In Vivo Fiber Tractography, a Mathematical Introduction

Diffusion tensor MRI (DT-MRI) is a in vivo imaging modality with the potential to generate three dimensional images of highly anisotropic anatomical structures such as nerves, muscles, ligaments, tendons, etc. This method is based on the observation that diffusion of water molecules in tissues is retarded by cell walls and other obstacles so that it happens mainly along the directions of axons, muscle fibres, etc. On the other hand, nuclear magnetic resonance can be used to measure water diffusivity in biological tissues. So we can, at least in theory, draw the axes of anisotropic structures following the diffusion of water molecules along them.