NAMIC Wiki - User contributions [en]

Algorithm:MIT

2008-05-20T19:09:12Z

Maddah: /* Fiber Tract Modeling, Clustering, and Quantitative Analysis */

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...]]

'''New: ''' 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. Best Paper Award MICCAI 2006 

|-

| | [[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...]]

'''New:''' B.T.T. Yeo, M.R. Sabuncu, R. Desikan, B. Fischl, P. Golland. Effects of Registration Regularization and Atlas Sharpness on Segmentation Accuracy. Accepted to Medical Image Analysis, 2008.

|-

| | [[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...]]

'''New: ''' M.R. Sabuncu, Serdar K. Balci and Polina Golland. Discovering Modes of an Image Population through Mixture Modeling. Accepted to MICCAI 2008.

|-

| | [[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...]]

'''New: ''' B.T.T. Yeo, P. Yu, P.E. Grant, B. Fischl, P. Golland. Shape Analysis with Overcomplete Spherical Wavelets. Accepted to MICCAI 2008.

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

|-

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

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

In this project we develop and validate a method for fully automated segmentation of the subfields of the hippocampus in ultra-high resolution in vivo MRI. [[Projects:HippocampalSubfieldSegmentation|More...]]

'''New:''' K. Van Leemput, A. Bakkour, T. Benner, G. Wiggins, L.L. Wald, J. Augustinack, B.C. Dickerson, P. Golland, B. Fischl. Model-Based Segmentation of Hippocampal Subfields in Ultra-High Resolution In Vivo MRI. Accepted to MICCAI 2008.

|-
| | [[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...]]

'''New: ''' D. Lashkari, N. Kanwisher, P. Golland. Discovering Structure in the Space of Activation
Profiles in fMRI. Accepted to 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...]]

'''New:''' 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...]]

'''New:''' 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 description in clustering and statistical analysis of fiber tracts. [[Projects:DTIModeling|More...]]

'''New:'''

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, to be presented in MICCAI 2008, NY, US.

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, to be presented at MMBIA 2008, Alaska, US.

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, Paris, France.

|-

| | [[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...]]

'''New:''' 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...]]

'''New:''' 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...]]

'''New:''' Mert R Sabuncu and Polina Golland. Structural Constellations for Population Analysis of Anatomical Variability.

|}

Algorithm:MIT

2008-05-20T19:07:07Z

Maddah: /* Fiber Tract Modeling, Clustering, and Quantitative Analysis */

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...]]

'''New: ''' 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. Best Paper Award MICCAI 2006 

|-

| | [[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...]]

'''New:''' B.T.T. Yeo, M.R. Sabuncu, R. Desikan, B. Fischl, P. Golland. Effects of Registration Regularization and Atlas Sharpness on Segmentation Accuracy. Accepted to Medical Image Analysis, 2008.

|-

| | [[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...]]

'''New: ''' M.R. Sabuncu, Serdar K. Balci and Polina Golland. Discovering Modes of an Image Population through Mixture Modeling. Accepted to MICCAI 2008.

|-

| | [[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...]]

'''New: ''' B.T.T. Yeo, P. Yu, P.E. Grant, B. Fischl, P. Golland. Shape Analysis with Overcomplete Spherical Wavelets. Accepted to MICCAI 2008.

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

|-

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

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

In this project we develop and validate a method for fully automated segmentation of the subfields of the hippocampus in ultra-high resolution in vivo MRI. [[Projects:HippocampalSubfieldSegmentation|More...]]

'''New:''' K. Van Leemput, A. Bakkour, T. Benner, G. Wiggins, L.L. Wald, J. Augustinack, B.C. Dickerson, P. Golland, B. Fischl. Model-Based Segmentation of Hippocampal Subfields in Ultra-High Resolution In Vivo MRI. Accepted to MICCAI 2008.

|-
| | [[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...]]

'''New: ''' D. Lashkari, N. Kanwisher, P. Golland. Discovering Structure in the Space of Activation
Profiles in fMRI. Accepted to 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...]]

'''New:''' 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...]]

'''New:''' 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 description in clustering and statistical analysis of fiber tracts. [[Projects:DTIModeling|More...]]

'''New:'''

|-

| | [[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...]]

'''New:''' 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...]]

'''New:''' 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...]]

'''New:''' Mert R Sabuncu and Polina Golland. Structural Constellations for Population Analysis of Anatomical Variability.

|}

Projects:DTIModeling

2008-05-20T19:01:06Z

Maddah: /* Key Investigators */

Back to [[NA-MIC_Internal_Collaborations:DiffusionImageAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]
__NOTOC__
= DTI Modeling =

We developed a novel approach for joint clustering and point-by-point mapping of white matter fiber pathways. Knowledge of the point correspondence along the fiber pathways is not only necessary for accurate clustering of the trajectories into fiber bundles, but also crucial for any tract-oriented quantitative analysis. The proposed approach is also capable of incorporating anatomical knowledge as prior information.

= Description =

We employ an expectation-maximization (EM) algorithm to cluster the trajectories in a Gamma mixture model context. The result of clustering is the probabilistic assignment of the fiber trajectories to each cluster and an estimate of the cluster parameters, i.e. spatial mean and variance, and point correspondences. The fiber bundles are modeled by the mean trajectory and its spatial variation. Point-by-point correspondence of the trajectories within a bundle is obtained by constructing a distance map and a label map from each cluster center at every iteration of the EM algorithm. This offers a time-efficient alternative to pairwise curve matching of all trajectories with respect to each cluster center.

