Estimation of Oxygen and Glucose Concentration Distribution in the Rat Brain Arterial System

Glucose and oxygen concentration gradients are the key indicators that form the trophic tissue supply in mammalian brain. To describe them in detail it is essential to combine the solution of both hemodynamics and the convection-diffusion-reaction problems in the tissue. Visualization of spatio-temporal distributions of the metabolites noted above can be carried out both using the gradients themselves and the corresponding probability density functions. In the case of considering large parts of the brain, as well as the entire organ as a whole, the second method for metabolite heterogeneity description is of greater interest for practical purposes. This paper presents an approach to obtain a probability density functions based on structural segmentation of the diffusion region using Delaunay triangulation and the spherical source diffusion field method. It is shown that the average values of the estimated distributions deviate by 8 % from the experimentally obtained results and it corresponds to the best match during the validation by the finite element method in the triangulation simplices of basic topology. Given the relatively low computational complexity of both the segmentation process and the estimation of concentration in a single segment, the proposed method to obtain integral distributions of various compounds, in particular glucose and oxygen, can be used as an affordable alternative to precise calculation of the concentration gradients in the whole brain and its distinct anatomical structures.