The case against the reservoir-wave approach

Carotid Reservoir Pressure Decrease After Prolonged Head Down Tilt Bed Rest in Young Healthy Subjects Is Associated With Reduction in Left Ventricular Ejection Time and Diastolic Length

Background

The arterial pressure waveform reflects the interaction between the heart and the arterial system and carries potentially relevant information about circulatory status. According to the commonly accepted 'wave transmission model', the net BP waveform results from the super-position of discrete forward and backward pressure waves, with the forward wave in systole determined mainly by the left ventricular (LV) ejection function and the backward by the wave reflection from the periphery, the timing and amplitude of which depend on arterial stiffness, the wave propagation speed and the extent of downstream admittance mismatching. However, this approach obscures the 'Windkessel function' of the elastic arteries. Recently, a 'reservoir-excess pressure' model has been proposed, which interprets the arterial BP waveform as a composite of a volume-related 'reservoir' pressure and a wave-related 'excess' pressure.

Methods

In this study we applied the reservoir-excess pressure approach to the analysis of carotid arterial pressure waveforms (applanation tonometry) in 10 young healthy volunteers before and after a 5-week head down tilt bed rest which induced a significant reduction in stroke volume (SV), end-diastolic LV volume and LV longitudinal function without significant changes in central blood pressure, cardiac output, total peripheral resistance and aortic stiffness. Forward and backward pressure components were also determined by wave separation analysis.

Results

Compared to the baseline state, bed rest induced a significant reduction in LV ejection time (LVET), diastolic time (DT), backward pressure amplitude (bP) and pressure reservoir integral (INTPR). INTPR correlated directly with LVET, DT, time to the peak of backward wave (bT) and stroke volume, while excess pressure integral (INTXSP) correlated directly with central pressure. Furthermore, Δ.INTPR correlated directly with Δ.LVET, and Δ.DT, and in multivariate analysis INTPR was independently related to LVET and DT and INTXSP to central systolic BP.

Conclusion

This is an hypothesis generating paper which adds support to the idea that the reservoir-wave hypothesis applied to non-invasively obtained carotid pressure waveforms is of potential clinical usefulness.

Increased Excess Pressure After Creation of an Arteriovenous Fistula in End-Stage Renal Disease

BACKGROUND

Reservoir-wave analysis (RWA) separates the arterial waveform into reservoir and excess pressure (XSP) components, where XSP is analogous to flow and related to left ventricular workload. RWA provides more detailed information about the arterial tree than traditional blood pressure (BP) parameters. In end-stage renal disease (ESRD), we have previously shown that XSP is associated with increased mortality and is higher in patients with arteriovenous fistula (AVF). In this study, we examined whether XSP increases after creation of an AVF in ESRD.

METHODS

Before and after a mean of 3.9 ± 1.2 months following creation of AVF, carotid pressure waves were recorded using arterial tonometry. XSP and its integral (XSPI) were derived using RWA through pressure wave analysis alone. Aortic stiffness was assessed by carotid-femoral pulse wave velocity (CF-PWV).

RESURLTS

In 38 patients (63% male, age 59 ± 15 years), after AVF creation, brachial diastolic BP decreased (79 ± 10 vs. 72 ± 12 mm Hg, P = 0.002), but the reduction in systolic BP, was not statistically significant (133 ± 20 vs. 127 ± 26 mm Hg, P = 0.137). However, carotid XSP (14 [12-19] to 17 [12-22] mm Hg, P = 0.031) and XSPI increased significantly (275 [212-335] to 334 [241-439] kPa∙s, P = 0.015), despite a reduction in CF-PWV (13 ± 3.6 vs. 12 ± 3.5 m/s, P = 0.025).

CONCLUSIONS

Creation of an AVF resulted in increased XSP in this population, despite improvement in diastolic BP and aortic stiffness. These findings underline the complex hemodynamic impact of AVF on the cardiovascular system.

