Wave transmission and input impedance of a model of skeletal muscle microvasculature

We analyzed wave transmission properties and input impedance of a microvascular network model. The model, derived from rat spinotrapezius muscle and previously described and validated by other investigators for steady pressure-flow relations, was expanded to include pulsatile phenomena. Microvessels are considered purely elastic, with compliances a function of vessel type; viscous dissipation follows Poiseuille's law. Linear and nonlinear results are presented. In the nonlinear case, shear rate-dependent viscosity of blood and transmural pressure-dependent vascular diameters were calculated and small signal perturbations were imposed around several working points. We investigated effects on input impedance of physiological variability of network parameters and structure: distribution of capillary diameters, capillary segment length, and presence or absence of cross-connecting capillaries. Results show that although wave transmission properties are complex, input impedance is simple. Apparent wave speeds differ substantially from phase velocities and change markedly from branch to branch; pressure and flow waves appear to travel at different speeds. These features result from the mesh-like structure of the network and the prominence of reflection at branchpoints. Input impedance displays a similar form under all conditions: Magnitude is a monotonically decreasing function of frequency, and phase decreases from 0 to approximately -45 degrees. Consideration of the characteristic impedance of a microvessel leads to modification of the three-element Windkessel as a reduced model of the observed input impedance.