The proposed method has the potential to benefit from an anatomical atlas of fiber tracts by incorporating it as prior information in the EM algorithm. The algorithm is also capable of handling outliers in a principled way. Here are some examples of modeling/clustering the bundles:

[[Image:models.jpg|Model of fiber tracts]]

[[Image:wholebrain.jpg|Model of fiber tracts|600px]]

One of the difficult bundles of fiber tracts to cluster is the cingulum. Even starting tractography from a user-defined ROI results in a set of disordered trajectories, mostly short in length because of low FA. Also, due to its adjacency to the corpus callosum, many callosal trajectories are included that adversely affect any further analysis of the bundle. As shown in the following figure for two subjects, our method is well capable of clustering these trajectories into the desired bundles. Two arbitrary trajectories, one from the the superior and one from the posterior part of the cingulum were selected as the initial cluster centers. Knowledge of the point correspondence and hence rigorous calculation of the similarity measure is essential for clustering of such a disordered set of trajectories.

[[Image:cingulum.jpg|400px]][[Image:Gamma.jpg|250px]]

Figure on the right illustrates the evolution of the Gamma distribution for the clusters of the first case shown the above figure. Convergence is achieved just after a few iterations of the EM algorithm.

The proposed algorithm is being applied on several datasets. Below are two examples:

'''Population Study on Patahogical Subjects'''

A population study on the cinglum bundle in controls and Schizophrenia cases:

[[Image:Populationstudy.jpg|400px]]

'''Brain Development'''

[[Image:braindevelopment.jpg|400px]][[Image:braindevelopment_qa.jpg|300px]]

FA-colored trajectories from (a), (d) cortico-spinal, (b), (e) cingulum and (c), (f) uncinate fasciculus at 32-wk (up) and 42-wk (down) postmenstrual age. part of the cingulum and at 32-wk (up) and 42-wk (down) postmenstrual age. Spatial patterns of the tract development are clearly seen.
On the right, the figure shows the box-plot of the FA variation along the tract arc length for part of the cingulum and at 32-wk (up) and 42-wk (down) postmenstrual age. Only the posterior part shows a significant FA increase. ROI-based analysis fails to detect such spatial dependencies.

''Software''

Currently, all of the codes are implemented in MATLAB.

= Key Investigators =

* MIT Algorithms: Mahnaz Maddah, Sandy Wells, Simon Warfield C-F Westin, and Eric Grimson.

= Publications =
''In Press''

* 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, to be presented in MICCAI 2008, NY, US.

* 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, to be presented at MMBIA 2008, Alaska, US.

* 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, Paris, France.

* M. Maddah, A. U. Mewes, H. Als, G. McAnulty, W. E. L. Grimson, and S. K. Warfield, Investigation of Neonate Brain Development Enabled by Tract-Oriented Quantification, ISMRM 2008, Toronto, Canada.

''In Print''

*[http://www.na-mic.org/pages/Special:Publications?text=Maddah+Tract&submit=Search&words=all&title=checked&keywords=checked&authors=checked&abstract=checked&sponsors=checked&searchbytag=checked| NA-MIC Publications Database]

[[Category: Shape Analysis]] [[Category:Schizophrenia]]

Projects:DTIModeling

2008-05-20T19:00:09Z

Maddah: /* Publications */

Back to [[NA-MIC_Internal_Collaborations:DiffusionImageAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]
__NOTOC__
= DTI Modeling =

We developed a novel approach for joint clustering and point-by-point mapping of white matter fiber pathways. Knowledge of the point correspondence along the fiber pathways is not only necessary for accurate clustering of the trajectories into fiber bundles, but also crucial for any tract-oriented quantitative analysis. The proposed approach is also capable of incorporating anatomical knowledge as prior information.

= Description =

We employ an expectation-maximization (EM) algorithm to cluster the trajectories in a Gamma mixture model context. The result of clustering is the probabilistic assignment of the fiber trajectories to each cluster and an estimate of the cluster parameters, i.e. spatial mean and variance, and point correspondences. The fiber bundles are modeled by the mean trajectory and its spatial variation. Point-by-point correspondence of the trajectories within a bundle is obtained by constructing a distance map and a label map from each cluster center at every iteration of the EM algorithm. This offers a time-efficient alternative to pairwise curve matching of all trajectories with respect to each cluster center.

The proposed method has the potential to benefit from an anatomical atlas of fiber tracts by incorporating it as prior information in the EM algorithm. The algorithm is also capable of handling outliers in a principled way. Here are some examples of modeling/clustering the bundles:

[[Image:models.jpg|Model of fiber tracts]]

[[Image:wholebrain.jpg|Model of fiber tracts|600px]]

One of the difficult bundles of fiber tracts to cluster is the cingulum. Even starting tractography from a user-defined ROI results in a set of disordered trajectories, mostly short in length because of low FA. Also, due to its adjacency to the corpus callosum, many callosal trajectories are included that adversely affect any further analysis of the bundle. As shown in the following figure for two subjects, our method is well capable of clustering these trajectories into the desired bundles. Two arbitrary trajectories, one from the the superior and one from the posterior part of the cingulum were selected as the initial cluster centers. Knowledge of the point correspondence and hence rigorous calculation of the similarity measure is essential for clustering of such a disordered set of trajectories.

