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| − | Quantifying magnetic susceptibility in the brain from the phase of the MR signal
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| − | provides a non-invasive means for measuring the accumulation
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| − | of iron believed to occur with aging and neurodegenerative disease.
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| − | Phase observations from local susceptibility distributions,
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| − | however, are corrupted by external biasfields, which
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| − | may be identical to the sources of interest. Furthermore,
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| − | limited observations of the phase makes the inversion ill-posed. We
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| − | describe a variational approach to susceptibility estimation that
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| − | incorporates a tissue-air atlas to resolve ambiguity in the forward model, while eliminating additional biasfields
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| − | through application of the Laplacian. Results show qualitative improvement
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| − | over two methods commonly used to infer underlying
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| − | susceptibility values, and quantitative susceptibility estimates
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| − | show better correlation with postmortem iron concentrations than
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| − | competing methods.
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| | | | |
| − | = Description =
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| − |
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| − | There is increasing evidence that excessive iron deposition in specific regions
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| − | of the brain is associated with neurodegenerative disorders such as Alzheimer's
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| − | and Parkinson's disease [1]. The role of iron in the pathogenesis of these diseases
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| − | remains unknown and is difficult to determine without a non-invasive method
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| − | to quantify its concentration in-vivo. Since iron is a ferromagnetic substance,
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| − | changes in iron concentration result in local changes in the magnetic susceptibility of tissue.
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| − | In magnetic resonance imaging (MRI) experiments, differences
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| − | in magnetic susceptibility cause perturbations in the local magnetic field, which
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| − | can be computed from the phase of the MR signal (in a gradient echo sequence, the observed field is proportional to the MR phase).
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| − |
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| − |
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| − | The field perturbations caused by magnetic susceptibility differences can be
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| − | modeled as the convolution of a dipole-like kernel with the spatial susceptibility
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| − | distribution. In the Fourier domain, the kernel exhibits zeros at the magic angle,
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| − | preventing direct inversion of the fieldmap [2]. Critically, limited observations of
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| − | the field make the problem ill-posed. The observed data is also corrupted by
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| − | confounding biasfields (ie. those from tissue-air interfaces, mis-set shims, and other
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| − | non-local sources). Eliminating these fields is critical for accurate susceptibility
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| − | estimation since they corrupt the phase contributions from local susceptibility
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| − | sources.
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| − |
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| − |
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| − | In general, methods that rely heavily on agreement between observed and
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| − | predicted field values computed using kernel-based forward models [2,3,4] are
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| − | inherently limited since they cannot distinguish between low frequency biasfields
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| − | and susceptibility distributions that are eigenfunctions of the model. Examples
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| − | of such distributions include constant, linear, and quadratic functions of
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| − | susceptibility along the main field (ie. 'z') direction. Applying the forward model to
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| − | these distributions results in predicted fields that are proportional to the local
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| − | susceptibility sources, but also identical in form to non-local biasfields (ie. those
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| − | produced by a z-shim). Therefore, removing all low frequency fields prior to
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| − | susceptibility estimation will eliminate the biasfield as well as fields due to the
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| − | sources of interest, potentially preventing accurate calculation of the underlying
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| − | susceptibility values. In contrast, inadequate removal of the biasfield may result
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| − | in the estimation of artifactual susceptibility eigenfunctions in areas where the
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| − | biasfield is strong, such as regions adjacent to tissue-air interfaces. This suggests
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| − | that additional information such as boundary conditions or priors may be necessary to
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| − | regularize an incomplete forward model and prevent the mis-estimation
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| − | of low frequency biasfields.
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| − |
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| − |
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| − | We present a variational approach for Atlas-based Susceptibility Mapping
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| − | (ASM) that performs simultaneous susceptibility estimation and biasfield
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| − | removal using the Laplacian operator and a tissue-air susceptibility atlas.
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| − | In [5,6,7] it was shown that applying the Laplacian to the observed field eliminates
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| − | non-local biasfields due to mis-set shims and remote susceptibility
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| − | distributions (ie. the neck/chest).
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| − | In this method, large deviations from the susceptibility atlas are penalized,
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| − | discouraging the estimation of artifactual susceptibility eigenfunctions in regions near
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| − | tissue-air boundaries where the Laplacian may not be sufficient to eliminate the
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| − | contribution of non-local sources and substantial signal loss corrupts the observed field.
