NAMIC Wiki - User contributions [en]

Projects:fMRIClustering

2010-02-16T20:37:11Z

Danial:

Back to [[NA-MIC_Internal_Collaborations:fMRIAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]
__NOTOC__
= fMRI Clustering =

One of the major goals in analysis of fMRI data is the detection of networks in the brain with similar functional behavior. A wide variety of methods including hypothesis-driven statistical tests, unsupervised learning methods such as PCA and ICA, and different clustering algorithms have been employed to find these networks. This project aims to particularly study application of model-based clustering algorithms in identification of functional connectivity in the brain.

= Clustering for the Exploration of Functional Connectivity =

'''''Generative Model for Functional Connectivity'''''

In the classical functional connectivity analysis, networks of interest are
defined based on correlation with the mean time course of a user-selected
`seed' region. Further, the user has to also specify a subject-specific threshold at which correlation
values are deemed significant. In this project, we simultaneously estimate the optimal
representative time courses that summarize the fMRI data well and
the partition of the volume into a set of disjoint regions that are best
explained by these representative time courses. This approach to functional connectivity analysis offers two
advantages. First, is removes the sensitivity of the analysis to the details
of the seed selection. Second, it substantially simplifies group analysis
by eliminating the need for the subject-specific threshold. Our experimental results indicate that
the functional segmentation provides a robust, anatomically meaningful
and consistent model for functional connectivity in fMRI.

We formulate the problem of characterizing connectivity as a partition of voxels into subsets that are well characterized by a certain number of representative hypotheses, or time courses, based on the similarity of their time courses to each hypothesis. We model the fMRI signal at each voxel as generated by a mixture of Gaussian distributions whose centers are the desired representative time courses. Using the EM algorithm to solve the corresponding model-fitting problem, we alternatively estimate the representative time courses and cluster assignments to improve our random initialization.

''' ''Experimental Results'' '''

We used data from 7 subjects with a diverse set of visual experiments including localizer, morphing, rest, internal tasks, and movie. The functional scans were pre-processed for motion artifacts, manually aligned into the Talairach coordinate system, detrended (removing linear trends in the
baseline activation) and smoothed (8mm kernel).

Fig. 1 shows the 2-system partition extracted in each subject independently
of all others. It also displays the boundaries of the intrinsic system determined
through the traditional seed selection, showing good agreement between the two
partitions. Fig. 2 presents the results of further clustering the stimulus-driven cluster into two clusters independently for each subject.

<table>
<tr> <th> '''Fig 1. 2-System Parcelation. Results for all 7 subjects.''' <th> '''Fig 2. 3-System Parcelation. Results for all 7 subjects.'''
<tr> <td align="center">
[[Image:mit_fmri_clustering_parcellation2_shb1_4.png |400px]]
[[Image:mit_fmri_clustering_parcellation2_shb5_6.png |400px]]
[[Image:mit_fmri_clustering_parcellation2_shb7.png |400px]]
<td align="center">
[[Image:mit_fmri_clustering_parcellation3_shb1_3.png |400px]]
[[Image:mit_fmri_clustering_parcellation3_shb4_5.png |400px]]
[[Image:mit_fmri_clustering_parcellation3_shb6.png |400px]]
[[Image:mit_fmri_clustering_parcellation3_shb7.png |400px]]
</table>

Fig.3 presents the group average of the subject-specific 2-system maps. Color shading shows the proportion of subjects whose clustering agreed with the majority label. Fig. 4 shows the group average of a further parcelation of the intrinsic system, i.e., one of two clusters associated with the non-stimulus-driven regions. In order to present a validation of the method, we compare these results with the conventional scheme for detection of visually responsive areas. In Fig. 5, color shows the statistical parametric map while solid lines indicate the boundaries of the visual system obtained through clustering. The result illustrate the agreement between the two methods.

<table>
<tr><th> '''Fig 3. 2-System Parcellation. Group-wise result.''' <th> '''Fig 4. Validation: Parcelation of the intrinsic system.'''
<tr> <td align="center">
[[Image:mit_fmri_clustering_parcellation2_xsub.png |thumb|570px]]
<td align="center">
[[Image:mit_fmri_clustering_intrinsicsystem.png |thumb|500px]]
</table>

{|
|+ '''Fig 5. Validation: Visual system.'''
|valign="top"|[[Image:mit_fmri_clustering_validation.png |thumb|1150px]]
|}

'''''Comparison between Different Clustering Schemes'''''

As a continuation to the above experiments, we apply two distinct clustering algorithms to functional connectivity analysis: K-Means clustering and Spectral Clustering. The K-Means algorithm assumes that each voxel time course is drawn independently from one of <em>k</em> multivariate Gaussian distributions with unique means and spherical covariances. In contrast, Spectral Clustering does not presume any parametric form for the data. Rather it captures the underlying signal geometry by inducing a low-dimensional representation based on a pairwise affinity matrix constructed from the data. Without placing any <em>a priori</em> constraints, both clustering methods yield partitions that are associated with brain systems traditionally identified via seed-based correlation analysis. Our empirical results suggest that clustering provides a valuable tool for functional connectivity analysis.

One downside of Spectral Clustering is that it relies on the eigen-decomposition of an <em>NxN</em> affinity matrix, where <em>N</em> is the number of voxels in the whole brain. Since <em>N</em> is on the order of ~200,000 voxels, it is infeasible to compute the full eigen-decomposition given realistic memory and time constraints. To solve this problem, we approximate the leading eigenvalues and eigenvectors of the affinity matrix via the Nystrom Method. This is done by selecting a random subset of "Nystrom Samples" from the data. The affinity matrix and spectral decomposition is computed only for this subset, and the results are projected onto the remaining data points.

'''''Experimental Results'''''

We validate these algorithms on resting state data collected from 45 healthy young adults (mean age 21.5, 26 female). Four 2mm isotropic functional runs were acquired from each subject. Each scan lasted for 6m20s with TR = 5s. The first 4 time points in each run were discarded, yielding 72 time samples per run. The entire brain volume is partitioned into an increasing number of clusters. We perform standard preprocessing on each of the four runs, including motion correction by rigid body alignment of the volumes, slice timing correction and registration to the MNI atlas space. The data is spatially smoothed with a 6mm 3D Gaussian filter, temporally low-pass filtered using a 0.08Hz cutoff, and motion corrected via linear regression. Next, we estimate and remove contributions from the white matter, ventricle and whole brain regions (assuming a linear signal model). We mask the data to include only brain voxels and normalized the time courses to have zero mean and unit variance. Finally, we concatenate the four runs into a single time course for analysis.

We first study the robustness of Spectral Clustering to the number of random samples. In this experiment, we start with a 4,000-sample Nystrom set, which is the computational limit of our machine. We then iteratively remove 500 samples and examine the effect on clustering performance. After matching the resulting clusters to those estimated with 4,000 samples, we compute the percentage of mismatched voxels between each trial and the 4,000-sample template. This procedure is repeated twice for each participant.

<table>
<tr> <th> '''Fig 6. Varying the number of Nystrom Samples''' <th> '''Fig 7. Nystrom consistency for 2,000 random samples'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_Samples_LogMedian2.jpeg |400px]]
<td align="center">
[[Image:mit_fmri_clustering_Consistency_Box.jpeg |400px]]
</table>

Fig 6. depicts the median clustering difference when varying the number of Nystrom samples. Values represent the percentage of mismatched voxels w.r.t. the 4,000-sample template. Error bars delineate the <em>10th</em>-<em>90</em> percentile region. The median clustering difference is less than 1% for 1,000 or more Nystrom samples, and the <em>90th</em> percentile difference is less than 1% for 1,500 or more samples. This experiment suggests that Nystrom-based SC converges to a stable clustering pattern as the number of samples increases. Based on these results, we chose to use 2,000 Nystrom samples for the remainder of this work. At this sample size, less than 5% of the runs for 2,4,5 clusters and approximately 8% of the runs for 3 clusters differed by more than 5% from the 4,000-sample template.

The box plot in Fig 7. summarizes the consistency of Nystrom-based Spectral Clustering across
different random samplings. The red lines indicate median values, the box corresponds to the upper and lower quartiles, and error bars denote the <em>10th</em> and <em>90th</em> percentiles. Here, we perform SC 10 times on each participant using 2,000 Nystrom samples. We then align the cluster maps and compute the percentage of mismatched voxels between each unique pair of runs. This yields a total of 45 comparisons per participant. In all cases, the median clustering difference is less than 1%, and the <em>90th</em> percentile value is less than 2.1%. Empirically, we find that Nystrom SC predictably converges to a second or third cluster pattern in only a handful of participants. This experiment suggests that we can obtain consistent clusterings with only 2,000 Nystrom samples.

<table>
<tr> ''' Fig 8. Clustering results across participants. The brain is partitioned into 5 clusters using Spectral Clustering/K-Means, and various seed are selected for Seed-Based Analysis. The color indicates the proportion of participants for whom the voxel was included in the detected system.'''
<tr> <th> '''Spectral Clustering''' <th> '''K-Means''' <th> '''Seed-Based'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Clust_2.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Clust_1.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Seed_PCC.jpeg |275px]]
<tr> <th> '''Cluster 1, Slice 37''' <th> '''Cluster 1, Slice 37''' <th> '''PCC, Slice 37'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Double.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Double.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Seed_vACC.jpeg |275px]]
<tr> <th> '''Cluster 1, Slice 55''' <th> '''Cluster 1, Slice 55''' <th> '''vACC, Slice 55'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Clust_3.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Clust_4.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Seed_V1.jpeg |275px]]
<tr> <th> '''Cluster 2, Slice 55''' <th> '''Cluster 2, Slice 55''' <th> '''Visual, Slice 55'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Clust_4.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Clust_3.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Seed_M1.jpeg |275px]]
<tr> <th> '''Cluster 3, Slice 31''' <th> '''Cluster 3, Slice 31''' <th> '''Motor, Slice 31'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Clust_1.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Clust_2.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Seed_IPS.jpeg |275px]]
<tr> <th> '''Cluster 4, Slice 31''' <th> '''Cluster 4, Slice 31''' <th> '''IPS, Slice 31'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Clust_5.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Clust_5.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Colorbar2.jpeg |64px]]
<tr> <th> '''Cluster 5, Slice 37''' <th> '''Cluster 5, Slice 37''' <th>
</table>

Fig 8. shows clearly that both Spectral Clustering and K-Means can identify well-known structures such as the default network, the visual cortex, the motor cortex, and the dorsal attention system. Spectral Clustering and K-Means also identified white matter. In general, one would not attempt to delineate this region using seed-based correlation analysis because we regress out the white matter signal during the preprocessing. In our experiments Spectral Clustering and K-Means achieve similar clustering results across participants. Furthermore, both methods identify the same functional systems as seed-based analysis without requiring <em>a priori</em> knowledge about the brain and without significant computation. Thus, clustering algorithms offer a viable alternative to standard functional connectivity analysis techniques.

''' ''Comparison of ICA and Clustering for the Identiﬁcation of Functional Connectivity in fMRI'' '''

Although ICA and clustering rely on very different assumptions on the underlying distributions, they produce surprisingly similar results for signals with large variation. Our main goal is to evaluate and compare the performance of ICA and clustering based on Gaussian mixture model (GMM) for identiﬁcation of functional connectivity. Using the synthetic data with artiﬁcial activations and artifacts under various levels of length of the time course and signal-to-noise ratio of the data, we compare both spatial maps and their associated time courses estimated by ICA and GMM to each other and to the ground truth. We choose the number of sources via the model selection scheme, and compare all of the resulting components of GMM and ICA, not just the task-related components, after we match them component-wise using the Hungarian algorithm. This comparison scheme is veriﬁed in a high level visual cortex fMRI study. We ﬁnd that ICA requires a smaller number of total components to extract the task-related components, but also needs a large number of total components to describe the entire data. We are currently applying ICA and clustering methods to connectivity analysis of schizophrenia patients.

= Clustering for Discovering Structure in the Space of Functional Selectivity =

''' ''Clustering Study of Domain Specificity in High Level Visual Cortex'' '''

As a more specific application of model-based clustering algorithms, we are devising clustering algorithms for discovering structure in the functional organization of the high-level visual cortex. It is suggested that there are regions in the visual cortex with high selectivity to certain categories of visual stimuli. Currently, the conventional method for detection of these methods is based on statistical tests comparing response of each voxel in the brain to different visual categories to see if it shows considerably higher activation to one category. For example, the well-known FFA (Fusiform Face Area) is the set of voxels which show high activation to face images. We use a model-based clustering approach to the analysis of this type of data as a means to make this analysis automatic and further discover new structures in the high-level visual cortex.

Introducing the notion of space of activation
profiles, we construct a representation of the data which explicitly
parametrizes all interesting patterns of activation. Mapping the data into
this space, we formulate a model-based clustering algorithm that simultaneously
finds a set of activation profiles and their spatial maps. We validate
our method on the data from studies of category selectivity in visual
cortex, demonstrating good agreement with the findings based on prior
hypothesis-driven methods. This model enables functional group analysis
independent of spatial correspondence among subjects. We are currently working on a co-clustering extension of this
algorithm which can simultaneously find a set of clusters of voxels and meta-categories
of stimuli in experiments with diverse sets of stimulus categories.

Fig. 9 compares the map of voxels assigned to a face-selective profile by our algorithm with the t-test's map of voxels with statistically significant (p<0.0001) response to faces when compared with object stimuli. Note that in contrast with the hypothesis testing method, we don't specify the existence of a face-selective region in our algorithm and the algorithm automatically discovers such a profile of activation in the data.

{|
|+ '''Fig 9. Spatial maps of the face selective regions found by the statistical test (red) and our mixture model (dark blue). Maps are presented in alternating rows for comparison. Visually responsive mask of voxels used in our experiment is illustrated in yellow and light blue.'''
|align="center"|[[Image:mit_fmri_clustering_mapffacompare.PNG |thumb|800px]]
|}

'''''Hierarchical Model for Exploratory fMRI Analysis without Spatial Normalization'''''

Building on the work on the clustering model for the domain specificity, we develop a hierarchical exploratory method for simultaneous parcellation of multisub ect fMRI data into functionally coherent areas. The method is based on a solely functional representation of the fMRI data and a hierarchical probabilistic model that accounts for both inter-subject and intra-subject forms of variability in fMRI response. We employ a Variational Bayes approximation to ﬁt the model to the data. The resulting algorithm ﬁnds a functional parcellation of the individual brains along with a set of population-level clusters, establishing correspondence between these two levels. The model eliminates the need for spatial normalization while still enabling us to fuse data from several subjects. We demonstrate the application of our method on the same visual fMRI study as before. Fig. 10 shows the scene-selective parcel in 2 different subjects. Parcel-level spatial correspondence is evident in the figure between the subjects.

<table>
<tr> <th> '''Fig 10. The map of the scene selective parcels in two different subjects. The rough location of the scene-selective areas PPA and TOS, identified by the expert, are shown on the maps by yellow and green circles, respectively.'''
<tr>
<td align="center">
[[Image:mit_fmriclustering_hierarchicalppamapsubject1.jpg |650px]]
<td align="center">
[[Image:mit_fmriclustering_hierarchicalppamapsubject2.jpg |650px]]
</table>

= Key Investigators =

* MIT: Danial Lashkari, Archana Venkataraman, Ed Vul, Nancy Kanwisher, Polina Golland.
* Harvard: J. Oh, Marek Kubicki, Carl-Fredrik Westin.

= Publications =

[http://www.na-mic.org/publications/pages/display?search=Projects%3AfMRIClustering&submit=Search&words=all&title=checked&keywords=checked&authors=checked&abstract=checked&sponsors=checked&searchbytag=checked| NA-MIC Publications Database]

Project Week Results: [[2008_Summer_Project_Week:fMRIconnectivity|June 2008]]

[[Category:fMRI]]

Projects:fMRIClustering

2010-02-16T20:35:21Z

Danial:

Back to [[NA-MIC_Internal_Collaborations:fMRIAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]
__NOTOC__
= fMRI Clustering =

One of the major goals in analysis of fMRI data is the detection of networks in the brain with similar functional behavior. A wide variety of methods including hypothesis-driven statistical tests, unsupervised learning methods such as PCA and ICA, and different clustering algorithms have been employed to find these networks. This project aims to particularly study application of model-based clustering algorithms in identification of functional connectivity in the brain.

= Clustering for Exploration of Functional Connectivity =

'''''Generative Model for Functional Connectivity'''''

In the classical functional connectivity analysis, networks of interest are
defined based on correlation with the mean time course of a user-selected
`seed' region. Further, the user has to also specify a subject-specific threshold at which correlation
values are deemed significant. In this project, we simultaneously estimate the optimal
representative time courses that summarize the fMRI data well and
the partition of the volume into a set of disjoint regions that are best
explained by these representative time courses. This approach to functional connectivity analysis offers two
advantages. First, is removes the sensitivity of the analysis to the details
of the seed selection. Second, it substantially simplifies group analysis
by eliminating the need for the subject-specific threshold. Our experimental results indicate that
the functional segmentation provides a robust, anatomically meaningful
and consistent model for functional connectivity in fMRI.

We formulate the problem of characterizing connectivity as a partition of voxels into subsets that are well characterized by a certain number of representative hypotheses, or time courses, based on the similarity of their time courses to each hypothesis. We model the fMRI signal at each voxel as generated by a mixture of Gaussian distributions whose centers are the desired representative time courses. Using the EM algorithm to solve the corresponding model-fitting problem, we alternatively estimate the representative time courses and cluster assignments to improve our random initialization.

''' ''Experimental Results'' '''

We used data from 7 subjects with a diverse set of visual experiments including localizer, morphing, rest, internal tasks, and movie. The functional scans were pre-processed for motion artifacts, manually aligned into the Talairach coordinate system, detrended (removing linear trends in the
baseline activation) and smoothed (8mm kernel).

Fig. 1 shows the 2-system partition extracted in each subject independently
of all others. It also displays the boundaries of the intrinsic system determined
through the traditional seed selection, showing good agreement between the two
partitions. Fig. 2 presents the results of further clustering the stimulus-driven cluster into two clusters independently for each subject.

<table>
<tr> <th> '''Fig 1. 2-System Parcelation. Results for all 7 subjects.''' <th> '''Fig 2. 3-System Parcelation. Results for all 7 subjects.'''
<tr> <td align="center">
[[Image:mit_fmri_clustering_parcellation2_shb1_4.png |400px]]
[[Image:mit_fmri_clustering_parcellation2_shb5_6.png |400px]]
[[Image:mit_fmri_clustering_parcellation2_shb7.png |400px]]
<td align="center">
[[Image:mit_fmri_clustering_parcellation3_shb1_3.png |400px]]
[[Image:mit_fmri_clustering_parcellation3_shb4_5.png |400px]]
[[Image:mit_fmri_clustering_parcellation3_shb6.png |400px]]
[[Image:mit_fmri_clustering_parcellation3_shb7.png |400px]]
</table>

Fig.3 presents the group average of the subject-specific 2-system maps. Color shading shows the proportion of subjects whose clustering agreed with the majority label. Fig. 4 shows the group average of a further parcelation of the intrinsic system, i.e., one of two clusters associated with the non-stimulus-driven regions. In order to present a validation of the method, we compare these results with the conventional scheme for detection of visually responsive areas. In Fig. 5, color shows the statistical parametric map while solid lines indicate the boundaries of the visual system obtained through clustering. The result illustrate the agreement between the two methods.

<table>
<tr><th> '''Fig 3. 2-System Parcellation. Group-wise result.''' <th> '''Fig 4. Validation: Parcelation of the intrinsic system.'''
<tr> <td align="center">
[[Image:mit_fmri_clustering_parcellation2_xsub.png |thumb|570px]]
<td align="center">
[[Image:mit_fmri_clustering_intrinsicsystem.png |thumb|500px]]
</table>

{|
|+ '''Fig 5. Validation: Visual system.'''
|valign="top"|[[Image:mit_fmri_clustering_validation.png |thumb|1150px]]
|}

'''''Comparison between Different Clustering Schemes'''''

As a continuation to the above experiments, we apply two distinct clustering algorithms to functional connectivity analysis: K-Means clustering and Spectral Clustering. The K-Means algorithm assumes that each voxel time course is drawn independently from one of <em>k</em> multivariate Gaussian distributions with unique means and spherical covariances. In contrast, Spectral Clustering does not presume any parametric form for the data. Rather it captures the underlying signal geometry by inducing a low-dimensional representation based on a pairwise affinity matrix constructed from the data. Without placing any <em>a priori</em> constraints, both clustering methods yield partitions that are associated with brain systems traditionally identified via seed-based correlation analysis. Our empirical results suggest that clustering provides a valuable tool for functional connectivity analysis.

One downside of Spectral Clustering is that it relies on the eigen-decomposition of an <em>NxN</em> affinity matrix, where <em>N</em> is the number of voxels in the whole brain. Since <em>N</em> is on the order of ~200,000 voxels, it is infeasible to compute the full eigen-decomposition given realistic memory and time constraints. To solve this problem, we approximate the leading eigenvalues and eigenvectors of the affinity matrix via the Nystrom Method. This is done by selecting a random subset of "Nystrom Samples" from the data. The affinity matrix and spectral decomposition is computed only for this subset, and the results are projected onto the remaining data points.

'''''Experimental Results'''''

We validate these algorithms on resting state data collected from 45 healthy young adults (mean age 21.5, 26 female). Four 2mm isotropic functional runs were acquired from each subject. Each scan lasted for 6m20s with TR = 5s. The first 4 time points in each run were discarded, yielding 72 time samples per run. The entire brain volume is partitioned into an increasing number of clusters. We perform standard preprocessing on each of the four runs, including motion correction by rigid body alignment of the volumes, slice timing correction and registration to the MNI atlas space. The data is spatially smoothed with a 6mm 3D Gaussian filter, temporally low-pass filtered using a 0.08Hz cutoff, and motion corrected via linear regression. Next, we estimate and remove contributions from the white matter, ventricle and whole brain regions (assuming a linear signal model). We mask the data to include only brain voxels and normalized the time courses to have zero mean and unit variance. Finally, we concatenate the four runs into a single time course for analysis.

We first study the robustness of Spectral Clustering to the number of random samples. In this experiment, we start with a 4,000-sample Nystrom set, which is the computational limit of our machine. We then iteratively remove 500 samples and examine the effect on clustering performance. After matching the resulting clusters to those estimated with 4,000 samples, we compute the percentage of mismatched voxels between each trial and the 4,000-sample template. This procedure is repeated twice for each participant.

<table>
<tr> <th> '''Fig 6. Varying the number of Nystrom Samples''' <th> '''Fig 7. Nystrom consistency for 2,000 random samples'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_Samples_LogMedian2.jpeg |400px]]
<td align="center">
[[Image:mit_fmri_clustering_Consistency_Box.jpeg |400px]]
</table>

Fig 6. depicts the median clustering difference when varying the number of Nystrom samples. Values represent the percentage of mismatched voxels w.r.t. the 4,000-sample template. Error bars delineate the <em>10th</em>-<em>90</em> percentile region. The median clustering difference is less than 1% for 1,000 or more Nystrom samples, and the <em>90th</em> percentile difference is less than 1% for 1,500 or more samples. This experiment suggests that Nystrom-based SC converges to a stable clustering pattern as the number of samples increases. Based on these results, we chose to use 2,000 Nystrom samples for the remainder of this work. At this sample size, less than 5% of the runs for 2,4,5 clusters and approximately 8% of the runs for 3 clusters differed by more than 5% from the 4,000-sample template.

The box plot in Fig 7. summarizes the consistency of Nystrom-based Spectral Clustering across
different random samplings. The red lines indicate median values, the box corresponds to the upper and lower quartiles, and error bars denote the <em>10th</em> and <em>90th</em> percentiles. Here, we perform SC 10 times on each participant using 2,000 Nystrom samples. We then align the cluster maps and compute the percentage of mismatched voxels between each unique pair of runs. This yields a total of 45 comparisons per participant. In all cases, the median clustering difference is less than 1%, and the <em>90th</em> percentile value is less than 2.1%. Empirically, we find that Nystrom SC predictably converges to a second or third cluster pattern in only a handful of participants. This experiment suggests that we can obtain consistent clusterings with only 2,000 Nystrom samples.

<table>
<tr> ''' Fig 8. Clustering results across participants. The brain is partitioned into 5 clusters using Spectral Clustering/K-Means, and various seed are selected for Seed-Based Analysis. The color indicates the proportion of participants for whom the voxel was included in the detected system.'''
<tr> <th> '''Spectral Clustering''' <th> '''K-Means''' <th> '''Seed-Based'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Clust_2.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Clust_1.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Seed_PCC.jpeg |275px]]
<tr> <th> '''Cluster 1, Slice 37''' <th> '''Cluster 1, Slice 37''' <th> '''PCC, Slice 37'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Double.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Double.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Seed_vACC.jpeg |275px]]
<tr> <th> '''Cluster 1, Slice 55''' <th> '''Cluster 1, Slice 55''' <th> '''vACC, Slice 55'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Clust_3.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Clust_4.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Seed_V1.jpeg |275px]]
<tr> <th> '''Cluster 2, Slice 55''' <th> '''Cluster 2, Slice 55''' <th> '''Visual, Slice 55'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Clust_4.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Clust_3.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Seed_M1.jpeg |275px]]
<tr> <th> '''Cluster 3, Slice 31''' <th> '''Cluster 3, Slice 31''' <th> '''Motor, Slice 31'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Clust_1.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Clust_2.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Seed_IPS.jpeg |275px]]
<tr> <th> '''Cluster 4, Slice 31''' <th> '''Cluster 4, Slice 31''' <th> '''IPS, Slice 31'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Clust_5.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Clust_5.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Colorbar2.jpeg |64px]]
<tr> <th> '''Cluster 5, Slice 37''' <th> '''Cluster 5, Slice 37''' <th>
</table>

Fig 8. shows clearly that both Spectral Clustering and K-Means can identify well-known structures such as the default network, the visual cortex, the motor cortex, and the dorsal attention system. Spectral Clustering and K-Means also identified white matter. In general, one would not attempt to delineate this region using seed-based correlation analysis because we regress out the white matter signal during the preprocessing. In our experiments Spectral Clustering and K-Means achieve similar clustering results across participants. Furthermore, both methods identify the same functional systems as seed-based analysis without requiring <em>a priori</em> knowledge about the brain and without significant computation. Thus, clustering algorithms offer a viable alternative to standard functional connectivity analysis techniques.

''' ''Comparison of ICA and Clustering for the Identiﬁcation of Functional Connectivity in fMRI'' '''

Although ICA and clustering rely on very different assumptions on the underlying distributions, they produce surprisingly similar results for signals with large variation. Our main goal is to evaluate and compare the performance of ICA and clustering based on Gaussian mixture model (GMM) for identiﬁcation of functional connectivity. Using the synthetic data with artiﬁcial activations and artifacts under various levels of length of the time course and signal-to-noise ratio of the data, we compare both spatial maps and their associated time courses estimated by ICA and GMM to each other and to the ground truth. We choose the number of sources via the model selection scheme, and compare all of the resulting components of GMM and ICA, not just the task-related components, after we match them component-wise using the Hungarian algorithm. This comparison scheme is veriﬁed in a high level visual cortex fMRI study. We ﬁnd that ICA requires a smaller number of total components to extract the task-related components, but also needs a large number of total components to describe the entire data. We are currently applying ICA and clustering methods to connectivity analysis of schizophrenia patients.

= Clustering for Discovering Structure in the Space of Functional Selectivity =

''' ''Clustering Study of Domain Specificity in High Level Visual Cortex'' '''

As a more specific application of model-based clustering algorithms, we are devising clustering algorithms for discovering structure in the functional organization of the high-level visual cortex. It is suggested that there are regions in the visual cortex with high selectivity to certain categories of visual stimuli. Currently, the conventional method for detection of these methods is based on statistical tests comparing response of each voxel in the brain to different visual categories to see if it shows considerably higher activation to one category. For example, the well-known FFA (Fusiform Face Area) is the set of voxels which show high activation to face images. We use a model-based clustering approach to the analysis of this type of data as a means to make this analysis automatic and further discover new structures in the high-level visual cortex.

