Algorithm:GATech:Finsler Active Contour DWI

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Objective:

We want to extract the white matter tracts from Diffusion Weighted MRI scans. The idea is to use directional information in a new anisotropic energy functional based on Finsler geometry.

Progress:

We have implemented the algorithm in Matlab/C using the Fast Sweeping algorithm. We are in the process of porting the code to ITK.

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.

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:

Fig 1. Results on Cingulum Bundle

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

Previously, this method was applied to full brain fiber tractography, as shown in the following images:

Fig 2. Results on full brain fiber tractograpy

Fiber tracking from high resolution data set.

Comparison of technique with streamline based on tensor field.

This method may also be used in pattern detection applications, such as vessel segmentation:

Fig 3. Results on Vessel Segmentation

Vessel Segmentation

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.

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.

References:

• 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.
• 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:

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

Links:

• Stony Brook University Algorithms
• NA-MIC Collaborations
• 4-block PPT Jan 2007
• June 2007 Project Week