Power-frequency relationship of wave dynamics in fluid-filled compliant tubes

The human heart pumps in a pulsatile fashion that generates pressure and flow waves in the cardiovascular system. These waves propagate and reflect through a fractal tree network composed of fluid-filled compliant tubes. The resulting complex pressure and flow waves create a pulsatile workload (an important contributor to the pumping efficiency of the heart). Although such load has been shown to be dependent on inflow wave frequency, the fundamental relationship between power and frequency has not been directly explored. Hence the general idea of this work is to address this by modeling wave propagation in a generic pulsatile system through a fluid-structure interaction solver (based on a reduced-order Navier-Stokes formulation) applied to a fluid-filled compliant tube terminated by a controlled reflection site. We analyze the impact of reflection on such pulse waves and their associated power-frequency relationships. Our analysis considers moderate frequencies and large wavelengths as inspired by cardiovascular flows. Examining pressure-flow dynamics reveals two distinct regimes as a function of inflow frequency: a pressure-leading regime and a flow-leading regime. We observe that the latter transitions into the former at particular “optimum frequencies” that minimize the pulsatile load on the inlet and create nonlinearity in power-frequency patterns. Results suggest that the values of these frequencies strongly depend on the reflection coefficient of the tube. Our findings highlight the significance of reflection as a key determinant in design that can provide control of optimum inflow frequencies toward minimizing destructive pulsatile loads.