Model Microvascular Networks Can Have Many Equilibria.
We show that large microvascular networks with realistic topologies, geometries, boundary conditions, and constitutive laws can exhibit many steady-state flow configurations. This is in direct contrast to most previous studies which have assumed, implicitly or explicitly, that a given network can only possess one equilibrium state. While our techniques are general and can be applied to any network, we focus on two distinct network types that model human tissues: perturbed honeycomb networks and random networks generated from Voronoi diagrams. We demonstrate that the disparity between observed and predicted flow directions reported in previous studies might be attributable to the presence of multiple equilibria. We show that the pathway effect, in which hematocrit is steadily increased along a series of diverging junctions, has important implications for equilibrium discovery, and that our estimates of the number of equilibria supported by these networks are conservative. If a more complete description of the plasma skimming effect that captures red blood cell allocation at junctions with high feed hematocrit were to be obtained empirically, then the number of equilibria found by our approach would at worst remain the same and would in all likelihood increase significantly.
Babson College, Wellesley, MA, 02457, USA. nkarst@babson.edu.
Nathaniel J
0000-0003-3838-1032
NJ
Karst
Olin College of Engineering, Needham, MA, 02492, USA.
John B
JB
Geddes
University of New Hampshire, Durham, NH, 03824, USA.
Russell T
RT
Carr
D001783:Blood Flow Velocity; D006400:Hematocrit; D018056:Hemorheology; D006801:Humans; D055641:Mathematical Concepts; D055806:Microvessels / Q000502:physiology*; D008955:Models, Cardiovascular; D017711:Nonlinear Dynamics; D009716:Numerical Analysis, Computer-Assisted
Microvascular blood flow; Multiple equilibria; Nonlinear dynamics; Numerical continuation