[[Image:cingulum.jpg|400px]][[Image:Gamma.jpg|250px]]

Figure on the right illustrates the evolution of the Gamma distribution for the clusters of the first case shown the above figure. Convergence is achieved just after a few iterations of the EM algorithm.

The proposed algorithm is being applied on several datasets. Below are two examples:

'''Population Study on Patahogical Subjects'''

A population study on the cinglum bundle in controls and Schizophrenia cases:

[[Image:Populationstudy.jpg|400px]]

'''Brain Development'''

[[Image:braindevelopment.jpg|400px]][[Image:braindevelopment_qa.jpg|300px]]

FA-colored trajectories from (a), (d) cortico-spinal, (b), (e) cingulum and (c), (f) uncinate fasciculus at 32-wk (up) and 42-wk (down) postmenstrual age. part of the cingulum and at 32-wk (up) and 42-wk (down) postmenstrual age. Spatial patterns of the tract development are clearly seen.
On the right, the figure shows the box-plot of the FA variation along the tract arc length for part of the cingulum and at 32-wk (up) and 42-wk (down) postmenstrual age. Only the posterior part shows a significant FA increase. ROI-based analysis fails to detect such spatial dependencies.

''Software''

Currently, all of the codes are implemented in MATLAB.

= Key Investigators =

* MIT Algorithms: Mahnaz Maddah, Sandy Wells, Simon Warfield and Eric Grimson.

= Publications =
''In Press''

* 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, to be presented in MICCAI 2008, NY, US.

* 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, to be presented at MMBIA 2008, Alaska, US.

* 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, Paris, France.

* M. Maddah, A. U. Mewes, H. Als, G. McAnulty, W. E. L. Grimson, and S. K. Warfield, Investigation of Neonate Brain Development Enabled by Tract-Oriented Quantification, ISMRM 2008, Toronto, Canada.

''In Print''

*[http://www.na-mic.org/pages/Special:Publications?text=Maddah+Tract&submit=Search&words=all&title=checked&keywords=checked&authors=checked&abstract=checked&sponsors=checked&searchbytag=checked| NA-MIC Publications Database]

[[Category: Shape Analysis]] [[Category:Schizophrenia]]

Projects:DTIModeling

2008-05-20T18:58:54Z

Maddah: /* Publications */

Back to [[NA-MIC_Internal_Collaborations:DiffusionImageAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]
__NOTOC__
= DTI Modeling =

We developed a novel approach for joint clustering and point-by-point mapping of white matter fiber pathways. Knowledge of the point correspondence along the fiber pathways is not only necessary for accurate clustering of the trajectories into fiber bundles, but also crucial for any tract-oriented quantitative analysis. The proposed approach is also capable of incorporating anatomical knowledge as prior information.

= Description =

We employ an expectation-maximization (EM) algorithm to cluster the trajectories in a Gamma mixture model context. The result of clustering is the probabilistic assignment of the fiber trajectories to each cluster and an estimate of the cluster parameters, i.e. spatial mean and variance, and point correspondences. The fiber bundles are modeled by the mean trajectory and its spatial variation. Point-by-point correspondence of the trajectories within a bundle is obtained by constructing a distance map and a label map from each cluster center at every iteration of the EM algorithm. This offers a time-efficient alternative to pairwise curve matching of all trajectories with respect to each cluster center.

The proposed method has the potential to benefit from an anatomical atlas of fiber tracts by incorporating it as prior information in the EM algorithm. The algorithm is also capable of handling outliers in a principled way. Here are some examples of modeling/clustering the bundles:

[[Image:models.jpg|Model of fiber tracts]]

[[Image:wholebrain.jpg|Model of fiber tracts|600px]]

One of the difficult bundles of fiber tracts to cluster is the cingulum. Even starting tractography from a user-defined ROI results in a set of disordered trajectories, mostly short in length because of low FA. Also, due to its adjacency to the corpus callosum, many callosal trajectories are included that adversely affect any further analysis of the bundle. As shown in the following figure for two subjects, our method is well capable of clustering these trajectories into the desired bundles. Two arbitrary trajectories, one from the the superior and one from the posterior part of the cingulum were selected as the initial cluster centers. Knowledge of the point correspondence and hence rigorous calculation of the similarity measure is essential for clustering of such a disordered set of trajectories.

[[Image:cingulum.jpg|400px]][[Image:Gamma.jpg|250px]]

Figure on the right illustrates the evolution of the Gamma distribution for the clusters of the first case shown the above figure. Convergence is achieved just after a few iterations of the EM algorithm.

The proposed algorithm is being applied on several datasets. Below are two examples:

'''Population Study on Patahogical Subjects'''

A population study on the cinglum bundle in controls and Schizophrenia cases:

[[Image:Populationstudy.jpg|400px]]

'''Brain Development'''

[[Image:braindevelopment.jpg|400px]][[Image:braindevelopment_qa.jpg|300px]]

FA-colored trajectories from (a), (d) cortico-spinal, (b), (e) cingulum and (c), (f) uncinate fasciculus at 32-wk (up) and 42-wk (down) postmenstrual age. part of the cingulum and at 32-wk (up) and 42-wk (down) postmenstrual age. Spatial patterns of the tract development are clearly seen.
On the right, the figure shows the box-plot of the FA variation along the tract arc length for part of the cingulum and at 32-wk (up) and 42-wk (down) postmenstrual age. Only the posterior part shows a significant FA increase. ROI-based analysis fails to detect such spatial dependencies.