Introducing the notion of space of activation
profiles, we construct a representation of the data which explicitly
parametrizes all interesting patterns of activation. Mapping the data into
this space, we formulate a model-based clustering algorithm that simultaneously
finds a set of activation profiles and their spatial maps. We validate
our method on the data from studies of category selectivity in visual
cortex, demonstrating good agreement with the findings based on prior
hypothesis-driven methods. This model enables functional group analysis
independent of spatial correspondence among subjects. We are currently working on a co-clustering extension of this
algorithm which can simultaneously find a set of clusters of voxels and meta-categories
of stimuli in experiments with diverse sets of stimulus categories.

Fig. 9 compares the map of voxels assigned to a face-selective profile by our algorithm with the t-test's map of voxels with statistically significant (p<0.0001) response to faces when compared with object stimuli. Note that in contrast with the hypothesis testing method, we don't specify the existence of a face-selective region in our algorithm and the algorithm automatically discovers such a profile of activation in the data.

{|
|+ '''Fig 9. Spatial maps of the face selective regions found by the statistical test (red) and our mixture model (dark blue). Maps are presented in alternating rows for comparison. Visually responsive mask of voxels used in our experiment is illustrated in yellow and light blue.'''
|align="center"|[[Image:mit_fmri_clustering_mapffacompare.PNG |thumb|800px]]
|}

'''''Hierarchical Model for Exploratory fMRI Analysis without Spatial Normalization'''''

Building on the work on the clustering model for the domain specificity, we develop a hierarchical exploratory method for simultaneous parcellation of multisub ect fMRI data into functionally coherent areas. The method is based on a solely functional representation of the fMRI data and a hierarchical probabilistic model that accounts for both inter-subject and intra-subject forms of variability in fMRI response. We employ a Variational Bayes approximation to ﬁt the model to the data. The resulting algorithm ﬁnds a functional parcellation of the individual brains along with a set of population-level clusters, establishing correspondence between these two levels. The model eliminates the need for spatial normalization while still enabling us to fuse data from several subjects. We demonstrate the application of our method on the same visual fMRI study as before. Fig. 10 shows the scene-selective parcel in 2 different subjects. Parcel-level spatial correspondence is evident in the figure between the subjects.

<table>
<tr> <th> '''Fig 10. The map of the scene selective parcels in two different subjects. The rough location of the scene-selective areas PPA and TOS, identified by the expert, are shown on the maps by yellow and green circles, respectively.'''
<tr>
<td align="center">
[[Image:mit_fmriclustering_hierarchicalppamapsubject1.jpg |650px]]
<td align="center">
[[Image:mit_fmriclustering_hierarchicalppamapsubject2.jpg |650px]]
</table>

= Key Investigators =

* MIT: Danial Lashkari, Archana Venkataraman, Ed Vul, Nancy Kanwisher, Polina Golland.
* Harvard: J. Oh, Marek Kubicki, Carl-Fredrik Westin.

= Publications =

[http://www.na-mic.org/publications/pages/display?search=Projects%3AfMRIClustering&submit=Search&words=all&title=checked&keywords=checked&authors=checked&abstract=checked&sponsors=checked&searchbytag=checked| NA-MIC Publications Database]

Project Week Results: [[2008_Summer_Project_Week:fMRIconnectivity|June 2008]]

[[Category:fMRI]]

Algorithm:MIT

2010-02-16T20:25:10Z

Danial:

Back to [[Algorithm:Main|NA-MIC Algorithms]]
__NOTOC__
= Overview of MIT Algorithms (PI: Polina Golland) =

Our group seeks to model statistical variability of anatomy and function across subjects and between populations and to utilize computational models of such variability to improve predictions for individual subjects, as well as characterize populations. Our long-term goal is to develop methods for joint modeling of anatomy and function and to apply them in clinical and scientific studies. We work primarily with anatomical, DTI and fMRI images. We actively contribute implementations of our algorithms to the NAMIC-kit.

= MIT Projects =

{| cellpadding="10" style="text-align:left;"
|| [[Image:Segmentation_example2.png|250px]]
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== [[Projects:NonparametricSegmentation| Nonparametric Models for Supervised Image Segmentation]] ==

We propose a non-parametric, probabilistic model for the automatic segmentation of medical images,
given a training set of images and corresponding label maps. The resulting inference algorithms we
develop rely on pairwise registrations between the test image and individual training images. The
training labels are then transferred to the test image and fused to compute a final segmentation of
the test subject. [[Projects:NonparametricSegmentation|More...]]

<font color="red">'''New: '''</font> Supervised Nonparametric Image Parcellation, M.R. Sabuncu, B.T. Thomas Yeo, K. Van Leemput, B. Fischl, and P. Golland. To appear in Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), 2009.

<font color="red">'''New: '''</font> Nonparametric Mixture Models for Supervised Image Parcellation, M.R. Sabuncu,
B.T.T. Yeo, K. Van Leemput, B. Fischl, and P. Golland. To be presented at PMMIA Workshop at MICCAI 2009.

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| | [[Image:TGIt.gif| 150px]]
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== [[Projects:LatentAtlasSegmentation|Joint Segmentation of Image Ensembles via Latent Atlases]] ==

Spatial priors, such as probabilistic atlases, play an important role in MRI segmentation. The atlases are typically generated by averaging manual labels of aligned brain regions across different subjects. However, the availability of comprehensive, reliable and suitable manual segmentations is limited. We therefore propose a joint segmentation of corresponding, aligned structures in the entire population that does not require a probability atlas.
[[Projects:LatentAtlasSegmentation|More...]]

<font color="red">'''New: '''</font> T. Riklin Raviv, K. Van Leemput, W.M. Wells III and P. Golland, Joint Segmentation of Image Ensembles via Latent Atlases, Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), 2009. '''Young Investigator Award'''.

<font color="red">'''New: '''</font>
T. Riklin Raviv, B.H. Menze, K. Van Leemput, B. Stieltjes, M.A. Weber, N. Ayache, W. M. Wells III and P. Golland, Joint Segmentation using Patient specific Latent Anatomy Model
MICCAI workshop for Probabilistic Models on Medical Image Analysis (PMMIA) 2009.

|-

{| cellpadding="10" style="text-align:left;"
|| [[Image:TetrahedralAtlasWarp.gif‎ |250px]]
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== [[Projects:BayesianMRSegmentation| Bayesian Segmentation of MRI Images]] ==

The aim of this project is to develop, implement, and validate a generic method for segmenting MRI images that automatically adapts to different acquisition sequences. [[Projects:BayesianMRSegmentation|More...]]

<font color="red">'''New: '''</font> Automated Segmentation of Hippocampal Subﬁelds from Ultra-High Resolution In Vivo MRI, K. Van Leemput, A. Bakkour, T. Benner, G. Wiggins, L.L. Wald, J. Augustinack, B.C. Dickerson, P. Golland, and B. Fischl. Hippocampus, vol. 19, no. 6, pp. 549-557, 2009.

<font color="red">'''New: '''</font> Encoding Probabilistic Atlases Using Bayesian Inference, K. Van Leemput. IEEE Transactions on Medical Imaging, vol. 28, no. 6, pp. 822-837, 2009.

|-

{| cellpadding="10" style="text-align:left;"
|| [[Image:lh.pm14686.BA2.gif|250px]]
||

== [[Projects:LearningRegistrationCostFunctions| Learning Task-Optimal Registration Cost Functions]] ==

We present a framework for learning the parameters of registration cost functions. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. We propose a principled approach to learn these parameters with respect to particular applications. [[Projects:LearningRegistrationCostFunctions|More...]]

<font color="red">'''New: '''</font> B.T.T. Yeo, M. Sabuncu, P. Golland, B. Fischl. Task-Optimal Registration Cost Functions. To appear in Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), 2009.

|-

| | [[Image:ICluster_templates.gif|250px]]
| |

== [[Projects:MultimodalAtlas|Multimodal Atlas]] ==

In this work, we propose and investigate an algorithm that jointly co-registers a collection of images while computing multiple templates. The algorithm, called '''iCluster''', is used to compute multiple atlases for a given population.
[[Projects:MultimodalAtlas|More...]]

<font color="red">'''New: '''</font> Image-driven Population Analysis through Mixture-Modeling, M.R. Sabuncu, S.K. Balci, M.E. Shenton and P. Golland. IEEE Transactions on Medical Imaging, 28(9):1473 - 1487, 2009.

|-

| | [[Image:Tumor_model.jpg‎|center|150px]]
| |

== [[Projects:TumorModeling|Modeling the growth of brain tumors]] ==

We are interested in developing computational methods for the assimilation of magnetic resonance image data into physiological models of glioma - the most frequent primary brain tumor - for a patient-adaptive modeling of tumor growth. [[Projects:TumorModeling|More...]]

<font color="red">'''New: '''</font> Joint Segmentation using Patient specific Latent Anatomy Model. T. Riklin Raviv, B.H. Menze, K. Van Leemput, B. Stieltjes, M.A. Weber, N. Ayache, W. M. Wells III and P. Golland. MICCAI workshop for Probabilistic Models on Medical Image Analysis (PMMIA), 2009.

|-

| | [[Image:CoordinateChart.png|250px]]
| |

== [[Projects:SphericalDemons|Spherical Demons: Fast Surface Registration]] ==

We present the fast Spherical Demons algorithm for registering two spherical images. By exploiting spherical vector spline interpolation theory, we show that a large class of regularizers for the modified demons objective function can be efficiently approximated on the sphere using convolution. Based on the one parameter subgroups of diffeomorphisms, [[Projects:SphericalDemons|More...]]

<font color="red">'''New: '''</font> B.T.T. Yeo, M. Sabuncu, T. Vercauteren, N. Ayache, B. Fischl, P. Golland. Spherical Demons: Fast Surface Registration. In Proc. MICCAI, volume 5241 of LNCS, 745--753, 2008.

<font color="red">'''New: '''</font> B.T.T. Yeo, M. Sabuncu, T. Vercauteren, N. Ayache, B. Fischl, P. Golland. Spherical Demons: Fast Surface Registration. IEEE TMI, In Press.

|-

| | [[Image:GroupwiseSummary.PNG|200px]]
| |

== [[Projects:GroupwiseRegistration|Groupwise Registration]] ==

We extend a previously demonstrated entropy based groupwise registration method to include a free-form deformation model based on B-splines. We provide an efficient implementation using stochastic gradient descents in a multi-resolution setting. We demonstrate the method in application to a set of 50 MRI brain scans and compare the results to a pairwise approach using segmentation labels to evaluate the quality of alignment.

In a related project, we develop a method that reconciles the practical advantages of symmetric registration with the asymmetric nature of image-template registration by adding a simple correction factor to the symmetric cost function. We instantiate our model within a log-domain diffeomorphic registration framework. Our experiments show exploiting the asymmetry in image-template registration improves alignment in the image coordinates. [[Projects:GroupwiseRegistration|More...]]

<font color="red">'''New: '''</font> Asymmetric Image-Template Registration, M.R. Sabuncu, B.T. Thomas Yeo, T. Vercauteren, K. Van Leemput, P. Golland. To appear in Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), 2009.

|-

| | [[Image:mit_fmri_clustering_parcellation2_xsub.png|200px]]
| |

== [[Projects:fMRIClustering|fMRI clustering]] ==

In this project we study the application of model-based clustering algorithms in identification of functional connectivity in the brain. [[Projects:fMRIClustering|More...]]

<font color="red">'''New: '''</font> D. Lashkari, E. Vul, N.G. Kanwisher, and P. Golland. Discovering structure in the space of fMRI selectivity profiles. NeuroImage, in press.

<font color="red">'''New: '''</font> A. Venkataraman, K.R.A Van Dijk, R.L. Buckner, and P. Golland. Exploring functional connectivity in fMRI via clustering. In Proc. ICASSP: IEEE International Conference on Acoustics, Speech and Signal Processing, 441-444, 2009.

<font color="red">'''New: '''</font> D. Lashkari and P. Golland. Exploratory fMRI Analysis without Spatial Normalization. In Proc. IPMI: International Conference on Information Processing and Medical Imaging, LNCS 5636:398-410, 2009. '''Honorable Mention for the Erbsmann Award'''.

|-

| | [[Image:epi_correction_small.jpg|200px]]
| |

== [[Projects:FieldmapFreeDistortionCorrection|Fieldmap-Free EPI Distortion Correction]] ==

In this project we aim to improve the EPI distortion correction algorithms. [[Projects:FieldmapFreeDistortionCorrection|More...]]

<font color="red">'''New: '''</font> Poynton C., Jenkinson M., Wells III W. Atlas-Based Improved Prediction of Magnetic Field Inhomogeneity for Distortion Correction of EPI Data. MICCAI 2009.

|-

| | [[Image:JointRegSeg.png|200px]]
| |

== [[Projects:RegistrationRegularization|Optimal Atlas Regularization in Image Segmentation]] ==

We propose a unified framework for computing atlases from manually labeled data sets at various degrees of “sharpness” and the joint registration and segmentation of a new brain with these atlases. Using this framework, we investigate the tradeoff between warp regularization and image ﬁdelity, i.e. the smoothness of the new subject warp and the sharpness of the atlas in a segmentation application.
[[Projects:RegistrationRegularization|More...]]

<font color="red">'''New:'''</font> B.T.T. Yeo, M.R. Sabuncu, R. Desikan, B. Fischl, P. Golland. Effects of Registration Regularization and Atlas Sharpness on Segmentation Accuracy. Medical Image Analysis, 12(5):603--615, 2008.

|-

| | [[Image:FoldingSpeedDetection.png|150px|]]
| |

== [[Projects:ShapeAnalysisWithOvercompleteWavelets|Shape Analysis With Overcomplete Wavelets]] ==

In this work, we extend the Euclidean wavelets to the sphere. The resulting over-complete spherical wavelets are invariant to the rotation of the spherical image parameterization. We apply the over-complete spherical wavelet to cortical folding development [[Projects:ShapeAnalysisWithOvercompleteWavelets|More...]]

<font color="red">'''New: '''</font> B.T.T. Yeo, P. Yu, P.E. Grant, B. Fischl, P. Golland. Shape Analysis with Overcomplete Spherical Wavelets. Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), volume 5241 of LNCS, 468--476, 2008.

B.T.T. Yeo, W. Ou, P. Golland. On the Construction of Invertible Filter Banks on the 2-Sphere. Yeo, Ou and Golland. IEEE Transactions on Image Processing. 17(3):283--300. 2008.

|-

| | [[Image:Models.jpg|200px]]
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== [[Projects:DTIModeling|Fiber Tract Modeling, Clustering, and Quantitative Analysis]] ==

The goal of this work is to model the shape of the fiber bundles and use this model description in clustering and statistical analysis of fiber tracts. [[Projects:DTIModeling|More...]]

<font color="red">'''New:'''</font> Mahnaz Maddah, Marek Kubicki, William M. Wells, Carl-Fredrik Westin, Martha E. Shenton and W. Eric L. Grimson, Findings in Schizophrenia by Tract-Oriented DT-MRI Analysis. MICCAI 2008.

M. Maddah, L. Zollei, W. E. L. Grimson, W. M. Wells, Modeling of Anatomical Information in Clustering of White Matter Fiber Trajectories Using Dirichlet Distribution. MMBIA 2008.

M. Maddah, L. Zollei, W. E. L. Grimson, C-F Westin, W. M. Wells, A Mathematical Framework for Incorporating Anatomical Knowledge in DT-MRI Analysis. ISBI 2008.

|-

| | [[Image:Progress_Registration_Segmentation_Shape.jpg|180px]]
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== [[Projects:ShapeBasedSegmentationAndRegistration|Shape Based Segmentation and Registration]] ==

This type of algorithm assigns a tissue type to each voxel in the volume. Incorporating prior shape information biases the label assignment towards contiguous regions that are consistent with the shape model. [[Projects:ShapeBasedSegmentationAndRegistration|More...]]

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| | [[Image:MIT_DTI_JointSegReg_atlas3D.jpg|200px]]
| |

== [[Projects:DTIFiberRegistration|Joint Registration and Segmentation of DWI Fiber Tractography]] ==

The goal of this work is to jointly register and cluster DWI fiber tracts obtained from a group of subjects. [[Projects:DTIFiberRegistration|More...]]

|-

| | [[Image:brain.png|200px]]
| |

== [[Projects:DTIClustering|DTI Fiber Clustering and Fiber-Based Analysis]] ==

The goal of this project is to provide structural description of the white matter architecture as a partition into coherent fiber bundles and clusters, and to use these bundles for quantitative measurement. [[Projects:DTIClustering|More...]]

|-

| | [[Image:FMRIEvaluationchart.jpg|200px]]
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== [[Projects:fMRIDetection|fMRI Detection and Analysis]] ==

We are exploring algorithms for improved fMRI detection and interpretation by incorporting spatial priors and anatomical information to guide the detection. [[Projects:fMRIDetection|More...]]

|-

| | [[Image:Thalamus_algo_outline.png|200px]]
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== [[Projects:DTISegmentation|DTI-based Segmentation]] ==

Unlike conventional MRI, DTI provides adequate contrast to segment the thalamic nuclei, which are gray matter structures. [[Projects:DTISegmentation|More...]]

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| | [[Image:ConnectivityMap.png|200px]]
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== [[Projects:DTIStochasticTractography|Stochastic Tractography]] ==

This work calculates posterior distributions of white matter fiber tract parameters given diffusion observations in a DWI volume. [[Projects:DTIStochasticTractography|More...]]

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| | [[Image:HippocampalShapeDifferences.gif|200px]]
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== [[Projects:ShapeAnalysis|Population Analysis of Anatomical Variability]] ==

Our goal is to develop mathematical approaches to modeling anatomical variability within and across populations using tools like local shape descriptors of specific regions of interest and global constellation descriptors of multiple ROI's. [[Projects:ShapeAnalysis|More...]]

|}

Projects:fMRIClustering

2009-09-10T18:47:17Z

Danial:

Back to [[NA-MIC_Internal_Collaborations:fMRIAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]
__NOTOC__
= fMRI Clustering =

One of the major goals in analysis of fMRI data is the detection of networks in the brain with similar functional behavior. A wide variety of methods including hypothesis-driven statistical tests, unsupervised learning methods such as PCA and ICA, and different clustering algorithms have been employed to find these networks. This project aims to particularly study application of model-based clustering algorithms in identification of functional connectivity in the brain.

= Description =

'''''Generative Model for Functional Connectivity'''''

In the classical functional connectivity analysis, networks of interest are
defined based on correlation with the mean time course of a user-selected
`seed' region. Further, the user has to also specify a subject-specific threshold at which correlation
values are deemed significant. In this project, we simultaneously estimate the optimal
representative time courses that summarize the fMRI data well and
the partition of the volume into a set of disjoint regions that are best
explained by these representative time courses. This approach to functional connectivity analysis offers two
advantages. First, is removes the sensitivity of the analysis to the details
of the seed selection. Second, it substantially simplifies group analysis
by eliminating the need for the subject-specific threshold. Our experimental results indicate that
the functional segmentation provides a robust, anatomically meaningful
and consistent model for functional connectivity in fMRI.

We formulate the problem of characterizing connectivity as a partition of voxels into subsets that are well characterized by a certain number of representative hypotheses, or time courses, based on the similarity of their time courses to each hypothesis. We model the fMRI signal at each voxel as generated by a mixture of Gaussian distributions whose centers are the desired representative time courses. Using the EM algorithm to solve the corresponding model-fitting problem, we alternatively estimate the representative time courses and cluster assignments to improve our random initialization.

''' ''Experimental Results'' '''

We used data from 7 subjects with a diverse set of visual experiments including localizer, morphing, rest, internal tasks, and movie. The functional scans were pre-processed for motion artifacts, manually aligned into the Talairach coordinate system, detrended (removing linear trends in the
baseline activation) and smoothed (8mm kernel).

Fig. 1 shows the 2-system partition extracted in each subject independently
of all others. It also displays the boundaries of the intrinsic system determined
through the traditional seed selection, showing good agreement between the two
partitions. Fig. 2 presents the results of further clustering the stimulus-driven cluster into two clusters independently for each subject.

<table>
<tr> <th> '''Fig 1. 2-System Parcelation. Results for all 7 subjects.''' <th> '''Fig 2. 3-System Parcelation. Results for all 7 subjects.'''
<tr> <td align="center">
[[Image:mit_fmri_clustering_parcellation2_shb1_4.png |400px]]
[[Image:mit_fmri_clustering_parcellation2_shb5_6.png |400px]]
[[Image:mit_fmri_clustering_parcellation2_shb7.png |400px]]
<td align="center">
[[Image:mit_fmri_clustering_parcellation3_shb1_3.png |400px]]
[[Image:mit_fmri_clustering_parcellation3_shb4_5.png |400px]]
[[Image:mit_fmri_clustering_parcellation3_shb6.png |400px]]
[[Image:mit_fmri_clustering_parcellation3_shb7.png |400px]]
</table>

Fig.3 presents the group average of the subject-specific 2-system maps. Color shading shows the proportion of subjects whose clustering agreed with the majority label. Fig. 4 shows the group average of a further parcelation of the intrinsic system, i.e., one of two clusters associated with the non-stimulus-driven regions. In order to present a validation of the method, we compare these results with the conventional scheme for detection of visually responsive areas. In Fig. 5, color shows the statistical parametric map while solid lines indicate the boundaries of the visual system obtained through clustering. The result illustrate the agreement between the two methods.

<table>
<tr><th> '''Fig 3. 2-System Parcellation. Group-wise result.''' <th> '''Fig 4. Validation: Parcelation of the intrinsic system.'''
<tr> <td align="center">
[[Image:mit_fmri_clustering_parcellation2_xsub.png |thumb|570px]]
<td align="center">
[[Image:mit_fmri_clustering_intrinsicsystem.png |thumb|500px]]
</table>

{|
|+ '''Fig 5. Validation: Visual system.'''
|valign="top"|[[Image:mit_fmri_clustering_validation.png |thumb|1150px]]
|}

'''''Exploring Functional Connectivity in fMRI via Clustering'''''

As a continuation to the above experiments, we apply two distinct clustering algorithms to functional connectivity analysis: K-Means clustering and Spectral Clustering. The K-Means algorithm assumes that each voxel time course is drawn independently from one of <em>k</em> multivariate Gaussian distributions with unique means and spherical covariances. In contrast, Spectral Clustering does not presume any parametric form for the data. Rather it captures the underlying signal geometry by inducing a low-dimensional representation based on a pairwise affinity matrix constructed from the data. Without placing any <em>a priori</em> constraints, both clustering methods yield partitions that are associated with brain systems traditionally identified via seed-based correlation analysis. Our empirical results suggest that clustering provides a valuable tool for functional connectivity analysis.

One downside of Spectral Clustering is that it relies on the eigen-decomposition of an <em>NxN</em> affinity matrix, where <em>N</em> is the number of voxels in the whole brain. Since <em>N</em> is on the order of ~200,000 voxels, it is infeasible to compute the full eigen-decomposition given realistic memory and time constraints. To solve this problem, we approximate the leading eigenvalues and eigenvectors of the affinity matrix via the Nystrom Method. This is done by selecting a random subset of "Nystrom Samples" from the data. The affinity matrix and spectral decomposition is computed only for this subset, and the results are projected onto the remaining data points.

'''''Experimental Results'''''

We validate these algorithms on resting state data collected from 45 healthy young adults (mean age 21.5, 26 female). Four 2mm isotropic functional runs were acquired from each subject. Each scan lasted for 6m20s with TR = 5s. The first 4 time points in each run were discarded, yielding 72 time samples per run. The entire brain volume is partitioned into an increasing number of clusters. We perform standard preprocessing on each of the four runs, including motion correction by rigid body alignment of the volumes, slice timing correction and registration to the MNI atlas space. The data is spatially smoothed with a 6mm 3D Gaussian filter, temporally low-pass filtered using a 0.08Hz cutoff, and motion corrected via linear regression. Next, we estimate and remove contributions from the white matter, ventricle and whole brain regions (assuming a linear signal model). We mask the data to include only brain voxels and normalized the time courses to have zero mean and unit variance. Finally, we concatenate the four runs into a single time course for analysis.

We first study the robustness of Spectral Clustering to the number of random samples. In this experiment, we start with a 4,000-sample Nystrom set, which is the computational limit of our machine. We then iteratively remove 500 samples and examine the effect on clustering performance. After matching the resulting clusters to those estimated with 4,000 samples, we compute the percentage of mismatched voxels between each trial and the 4,000-sample template. This procedure is repeated twice for each participant.

<table>
<tr> <th> '''Fig 6. Varying the number of Nystrom Samples''' <th> '''Fig 7. Nystrom consistency for 2,000 random samples'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_Samples_LogMedian2.jpeg |400px]]
<td align="center">
[[Image:mit_fmri_clustering_Consistency_Box.jpeg |400px]]
</table>

Fig 6. depicts the median clustering difference when varying the number of Nystrom samples. Values represent the percentage of mismatched voxels w.r.t. the 4,000-sample template. Error bars delineate the <em>10th</em>-<em>90</em> percentile region. The median clustering difference is less than 1% for 1,000 or more Nystrom samples, and the <em>90th</em> percentile difference is less than 1% for 1,500 or more samples. This experiment suggests that Nystrom-based SC converges to a stable clustering pattern as the number of samples increases. Based on these results, we chose to use 2,000 Nystrom samples for the remainder of this work. At this sample size, less than 5% of the runs for 2,4,5 clusters and approximately 8% of the runs for 3 clusters differed by more than 5% from the 4,000-sample template.

The box plot in Fig 7. summarizes the consistency of Nystrom-based Spectral Clustering across
different random samplings. The red lines indicate median values, the box corresponds to the upper and lower quartiles, and error bars denote the <em>10th</em> and <em>90th</em> percentiles. Here, we perform SC 10 times on each participant using 2,000 Nystrom samples. We then align the cluster maps and compute the percentage of mismatched voxels between each unique pair of runs. This yields a total of 45 comparisons per participant. In all cases, the median clustering difference is less than 1%, and the <em>90th</em> percentile value is less than 2.1%. Empirically, we find that Nystrom SC predictably converges to a second or third cluster pattern in only a handful of participants. This experiment suggests that we can obtain consistent clusterings with only 2,000 Nystrom samples.

<table>
<tr> ''' Fig 8. Clustering results across participants. The brain is partitioned into 5 clusters using Spectral Clustering/K-Means, and various seed are selected for Seed-Based Analysis. The color indicates the proportion of participants for whom the voxel was included in the detected system.'''
<tr> <th> '''Spectral Clustering''' <th> '''K-Means''' <th> '''Seed-Based'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Clust_2.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Clust_1.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Seed_PCC.jpeg |275px]]
<tr> <th> '''Cluster 1, Slice 37''' <th> '''Cluster 1, Slice 37''' <th> '''PCC, Slice 37'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Double.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Double.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Seed_vACC.jpeg |275px]]
<tr> <th> '''Cluster 1, Slice 55''' <th> '''Cluster 1, Slice 55''' <th> '''vACC, Slice 55'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Clust_3.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Clust_4.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Seed_V1.jpeg |275px]]
<tr> <th> '''Cluster 2, Slice 55''' <th> '''Cluster 2, Slice 55''' <th> '''Visual, Slice 55'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Clust_4.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Clust_3.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Seed_M1.jpeg |275px]]
<tr> <th> '''Cluster 3, Slice 31''' <th> '''Cluster 3, Slice 31''' <th> '''Motor, Slice 31'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Clust_1.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Clust_2.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Seed_IPS.jpeg |275px]]
<tr> <th> '''Cluster 4, Slice 31''' <th> '''Cluster 4, Slice 31''' <th> '''IPS, Slice 31'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Clust_5.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Clust_5.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Colorbar2.jpeg |64px]]
<tr> <th> '''Cluster 5, Slice 37''' <th> '''Cluster 5, Slice 37''' <th>
</table>

Fig 8. shows clearly that both Spectral Clustering and K-Means can identify well-known structures such as the default network, the visual cortex, the motor cortex, and the dorsal attention system. Spectral Clustering and K-Means also identified white matter. In general, one would not attempt to delineate this region using seed-based correlation analysis because we regress out the white matter signal during the preprocessing. In our experiments Spectral Clustering and K-Means achieve similar clustering results across participants. Furthermore, both methods identify the same functional systems as seed-based analysis without requiring <em>a priori</em> knowledge about the brain and without significant computation. Thus, clustering algorithms offer a viable alternative to standard functional connectivity analysis techniques.

