The modified arterial reservoir: An update with consideration of asymptotic pressure (P_∞) and zero-flow pressure (P_zf)

Abstract

This article describes the modified arterial reservoir in detail. The modified arterial reservoir makes explicit the wave nature of both reservoir ( Pres) and excess pressure ( Pxs). The mathematical derivation and methods for estimating Pres in the absence of flow velocity data are described. There is also discussion of zero-flow pressure ( Pzf), the pressure at which flow through the circulation ceases; its relationship to asymptotic pressure ( P∞) estimated by the reservoir model; and the physiological interpretation of Pzf . A systematic review and meta-analysis provides evidence that Pzf differs from mean circulatory filling pressure.

Feasibility of estimation of aortic wave intensity using non-invasive pressure recordings in the absence of flow velocity in man

“…Details of the reservoir approach are provided elsewhere (Hughes and Parker, 2020). In brief, it is assumed that reservoir pressure, P res , satisfies overall conservation of mass for the circulation: where Q in is the volumetric flow rate into the aortic root, C is the net compliance of the arteries, k d is the diastolic rate constant (the reciprocal of the diastolic time constant τ = RC , where R is the resistance to outflow through the microcirculation, and P zf is the pressure at which outflow through the microcirculation ceases.…”

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

“…In addition, although AIx increases with age, it plateaus and may even decrease around middle age ( Kelly et al, 1989 ; Mitchell et al, 2004 ; Fantin et al, 2006 ); it has been argued that this plateau does not necessarily mean that wave reflection is decreasing, but is a result of mathematical division between two linearly increasing curves (AP and PP) ( Namasivayam et al, 2010 ). Davies et al (2010) concluded that systolic augmentation was mainly related to reservoir pressure, with only a minor contribution from reflected waves; however, this interpretation now appears moot because current (revised) views acknowledge that wave reflection produces the reservoir pressure ( Hughes and Parker, 2020 ). Nevertheless, AIx has also been shown to depend on ventricular outflow patterns ( Karamanoglu and Feneley, 1999 ), preload ( van de Velde et al, 2017 ), contractility/relaxation properties ( Cheng et al, 2012 ) and forward waves ( Fok et al, 2014 ), although these dependencies may relate in part to re-reflection of backward-traveling waves when they return to the ventricle ( Phan et al, 2016a ).…”

“…The latter signifies the pressure that would exist if no pressure differentials existed throughout the circulation, and may therefore be identified with mean circulatory pressure ( P mc ) ( Mynard and Smolich, 2014b ). Alternatively, P ud could be identified with the zero-flow or asymptotic pressure that is reached after a long period of asystole, which may not be equal to P mc ( Hughes and Parker, 2020 ).…”

“…In response to some of the criticisms raised, Parker et al proposed a ‘modified’ reservoir pressure ( P res ) and revised concepts around how this reservoir pressure relates to waves ( Parker et al, 2012 ; Parker, 2017 ; Hughes and Parker, 2020 ). The new P res is distinct from a windkessel pressure in that it incorporates a propagation delay but is otherwise uniform in space.…”

“…The new P res is distinct from a windkessel pressure in that it incorporates a propagation delay but is otherwise uniform in space. Moreover, rather than being considered exclusive to wave reflection, it is now broadly agreed that the P res in fact arises entirely from wave reflection, with Hughes and Parker (2020) stating that “the reservoir pressure can be understood as the pressure due to the cumulative effect of … reflected and re-reflected waves.” Indeed, it has been shown that in the aorta, P res is approximately equal to twice the backward component of pressure ( Hametner et al, 2014 ), while excess pressure ( P ex = P − P res ) is approximately equal to flow multiplied by characteristic impedance, which is the pressure that would theoretically exist in the absence of any wave reflection. The debate regarding wave intensity analysis appears to have been resolved, with recent literature reflecting a consensus that measured pressure (or an appropriate distension-based surrogate) should be used for wave intensity, not P ex ( Segers et al, 2017 ; Su et al, 2017 ; Pomella et al, 2018 ; Bhuva et al, 2019 ; Chiesa et al, 2019 ; Kowalski et al, 2019b ; Hughes et al, 2020 ).…”