A Novel Three-Phase Model of Brain Tissue Microstructure

We propose a novel biologically constrained three-phase model of the brain microstructure. Designing a realistic model is tantamount to a packing problem, and for this reason, a number of techniques from the theory of random heterogeneous materials can be brought to bear on this problem. Our analysis strongly suggests that previously developed two-phase models in which cells are packed in the extracellular space are insufficient representations of the brain microstructure. These models either do not preserve realistic geometric and topological features of brain tissue or preserve these properties while overestimating the brain's effective diffusivity, an average measure of the underlying microstructure. In light of the highly connected nature of three-dimensional space, which limits the minimum diffusivity of biologically constrained two-phase models, we explore the previously proposed hypothesis that the extracellular matrix is an important factor that contributes to the diffusivity of brain tissue. Using accurate first-passage-time techniques, we support this hypothesis by showing that the incorporation of the extracellular matrix as the third phase of a biologically constrained model gives the reduction in the diffusion coefficient necessary for the three-phase model to be a valid representation of the brain microstructure.
Author Summary The goal of the present work is to develop a biologically constrained three-dimensional model of the brain microstructure. This is an important task because the brain's three-dimensional microstructure cannot be directly visualized, yet a knowledge of its structure is essential for understanding normal brain functioning. We first explore the shortcomings of the conventional modeling approach that treats brain tissue as a two-phase material. These models either do not preserve realistic features of brain tissue or preserve these properties while overestimating the brain's effective diffusivity, an average measure of the underlying microstructure. We thus developed a biologically constrained two-phase model that, upon analysis, achieves a lower diffusion coefficient than other constrained models yet proves to not have a low enough diffusion coefficient to be a valid representation of the brain microstructure. We then show that if the extracellular matrix is incorporated as a third phase in this model, then the reduction in the diffusion coefficient achieved allows the proposed model to be a valid representation of the brain microstructure. Using this model, we can test the impact that microstructural changes have on the transport of nutrients and signaling molecules in the brain.