''' ''Clustering Study of Domain Specificity in High Level Visual Cortex'' '''

As a more specific application of model-based clustering algorithms, we are devising clustering algorithms for detection of functional connectivity in high-level visual cortex. It is suggested that there are regions in the visual cortex with high selectivity to certain categories of visual stimuli. Currently, the conventional method for detection of these methods is based on statistical tests comparing response of each voxel in the brain to different visual categories to see if it shows considerably higher activation to one category. For example, the well-known FFA (Fusiform Face Area) is the set of voxels which show high activation to face images. We use a model-based clustering approach to the analysis of this type of data as a means to make this analysis automatic and further discover new structures in the high-level visual cortex.

Introducing the notion of space of activation
profiles, we construct a representation of the data which explicitly
parametrizes all interesting patterns of activation. Mapping the data into
this space, we formulate a model-based clustering algorithm that simultaneously
finds a set of activation profiles and their spatial maps. We validate
our method on the data from studies of category selectivity in visual
cortex, demonstrating good agreement with the findings based on prior
hypothesis-driven methods. This model enables functional group analysis
independent of spatial correspondence among subjects. We are currently working on a co-clustering extension of this
algorithm which can simultaneously find a set of clusters of voxels and meta-categories
of stimuli in experiments with diverse sets of stimulus categories.

Fig. 9 compares the map of voxels assigned to a face-selective profile by our algorithm with the t-test's map of voxels with statistically significant (p<0.0001) response to faces when compared with object stimuli. Note that in contrast with the hypothesis testing method, we don't specify the existence of a face-selective region in our algorithm and the algorithm automatically discovers such a profile of activation in the data.

{|
|+ '''Fig 9. Spatial maps of the face selective regions found by the statistical test (red) and our mixture model (dark blue). Maps are presented in alternating rows for comparison. Visually responsive mask of voxels used in our experiment is illustrated in yellow and light blue.'''
|align="center"|[[Image:mit_fmri_clustering_mapffacompare.PNG |thumb|800px]]
|}

''' ''Comparison of Data-Driven Analysis Methods for Identiﬁcation of Functional Connectivity in fMRI'' '''

Although ICA and clustering rely on very different assumptions on the underlying distributions, they produce surprisingly similar results for signals with large variation. Our main goal is to evaluate and compare the performance of ICA and clustering based on Gaussian mixture model (GMM) for identiﬁcation of functional connectivity. Using the synthetic data with artiﬁcial activations and artifacts under various levels of length of the time course and signal-to-noise ratio of the data, we compare both spatial maps and their associated time courses estimated by ICA and GMM to each other and to the ground truth. We choose the number of sources via the model selection scheme, and compare all of the resulting components of GMM and ICA, not just the task-related components, after we match them component-wise using the Hungarian algorithm. This comparison scheme is veriﬁed in a high level visual cortex fMRI study. We ﬁnd that ICA requires a smaller number of total components to extract the task-related components, but also needs a large number of total components to describe the entire data. We are currently applying ICA and clustering methods to connectivity analysis of schizophrenia patients.

'''''Hierarchical Model for Exploratory fMRI Analysis without Spatial Normalization'''''

Building on the work on the clustering model for the domain specificity, we develop a hierarchical exploratory method for simultaneous parcellation of multisub ect fMRI data into functionally coherent areas. The method is based on a solely functional representation of the fMRI data and a hierarchical probabilistic model that accounts for both inter-subject and intra-subject forms of variability in fMRI response. We employ a Variational Bayes approximation to ﬁt the model to the data. The resulting algorithm ﬁnds a functional parcellation of the individual brains along with a set of population-level clusters, establishing correspondence between these two levels. The model eliminates the need for spatial normalization while still enabling us to fuse data from several subjects. We demonstrate the application of our method on the same visual fMRI study as before. Fig. 10 shows the scene-selective parcel in 2 different subjects. Parcel-level spatial correspondence is evident in the figure between the subjects.

<table>
<tr> <th> '''Fig 10. The map of the scene selective parcels in two different subjects. The rough location of the scene-selective areas PPA and TOS, identified by the expert, are shown on the maps by yellow and green circles, respectively.'''
<tr>
<td align="center">
[[Image:mit_fmriclustering_hierarchicalppamapsubject1.jpg |650px]]
<td align="center">
[[Image:mit_fmriclustering_hierarchicalppamapsubject2.jpg |650px]]
</table>

= Key Investigators =

* MIT Algorithms: Danial Lashkari, Y. Bryce Kim, Archana Venkataraman, Polina Golland, Nancy Kanwisher.
* Harvard DBP 2: J. Oh, Marek Kubicki.

= Publications =

''In print''

* [http://www.na-mic.org/publications/pages/display?search=Projects%3AfMRIClustering&submit=Search&words=all&title=checked&keywords=checked&authors=checked&abstract=checked&sponsors=checked&searchbytag=checked| NA-MIC Publications Database]

''In press''

D. Lashkari and P. Golland, Exploratory fMRI Analysis without Spatial Normalization. To appear in Proc. IPMI: International Conference on Information Processing and Medical Imaging, 2009.

Project Week Results: [[2008_Summer_Project_Week:fMRIconnectivity|June 2008]]

[[Category:fMRI]]

Projects:fMRIClustering

2009-09-10T18:46:20Z

Danial:

Back to [[NA-MIC_Internal_Collaborations:fMRIAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]
__NOTOC__
= fMRI Clustering =

One of the major goals in analysis of fMRI data is the detection of networks in the brain with similar functional behavior. A wide variety of methods including hypothesis-driven statistical tests, unsupervised learning methods such as PCA and ICA, and different clustering algorithms have been employed to find these networks. This project aims to particularly study application of model-based clustering algorithms in identification of functional connectivity in the brain.

= Description =

'''''Generative Model for Functional Connectivity'''''

In the classical functional connectivity analysis, networks of interest are
defined based on correlation with the mean time course of a user-selected
`seed' region. Further, the user has to also specify a subject-specific threshold at which correlation
values are deemed significant. In this project, we simultaneously estimate the optimal
representative time courses that summarize the fMRI data well and
the partition of the volume into a set of disjoint regions that are best
explained by these representative time courses. This approach to functional connectivity analysis offers two
advantages. First, is removes the sensitivity of the analysis to the details
of the seed selection. Second, it substantially simplifies group analysis
by eliminating the need for the subject-specific threshold. Our experimental results indicate that
the functional segmentation provides a robust, anatomically meaningful
and consistent model for functional connectivity in fMRI.

We formulate the problem of characterizing connectivity as a partition of voxels into subsets that are well characterized by a certain number of representative hypotheses, or time courses, based on the similarity of their time courses to each hypothesis. We model the fMRI signal at each voxel as generated by a mixture of Gaussian distributions whose centers are the desired representative time courses. Using the EM algorithm to solve the corresponding model-fitting problem, we alternatively estimate the representative time courses and cluster assignments to improve our random initialization.

''' ''Experimental Results'' '''

We used data from 7 subjects with a diverse set of visual experiments including localizer, morphing, rest, internal tasks, and movie. The functional scans were pre-processed for motion artifacts, manually aligned into the Talairach coordinate system, detrended (removing linear trends in the
baseline activation) and smoothed (8mm kernel).

Fig. 1 shows the 2-system partition extracted in each subject independently
of all others. It also displays the boundaries of the intrinsic system determined
through the traditional seed selection, showing good agreement between the two
partitions. Fig. 2 presents the results of further clustering the stimulus-driven cluster into two clusters independently for each subject.

<table>
<tr> <th> '''Fig 1. 2-System Parcelation. Results for all 7 subjects.''' <th> '''Fig 2. 3-System Parcelation. Results for all 7 subjects.'''
<tr> <td align="center">
[[Image:mit_fmri_clustering_parcellation2_shb1_4.png |400px]]
[[Image:mit_fmri_clustering_parcellation2_shb5_6.png |400px]]
[[Image:mit_fmri_clustering_parcellation2_shb7.png |400px]]
<td align="center">
[[Image:mit_fmri_clustering_parcellation3_shb1_3.png |400px]]
[[Image:mit_fmri_clustering_parcellation3_shb4_5.png |400px]]
[[Image:mit_fmri_clustering_parcellation3_shb6.png |400px]]
[[Image:mit_fmri_clustering_parcellation3_shb7.png |400px]]
</table>

Fig.3 presents the group average of the subject-specific 2-system maps. Color shading shows the proportion of subjects whose clustering agreed with the majority label. Fig. 4 shows the group average of a further parcelation of the intrinsic system, i.e., one of two clusters associated with the non-stimulus-driven regions. In order to present a validation of the method, we compare these results with the conventional scheme for detection of visually responsive areas. In Fig. 5, color shows the statistical parametric map while solid lines indicate the boundaries of the visual system obtained through clustering. The result illustrate the agreement between the two methods.

<table>
<tr><th> '''Fig 3. 2-System Parcellation. Group-wise result.''' <th> '''Fig 4. Validation: Parcelation of the intrinsic system.'''
<tr> <td align="center">
[[Image:mit_fmri_clustering_parcellation2_xsub.png |thumb|570px]]
<td align="center">
[[Image:mit_fmri_clustering_intrinsicsystem.png |thumb|500px]]
</table>

{|
|+ '''Fig 5. Validation: Visual system.'''
|valign="top"|[[Image:mit_fmri_clustering_validation.png |thumb|1150px]]
|}

'''''Exploring Functional Connectivity in fMRI via Clustering'''''

As a continuation to the above experiments, we apply two distinct clustering algorithms to functional connectivity analysis: K-Means clustering and Spectral Clustering. The K-Means algorithm assumes that each voxel time course is drawn independently from one of <em>k</em> multivariate Gaussian distributions with unique means and spherical covariances. In contrast, Spectral Clustering does not presume any parametric form for the data. Rather it captures the underlying signal geometry by inducing a low-dimensional representation based on a pairwise affinity matrix constructed from the data. Without placing any <em>a priori</em> constraints, both clustering methods yield partitions that are associated with brain systems traditionally identified via seed-based correlation analysis. Our empirical results suggest that clustering provides a valuable tool for functional connectivity analysis.

One downside of Spectral Clustering is that it relies on the eigen-decomposition of an <em>NxN</em> affinity matrix, where <em>N</em> is the number of voxels in the whole brain. Since <em>N</em> is on the order of ~200,000 voxels, it is infeasible to compute the full eigen-decomposition given realistic memory and time constraints. To solve this problem, we approximate the leading eigenvalues and eigenvectors of the affinity matrix via the Nystrom Method. This is done by selecting a random subset of "Nystrom Samples" from the data. The affinity matrix and spectral decomposition is computed only for this subset, and the results are projected onto the remaining data points.

'''''Experimental Results'''''

We validate these algorithms on resting state data collected from 45 healthy young adults (mean age 21.5, 26 female). Four 2mm isotropic functional runs were acquired from each subject. Each scan lasted for 6m20s with TR = 5s. The first 4 time points in each run were discarded, yielding 72 time samples per run. The entire brain volume is partitioned into an increasing number of clusters. We perform standard preprocessing on each of the four runs, including motion correction by rigid body alignment of the volumes, slice timing correction and registration to the MNI atlas space. The data is spatially smoothed with a 6mm 3D Gaussian filter, temporally low-pass filtered using a 0.08Hz cutoff, and motion corrected via linear regression. Next, we estimate and remove contributions from the white matter, ventricle and whole brain regions (assuming a linear signal model). We mask the data to include only brain voxels and normalized the time courses to have zero mean and unit variance. Finally, we concatenate the four runs into a single time course for analysis.

We first study the robustness of Spectral Clustering to the number of random samples. In this experiment, we start with a 4,000-sample Nystrom set, which is the computational limit of our machine. We then iteratively remove 500 samples and examine the effect on clustering performance. After matching the resulting clusters to those estimated with 4,000 samples, we compute the percentage of mismatched voxels between each trial and the 4,000-sample template. This procedure is repeated twice for each participant.

<table>
<tr> <th> '''Fig 6. Varying the number of Nystrom Samples''' <th> '''Fig 7. Nystrom consistency for 2,000 random samples'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_Samples_LogMedian2.jpeg |400px]]
<td align="center">
[[Image:mit_fmri_clustering_Consistency_Box.jpeg |400px]]
</table>

Fig 6. depicts the median clustering difference when varying the number of Nystrom samples. Values represent the percentage of mismatched voxels w.r.t. the 4,000-sample template. Error bars delineate the <em>10th</em>-<em>90</em> percentile region. The median clustering difference is less than 1% for 1,000 or more Nystrom samples, and the <em>90th</em> percentile difference is less than 1% for 1,500 or more samples. This experiment suggests that Nystrom-based SC converges to a stable clustering pattern as the number of samples increases. Based on these results, we chose to use 2,000 Nystrom samples for the remainder of this work. At this sample size, less than 5% of the runs for 2,4,5 clusters and approximately 8% of the runs for 3 clusters differed by more than 5% from the 4,000-sample template.

The box plot in Fig 7. summarizes the consistency of Nystrom-based Spectral Clustering across
different random samplings. The red lines indicate median values, the box corresponds to the upper and lower quartiles, and error bars denote the <em>10th</em> and <em>90th</em> percentiles. Here, we perform SC 10 times on each participant using 2,000 Nystrom samples. We then align the cluster maps and compute the percentage of mismatched voxels between each unique pair of runs. This yields a total of 45 comparisons per participant. In all cases, the median clustering difference is less than 1%, and the <em>90th</em> percentile value is less than 2.1%. Empirically, we find that Nystrom SC predictably converges to a second or third cluster pattern in only a handful of participants. This experiment suggests that we can obtain consistent clusterings with only 2,000 Nystrom samples.

<table>
<tr> ''' Fig 8. Clustering results across participants. The brain is partitioned into 5 clusters using Spectral Clustering/K-Means, and various seed are selected for Seed-Based Analysis. The color indicates the proportion of participants for whom the voxel was included in the detected system.'''
<tr> <th> '''Spectral Clustering''' <th> '''K-Means''' <th> '''Seed-Based'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Clust_2.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Clust_1.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Seed_PCC.jpeg |275px]]
<tr> <th> '''Cluster 1, Slice 37''' <th> '''Cluster 1, Slice 37''' <th> '''PCC, Slice 37'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Double.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Double.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Seed_vACC.jpeg |275px]]
<tr> <th> '''Cluster 1, Slice 55''' <th> '''Cluster 1, Slice 55''' <th> '''vACC, Slice 55'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Clust_3.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Clust_4.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Seed_V1.jpeg |275px]]
<tr> <th> '''Cluster 2, Slice 55''' <th> '''Cluster 2, Slice 55''' <th> '''Visual, Slice 55'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Clust_4.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Clust_3.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Seed_M1.jpeg |275px]]
<tr> <th> '''Cluster 3, Slice 31''' <th> '''Cluster 3, Slice 31''' <th> '''Motor, Slice 31'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Clust_1.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Clust_2.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Seed_IPS.jpeg |275px]]
<tr> <th> '''Cluster 4, Slice 31''' <th> '''Cluster 4, Slice 31''' <th> '''IPS, Slice 31'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Clust_5.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Clust_5.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Colorbar2.jpeg |64px]]
<tr> <th> '''Cluster 5, Slice 37''' <th> '''Cluster 5, Slice 37''' <th>
</table>

Fig 8. shows clearly that both Spectral Clustering and K-Means can identify well-known structures such as the default network, the visual cortex, the motor cortex, and the dorsal attention system. Spectral Clustering and K-Means also identified white matter. In general, one would not attempt to delineate this region using seed-based correlation analysis because we regress out the white matter signal during the preprocessing. In our experiments Spectral Clustering and K-Means achieve similar clustering results across participants. Furthermore, both methods identify the same functional systems as seed-based analysis without requiring <em>a priori</em> knowledge about the brain and without significant computation. Thus, clustering algorithms offer a viable alternative to standard functional connectivity analysis techniques.

''' ''Clustering Study of Domain Specificity in High Level Visual Cortex'' '''

As a more specific application of model-based clustering algorithms, we are devising clustering algorithms for detection of functional connectivity in high-level visual cortex. It is suggested that there are regions in the visual cortex with high selectivity to certain categories of visual stimuli. Currently, the conventional method for detection of these methods is based on statistical tests comparing response of each voxel in the brain to different visual categories to see if it shows considerably higher activation to one category. For example, the well-known FFA (Fusiform Face Area) is the set of voxels which show high activation to face images. We use a model-based clustering approach to the analysis of this type of data as a means to make this analysis automatic and further discover new structures in the high-level visual cortex.

Introducing the notion of space of activation
profiles, we construct a representation of the data which explicitly
parametrizes all interesting patterns of activation. Mapping the data into
this space, we formulate a model-based clustering algorithm that simultaneously
finds a set of activation profiles and their spatial maps. We validate
our method on the data from studies of category selectivity in visual
cortex, demonstrating good agreement with the findings based on prior
hypothesis-driven methods. This model enables functional group analysis
independent of spatial correspondence among subjects. We are currently working on a co-clustering extension of this
algorithm which can simultaneously find a set of clusters of voxels and meta-categories
of stimuli in experiments with diverse sets of stimulus categories.

Fig. 9 compares the map of voxels assigned to a face-selective profile by our algorithm with the t-test's map of voxels with statistically significant (p<0.0001) response to faces when compared with object stimuli. Note that in contrast with the hypothesis testing method, we don't specify the existence of a face-selective region in our algorithm and the algorithm automatically discovers such a profile of activation in the data.

{|
|+ '''Fig 9. Spatial maps of the face selective regions found by the statistical test (red) and our mixture model (dark blue). Maps are presented in alternating rows for comparison. Visually responsive mask of voxels used in our experiment is illustrated in yellow and light blue.'''
|align="center"|[[Image:mit_fmri_clustering_mapffacompare.PNG |thumb|800px]]
|}

''' ''Comparison of Data-Driven Analysis Methods for Identiﬁcation of Functional Connectivity in fMRI'' '''

Although ICA and clustering rely on very different assumptions on the underlying distributions, they produce surprisingly similar results for signals with large variation. Our main goal is to evaluate and compare the performance of ICA and clustering based on Gaussian mixture model (GMM) for identiﬁcation of functional connectivity. Using the synthetic data with artiﬁcial activations and artifacts under various levels of length of the time course and signal-to-noise ratio of the data, we compare both spatial maps and their associated time courses estimated by ICA and GMM to each other and to the ground truth. We choose the number of sources via the model selection scheme, and compare all of the resulting components of GMM and ICA, not just the task-related components, after we match them component-wise using the Hungarian algorithm. This comparison scheme is veriﬁed in a high level visual cortex fMRI study. We ﬁnd that ICA requires a smaller number of total components to extract the task-related components, but also needs a large number of total components to describe the entire data. We are currently applying ICA and clustering methods to connectivity analysis of schizophrenia patients.

'''''Hierarchical Model for Exploratory fMRI Analysis without Spatial Normalization'''''

Building on the work on the clustering model for the domain specificity, we develop a hierarchical exploratory method for simultaneous parcellation of multisub ect fMRI data into functionally coherent areas. The method is based on a solely functional representation of the fMRI data and a hierarchical probabilistic model that accounts for both inter-subject and intra-subject forms of variability in fMRI response. We employ a Variational Bayes approximation to ﬁt the model to the data. The resulting algorithm ﬁnds a functional parcellation of the individual brains along with a set of population-level clusters, establishing correspondence between these two levels. The model eliminates the need for spatial normalization while still enabling us to fuse data from several subjects. We demonstrate the application of our method on the same visual fMRI study as before. Fig. 10 shows the scene-selective parcel in 2 different subjects. Parcel-level spatial correspondence is evident in the figure between the subjects.

<table>
<tr> <th> '''Fig 10. Map of the scene selective parcels in two different subjects. The rough location of the scene-selective areas PPA and TOS, identified by the expert, are shown on the maps by yellow and green circles, respectively.'''
<tr>
<td align="center">
[[Image:mit_fmriclustering_hierarchicalppamapsubject1.jpg |650px]]
<td align="center">
[[Image:mit_fmriclustering_hierarchicalppamapsubject2.jpg |650px]]
</table>

= Key Investigators =

* MIT Algorithms: Danial Lashkari, Y. Bryce Kim, Archana Venkataraman, Polina Golland, Nancy Kanwisher.
* Harvard DBP 2: J. Oh, Marek Kubicki.

= Publications =

''In print''

* [http://www.na-mic.org/publications/pages/display?search=Projects%3AfMRIClustering&submit=Search&words=all&title=checked&keywords=checked&authors=checked&abstract=checked&sponsors=checked&searchbytag=checked| NA-MIC Publications Database]

''In press''

D. Lashkari and P. Golland, Exploratory fMRI Analysis without Spatial Normalization. To appear in Proc. IPMI: International Conference on Information Processing and Medical Imaging, 2009.

Project Week Results: [[2008_Summer_Project_Week:fMRIconnectivity|June 2008]]

[[Category:fMRI]]

Projects:fMRIClustering

2009-09-10T18:44:48Z

Danial:

Back to [[NA-MIC_Internal_Collaborations:fMRIAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]
__NOTOC__
= fMRI Clustering =

One of the major goals in analysis of fMRI data is the detection of networks in the brain with similar functional behavior. A wide variety of methods including hypothesis-driven statistical tests, unsupervised learning methods such as PCA and ICA, and different clustering algorithms have been employed to find these networks. This project aims to particularly study application of model-based clustering algorithms in identification of functional connectivity in the brain.

= Description =

'''''Generative Model for Functional Connectivity'''''

In the classical functional connectivity analysis, networks of interest are
defined based on correlation with the mean time course of a user-selected
`seed' region. Further, the user has to also specify a subject-specific threshold at which correlation
values are deemed significant. In this project, we simultaneously estimate the optimal
representative time courses that summarize the fMRI data well and
the partition of the volume into a set of disjoint regions that are best
explained by these representative time courses. This approach to functional connectivity analysis offers two
advantages. First, is removes the sensitivity of the analysis to the details
of the seed selection. Second, it substantially simplifies group analysis
by eliminating the need for the subject-specific threshold. Our experimental results indicate that
the functional segmentation provides a robust, anatomically meaningful
and consistent model for functional connectivity in fMRI.

We formulate the problem of characterizing connectivity as a partition of voxels into subsets that are well characterized by a certain number of representative hypotheses, or time courses, based on the similarity of their time courses to each hypothesis. We model the fMRI signal at each voxel as generated by a mixture of Gaussian distributions whose centers are the desired representative time courses. Using the EM algorithm to solve the corresponding model-fitting problem, we alternatively estimate the representative time courses and cluster assignments to improve our random initialization.

''' ''Experimental Results'' '''

We used data from 7 subjects with a diverse set of visual experiments including localizer, morphing, rest, internal tasks, and movie. The functional scans were pre-processed for motion artifacts, manually aligned into the Talairach coordinate system, detrended (removing linear trends in the
baseline activation) and smoothed (8mm kernel).

Fig. 1 shows the 2-system partition extracted in each subject independently
of all others. It also displays the boundaries of the intrinsic system determined
through the traditional seed selection, showing good agreement between the two
partitions. Fig. 2 presents the results of further clustering the stimulus-driven cluster into two clusters independently for each subject.

<table>
<tr> <th> '''Fig 1. 2-System Parcelation. Results for all 7 subjects.''' <th> '''Fig 2. 3-System Parcelation. Results for all 7 subjects.'''
<tr> <td align="center">
[[Image:mit_fmri_clustering_parcellation2_shb1_4.png |400px]]
[[Image:mit_fmri_clustering_parcellation2_shb5_6.png |400px]]
[[Image:mit_fmri_clustering_parcellation2_shb7.png |400px]]
<td align="center">
[[Image:mit_fmri_clustering_parcellation3_shb1_3.png |400px]]
[[Image:mit_fmri_clustering_parcellation3_shb4_5.png |400px]]
[[Image:mit_fmri_clustering_parcellation3_shb6.png |400px]]
[[Image:mit_fmri_clustering_parcellation3_shb7.png |400px]]
</table>

Fig.3 presents the group average of the subject-specific 2-system maps. Color shading shows the proportion of subjects whose clustering agreed with the majority label. Fig. 4 shows the group average of a further parcelation of the intrinsic system, i.e., one of two clusters associated with the non-stimulus-driven regions. In order to present a validation of the method, we compare these results with the conventional scheme for detection of visually responsive areas. In Fig. 5, color shows the statistical parametric map while solid lines indicate the boundaries of the visual system obtained through clustering. The result illustrate the agreement between the two methods.

<table>
<tr><th> '''Fig 3. 2-System Parcellation. Group-wise result.''' <th> '''Fig 4. Validation: Parcelation of the intrinsic system.'''
<tr> <td align="center">
[[Image:mit_fmri_clustering_parcellation2_xsub.png |thumb|570px]]
<td align="center">
[[Image:mit_fmri_clustering_intrinsicsystem.png |thumb|500px]]
</table>

{|
|+ '''Fig 5. Validation: Visual system.'''
|valign="top"|[[Image:mit_fmri_clustering_validation.png |thumb|1150px]]
|}

'''''Exploring Functional Connectivity in fMRI via Clustering'''''

As a continuation to the above experiments, we apply two distinct clustering algorithms to functional connectivity analysis: K-Means clustering and Spectral Clustering. The K-Means algorithm assumes that each voxel time course is drawn independently from one of <em>k</em> multivariate Gaussian distributions with unique means and spherical covariances. In contrast, Spectral Clustering does not presume any parametric form for the data. Rather it captures the underlying signal geometry by inducing a low-dimensional representation based on a pairwise affinity matrix constructed from the data. Without placing any <em>a priori</em> constraints, both clustering methods yield partitions that are associated with brain systems traditionally identified via seed-based correlation analysis. Our empirical results suggest that clustering provides a valuable tool for functional connectivity analysis.

One downside of Spectral Clustering is that it relies on the eigen-decomposition of an <em>NxN</em> affinity matrix, where <em>N</em> is the number of voxels in the whole brain. Since <em>N</em> is on the order of ~200,000 voxels, it is infeasible to compute the full eigen-decomposition given realistic memory and time constraints. To solve this problem, we approximate the leading eigenvalues and eigenvectors of the affinity matrix via the Nystrom Method. This is done by selecting a random subset of "Nystrom Samples" from the data. The affinity matrix and spectral decomposition is computed only for this subset, and the results are projected onto the remaining data points.

'''''Experimental Results'''''

We validate these algorithms on resting state data collected from 45 healthy young adults (mean age 21.5, 26 female). Four 2mm isotropic functional runs were acquired from each subject. Each scan lasted for 6m20s with TR = 5s. The first 4 time points in each run were discarded, yielding 72 time samples per run. The entire brain volume is partitioned into an increasing number of clusters. We perform standard preprocessing on each of the four runs, including motion correction by rigid body alignment of the volumes, slice timing correction and registration to the MNI atlas space. The data is spatially smoothed with a 6mm 3D Gaussian filter, temporally low-pass filtered using a 0.08Hz cutoff, and motion corrected via linear regression. Next, we estimate and remove contributions from the white matter, ventricle and whole brain regions (assuming a linear signal model). We mask the data to include only brain voxels and normalized the time courses to have zero mean and unit variance. Finally, we concatenate the four runs into a single time course for analysis.

We first study the robustness of Spectral Clustering to the number of random samples. In this experiment, we start with a 4,000-sample Nystrom set, which is the computational limit of our machine. We then iteratively remove 500 samples and examine the effect on clustering performance. After matching the resulting clusters to those estimated with 4,000 samples, we compute the percentage of mismatched voxels between each trial and the 4,000-sample template. This procedure is repeated twice for each participant.

<table>
<tr> <th> '''Fig 6. Varying the number of Nystrom Samples''' <th> '''Fig 7. Nystrom consistency for 2,000 random samples'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_Samples_LogMedian2.jpeg |400px]]
<td align="center">
[[Image:mit_fmri_clustering_Consistency_Box.jpeg |400px]]
</table>

Fig 6. depicts the median clustering difference when varying the number of Nystrom samples. Values represent the percentage of mismatched voxels w.r.t. the 4,000-sample template. Error bars delineate the <em>10th</em>-<em>90</em> percentile region. The median clustering difference is less than 1% for 1,000 or more Nystrom samples, and the <em>90th</em> percentile difference is less than 1% for 1,500 or more samples. This experiment suggests that Nystrom-based SC converges to a stable clustering pattern as the number of samples increases. Based on these results, we chose to use 2,000 Nystrom samples for the remainder of this work. At this sample size, less than 5% of the runs for 2,4,5 clusters and approximately 8% of the runs for 3 clusters differed by more than 5% from the 4,000-sample template.