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| − | Agreement of predicted and observed fields
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| − | within the brain is also enforced, but deviations in estimated susceptibility values outside the
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| − | brain are not penalized, allowing values at the boundary to vary from
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| − | the atlas-based prior to account for unmodeled external field sources (ie. shims).
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| − |
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| − | = Results =
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| − |
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| − | The method is evaluated by comparison of susceptibility maps estimated using ASM to results from Susceptibility Weighted Imaging (SWI) and Field Dependent Relaxation Imaging (FDRI). In SWI, a filtered phase map is obtained by applying a high-pass filter to the phase data, and the resulting SWI map is commonly used as a proxy for susceptibility.
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| − | While SWI has shown some correlation with magnetic susceptibility differences
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| − | due to iron and other sources, the phase maps it yields are only an indirect
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| − | measure of susceptibility due to the non-local effects of the convolution kernel.
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| − | In addition, the filtering process may remove some low frequency fields due to
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| − | sources inside the brain. In FDRI, R2 maps are acquired at two different field strengths (ie. 1.5
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| − | and 3 Tesla) and the difference in R2 divided by the difference in field strength
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| − | gives the FDRI. The mean FDRI in several regions of interest was previously compared
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| − | to the mean iron concentration obtained from postmortem analysis and showed
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| − | stronger correlation with iron content than the SWI maps computed for the same
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| − | subjects. Obtaining FDRI measurements would be impractical for most studies,
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| − | however, since it requires images to be collected on two separate scanners.
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| − | In this work, quantitative results are obtained by comparison of mean susceptibility
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| − | values in the thalamus (TH), caudate (CD), putamen (PT)
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| − | and globus pallidus (GP) to corresponding results from SWI, FDRI and postmortem data.
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| − |
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| − | ASM results for a young subject are shown in Fig. 1. Column 1 shows the T1
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| − | structural (row 1) and acquired fieldmap (row 2). Application of the Laplacian
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| − | to the field map (row 2, column 2) removes substantial B0 inhomogeneities that
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| − | bias the observed field. The susceptibility atlas is shown in row 1, column 2
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| − | and estimated external sources are shown in row 1, column 3. The estimated
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| − | susceptibility map (row2, column 3) shares high frequency structure with the
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| − | Laplacian of the observed field, while low frequency structure is preserved by
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| − | enforcing agreement with additional information provided by the atlas-based
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| − | prior and observed field.
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| − |
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| − |
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| − | {|
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| − | |[[File:Fig1 compound lighter v2.png|400px|thumb|Fig. 1: ASM Results.
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| − | The first column shows the T1 structural image (row 1) and field
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| − | map (row 2) with substantial inhomogeneity that was obtained from a young subject.
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| − | Column 2 shows the susceptibility atlas (row 1), in which voxels take continuous values
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| − | between [0,1] corresponding to susceptibility values between air and tissue. Taking
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| − | the Laplacian of the fieldmap successfully eliminates biasfields (row 2, column 2).
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| − | Estimates of external sources are shown in row 1, column 3. The estimated susceptibility
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| − | map (row 2, column 3) shares similar high frequency structure with the Laplacian of
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| − | the observed field while low frequency structure is preserved by enforcing agreement
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| − | with the atlas and observed field.]]
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| − | |}
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| − | Fig. 2 shows the T1 structural image (row 1, column 1) and results from FDRI (row 1, column 2), SWI (row 1,column 3),
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| − | and ASM (row 2, column 3) for a young subject. ASM results for 2 elderly
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| − | subjects are shown in row 2, columns 1-2. The FDRI shows strong constrast between the
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| − | ROIs and surrounding tissue, but less high frequency structure than the SWI.
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| − | The SWI retains high frequency phase effects, but indiscriminately removes low
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| − | order fields from both internal and external sources, resulting in artifactual low
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| − | frequency structure. The ASM method accurately preserves the high frequency
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| − | phase effects seen in SWI while showing improved estimation of low order susceptibility
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| − | distributions. In addition, ASM provides direct estimates of susceptibility
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| − | values rather than filtered phase values that serve as proxies for susceptibility.
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| − |
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| − |
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| − | {|
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| − | |[[File:Fig2 compound lighter.png|400px|thumb|Fig. 2: Comparison of Results.