Novel Pressure Wave Separation Analysis for Cardiovascular Function Assessment Highlights Major Role of Aortic Root

Objective

A novel method was presented to separate the central blood pressure wave (CBPW) into five components with different biophysical and temporal origins. It includes a time-varying emission coefficient (γ) that quantifies pulse wave generation and reflection at the aortic root.

Methods

The method was applied to normotensive subjects with modulated physiology by inotropic/vasoactive drugs (n = 13), hypertensive subjects (n = 158), and virtual subjects (n = 4,374).

Results

γ is directly proportional to aortic flow throughout the cardiac cycle. Mean peak γ increased with increasing pulse pressure (from <30 to >70 mmHg) in the hypertensive (from 1.6 to 2.5, P < 0.001) and in silico (from 1.4 to 2.8, P < 0.001) groups, dobutamine dose (from baseline to 7.5 μg/kg/min) in the normotensive group (from 2.1 to 2.7, P < 0.05), and remained unchanged when peripheral wave reflections were suppressed in silico. This was accompanied by an increase in the percentage contribution of the cardiac-aortic-coupling component of CBPW in systole: from 11% to 23% (P < 0.001) in the hypertensive group, 9% to 21% (P < 0.001) in the in silico group, and 17% to 23% (P < 0.01) in the normotensive group.

Conclusion

These results suggest that the aortic root is a major reflection site in the systemic arterial network and ventricular-aortic coupling is the main determinant in the elevation of pulsatile pulse pressure.

Significance

Ventricular-aortic coupling is a prime therapeutic target for preventing/treating systolic hypertension.

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

The optimal performance of the cardiovascular system, as well as the break-down of this performance with disease, both involve complex biomechanical interactions between the heart, conduit vascular networks and microvascular beds. ‘Wave analysis’ refers to a group of techniques that provide valuable insight into these interactions by scrutinizing the shape of blood pressure and flow/velocity waveforms. The aim of this review paper is to provide a comprehensive introduction to wave analysis, with a focus on key concepts and practical application rather than mathematical derivations. We begin with an overview of invasive and non-invasive measurement techniques that can be used to obtain the signals required for wave analysis. We then review the most widely used wave analysis techniques—pulse wave analysis, wave separation and wave intensity analysis—and associated methods for estimating local wave speed or characteristic impedance that are required for decomposing waveforms into forward and backward wave components. This is followed by a discussion of the biomechanical phenomena that generate waves and the processes that modulate wave amplitude, both of which are critical for interpreting measured wave patterns. Finally, we provide a brief update on several emerging techniques/concepts in the wave analysis field, namely wave potential and the reservoir-excess pressure approach.

Conduit arterial wave reflection promotes pressure transmission but impedes hydraulic energy transmission to the microvasculature

With aging, a reduction in the stiffness gradient between elastic and muscular arteries is thought to reduce wave reflection in conduit arteries, leading to increased pulsatile pressure transmission into the microvasculature. This assumes that wave reflection limits pressure transmission in arteries. However, using a computational model, we showed that wave reflection promotes pulsatile pressure transmission, although it does limit hydraulic energy transmission. Increased microvascular pulse pressure with aging is instead related to decreasing arterial compliance.

Changes in hemodynamics associated with metabolic syndrome are more pronounced in women than in men

The increase in cardiovascular risk associated with metabolic syndrome (MS) seems higher in women than in men. We examined hemodynamics during head-up tilt in 252 men and 250 women without atherosclerosis, diabetes, or antihypertensive medication, mean age 48 years, using whole-body impedance cardiography and radial pulse wave analysis. MS was defined according to Alberti et al. 2009. Men and women with MS presented with corresponding elevations of systolic and diastolic blood pressure (10-14%, p ≤ 0.001) versus controls. Supine pulse wave velocity (16-17%, p < 0.001) and systemic vascular resistance (7-9%, p ≤ 0.026), and upright cardiac output (6-11%, p ≤ 0.008) were higher in both MS groups than controls. Elevation of supine aortic characteristic impedance was higher in women than in men with MS (16% vs. 8%, p = 0.026), and in contrast to men, no upright impedance reduction was observed in women. When upright, women but not men with MS showed faster return of reflected pressure wave (p = 0.036), and smaller decrease in left cardiac work (p = 0.035) versus controls. The faster upright return of reflected pressure, lower upright decrease in left cardiac work, and higher elevation of aortic characteristic impedance may contribute to the greater increase in MS-related cardiovascular risk in women than in men.

