Oxygen advection and diffusion in a three-dimensional vascular anatomical network

TLDR

There is an increasing need for quantitative and computationally affordable models for analyzing tissue metabolism and hemodynamics in microvascular networks. This work develops a hybrid model to solve the time‑varying oxygen advection‑diffusion equation in vessels and tissue. The model couples a graph‑based advection scheme with a finite‑element diffusion solver and an implicit time‑advancing algorithm, is validated under static and dynamic conditions, and is applied to a rodent somatosensory cortex vascular network. The model’s predictions qualitatively agree with in‑vivo experiments.

Abstract

There is an increasing need for quantitative and computationally affordable models for analyzing tissue metabolism and hemodynamics in microvascular networks. In this work, we develop a hybrid model to solve for the time-varying oxygen advection-diffusion equation in the vessels and tissue. To obtain a three-dimensional temporal evolution of tissue oxygen concentration for realistic complex vessel networks, we used a graph-based advection model combined with a finite-element based diffusion model and an implicit time-advancing scheme. We validated this algorithm for both static and dynamic conditions. We also applied it to a complex vascular network obtained from a rodent somatosensory cortex. Qualitative agreement was found with in-vivo experiments.