Difference between revisions of "Projects:GeodesicTractographySegmentation"

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  Back to [[NA-MIC_Collaborations|NA-MIC_Collaborations]]
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  Back to [[Algorithm:Stony Brook|Stony Brook University Algorithms]], [[DBP2:Harvard|Harvard DBP 2]]
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__NOTOC__
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= Geodesic Tractography Segmentation =
  
'''Objective:'''
+
The purpose of this work is to extract white matter tracts and volumetric fiber bundles from Diffusion-Weighted MRI (DW-MRI) in order to study clinically relevant outcomes related to these structures. The idea is to use directional information in an anisotropic energy functional based on the Finsler metric (remember that the Riemannian metric is one particular Finsler metric of interest) in order to extract the best geodesic (i.e. optimal) path, which we dub "the anchor tract", between two regions of interest.  Subsequently, region-based active contours are used to segment the associated volumetric fiber bundle.  Finally, statistics are computed along both the anchor tract and the volumetric fiber bundle which may be used to compare different clinical populations.
  
We want to extract the white matter tracts and volumetric fiber bundles from Diffusion-Weighted MRI scans. The idea is to use directional information in a new anisotropic energy functional based on Finsler geometry to extract optimal tracts and then to use region-based active contours to segment the full fiber bundle.
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= Description =
 
 
'''Progress:'''
 
  
 
''Fiber Tractography''
 
''Fiber Tractography''
  
We have implemented the algorithm in Matlab/C using the Fast Sweeping algorithm. We are in the process of porting the code to ITK.
+
The goal of fiber tractography is to find open curves (i.e. paths without volume) in the white matter which correspond to something anatomically significant. In our framework, a direction-dependent Finsler manifold is constructed.  Note that Riemannian manifolds based on tensors comprise a subset of all possible Finsler manifolds and are most commonly used in this framework.  Then, the best geodesic path connecting the input ROIs is computed on the manifold. This minimum cost geodesic curve is determined by solving a Hamilton-Jacobi-Bellman (HJB) equation using the Fast Sweeping algorithm. The resulting solution is the anchor tract connecting the two ROIs.
 
 
We are continuing to work on our new framework for white matter tractography in high angular resolution diffusion data. We base our work on concepts from Finsler geometry. Namely, a direction-dependent local cost is defined based on the diffusion data for every direction on the unit sphere. Minimum cost curves are determined by solving the Hamilton-Jacobi-Bellman using the Fast Sweeping algorithm. Classical costs based on the diffusion tensor field can be seen as a special case. While the minimum cost (or equivalently the travel time of a particle moving along the curve) and the anisotropic front propagation frameworks are related, front speed is related to particle speed through a Legendre transformation which can severely impact anisotropy information for front propagation techniques. Implementation details and results on high angular diffusion data show that this method can successfully take advantage of the increased angular resolution in high b-value diffusion weighted data despite lower signal to noise ratio.
 
  
''Fiber Bundle Segmentation''
+
Clinically speaking, the anchor tract has little meaning.  However, during the computation of the anchor tract, connectivity maps are generated as a useful by-product which represent the connectivity of the brain volume to the input ROIs.
  
We have developed a locally-constrained region-based approach which, when initialized on the fiber tracts, is able to provide volumetric fiber segmentations of the full diffusion bundles.
+
Also, note that in this framework, special care is taken so that the minimum cost (or equivalently the fastest travel time of a particle moving along the curve in the given manifold) and the anisotropic front propagation used to solve the HJB equation are appropriately related through a Legendre transformation. Algorithms which inappropriately ignore the Legendre transformation can severely impact the anisotropy information in front propagation based PDE solvers.
 
 
''Data''
 
 
 
We are using Harvard's high angular resolution datasets which currently consist of a population of 12 schizophrenics and 12 normal controls.
 
