Nonlinear dynamics of microvascular blood flow

Kiani et al. (Kiani, M. F., A. R. Pries, L. L. Hsu, I. H. Sarelius, and G. R. Cokelet, Am. J. Physics. 266: H1822-H1828, 1994) suggested that blood velocity, hematocrit, and nodal pressures can oscillate spontaneously in large microvascular networks in the absence of biological control. This paper presents a model of blood flow in microvascular networks that shows the possibility of sustained spontaneous oscillations in small networks (less than 15 vessel segments). The paper explores mechanisms which cause spontaneous oscillations under some conditions and steady states under others. The existence of sustained oscillations in the absence of biological control provides alternative interpretations of dynamic behavior in the microcirculation. The model includes the Fåhraeus-Lindqvist effect and plasma skimming but no biological control mechanisms. The model is a set of coupled nonlinear partial differential equations. The equations have been solved numerically with the direct marching numerical method of characteristics. The model shows steady-state fixed point and limit cycle dynamics (sometimes showing period doubling). Plasma skimming, and the Fåhraeus-Lindqvist effect, along with arcade type topology are necessary for oscillations to occur. Depending on network parameters, nonoscillating, damped oscillating and sustaining oscillating dynamics have been demonstrated. Oscillations are damped when the residence time one of the vessels is large compared to the residence times for the other vessels. When the residence times for all vessels are comparable, sustained oscillations are possible.