Reservoir pressure analysis of aortic blood pressure: an in-vivo study at five locations in humans

INTRODUCTION

The development and propagation of the aortic blood pressure wave remains poorly understood, despite its clear relevance to major organ blood flow and potential association with cardiovascular outcomes. The reservoir pressure model provides a unified description of the dual conduit and reservoir functions of the aorta. Reservoir waveform analysis resolves the aortic pressure waveform into an excess (wave related) and reservoir (compliance related) pressure. The applicability of this model to the pressure waveform as it propagates along the aorta has not been investigated in humans.

METHODS

We analysed invasively acquired high-fidelity aortic pressure waveforms from 40 patients undergoing clinically indicated coronary catheterization. Aortic waveforms were measured using a solid-state pressure catheter at five anatomical sites: the ascending aorta, the transverse aortic arch, the diaphragm, the level of the renal arteries, and at the aortic bifurcation. Ensemble average pressure waveforms were obtained for these sites for each patient and analysed to obtain the reservoir pressure [Pr(t)] and the excess pressure [Px(t)] at each aortic position.

RESULTS

Systolic blood pressure increased at a rate of 2.1 mmHg per site along the aorta, whereas diastolic blood pressure was effectively constant. Maximum Pr decreased only slightly along the aorta (changing by -0.7 mmHg per site), whereas the maximum of Px increased from the proximal to distal aorta (+4.1 mmHg per site; P < 0.001). The time, relative to the start of systolic upstroke, of the occurrence of the maximum excess pressure did not vary along the aorta. Of the parameters used to derive the reservoir pressure waveform the systolic and diastolic rate constants showed divergent changes with the systolic rate constant (ks) decreasing and the diastolic rate constant (kd) increasing along the aorta.

CONCLUSIONS

This analysis confirms the proposition that the magnitude of the calculated reservoir pressure waveform, despite known changes in aortic structure, is effectively constant throughout the aorta. A progressive increase of excess pressure accounts for the increase in pulse pressure from the proximal to distal aorta. The reservoir pressure rate constants seem to behave as arterial functional parameters. The accompanying decrease in ks and increase in kd are consistent with a progressive decrease in aortic compliance and increase in impedance. The reservoir pressure waveform therefore provides a model that might have utility in understanding the generation of central blood pressure and in specific cases might have clinical utility.

Major contribution of central pulmonary reservoir discharge to increased pulmonary arterial diastolic blood flow after birth in near-term lambs

Recent fetal lamb data have suggested that the pulmonary trunk (PT) region displays a reservoir function and that a pharmacologically induced fall in pulmonary vascular resistance (PVR) increases and redistributes diastolic discharge from this central pulmonary reservoir toward the lungs, thereby producing a positive diastolic offset in the pulmonary arterial (PA) blood flow profile. As a similar offset in PA flow characteristically occurs after birth, this study tested the hypotheses that 1) central pulmonary reservoir discharge is both redistributed toward the lungs and increased in magnitude during the birth transition and 2) discharge from this reservoir constitutes a major component of increased PA diastolic blood flow after birth. Six anesthetized near-term fetal lambs were instrumented with PT, ductal and left PA transit-time flow probes, and aortic, PT and left atrial catheters. Hemodynamic data were recorded in fetuses and at regular intervals during 2-h mechanical ventilation following cesarean section delivery. Diastolic PA blood flow rose from near zero in fetuses to 468 ± 188 ml/min by 15 min ( P < 0.001). Central pulmonary reservoir discharge in fetuses (99 ± 44 ml/min) passed primarily right-to-left across the ductus. However, this reservoir discharge redistributed entirely to the lungs by 1 min after birth, and then doubled to a peak of 214 ± 167 ml/min at 15 min ( P < 0.001). Reservoir discharge subsequently stabilized at 151 ± 60 ml/min at 30–120 min, which comprised ∼50% of diastolic and ∼20% of mean PA blood flow. These findings suggest that enhanced diastolic central pulmonary reservoir discharge plays a major role in supporting an increased pulmonary perfusion after birth.