 
 
''Visual Results''
 
  
 
Recently, we have applied this method to the cingulum bundle, as shown in the following images:
 
Recently, we have applied this method to the cingulum bundle, as shown in the following images:
 
 
  
 
{|
 
{|
|+ '''Fig 1. Results on Cingulum Bundle'''
+
|+ '''Fig 1. Cingulum Bundle Anchor Tracts'''
 
|valign="top"|[[Image:Case24-coronal-tensors-edit.png |thumb|250px|Detailed View of the Cingulum Bundle Anchor Tract]]
 
|valign="top"|[[Image:Case24-coronal-tensors-edit.png |thumb|250px|Detailed View of the Cingulum Bundle Anchor Tract]]
 
|valign="top"|[[Image:Case25-sagstream-tensors-edit.png|thumb|250px|Streamline Comparison]]
 
|valign="top"|[[Image:Case25-sagstream-tensors-edit.png|thumb|250px|Streamline Comparison]]
Line 36: Line 26:
 
|}
 
|}
  
Previously, this method was applied to full brain fiber tractography, as shown in the following images:
+
''Fiber Bundle Segmentation''
 +
 
 +
We have developed a region-based active contour segmentation algorithm which provides volumetric fiber segmentations of fiber bundles.  These active contours are initialized on the anchor tract and are expanded away from the anchor tract to capture the volumetric fiber bundle.  The basic idea is to evolve the front away from the contour capturing only those voxels which are locally "connected" to the anchor tract.  Cast in a Bayesian framework, this technique includes prior clinical knowledge penalizing bundles with abnormal radii and image-driven likelihood information to accurately capture edges in the directional information.
 +
 
 +
{|
 +
|+ '''Fig 2. Cingulum Bundle Volumetric Fiber Bundles Segmentation Results'''
 +
|valign="top"|[[Image:ResultZoomedOut.png |thumb|250px|Zoomed Out View]]
 +
|valign="top"|[[Image:ZoomedResultWithModel.png |thumb|250px|Zoomed In View]]
 +
|}
  
 
{|
 
{|
|+ '''Fig 2. Results on full brain fiber tractograpy'''
+
|+ '''Fig 3. Cingulum Bundle Volumetric Fiber Bundles Surface Evolution'''
|valign="top"|[[Image:Tracts1.png |thumb|250px|Fiber tracking from high resolution data set.]]
+
|valign="top"|[[Image:PriorFiberResultOverBaseline001.png |thumb|250px|Result from Priors Only (t=1)]]
|valign="top"|[[Image:Tracts2.png|thumb|250px|Comparison of technique with streamline based on tensor field.]]
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|valign="top"|[[Image:PriorFiberResultOverBaseline003.png |thumb|250px|Result from Priors Only (t=3)]]
 +
|valign="top"|[[Image:PriorFiberResultOverBaseline008.png |thumb|250px|Result from Priors Only (t=8)]]
 +
|-
 +
|valign="top"|[[Image:LikelihoodsFiberResultOverBaseline001.png |thumb|250px|Result from Likelihoods Only (t=1)]]
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|valign="top"|[[Image:LikelihoodsFiberResultOverBaseline003.png |thumb|250px|Result from Likelihoods Only (t=3)]]
 +
|valign="top"|[[Image:LikelihoodsFiberResultOverBaseline008.png |thumb|250px|Result from Likelihoods Only (t=8)]]
 +
|-
 +
|valign="top"|[[Image:FinalFiberResultOverBaseline001.png |thumb|250px|Result from Combined Likelihoods and Priors (t=1)]]
 +
|valign="top"|[[Image:FinalFiberResultOverBaseline003.png |thumb|250px|Result from Combined Likelihoods and Priors (t=3)]]
 +
|valign="top"|[[Image:FinalFiberResultOverBaseline008.png |thumb|250px|Result from Combined Likelihoods and Priors (t=8)]]
 
|}
 
|}
  
 +
''Data''
  
This method may also be used in pattern detection applications, such as vessel segmentation:
+
We are using Harvard's high angular resolution datasets which currently consist of a population of 12 schizophrenics and 12 normal controls.
  
