Dynamic viscous flow in distensible vessels of skeletal muscle microcirculation: application to pressure and flow transients

Blood flow in the microcirculation of the rat skeletal muscle during transient changes of arterial pressure is analyzed theoretically. Although flow in such small vessels is quasi-steady and has a very low Reynolds number, time-dependent nonuniform flows along the length of the blood vessels can be observed due to vessel distensibility. The governing equations for a single microvessel are derived using previously measured microvessel elasticity, and several solutions to different inflow and outflow pressures and flow conditions are investigated. The results indicate that when such distensible microvessels are subjected to a step increase of arterial pressure, the arterial flow shows a rapid overshoot followed by a progressive decay to steady-state. An arterial step flow induces a different response which takes the form of a monotonically increasing pressure. Pressure and flows are nonuniform along the vessel length during such transients. In-vitro whole organ pressure-flow data are presented in the dilated rat gracilis muscle which qualitatively agree with the theoretical predictions.