''Software''

Currently, all of the codes are implemented in MATLAB.

= Key Investigators =

* MIT Algorithms: Mahnaz Maddah, Sandy Wells, Simon Warfield and Eric Grimson.

= Publications =
''In Press''

* 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, to be presented in MICCAI 2008, NY, US.

* 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,
to be presented at MMBIA 2008, Alaska, US.

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

* M. Maddah, A. U. Mewes, H. Als, G. McAnulty, W. E. L. Grimson, and S. K. Warfield,
Investigation of Neonate Brain Development Enabled by Tract-Oriented Quantification,
ISMRM 2008, Toronto, Canada.

''In Print''

*[http://www.na-mic.org/pages/Special:Publications?text=Maddah+Tract&submit=Search&words=all&title=checked&keywords=checked&authors=checked&abstract=checked&sponsors=checked&searchbytag=checked| NA-MIC Publications Database]

[[Category: Shape Analysis]] [[Category:Schizophrenia]]

Projects:DTIModeling

2007-11-11T03:10:22Z

Maddah: /* DTI Modeling */

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

= DTI Modeling =

We developed a novel approach for joint clustering and point-by-point mapping of white matter fiber pathways. Knowledge of the point correspondence along the fiber pathways is not only necessary for accurate clustering of the trajectories into fiber bundles, but also crucial for any tract-oriented quantitative analysis. The proposed approach is also capable of incorporating anatomical knowledge as prior information.

= Description =

We employ an expectation-maximization (EM) algorithm to cluster the trajectories in a Gamma mixture model context. The result of clustering is the probabilistic assignment of the fiber trajectories to each cluster and an estimate of the cluster parameters, i.e. spatial mean and variance, and point correspondences. The fiber bundles are modeled by the mean trajectory and its spatial variation. Point-by-point correspondence of the trajectories within a bundle is obtained by constructing a distance map and a label map from each cluster center at every iteration of the EM algorithm. This offers a time-efficient alternative to pairwise curve matching of all trajectories with respect to each cluster center.

The proposed method has the potential to benefit from an anatomical atlas of fiber tracts by incorporating it as prior information in the EM algorithm. The algorithm is also capable of handling outliers in a principled way. Here are some examples of modeling/clustering the bundles:

[[Image:models.jpg|Model of fiber tracts]]

[[Image:wholebrain.jpg|Model of fiber tracts|600px]]

One of the difficult bundles of fiber tracts to cluster is the cingulum. Even starting tractography from a user-defined ROI results in a set of disordered trajectories, mostly short in length because of low FA. Also, due to its adjacency to the corpus callosum, many callosal trajectories are included that adversely affect any further analysis of the bundle. As shown in the following figure for two subjects, our method is well capable of clustering these trajectories into the desired bundles. Two arbitrary trajectories, one from the the superior and one from the posterior part of the cingulum were selected as the initial cluster centers. Knowledge of the point correspondence and hence rigorous calculation of the similarity measure is essential for clustering of such a disordered set of trajectories.

[[Image:cingulum.jpg|400px]][[Image:Gamma.jpg|250px]]

Figure on the right illustrates the evolution of the Gamma distribution for the clusters of the first case shown the above figure. Convergence is achieved just after a few iterations of the EM algorithm.

The proposed algorithm is being applied on several datasets. Below are two examples:

'''Population Study on Patahogical Subjects'''

A population study on the cinglum bundle in controls and Schizophrenia cases:

[[Image:Populationstudy.jpg|400px]]

'''Brain Development'''

[[Image:braindevelopment.jpg|400px]][[Image:braindevelopment_qa.jpg|300px]]

FA-colored trajectories from (a), (d) cortico-spinal, (b), (e) cingulum and (c), (f) uncinate fasciculus at 32-wk (up) and 42-wk (down) postmenstrual age. part of the cingulum and at 32-wk (up) and 42-wk (down) postmenstrual age. Spatial patterns of the tract development are clearly seen.
On the right, the figure shows the box-plot of the FA variation along the tract arc length for part of the cingulum and at 32-wk (up) and 42-wk (down) postmenstrual age. Only the posterior part shows a significant FA increase. ROI-based analysis fails to detect such spatial dependencies.

''Software''

Currently, all of the codes are implemented in MATLAB.

= Key Investigators =

Mahnaz Maddah, Sandy Wells, Simon Warfield and Eric Grimson.

= Publications =

[1] 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.

[2] 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.

[3] M. Maddah, W. M. Wells, S. K. Warfield, C-F. Westin, and W. E. L. Grimson, A Spatial Model of White Matter Fiber Tracts to be presented at ISMRM 2007, Berlin.

[4] M. Maddah, W. E. L. Grimson, and S. Warfield, Statistical Modeling and EM Clustering of White Matter Fiber Tracts 3rd IEEE International Symposium on Biomedical Imaging: Macro to Nano (ISBI) 2006, pp. 53-56.

[5] D. Goldberg-Zimring, A. U. J. Mewes, M. Maddah, S. K. Warfield, Diffusion Tensor Magnetic Resonance Imaging in Multiple Sclerosis J Neuroimaging, vol. 15, pp. 68S-81S, 2005.