The box plot in Fig 7. summarizes the consistency of Nystrom-based Spectral Clustering across
different random samplings. The red lines indicate median values, the box corresponds to the upper and lower quartiles, and error bars denote the <em>10th</em> and <em>90th</em> percentiles. Here, we perform SC 10 times on each participant using 2,000 Nystrom samples. We then align the cluster maps and compute the percentage of mismatched voxels between each unique pair of runs. This yields a total of 45 comparisons per participant. In all cases, the median clustering difference is less than 1%, and the <em>90th</em> percentile value is less than 2.1%. Empirically, we find that Nystrom SC predictably converges to a second or third cluster pattern in only a handful of participants. This experiment suggests that we can obtain consistent clusterings with only 2,000 Nystrom samples.

<table>
<tr> ''' Fig 8. Clustering results across participants. The brain is partitioned into 5 clusters using Spectral Clustering/K-Means, and various seed are selected for Seed-Based Analysis. The color indicates the proportion of participants for whom the voxel was included in the detected system.'''
<tr> <th> '''Spectral Clustering''' <th> '''K-Means''' <th> '''Seed-Based'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Clust_2.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Clust_1.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Seed_PCC.jpeg |275px]]
<tr> <th> '''Cluster 1, Slice 37''' <th> '''Cluster 1, Slice 37''' <th> '''PCC, Slice 37'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Double.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Double.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Seed_vACC.jpeg |275px]]
<tr> <th> '''Cluster 1, Slice 55''' <th> '''Cluster 1, Slice 55''' <th> '''vACC, Slice 55'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Clust_3.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Clust_4.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Seed_V1.jpeg |275px]]
<tr> <th> '''Cluster 2, Slice 55''' <th> '''Cluster 2, Slice 55''' <th> '''Visual, Slice 55'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Clust_4.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Clust_3.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Seed_M1.jpeg |275px]]
<tr> <th> '''Cluster 3, Slice 31''' <th> '''Cluster 3, Slice 31''' <th> '''Motor, Slice 31'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Clust_1.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Clust_2.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Seed_IPS.jpeg |275px]]
<tr> <th> '''Cluster 4, Slice 31''' <th> '''Cluster 4, Slice 31''' <th> '''IPS, Slice 31'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Clust_5.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Clust_5.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Colorbar2.jpeg |64px]]
<tr> <th> '''Cluster 5, Slice 37''' <th> '''Cluster 5, Slice 37''' <th>
</table>

Fig 8. shows clearly that both Spectral Clustering and K-Means can identify well-known structures such as the default network, the visual cortex, the motor cortex, and the dorsal attention system. Spectral Clustering and K-Means also identified white matter. In general, one would not attempt to delineate this region using seed-based correlation analysis because we regress out the white matter signal during the preprocessing. In our experiments Spectral Clustering and K-Means achieve similar clustering results across participants. Furthermore, both methods identify the same functional systems as seed-based analysis without requiring <em>a priori</em> knowledge about the brain and without significant computation. Thus, clustering algorithms offer a viable alternative to standard functional connectivity analysis techniques.

''' ''Clustering Study of Domain Specificity in High Level Visual Cortex'' '''

As a more specific application of model-based clustering algorithms, we are devising clustering algorithms for detection of functional connectivity in high-level visual cortex. It is suggested that there are regions in the visual cortex with high selectivity to certain categories of visual stimuli. Currently, the conventional method for detection of these methods is based on statistical tests comparing response of each voxel in the brain to different visual categories to see if it shows considerably higher activation to one category. For example, the well-known FFA (Fusiform Face Area) is the set of voxels which show high activation to face images. We use a model-based clustering approach to the analysis of this type of data as a means to make this analysis automatic and further discover new structures in the high-level visual cortex.

Introducing the notion of space of activation
profiles, we construct a representation of the data which explicitly
parametrizes all interesting patterns of activation. Mapping the data into
this space, we formulate a model-based clustering algorithm that simultaneously
finds a set of activation profiles and their spatial maps. We validate
our method on the data from studies of category selectivity in visual
cortex, demonstrating good agreement with the findings based on prior
hypothesis-driven methods. This model enables functional group analysis
independent of spatial correspondence among subjects. We are currently working on a co-clustering extension of this
algorithm which can simultaneously find a set of clusters of voxels and meta-categories
of stimuli in experiments with diverse sets of stimulus categories.

Fig. 9 compares the map of voxels assigned to a face-selective profile by our algorithm with the t-test's map of voxels with statistically significant (p<0.0001) response to faces when compared with object stimuli. Note that in contrast with the hypothesis testing method, we don't specify the existence of a face-selective region in our algorithm and the algorithm automatically discovers such a profile of activation in the data.

{|
|+ '''Fig 9. Spatial maps of the face selective regions found by the statistical test (red) and our mixture model (dark blue). Maps are presented in alternating rows for comparison. Visually responsive mask of voxels used in our experiment is illustrated in yellow and light blue.'''
|align="center"|[[Image:mit_fmri_clustering_mapffacompare.PNG |thumb|800px]]
|}

''' ''Comparison of Data-Driven Analysis Methods for Identiﬁcation of Functional Connectivity in fMRI'' '''

Although ICA and clustering rely on very different assumptions on the underlying distributions, they produce surprisingly similar results for signals with large variation. Our main goal is to evaluate and compare the performance of ICA and clustering based on Gaussian mixture model (GMM) for identiﬁcation of functional connectivity. Using the synthetic data with artiﬁcial activations and artifacts under various levels of length of the time course and signal-to-noise ratio of the data, we compare both spatial maps and their associated time courses estimated by ICA and GMM to each other and to the ground truth. We choose the number of sources via the model selection scheme, and compare all of the resulting components of GMM and ICA, not just the task-related components, after we match them component-wise using the Hungarian algorithm. This comparison scheme is veriﬁed in a high level visual cortex fMRI study. We ﬁnd that ICA requires a smaller number of total components to extract the task-related components, but also needs a large number of total components to describe the entire data. We are currently applying ICA and clustering methods to connectivity analysis of schizophrenia patients.

'''''Hierarchical Model for Exploratory fMRI Analysis
without Spatial Normalization'''''

Building on the work on the clustering model for the domain specificity, we develop a hierarchical exploratory method for simultaneous parcellation of multisub ect fMRI data into functionally coherent areas. The method is based on a solely functional representation of the fMRI data and a hierarchical probabilistic model that accounts for both inter-subject and intra-subject forms of variability in fMRI response. We employ a Variational Bayes approximation to ﬁt the model to the data. The resulting algorithm ﬁnds a functional parcellation of the individual brains along with a set of population-level clusters, establishing correspondence between these two levels. The model eliminates the need for spatial normalization while still enabling us to fuse data from several subjects. We demonstrate the application of our method on the same visual fMRI study as before. Fig. 10 shows the scene-selective parcel in 2 different subjects. The rough location of the scene-selective areas PPA and TOS, identified by the expert, are shown on the maps by yellow and green circles, respectively. Parcel-level spatial correspondence is evident in the figure between the subjects.

<table>
<tr> <th> '''Fig 10. Map of the scene selective parcels in two different subjects'''
<tr>
<td align="center">
[[Image:mit_fmriclustering_hierarchicalppamapsubject1.jpg |650px]]
<td align="center">
[[Image:mit_fmriclustering_hierarchicalppamapsubject2.jpg |650px]]
</table>

= Key Investigators =

* MIT Algorithms: Danial Lashkari, Y. Bryce Kim, Archana Venkataraman, Polina Golland, Nancy Kanwisher.
* Harvard DBP 2: J. Oh, Marek Kubicki.

= Publications =

''In print''

* [http://www.na-mic.org/publications/pages/display?search=Projects%3AfMRIClustering&submit=Search&words=all&title=checked&keywords=checked&authors=checked&abstract=checked&sponsors=checked&searchbytag=checked| NA-MIC Publications Database]

''In press''

D. Lashkari and P. Golland, Exploratory fMRI Analysis without Spatial Normalization. To appear in Proc. IPMI: International Conference on Information Processing and Medical Imaging, 2009.

Project Week Results: [[2008_Summer_Project_Week:fMRIconnectivity|June 2008]]

[[Category:fMRI]]

Projects:fMRIClustering

2009-09-10T18:42:45Z

Danial:

Back to [[NA-MIC_Internal_Collaborations:fMRIAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]
__NOTOC__
= fMRI Clustering =

One of the major goals in analysis of fMRI data is the detection of networks in the brain with similar functional behavior. A wide variety of methods including hypothesis-driven statistical tests, unsupervised learning methods such as PCA and ICA, and different clustering algorithms have been employed to find these networks. This project aims to particularly study application of model-based clustering algorithms in identification of functional connectivity in the brain.

= Description =

'''''Generative Model for Functional Connectivity'''''

In the classical functional connectivity analysis, networks of interest are
defined based on correlation with the mean time course of a user-selected
`seed' region. Further, the user has to also specify a subject-specific threshold at which correlation
values are deemed significant. In this project, we simultaneously estimate the optimal
representative time courses that summarize the fMRI data well and
the partition of the volume into a set of disjoint regions that are best
explained by these representative time courses. This approach to functional connectivity analysis offers two
advantages. First, is removes the sensitivity of the analysis to the details
of the seed selection. Second, it substantially simplifies group analysis
by eliminating the need for the subject-specific threshold. Our experimental results indicate that
the functional segmentation provides a robust, anatomically meaningful
and consistent model for functional connectivity in fMRI.

We formulate the problem of characterizing connectivity as a partition of voxels into subsets that are well characterized by a certain number of representative hypotheses, or time courses, based on the similarity of their time courses to each hypothesis. We model the fMRI signal at each voxel as generated by a mixture of Gaussian distributions whose centers are the desired representative time courses. Using the EM algorithm to solve the corresponding model-fitting problem, we alternatively estimate the representative time courses and cluster assignments to improve our random initialization.

''' ''Experimental Results'' '''

We used data from 7 subjects with a diverse set of visual experiments including localizer, morphing, rest, internal tasks, and movie. The functional scans were pre-processed for motion artifacts, manually aligned into the Talairach coordinate system, detrended (removing linear trends in the
baseline activation) and smoothed (8mm kernel).

Fig. 1 shows the 2-system partition extracted in each subject independently
of all others. It also displays the boundaries of the intrinsic system determined
through the traditional seed selection, showing good agreement between the two
partitions. Fig. 2 presents the results of further clustering the stimulus-driven cluster into two clusters independently for each subject.

<table>
<tr> <th> '''Fig 1. 2-System Parcelation. Results for all 7 subjects.''' <th> '''Fig 2. 3-System Parcelation. Results for all 7 subjects.'''
<tr> <td align="center">
[[Image:mit_fmri_clustering_parcellation2_shb1_4.png |400px]]
[[Image:mit_fmri_clustering_parcellation2_shb5_6.png |400px]]
[[Image:mit_fmri_clustering_parcellation2_shb7.png |400px]]
<td align="center">
[[Image:mit_fmri_clustering_parcellation3_shb1_3.png |400px]]
[[Image:mit_fmri_clustering_parcellation3_shb4_5.png |400px]]
[[Image:mit_fmri_clustering_parcellation3_shb6.png |400px]]
[[Image:mit_fmri_clustering_parcellation3_shb7.png |400px]]
</table>

Fig.3 presents the group average of the subject-specific 2-system maps. Color shading shows the proportion of subjects whose clustering agreed with the majority label. Fig. 4 shows the group average of a further parcelation of the intrinsic system, i.e., one of two clusters associated with the non-stimulus-driven regions. In order to present a validation of the method, we compare these results with the conventional scheme for detection of visually responsive areas. In Fig. 5, color shows the statistical parametric map while solid lines indicate the boundaries of the visual system obtained through clustering. The result illustrate the agreement between the two methods.

<table>
<tr><th> '''Fig 3. 2-System Parcellation. Group-wise result.''' <th> '''Fig 4. Validation: Parcelation of the intrinsic system.'''
<tr> <td align="center">
[[Image:mit_fmri_clustering_parcellation2_xsub.png |thumb|570px]]
<td align="center">
[[Image:mit_fmri_clustering_intrinsicsystem.png |thumb|500px]]
</table>

{|
|+ '''Fig 5. Validation: Visual system.'''
|valign="top"|[[Image:mit_fmri_clustering_validation.png |thumb|1150px]]
|}

'''''Exploring Functional Connectivity in fMRI via Clustering'''''

As a continuation to the above experiments, we apply two distinct clustering algorithms to functional connectivity analysis: K-Means clustering and Spectral Clustering. The K-Means algorithm assumes that each voxel time course is drawn independently from one of <em>k</em> multivariate Gaussian distributions with unique means and spherical covariances. In contrast, Spectral Clustering does not presume any parametric form for the data. Rather it captures the underlying signal geometry by inducing a low-dimensional representation based on a pairwise affinity matrix constructed from the data. Without placing any <em>a priori</em> constraints, both clustering methods yield partitions that are associated with brain systems traditionally identified via seed-based correlation analysis. Our empirical results suggest that clustering provides a valuable tool for functional connectivity analysis.

One downside of Spectral Clustering is that it relies on the eigen-decomposition of an <em>NxN</em> affinity matrix, where <em>N</em> is the number of voxels in the whole brain. Since <em>N</em> is on the order of ~200,000 voxels, it is infeasible to compute the full eigen-decomposition given realistic memory and time constraints. To solve this problem, we approximate the leading eigenvalues and eigenvectors of the affinity matrix via the Nystrom Method. This is done by selecting a random subset of "Nystrom Samples" from the data. The affinity matrix and spectral decomposition is computed only for this subset, and the results are projected onto the remaining data points.

'''''Experimental Results'''''

We validate these algorithms on resting state data collected from 45 healthy young adults (mean age 21.5, 26 female). Four 2mm isotropic functional runs were acquired from each subject. Each scan lasted for 6m20s with TR = 5s. The first 4 time points in each run were discarded, yielding 72 time samples per run. The entire brain volume is partitioned into an increasing number of clusters. We perform standard preprocessing on each of the four runs, including motion correction by rigid body alignment of the volumes, slice timing correction and registration to the MNI atlas space. The data is spatially smoothed with a 6mm 3D Gaussian filter, temporally low-pass filtered using a 0.08Hz cutoff, and motion corrected via linear regression. Next, we estimate and remove contributions from the white matter, ventricle and whole brain regions (assuming a linear signal model). We mask the data to include only brain voxels and normalized the time courses to have zero mean and unit variance. Finally, we concatenate the four runs into a single time course for analysis.

We first study the robustness of Spectral Clustering to the number of random samples. In this experiment, we start with a 4,000-sample Nystrom set, which is the computational limit of our machine. We then iteratively remove 500 samples and examine the effect on clustering performance. After matching the resulting clusters to those estimated with 4,000 samples, we compute the percentage of mismatched voxels between each trial and the 4,000-sample template. This procedure is repeated twice for each participant.

<table>
<tr> <th> '''Fig 6. Varying the number of Nystrom Samples''' <th> '''Fig 7. Nystrom consistency for 2,000 random samples'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_Samples_LogMedian2.jpeg |400px]]
<td align="center">
[[Image:mit_fmri_clustering_Consistency_Box.jpeg |400px]]
</table>

Fig 6. depicts the median clustering difference when varying the number of Nystrom samples. Values represent the percentage of mismatched voxels w.r.t. the 4,000-sample template. Error bars delineate the <em>10th</em>-<em>90</em> percentile region. The median clustering difference is less than 1% for 1,000 or more Nystrom samples, and the <em>90th</em> percentile difference is less than 1% for 1,500 or more samples. This experiment suggests that Nystrom-based SC converges to a stable clustering pattern as the number of samples increases. Based on these results, we chose to use 2,000 Nystrom samples for the remainder of this work. At this sample size, less than 5% of the runs for 2,4,5 clusters and approximately 8% of the runs for 3 clusters differed by more than 5% from the 4,000-sample template.

The box plot in Fig 7. summarizes the consistency of Nystrom-based Spectral Clustering across
different random samplings. The red lines indicate median values, the box corresponds to the upper and lower quartiles, and error bars denote the <em>10th</em> and <em>90th</em> percentiles. Here, we perform SC 10 times on each participant using 2,000 Nystrom samples. We then align the cluster maps and compute the percentage of mismatched voxels between each unique pair of runs. This yields a total of 45 comparisons per participant. In all cases, the median clustering difference is less than 1%, and the <em>90th</em> percentile value is less than 2.1%. Empirically, we find that Nystrom SC predictably converges to a second or third cluster pattern in only a handful of participants. This experiment suggests that we can obtain consistent clusterings with only 2,000 Nystrom samples.

<table>
<tr> ''' Fig 8. Clustering results across participants. The brain is partitioned into 5 clusters using Spectral Clustering/K-Means, and various seed are selected for Seed-Based Analysis. The color indicates the proportion of participants for whom the voxel was included in the detected system.'''
<tr> <th> '''Spectral Clustering''' <th> '''K-Means''' <th> '''Seed-Based'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Clust_2.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Clust_1.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Seed_PCC.jpeg |275px]]
<tr> <th> '''Cluster 1, Slice 37''' <th> '''Cluster 1, Slice 37''' <th> '''PCC, Slice 37'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Double.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Double.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Seed_vACC.jpeg |275px]]
<tr> <th> '''Cluster 1, Slice 55''' <th> '''Cluster 1, Slice 55''' <th> '''vACC, Slice 55'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Clust_3.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Clust_4.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Seed_V1.jpeg |275px]]
<tr> <th> '''Cluster 2, Slice 55''' <th> '''Cluster 2, Slice 55''' <th> '''Visual, Slice 55'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Clust_4.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Clust_3.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Seed_M1.jpeg |275px]]
<tr> <th> '''Cluster 3, Slice 31''' <th> '''Cluster 3, Slice 31''' <th> '''Motor, Slice 31'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Clust_1.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Clust_2.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Seed_IPS.jpeg |275px]]
<tr> <th> '''Cluster 4, Slice 31''' <th> '''Cluster 4, Slice 31''' <th> '''IPS, Slice 31'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Clust_5.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Clust_5.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Colorbar2.jpeg |64px]]
<tr> <th> '''Cluster 5, Slice 37''' <th> '''Cluster 5, Slice 37''' <th>
</table>

Fig 8. shows clearly that both Spectral Clustering and K-Means can identify well-known structures such as the default network, the visual cortex, the motor cortex, and the dorsal attention system. Spectral Clustering and K-Means also identified white matter. In general, one would not attempt to delineate this region using seed-based correlation analysis because we regress out the white matter signal during the preprocessing. In our experiments Spectral Clustering and K-Means achieve similar clustering results across participants. Furthermore, both methods identify the same functional systems as seed-based analysis without requiring <em>a priori</em> knowledge about the brain and without significant computation. Thus, clustering algorithms offer a viable alternative to standard functional connectivity analysis techniques.

''' ''Clustering Study of Domain Specificity in High Level Visual Cortex'' '''

As a more specific application of model-based clustering algorithms, we are devising clustering algorithms for detection of functional connectivity in high-level visual cortex. It is suggested that there are regions in the visual cortex with high selectivity to certain categories of visual stimuli. Currently, the conventional method for detection of these methods is based on statistical tests comparing response of each voxel in the brain to different visual categories to see if it shows considerably higher activation to one category. For example, the well-known FFA (Fusiform Face Area) is the set of voxels which show high activation to face images. We use a model-based clustering approach to the analysis of this type of data as a means to make this analysis automatic and further discover new structures in the high-level visual cortex.

Introducing the notion of space of activation
profiles, we construct a representation of the data which explicitly
parametrizes all interesting patterns of activation. Mapping the data into
this space, we formulate a model-based clustering algorithm that simultaneously
finds a set of activation profiles and their spatial maps. We validate
our method on the data from studies of category selectivity in visual
cortex, demonstrating good agreement with the findings based on prior
hypothesis-driven methods. This model enables functional group analysis
independent of spatial correspondence among subjects. We are currently working on a co-clustering extension of this
algorithm which can simultaneously find a set of clusters of voxels and meta-categories
of stimuli in experiments with diverse sets of stimulus categories.

Fig. 9 compares the map of voxels assigned to a face-selective profile by our algorithm with the t-test's map of voxels with statistically significant (p<0.0001) response to faces when compared with object stimuli. Note that in contrast with the hypothesis testing method, we don't specify the existence of a face-selective region in our algorithm and the algorithm automatically discovers such a profile of activation in the data.

{|
|+ '''Fig 9. Spatial maps of the face selective regions found by the statistical test (red) and our mixture model (dark blue). Maps are presented in alternating rows for comparison. Visually responsive mask of voxels used in our experiment is illustrated in yellow and light blue.'''
|align="center"|[[Image:mit_fmri_clustering_mapffacompare.PNG |thumb|800px]]
|}

''' ''Comparison of Data-Driven Analysis Methods for Identiﬁcation of Functional Connectivity in fMRI'' '''

Although ICA and clustering rely on very diﬀerent assumptions on the underlying distributions, they produce surprisingly similar results for signals with large variation. Our main goal is to evaluate and compare the performance of ICA and clustering based on Gaussian mixture model (GMM) for identiﬁcation of functional connectivity. Using the synthetic data with artiﬁcial activations and artifacts under various levels of length of the time course and signal-to-noise ratio of the data, we compare both spatial maps and their associated time courses estimated by ICA and GMM to each other and to the ground truth. We choose the number of sources via the model selection scheme, and compare all of the resulting components of GMM and ICA, not just the task-related components, after we match them component-wise using the Hungarian algorithm. This comparison scheme is veriﬁed in a high level visual cortex fMRI study. We ﬁnd that ICA requires a smaller number of total components to extract the task-related components, but also needs a large number of total components to describe the entire data. We are currently applying ICA and clustering methods to connectivity analysis of schizophrenia patients.

'''''Hierarchical Model for Exploratory fMRI Analysis
without Spatial Normalization'''''

Building on the work on the clustering model for the domain specificity, we develop a hierarchical exploratory method for simultaneous parcellation of multisub ect fMRI data into functionally coherent areas. The method is based on a solely functional representation of the fMRI data and a hierarchical probabilistic model that accounts for both inter-subject and intra-subject forms of variability in fMRI response. We employ a Variational Bayes approximation to ﬁt the model to the data. The resulting algorithm ﬁnds a functional parcellation of the individual brains along with a set of population-level clusters, establishing correspondence between these two levels. The model eliminates the need for spatial normalization while still enabling us to fuse data from several sub jects.

We demonstrate the application of our method on the same visual fMRI study as before. Fig. 10 shows the scene-selective parcel in 2 different subjects. The rough location of the scene-selective areas PPA and TOS, identified by the expert, are shown on the maps by yellow and green circles, respectively.

<table>
<tr> <th> '''Fig 10. Map of the scene selective parcels in two different subjects'''
<tr>
<td align="center">
[[Image:mit_fmriclustering_hierarchicalppamapsubject1.jpg |650px]]
<td align="center">
[[Image:mit_fmriclustering_hierarchicalppamapsubject2.jpg |650px]]
</table>

= Key Investigators =

* MIT Algorithms: Danial Lashkari, Y. Bryce Kim, Archana Venkataraman, Polina Golland, Nancy Kanwisher.
* Harvard DBP 2: J. Oh, Marek Kubicki.

= Publications =

''In print''

* [http://www.na-mic.org/publications/pages/display?search=Projects%3AfMRIClustering&submit=Search&words=all&title=checked&keywords=checked&authors=checked&abstract=checked&sponsors=checked&searchbytag=checked| NA-MIC Publications Database]

''In press''

D. Lashkari and P. Golland, Exploratory fMRI Analysis without Spatial Normalization. To appear in Proc. IPMI: International Conference on Information Processing and Medical Imaging, 2009.

Project Week Results: [[2008_Summer_Project_Week:fMRIconnectivity|June 2008]]

[[Category:fMRI]]

File:Mit fmriclustering hierarchicalppamapsubject2.jpg

2009-09-10T18:36:17Z

Danial:

File:Mit fmriclustering hierarchicalppamapsubject1.jpg

2009-09-10T18:35:31Z

Danial:

File:Hierarchical-Ppamapsubject2.pdf

2009-09-10T18:31:32Z

Danial:

Projects:fMRIClustering

2009-09-10T18:30:47Z

Danial:

Back to [[NA-MIC_Internal_Collaborations:fMRIAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]
__NOTOC__
= fMRI Clustering =

One of the major goals in analysis of fMRI data is the detection of networks in the brain with similar functional behavior. A wide variety of methods including hypothesis-driven statistical tests, unsupervised learning methods such as PCA and ICA, and different clustering algorithms have been employed to find these networks. This project aims to particularly study application of model-based clustering algorithms in identification of functional connectivity in the brain.

= Description =

'''''Generative Model for Functional Connectivity'''''

In the classical functional connectivity analysis, networks of interest are
defined based on correlation with the mean time course of a user-selected
`seed' region. Further, the user has to also specify a subject-specific threshold at which correlation
values are deemed significant. In this project, we simultaneously estimate the optimal
representative time courses that summarize the fMRI data well and
the partition of the volume into a set of disjoint regions that are best
explained by these representative time courses. This approach to functional connectivity analysis offers two
advantages. First, is removes the sensitivity of the analysis to the details
of the seed selection. Second, it substantially simplifies group analysis
by eliminating the need for the subject-specific threshold. Our experimental results indicate that
the functional segmentation provides a robust, anatomically meaningful
and consistent model for functional connectivity in fMRI.

We formulate the problem of characterizing connectivity as a partition of voxels into subsets that are well characterized by a certain number of representative hypotheses, or time courses, based on the similarity of their time courses to each hypothesis. We model the fMRI signal at each voxel as generated by a mixture of Gaussian distributions whose centers are the desired representative time courses. Using the EM algorithm to solve the corresponding model-fitting problem, we alternatively estimate the representative time courses and cluster assignments to improve our random initialization.

''' ''Experimental Results'' '''

We used data from 7 subjects with a diverse set of visual experiments including localizer, morphing, rest, internal tasks, and movie. The functional scans were pre-processed for motion artifacts, manually aligned into the Talairach coordinate system, detrended (removing linear trends in the
baseline activation) and smoothed (8mm kernel).

Fig. 1 shows the 2-system partition extracted in each subject independently
of all others. It also displays the boundaries of the intrinsic system determined
through the traditional seed selection, showing good agreement between the two
partitions. Fig. 2 presents the results of further clustering the stimulus-driven cluster into two clusters independently for each subject.

<table>
<tr> <th> '''Fig 1. 2-System Parcelation. Results for all 7 subjects.''' <th> '''Fig 2. 3-System Parcelation. Results for all 7 subjects.'''
<tr> <td align="center">
[[Image:mit_fmri_clustering_parcellation2_shb1_4.png |400px]]
[[Image:mit_fmri_clustering_parcellation2_shb5_6.png |400px]]
[[Image:mit_fmri_clustering_parcellation2_shb7.png |400px]]
<td align="center">
[[Image:mit_fmri_clustering_parcellation3_shb1_3.png |400px]]
[[Image:mit_fmri_clustering_parcellation3_shb4_5.png |400px]]
[[Image:mit_fmri_clustering_parcellation3_shb6.png |400px]]
[[Image:mit_fmri_clustering_parcellation3_shb7.png |400px]]
</table>

Fig.3 presents the group average of the subject-specific 2-system maps. Color shading shows the proportion of subjects whose clustering agreed with the majority label. Fig. 4 shows the group average of a further parcelation of the intrinsic system, i.e., one of two clusters associated with the non-stimulus-driven regions. In order to present a validation of the method, we compare these results with the conventional scheme for detection of visually responsive areas. In Fig. 5, color shows the statistical parametric map while solid lines indicate the boundaries of the visual system obtained through clustering. The result illustrate the agreement between the two methods.

