Self-sustained oscillations in blood flow through a honeycomb capillary network

Numerical simulations of unsteady blood flow through a honeycomb network originating at multiple inlets and terminating at multiple outlets are presented and discussed under the assumption that blood behaves as a continuum with variable constitution. Unlike a tree network, the honeycomb network exhibits both diverging and converging bifurcations between branching capillary segments. Numerical results based on a finite difference method demonstrate that as in the case of tree networks considered in previous studies, the cell partitioning law at diverging bifurcations is an important parameter in both steady and unsteady flow. Specifically, a steady flow may spontaneously develop self-sustained oscillations at critical conditions by way of a Hopf bifurcation. Contrary to tree-like networks comprised entirely of diverging bifurcations, the critical parameters for instability in honeycomb networks depend weakly on the system size. The blockage of one or more network segments due to the presence of large cells or the occurrence of capillary constriction may cause flow reversal or trigger a transition to unsteady flow.