Unraveling the Stochastic Geometry of the Human Brain

Diffusion-weighted magnetic resonance imaging (MRI) uses measurements of the diffusion of the water molecules in biological tissue to map out structural changes in the tissue at microscopic scales. To investigate and interpret this clinically relevant microstructural information, current methods model the tissue as an arrangement of basic building blocks such as cylinders. While these models do give a rough idea of the microstructure of the tissue, there is evidence that they are too limited for, e.g., the mapping of nervous fibers in the human brain.

Here I consider a different approach. Just like diffusion is most naturally understood as a stochastic process – where it is not necessary to keep track of each individual particle in a fluid – a stochastic view of the tissue microstructure may better explain emergent properties of larger scale structures. By treating the structure of the tissue itself as a random entity, I aim to construct more realistic models of biological tissue.