<table>
<tr><th> '''Fig 3. 2-System Parcellation. Group-wise result.''' <th> '''Fig 4. Validation: Parcelation of the intrinsic system.'''
<tr> <td align="center">
[[Image:mit_fmri_clustering_parcellation2_xsub.png |thumb|570px]]
<td align="center">
[[Image:mit_fmri_clustering_intrinsicsystem.png |thumb|500px]]
</table>

{|
|+ '''Fig 5. Validation: Visual system.'''
|valign="top"|[[Image:mit_fmri_clustering_validation.png |thumb|1150px]]
|}

'''''Exploring Functional Connectivity in fMRI via Clustering'''''

As a continuation to the above experiments, we apply two distinct clustering algorithms to functional connectivity analysis: K-Means clustering and Spectral Clustering. The K-Means algorithm assumes that each voxel time course is drawn independently from one of <em>k</em> multivariate Gaussian distributions with unique means and spherical covariances. In contrast, Spectral Clustering does not presume any parametric form for the data. Rather it captures the underlying signal geometry by inducing a low-dimensional representation based on a pairwise affinity matrix constructed from the data. Without placing any <em>a priori</em> constraints, both clustering methods yield partitions that are associated with brain systems traditionally identified via seed-based correlation analysis. Our empirical results suggest that clustering provides a valuable tool for functional connectivity analysis.

One downside of Spectral Clustering is that it relies on the eigen-decomposition of an <em>NxN</em> affinity matrix, where <em>N</em> is the number of voxels in the whole brain. Since <em>N</em> is on the order of ~200,000 voxels, it is infeasible to compute the full eigen-decomposition given realistic memory and time constraints. To solve this problem, we approximate the leading eigenvalues and eigenvectors of the affinity matrix via the Nystrom Method. This is done by selecting a random subset of "Nystrom Samples" from the data. The affinity matrix and spectral decomposition is computed only for this subset, and the results are projected onto the remaining data points.

'''''Experimental Results'''''

We validate these algorithms on resting state data collected from 45 healthy young adults (mean age 21.5, 26 female). Four 2mm isotropic functional runs were acquired from each subject. Each scan lasted for 6m20s with TR = 5s. The first 4 time points in each run were discarded, yielding 72 time samples per run. The entire brain volume is partitioned into an increasing number of clusters. We perform standard preprocessing on each of the four runs, including motion correction by rigid body alignment of the volumes, slice timing correction and registration to the MNI atlas space. The data is spatially smoothed with a 6mm 3D Gaussian filter, temporally low-pass filtered using a 0.08Hz cutoff, and motion corrected via linear regression. Next, we estimate and remove contributions from the white matter, ventricle and whole brain regions (assuming a linear signal model). We mask the data to include only brain voxels and normalized the time courses to have zero mean and unit variance. Finally, we concatenate the four runs into a single time course for analysis.

We first study the robustness of Spectral Clustering to the number of random samples. In this experiment, we start with a 4,000-sample Nystrom set, which is the computational limit of our machine. We then iteratively remove 500 samples and examine the effect on clustering performance. After matching the resulting clusters to those estimated with 4,000 samples, we compute the percentage of mismatched voxels between each trial and the 4,000-sample template. This procedure is repeated twice for each participant.

<table>
<tr> <th> '''Fig 1. Varying the number of Nystrom Samples''' <th> '''Fig 2. Nystrom consistency for 2,000 random samples'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_Samples_LogMedian2.jpeg |400px]]
<td align="center">
[[Image:mit_fmri_clustering_Consistency_Box.jpeg |400px]]
</table>

Fig 1. depicts the median clustering difference when varying the number of Nystrom samples. Values represent the percentage of mismatched voxels w.r.t. the 4,000-sample template. Error bars delineate the <em>10th</em>-<em>90</em> percentile region. The median clustering difference is less than 1% for 1,000 or more Nystrom samples, and the <em>90th</em> percentile difference is less than 1% for 1,500 or more samples. This experiment suggests that Nystrom-based SC converges to a stable clustering pattern as the number of samples increases. Based on these results, we chose to use 2,000 Nystrom samples for the remainder of this work. At this sample size, less than 5% of the runs for 2,4,5 clusters and approximately 8% of the runs for 3 clusters differed by more than 5% from the 4,000-sample template.

The box plot in Fig 2. summarizes the consistency of Nystrom-based Spectral Clustering across
different random samplings. The red lines indicate median values, the box corresponds to the upper and lower quartiles, and error bars denote the <em>10th</em> and <em>90th</em> percentiles. Here, we perform SC 10 times on each participant using 2,000 Nystrom samples. We then align the cluster maps and compute the percentage of mismatched voxels between each unique pair of runs. This yields a total of 45 comparisons per participant. In all cases, the median clustering difference is less than 1%, and the <em>90th</em> percentile value is less than 2.1%. Empirically, we find that Nystrom SC predictably converges to a second or third cluster pattern in only a handful of participants. This experiment suggests that we can obtain consistent clusterings with only 2,000 Nystrom samples.

<table>
<tr> ''' Fig 3. Clustering results across participants. The brain is partitioned into 5 clusters using Spectral Clustering/K-Means, and various seed are selected for Seed-Based Analysis. The color indicates the proportion of participants for whom the voxel was included in the detected system.'''
<tr> <th> '''Spectral Clustering''' <th> '''K-Means''' <th> '''Seed-Based'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Clust_2.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Clust_1.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Seed_PCC.jpeg |275px]]
<tr> <th> '''Cluster 1, Slice 37''' <th> '''Cluster 1, Slice 37''' <th> '''PCC, Slice 37'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Double.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Double.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Seed_vACC.jpeg |275px]]
<tr> <th> '''Cluster 1, Slice 55''' <th> '''Cluster 1, Slice 55''' <th> '''vACC, Slice 55'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Clust_3.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Clust_4.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Seed_V1.jpeg |275px]]
<tr> <th> '''Cluster 2, Slice 55''' <th> '''Cluster 2, Slice 55''' <th> '''Visual, Slice 55'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Clust_4.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Clust_3.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Seed_M1.jpeg |275px]]
<tr> <th> '''Cluster 3, Slice 31''' <th> '''Cluster 3, Slice 31''' <th> '''Motor, Slice 31'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Clust_1.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Clust_2.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Seed_IPS.jpeg |275px]]
<tr> <th> '''Cluster 4, Slice 31''' <th> '''Cluster 4, Slice 31''' <th> '''IPS, Slice 31'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Clust_5.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Clust_5.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Colorbar2.jpeg |64px]]
<tr> <th> '''Cluster 5, Slice 37''' <th> '''Cluster 5, Slice 37''' <th>
</table>

Fig 3. shows clearly that both Spectral Clustering and K-Means can identify well-known structures such as the default network, the visual cortex, the motor cortex, and the dorsal attention system. Spectral Clustering and K-Means also identified white matter. In general, one would not attempt to delineate this region using seed-based correlation analysis because we regress out the white matter signal during the preprocessing. In our experiments Spectral Clustering and K-Means achieve similar clustering results across participants. Furthermore, both methods identify the same functional systems as seed-based analysis without requiring <em>a priori</em> knowledge about the brain and without significant computation. Thus, clustering algorithms offer a viable alternative to standard functional connectivity analysis techniques.

''' ''Clustering Study of Domain Specificity in High Level Visual Cortex'' '''

As a more specific application of model-based clustering algorithms, we are devising clustering algorithms for detection of functional connectivity in high-level visual cortex. It is suggested that there are regions in the visual cortex with high selectivity to certain categories of visual stimuli. Currently, the conventional method for detection of these methods is based on statistical tests comparing response of each voxel in the brain to different visual categories to see if it shows considerably higher activation to one category. For example, the well-known FFA (Fusiform Face Area) is the set of voxels which show high activation to face images. We use a model-based clustering approach to the analysis of this type of data as a means to make this analysis automatic and further discover new structures in the high-level visual cortex.

Introducing the notion of space of activation
profiles, we construct a representation of the data which explicitly
parametrizes all interesting patterns of activation. Mapping the data into
this space, we formulate a model-based clustering algorithm that simultaneously
finds a set of activation profiles and their spatial maps. We validate
our method on the data from studies of category selectivity in visual
cortex, demonstrating good agreement with the findings based on prior
hypothesis-driven methods. This model enables functional group analysis
independent of spatial correspondence among subjects. We are currently working on a co-clustering extension of this
algorithm which can simultaneously find a set of clusters of voxels and meta-categories
of stimuli in experiments with diverse sets of stimulus categories.

Fig. 6 compares the map of voxels assigned to a face-selective profile by our algorithm with the t-test's map of voxels with statistically significant (p<0.0001) response to faces when compared with object stimuli. Note that in contrast with the hypothesis testing method, we don't specify the existence of a face-selective region in our algorithm and the algorithm automatically discovers such a profile of activation in the data.

{|
|+ '''Fig 6. Spatial maps of the face selective regions found by the statistical test (red) and our mixture model (dark blue). Maps are presented in alternating rows for comparison. Visually responsive mask of voxels used in our experiment is illustrated in yellow and light blue.'''
|align="center"|[[Image:mit_fmri_clustering_mapffacompare.PNG |thumb|800px]]
|}

''' ''Comparison of Data-Driven Analysis Methods for Identiﬁcation of Functional Connectivity in fMRI'' '''

Although ICA and clustering rely on very diﬀerent assumptions on the underlying distributions, they produce surprisingly similar results for signals with large variation. Our main goal is to evaluate and compare the performance of ICA and clustering based on Gaussian mixture model (GMM) for identiﬁcation of functional connectivity. Using the synthetic data with artiﬁcial activations and artifacts under various levels of length of the time course and signal-to-noise ratio of the data, we compare both spatial maps and their associated time courses estimated by ICA and GMM to each other and to the ground truth. We choose the number of sources via the model selection scheme, and compare all of the resulting components of GMM and ICA, not just the task-related components, after we match them component-wise using the Hungarian algorithm. This comparison scheme is veriﬁed in a high level visual cortex fMRI study. We ﬁnd that ICA requires a smaller number of total components to extract the task-related components, but also needs a large number of total components to describe the entire data. We are currently applying ICA and clustering methods to connectivity analysis of schizophrenia patients.

'''''Hierarchical Model for Exploratory fMRI Analysis
without Spatial Normalization'''''

Building on the work on the clustering model for the domain specificity, we develop a hierarchical exploratory method for simultaneous parcellation of multisub ect fMRI data into functionally coherent areas. The method is based on a solely functional representation of the fMRI data and a hierarchical probabilistic model that accounts for both inter-subject and intra-subject forms of variability in fMRI response. We employ a Variational Bayes approximation to ﬁt the model to the data. The resulting algorithm ﬁnds a functional parcellation of the individual brains along with a set of population-level clusters, establishing correspondence between these two levels. The model eliminates the need for spatial normalization while still enabling us to fuse data from several sub jects.

We demonstrate the application of our method on the same visual fMRI study as before.

hierarchical-Ppamapsubject1.pdf

<table>
<tr> <th> '''Fig 1. Varying the number of Nystrom Samples''' <th> '''Fig 2. Nystrom consistency for 2,000 random samples'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_Samples_LogMedian2.jpeg |400px]]
<td align="center">
[[Image:mit_fmri_clustering_Consistency_Box.jpeg |400px]]
</table>

= Key Investigators =

* MIT Algorithms: Danial Lashkari, Y. Bryce Kim, Archana Venkataraman, Polina Golland, Nancy Kanwisher.
* Harvard DBP 2: J. Oh, Marek Kubicki.

= Publications =

''In print''

* [http://www.na-mic.org/publications/pages/display?search=Projects%3AfMRIClustering&submit=Search&words=all&title=checked&keywords=checked&authors=checked&abstract=checked&sponsors=checked&searchbytag=checked| NA-MIC Publications Database]

''In press''

D. Lashkari and P. Golland, Exploratory fMRI Analysis without Spatial Normalization. To appear in Proc. IPMI: International Conference on Information Processing and Medical Imaging, 2009.

Project Week Results: [[2008_Summer_Project_Week:fMRIconnectivity|June 2008]]

[[Category:fMRI]]

File:Hierarchical-Ppamapsubject1.pdf

2009-09-10T18:29:55Z

Danial:

Projects:fMRIClustering

2009-04-23T18:26:17Z

Danial:

Back to [[NA-MIC_Internal_Collaborations:fMRIAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]
__NOTOC__

= fMRI Clustering =

One of the major goals in analysis of fMRI data is the detection of networks in the brain with similar functional behavior. A wide variety of methods including hypothesis-driven statistical tests, unsupervised learning methods such as PCA and ICA, and different clustering algorithms have been employed to find these networks. This project aims to particularly study application of model-based clustering algorithms in identification of functional connectivity in the brain.

= Description =

'''''Generative Model for Functional Connectivity'''''

In the classical functional connectivity analysis, networks of interest are
defined based on correlation with the mean time course of a user-selected
`seed' region. Further, the user has to also specify a subject-specific threshold at which correlation
values are deemed significant. In this project, we simultaneously estimate the optimal
representative time courses that summarize the fMRI data well and
the partition of the volume into a set of disjoint regions that are best
explained by these representative time courses. This approach to functional connectivity analysis offers two
advantages. First, is removes the sensitivity of the analysis to the details
of the seed selection. Second, it substantially simplifies group analysis
by eliminating the need for the subject-specific threshold. Our experimental results indicate that
the functional segmentation provides a robust, anatomically meaningful
and consistent model for functional connectivity in fMRI.

We formulate the problem of characterizing connectivity as a partition of voxels into subsets that are well characterized by a certain number of representative hypotheses, or time courses, based on the similarity of their time courses to each hypothesis. We model the fMRI signal at each voxel as generated by a mixture of Gaussian distributions whose centers are the desired representative time courses. Using the EM algorithm to solve the corresponding model-fitting problem, we alternatively estimate the representative time courses and cluster assignments to improve our random initialization.

''' ''Experimental Results'' '''

We used data from 7 subjects with a diverse set of visual experiments including localizer, morphing, rest, internal tasks, and movie. The functional scans were pre-processed for motion artifacts, manually aligned into the Talairach coordinate system, detrended (removing linear trends in the
baseline activation) and smoothed (8mm kernel).

Fig. 1 shows the 2-system partition extracted in each subject independently
of all others. It also displays the boundaries of the intrinsic system determined
through the traditional seed selection, showing good agreement between the two
partitions. Fig. 2 presents the results of further clustering the stimulus-driven cluster into two clusters independently for each subject.

<table>
<tr> <th> '''Fig 1. 2-System Parcelation. Results for all 7 subjects.''' <th> '''Fig 2. 3-System Parcelation. Results for all 7 subjects.'''
<tr> <td align="center">
[[Image:mit_fmri_clustering_parcellation2_shb1_4.png |400px]]
[[Image:mit_fmri_clustering_parcellation2_shb5_6.png |400px]]
[[Image:mit_fmri_clustering_parcellation2_shb7.png |400px]]
<td align="center">
[[Image:mit_fmri_clustering_parcellation3_shb1_3.png |400px]]
[[Image:mit_fmri_clustering_parcellation3_shb4_5.png |400px]]
[[Image:mit_fmri_clustering_parcellation3_shb6.png |400px]]
[[Image:mit_fmri_clustering_parcellation3_shb7.png |400px]]
</table>

Fig.3 presents the group average of the subject-specific 2-system maps. Color shading shows the proportion of subjects whose clustering agreed with the majority label. Fig. 4 shows the group average of a further parcelation of the intrinsic system, i.e., one of two clusters associated with the non-stimulus-driven regions. In order to present a validation of the method, we compare these results with the conventional scheme for detection of visually responsive areas. In Fig. 5, color shows the statistical parametric map while solid lines indicate the boundaries of the visual system obtained through clustering. The result illustrate the agreement between the two methods.

<table>
<tr><th> '''Fig 3. 2-System Parcellation. Group-wise result.''' <th> '''Fig 4. Validation: Parcelation of the intrinsic system.'''
<tr> <td align="center">
[[Image:mit_fmri_clustering_parcellation2_xsub.png |thumb|570px]]
<td align="center">
[[Image:mit_fmri_clustering_intrinsicsystem.png |thumb|500px]]
</table>

{|
|+ '''Fig 5. Validation: Visual system.'''
|valign="top"|[[Image:mit_fmri_clustering_validation.png |thumb|1150px]]
|}

'''''Exploring Functional Connectivity in fMRI via Clustering'''''

As a continuation to the above experiments, we apply two distinct clustering algorithms to functional connectivity analysis: K-Means clustering and Spectral Clustering. The K-Means algorithm assumes that each voxel time course is drawn independently from one of <em>k</em> multivariate Gaussian distributions with unique means and spherical covariances. In contrast, Spectral Clustering does not presume any parametric form for the data. Rather it captures the underlying signal geometry by inducing a low-dimensional representation based on a pairwise affinity matrix constructed from the data. Without placing any <em>a priori</em> constraints, both clustering methods yield partitions that are associated with brain systems traditionally identified via seed-based correlation analysis. Our empirical results suggest that clustering provides a valuable tool for functional connectivity analysis.

One downside of Spectral Clustering is that it relies on the eigen-decomposition of an <em>NxN</em> affinity matrix, where <em>N</em> is the number of voxels in the whole brain. Since <em>N</em> is on the order of ~200,000 voxels, it is infeasible to compute the full eigen-decomposition given realistic memory and time constraints. To solve this problem, we approximate the leading eigenvalues and eigenvectors of the affinity matrix via the Nystrom Method. This is done by selecting a random subset of "Nystrom Samples" from the data. The affinity matrix and spectral decomposition is computed only for this subset, and the results are projected onto the remaining data points.

'''''Experimental Results'''''

We validate these algorithms on resting state data collected from 45 healthy young adults (mean age 21.5, 26 female). Four 2mm isotropic functional runs were acquired from each subject. Each scan lasted for 6m20s with TR = 5s. The first 4 time points in each run were discarded, yielding 72 time samples per run. The entire brain volume is partitioned into an increasing number of clusters. We perform standard preprocessing on each of the four runs, including motion correction by rigid body alignment of the volumes, slice timing correction and registration to the MNI atlas space. The data is spatially smoothed with a 6mm 3D Gaussian filter, temporally low-pass filtered using a 0.08Hz cutoff, and motion corrected via linear regression. Next, we estimate and remove contributions from the white matter, ventricle and whole brain regions (assuming a linear signal model). We mask the data to include only brain voxels and normalized the time courses to have zero mean and unit variance. Finally, we concatenate the four runs into a single time course for analysis.

We first study the robustness of Spectral Clustering to the number of random samples. In this experiment, we start with a 4,000-sample Nystrom set, which is the computational limit of our machine. We then iteratively remove 500 samples and examine the effect on clustering performance. After matching the resulting clusters to those estimated with 4,000 samples, we compute the percentage of mismatched voxels between each trial and the 4,000-sample template. This procedure is repeated twice for each participant.

<table>
<tr> <th> '''Fig 1. Varying the number of Nystrom Samples''' <th> '''Fig 2. Nystrom consistency for 2,000 random samples'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_Samples_LogMedian2.jpeg |400px]]
<td align="center">
[[Image:mit_fmri_clustering_Consistency_Box.jpeg |400px]]
</table>

Fig 1. depicts the median clustering difference when varying the number of Nystrom samples. Values represent the percentage of mismatched voxels w.r.t. the 4,000-sample template. Error bars delineate the <em>10th</em>-<em>90</em> percentile region. The median clustering difference is less than 1% for 1,000 or more Nystrom samples, and the <em>90th</em> percentile difference is less than 1% for 1,500 or more samples. This experiment suggests that Nystrom-based SC converges to a stable clustering pattern as the number of samples increases. Based on these results, we chose to use 2,000 Nystrom samples for the remainder of this work. At this sample size, less than 5% of the runs for 2,4,5 clusters and approximately 8% of the runs for 3 clusters differed by more than 5% from the 4,000-sample template.

The box plot in Fig 2. summarizes the consistency of Nystrom-based Spectral Clustering across
different random samplings. The red lines indicate median values, the box corresponds to the upper and lower quartiles, and error bars denote the <em>10th</em> and <em>90th</em> percentiles. Here, we perform SC 10 times on each participant using 2,000 Nystrom samples. We then align the cluster maps and compute the percentage of mismatched voxels between each unique pair of runs. This yields a total of 45 comparisons per participant. In all cases, the median clustering difference is less than 1%, and the <em>90th</em> percentile value is less than 2.1%. Empirically, we find that Nystrom SC predictably converges to a second or third cluster pattern in only a handful of participants. This experiment suggests that we can obtain consistent clusterings with only 2,000 Nystrom samples.

<table>
<tr> ''' Fig 3. Clustering results across participants. The brain is partitioned into 5 clusters using Spectral Clustering/K-Means, and various seed are selected for Seed-Based Analysis. The color indicates the proportion of participants for whom the voxel was included in the detected system.'''
<tr> <th> '''Spectral Clustering''' <th> '''K-Means''' <th> '''Seed-Based'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Clust_2.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Clust_1.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Seed_PCC.jpeg |275px]]
<tr> <th> '''Cluster 1, Slice 37''' <th> '''Cluster 1, Slice 37''' <th> '''PCC, Slice 37'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Double.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Double.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Seed_vACC.jpeg |275px]]
<tr> <th> '''Cluster 1, Slice 55''' <th> '''Cluster 1, Slice 55''' <th> '''vACC, Slice 55'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Clust_3.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Clust_4.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Seed_V1.jpeg |275px]]
<tr> <th> '''Cluster 2, Slice 55''' <th> '''Cluster 2, Slice 55''' <th> '''Visual, Slice 55'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Clust_4.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Clust_3.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Seed_M1.jpeg |275px]]
<tr> <th> '''Cluster 3, Slice 31''' <th> '''Cluster 3, Slice 31''' <th> '''Motor, Slice 31'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Clust_1.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Clust_2.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Seed_IPS.jpeg |275px]]
<tr> <th> '''Cluster 4, Slice 31''' <th> '''Cluster 4, Slice 31''' <th> '''IPS, Slice 31'''
<tr>
<td align="center">
[[Image:mit_fmri_clustering_SC_5Clust_5.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_KM_5Clust_5.jpeg |275px]]
<td align="center">
[[Image:mit_fmri_clustering_Colorbar2.jpeg |64px]]
<tr> <th> '''Cluster 5, Slice 37''' <th> '''Cluster 5, Slice 37''' <th>
</table>

Fig 3. shows clearly that both Spectral Clustering and K-Means can identify well-known structures such as the default network, the visual cortex, the motor cortex, and the dorsal attention system. Spectral Clustering and K-Means also identified white matter. In general, one would not attempt to delineate this region using seed-based correlation analysis because we regress out the white matter signal during the preprocessing. In our experiments Spectral Clustering and K-Means achieve similar clustering results across participants. Furthermore, both methods identify the same functional systems as seed-based analysis without requiring <em>a priori</em> knowledge about the brain and without significant computation. Thus, clustering algorithms offer a viable alternative to standard functional connectivity analysis techniques.

''' ''Clustering Study of Domain Specificity in High Level Visual Cortex'' '''

As a more specific application of model-based clustering algorithms, we are devising clustering algorithms for detection of functional connectivity in high-level visual cortex. It is suggested that there are regions in the visual cortex with high selectivity to certain categories of visual stimuli. Currently, the conventional method for detection of these methods is based on statistical tests comparing response of each voxel in the brain to different visual categories to see if it shows considerably higher activation to one category. For example, the well-known FFA (Fusiform Face Area) is the set of voxels which show high activation to face images. We use a model-based clustering approach to the analysis of this type of data as a means to make this analysis automatic and further discover new structures in the high-level visual cortex.

Introducing the notion of space of activation
profiles, we construct a representation of the data which explicitly
parametrizes all interesting patterns of activation. Mapping the data into
this space, we formulate a model-based clustering algorithm that simultaneously
finds a set of activation profiles and their spatial maps. We validate
our method on the data from studies of category selectivity in visual
cortex, demonstrating good agreement with the findings based on prior
hypothesis-driven methods. This model enables functional group analysis
independent of spatial correspondence among subjects. We are currently working on a co-clustering extension of this
algorithm which can simultaneously find a set of clusters of voxels and meta-categories
of stimuli in experiments with diverse sets of stimulus categories.

Fig. 6 compares the map of voxels assigned to a face-selective profile by our algorithm with the t-test's map of voxels with statistically significant (p<0.0001) response to faces when compared with object stimuli. Note that in contrast with the hypothesis testing method, we don't specify the existence of a face-selective region in our algorithm and the algorithm automatically discovers such a profile of activation in the data.

{|
|+ '''Fig 6. Spatial maps of the face selective regions found by the statistical test (red) and our mixture model (dark blue). Maps are presented in alternating rows for comparison. Visually responsive mask of voxels used in our experiment is illustrated in yellow and light blue.'''
|align="center"|[[Image:mit_fmri_clustering_mapffacompare.PNG |thumb|800px]]
|}

''' ''Comparison of Data-Driven Analysis Methods for Identiﬁcation of Functional Connectivity in fMRI'' '''

Although ICA and clustering rely on very diﬀerent assumptions on the underlying distributions, they produce surprisingly similar results for signals with large variation. Our main goal is to evaluate and compare the performance of ICA and clustering based on Gaussian mixture model (GMM) for identiﬁcation of functional connectivity. Using the synthetic data with artiﬁcial activations and artifacts under various levels of length of the time course and signal-to-noise ratio of the data, we compare both spatial maps and their associated time courses estimated by ICA and GMM to each other and to the ground truth. We choose the number of sources via the model selection scheme, and compare all of the resulting components of GMM and ICA, not just the task-related components, after we match them component-wise using the Hungarian algorithm. This comparison scheme is veriﬁed in a high level visual cortex fMRI study. We ﬁnd that ICA requires a smaller number of total components to extract the task-related components, but also needs a large number of total components to describe the entire data. We are currently applying ICA and clustering methods to connectivity analysis of schizophrenia patients.

= Key Investigators =

* MIT Algorithms: Danial Lashkari, Y. Bryce Kim, Archana Venkataraman, Polina Golland, Nancy Kanwisher.
* Harvard DBP 2: J. Oh, Marek Kubicki.

= Publications =

''In print''

* [http://www.na-mic.org/publications/pages/display?search=Projects%3AfMRIClustering&submit=Search&words=all&title=checked&keywords=checked&authors=checked&abstract=checked&sponsors=checked&searchbytag=checked| NA-MIC Publications Database]

''In press''

D. Lashkari and P. Golland, Exploratory fMRI Analysis without Spatial Normalization. To appear in Proc. IPMI: International Conference on Information Processing and Medical Imaging, 2009.

[[Category:fMRI]]

Projects:fMRIClustering

2008-10-09T22:45:56Z

Danial:

Projects:fMRIClustering

2008-05-16T22:04:56Z

Danial:

Projects:fMRIClustering

2008-05-16T22:04:37Z

Danial:

Projects:fMRIClustering

2008-05-16T22:03:05Z

Danial:

File:Mit fmri clustering mapffacompare.PNG

2008-05-16T21:55:39Z

Danial:

Projects:fMRIClustering

2008-05-16T21:54:31Z

Danial:

Algorithm:MIT

2008-05-16T21:50:58Z

Danial:

Back to [[Algorithm:Main|NA-MIC Algorithms]]
__NOTOC__
= Overview of MIT Algorithms =

Our group seeks to model statistical variability of anatomy and function across subjects and between populations and to utilize computational models of such variability to improve predictions for individual subjects, as well as characterize populations. Our long-term goal is to develop methods for joint modeling of anatomy and function and to apply them in clinical and scientific studies. We work primarily with anatomical, DTI and fMRI images. We actively contribute implementations of our algorithms to the NAMIC-kit.

= MIT Projects =

{| cellpadding="10"
| style="width:15%" | [[Image:Progress_Registration_Segmentation_Shape.jpg|200px]]
| style="width:85%" |

== [[Projects:ShapeBasedSegmentationAndRegistration|Shape Based Segmentation and Registration]] ==

This type of algorithm assigns a tissue type to each voxel in the volume. Incorporating prior shape information biases the label assignment towards contiguous regions that are consistent with the shape model. [[Projects:ShapeBasedSegmentationAndRegistration|More...]]

<font color="red">'''New: '''</font> K.M. Pohl, J. Fisher, S. Bouix, M. Shenton, R. W. McCarley, W.E.L. Grimson, R. Kikinis, and W.M. Wells. Using the Logarithm of Odds to Define a Vector Space on Probabilistic Atlases. Medical Image Analysis,11(6), pp. 465-477, 2007. <b>Best Paper Award MICCAI 2006 </b>

|-

| | [[Image:JointRegSeg.png|200px]]
| |

== [[Projects:RegistrationRegularization|Optimal Atlas Regularization in Image Segmentation]] ==

We propose a unified framework for computing atlases from manually labeled data sets at various degrees of “sharpness” and the joint registration and segmentation of a new brain with these atlases. Using this framework, we investigate the tradeoff between warp regularization and image ﬁdelity, i.e. the smoothness of the new subject warp and the sharpness of the atlas in a segmentation application.
[[Projects:RegistrationRegularization|More...]]

