Structural adaptation and stability of microvascular networks: theory and simulations

1 Deutsches Herzzentrum Berlin, D-13353 Berlin, Germany; 2 Department of Physiology, University of Arizona, Tucson, Arizona 85724; and 3 Department of Physiology, Freie Universität Berlin, D-14195 Berlin, Germany A theoretical model was developed to simulate long-term changes of vessel diameters during structural adaptation of microvascular networks in response to tissue needs. The diameter of each vascular segment was assumed to change with time in response to four local stimuli: endothelial wall shear stress ( w ), intravascular pressure (P), a flow-dependent metabolic stimulus (M), and a stimulus conducted from distal to proximal segments along vascular walls (C). Increases in w , M, or C or decreases in P were assumed to stimulate diameter increases. Hemodynamic quantities were estimated using a mathematical model of network flow. Simulations were continued until equilibrium states were reached in which the stimuli were in balance. Predictions were compared with data from intravital microscopy of the rat mesentery, including topological position, diameter, length, and flow velocity for each segment of complete networks. Stable equilibrium states, with realistic distributions of velocities and diameters, were achieved only when all four stimuli were included. According to the model, responses to w and P ensure that diameters are smaller in peripheral than in proximal segments and are larger in venules than in corresponding arterioles, whereas M prevents collapse of networks to single pathways and C suppresses generation of large proximal shunts. shear stress; pressure; conducted response; mathematical modeling