Fiber tractography using entropy spectrum pathways
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.
1. A method for fiber tractography, comprising:
acquiring, via an imaging system, diffusion weighted MRI data comprising a plurality of voxels, wherein the plurality of voxels defines a lattice, each voxel connected by a path;
inputting the MRI data into a computer processor having instructions stored therein for causing the computer processor to execute the steps of:
calculating intravoxel diffusion characteristics from the MRI data;
calculating a transition probability for each path on the lattice, wherein the transition probability is weighted according the intravoxel characteristics;
calculating an entropy for each path;
ranking the paths between two voxels according to entropy to determine a maximum entropy;
calculating a connection between a global structure of the probability with a local structure of the lattice by applying the Fokker-Planck equation to one or more highest ranked paths, wherein potential equals entropy;
calculating a location and direction of one or more fiber tracts by applying geometric optics algorithms to the results of the Fokker-Planck equation; and
generating an output comprising a display corresponding to the one or more fiber tracts.
2. The method of claim 1 , wherein the Fokker-Planck equation is
∂ t P+∇ ·( LP∇S )=∇· D∇P,
where P is probability=P 0 +P 1 , S is the entropy, D is a diffusion coefficient, and L is a local diffusion tensor, where L=κD, where κ is the Onsager coefficient.
3. The method of claim 1 , where the geometric optics algorithms comprise
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4. A method for fiber tractography, comprising:
acquiring, via an imaging system, diffusion weighted MRI data comprising a plurality of voxels, wherein the plurality of voxels defines a lattice, each voxel connected by a path;
inputting the MRI data into a computer processor having instructions stored therein for causing the computer processor to execute the steps of:
calculating intravoxel diffusion characteristics from the MRI data;
calculating a transition probability for each path on the lattice, wherein the transition probability is weighted according the intravoxel characteristics;
calculating an entropy for each path;
ranking the paths between two voxels according to entropy to determine a maximum entropy;
calculating a connection between a global structure of the probability with a local structure of the lattice for one or more highest ranked paths;
determining one or more fiber tracts corresponding to the highest ranked paths using ray tracing, wherein potential equals entropy; and
generating an output comprising a display corresponding to the one or more fiber tracts.
5. The method of claim 4 , wherein calculating a connection comprises applying the relationship ∂ t P+∇·(LP∇S)=∇·D∇P to the one or more highest ranked paths, where P is probability=P 0 +P 1 , S is the entropy, D is a diffusion coefficient, and L is a local diffusion tensor, where L=κ, where κ is the Onsager coefficient.
6. The method of claim 4 , wherein ray tracing comprising applying geometric optics algorithms to the highest ranked paths according to the relationships
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where r is the location, R is displacement, k is the direction, t is time, X=∇P 0 (2+ln P 0 )+∇(P 0 (1+ln P 0 )), Y=P 0 (1+ln P 0 ), and Z=∇·∇P 0 (2+ln P 0 ).
7. A method for fiber tractography, comprising:
acquiring, via an imaging system, multi-shell diffusion weighted MRI data comprising a plurality of voxels, wherein the plurality of voxels define locations on a lattice, each location connected by a path;
in a computing device, executing the steps of:
performing a spherical wave decomposition on the data to define a set of spherical wave decomposition coefficients;
using the spherical wave decomposition coefficients, generating a coupling matrix for diffusion connectivity at multiple scales, wherein the coupling matrix defines interactions between locations on the lattice;
using the coupling matrix, computing transition probabilities and equilibrium probabilities for a plurality of interactions between locations on the lattice;
using the computed transition probabilities to represent angular and scale distributions of potential paths between locations on the lattice;
applying a geometric optics tractography algorithm to the transition probabilities to construct possible pathways, each possible pathway having an eigenvector and an eigenvalue;
calculating eigenmodes for the possible pathways;
ranking the possible pathways according to their eigenmode;
defining a preselected number of pathways from the ranked pathways; and
displaying the preselected number of pathways on a visual display.
8. The method of claim 7 , wherein using the computed transition probabilities comprises applying the relationship ∂ t P+∇·(LP∇S)=∇·D∇P to the one or more highest ranked paths, where P is probability=P 0 −P 1 , S is the entropy, D is a diffusion coefficient, and L is a local diffusion tensor, where L=κD, where κ is the Onsager coefficient.
9. The method of claim 7 , wherein the geometric optics tractography algorithm comprises
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