<font color="red">'''New:'''</font> B.T.T. Yeo, M.R. Sabuncu, R. Desikan, B. Fischl, P. Golland. Effects of Registration Regularization and Atlas Sharpness on Segmentation Accuracy. In Proceedings of MICCAI: International Conference on Medical Image Computing and Computer Assisted Intervention, 683-691, 2007. '''MICCAI Young Scientist Award.'''

|-

| | [[Image:ICluster_templates.gif|200px]]
| |

== [[Projects:MultimodalAtlas|Multimodal Atlas]] ==

In this work, we propose and investigate an algorithm that jointly co-registers a collection of images while computing multiple templates. The algorithm, called '''iCluster''', is used to compute multiple atlases for a given population.
[[Projects:MultimodalAtlas|More...]]

<font color="red">'''New: '''</font> M.R. Sabuncu, Serdar K. Balci and Polina Golland. Discovering Modes of an Image Population through Mixture. Accepted to MICCAI 2008.
'''In Press:''' M.R. Sabuncu, M.E. Shenton, P. Golland. Joint Registration and Clustering of Images. In Proceedings of MICCAI 2007 Statistical Registration Workshop: Pair-wise and Group-wise Alignment and Atlas Formation, 47-54, 2007.

|-

| | [[Image:GroupwiseSummary.PNG|200px]]
| |

== [[Projects:GroupwiseRegistration|Groupwise Registration]] ==

We extend a previously demonstrated entropy based groupwise registration method to include a free-form deformation model based on B-splines. We provide an efficient implementation using stochastic gradient descents in a multi-resolution setting. We demonstrate the method in application to a set of 50 MRI brain scans and compare the results to a pairwise approach using segmentation labels to evaluate the quality of alignment.
[[Projects:GroupwiseRegistration|More...]]

S.K. Balci, P. Golland, M.E. Shenton, W.M. Wells III. Free-Form B-spline Deformation Model for Groupwise Registration. In Proceedings of MICCAI 2007 Statistical Registration Workshop: Pair-wise and Group-wise Alignment and Atlas Formation, 23-30, 2007.

|-

| | [[Image:FoldingSpeedDetection.png|200px|]]
| |

== [[Projects:ShapeAnalysisWithOvercompleteWavelets|Shape Analysis With Overcomplete Wavelets]] ==

In this work, we extend the Euclidean wavelets to the sphere. The resulting over-complete spherical wavelets are invariant to the rotation of the spherical image parameterization. We apply the over-complete spherical wavelet to cortical folding development [[Projects:ShapeAnalysisWithOvercompleteWavelets|More...]]

<font color="red">'''New: '''</font> B.T.T. Yeo, W. Ou, P. Golland. On the Construction of Invertible Filter Banks on the 2-Sphere. Yeo, Ou and Golland. Accepted to the IEEE Transactions on Image Processing.

P. Yu, B.T.T. Yeo, P.E. Grant, B. Fischl, P. Golland. Cortical Folding Development Study based on Over-Complete Spherical Wavelets. In Proceedings of MMBIA: IEEE Computer Society Workshop on Mathematical Methods in Biomedical Image Analysis, 2007.

|-

| | [[Image:mit_fmri_clustering_parcellation2_xsub.png|200px]]
| |

== [[Projects:fMRIClustering|fMRI clustering]] ==

In this project we study the application of model-based clustering algorithms in identification of functional connectivity in the brain. [[Projects:fMRIClustering|More...]]

<font color="red">'''New: '''</font> D. Lashkari, N. Kanwisher, P. Golland. Discovering Structure in the Space of Activation
Profiles in fMRI. Accpeted in MICCAI 2008.

|-

| | [[Image:MIT_DTI_JointSegReg_atlas3D.jpg|200px]]
| |

== [[Projects:DTIFiberRegistration|Joint Registration and Segmentation of DWI Fiber Tractography]] ==

The goal of this work is to jointly register and cluster DWI fiber tracts obtained from a group of subjects. [[Projects:DTIFiberRegistration|More...]]

<font color="red">'''New:'''</font> U. Ziyan, M. R. Sabuncu, W. E. L. Grimson, Carl-Fredrik Westin. A Robust Algorithm for Fiber-Bundle Atlas Construction. MMBIA 2007

|-

| | [[Image:brain.png|200px]]
| |

== [[Projects:DTIClustering|DTI Fiber Clustering and Fiber-Based Analysis]] ==

The goal of this project is to provide structural description of the white matter architecture as a partition into coherent fiber bundles and clusters, and to use these bundles for quantitative measurement. [[Projects:DTIClustering|More...]]

<font color="red">'''New:'''</font> Monica E. Lemmond, Lauren J. O'Donnell, Stephen Whalen, Alexandra J. Golby. Characterizing Diffusion Along White Matter Tracts Affected by Primary Brain Tumors. Accepted to HBM 2007.

|-

| | [[Image:Models.jpg|200px]]
| |

== [[Projects:DTIModeling|Fiber Tract Modeling, Clustering, and Quantitative Analysis]] ==

The goal of this work is to model the shape of the fiber bundles and use this model discription in clustering and statistical analysis of fiber tracts. [[Projects:DTIModeling|More...]]

<font color="red">'''New:'''</font>
M. Maddah, W. E. L. Grimson, S. K. Warfield, W. M. Wells, A Unified Framework for Clustering and Quantitative Analysis of White Matter Fiber Tracts. Medical Image Analysis, in press.

M. Maddah, W. M. Wells, S. K. Warfield, C.-F. Westin, and W. E. L. Grimson, Probabilistic Clustering and Quantitative Analysis of White Matter Fiber Tracts, IPMI 2007, Netherlands.

|-

| | [[Image:FMRIEvaluationchart.jpg|200px]]
| |

== [[Projects:fMRIDetection|fMRI Detection and Analysis]] ==

We are exploring algorithms for improved fMRI detection and interpretation by incorporting spatial priors and anatomical information to guide the detection. [[Projects:fMRIDetection|More...]]

<font color="red">'''New:'''</font> Wanmei Ou, Sandy Wells, Polina Golland. Bridging Spatial Regularization And Anatomical Priors in fMRI Detection. In preparation for submission to IEEE TMI.

|-

| | [[Image:Thalamus_algo_outline.png|200px]]
| |

== [[Projects:DTISegmentation|DTI-based Segmentation]] ==

Unlike conventional MRI, DTI provides adequate contrast to segment the thalamic nuclei, which are gray matter structures. [[Projects:DTISegmentation|More...]]

<font color="red">'''New:'''</font> Ulas Ziyan, David Tuch, Carl-Fredrik Westin. Segmentation of Thalamic Nuclei from DTI using Spectral Clustering. Accepted to MICCAI 2006.

|-

| | [[Image:ConnectivityMap.png|200px]]
| |

== [[Projects:DTIStochasticTractography|Stochastic Tractography]] ==

This work calculates posterior distributions of white matter fiber tract parameters given diffusion observations in a DWI volume. [[Projects:DTIStochasticTractography|More...]]

|-

| | [[Image:HippocampalShapeDifferences.gif|200px]]
| |

== [[Projects:ShapeAnalysis|Population Analysis of Anatomical Variability]] ==

Our goal is to develop mathematical approaches to modeling anatomical variability within and across populations using tools like local shape descriptors of specific regions of interest and global constellation descriptors of multiple ROI's. [[Projects:ShapeAnalysis|More...]]

<font color="red">'''New:'''</font> Mert R Sabuncu and Polina Golland. Structural Constellations for Population Analysis of Anatomical Variability.

== [[Projects:HippocampalSubfieldSegmentation|Model-Based Segmentation of Hippocampal Subﬁelds in In Vivo MRI]] ==

|}

Projects:fMRIClustering

2008-05-16T21:49:09Z

Danial:

Projects:fMRIClustering

2008-05-16T21:48:29Z

Danial:

File:Mapffacompare2.TIF

2008-05-16T21:45:19Z

Danial:

Projects:fMRIClustering

2008-05-16T21:17:43Z

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Projects:fMRIClustering

2008-05-16T21:17:30Z

Danial:

Projects:fMRIClustering

2008-05-16T21:15:37Z

Danial:

Projects:fMRIClustering

2007-11-10T18:40:15Z

Danial:

Back to [[NA-MIC_Collaborations|NA-MIC_Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

= fMRI Clustering =

One of the major goals in analysis of fMRI data is the detection of networks in the brain with similar functional behavior. A wide variety of methods including hypothesis-driven statistical tests, unsupervised learning methods such as PCA and ICA, and different clustering algorithms have been employed to find these networks. This project aims to particularly study application of model-based clustering algorithms in identification of functional connectivity in the brain.

= Description =

'''''Generative Model for Functional Connectivity'''''

In the classical functional connectivity analysis, networks of interest are
defined based on correlation with the mean time course of a user-selected
`seed' region. Further, the user has to also specify a subject-specific threshold at which correlation
values are deemed significant. In this project, we simultaneously estimate the optimal
representative time courses that summarize the fMRI data well and
the partition of the volume into a set of disjoint regions that are best
explained by these representative time courses. This approach to functional connectivity analysis offers two
advantages. First, is removes the sensitivity of the analysis to the details
of the seed selection. Second, it substantially simplifies group analysis
by eliminating the need for the subject-specific threshold. Our experimental results indicate that
the functional segmentation provides a robust, anatomically meaningful
and consistent model for functional connectivity in fMRI.

We formulate the problem of characterizing connectivity as a partition of voxels into subsets that are well characterized by a certain number of representative hypotheses, or time courses, based on the similarity of their time courses to each hypothesis. We model the fMRI signal at each voxel as generated by a mixture of Gaussian distributions whose centers are the desired representative time courses. Using the EM algorithm to solve the corresponding model-fitting problem, we alternatively estimate the representative time courses and cluster assignments to improve our random initialization.

''' ''Experimental Results'' '''

We used data from 7 subjects with a diverse set of visual experiments including localizer, morphing, rest, internal tasks, and movie. The functional scans were pre-processed for motion artifacts, manually aligned into the Talairach coordinate system, detrended (removing linear trends in the
baseline activation) and smoothed (8mm kernel).

Fig. 1 shows the 2-system partition extracted in each subject independently
of all others. It also displays the boundaries of the intrinsic system determined
through the traditional seed selection, showing good agreement between the two
partitions. Fig. 2 presents the results of further clustering the stimulus-driven cluster into two clusters independently for each subject.

<table>
<tr> <th> '''Fig 1. 2-System Parcelation. Results for all 7 subjects.''' <th> '''Fig 2. 3-System Parcelation. Results for all 7 subjects.'''
<tr> <td align="center">
[[Image:mit_fmri_clustering_parcellation2_shb1_4.png |400px]]
[[Image:mit_fmri_clustering_parcellation2_shb5_6.png |400px]]
[[Image:mit_fmri_clustering_parcellation2_shb7.png |400px]]
<td align="center">
[[Image:mit_fmri_clustering_parcellation3_shb1_3.png |400px]]
[[Image:mit_fmri_clustering_parcellation3_shb4_5.png |400px]]
[[Image:mit_fmri_clustering_parcellation3_shb6.png |400px]]
[[Image:mit_fmri_clustering_parcellation3_shb7.png |400px]]
</table>

Fig.3 presents the group average of the subject-specific 2-system maps. Color shading shows the proportion of subjects whose clustering agreed with the majority label. Fig. 4 shows the group average of a further parcelation of the intrinsic system, i.e., one of two clusters associated with the non-stimulus-driven regions. In order to present a validation of the method, we compare these results with the conventional scheme for detection of visually responsive areas. In Fig. 5, color shows the statistical parametric map while solid lines indicate the boundaries of the visual system obtained through clustering. The result illustrate the agreement between the two methods.

<table>
<tr><th> '''Fig 3. 2-System Parcellation. Group-wise result.'''
<tr> <td align="center">
{|
|+
|valign="top"|[[Image:mit_fmri_clustering_parcellation2_xsub.png |thumb|700px]]
|}
</table>

{|
|+ '''Fig 4. Validation: Parcelation of the intrinsic system.'''
|valign="top"|[[Image:mit_fmri_clustering_intrinsicsystem.png |thumb|650px]]
|}

{|
|+ '''Fig 5. Validation: Visual system.'''
|valign="top"|[[Image:mit_fmri_clustering_validation.png |thumb|1150px]]
|}

''' ''Clustering Study of Domain Specificity in High Level Visual Cortex'' '''

As a more specific application of clustering model-based algorithms, we are currently investigating devising clustering algorithms for detection of functional connectivity in high-level visual cortex. It is suggested that there are regions in the visual cortex with high selectivity to certain categories of visual stimuli. Currently, the conventional method for detection of these methods is based on statistical tests comparing response of each voxel in the brain to different visual categories to see if it shows considerably higher activation to one category. For example, the well-known FFA (Fusiform Face Area) is the set of voxels which show high activation to faces when compared to objects. We are working on using the clustering the visual cortex as a means to make this analysis automatic and further discover new structures in the high-level visual cortex.

= Key Investigators =

* MIT: Danial Lashkari, Polina Golland, Nancy Kanwisher

= Publications =

''In print''

* P. Golland, Y. Golland, R. Malach. Detection of Spatial Activation Patterns As Unsupervised Segmentation of fMRI Data. In Proceedings of MICCAI: International Conference on Medical Image Computing and Computer Assisted Intervention, 110-118, 2007.

''In press''

* D. Lashkari, P. Golland. Convex Clustering with Exemplar-Based Models. In NIPS: Advances in Neural Information Processing Systems, 2007.

= Links =

Projects:fMRIClustering

2007-11-10T18:34:16Z

Danial:

Back to [[NA-MIC_Collaborations|NA-MIC_Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

= fMRI Clustering =

One of the major goals in analysis of fMRI data is the detection of networks in the brain with similar functional behavior. A wide variety of methods including hypothesis-driven statistical tests, unsupervised learning methods such as PCA and ICA, and different clustering algorithms have been employed to find these networks. This project aims to particularly study application of model-based clustering algorithms in identification of functional connectivity in the brain.

= Description =

'''''Generative Model for Functional Connectivity'''''

In the classical functional connectivity analysis, networks of interest are
defined based on correlation with the mean time course of a user-selected
`seed' region. Further, the user has to also specify a subject-specific threshold at which correlation
values are deemed significant. In this project, we simultaneously estimate the optimal
representative time courses that summarize the fMRI data well and
the partition of the volume into a set of disjoint regions that are best
explained by these representative time courses. This approach to functional connectivity analysis offers two
advantages. First, is removes the sensitivity of the analysis to the details
of the seed selection. Second, it substantially simplifies group analysis
by eliminating the need for the subject-specific threshold. Our experimental results indicate that
the functional segmentation provides a robust, anatomically meaningful
and consistent model for functional connectivity in fMRI.

We formulate the problem of characterizing connectivity as a partition of voxels into subsets that are well characterized by a certain number of representative hypotheses, or time courses, based on the similarity of their time courses to each hypothesis. We model the fMRI signal at each voxel as generated by a mixture of Gaussian distributions whose centers are the desired representative time courses. Using the EM algorithm to solve the corresponding model-fitting problem, we alternatively estimate the representative time courses and cluster assignments to improve our random initialization.

''' ''Experimental Results'' '''

We used data from 7 subjects with a diverse set of visual experiments including localizer, morphing, rest, internal tasks, and movie. The functional scans were pre-processed for motion artifacts, manually aligned into the Talairach coordinate system, detrended (removing linear trends in the
baseline activation) and smoothed (8mm kernel).

Fig. 1 shows the 2-system partition extracted in each subject independently
of all others. It also displays the boundaries of the intrinsic system determined
through the traditional seed selection, showing good agreement between the two
partitions. Fig. 2 presents the results of further clustering the stimulus-driven cluster into two clusters independently for each subject.

<table>
<tr> <th> '''Fig 1. 2-System Parcelation. Results for all 7 subjects.''' <th> '''Fig 2. 3-System Parcelation. Results for all 7 subjects.'''
<tr> <td align="center">
[[Image:mit_fmri_clustering_parcellation2_shb1_4.png |400px]]
[[Image:mit_fmri_clustering_parcellation2_shb5_6.png |400px]]
[[Image:mit_fmri_clustering_parcellation2_shb7.png |400px]]
<td align="center">
[[Image:mit_fmri_clustering_parcellation3_shb1_3.png |400px]]
[[Image:mit_fmri_clustering_parcellation3_shb4_5.png |400px]]
[[Image:mit_fmri_clustering_parcellation3_shb6.png |400px]]
[[Image:mit_fmri_clustering_parcellation3_shb7.png |400px]]
</table>

Fig.3 presents the group average of the subject-specific 2-system maps. Color shading shows the proportion of subjects whose clustering agreed with the majority label. Fig. 4 shows the group average of a further parcelation of the intrinsic system, i.e., one of two clusters associated with the non-stimulus-driven regions. In order to present a validation of the method, we compare these results with the conventional scheme for detection of visually responsive areas. In Fig. 5, color shows the statistical parametric map while solid lines indicate the boundaries of the visual system obtained through clustering. The result illustrate the agreement between the two methods.

{|
|+ '''Fig 3. 2-System Parcellation. Group-wise result.'''
|valign="top"|[[Image:mit_fmri_clustering_parcellation2_xsub.png |thumb|700px]]
|}

{|
|+ '''Fig 4. Validation: Parcelation of the intrinsic system.'''
|valign="top"|[[Image:mit_fmri_clustering_intrinsicsystem.png |thumb|650px]]
|}

{|
|+ '''Fig 5. Validation: Visual system.'''
|valign="top"|[[Image:mit_fmri_clustering_validation.png |thumb|1150px]]
|}

''' ''Clustering Study of Domain Specificity in High Level Visual Cortex'' '''

As a more specific application of clustering model-based algorithms, we are currently investigating devising clustering algorithms for detection of functional connectivity in high-level visual cortex. It is suggested that there are regions in the visual cortex with high selectivity to certain categories of visual stimuli. Currently, the conventional method for detection of these methods is based on statistical tests comparing response of each voxel in the brain to different visual categories to see if it shows considerably higher activation to one category. For example, the well-known FFA (Fusiform Face Area) is the set of voxels which show high activation to faces when compared to objects. We are working on using the clustering the visual cortex as a means to make this analysis automatic and further discover new structures in the high-level visual cortex.

= Key Investigators =

* MIT: Danial Lashkari, Polina Golland, Nancy Kanwisher

= Publications =

''In print''

* P. Golland, Y. Golland, R. Malach. Detection of Spatial Activation Patterns As Unsupervised Segmentation of fMRI Data. In Proceedings of MICCAI: International Conference on Medical Image Computing and Computer Assisted Intervention, 110-118, 2007.

''In press''

* D. Lashkari, P. Golland. Convex Clustering with Exemplar-Based Models. In NIPS: Advances in Neural Information Processing Systems, 2007.

= Links =

Algorithm:MIT:New

2007-11-10T17:43:07Z

Danial: /* fMRI clustering */

Back to [[Algorithm:Main|NA-MIC Algorithms]]

= Overview of MIT Algorithms =

A brief overview of the MIT's algorithms goes here. This should not be much longer than a paragraph. Remember that people visiting your site want to be able to understand very quickly what you're all about and then they want to jump into your site's projects. The projects below are organized into a two column table: the left column is for representative images and the right column is for project overviews. The number of rows corresponds to the number of projects at your site. Put the most interesting and relevant projects at the top of the table. You do not need to organize the table according to subject matter (i.e. do not group all segmentation projects together and all DWI projects together).

[[#Shape_Based_Segmentation_and_Registration|Shape Based Segmentation and Registration]]

[[#Effects_of_Registration_Regularization_on_Segmentation_Accuracy|Effects of Registration Regularization on Segmentation Accuracy]]

[[#Multimodal_Atlas|Multimodal Atlas]]

[[#Shape_Analysis_With_Overcomplete_Wavelets|Shape Analysis With Overcomplete Wavelets]]

[[#fMRI_clustering|fMRI clustering]]

[[#Joint_Registration_and_Segmentation_of_DWI_Fiber_Tractography|Joint Registration and Segmentation of DWI Fiber Tractography]]

[[#Shape_Based_Level_Segmentation|Shape Based Level Segmentation]]

[[#DTI_Fiber_Clustering_and_Fiber-Based_Analysis|DTI Fiber Clustering and Fiber-Based Analysis]]

[[#Fiber_Tract_Modeling.2C_Clustering.2C_and_Quantitative_Analysis|Fiber Tract Modeling, Clustering and Quantitative Analysis]]

[[#DTI-based_Segmentation|DTI-based Segmentation]]

[[#Stochastic_Tractography|Stochastic Tractography]]

[[#fMRI_Detection_and_Analysis|fMRI Detection and Analysis]]

[[#Population_Analysis_of_Anatomical_Variability|Population Analysis of Anatomical Variability]]

[[#Groupwise_Registration|Groupwise Registration]]

= MIT Projects =

{|
| style="width:10%" | [[Image:Progress_Registration_Segmentation_Shape.jpg|left|200px]]
| style="width:90%" |

== [[Algorithm:MIT:Shape_Based_Segmentation_And_Registration|Shape Based Segmentation and Registration]] ==

This type of algorithms assigns a tissue type to each voxel in the volume. Incorporating prior shape information biases the label assignment towards contiguous regions that are consistent with the shape model. [[Algorithm:MIT:Shape_Based_Segmentation_And_Registration|More...]]

<font color="red">'''New: '''</font> K.M. Pohl, J. Fisher, S. Bouix, M. Shenton, R. W. McCarley, W.E.L. Grimson, R. Kikinis, and W.M. Wells. Using the Logarithm of Odds to Define a Vector Space on Probabilistic Atlases. Medical Image Analysis,11(6), pp. 465-477, 2007. <b>Best Paper Award MICCAI 2006 </b> [[Algorithm:MIT:Shape_Based_Segmentation_And_Registration#Publications|More...]]

|-

| | [[Image:JointRegSeg.png|left|200px]]
| |

== [[Algorithm:MIT:RegistrationRegularization|Optimal Atlas Regularization in Image Segmentation]] ==

We propose a unified framework for computing atlases from manually labeled data sets at various degrees of “sharpness” and the joint registration and segmentation of a new brain with these atlases. Using this framework, we investigate the tradeoff between warp regularization and image ﬁdelity, i.e. the smoothness of the new subject warp and the sharpness of the atlas in a segmentation application.
[[Algorithm:MIT:RegistrationRegularization|More...]]

<font color="red">'''New:'''</font> B.T.T. Yeo, M.R. Sabuncu, R. Desikan, B. Fischl, P. Golland. Effects of Registration Regularization and Atlas Sharpness on Segmentation Accuracy. In Proceedings of MICCAI: International Conference on Medical Image Computing and Computer Assisted Intervention, 683-691, 2007. '''MICCAI Young Scientist Award.'''

|-

| | [[Image:ICluster_templates.gif|left|200px]]
| |

== [[Algorithm:MIT:Multimodal Atlas |Multimodal Atlas]] ==

In this work, we propose and investigate an algorithm that jointly co-registers a collection of images while computing multiple templates. The algorithm, called '''iCluster''', is used to compute multiple atlases for a given population.
[[Algorithm:MIT:Multimodal Atlas|More...]]

<font color="red">'''New: '''</font> M.R. Sabuncu, M.E. Shenton, P. Golland. Joint Registration and Clustering of Images. In Proceedings of MICCAI 2007 Statistical Registration Workshop: Pair-wise and Group-wise Alignment and Atlas Formation, 47-54, 2007.
[[Algorithm:MIT:Multimodal Atlas#Publications|More...]]

|-

| | [[Image:GroupwiseSummary.PNG|left|200px]]
| |

== [[Algorithm:MIT:Groupwise_Registration#Introduction|Groupwise Registration]] ==

We extend a previously demonstrated entropy based groupwise registration method to include a free-form deformation model based on B-splines. We provide an efficient implementation using stochastic gradient descents in a multi-resolution setting. We demonstrate the method in application to a set of 50 MRI brain scans and compare the results to a pairwise approach using segmentation labels to evaluate the quality of alignment.
[[Algorithm:MIT:Groupwise_Registration|More...]]

<font color="red">'''New:'''</font> S.K. Balci, P. Golland, M.E. Shenton, W.M. Wells III. Free-Form B-spline Deformation Model for Groupwise Registration. In Proceedings of MICCAI 2007 Statistical Registration Workshop: Pair-wise and Group-wise Alignment and Atlas Formation, 23-30, 2007.

|-

| | [[Image:FoldingSpeedDetection.png|center|150px|]]
| |

== [[Algorithm:MIT:ShapeAnalysisWithOvercompleteWavelets|Shape Analysis With Overcomplete Wavelets]] ==

In this work, we extend the Euclidean wavelets to the sphere. The resulting over-complete spherical wavelets are invariant to the rotation of the spherical image parameterization. We apply the over-complete spherical wavelet to cortical folding development [[Algorithm:MIT:Shape_Based_Segmentation_And_Registration|More...]]

<font color="red">'''New: '''</font> B.T.T. Yeo, W. Ou, P. Golland. On the Construction of Invertible Filter Banks on the 2-Sphere. Yeo, Ou and Golland. Accepted to the IEEE Transactions on Image Processing.

P. Yu, B.T.T. Yeo, P.E. Grant, B. Fischl, P. Golland. Cortical Folding Development Study based on Over-Complete Spherical Wavelets. In Proceedings of MMBIA: IEEE Computer Society Workshop on Mathematical Methods in Biomedical Image Analysis, 2007. [[Algorithm:MIT:ShapeAnalysisWithOvercompleteWavelets#Publication|More...]]

|-

| | [[Image:mit_fmri_clustering_parcellation2_xsub.png|center|200px]]
| |

== [[Algorithm:MIT:fMRI Clustering |fMRI clustering]] ==

In this project we study the application of model-based clustering algorithms in identification of functional connectivity in the brain. [[Algorithm:MIT:fMRI_Clustering|More...]]

<font color="red">'''New: '''</font> P. Golland, Y. Golland, R. Malach. Detection of Spatial Activation Patterns As Unsupervised Segmentation of fMRI Data. In Proceedings of MICCAI: International Conference on Medical Image Computing and Computer Assisted Intervention, 110-118, 2007.

|-

| | [[Image:MIT_DTI_JointSegReg_atlas3D.jpg|center|200px]]
| |

== [[Algorithm:MIT:DTI_FiberRegistration|Joint Registration and Segmentation of DWI Fiber Tractography]] ==

The goal of this work is to jointly register and cluster DWI fiber tracts obtained from a group of subjects. [[Algorithm:MIT:DTI_FiberRegistration|More...]]

<font color="red">'''New:'''</font> U. Ziyan, M. R. Sabuncu, W. E. L. Grimson, Carl-Fredrik Westin. A Robust Algorithm for Fiber-Bundle Atlas Construction. MMBIA 2007



|-

| | [[Image:Wholebrain.jpg|center|200px]]
| |

== [[Algorithm:MIT:DTI_Clustering|DTI Fiber Clustering and Fiber-Based Analysis]] ==

The goal of this project is to provide structural description of the white matter architecture as a partition into coherent fiber bundles and clusters, and to use these bundles for quantitative measurement. [[Algorithm:MIT:DTI_Clustering|More...]]

<font color="red">'''New:'''</font>
Monica E. Lemmond, Lauren J. O'Donnell, Stephen Whalen, Alexandra J. Golby.
Characterizing Diffusion Along White Matter Tracts Affected by Primary Brain Tumors.
Accepted to HBM 2007.

|-

| | [[Image:Models.jpg|center|200px]]
| |

== [[Algorithm:MIT:DTI_Modeling|Fiber Tract Modeling, Clustering, and Quantitative Analysis]] ==

The goal of this work is to model the shape of the fiber bundles and use this model discription in clustering and statistical analysis of fiber tracts. [[Algorithm:MIT:DTI_Modeling|More...]]