[6] M. Maddah, A. Mewes, S. Haker, W. E. L. Grimson, and S. Warfield, Automated Atlas-Based Clustering of White Matter Fiber Tracts from DTMRI. MICCAI05, Palm Spring, CA, pp. 188-195, 2005.

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

= Links =

Projects:DTIModeling

2007-11-11T03:04:00Z

Maddah: /* Description */

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

= DTI Modeling =

We developed a novel approach for joint clustering and point-by-point mapping of white matter fiber pathways. Knowledge of the point correspondence along the fiber pathways is not only necessary for accurate clustering of the trajectories into fiber bundles, but also crucial for any tract-oriented quantitative analysis.

= Description =

We employ an expectation-maximization (EM) algorithm to cluster the trajectories in a Gamma mixture model context. The result of clustering is the probabilistic assignment of the fiber trajectories to each cluster and an estimate of the cluster parameters, i.e. spatial mean and variance, and point correspondences. The fiber bundles are modeled by the mean trajectory and its spatial variation. Point-by-point correspondence of the trajectories within a bundle is obtained by constructing a distance map and a label map from each cluster center at every iteration of the EM algorithm. This offers a time-efficient alternative to pairwise curve matching of all trajectories with respect to each cluster center.

The proposed method has the potential to benefit from an anatomical atlas of fiber tracts by incorporating it as prior information in the EM algorithm. The algorithm is also capable of handling outliers in a principled way. Here are some examples of modeling/clustering the bundles:

[[Image:models.jpg|Model of fiber tracts]]

[[Image:wholebrain.jpg|Model of fiber tracts|600px]]

One of the difficult bundles of fiber tracts to cluster is the cingulum. Even starting tractography from a user-defined ROI results in a set of disordered trajectories, mostly short in length because of low FA. Also, due to its adjacency to the corpus callosum, many callosal trajectories are included that adversely affect any further analysis of the bundle. As shown in the following figure for two subjects, our method is well capable of clustering these trajectories into the desired bundles. Two arbitrary trajectories, one from the the superior and one from the posterior part of the cingulum were selected as the initial cluster centers. Knowledge of the point correspondence and hence rigorous calculation of the similarity measure is essential for clustering of such a disordered set of trajectories.

[[Image:cingulum.jpg|400px]][[Image:Gamma.jpg|250px]]

Figure on the right illustrates the evolution of the Gamma distribution for the clusters of the first case shown the above figure. Convergence is achieved just after a few iterations of the EM algorithm.

The proposed algorithm is being applied on several datasets. Below are two examples:

'''Population Study on Patahogical Subjects'''

A population study on the cinglum bundle in controls and Schizophrenia cases:

[[Image:Populationstudy.jpg|400px]]

'''Brain Development'''

[[Image:braindevelopment.jpg|400px]][[Image:braindevelopment_qa.jpg|300px]]

FA-colored trajectories from (a), (d) cortico-spinal, (b), (e) cingulum and (c), (f) uncinate fasciculus at 32-wk (up) and 42-wk (down) postmenstrual age. part of the cingulum and at 32-wk (up) and 42-wk (down) postmenstrual age. Spatial patterns of the tract development are clearly seen.
On the right, the figure shows the box-plot of the FA variation along the tract arc length for part of the cingulum and at 32-wk (up) and 42-wk (down) postmenstrual age. Only the posterior part shows a significant FA increase. ROI-based analysis fails to detect such spatial dependencies.

''Software''

Currently, all of the codes are implemented in MATLAB.

= Key Investigators =

Mahnaz Maddah, Sandy Wells, Simon Warfield and Eric Grimson.

= Publications =

[1] 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.

[2] 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.

[3] M. Maddah, W. M. Wells, S. K. Warfield, C-F. Westin, and W. E. L. Grimson, A Spatial Model of White Matter Fiber Tracts to be presented at ISMRM 2007, Berlin.

[4] M. Maddah, W. E. L. Grimson, and S. Warfield, Statistical Modeling and EM Clustering of White Matter Fiber Tracts 3rd IEEE International Symposium on Biomedical Imaging: Macro to Nano (ISBI) 2006, pp. 53-56.

[5] D. Goldberg-Zimring, A. U. J. Mewes, M. Maddah, S. K. Warfield, Diffusion Tensor Magnetic Resonance Imaging in Multiple Sclerosis J Neuroimaging, vol. 15, pp. 68S-81S, 2005.

[6] M. Maddah, A. Mewes, S. Haker, W. E. L. Grimson, and S. Warfield, Automated Atlas-Based Clustering of White Matter Fiber Tracts from DTMRI. MICCAI05, Palm Spring, CA, pp. 188-195, 2005.

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

= Links =

Projects:DTIModeling

2007-11-11T02:58:05Z

Maddah: /* Description */

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

= DTI Modeling =

We developed a novel approach for joint clustering and point-by-point mapping of white matter fiber pathways. Knowledge of the point correspondence along the fiber pathways is not only necessary for accurate clustering of the trajectories into fiber bundles, but also crucial for any tract-oriented quantitative analysis.