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| − | Row 1 shows the T1 structural image (column 1), FDRI
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| − | (column 2) and SWI (column 3) results for a young subject. ASM results are shown in
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| − | row 2 for young (column 3) and elderly (columns 1,2) subjects. The FDRI shows strong
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| − | constrast between ROIs and adjacent tissue, but less high frequency structure than
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| − | the SWI. The SWI retains high frequency phase effects, but indiscriminately removes
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| − | low order fields from both internal and external sources, resulting in artifactual low
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| − | frequency structure. ASM accurately preserves the high frequency structure seen in
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| − | SWI while showing improved estimation of low order susceptibility distributions.]]
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| − | |}
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| − |
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| − | Quantitative results from ASM and previously reported results from FDRI
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| − | and SWI for the same 12 elderly subjects are shown in Fig. 3. The mean
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| − | susceptibility values (relative to tissue susceptibility) in each ROI from all elderly subjects are plotted
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| − | against the corresponding iron concentrations from postmortem analysis (only
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| − | the mean and SD in each ROI was reported in [8]). ASM shows a high
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| − | correlation with postmortem values, which is comparable to that seen in FDRI and
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| − | substantially better than the correlation between phase and iron concentration
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| − | obtained with SWI. In addition, for the structures that we analyzed (TH, CD, PT, and GP), ASM results
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| − | compare favorably to the correlation between postmortem iron and
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| − | susceptibility estimates in corresponding ROIs computed from multi-angle acquisitions [4].
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| − |
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| − |
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| − | {|
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| − | |[[File:Fig3 elderly compound.png|800px|thumb|Fig. 3: Quantitative Results. The Mean +/- SD iron concentration
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| − | (mg/100g fresh weight)
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| − | in each ROI determined from postmortem analysis [17] is plotted on the x-axis. The y-
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| − | axes show the Mean +/- SD FDRI (s^{-1}/Tesla), Mean +/- SD SWI (radians), and Mean +/- SD
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| − | ASM susceptibility (ppm). Mean susceptibility values from ASM show a high
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| − | correlation with the postmortem data, which agrees well with previous results from FDRI
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| − | and shows improvement over SWI values reported for the same data [5].]]
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| − | |}
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| − | [1] Zecca L; Youdim MB; Riederer P; Connor JR; and Crichton RR. Iron, brain ageing and neurodegenerative disorders. Nat Rev Neurosci, 5:863{73, Nov 2004.
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| − |
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| − | [2] Liu T; Spincemaille P; de Rochefort L; Kressler B; and Wang Y. Calculation of susceptibility through multiple orientation sampling (cosmos): a method for conditioning the inverse problem from measured magnetic field map to susceptibility source image in mri. Magn Reson Med, 61:196{204, Jan 2009.
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| − |
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| − | [3] Wu J; Wang Y de Rochefort L; Liu T; Kressler B; Liu J; Spincemaille P; Lebon V. Quantitative susceptibility map reconstruction from mr phase data using bayesian regularization: validation and application to brain imaging. Magn Reson Med, 63:194{206, Jan 2010.
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| − |
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| − | [4] Haacke EM; Xu Y; Cheng YC; and Reichenbach JR. Susceptibility weighted imaging (swi). Magn Reson Med, 52:612{8, Sep 2004.
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| − |
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| − | [5] Ismrm here
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| − |
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| − | [6] Li L; and Leigh JS. High-precision mapping of the magnetic field utilizing the harmonic function mean value property.
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| − | J Magn Reson, 148:442-8,Feb 2001.
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| − |
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| − | [7] Schweser F; Deistung A; Lehr BW; and Reichenbach JR. Quantitative imaging of intrinsic magnetic tissue properties using mri signal phase: an approach to in-vivo brain iron metabolism. Neuroimage, 54:2789-807, Feb 2011.
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| − |
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| − | [8] Hallgren B; and Sourander P. The effect of age on the non-haemin iron in the human brain. J Neurochemistry, 3:41{51, 1958.
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| − |
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| − | = Key Investigators =
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| − | * MIT: Clare Poynton, Elfar Adalsteinsson, Polina Golland
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| − | * BWH/Harvard: William Wells
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| − | * Stanford: Adolf Pfefferbaum, Edith Sullivan
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