<font color="red">'''New:'''</font>
M. Maddah, W. M. Wells, S. K. Warfield, C.-F. Westin, and W. E. L. Grimson, Probabilistic Clustering and Quantitative Analysis of White Matter Fiber Tracts,IPMI 2007, Netherlands.

|-

| | [[Image:Thalamus_algo_outline.png|center|200px]]
| |

== [[Algorithm:MIT:DTI_Segmentation|DTI-based Segmentation]] ==

Unlike conventional MRI, DTI provides adequate contrast to segment the thalamic nuclei, which are gray matter structures. [[Algorithm:MIT:DTI_Segmentation|More...]]



|-

|-

| | [[Image:ConnectivityMap.png|center|200px]]
| |

== [[Algorithm:MIT:DTI_StochasticTractography|Stochastic Tractography]] ==

This work calculates posterior distributions of white matter fiber tract parameters given diffusion observations in a DWI volume. [[Algorithm:MIT:DTI_StochasticTractography|More...]]



|-

| | [[Image:FMRIEvaluationchart.jpg|center|200px]]
| |

== [[Algorithm:MIT:fMRI_Detection|fMRI Detection and Analysis]] ==

We are exploring algorithms for improved fMRI detection and interpretation by incorporting spatial priors and anatomical information to guide the detection. [[Algorithm:MIT:fMRI_Detection|More...]]

<font color="red">'''New:'''</font> Wanmei Ou, Sandy Wells, Polina Golland. Bridging Spatial Regularization And Anatomical Priors in fMRI Detection. In preparation for submission to IEEE TMI.

|-

| | [[Image:HippocampalShapeDifferences.gif|center|200px]]
| |

== [[Algorithm:MIT:Shape_Analisys|Population Analysis of Anatomical Variability]] ==

Our goal is to develop mathematical approaches to modeling anatomical variability within and across populations using tools like local shape descriptors of specific regions of interest and global constellation descriptors of multiple ROI's. [[Algorithm:MIT:Shape_Analisys|More...]]

Algorithm:MIT:New

2007-11-10T17:41:16Z

Danial: /* fMRI clustering */

Back to [[Algorithm:Main|NA-MIC Algorithms]]

= Overview of MIT Algorithms =

A brief overview of the MIT's algorithms goes here. This should not be much longer than a paragraph. Remember that people visiting your site want to be able to understand very quickly what you're all about and then they want to jump into your site's projects. The projects below are organized into a two column table: the left column is for representative images and the right column is for project overviews. The number of rows corresponds to the number of projects at your site. Put the most interesting and relevant projects at the top of the table. You do not need to organize the table according to subject matter (i.e. do not group all segmentation projects together and all DWI projects together).

[[#Shape_Based_Segmentation_and_Registration|Shape Based Segmentation and Registration]]

[[#Effects_of_Registration_Regularization_on_Segmentation_Accuracy|Effects of Registration Regularization on Segmentation Accuracy]]

[[#Multimodal_Atlas|Multimodal Atlas]]

[[#Shape_Analysis_With_Overcomplete_Wavelets|Shape Analysis With Overcomplete Wavelets]]

[[#fMRI_clustering|fMRI clustering]]

[[#Joint_Registration_and_Segmentation_of_DWI_Fiber_Tractography|Joint Registration and Segmentation of DWI Fiber Tractography]]

[[#Shape_Based_Level_Segmentation|Shape Based Level Segmentation]]

[[#DTI_Fiber_Clustering_and_Fiber-Based_Analysis|DTI Fiber Clustering and Fiber-Based Analysis]]

[[#Fiber_Tract_Modeling.2C_Clustering.2C_and_Quantitative_Analysis|Fiber Tract Modeling, Clustering and Quantitative Analysis]]

[[#DTI-based_Segmentation|DTI-based Segmentation]]

[[#Stochastic_Tractography|Stochastic Tractography]]

[[#fMRI_Detection_and_Analysis|fMRI Detection and Analysis]]

[[#Population_Analysis_of_Anatomical_Variability|Population Analysis of Anatomical Variability]]

[[#Groupwise_Registration|Groupwise Registration]]

= MIT Projects =

{|
| style="width:10%" | [[Image:Progress_Registration_Segmentation_Shape.jpg|left|200px]]
| style="width:90%" |

== [[Algorithm:MIT:Shape_Based_Segmentation_And_Registration|Shape Based Segmentation and Registration]] ==

This type of algorithms assigns a tissue type to each voxel in the volume. Incorporating prior shape information biases the label assignment towards contiguous regions that are consistent with the shape model. [[Algorithm:MIT:Shape_Based_Segmentation_And_Registration|More...]]

<font color="red">'''New: '''</font> K.M. Pohl, J. Fisher, S. Bouix, M. Shenton, R. W. McCarley, W.E.L. Grimson, R. Kikinis, and W.M. Wells. Using the Logarithm of Odds to Define a Vector Space on Probabilistic Atlases. Medical Image Analysis,11(6), pp. 465-477, 2007. <b>Best Paper Award MICCAI 2006 </b> [[Algorithm:MIT:Shape_Based_Segmentation_And_Registration#Publications|More...]]

|-

| | [[Image:JointRegSeg.png|left|200px]]
| |

== [[Algorithm:MIT:RegistrationRegularization|Optimal Atlas Regularization in Image Segmentation]] ==

We propose a unified framework for computing atlases from manually labeled data sets at various degrees of “sharpness” and the joint registration and segmentation of a new brain with these atlases. Using this framework, we investigate the tradeoff between warp regularization and image ﬁdelity, i.e. the smoothness of the new subject warp and the sharpness of the atlas in a segmentation application.
[[Algorithm:MIT:RegistrationRegularization|More...]]

<font color="red">'''New:'''</font> B.T.T. Yeo, M.R. Sabuncu, R. Desikan, B. Fischl, P. Golland. Effects of Registration Regularization and Atlas Sharpness on Segmentation Accuracy. In Proceedings of MICCAI: International Conference on Medical Image Computing and Computer Assisted Intervention, 683-691, 2007. '''MICCAI Young Scientist Award.'''

|-

| | [[Image:ICluster_templates.gif|left|200px]]
| |

== [[Algorithm:MIT:Multimodal Atlas |Multimodal Atlas]] ==

In this work, we propose and investigate an algorithm that jointly co-registers a collection of images while computing multiple templates. The algorithm, called '''iCluster''', is used to compute multiple atlases for a given population.
[[Algorithm:MIT:Multimodal Atlas|More...]]

<font color="red">'''New: '''</font> M.R. Sabuncu, M.E. Shenton, P. Golland. Joint Registration and Clustering of Images. In Proceedings of MICCAI 2007 Statistical Registration Workshop: Pair-wise and Group-wise Alignment and Atlas Formation, 47-54, 2007.
[[Algorithm:MIT:Multimodal Atlas#Publications|More...]]

|-

| | [[Image:GroupwiseSummary.PNG|left|200px]]
| |

== [[Algorithm:MIT:Groupwise_Registration#Introduction|Groupwise Registration]] ==

We extend a previously demonstrated entropy based groupwise registration method to include a free-form deformation model based on B-splines. We provide an efficient implementation using stochastic gradient descents in a multi-resolution setting. We demonstrate the method in application to a set of 50 MRI brain scans and compare the results to a pairwise approach using segmentation labels to evaluate the quality of alignment.
[[Algorithm:MIT:Groupwise_Registration|More...]]

<font color="red">'''New:'''</font> S.K. Balci, P. Golland, M.E. Shenton, W.M. Wells III. Free-Form B-spline Deformation Model for Groupwise Registration. In Proceedings of MICCAI 2007 Statistical Registration Workshop: Pair-wise and Group-wise Alignment and Atlas Formation, 23-30, 2007.

|-

| | [[Image:FoldingSpeedDetection.png|center|150px|]]
| |

== [[Algorithm:MIT:ShapeAnalysisWithOvercompleteWavelets|Shape Analysis With Overcomplete Wavelets]] ==

In this work, we extend the Euclidean wavelets to the sphere. The resulting over-complete spherical wavelets are invariant to the rotation of the spherical image parameterization. We apply the over-complete spherical wavelet to cortical folding development [[Algorithm:MIT:Shape_Based_Segmentation_And_Registration|More...]]

<font color="red">'''New: '''</font> B.T.T. Yeo, W. Ou, P. Golland. On the Construction of Invertible Filter Banks on the 2-Sphere. Yeo, Ou and Golland. Accepted to the IEEE Transactions on Image Processing.

P. Yu, B.T.T. Yeo, P.E. Grant, B. Fischl, P. Golland. Cortical Folding Development Study based on Over-Complete Spherical Wavelets. In Proceedings of MMBIA: IEEE Computer Society Workshop on Mathematical Methods in Biomedical Image Analysis, 2007. [[Algorithm:MIT:ShapeAnalysisWithOvercompleteWavelets#Publication|More...]]

|-

| | [[Image:mit_fmri_clustering_parcellation2_xsub.png|center|200px]]
| |

== [[Algorithm:MIT:fMRI Clustering |fMRI clustering]] ==

In this project we study the application of model-based clustering algorithms in identification of functional connectivity in the brain. [[Algorithm:MIT:Algorithm:MIT:fMRI_Clustering|More...]]

<font color="red">'''New: '''</font> P. Golland, Y. Golland, R. Malach. Detection of Spatial Activation Patterns As Unsupervised Segmentation of fMRI Data. In Proceedings of MICCAI: International Conference on Medical Image Computing and Computer Assisted Intervention, 110-118, 2007. [[Algorithm:MIT:Shape_Based_Segmentation_And_Registration#Publications|More...]]

|-

| | [[Image:MIT_DTI_JointSegReg_atlas3D.jpg|center|200px]]
| |

== [[Algorithm:MIT:DTI_FiberRegistration|Joint Registration and Segmentation of DWI Fiber Tractography]] ==

The goal of this work is to jointly register and cluster DWI fiber tracts obtained from a group of subjects. [[Algorithm:MIT:DTI_FiberRegistration|More...]]

<font color="red">'''New:'''</font> U. Ziyan, M. R. Sabuncu, W. E. L. Grimson, Carl-Fredrik Westin. A Robust Algorithm for Fiber-Bundle Atlas Construction. MMBIA 2007



|-

| | [[Image:Wholebrain.jpg|center|200px]]
| |

== [[Algorithm:MIT:DTI_Clustering|DTI Fiber Clustering and Fiber-Based Analysis]] ==

The goal of this project is to provide structural description of the white matter architecture as a partition into coherent fiber bundles and clusters, and to use these bundles for quantitative measurement. [[Algorithm:MIT:DTI_Clustering|More...]]

<font color="red">'''New:'''</font>
Monica E. Lemmond, Lauren J. O'Donnell, Stephen Whalen, Alexandra J. Golby.
Characterizing Diffusion Along White Matter Tracts Affected by Primary Brain Tumors.
Accepted to HBM 2007.

|-

| | [[Image:Models.jpg|center|200px]]
| |

== [[Algorithm:MIT:DTI_Modeling|Fiber Tract Modeling, Clustering, and Quantitative Analysis]] ==

The goal of this work is to model the shape of the fiber bundles and use this model discription in clustering and statistical analysis of fiber tracts. [[Algorithm:MIT:DTI_Modeling|More...]]

<font color="red">'''New:'''</font>
M. Maddah, W. M. Wells, S. K. Warfield, C.-F. Westin, and W. E. L. Grimson, Probabilistic Clustering and Quantitative Analysis of White Matter Fiber Tracts,IPMI 2007, Netherlands.

|-

| | [[Image:Thalamus_algo_outline.png|center|200px]]
| |

== [[Algorithm:MIT:DTI_Segmentation|DTI-based Segmentation]] ==

Unlike conventional MRI, DTI provides adequate contrast to segment the thalamic nuclei, which are gray matter structures. [[Algorithm:MIT:DTI_Segmentation|More...]]



|-

|-

| | [[Image:ConnectivityMap.png|center|200px]]
| |

== [[Algorithm:MIT:DTI_StochasticTractography|Stochastic Tractography]] ==

This work calculates posterior distributions of white matter fiber tract parameters given diffusion observations in a DWI volume. [[Algorithm:MIT:DTI_StochasticTractography|More...]]



|-

| | [[Image:FMRIEvaluationchart.jpg|center|200px]]
| |

== [[Algorithm:MIT:fMRI_Detection|fMRI Detection and Analysis]] ==

We are exploring algorithms for improved fMRI detection and interpretation by incorporting spatial priors and anatomical information to guide the detection. [[Algorithm:MIT:fMRI_Detection|More...]]

<font color="red">'''New:'''</font> Wanmei Ou, Sandy Wells, Polina Golland. Bridging Spatial Regularization And Anatomical Priors in fMRI Detection. In preparation for submission to IEEE TMI.

|-

| | [[Image:HippocampalShapeDifferences.gif|center|200px]]
| |

== [[Algorithm:MIT:Shape_Analisys|Population Analysis of Anatomical Variability]] ==

Our goal is to develop mathematical approaches to modeling anatomical variability within and across populations using tools like local shape descriptors of specific regions of interest and global constellation descriptors of multiple ROI's. [[Algorithm:MIT:Shape_Analisys|More...]]

Projects:fMRIClustering

2007-11-10T17:37:56Z

Danial:

Back to [[NA-MIC_Collaborations|NA-MIC_Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

= fMRI Clustering =

One of the major goals in analysis of fMRI data is the detection of networks in the brain with similar functional behavior. A wide variety of methods including hypothesis-driven statistical tests, unsupervised learning methods such as PCA and ICA, and different clustering algorithms have been employed to find these networks. This project aims to particularly study application of model-based clustering algorithms in identification of functional connectivity in the brain.

= Description =

'''''Generative Model for Functional Connectivity'''''

In the classical functional connectivity analysis, networks of interest are
defined based on correlation with the mean time course of a user-selected
`seed' region. Further, the user has to also specify a subject-specific threshold at which correlation
values are deemed significant. In this project, we simultaneously estimate the optimal
representative time courses that summarize the fMRI data well and
the partition of the volume into a set of disjoint regions that are best
explained by these representative time courses. This approach to functional connectivity analysis offers two
advantages. First, is removes the sensitivity of the analysis to the details
of the seed selection. Second, it substantially simplifies group analysis
by eliminating the need for the subject-specific threshold. Our experimental results indicate that
the functional segmentation provides a robust, anatomically meaningful
and consistent model for functional connectivity in fMRI.

We formulate the problem of characterizing connectivity as a partition of voxels into subsets that are well characterized by a certain number of representative hypotheses, or time courses, based on the similarity of their time courses to each hypothesis. We model the fMRI signal at each voxel as generated by a mixture of Gaussian distributions whose centers are the desired representative time courses. Using the EM algorithm to solve the corresponding model-fitting problem, we alternatively estimate the representative time courses and cluster assignments to improve our random initialization.

''' ''Experimental Results'' '''

We used data from 7 subjects with a diverse set of visual experiments including localizer, morphing, rest, internal tasks, and movie. The functional scans were pre-processed for motion artifacts, manually aligned into the Talairach coordinate system, detrended (removing linear trends in the
baseline activation) and smoothed (8mm kernel).

Fig. 1 shows the 2-system partition extracted in each subject independently
of all others. It also displays the boundaries of the intrinsic system determined
through the traditional seed selection, showing good agreement between the two
partitions. Fig.2 presents the group average of the subject-specific 2-system maps. Color shading shows the proportion of subjects whose clustering agreed with the majority label. Fig.3 shows the group average of a further parcelation of the intrinsic system.

{|
|+ '''Fig 1. 2-System Parcelation. Results for all 7 subjects.'''
|valign="top"|[[Image:mit_fmri_clustering_parcellation2_shb1_4.png |400px]]
|-
|valign="top"|[[Image:mit_fmri_clustering_parcellation2_shb5_6.png |400px]]
|-
|valign="top"|[[Image:mit_fmri_clustering_parcellation2_shb7.png |400px]]
|}

{|
|+ '''Fig 2. 2-System Parcellation. Group-wise result.'''
|valign="top"|[[Image:mit_fmri_clustering_parcellation2_xsub.png |thumb|700px]]
|}

{|
|+ '''Fig 3. Validation: Parcelation of the intrinsic system.'''
|valign="top"|[[Image:mit_fmri_clustering_intrinsicsystem.png |thumb|650px]]
|}

Fig. 4 shows the results of further clustering the stimulus-driven cluster into two clusters independently for each subject. In order to present a validation of the method, we compare these results with the conventional scheme for detection of visually responsive areas. In Fig. 5, color shows the statistical parametric map while solid lines indicate the boundaries of the visual system obtained through clustering. The results illustrate the agreement between the two methods. Fig. 5 is presenting

{|
|+ '''Fig 4. 3-System Parcelation. Results for all 7 subjects.'''
|valign="top"|[[Image:mit_fmri_clustering_parcellation3_shb1_3.png |400px]]
|-
|valign="top"|[[Image:mit_fmri_clustering_parcellation3_shb4_5.png |400px]]
|-
|valign="top"|[[Image:mit_fmri_clustering_parcellation3_shb6.png |400px]]
|-
|valign="top"|[[Image:mit_fmri_clustering_parcellation3_shb7.png |400px]]
|}

{|
|+ '''Fig 5. Validation: Visual system.'''
|valign="top"|[[Image:mit_fmri_clustering_validation.png |thumb|1150px]]
|}

''' ''Clustering Study of Domain Specificity in High Level Visual Cortex'' '''

As a more specific application of clustering model-based algorithms, we are currently investigating devising clustering algorithms for detection of functional connectivity in high-level visual cortex. It is suggested that there are regions in the visual cortex with high selectivity to certain categories of visual stimuli. Currently, the conventional method for detection of these methods is based on statistical tests comparing response of each voxel in the brain to different visual categories to see if it shows considerably higher activation to one category. For example, the well-known FFA (Fusiform Face Area) is the set of voxels which show high activation to faces when compared to objects. We are working on using the clustering the visual cortex as a means to make this analysis automatic and further discover new structures in the high-level visual cortex.

= Key Investigators =

* MIT: Danial Lashkari, Polina Golland, Nancy Kanwisher

= Publications =

''In print''

* P. Golland, Y. Golland, R. Malach. Detection of Spatial Activation Patterns As Unsupervised Segmentation of fMRI Data. In Proceedings of MICCAI: International Conference on Medical Image Computing and Computer Assisted Intervention, 110-118, 2007.

''In press''

* D. Lashkari, P. Golland. Convex Clustering with Exemplar-Based Models. In NIPS: Advances in Neural Information Processing Systems, 2007.

= Links =

Projects:fMRIClustering

2007-11-10T17:20:59Z

Danial:

Back to [[NA-MIC_Collaborations|NA-MIC_Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

= fMRI Clustering =

One of the major goals in analysis of fMRI data is the detection of networks in the brain with similar functional behavior. A wide variety of methods including hypothesis-driven statistical tests, unsupervised learning methods such as PCA and ICA, and different clustering algorithms have been employed to find these networks. This project aims to more specifically study application of model-based clustering algorithms in identification of functional connectivity in the brain.

= Description =

''Generative Model for Functional Connectivity''

In the classical functional connectivity analysis, networks of interest are
defined based on correlation with the mean time course of a user-selected
`seed' region. Further, the user has to also specify a subject-specific threshold at which correlation
values are deemed significant. In this project, we simultaneously estimate the optimal
representative time courses that summarize the fMRI data well and
the partition of the volume into a set of disjoint regions that are best
explained by these representative time courses. This approach to functional connectivity analysis offers two
advantages. First, is removes the sensitivity of the analysis to the details
of the seed selection. Second, it substantially simplifies group analysis
by eliminating the need for the subject-specific threshold. Our experimental results indicate that
the functional segmentation provides a robust, anatomically meaningful
and consistent model for functional connectivity in fMRI.

We formulate the problem of characterizing connectivity as a partition of voxels into subsets that are well characterized by a certain number of representative hypotheses, or time courses, based on the similarity of their time courses to each hypothesis. We model the fMRI signal at each voxel as generated by a mixture of Gaussian distributions whose centers are the desired representative time courses. Using the EM algorithm to solve the corresponding model-fitting problem, we alternatively estimate the representative time courses and cluster assignments to improve our random initialization.

''Experimental Results''

We used data from 7 subjects with a diverse set of visual experiments including localizer, morphing, rest, internal tasks, and movie. The functional scans were pre-processed for motion artifacts, manually aligned into the Talairach coordinate system, detrended (removing linear trends in the
baseline activation) and smoothed (8mm kernel).

Fig. 1 shows the 2-system partition extracted in each subject independently
of all others. It also displays the boundaries of the intrinsic system determined
through the traditional seed selection, showing good agreement between the two
partitions. Fig.2 presents the group average of the subject-specific 2-system maps. Color shading shows the proportion of subjects whose clustering agreed with the majority label. Fig.3 shows the group average of a further parcelation of the intrinsic system.

{|
|+ '''Fig 1. 2-System Parcelation. Results for all 7 subjects.'''
|valign="top"|[[Image:mit_fmri_clustering_parcellation2_shb1_4.png |400px]]
|-
|valign="top"|[[Image:mit_fmri_clustering_parcellation2_shb5_6.png |400px]]
|-
|valign="top"|[[Image:mit_fmri_clustering_parcellation2_shb7.png |400px]]
|}

{|
|+ '''Fig 2. 2-System Parcellation. Group-wise result.'''
|valign="top"|[[Image:mit_fmri_clustering_parcellation2_xsub.png |thumb|700px]]
|}

{|
|+ '''Fig 3. Validation: Parcelation of the intrinsic system.'''
|valign="top"|[[Image:mit_fmri_clustering_intrinsicsystem.png |thumb|900px]]
|}

Fig. 4 shows the results of further clustering the stimulus-driven cluster into two clusters independently for each subject. In order to present a validation of the method, we compare these results with the conventional scheme for detection of visually responsive areas. In Fig. 5, color shows the statistical parametric map while solid lines indicate the boundaries of the visual system obtained through clustering. The results illustrate the agreement between the two methods. Fig. 5 is presenting

{|
|+ '''Fig 4. 3-System Parcelation. Results for all 7 subjects.'''
|valign="top"|[[Image:mit_fmri_clustering_parcellation3_shb1_3.png |400px]]
|-
|valign="top"|[[Image:mit_fmri_clustering_parcellation3_shb4_5.png |400px]]
|-
|valign="top"|[[Image:mit_fmri_clustering_parcellation3_shb6.png |400px]]
|-
|valign="top"|[[Image:mit_fmri_clustering_parcellation3_shb7.png |400px]]
|}

{|
|+ '''Fig 5. Validation: Visual system.'''
|valign="top"|[[Image:mit_fmri_clustering_validation.png |thumb|1000px]]
|}

''Clustering Study of Domain Specificity in High Level Visual Cortex''

blah blah ...

''Project Status''

* Working 3D implementation in Matlab using the C-based Mex functions.
* Currently porting to ITK. (last updated 18/Apr/2007)

= Key Investigators =

* MIT: Danial Lashkari, Polina Golland, Nancy Kanwisher

= Publications =

''In print''

* P. Golland, Y. Golland, R. Malach. Detection of Spatial Activation Patterns As Unsupervised Segmentation of fMRI Data. In Proceedings of MICCAI: International Conference on Medical Image Computing and Computer Assisted Intervention, 110-118, 2007.

''In press''

* D. Lashkari, P. Golland. Convex Clustering with Exemplar-Based Models. In NIPS: Advances in Neural Information Processing Systems, 2007.

= Links =

File:Mit fmri clustering intrinsicsystem.png

2007-11-10T17:00:43Z

Danial:

Projects:fMRIClustering

2007-11-09T23:10:51Z

Danial:

Back to [[NA-MIC_Collaborations|NA-MIC_Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

= fMRI Clustering =

In the classical functional connectivity analysis, networks of interest are
defined based on correlation with the mean time course of a user-selected
`seed' region. Further, the user has to also specify a subject-specific threshold at which correlation
values are deemed significant. In this project, we simultaneously estimate the optimal
representative time courses that summarize the fMRI data well and
the partition of the volume into a set of disjoint regions that are best
explained by these representative time courses. This approach to functional connectivity analysis offers two
advantages. First, is removes the sensitivity of the analysis to the details
of the seed selection. Second, it substantially simplifies group analysis
by eliminating the need for the subject-specific threshold. Our experimental results indicate that
the functional segmentation provides a robust, anatomically meaningful
and consistent model for functional connectivity in fMRI.

Currently, we are investigating the application of such clustering algorithms in detection of functional connectivity in high-level

= Description =

''Generative Model for Functional Connectivity''

In the classical functional connectivity analysis, networks of interest are
defined based on correlation with the mean time course of a user-selected
`seed' region. Further, the user has to also specify a subject-specific threshold at which correlation
values are deemed significant. In this project, we simultaneously estimate the optimal
representative time courses that summarize the fMRI data well and
the partition of the volume into a set of disjoint regions that are best
explained by these representative time courses. This approach to functional connectivity analysis offers two
advantages. First, is removes the sensitivity of the analysis to the details
of the seed selection. Second, it substantially simplifies group analysis
by eliminating the need for the subject-specific threshold. Our experimental results indicate that
the functional segmentation provides a robust, anatomically meaningful
and consistent model for functional connectivity in fMRI.

We formulate the problem of characterizing connectivity as a partition of voxels into subsets that are well characterized by a certain number of representative hypotheses, or time courses, based on the similarity of their time courses to each hypothesis. We model the fMRI signal at each voxel as generated by a mixture of Gaussian distributions whose centers are the desired representative time courses. Using the EM algorithm to solve the corresponding model-fitting problem, we alternatively estimate the representative time courses and cluster assignments to improve our random initialization.

''Experimental Results''

We used data from 7 subjects with a diverse set of visual experiments including localizer, morphing, rest, internal tasks, and movie. The functional scans were pre-processed for motion artifacts, manually aligned into the Talairach coordinate system, detrended (removing linear trends in the
baseline activation) and smoothed (8mm kernel).

Fig. 1 shows the 2-system partition extracted in each subject independently
of all others. It also displays the boundaries of the intrinsic system determined
through the traditional seed selection, showing good agreement between the two
partitions. Fig.2 presents the group average of the subject-specific 2-system maps. Color shading shows the proportion of subjects whose clustering agreed with the majority label.

{|
|+ '''Fig 1. 2-System Parcelation. Results for all 7 subjects.'''
|valign="top"|[[Image:mit_fmri_clustering_parcellation2_shb1_4.png |400px]]
|-
|valign="top"|[[Image:mit_fmri_clustering_parcellation2_shb5_6.png |400px]]
|-
|valign="top"|[[Image:mit_fmri_clustering_parcellation2_shb7.png |400px]]
|}

{|
|+ '''Fig 2. 2-System Parcellation. Group-wise result.'''
|valign="top"|[[Image:mit_fmri_clustering_parcellation2_xsub.png |thumb|700px]]
|}

Fig. 3 shows the results of further clustering the stimulus-driven cluster into two clusters independently for each subject. In order to present a validation of the method, we compare these results with the conventional scheme for detection of visually responsive areas. In Fig. 4, color shows the statistical parametric map while solid lines indicate the boundaries of the visual system obtained through clustering. The results illustrate the agreement between the two methods.

{|
|+ '''Fig 3. 3-System Parcelation. Results for all 7 subjects.'''
|valign="top"|[[Image:mit_fmri_clustering_parcellation3_shb1_3.png |400px]]
|-
|valign="top"|[[Image:mit_fmri_clustering_parcellation3_shb4_5.png |400px]]
|-
|valign="top"|[[Image:mit_fmri_clustering_parcellation3_shb6.png |400px]]
|-
|valign="top"|[[Image:mit_fmri_clustering_parcellation3_shb7.png |400px]]
|}

{|
|+ '''Fig 4. Validation: Visual system.'''
|valign="top"|[[Image:mit_fmri_clustering_validation.png |thumb|1000px]]
|}

''Clustering Study of Domain Specificity in High Level Visual Cortex''

blah blah ...

''Project Status''

* Working 3D implementation in Matlab using the C-based Mex functions.
* Currently porting to ITK. (last updated 18/Apr/2007)

= Key Investigators =

* MIT: Danial Lashkari, Polina Golland, Nancy Kanwisher

= Publications =

''In print''

* P. Golland, Y. Golland, R. Malach. Detection of Spatial Activation Patterns As Unsupervised Segmentation of fMRI Data. In Proceedings of MICCAI: International Conference on Medical Image Computing and Computer Assisted Intervention, 110-118, 2007.

''In press''

* D. Lashkari, P. Golland. Convex Clustering with Exemplar-Based Models. In NIPS: Advances in Neural Information Processing Systems, 2007.

