Mathematical modeling of cerebral capillary blood flow heterogeneity and its effect on brain tissue oxygen levels

Maintaining cerebral blood flow is critical for adequate neuronal function. Previous computational models of brain capillary networks have predicted that heterogeneous cerebral capillary flow patterns result in lower brain tissue partial oxygen pressures PO2). However, these previous models have often considered simple capillary networks in terms of their geometric properties. In this current work, we developed and analyzed computational models of brain capillary networks to determine how perturbations of network properties impact tissue oxygen levels. The models include variabilities in both their geometric (segment lengths and diameters) and three-dimensional, topological structure. Two classes of capillary network models are considered. The first consists of equations for the oxygen partial pressure, PO₂, in both a capillary network and the surrounding tissue. In order to gain insight into the behavior of this detailed model, we also consider a reduced model for changes in PO₂ in just the capillary network. The main result is that for a general class of networks, random perturbations of either segment diameters or conductances will always, on average, decrease the average tissue oxygen levels. This result is supported through both simulations of the models and mathematical analysis. Our results promise to expand our understanding of cerebral capillary blood flow and its impact on the brain function in health and disease.