Oscillations in a simple microvascular network

We have identified the simplest topology that will permit spontaneous oscillations in a model of microvascular blood flow that includes the plasma skimming effect and the Fahraeus-Lindqvist effect and assumes that the flow can be described by a first-order wave equation in blood hematocrit. Our analysis is based on transforming the governing partial differential equations into delay differential equations and analyzing the associated linear stability problem. In doing so we have discovered three dimensionless parameters, which can be used to predict the occurrence of nonlinear oscillations. Two of these parameters are related to the response of the hydraulic resistances in the branches to perturbations. The other parameter is related to the amount of time necessary for the blood to pass through each of the branches. The simple topology used in this study is much simpler than networks found in vivo. However, we believe our analysis will form the basis for understanding more complex networks.