2D Diffusion Tensor Field: Crossing-Fiber Tractography

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 on a single imaging plane — two bundles overlapping at the center, a standard test case for diffusion algorithms — computes each point's 2×2 diffusion tensor from the mixture, diagonalizes it in closed form 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 fiber tracts exactly as one slice of a clinical tractography pipeline would.