CrossTalk proposal: Forward and backward pressure waves in the arterial system do represent reality

The nature of waves in the arteries in memoriam: Nico Westerhof and John Tyberg

This memorial remembers the lives of two distinguished researchers who made major contributions to cardiovascular physiology; Nico Westerhof (1937-2022) and John Tyberg (1938-2022). It is a joint memorial not because they collaborated closely but because they held very different views about the nature of waves in the arteries. Their papers and particularly their lively discussions at many scientific meetings stimulated interest in the subject. Both were thoughtful and articulate about their views and the debates were polite and dignified. They never resolved their differences and, after outlining what these differences were, we will suggest that perhaps there is no resolution. The authors of this memorial were close to one or the other protagonist; a son, a son-in-law and two close collaborators. We all have different views about the nature of waves in the arteries but we all share great respect for both men and felt that a joint memorial was a fitting way to remember them and their many contributions. All of the authors knew the subjects of this memorial as 'Nico' and 'John' and we will use these informal names throughout. This article is protected by copyright. All rights reserved.

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

This article describes the modified arterial reservoir in detail. The modified arterial reservoir makes explicit the wave nature of both reservoir (P_res) and excess pressure (P_xs). The mathematical derivation and methods for estimating P_res in the absence of flow velocity data are described. There is also discussion of zero-flow pressure (P_zf), 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 P_zf . A systematic review and meta-analysis provides evidence that P_zf differs from mean circulatory filling pressure.

Acute Tachycardia Increases Aortic Distensibility, but Reduces Total Arterial Compliance Up to a Moderate Heart Rate

Background: The differential effects of rapid cardiac pacing on small and large vessels have not been well-established. The objective of this study was to investigate the effect of pacing-induced acute tachycardia on hemodynamics and arterial stiffness.

Methods: The pressure and flow waves in ascending aorta and femoral artery of six domestic swine were recorded simultaneously at baseline and heart rates (HR) of 135 and 155 beats per minutes (bpm) and analyzed by the models of Windkessel and Womersley types. Accordingly, the flow waves were simultaneously measured at carotid and femoral arteries to quantify aortic pulse wave velocity (PWV). The arterial distensibility was identified in small branches of coronary, carotid and femoral arteries with diameters of 300–600 μm by ex vivo experiments.

Results: The rapid pacing in HR up to 135 bpm reduced the total arterial compliance, stroke volume, systemic pulse pressure, and central systolic pressure by 36 ± 17, 38 ± 26, 29 ± 16, and 23 ± 12%, respectively, despite no statistical difference of mean aortic pressure, cardiac output, peripheral resistance, and vascular flow patterns. The pacing also resulted in a decrease of distensibility of small muscular arteries, but an increase of aortic distensibility. Pacing from 135 to 155 bpm had negligible effects on systemic and local hemodynamics and arterial stiffness.

Conclusions: There is an acute mismatch in the response of aorta and small arteries to pacing from basal HR to 135 bpm, which may have important pathological implications under chronic tachycardia conditions.

Modeling Arterial Pulse Pressure From Heart Rate During Sympathetic Activation by Progressive Central Hypovolemia

Heart rate (HR) has an impact on the central blood pressure (BP) wave shape and is related to pulse wave velocity and therefore to timing and duration of systole and diastole. This study tested the hypothesis that in healthy subjects both in rest and during sympathetic stimulation the relation between HR and pulse pressure (PP) is described by a linear effect model. Forty-four healthy volunteers were subjected to sympathetic stimulation by continuous lower body negative pressure (LBNP) until the onset of pre-syncopal symptoms. Changes in PP and HR were tracked non-invasively and modeled by linear mixed effect (LME) models. The dataset was split into two groups: the first was used for creating a model and the second for its evaluation. Models were created on the data obtained during LBNP. Model performance was expressed as absolute median error (1st; 3rd quantiles) and bias with limits of agreement (LOA) between modeled and measured PP. From rest to sympathetic stimulation, mean BP was maintained while HR increased (~30%) and PP decreased gradually (~20%). During baseline, PP could be modeled with an absolute error of 6 (4; 10) mm Hg and geometric mean ratio of the bias was 0.97 (LOA: 0.8–1.1). During LBNP, absolute median model error was 5 (4; 8) mmHg with geometric mean ratio 1.02 (LOA: 0.8–1.3). In conclusion, both during rest and during sustained sympathetic outflow induced by progressive central hypovolemia, a LME model of HR provides for an estimate of PP in healthy young adults.