= Links =

Projects:fMRIClustering

2007-11-09T23:07:28Z

Danial:

Back to [[NA-MIC_Collaborations|NA-MIC_Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

= fMRI Clustering =

In the classical functional connectivity analysis, networks of interest are
defined based on correlation with the mean time course of a user-selected
`seed' region. Further, the user has to also specify a subject-specific threshold at which correlation
values are deemed significant. In this project, we simultaneously estimate the optimal
representative time courses that summarize the fMRI data well and
the partition of the volume into a set of disjoint regions that are best
explained by these representative time courses. This approach to functional connectivity analysis offers two
advantages. First, is removes the sensitivity of the analysis to the details
of the seed selection. Second, it substantially simplifies group analysis
by eliminating the need for the subject-specific threshold. Our experimental results indicate that
the functional segmentation provides a robust, anatomically meaningful
and consistent model for functional connectivity in fMRI.

Currently, we are investigating the application of such clustering algorithms in detection of functional connectivity in high-level

= Description =

''Generative Model for Functional Connectivity''

In the classical functional connectivity analysis, networks of interest are
defined based on correlation with the mean time course of a user-selected
`seed' region. Further, the user has to also specify a subject-specific threshold at which correlation
values are deemed significant. In this project, we simultaneously estimate the optimal
representative time courses that summarize the fMRI data well and
the partition of the volume into a set of disjoint regions that are best
explained by these representative time courses. This approach to functional connectivity analysis offers two
advantages. First, is removes the sensitivity of the analysis to the details
of the seed selection. Second, it substantially simplifies group analysis
by eliminating the need for the subject-specific threshold. Our experimental results indicate that
the functional segmentation provides a robust, anatomically meaningful
and consistent model for functional connectivity in fMRI.

We formulate the problem of characterizing connectivity as a partition of voxels into subsets that are well characterized by a certain number of representative hypotheses, or time courses, based on the similarity of their time courses to each hypothesis. We model the fMRI signal at each voxel as generated by a mixture of Gaussian distributions whose centers are the desired representative time courses. Using the EM algorithm to solve the corresponding model-fitting problem, we alternatively estimate the representative time courses and cluster assignments to improve our random initialization.

''Experimental Results''

We used data from 7 subjects with a diverse set of visual experiments including localizer, morphing, rest, internal tasks, and movie. The functional scans were pre-processed for motion artifacts, manually aligned into the Talairach coordinate system, detrended (removing linear trends in the
baseline activation) and smoothed (8mm kernel).

Fig. 1 shows the 2-system partition extracted in each subject independently
of all others. It also displays the boundaries of the intrinsic system determined
through the traditional seed selection, showing good agreement between the two
partitions. Fig.2 presents the group average of the subject-specific 2-system maps. Color shading shows the proportion of subjects whose clustering agreed with the majority label.

{|
|+ '''Fig 1. 2-System Parcelation. Results for all 7 subjects.'''
|valign="top"|[[Image:mit_fmri_clustering_parcellation2_shb1_4.png |400px]]
|-
|valign="top"|[[Image:mit_fmri_clustering_parcellation2_shb5_6.png |400px]]
|-
|valign="top"|[[Image:mit_fmri_clustering_parcellation2_shb7.png |400px]]
|}

{|
|+ '''Fig 2. 2-System Parcellation. Group-wise result.'''
|valign="top"|[[Image:mit_fmri_clustering_parcellation2_xsub.png |thumb|700px]]
|}

Fig. 3 shows the results of further clustering the stimulus-driven cluster into two clusters independently for each subject. In order to present a validation of the method, we compare these results with the conventional scheme for detection of visually responsive areas. In Fig. 4, color shows the statistical parametric map while solid lines indicate the boundaries of the visual system obtained through clustering. The results illustrate the agreement between the two methods.

{|
|+ '''Fig 3. 3-System Parcelation. Results for all 7 subjects.'''
|valign="top"|[[Image:mit_fmri_clustering_parcellation3_shb1_3.png |400px]]
|-
|valign="top"|[[Image:mit_fmri_clustering_parcellation3_shb4_5.png |400px]]
|-
|valign="top"|[[Image:mit_fmri_clustering_parcellation3_shb6.png |400px]]
|-
|valign="top"|[[Image:mit_fmri_clustering_parcellation3_shb7.png |400px]]
|}

{|
|+ '''Fig 4. Validation: Visual system.'''
|valign="top"|[[Image:mit_fmri_clustering_validation.png |thumb|1000px|blah blah]]
|}

''Project Status''

*Working 3D implementation in Matlab using the C-based Mex functions.
*Currently porting to ITK. (last updated 18/Apr/2007)

= Key Investigators =

* MIT: Danial Lashkari, Polina Golland, Nancy Kanwisher

= Publications =

''In print''

* P. Golland, Y. Golland, R. Malach. Detection of Spatial Activation Patterns As Unsupervised Segmentation of fMRI Data. In Proceedings of MICCAI: International Conference on Medical Image Computing and Computer Assisted Intervention, 110-118, 2007.

''In press''

* D. Lashkari, P. Golland. Convex Clustering with Exemplar-Based Models. In NIPS: Advances in Neural Information Processing Systems, 2007.

= Links =

Algorithm:MIT:New

2007-11-09T22:47:36Z

Danial: /* Shape Analysis With Overcomplete Wavelets */

Back to [[Algorithm:Main|NA-MIC Algorithms]]

= Overview of MIT Algorithms =

A brief overview of the MIT's algorithms goes here. This should not be much longer than a paragraph. Remember that people visiting your site want to be able to understand very quickly what you're all about and then they want to jump into your site's projects. The projects below are organized into a two column table: the left column is for representative images and the right column is for project overviews. The number of rows corresponds to the number of projects at your site. Put the most interesting and relevant projects at the top of the table. You do not need to organize the table according to subject matter (i.e. do not group all segmentation projects together and all DWI projects together).

[[#Shape_Based_Segmentation_and_Registration|Shape Based Segmentation and Registration]]

[[#Effects_of_Registration_Regularization_on_Segmentation_Accuracy|Effects of Registration Regularization on Segmentation Accuracy]]

[[#Multimodal_Atlas|Multimodal Atlas]]

[[#Shape_Analysis_With_Overcomplete_Wavelets|Shape Analysis With Overcomplete Wavelets]]

[[#fMRI_clustering|fMRI clustering]]

[[#Joint_Registration_and_Segmentation_of_DWI_Fiber_Tractography|Joint Registration and Segmentation of DWI Fiber Tractography]]

[[#Shape_Based_Level_Segmentation|Shape Based Level Segmentation]]

[[#DTI_Fiber_Clustering_and_Fiber-Based_Analysis|DTI Fiber Clustering and Fiber-Based Analysis]]

[[#Fiber_Tract_Modeling.2C_Clustering.2C_and_Quantitative_Analysis|Fiber Tract Modeling, Clustering and Quantitative Analysis]]

[[#DTI-based_Segmentation|DTI-based Segmentation]]

[[#Stochastic_Tractography|Stochastic Tractography]]

[[#fMRI_Detection_and_Analysis|fMRI Detection and Analysis]]

[[#Population_Analysis_of_Anatomical_Variability|Population Analysis of Anatomical Variability]]

[[#Groupwise_Registration|Groupwise Registration]]

= MIT Projects =

{|
| style="width:10%" | [[Image:Progress_Registration_Segmentation_Shape.jpg|left|200px]]
| style="width:90%" |

== [[Algorithm:MIT:Shape_Based_Segmentation_And_Registration|Shape Based Segmentation and Registration]] ==

This type of algorithms assigns a tissue type to each voxel in the volume. Incorporating prior shape information biases the label assignment towards contiguous regions that are consistent with the shape model. [[Algorithm:MIT:Shape_Based_Segmentation_And_Registration|More...]]

<font color="red">'''New: '''</font> K.M. Pohl, J. Fisher, S. Bouix, M. Shenton, R. W. McCarley, W.E.L. Grimson, R. Kikinis, and W.M. Wells. Using the Logarithm of Odds to Define a Vector Space on Probabilistic Atlases. Accepted to the Special Issue of Best Selected Papers from MICCAI 06 in Medical Image Analysis [[Algorithm:MIT:Shape_Based_Segmentation_And_Registration#Publications|More...]]

|-

| | [[Image:JointRegSeg.png|left|200px]]
| |

== [[Algorithm:MIT:RegistrationRegularization|Optimal Atlas Regularization in Image Segmentation]] ==

We propose a unified framework for computing atlases from manually labeled data sets at various degrees of “sharpness” and the joint registration and segmentation of a new brain with these atlases. Using this framework, we investigate the tradeoff between warp regularization and image ﬁdelity, i.e. the smoothness of the new subject warp and the sharpness of the atlas in a segmentation application.
[[Algorithm:MIT:RegistrationRegularization|More...]]

<font color="red">'''New:'''</font> B.T.T. Yeo, M.R. Sabuncu, R. Desikan, B. Fischl, P. Golland. Effects of Registration Regularization and Atlas Sharpness on Segmentation Accuracy. In Proceedings of MICCAI: International Conference on Medical Image Computing and Computer Assisted Intervention, 683-691, 2007. '''MICCAI Young Scientist Award.'''

|-

| | [[Image:ICluster_templates.gif|left|200px]]
| |

== [[Algorithm:MIT:Multimodal Atlas |Multimodal Atlas]] ==

In this work, we propose and investigate an algorithm that jointly co-registers a collection of images while computing multiple templates. The algorithm, called '''iCluster''', is used to compute multiple atlases for a given population.
[[Algorithm:MIT:Multimodal Atlas|More...]]

<font color="red">'''New: '''</font> M.R. Sabuncu, M.E. Shenton, P. Golland. Joint Registration and Clustering of Images. In Proceedings of MICCAI 2007 Statistical Registration Workshop: Pair-wise and Group-wise Alignment and Atlas Formation, 47-54, 2007.
[[Algorithm:MIT:Multimodal Atlas#Publications|More...]]

|-

| | [[Image:GroupwiseSummary.PNG|left|200px]]
| |

== [[Algorithm:MIT:Groupwise_Registration#Introduction|Groupwise Registration]] ==

We are exploring algorithms for groupwise registration of medical data. [[Algorithm:MIT:Groupwise_Registration|More...]]

<font color="red">'''New:'''</font> Serdar K Balci, Polina Golland, Sandy Wells, Lilla Zollei, Mert R Sabuncu and Kinh Tieu. Groupwise registration of medical data.

|-

| | [[Image:FoldingSpeedDetection.png|center|150px|]]
| |

== [[Algorithm:MIT:ShapeAnalysisWithOvercompleteWavelets|Shape Analysis With Overcomplete Wavelets]] ==

In this work, we extend the Euclidean wavelets to the sphere. The resulting over-complete spherical wavelets are invariant to the rotation of the spherical image parameterization. We apply the over-complete spherical wavelet to cortical folding development [[Algorithm:MIT:Shape_Based_Segmentation_And_Registration|More...]]

<font color="red">'''New: '''</font> B.T.T. Yeo, W. Ou, P. Golland. On the Construction of Invertible Filter Banks on the 2-Sphere. Yeo, Ou and Golland. Accepted to the IEEE Transactions on Image Processing.

P. Yu, B.T.T. Yeo, P.E. Grant, B. Fischl, P. Golland. Cortical Folding Development Study based on Over-Complete Spherical Wavelets. In Proceedings of MMBIA: IEEE Computer Society Workshop on Mathematical Methods in Biomedical Image Analysis, 2007. [[Algorithm:MIT:ShapeAnalysisWithOvercompleteWavelets#Publication|More...]]

|-

| | [[Image:mit_fmri_clustering_parcellation2_xsub.png|thumb|left|200px]]
| |

== [[Algorithm:MIT:fMRI Clustering |fMRI clustering]] ==

This type of algorithms assigns a tissue type to each voxel in the volume. Incorporating prior shape information biases the label assignment towards contiguous regions that are consistent with the shape model. [[Algorithm:MIT:Shape_Based_Segmentation_And_Registration|More...]]

<font color="red">'''New: '''</font> K.M. Pohl, J. Fisher, S. Bouix, M. Shenton, R. W. McCarley, W.E.L. Grimson, R. Kikinis, and W.M. Wells. Using the Logarithm of Odds to Define a Vector Space on Probabilistic Atlases. Accepted to the Special Issue of Best Selected Papers from MICCAI 06 in Medical Image Analysis [[Algorithm:MIT:Shape_Based_Segmentation_And_Registration#Publications|More...]]

|-

| | [[Image:MIT_DTI_JointSegReg_atlas3D.jpg|thumb|left|200px]]
| |

== [[Algorithm:MIT:DTI_FiberRegistration|Joint Registration and Segmentation of DWI Fiber Tractography]] ==

The goal of this work is to jointly register and cluster DWI fiber tracts obtained from a group of subjects. [[Algorithm:MIT:DTI_FiberRegistration|More...]]

<font color="red">'''New:'''</font> U. Ziyan, M. R. Sabuncu, W. E. L. Grimson, Carl-Fredrik Westin. A Robust Algorithm for Fiber-Bundle Atlas Construction. MMBIA 2007

|-

| | [[Image:brain.png|thumb|left|200px]]
| |

== [[Algorithm:MIT:Shape_Based_Level_Set_Segmentation|Shape Based Level Segmentation]] ==

This class of algorithms explicitly manipulates the representation of the object boundary to fit the strong gradients in the image, indicative of the object outline. Bias in the boundary evolution towards the likely shapes improves the robustness of the segmentation results when the intensity information alone is insufficient for boundary detection. [[Algorithm:MIT:Shape_Based_Level_Set_Segmentation|More...]]

<font color="red">'''New: '''</font>

|-

| | [[Image:Wholebrain.jpg|thumb|left|200px]]
| |

== [[Algorithm:MIT:DTI_Clustering|DTI Fiber Clustering and Fiber-Based Analysis]] ==

The goal of this project is to provide structural description of the white matter architecture as a partition into coherent fiber bundles and clusters, and to use these bundles for quantitative measurement. [[Algorithm:MIT:DTI_Clustering|More...]]

<font color="red">'''New:'''</font>
Monica E. Lemmond, Lauren J. O'Donnell, Stephen Whalen, Alexandra J. Golby.
Characterizing Diffusion Along White Matter Tracts Affected by Primary Brain Tumors.
Accepted to HBM 2007.

|-

| | [[Image:Models.jpg|thumb|left|200px]]
| |

== [[Algorithm:MIT:DTI_Modeling|Fiber Tract Modeling, Clustering, and Quantitative Analysis]] ==

The goal of this work is to model the shape of the fiber bundles and use this model discription in clustering and statistical analysis of fiber tracts. [[Algorithm:MIT:DTI_Modeling|More...]]

<font color="red">'''New:'''</font>
M. Maddah, W. M. Wells, S. K. Warfield, C.-F. Westin, and W. E. L. Grimson, Probabilistic Clustering and Quantitative Analysis of White Matter Fiber Tracts,IPMI 2007, Netherlands.

|-

| | [[Image:Thalamus_algo_outline.png|thumb|left|200px]]
| |

== [[Algorithm:MIT:DTI_Segmentation|DTI-based Segmentation]] ==

Unlike conventional MRI, DTI provides adequate contrast to segment the thalamic nuclei, which are gray matter structures. [[Algorithm:MIT:DTI_Segmentation|More...]]

<font color="red">'''New:'''</font> Ulas Ziyan, David Tuch, Carl-Fredrik Westin. Segmentation of Thalamic Nuclei from DTI using Spectral Clustering. Accepted to MICCAI 2006.

|-

|-

| | [[Image:ConnectivityMap.png|thumb|left|200px]]
| |

== [[Algorithm:MIT:DTI_StochasticTractography|Stochastic Tractography]] ==

This work calculates posterior distributions of white matter fiber tract parameters given diffusion observations in a DWI volume. [[Algorithm:MIT:DTI_StochasticTractography|More...]]

<font color="red">'''New: '''</font>

|-

| | [[Image:FMRIEvaluationchart.jpg|thumb|left|200px]]
| |

== [[Algorithm:MIT:fMRI_Detection|fMRI Detection and Analysis]] ==

We are exploring algorithms for improved fMRI detection and interpretation by incorporting spatial priors and anatomical information to guide the detection. [[Algorithm:MIT:fMRI_Detection|More...]]

<font color="red">'''New:'''</font> Wanmei Ou, Sandy Wells, Polina Golland. Bridging Spatial Regularization And Anatomical Priors in fMRI Detection. In preparation for submission to IEEE TMI.

|-

| | [[Image:HippocampalShapeDifferences.gif|thumb|left|200px]]
| |

== [[Algorithm:MIT:Shape_Analisys|Population Analysis of Anatomical Variability]] ==

Our goal is to develop mathematical approaches to modeling anatomical variability within and across populations using tools like local shape descriptors of specific regions of interest and global constellation descriptors of multiple ROI's. [[Algorithm:MIT:Shape_Analisys|More...]]

<font color="red">'''New:'''</font> Mert R Sabuncu and Polina Golland. Structural Constellations for Population Analysis of Anatomical Variability.

File:Mit fmri clustering parcellation3 shb1 3.png

2007-11-09T22:01:54Z

Danial:

Projects:fMRIClustering

2007-11-09T22:00:39Z

Danial:

File:Mit fmri clustering validation.png

2007-11-09T21:59:02Z

Danial:

File:Mit fmri clustering parcellation3 shb7.png

2007-11-09T21:56:25Z

Danial:

File:Mit fmri clustering parcellation3 shb6.png

2007-11-09T21:56:05Z

Danial:

File:Mit fmri clustering parcellation3 shb4 5.png

2007-11-09T21:55:37Z

Danial:

File:Mit fmri clustering parcellation3 shb1 4.png

2007-11-09T21:55:08Z

Danial:

Projects:fMRIClustering

2007-11-09T21:38:41Z

Danial:

Projects:fMRIClustering

2007-11-09T21:30:01Z

Danial:

Back to [[NA-MIC_Collaborations|NA-MIC_Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

= fMRI Clustering =

In the classical functional connectivity analysis, networks of interest are
defined based on correlation with the mean time course of a user-selected
`seed' region. Further, the user has to also specify a subject-specific threshold at which correlation
values are deemed significant. In this project, we simultaneously estimate the optimal
representative time courses that summarize the fMRI data well and
the partition of the volume into a set of disjoint regions that are best
explained by these representative time courses. This approach to functional connectivity analysis offers two
advantages. First, is removes the sensitivity of the analysis to the details
of the seed selection. Second, it substantially simplifies group analysis
by eliminating the need for the subject-specific threshold. Our experimental results indicate that
the functional segmentation provides a robust, anatomically meaningful
and consistent model for functional connectivity in fMRI.

Currently, we are investigating the application of such clustering algorithms in detection of functional connectivity in high-level

= Description =

''Generative Model for Functional Connectivity''

We formulate the problem of characterizing connectivity as a partition of voxels into subsets
Spatial Activation Patterns in fMRI that are well characterized by Ns representative hypotheses, or time courses,
m1; : : : mNs based on the similarity of their time courses to each hypothesis.
We model the fMRI signal Y at each voxel as generated by the mixture pY(y) =
PNs
s=1 �spYjS(yjs) over Ns conditional likelihoods pYjS(yjs) [15]. �s is the prior
probability that a voxel belongs to system s 2 f1; : : : ;Nsg. Following a commonly
used approach in fMRI analysis, we model the class-conditional densities
as normal distributions centered around the system mean time course, i.e.,
pYjS(yjs) = N(y;ms;�s). The high dimensionality of the fMRI data makes modeling
a full covariance matrix impractical. Instead, most methods either limit the
modeling to estimating variance elements, or model the time course dynamics as
an auto-regressive (AR) process. At this stage, we take the simpler approach of
modeling variance and note that the mixture model estimation can be straightforwardly
extended to include an AR model. Unlike separate dimensionality reduction
procedures, this approach follows closely the notions of functional similarity
used by the detection methods in fMRI. In other words, we keep the notion of
co-activation consistent with the standard analysis and instead rede�ne how the
co-activation patterns are represented and extracted from images.
This unsupervised technique generalizes
connectivity analysis to situations where candidate seeds are difficult to
identify reliably or are unknown.

Recently, we have applied this method to the cingulum bundle, as shown in the following images:

''Fiber Bundle Segmentation''

{|
|+ '''Fig 2. Cingulum Bundle Volumetric Fiber Bundles Segmentation Results'''
|valign="top"|[[Image:ResultZoomedOut.png |thumb|250px|Zoomed Out View]]
|valign="top"|[[Image:ZoomedResultWithModel.png |thumb|250px|Zoomed In View]]
|}

''Experimental Result''

We used data from 7 subjects with a diverse set of visual experiments including localizer, morphing, rest, internal tasks, and movie. The functional scans were pre-processed for motion artifacts, manually aligned into the Talairach coordinate system, detrended (removing linear trends in the
baseline activation) and smoothed (8mm kernel).

{|
|+ '''Fig 1. 2-System Parcellation. Group-wise result.'''
|valign="top"|[[Image:mit_fmri_clustering_parcellation2_xsub.png |thumb|700px|Detailed View of the Cingulum Bundle Anchor Tract]]
|}

{|
|+ '''Fig 2. 2-System Parcelation. Results for all 7 subjects.'''
|valign="top"|[[Image:mit_fmri_clustering_parcellation2_shb1_4.png |400px]]
|-
|valign="top"|[[Image:mit_fmri_clustering_parcellation2_shb5_6.png |400px]]
|-
|valign="top"|[[Image:mit_fmri_clustering_parcellation2_shb7.png |400px]]
|}

''Project Status''

*Working 3D implementation in Matlab using the C-based Mex functions.
*Currently porting to ITK. (last updated 18/Apr/2007)

= Key Investigators =

* MIT: Danial Lashkari, Polina Golland, Nancy Kanwisher

= Publications =

''In print''

* P. Golland, Y. Golland, R. Malach. Detection of Spatial Activation Patterns As Unsupervised Segmentation of fMRI Data. In Proceedings of MICCAI: International Conference on Medical Image Computing and Computer Assisted Intervention, 110-118, 2007.

''In press''

* D. Lashkari, P. Golland. Convex Clustering with Exemplar-Based Models. In NIPS: Advances in Neural Information Processing Systems, 2007.

= Links =

File:Mit fmri clustering parcellation2 shb7.png

2007-11-09T21:17:14Z

Danial:

File:Mit fmri clustering parcellation2 shb5 6.png

2007-11-09T21:16:51Z

Danial:

File:Mit fmri clustering parcellation2 shb1 4.png

2007-11-09T21:13:10Z

Danial:

File:Mit fmri clustering parcellation2 xsub.png

2007-11-09T21:12:24Z

Danial:

Projects:fMRIClustering

2007-11-09T20:56:26Z

Danial:

Back to [[NA-MIC_Collaborations|NA-MIC_Collaborations]], [[Algorithm:MIT|MIT Algorithms]]

= fMRI Clustering =

In the classical functional connectivity analysis, networks of interest are
defined based on correlation with the mean time course of a user-selected
`seed' region. Further, the user has to also specify a subject-specific threshold at which correlation
values are deemed significant. In this project, we simultaneously estimate the optimal
representative time courses that summarize the fMRI data well and
the partition of the volume into a set of disjoint regions that are best
explained by these representative time courses. This approach to functional connectivity analysis offers two
advantages. First, is removes the sensitivity of the analysis to the details
of the seed selection. Second, it substantially simplifies group analysis
by eliminating the need for the subject-specific threshold. Our experimental results indicate that
the functional segmentation provides a robust, anatomically meaningful
and consistent model for functional connectivity in fMRI.

Currently, we are investigating the application of such clustering algorithms in detection of functional connectivity in high-level

= Description =

''Generative Model for Functional Connectivity''

We formulate the problem of characterizing connectivity as a partition of voxels into subsets
Spatial Activation Patterns in fMRI that are well characterized by Ns representative hypotheses, or time courses,
m1; : : : mNs based on the similarity of their time courses to each hypothesis.
We model the fMRI signal Y at each voxel as generated by the mixture pY(y) =
PNs
s=1 �spYjS(yjs) over Ns conditional likelihoods pYjS(yjs) [15]. �s is the prior
probability that a voxel belongs to system s 2 f1; : : : ;Nsg. Following a commonly
used approach in fMRI analysis, we model the class-conditional densities
as normal distributions centered around the system mean time course, i.e.,
pYjS(yjs) = N(y;ms;�s). The high dimensionality of the fMRI data makes modeling
a full covariance matrix impractical. Instead, most methods either limit the
modeling to estimating variance elements, or model the time course dynamics as
an auto-regressive (AR) process. At this stage, we take the simpler approach of
modeling variance and note that the mixture model estimation can be straightforwardly
extended to include an AR model. Unlike separate dimensionality reduction
procedures, this approach follows closely the notions of functional similarity
used by the detection methods in fMRI. In other words, we keep the notion of
co-activation consistent with the standard analysis and instead rede�ne how the
co-activation patterns are represented and extracted from images.
This unsupervised technique generalizes
connectivity analysis to situations where candidate seeds are difficult to
identify reliably or are unknown.

Recently, we have applied this method to the cingulum bundle, as shown in the following images:

{|
|+ '''Fig 1. 2-System Parcellation'''
|valign="top"|[[Image:Case24-coronal-tensors-edit.png |thumb|250px|Detailed View of the Cingulum Bundle Anchor Tract]]
|valign="top"|[[Image:Case25-sagstream-tensors-edit.png|thumb|250px|Streamline Comparison]]
|-
|valign="top"|[[Image:Case26-anterior.png |thumb|250px|Anterior View of the Cingulum Bundle Anchor Tract]]
|valign="top"|[[Image:Case26-posterior.png|thumb|250px|Posterior View of the Cingulum Bundle Anchor Tract]]
|}

''Fiber Bundle Segmentation''

{|
|+ '''Fig 2. Cingulum Bundle Volumetric Fiber Bundles Segmentation Results'''
|valign="top"|[[Image:ResultZoomedOut.png |thumb|250px|Zoomed Out View]]
|valign="top"|[[Image:ZoomedResultWithModel.png |thumb|250px|Zoomed In View]]
|}

{|
|+ '''Fig 3. Cingulum Bundle Volumetric Fiber Bundles Surface Evolution'''
|valign="top"|[[Image:PriorFiberResultOverBaseline001.png |thumb|250px|Result from Priors Only (t=1)]]
|valign="top"|[[Image:PriorFiberResultOverBaseline003.png |thumb|250px|Result from Priors Only (t=3)]]
|valign="top"|[[Image:PriorFiberResultOverBaseline008.png |thumb|250px|Result from Priors Only (t=8)]]
|-
|valign="top"|[[Image:LikelihoodsFiberResultOverBaseline001.png |thumb|250px|Result from Likelihoods Only (t=1)]]
|valign="top"|[[Image:LikelihoodsFiberResultOverBaseline003.png |thumb|250px|Result from Likelihoods Only (t=3)]]
|valign="top"|[[Image:LikelihoodsFiberResultOverBaseline008.png |thumb|250px|Result from Likelihoods Only (t=8)]]
|-
|valign="top"|[[Image:FinalFiberResultOverBaseline001.png |thumb|250px|Result from Combined Likelihoods and Priors (t=1)]]
|valign="top"|[[Image:FinalFiberResultOverBaseline003.png |thumb|250px|Result from Combined Likelihoods and Priors (t=3)]]
|valign="top"|[[Image:FinalFiberResultOverBaseline008.png |thumb|250px|Result from Combined Likelihoods and Priors (t=8)]]
|}

''Experimental Result''

We used data from 7 subjects with a diverse set of visual experiments including localizer, morphing, rest, internal tasks, and movie. The functional scans were pre-processed for motion artifacts, manually aligned into the Talairach coordinate system, detrended (removing linear trends in the
baseline activation) and smoothed (8mm kernel).

''Project Status''

*Working 3D implementation in Matlab using the C-based Mex functions.
*Currently porting to ITK. (last updated 18/Apr/2007)

= Key Investigators =

* MIT: Danial Lashkari, Polina Golland, Nancy Kanwisher

= Publications =

''In print''

* P. Golland, Y. Golland, R. Malach. Detection of Spatial Activation Patterns As Unsupervised Segmentation of fMRI Data. In Proceedings of MICCAI: International Conference on Medical Image Computing and Computer Assisted Intervention, 110-118, 2007.

''In press''

* D. Lashkari, P. Golland. Convex Clustering with Exemplar-Based Models. In NIPS: Advances in Neural Information Processing Systems, 2007.

= Links =