Theoretical Models for Blood Flow Regulation in Heterogeneous Microvascular Networks

Abstract

Proper distribution of blood flow in the microcirculation is necessary to match changing oxygen demands in various tissues. How this coordination of perfusion and consumption occurs in heterogeneous microvascular networks remains incompletely understood. Theoretical models are powerful tools that can help bridge this knowledge gap by simulating a range of conditions difficult to obtain experimentally. Here, an algorithm is first developed to estimate blood flow rates in large microvascular networks. Then, a theoretical model is presented for metabolic blood flow regulation in a realistic heterogeneous network structure, derived from experimental results from hamster cremaster muscle in control and dilated states. The model is based on modulation of arteriolar diameters according to the length-tension characteristics of vascular smooth muscle. Responses of smooth muscle cell tone to myogenic, shear-dependent, and metabolic stimuli are included. Blood flow is simulated including unequal hematocrit partition at diverging vessel bifurcations. Convective and diffusive oxygen transport in the network is simulated, and oxygen-dependent metabolic signals are assumed to be conducted upstream from distal vessels to arterioles. Simulations are carried out over a range of tissue oxygen demand. With increasing demand, arterioles dilate, blood flow increases, and the numbers of flowing arterioles and capillaries, as defined by red-blood-cell flux above a small threshold value, increase. Unequal hematocrit partition at diverging bifurcations contributes to capillary recruitment and enhances tissue oxygenation. The results imply that microvessel recruitment can occur as a consequence of local control of arteriolar tone. The effectiveness of red-blood-cell-dependent and independent mechanisms for the metabolic response of local blood flow regulation is examined over a range of tissue oxygen demands. Model results suggest that although a red-blood-cell-independent mechanism is most effective in increasing flow and preventing hypoxia, the addition of a red-blood-cell-dependent mechanism leads to a higher median tissue oxygen level, indicating distinct roles for the two mechanisms. In summary, flow rates in large microvessel networks can be estimated with the proposed algorithm, and the theoretical model for flow regulation predicts a mechanism for capillary recruitment, as well as roles for red-blood-cell-dependent and independent mechanisms in the metabolic regulation of blood flow in heterogeneous microvascular networks.