= Description =

We employ an expectation-maximization (EM) algorithm to cluster the trajectories in a Gamma mixture model context. The result of clustering is the probabilistic assignment of the fiber trajectories to each cluster and an estimate of the cluster parameters, i.e. spatial mean and variance, and point correspondences. The fiber bundles are modeled by the mean trajectory and its spatial variation. Point-by-point correspondence of the trajectories within a bundle is obtained by constructing a distance map and a label map from each cluster center at every iteration of the EM algorithm. This offers a time-efficient alternative to pairwise curve matching of all trajectories with respect to each cluster center.

The proposed method has the potential to benefit from an anatomical atlas of fiber tracts by incorporating it as prior information in the EM algorithm. The algorithm is also capable of handling outliers in a principled way. Here are some examples of modeling/clustering the bundles:

[[Image:models.jpg|Model of fiber tracts]]

[[Image:wholebrain.jpg|Model of fiber tracts]]

One of the difficult bundles of fiber tracts to cluster is the cingulum. Even starting tractography from a user-defined ROI results in a set of disordered trajectories, mostly short in length because of low FA. Also, due to its adjacency to the corpus callosum, many callosal trajectories are included that adversely affect any further analysis of the bundle. As shown in the following figure for two subjects, our method is well capable of clustering these trajectories into the desired bundles. Two arbitrary trajectories, one from the the superior and one from the posterior part of the cingulum were selected as the initial cluster centers. Knowledge of the point correspondence and hence rigorous calculation of the similarity measure is essential for clustering of such a disordered set of trajectories.

[[Image:cingulum.jpg|400px]][[Image:Gamma.jpg|250px]]

Figure on the right illustrates the evolution of the Gamma distribution for the clusters of the first case shown the above figure. Convergence is achieved just after a few iterations of the EM algorithm.

The proposed algorithm is being applied on several datasets. Below are two examples:

[[Image:braindevelopment.jpg|400px]][[Image:braindevelopment_qa.jpg|300px]]

FA-colored trajectories from (a), (d) cortico-spinal, (b), (e) cingulum and (c), (f) uncinate fasciculus at 32-wk (up) and 42-wk (down) postmenstrual age. part of the cingulum and at 32-wk (up) and 42-wk (down) postmenstrual age. Spatial patterns of the tract development are clearly seen.
On the right, the figure shows the box-plot of the FA variation along the tract arc length for part of the cingulum and at 32-wk (up) and 42-wk (down) postmenstrual age. Only the posterior part shows a significant FA increase. ROI-based analysis fails to detect such spatial dependencies.

And a population study on the cinglum bundle in controls and schizopherenia cases:
[[Image:Populationstudy.jpg|400px]]

''Software''

Currently, all of the codes are implemented in MATLAB.

= Key Investigators =

Mahnaz Maddah, Sandy Wells, Simon Warfield and Eric Grimson.

= Publications =

[1] 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.

[2] 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.

[3] M. Maddah, W. M. Wells, S. K. Warfield, C-F. Westin, and W. E. L. Grimson, A Spatial Model of White Matter Fiber Tracts to be presented at ISMRM 2007, Berlin.

[4] M. Maddah, W. E. L. Grimson, and S. Warfield, Statistical Modeling and EM Clustering of White Matter Fiber Tracts 3rd IEEE International Symposium on Biomedical Imaging: Macro to Nano (ISBI) 2006, pp. 53-56.

[5] D. Goldberg-Zimring, A. U. J. Mewes, M. Maddah, S. K. Warfield, Diffusion Tensor Magnetic Resonance Imaging in Multiple Sclerosis J Neuroimaging, vol. 15, pp. 68S-81S, 2005.

[6] M. Maddah, A. Mewes, S. Haker, W. E. L. Grimson, and S. Warfield, Automated Atlas-Based Clustering of White Matter Fiber Tracts from DTMRI. MICCAI05, Palm Spring, CA, pp. 188-195, 2005.

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

= Links =

File:Populationstudy.jpg

2007-11-11T02:54:42Z

Maddah:

Projects:DTIModeling

2007-11-11T02:49:25Z

Maddah: /* Description */

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

= DTI Modeling =

We developed a novel approach for joint clustering and point-by-point mapping of white matter fiber pathways. Knowledge of the point correspondence along the fiber pathways is not only necessary for accurate clustering of the trajectories into fiber bundles, but also crucial for any tract-oriented quantitative analysis.

= Description =

We employ an expectation-maximization (EM) algorithm to cluster the trajectories in a Gamma mixture model context. The result of clustering is the probabilistic assignment of the fiber trajectories to each cluster and an estimate of the cluster parameters, i.e. spatial mean and variance, and point correspondences. The fiber bundles are modeled by the mean trajectory and its spatial variation. Point-by-point correspondence of the trajectories within a bundle is obtained by constructing a distance map and a label map from each cluster center at every iteration of the EM algorithm. This offers a time-efficient alternative to pairwise curve matching of all trajectories with respect to each cluster center.

The proposed method has the potential to benefit from an anatomical atlas of fiber tracts by incorporating it as prior information in the EM algorithm. The algorithm is also capable of handling outliers in a principled way. Here are some examples of modeling/clustering the bundles:

[[Image:models.jpg|Model of fiber tracts]]

[[Image:wholebrain.jpg|Model of fiber tracts]]

One of the difficult bundles of fiber tracts to cluster is the cingulum. Even starting tractography from a user-defined ROI results in a set of disordered trajectories, mostly short in length because of low FA. Also, due to its adjacency to the corpus callosum, many callosal trajectories are included that adversely affect any further analysis of the bundle. As shown in the following figure for two subjects, our method is well capable of clustering these trajectories into the desired bundles. Two arbitrary trajectories, one from the the superior and one from the posterior part of the cingulum were selected as the initial cluster centers. Knowledge of the point correspondence and hence rigorous calculation of the similarity measure is essential for clustering of such a disordered set of trajectories.

