Reliable shape modeling and clustering of white matter fiber tracts is essential for clinical and anatomical studies that use diffusion tensor imaging (DTI) tractography techniques. In this work we present a novel scheme to model the shape of white matter fiber tracts reconstructed from DTI and cluster them into bundles using Fourier descriptors. We characterize a tract's shape by using Fourier descriptors which are effective in capturing shape properties of fiber tracts. Fourier descriptors derived from different shape signatures are analyzed. Clustering is then performed on these multi-dimensional features in conjunction with mass centers using a k-means like threshold based approach. The advantage of this method lies in the fact that Fourier descriptors achieve spatial independent representation and normalization of white matter fiber tracts which makes it useful for tract comparison across subjects. It also eliminates the need to find matching correspondences between two randomly organized tracts from whole brain tracking. Several issues related to tract shape representation and normalization are also discussed. Real DTI datasets are used to test this technique. Experiment results show that this technique can effectively separate multiple fascicles into plausible bundles.

Shape modeling and clustering of white matter fiber tracts using fourier descriptors

We introduce a method for estimating regional connectivity in diffusion tensor magnetic resonance imaging (DT-MRI) based on a fluid mechanics model. We customize the Navier-Stokes equations to include information from the diffusion tensor and simulate an artificial fluid flow. The velocity vector field of this fluid construct is then used as a connectivity metric. We generate probable connection paths by maximizing the fluid velocity along a path between two regions of interest while constraining its bending energy. Our method is based on a second-order nonlinear partial differential equation (PDE) and incorporates local anisotropy and similarity measurements into a viscosity term, which extends previous linear first-order methods. We tested our algorithm on a digital DTI phantom. Our method was able to correctly segment the structure of the phantom with various levels of noise, despite local distortion of the image pattern. We applied our method to DTI volumes from a normal human subject. Seed points were chosen along the corticospinal tracts, white matter regions with well-known connectivity. Our method produced paths that were consistent with both known anatomy and directionally encoded color (DEC) images of the DTI volumes. Applying our method to a digital phantom that simulates discrete white matter lesions, we also demonstrate that the fluid velocity field around areas of simulated localized white matter disruption becomes dampened and turbulent compared to the heat flow field from a first order PDE method. This provides a means for identifying lesion position from the fluid velocity field.

A diffusion tensor imaging tractography algorithm based on Navier-Stokes fluid mechanics

We present a new analysis scheme to measure regional micro structural white matter (WM) changes along the major cingulum fiber bundles which may not be effectively performed by existing methods due to its curved geospatial feature. The primary advantages of the technique lie in the diffusion tensor imaging tractography and geodesic distance mapping. The volumetric major cingulum is represented by a reconstructed fiber bundle. Quantitative analysis of regional micro structural WM alterations is based on the geodesic distance mapping, which allows cross-subject evaluation of diffusion properties by establishing correspondences through reparameterizing the space of reconstructed fiber bundle as a function of geodesic distance. Evaluation of the technique explores regional fractional anisotropy degradations along the left cingulum path in amnestic mild cognitive impairment subjects. Our experimental results indicate that this approach is effective and may provide a more sensitive alternative to examining the WM integrity of brain neuronal connectivity.

White Matter Integrity Analysis along Cingulum Paths in Mild Cognitive Impairment - A Geodesic Distance Approach

Accurate and efficient white matter fiber tract segmentation is an important step in clinical and anatomical studies that use diffusion tensor magnetic resonance imaging (DTI) tractography techniques. In this work, we present a novel technique to group white matter fiber tracts reconstructed from DTI into bundles using Nonnegative Matrix Factorization (NMF) of the frequency-tract matrix. A fiber tract is quantified by Fourier descriptors in terms of frequencies. Fourier descriptors derived from the shape signature, the central angle dot product, are used to construct the nonnegative frequency-tract matrix which is analogous to the term-document matrix in the document clustering context. In the NMF derived feature space, each basis vector captures the base shape of a particular fiber tract bundle. Each fiber tract is represented as an additive combination of the base shapes. The cluster label of each fiber tract is easily determined by finding the basis vector with which a fiber tract has the largest projection value. Preliminary experimental results with real DTI data show that this method efficiently groups tracts into plausible bundles. This indicates that NMF may be used in fiber tract segmentation with appropriate fiber tract encodings.

http://www.cs.engr.uky.edu/~jzhang/pub/MRI/liang5.pdf

White Matter Fiber Tract Segmentation Using Nonnegative Matrix Factorization

In this paper, we present a novel set of features which mainly comprises Fourier descriptors to facilitate the classification of white matter (WM) fiber tracts reconstructed from diffusion tensor imaging (DTI) tractography. Particularly, Fourier descriptors composing the feature vectors are different frequency terms of the discrete Fourier transform of the Euclidean coordinates of the step points of WM fiber tracts. This approach can effectively reduce the computing cost in WM fiber tract classification due to the decreased feature vector dimensionality. As integrals, Fourier descriptor features make the algorithm less sensitive to DTI noise. The fact that Fourier descriptors achieve spatial independent representation and normalization of WM fiber tracts makes it useful for group studies of WM fiber tracts. Specially, a new strategy for using Fourier descriptors is proposed. Experimental results with real datasets show that this technique is feasible and may be an alternative to existing approaches.

Using Fourier Descriptor Features in the Classification of White Matter Fiber Tracts in DTI

We present a new technique for noninvasively tracing brain white matter fiber tracts using diffusion tensor magnetic resonance imaging (DT-MRI). This technique is based on performing diffusion simulations over a series of overlapping three dimensional diffusion kernels that cover only a small portion of the human brain volume and are geometrically centered upon selected starting voxels where a seed is placed. Synthetic and real DT-MRI data are employed to demonstrate the tracking scheme. It is shown that the synthetic tracts can be accurately replicated, while several major white matter fiber pathways in the human brain can be reproduced noninvasively as well. The primary advantages of the algorithm lie in the handling of fiber branching and crossing and its seamless adaptation to the platform established by new imaging techniques, such as high angular, q-space, or generalized diffusion tensor imaging.

Ning Kang

Papers

Approximating anatomical brain connectivity with diffusion tensor MRI using kernel-based diffusion simulations