{|
+
''Associated Results''
|+ '''Fig 3. Results on Vessel Segmentation'''
+
 
|valign="top"|[[Image:Vessels1.png |thumb|250px|Vessel Segmentation]]
+
For previous results showing comparisons of this framework to traditional streamline frameworks and results showing the application of this framework to the segmentation of blood vessels, see [[Algorithm:GATech:DWMRI_Geodesic_Active_Contours_Archive| Associated Results]].
|}
 
  
 
''Statistical Results''
 
''Statistical Results''
  
We are currently investigating Cingulum Bundle fractional anisotropy (FA) differences between a population of 12 schizophrenics and 12 normal controls.  We find the anchor tracts as described above and then compute statistics for FA inside a tube of radii 1-3mm centered on the anchor tract.  So far using this method we have been unable to find a statistical difference between the normal controls and the schizophrenics.  Therefore, we are investigating a more precise extraction of the cingulum bundle using Finsler Levelsets, rather than using the primitive cylinder as is currently done.
+
We are currently investigating Cingulum Bundle fractional anisotropy (FA) differences between a population of 12 schizophrenics and 12 normal controls.  We find the anchor tracts as described above and then compute statistics for FA inside a tube of radii 1-3mm centered on the anchor tract.  So far using this method we have been unable to find a statistical difference between the normal controls and the schizophrenics.  Once we have processed the entire population using our volumetric segmenter, we will rerun the statistics on the full fiber bundle.
  
 
Download the current statistical results [[Media:ResultsAnchorTube.txt|here.‎]] (last updated 18/Apr/2007)
 
Download the current statistical results [[Media:ResultsAnchorTube.txt|here.‎]] (last updated 18/Apr/2007)
 
  
 
''Project Status''
 
''Project Status''
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*Currently porting to ITK.
 
*Currently porting to ITK.
  
''References:''
+
= Publications =
* V. Mohan, J. Melonakos, M. Niethammer, M. Kubicki, and A. Tannenbaum. Finsler Level Set Segmentation for Imagery in Oriented Domains. BMVC 2007. Under review.
+
 
* J. Melonakos, V. Mohan, M. Niethammer, K. Smith, M. Kubicki, and A. Tannenbaum. Finsler Tractography for White Matter Connectivity Analysis of the Cingulum Bundle. MICCAI 2007. Under review.
+
[http://www.na-mic.org/publications/pages/display?search=GeodesicTractographySegmentation NA-MIC Publications Database on Geodesic Tractography Segmentation]
* J. Melonakos, E. Pichon, S. Angenet, and A. Tannenbaum. Finsler Active Contours. IEEE Transactions on Pattern Analysis and Machine Intelligence, to appear in 2007.
 
* E. Pichon and A. Tannenbaum. Curve segmentation using directional information, relation to pattern detection. In IEEE International Conference on Image Processing (ICIP), volume 2, pages 794-797, 2005.
 
* E. Pichon, C-F Westin, and A. Tannenbaum. A Hamilton-Jacobi-Bellman approach to high angular resolution diffusion tractography. In International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), pages 180-187, 2005.
 
  
'''Key Investigators:'''
+
= Key Investigators =
  
 
* Georgia Tech: John Melonakos, Vandana Mohan, Sam Dambreville, Allen Tannenbaum
 
* Georgia Tech: John Melonakos, Vandana Mohan, Sam Dambreville, Allen Tannenbaum
 
* Harvard/BWH: Marek Kubicki, Marc Niethammer, Kate Smith, C-F Westin, Martha Shenton
 
* Harvard/BWH: Marek Kubicki, Marc Niethammer, Kate Smith, C-F Westin, Martha Shenton
  
'''Links:'''
+
= Links =
 +
 
 +
* For some additional diffusion-related thoughts, see: [[Algorithm:GATech:DWMRI_Musings | DW-MRI Musings]]
 +
 
 +
Project Week Results: [[Media:2007_Project_Half_Week_FinslerTractography.ppt|Jan 2007]], [[Projects/Diffusion/2007_Project_Week_Geodesic_Tractography|June 2007]]
  
* [[Algorithm:GATech|Georgia Tech Algorithms]]
+
[[Category:Segmentation]] [[Category:Diffusion MRI]] [[Category:Schizophrenia]]
* [[NA-MIC_Collaborations|NA-MIC Collaborations]]
 
* [[Media:2007_Project_Half_Week_FinslerTractography.ppt| 4-block PPT Jan 2007]]
 
* [[Projects/Diffusion/2007_Project_Week_Geodesic_Tractography| June 2007 Project Week]]
 

Latest revision as of 00:59, 16 November 2013

Home < Projects:GeodesicTractographySegmentation
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Geodesic Tractography Segmentation

The purpose of this work is to extract white matter tracts and volumetric fiber bundles from Diffusion-Weighted MRI (DW-MRI) in order to study clinically relevant outcomes related to these structures. The idea is to use directional information in an anisotropic energy functional based on the Finsler metric (remember that the Riemannian metric is one particular Finsler metric of interest) in order to extract the best geodesic (i.e. optimal) path, which we dub "the anchor tract", between two regions of interest. Subsequently, region-based active contours are used to segment the associated volumetric fiber bundle. Finally, statistics are computed along both the anchor tract and the volumetric fiber bundle which may be used to compare different clinical populations.