[[Image:cingulum.jpg|400px]][[Image:Gamma.jpg|250px]]

Figure on the right illustrates the evolution of the Gamma distribution for the clusters of the first case shown the above figure. Convergence is achieved just after a few iterations of the EM algorithm.

The proposed algorithm is being applied on several datasets. Below are two examples:

[[Image:braindevelopment.jpg|300px]][[Image:braindevelopment_qa.jpg|300px]]

FA-colored trajectories from (a), (d) cortico-spinal, (b), (e) cingulum and (c), (f) uncinate fasciculus at 32-wk (up) and 42-wk (down) postmenstrual age. part of the cingulum and at 32-wk (up) and 42-wk (down) postmenstrual age. Spatial patterns of the tract development are clearly seen.
On the right, the figure shows the box-plot of the FA variation along the tract arc length for part of the cingulum and at 32-wk (up) and 42-wk (down) postmenstrual age. Only the posterior part shows a significant FA increase. ROI-based analysis fails to detect such spatial dependencies.

''Software''

Currently, all of the codes are implemented in MATLAB.

= Key Investigators =

Mahnaz Maddah, Sandy Wells, Simon Warfield and Eric Grimson.

= Publications =

[1] 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.

[2] 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.

[3] M. Maddah, W. M. Wells, S. K. Warfield, C-F. Westin, and W. E. L. Grimson, A Spatial Model of White Matter Fiber Tracts to be presented at ISMRM 2007, Berlin.

[4] M. Maddah, W. E. L. Grimson, and S. Warfield, Statistical Modeling and EM Clustering of White Matter Fiber Tracts 3rd IEEE International Symposium on Biomedical Imaging: Macro to Nano (ISBI) 2006, pp. 53-56.

[5] D. Goldberg-Zimring, A. U. J. Mewes, M. Maddah, S. K. Warfield, Diffusion Tensor Magnetic Resonance Imaging in Multiple Sclerosis J Neuroimaging, vol. 15, pp. 68S-81S, 2005.

[6] M. Maddah, A. Mewes, S. Haker, W. E. L. Grimson, and S. Warfield, Automated Atlas-Based Clustering of White Matter Fiber Tracts from DTMRI. MICCAI05, Palm Spring, CA, pp. 188-195, 2005.

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

= Links =

Projects:DTIModeling

2007-11-11T02:42:11Z

Maddah: /* Description */

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

= DTI Modeling =

We developed a novel approach for joint clustering and point-by-point mapping of white matter fiber pathways. Knowledge of the point correspondence along the fiber pathways is not only necessary for accurate clustering of the trajectories into fiber bundles, but also crucial for any tract-oriented quantitative analysis.

= Description =

We employ an expectation-maximization (EM) algorithm to cluster the trajectories in a Gamma mixture model context. The result of clustering is the probabilistic assignment of the fiber trajectories to each cluster and an estimate of the cluster parameters, i.e. spatial mean and variance, and point correspondences. The fiber bundles are modeled by the mean trajectory and its spatial variation. Point-by-point correspondence of the trajectories within a bundle is obtained by constructing a distance map and a label map from each cluster center at every iteration of the EM algorithm. This offers a time-efficient alternative to pairwise curve matching of all trajectories with respect to each cluster center.

The proposed method has the potential to benefit from an anatomical atlas of fiber tracts by incorporating it as prior information in the EM algorithm. The algorithm is also capable of handling outliers in a principled way. Here are some examples of modeling/clustering the bundles:

[[Image:models.jpg|Model of fiber tracts]]

[[Image:wholebrain.jpg|Model of fiber tracts]]

One of the difficult bundles of fiber tracts to cluster is the cingulum. Even starting tractography from a user-defined ROI results in a set of disordered trajectories, mostly short in length because of low FA. Also, due to its adjacency to the corpus callosum, many callosal trajectories are included that adversely affect any further analysis of the bundle. As shown in the following figure for two subjects, our method is well capable of clustering these trajectories into the desired bundles. Two arbitrary trajectories, one from the the superior and one from the posterior part of the cingulum were selected as the initial cluster centers. Knowledge of the point correspondence and hence rigorous calculation of the similarity measure is essential for clustering of such a disordered set of trajectories.

[[Image:cingulum.jpg|400px]][[Image:Gamma.jpg|250px]]

Figure on the right illustrates the evolution of the Gamma distribution for the clusters of the first case shown the above figure. Convergence is achieved just after a few iterations of the EM algorithm.

The proposed algorithm is being applied on several datasets. Below are two examples:

[[Image:braindevelopment.jpg|300px]][[Image:braindevelopment_qa.jpg|300px]]

''Software''

Currently, all of the codes are implemented in MATLAB.

= Key Investigators =

Mahnaz Maddah, Sandy Wells, Simon Warfield and Eric Grimson.

= Publications =

[1] 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.

[2] 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.

[3] M. Maddah, W. M. Wells, S. K. Warfield, C-F. Westin, and W. E. L. Grimson, A Spatial Model of White Matter Fiber Tracts to be presented at ISMRM 2007, Berlin.