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.

Areas under peripheral pulse waves: a potential marker of atherosclerotic changes

OBJECTIVE

In this study, we propose a method for finding atherosclerotic changes based on the ratios of areas under peripheral arterial pulse wave (PW) contours and analyze its performance.

APPROACH

The PW signals were recorded with force sensors and photoplethysmographic sensors from ankle, wrist, cubital fossa, index finger and second toe from 30 atherosclerotic patients and 52 control subjects. In addition, the day-to-day repeatability of the method was studied with 10 test subjects examined on three different days. The ratios of areas under the PWs were computed and the results were evaluated by means of receiver operating characteristic (ROC) analysis, intra-class correlation (ICC) coefficient and multiple linear regression analysis.

MAIN RESULTS

Areas under ROC curves of 0.802-0.906 were found for different area ratios having statistically significant differences between the atheroslerotic group and control groups. ICCs over 0.80 were found widely for the beat-by-beat analyzed data and over 0.95 for the data based on the averages over different numbers of PWs. Multiple linear regression analysis showed linear dependence between the area ratios and age and the diagnosis of atherosclerosis.

SIGNIFICANCE

Our findings may facilitate development of novel diagnostic approaches and preventive strategies against cardiovascular disorders. However, further studies are needed to confirm the results. The presented study demonstrates the potential of arterial PW analysis in finding vascular abnormalities.

Pulse Waveform Analysis: Is It Ready for Prime Time?

PURPOSE OF REVIEW

Arterial pulse waveform analysis has a long tradition but has not pervaded medical routine yet. This review aims to answer the question whether the methodology is ready for prime time use. The current methodological consensus is assessed, existing technologies for waveform measurement and pulse wave analysis are discussed, and further needs for a widespread use are proposed.

RECENT FINDINGS

A consensus document on the understanding and analysis of the pulse waveform was published recently. Although still some discrepancies remain, the analysis using both pressure and flow waves is favoured. However, devices which enable pulse wave measurement are limited, and the comparability between devices is not sufficiently given. Pulse waveform analysis has the potential for prime time. It is currently on a way towards broader use, but still needs to overcome challenges before settling its role in medical routine.

Towards a consensus on the understanding and analysis of the pulse waveform: Results from the 2016 Workshop on Arterial Hemodynamics: Past, present and future

This paper aims to summarize and map contemporary views on some contentious aspects of arterial hemodynamics that have remained unresolved despite years of research. These were discussed during a workshop entitled Arterial hemodynamics: past, present and future held in London on June 14 and 15, 2016. To do this we formulated a list of potential consensus statements informed by discussion at the meeting in London and quantified the degree of agreement and invited comments from the participants of the workshop. Overall the responses and comments show a high measure of quantitative agreement with the various proposed 'consensus' statements. Taken together, these statements seem a useful basis for proceeding with a more detailed and comprehensive consensus document on the current understanding and approaches to analysis of the pulse waveform. Future efforts should be directed at identifying remaining areas of dispute and future topics for research.

The aortic reservoir-wave as a paradigm for arterial haemodynamics: insights from three-dimensional fluid-structure interaction simulations in a model of aortic coarctation

BACKGROUND

The reservoir-wave paradigm considers aortic pressure as the superposition of a 'reservoir pressure', directly related to changes in reservoir volume, and an 'excess' component ascribed to wave dynamics. The change in reservoir pressure is assumed to be proportional to the difference between aortic inflow and outflow (i.e. aortic volume changes), an assumption that is virtually impossible to validate in vivo. The aim of this study is therefore to apply the reservoir-wave paradigm to aortic pressure and flow waves obtained from three-dimensional fluid-structure interaction simulations in a model of a normal aorta, aortic coarctation (narrowed descending aorta) and stented coarctation (stiff segment in descending aorta).