Description

Fiber Tractography

The goal of fiber tractography is to find open curves (i.e. paths without volume) in the white matter which correspond to something anatomically significant. In our framework, a direction-dependent Finsler manifold is constructed. Note that Riemannian manifolds based on tensors comprise a subset of all possible Finsler manifolds and are most commonly used in this framework. Then, the best geodesic path connecting the input ROIs is computed on the manifold. This minimum cost geodesic curve is determined by solving a Hamilton-Jacobi-Bellman (HJB) equation using the Fast Sweeping algorithm. The resulting solution is the anchor tract connecting the two ROIs.

Clinically speaking, the anchor tract has little meaning. However, during the computation of the anchor tract, connectivity maps are generated as a useful by-product which represent the connectivity of the brain volume to the input ROIs.

Also, note that in this framework, special care is taken so that the minimum cost (or equivalently the fastest travel time of a particle moving along the curve in the given manifold) and the anisotropic front propagation used to solve the HJB equation are appropriately related through a Legendre transformation. Algorithms which inappropriately ignore the Legendre transformation can severely impact the anisotropy information in front propagation based PDE solvers.

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

Fig 1. Cingulum Bundle Anchor Tracts
Detailed View of the Cingulum Bundle Anchor Tract
Streamline Comparison
Anterior View of the Cingulum Bundle Anchor Tract
Posterior View of the Cingulum Bundle Anchor Tract

Fiber Bundle Segmentation

We have developed a region-based active contour segmentation algorithm which provides volumetric fiber segmentations of fiber bundles. These active contours are initialized on the anchor tract and are expanded away from the anchor tract to capture the volumetric fiber bundle. The basic idea is to evolve the front away from the contour capturing only those voxels which are locally "connected" to the anchor tract. Cast in a Bayesian framework, this technique includes prior clinical knowledge penalizing bundles with abnormal radii and image-driven likelihood information to accurately capture edges in the directional information.

Fig 2. Cingulum Bundle Volumetric Fiber Bundles Segmentation Results
Zoomed Out View
Zoomed In View
Fig 3. Cingulum Bundle Volumetric Fiber Bundles Surface Evolution
Result from Priors Only (t=1)
Result from Priors Only (t=3)
Result from Priors Only (t=8)
Result from Likelihoods Only (t=1)
Result from Likelihoods Only (t=3)
Result from Likelihoods Only (t=8)
Result from Combined Likelihoods and Priors (t=1)
Result from Combined Likelihoods and Priors (t=3)
Result from Combined Likelihoods and Priors (t=8)

Data

We are using Harvard's high angular resolution datasets which currently consist of a population of 12 schizophrenics and 12 normal controls.

Associated Results

For previous results showing comparisons of this framework to traditional streamline frameworks and results showing the application of this framework to the segmentation of blood vessels, see Associated Results.

Statistical Results

We are currently investigating Cingulum Bundle fractional anisotropy (FA) differences between a population of 12 schizophrenics and 12 normal controls. We find the anchor tracts as described above and then compute statistics for FA inside a tube of radii 1-3mm centered on the anchor tract. So far using this method we have been unable to find a statistical difference between the normal controls and the schizophrenics. Once we have processed the entire population using our volumetric segmenter, we will rerun the statistics on the full fiber bundle.

Download the current statistical results here.‎ (last updated 18/Apr/2007)

Project Status

  • Working 3D implementation in Matlab using the C-based Mex functions.
  • Currently porting to ITK.

Publications

NA-MIC Publications Database on Geodesic Tractography Segmentation

Key Investigators

  • Georgia Tech: John Melonakos, Vandana Mohan, Sam Dambreville, Allen Tannenbaum
  • Harvard/BWH: Marek Kubicki, Marc Niethammer, Kate Smith, C-F Westin, Martha Shenton

Links

Project Week Results: Jan 2007, June 2007