BME Seminar Series: Russell Carr, Ph.D.
Putting Dynamics into Hemodynamics
Chemical Engineering Department, The University of New Hampshire
Nobel Laureate August Krogh noted the remarkable spatial and temporal variability of flow in the microcirculation in his papers on the anatomy and physiology of capillaries. Fifty years later, Professor YC Fung suggested that passive temporal fluctuation in the microcirculation could be due to random differences in the sizes and mechanical properties of blood cells and blood vessels (Stochastic Flow in Capillary Blood Vessels, MVR 5, 34-48, 1973). Twenty years after that Kiani et al. published a computer simulation indicating that spontaneous oscillations in blood flow can be a result of purely rheological factors (Fluctuations in microvascular blood flow parameters caused by hemodynamic mechanisms, Am J Physiol 266, H1822-H1828, 1994).
We show that blood flow in the microvascular is described by nonlinear physics and that the oscillations discovered by Kiani et al. can be explained by the ideas of nonlinear dynamics. The rheological properties of the Fahraeus Lindqvist effect and plasma skimming are two sources of nonlinearity. These lead to the existence of multiple steady states (fixed points) and hysteresis. We have found multiple fixed points that arise from what are called saddle node bifurcations in the dynamics literature. Kiani et al.âs model can be thought of as pulses of red cell packets propagating through the vessels. Another source on nonlinearity is the fact that the wave speed of the hematocrit pulses is a function of the hematocrit distribution in the network. This fact leads to the derivation of state dependent delay equations. Such equations can exhibit spontaneous oscillations. These oscillations are often limit cycles, the result of supercritical Hopf bifurcations.
In vitro experiments on simple network flows have verified some of the predictions of this nonlinear model of microvascular network blood flow. Multiple steady states and bistability with hysteresis has been demonstrated (Bistability in a simple fluid network due to viscosity contrast Physical Review E 81, Art 04316, 2010). Sustained spontaneous oscillations in a simple microfluidic network with RBC suspensions has also been shown (Blood flow in microvascular networks: A study in nonlinear biology, Chaos 20 Art 045123, 2010). Experiments in more complex networks are planned.
Hemodynamics is clearly dynamic (and nonlinear as well).