Novel wave power analysis linking pressure-flow waves, wave potential, and the forward and backward components of hydraulic power

Abstract

Wave intensity analysis provides detailed insights into factors influencing hemodynamics. However, wave intensity is not a conserved quantity, so it is sensitive to diameter variations and is not distributed among branches of a junction. Moreover, the fundamental relation between waves and hydraulic power is unclear. We, therefore, propose an alternative to wave intensity called “wave power,” calculated via incremental changes in pressure and flow (dPdQ) and a novel time-domain separation of hydraulic pressure power and kinetic power into forward and backward wave-related components (ΠP± and ΠQ±). Wave power has several useful properties: 1) it is obtained directly from flow measurements, without requiring further calculation of velocity; 2) it is a quasi-conserved quantity that may be used to study the relative distribution of waves at junctions; and 3) it has the units of power (Watts). We also uncover a simple relationship between wave power and changes in ΠP± and show that wave reflection reduces transmitted power. Absolute values of ΠP± represent wave potential, a recently introduced concept that unifies steady and pulsatile aspects of hemodynamics. We show that wave potential represents the hydraulic energy potential stored in a compliant pressurized vessel, with spatial gradients producing waves that transfer this energy. These techniques and principles are verified numerically and also experimentally with pressure/flow measurements in all branches of a central bifurcation in sheep, under a wide range of hemodynamic conditions. The proposed “wave power analysis,” encompassing wave power, wave potential, and wave separation of hydraulic power provides a potent time-domain approach for analyzing hemodynamics.