METHOD AND RESULTS

We found no unequivocal relation between the intraaortic volume and the reservoir pressure for any of the simulated cases. When plotted in a pressure-volume diagram, hysteresis loops are found that are looped in a clockwise way indicating that the reservoir pressure is lower than the pressure associated with the change in volume. The reservoir-wave analysis leads to very high excess pressures, especially for the coarctation models, but to surprisingly little changes of the reservoir component despite the impediment of the buffer capacity of the aorta.

CONCLUSION

With the observation that reservoir pressure is not related to the volume in the aortic reservoir in systole, an intrinsic assumption in the wave-reservoir concept is invalidated and, consequently, also the assumption that the excess pressure is the component of pressure that can be attributed to wave travel and reflection.

Attenuation of reflected waves in man during retrograde propagation from femoral artery to proximal aorta

BACKGROUND

Wave reflection may be an important influence on blood pressure, but the extent to which reflections undergo attenuation during retrograde propagation has not been studied. We quantified retrograde transmission of a reflected wave created by occlusion of the left femoral artery in man.

METHODS

20 subjects (age 31-83 years; 14 male) underwent invasive measurement of pressure and flow velocity with a sensor-tipped intra-arterial wire at multiple locations distal to the proximal aorta before, during and following occlusion of the left femoral artery by thigh cuff inflation. A numerical model of the circulation was also used to predict reflected wave transmission. Wave reflection was measured as the ratio of backward to forward wave energy (WRI) and the ratio of peak backward to forward pressure (Pb/Pf).

RESULTS

Cuff inflation caused a marked reflection which was largest at 5-10 cm from the cuff (change (Δ) in WRI=0.50 (95% CI 0.38, 0.62); p<0.001, ΔPb/Pf=0.23 (0.18-0.29); p<0.001). The magnitude of the cuff-induced reflection decreased progressively at more proximal locations and was barely discernible at sites>40 cm from the cuff including in the proximal aorta. Numerical modelling gave similar predictions to those observed experimentally.

CONCLUSIONS

Reflections due to femoral artery occlusion are markedly attenuated by the time they reach the proximal aorta. This is due to impedance mismatches of bifurcations traversed in the backward direction. This degree of attenuation is inconsistent with the idea of a large discrete reflected wave arising from the lower limb and propagating back into the aorta.

Associations and clinical relevance of aortic-brachial artery stiffness mismatch, aortic reservoir function, and central pressure augmentation

Central augmentation pressure (AP) and index (AIx) predict cardiovascular events and mortality, but underlying physiological mechanisms remain disputed. While traditionally believed to relate to wave reflections arising from proximal arterial impedance (and stiffness) mismatching, recent evidence suggests aortic reservoir function may be a more dominant contributor to AP and AIx. Our aim was therefore to determine relationships among aortic-brachial stiffness mismatching, AP, AIx, aortic reservoir function, and end-organ disease. Aortic (aPWV) and brachial (bPWV) pulse wave velocity were measured in 359 individuals (aged 61 ± 9, 49% male). Central AP, AIx, and aortic reservoir indexes were derived from radial tonometry. Participants were stratified by positive (bPWV > aPWV), negligible (bPWV ≈ aPWV), or negative stiffness mismatch (bPWV < aPWV). Left-ventricular mass index (LVMI) was measured by two-dimensional-echocardiography. Central AP and AIx were higher with negative stiffness mismatch vs. negligible or positive stiffness mismatch (11 ± 6 vs. 10 ± 6 vs. 8 ± 6 mmHg, P < 0.001 and 24 ± 10 vs. 24 ± 11 vs. 21 ± 13%, P = 0.042). Stiffness mismatch (bPWV-aPWV) was negatively associated with AP (r = -0.18, P = 0.001) but not AIx (r = -0.06, P = 0.27). Aortic reservoir pressure strongly correlated to AP (r = 0.81, P < 0.001) and AIx (r = 0.62, P < 0.001) independent of age, sex, heart rate, mean arterial pressure, and height (standardized β = 0.61 and 0.12, P ≤ 0.001). Aortic reservoir pressure independently predicted abnormal LVMI (β = 0.13, P = 0.024). Positive aortic-brachial stiffness mismatch does not result in higher AP or AIx. Aortic reservoir function, rather than discrete wave reflection from proximal arterial stiffness mismatching, provides a better model description of AP and AIx and also has clinical relevance as evidenced by an independent association of aortic reservoir pressure with LVMI.

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.