Effects of pacing modality on noninvasive assessment of heart rate dependency of indices of large artery function

Studies investigating the relationship between heart rate (HR) and arterial stiffness or wave reflections have commonly induced HR changes through in situ cardiac pacing. Although pacing produces consistent HR changes, hemodynamics can be different with different pacing modalities. Whether the differences affect the HR relationship with arterial stiffness or wave reflections is unknown. In the present study, 48 subjects [mean age, 78 ± 10 (SD), 9 women] with in situ cardiac pacemakers were paced at 60, 70, 80, 90, and 100 beats per min under atrial, atrioventricular, or ventricular pacing. At each paced HR, brachial cuff-based pulse wave analysis was used to determine central hemodynamic parameters, including ejection duration (ED) and augmentation index (AIx). Wave separation analysis was used to determine wave reflection magnitude (RM) and reflection index (RI). Arterial stiffness was assessed by carotid-femoral pulse wave velocity (cfPWV). Pacing modality was found to have significant effects on the HR relationship with ED (P = 0.01), central aortic pulse pressure (P = 0.01), augmentation pressure (P < 0.0001), and magnitudes of both forward and reflected waves (P = 0.05 and P = 0.003, respectively), but not cfPWV (P = 0.57) or AIx (P = 0.38). However, at a fixed HR, significant differences in pulse pressure amplification (P < 0.001), AIx (P < 0.0001), RM (P = 0.03), and RI (P = 0.03) were observed with different pacing modalities. These results demonstrate that although the HR relationships with arterial stiffness and systolic loading as measured by cfPWV and AIx were unaffected by pacing modality, it should still be taken into account for studies in which mixed pacing modalities are present, in particular, for wave reflection studies.

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

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.

Wave Separation, Wave Intensity, the Reservoir-Wave Concept, and the Instantaneous Wave-Free Ratio

Wave separation analysis and wave intensity analysis (WIA) use (aortic) pressure and flow to separate them in their forward and backward (reflected) waves. While wave separation analysis uses measured pressure and flow, WIA uses their derivatives. Because differentiation emphasizes rapid changes, WIA suppresses slow (diastolic) fluctuations of the waves and renders diastole a seemingly wave-free period. However, integration of the WIA-obtained forward and backward waves is equal to the wave separation analysis–obtained waves. Both the methods thus give similar results including backward waves spanning systole and diastole. Nevertheless, this seemingly wave-free period in diastole formed the basis of both the reservoir-wave concept and the Instantaneous wave-Free Ratio of (iFR) pressure and flow. The reservoir-wave concept introduces a reservoir pressure, P res , (Frank Windkessel) as a wave-less phenomenon. Because this Windkessel model falls short in systole an excess pressure, P exc , is introduced, which is assumed to have wave properties. The reservoir-wave concept, however, is internally inconsistent. The presumed wave-less P res equals twice the backward pressure wave and travels, arriving later in the distal aorta. Hence, in contrast, P exc is minimally affected by wave reflections. Taken together, P res seems to behave as a wave, rather than P exc . The iFR is also not without flaws, as easily demonstrated when applied to the aorta. The ratio of diastolic aortic pressure and flow implies division by zero giving nonsensical results. In conclusion, presumptions based on WIA have led to misconceptions that violate physical principles, and reservoir-wave concept and iFR should be abandoned.