Fiber tractography using entropy spectrum pathways
Inventors
Frank, Lawrence R. • GALINSKY, Vitaly L.
Assignees
Office of General Counsel of VA • University of California San Diego UCSD
Publication Number
US-9645212-B2
Publication Date
2017-05-09
Expiration Date
2035-10-21
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Abstract
A method for fiber tractography processes multi-shell diffusion weighted MRI data to identify fiber tracts by calculating intravoxel diffusion characteristics from the MRI data. A transition probability is calculated for each possible path on the lattice, with the transition probability weighted according the intravoxel characteristics. Entropy is calculated for each path and the paths are ranked according to entropy. A geometrical optics algorithm is applied to the entropy data to define pathways, which are ranked according to their significance to generate a map of the pathways.
Core Innovation
The invention described is a computer-implemented method and system for fiber tractography that identifies neural pathways within multi-shell diffusion weighted MRI data by calculating intravoxel diffusion characteristics, computing transition probabilities weighted by those characteristics, calculating entropy for each path on a lattice of voxels, ranking the paths by entropy, and applying a geometric optics algorithm to define and rank significant pathways, which together produce a map of fiber tracts.
The problem being solved arises from challenges in diffusion MRI and tractography where local voxel diffusion measurements are noisy, spatially coarse relative to underlying fibers, and there are many possible neural pathways between two points consistent with the data. Traditional methods separate local diffusion estimation and global tractography steps, which is limiting, and often rely on local computations without assessing global path probabilities. There is a need for a method that integrates local and global information, ranks paths rigorously, and addresses multiple spatial and temporal scales of diffusion.
The invention innovates by generalizing the maximum entropy random walk (MERW) approach to a framework called Entropy Spectrum Pathways (ESP), which models information flow on a lattice by maximizing entropy subject to prior information. This yields transition probabilities from global eigenvector solutions of a coupling matrix derived from spherical wave decomposition of diffusion data at multiple scales. The method solves an eigenvector problem, applies a Fokker-Planck equation with entropy as the potential to connect global and local structures, and uses geometric optics-like ray tracing to determine fiber tract location and direction. This simultaneously estimates local diffusion and global fiber tracts, incorporating multi-scale, multi-modal data and overcoming limitations of prior local-only or two-step methods.
Claims Coverage
The patent includes three independent claims focused on a method for fiber tractography using diffusion weighted MRI data, incorporating intravoxel diffusion characteristic calculations, transition probability computations, entropy calculations for paths, and applying mathematical models and algorithms to define fiber tracts.
Integration of local intravoxel diffusion characteristics with global pathway probabilities
The method calculates intravoxel diffusion characteristics from diffusion weighted MRI data, then computes transition probabilities for lattice paths weighted by these characteristics, calculates entropy for each path, and ranks the paths to determine maximum entropy pathways.
Application of Fokker-Planck equation with entropy as potential to link global and local structures
The method applies the Fokker-Planck equation ∂tP+∇·(LP∇S)=∇·D∇P, where P is probability, S is entropy, D is diffusion coefficient, and L is a local diffusion tensor (L=κD), to one or more highest ranked paths, establishing potential as entropy.
Use of geometric optics-based algorithms for fiber tract location and direction determination
The method applies geometric optics tractography algorithms to the results from the Fokker-Planck equation or ray tracing on the highest ranked paths, represented by specific mathematical formulations, to calculate the location and direction of fiber tracts and generate display outputs.
Multi-scale spherical wave decomposition-based coupling matrix formulation
The method performs spherical wave decomposition on multi-shell diffusion weighted MRI data to compute spherical wave decomposition coefficients, generates a coupling matrix defining interactions between lattice locations for multiple scales, then computes transition and equilibrium probabilities representing angular and scale distributions used in geometric optics tractography.
Ranking and selection of fiber pathways based on eigenmodes and entropy spectrum
Possible fiber pathways constructed via geometric optics tractography are characterized by eigenvectors and eigenvalues (eigenmodes), which are calculated and ranked to select a preselected number of pathways for visualization.
Together, these inventive features disclose a novel fiber tractography method that integrates local diffusion data with global probabilistic path characterization using entropy-based mathematical formalism, applies multi-scale decomposition and sophisticated algorithms to compute transition probabilities, and employs geometric optics principles for fiber pathway extraction and ranking.
Stated Advantages
Provides a global approach that explicitly considers the neighborhood of paths rather than just local voxel information.
Allows simultaneous estimation of local diffusion and global fiber tracts incorporating multi-scale and multi-modal data from multi-shell diffusion MRI.
Improves accuracy and completeness of fiber pathway extraction compared to traditional methods that separate local and global estimation.
Avoids expensive front evolution computation steps common in current tractography methods, increasing efficiency.
Capable of resolving fiber crossings and complex intravoxel fiber architecture by utilizing multiple scales and global connectivity information.
Offers scientifically rigorous ranking of fiber pathways based on entropy spectrum instead of heuristic or single-scale approaches.
Documented Applications
Quantification of neural fiber connectivity in the human brain using diffusion tensor imaging.
Assessment of functional connectivity using functional MRI (fMRI).
Anatomical connectivity analysis using segmentation methods.
Characterization of connectivity in complex networks such as internet and communication systems.
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