Genesis of the characteristic pulmonary venous pressure waveform as described by the reservoir-wave model

Conventional haemodynamic analysis of pulmonary venous and left atrial (LA) pressure waveforms yields substantial forward and backward waves throughout the cardiac cycle; the reservoir wave model provides an alternative analysis with minimal waves during diastole. Pressure and flow in a single pulmonary vein (PV) and the main pulmonary artery (PA) were measured in anaesthetized dogs and the effects of hypoxia and nitric oxide, volume loading, and positive-end expiratory pressure (PEEP) were observed. The reservoir wave model was used to determine the reservoir contribution to PV pressure and flow. Subtracting reservoir pressure and flow resulted in 'excess' quantities which were treated as wave-related.Wave intensity analysis of excess pressure and flow quantified the contributions of waves originating upstream (from the PA) and downstream (from the LA and/or left ventricle (LV)).Major features of the characteristic PV waveform are caused by sequential LA and LV contraction and relaxation creating backward compression (i.e.pressure-increasing) waves followed by decompression (i.e. pressure-decreasing) waves. Mitral valve opening is linked to a backwards decompression wave (i.e. diastolic suction). During late systole and early diastole, forward waves originating in the PA are significant. These waves were attenuated less with volume loading and delayed with PEEP. The reservoir wave model shows that the forward and backward waves are negligible during LV diastasis and that the changes in pressure and flow can be accounted for by the discharge of upstream reservoirs. In sharp contrast, conventional analysis posits forward and backward waves such that much of the energy of the forward wave is opposed by the backward wave.

Wave reflections in the pulmonary arteries analysed with the reservoir-wave model

Conventional haemodynamic analysis of pressure and flow in the pulmonary circulation yields incident and reflected waves throughout the cardiac cycle, even during diastole. The reservoir-wave model provides an alternative haemodynamic analysis consistent with minimal wave activity during diastole. Pressure and flow in the main pulmonary artery were measured in anaesthetized dogs and the effects of hypoxia and nitric oxide, volume loading and positive end-expiratory pressure were observed. The reservoir-wave model was used to determine the reservoir contribution to pressure and flow and once subtracted, resulted in 'excess' quantities, which were treated as wave-related. Wave intensity analysis quantified the contributions of waves originating upstream (forward-going waves) and downstream (backward-going waves). In the pulmonary artery, negative reflections of incident waves created by the right ventricle were observed. Overall, the distance from the pulmonary artery valve to this reflection site was calculated to be 5.7 ± 0.2 cm. During 100% O2 ventilation, the strength of these reflections increased 10% with volume loading and decreased 4% with 10 cmH2O positive end-expiratory pressure. In the pulmonary arterial circulation, negative reflections arise from the junction of lobar arteries from the left and right pulmonary arteries. This mechanism serves to reduce peak systolic pressure, while increasing blood flow.

Hemodynamic and arterial stiffness differences between African-Americans and Caucasians after maximal exercise

African-American (AA) men have higher arterial stiffness and augmentation index (AIx) than Caucasian-American (CA) men. Women have greater age-associated increases in arterial stiffness and AIx than men. This study examined racial and sex differences in arterial stiffness and central hemodynamics at rest and after an acute bout of maximal exercise in young healthy individuals. One hundred young, healthy individuals (28 AA men, 24 AA women, 25 CA men, and 23 CA women) underwent measurements of aortic blood pressure (BP) and arterial stiffness at rest and 15 and 30 min after an acute bout of graded maximal aerobic exercise. Aortic BP and AIx were derived from radial artery applanation tonometry. Aortic stiffness (carotid-femoral) was measured via pulse wave velocity. Aortic stiffness was increased in AA subjects but not in CA subjects (P < 0.05) after an acute bout of maximal cycling exercise, after controlling for body mass index. Aortic BP decreased after exercise in CA subjects but not in AA subjects (P < 0.05). Women exhibited greater reductions in AIx after maximal aerobic exercise compared with men (P < 0.05). In conclusion, race and sex impact vascular and central hemodynamic responses to exercise. Young AA and CA subjects exhibited differential responses in central stiffness and central BP after acute maximal exercise. Premenopausal women had greater augmented pressure at rest and after maximal aerobic exercise than men. Future research is needed to examine the potential mechanisms.