Diffusion MRI Tractography: Tracking White-Matter Fibers

Diffusion-tensor MRI infers the microscopic orientation of white-matter fiber bundles from how quickly water molecules diffuse in different directions, since myelinated axons let water travel freely along a fiber but block it across one. This simulator builds a synthetic crossing-fiber phantom — two bundles overlapping at the center, a standard test case for diffusion algorithms — computes each voxel's diffusion tensor from the mixture, diagonalizes it live with a Jacobi eigenvalue solver to get its principal direction and fractional anisotropy, and then runs FACT-style streamline tractography that follows the principal eigenvector step by step until anisotropy drops or the path bends too sharply, reconstructing the fiber tracts in 3D exactly as a clinical tractography pipeline would.