[4] M. Maddah, W. E. L. Grimson, and S. Warfield, Statistical Modeling and EM Clustering of White Matter Fiber Tracts 3rd IEEE International Symposium on Biomedical Imaging: Macro to Nano (ISBI) 2006, pp. 53-56.

[5] D. Goldberg-Zimring, A. U. J. Mewes, M. Maddah, S. K. Warfield, Diffusion Tensor Magnetic Resonance Imaging in Multiple Sclerosis J Neuroimaging, vol. 15, pp. 68S-81S, 2005.

[6] M. Maddah, A. Mewes, S. Haker, W. E. L. Grimson, and S. Warfield, Automated Atlas-Based Clustering of White Matter Fiber Tracts from DTMRI. MICCAI05, Palm Spring, CA, pp. 188-195, 2005.

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

= Links =

File:Braindevelopment qa.jpg

2007-11-11T02:37:14Z

Maddah:

File:Braindevelopment.jpg

2007-11-11T02:33:52Z

Maddah:

Projects:DTIModeling

2007-11-11T02:14:23Z

Maddah: /* Publications */

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

= DTI Modeling =

We developed a novel approach for joint clustering and point-by-point mapping of white matter fiber pathways. Knowledge of the point correspondence along the fiber pathways is not only necessary for accurate clustering of the trajectories into fiber bundles, but also crucial for any tract-oriented quantitative analysis.

= Description =

We employ an expectation-maximization (EM) algorithm to cluster the trajectories in a Gamma mixture model context. The result of clustering is the probabilistic assignment of the fiber trajectories to each cluster and an estimate of the cluster parameters, i.e. spatial mean and variance, and point correspondences. The fiber bundles are modeled by the mean trajectory and its spatial variation. Point-by-point correspondence of the trajectories within a bundle is obtained by constructing a distance map and a label map from each cluster center at every iteration of the EM algorithm. This offers a time-efficient alternative to pairwise curve matching of all trajectories with respect to each cluster center.

The proposed method has the potential to benefit from an anatomical atlas of fiber tracts by incorporating it as prior information in the EM algorithm. The algorithm is also capable of handling outliers in a principled way. Here are some examples of modeling/clustering the bundles:

[[Image:models.jpg|Model of fiber tracts]]

[[Image:wholebrain.jpg|Model of fiber tracts]]

One of the difficult bundles of fiber tracts to cluster is the cingulum. Even starting tractography from a user-defined ROI results in a set of disordered trajectories, mostly short in length because of low FA. Also, due to its adjacency to the corpus callosum, many callosal trajectories are included that adversely affect any further analysis of the bundle. As shown in the following figure for two subjects, our method is well capable of clustering these trajectories into the desired bundles. Two arbitrary trajectories, one from the the superior and one from the posterior part of the cingulum were selected as the initial cluster centers. Knowledge of the point correspondence and hence rigorous calculation of the similarity measure is essential for clustering of such a disordered set of trajectories.

[[Image:cingulum.jpg]]

Figure below illustrates the evolution of the Gamma distribution for the clusters of the first case shown the above figure. Convergence is achieved just after a few iterations of the EM algorithm.

[[Image:Gamma.jpg|300px]]

An example of tract-based quantitative analysis is shown below for five bundles of fiber tracts. The FA is plotted vs. the arc length. Note that since the point correspondance between the trajectories is already known with our clustering algorithm, no further aligining is needed for performing quantitative analysis along the tracts.

[[Image:5bundles.jpg|200px]]
[[Image:FAs.jpg]]

''Software''

Currently, all of the codes are implemented in MATLAB.

= Key Investigators =

Mahnaz Maddah, Sandy Wells, Simon Warfield and Eric Grimson.

= Publications =

[1] 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.

[2] 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.

[3] M. Maddah, W. M. Wells, S. K. Warfield, C-F. Westin, and W. E. L. Grimson, A Spatial Model of White Matter Fiber Tracts to be presented at ISMRM 2007, Berlin.

[4] M. Maddah, W. E. L. Grimson, and S. Warfield, Statistical Modeling and EM Clustering of White Matter Fiber Tracts 3rd IEEE International Symposium on Biomedical Imaging: Macro to Nano (ISBI) 2006, pp. 53-56.

[5] D. Goldberg-Zimring, A. U. J. Mewes, M. Maddah, S. K. Warfield, Diffusion Tensor Magnetic Resonance Imaging in Multiple Sclerosis J Neuroimaging, vol. 15, pp. 68S-81S, 2005.

[6] M. Maddah, A. Mewes, S. Haker, W. E. L. Grimson, and S. Warfield, Automated Atlas-Based Clustering of White Matter Fiber Tracts from DTMRI. MICCAI05, Palm Spring, CA, pp. 188-195, 2005.

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

= Links =

Algorithm:MIT:New

2007-11-10T21:34:58Z

Maddah: /* Fiber Tract Modeling, Clustering, and Quantitative Analysis */

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...]]

'''New: ''' 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. Best Paper Award MICCAI 2006 [[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...]]

'''New:''' 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...]]

'''New: ''' 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...]]

'''New:''' 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...]]

'''New: ''' 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...]]

'''New: ''' 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...]]

'''New:''' 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...]]

'''New:'''
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...]]

'''New:'''
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: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...]]

'''New:''' 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...]]