A three‐dimensional, discrete‐continuum model of blood pressure in microvascular networks

Abstract

We present a 3D discrete‐continuum model to simulate blood pressure in large microvascular tissues in the absence of known capillary network architecture. Our hybrid approach combines a 1D Poiseuille flow description for large, discrete arteriolar and venular networks coupled to a continuum‐based Darcy model, point sources of flux, for transport in the capillary bed. We evaluate our hybrid approach using a vascular network imaged from the mouse brain medulla/pons using multi‐fluorescence high‐resolution episcopic microscopy (MF‐HREM). We use the fully‐resolved vascular network to predict the hydraulic conductivity of the capillary network and generate a fully‐discrete pressure solution to benchmark against. Our results demonstrate that the discrete‐continuum methodology is a computationally feasible and effective tool for predicting blood pressure in real‐world microvascular tissues when capillary microvessels are poorly defined.