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; and3) 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.

Major influence of a ‘smoke and mirrors’ effect caused by wave reflection on early diastolic coronary arterial wave intensity

“…Cumulative wave intensity (CI), related to the energy of a wave (Davies et al . ; Mynard & Smolich, ), is defined as the integral of WI ± over the duration of a given wave. Waves that have a pressure‐increasing effect are called ‘compression waves’, whereas waves that have a pressure‐decreasing effect are called ‘decompression waves’ (sometimes also referred to as ‘suction’ or ‘expansion’ waves).…”

“…The forward component (WI + ) and backward component (WI − ) of wave intensity are calculated via WI ± = ±(dP/dt ± ρc dU/dt) 2 /(4ρc), with forward waves having positive WI and backward waves having negative WI. Cumulative wave intensity (CI), related to the energy of a wave (Davies et al 2006a;Mynard & Smolich, 2016b), is defined as the integral of WI ± over the duration of a given wave. Waves that have a pressure-increasing effect are called 'compression waves' , whereas waves that have a pressure-decreasing effect are called 'decompression waves' (sometimes also referred to as 'suction' or 'expansion' waves).…”

Measurement, Analysis and Interpretation of Pressure/Flow Waves in Blood Vessels

“…While we have discussed wave separation for pressure, a similar approach can also be applied to calculate forward and backward components of flow (Westerhof et al, 1972), velocity (Parker, 2009), diameter or area distension (Feng and Khir, 2010;Biglino et al, 2012), wave intensity (Parker and Jones, 1990), wave power, and hydraulic power (Mynard and Smolich, 2016). As can be seen in Table 1, all of these calculations rely on the estimation of local characteristic impedance or wave speed.…”

“…Wave power is an alternative to wave intensity that uses pressure and volumetric flow signals (dπ = dPdQ) and has a number of advantages (Mynard and Smolich, 2016). First, as the name suggests, wave power has the physically meaningful units of power (Watts) and is therefore not sensitive to cross-sectional area variations (e.g., within vessels or between individuals).…”

“…Finally, wave power is linked to the hydraulic pressure power of flowing blood ( P = PQ), which determines total ventricular workload (Laskey et al, 1985). While hydraulic power has traditionally been decomposed into steady and oscillatory components (Milnor et al, 1966;Burattini and Campbell, 1999), Mynard and Smolich (2016) showed that power can also be separated into forward and backward wave components ( P± , see Table 1). Moreover, an incremental change in P± is proportional to wave power divided by the associated fractional change in pressure or flow components.…”