Blood flow in microvascular networks: A study in nonlinear biology

Abstract

Plasma skimming and the Fahraeus-Lindqvist effect are well-known phenomena in blood rheology. By combining these peculiarities of blood flow in the microcirculation with simple topological models of microvascular networks, we have uncovered interesting nonlinear behavior regarding blood flow in networks. Nonlinearity manifests itself in the existence of multiple steady states. This is due to the nonlinear dependence of viscosity on blood cell concentration. Nonlinearity also appears in the form of spontaneous oscillations in limit cycles. These limit cycles arise from the fact that the physics of blood flow can be modeled in terms of state dependent delay equations with multiple interacting delay times. In this paper we extend our previous work on blood flow in a simple two node network and begin to explore how topological complexity influences the dynamics of network blood flow. In addition we present initial evidence that the nonlinear phenomena predicted by our model are observed experimentally. © 2010 American Institute of Physics. ͓doi:10.1063/1.3530122͔Nonlinear phenomena are very common in nature. Here we explore one example from biology, the flow of blood in small blood vessel networks. Nonlinearity is revealed in this case by the existence of multiple steady state solutions and by the evolution of spontaneous fluctuations in network flow. These nonlinear phenomena are not dependent on any biological control mechanisms but are solely due to the interaction of well-known blood rheological properties and network geometry. We examine these interactions through analysis and numerical computation. We also present our first in vitro experimental data on spontaneous oscillations in blood flow in this paper.

Testicular ischemia-reperfusion may alter micro-rheological parameters in laboratory rats

“…In this approach, the hemorheological approach is inseparable, since it is well known, that blood and plasma viscosity, hematocrit, red blood cell deformability as well as red blood cell aggregation are major determinants of the microcirculatory flow [e.g. 2,3,10,17,24].…”

Oscillations and Multiple Equilibria in Microvascular Blood Flow

“…We will consider two cases, d C = 5 µm and d C = 10 µm, in order to highlight the role that the diameter of this middle vessel plays in the formation of multiple equilibria and sustained oscillations. Geddes et al (2010) showed that the network under consideration can exhibit multiple equilibria under different plasma skimming and viscosity assumptions than those used here. Their approach centered on plotting the solution curves to Eqs.…”

Haemoglobin

“…These properties will also affect blood transport and gas diffusion characteristics. The interaction of these phenoma in microcirculatory beds is complex and highly nonlinear, such that it could lead to the presence of chaotic states with spontaneous oscillations in vessel calibre [11]. An important regulator of calibre and tone of retinal blood flow has been found to be nitric oxide (NO) [12].…”

“…It is not immediately obvious why increases in systolic pressure would be associated with a reduced vasodilatory response to flicker light exposure. One of the possible mechanisms might be related to the interaction of retinal haemodynamics with cerebrovascular and cerebrospinal fluid dynamics [6] as well as the complex particulate properties of blood in small calibre vessels being affected by intravascular flow conditions modulating erythrocyte and plasma separation [11,18].…”