The case for the reservoir-wave approach

Generalization Error of a Regression Model for Non-Invasive Blood Pressure Monitoring using a Single Photoplethysmography (PPG) Signal

Photoplethysmography (PPG) sensors integrated in wearable devices offer the potential to monitor arterial blood pressure (ABP) in patients. Such cuffless, non-invasive, and continuous solution is suitable for remote and ambulatory monitoring. A machine learning model based on PPG signal can be used to detect hypertension, estimate beat-by-beat ABP values, and even reconstruct the shape of the ABP. Overall, models presented in literature have shown good performance, but there is a gap between research and potential real-world use cases. Usually, models are trained and tested on data from the same dataset and same subjects, which may lead to overestimating their accuracy. In this paper: we compare cross-validation, where the test data are from the same dataset as training data, and external validation, where the model is tested on samples from a new dataset, on a regression model which predicts diastolic blood pressure from PPG features. The results show that, in the cross-validation, the predicted and the real values are linearly dependent, while in the external validation, the predicted values are not related to the real ones, but probably just through an average value.

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.

Aortic Biomechanics and Clinical Applications

The aorta contributes to cardiovascular physiology and function. Understanding biomechanics in health, disease, and after aortic interventions will facilitate optimization of perioperative patient care.

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.

Wave propagation and reflection in the aorta and implications of the aortic Windkessel

Some have said that it is inappropriate and perhaps impossible to consider wave and Windkessel phenomena simultaneously. For 50 years, arterial hemodynamics has been dominated by the frequency-domain “impedance analysis” in which it was assumed that all variations in aortic pressure and flow were caused only by forward- and backward-going waves. This paper is a review of the results of incorporating the effects of Frank’s Windkessel. We have taken the view that measured aortic pressure is the sum of a Windkessel component and forward-going and backward-going wave components. When the Windkessel component is initially subtracted out, the pattern of propagation and reflection of wave components becomes clear. Furthermore, this analysis obviates the implications of impedance analysis that have not been explained satisfactorily.

Impact of varying diastolic pressure fitting technique for the reservoir-wave model on wave intensity analysis

The reservoir-wave model assumes that the measured arterial pressure is made of two components: reservoir and excess. The effect of the reservoir volume should be excluded to quantify the effects of forward and backward traveling waves on blood pressure. Whilst the validity of the reservoir-wave concept is still debated, there is no consensus on the best fitting method for the calculation of the reservoir pressure waveform. Therefore, the aim of this parametric study is to examine the effects of varying the fitting technique on the calculation of reservoir and excess components of pressure and velocity waveforms. Common carotid pressure and flow velocity were measured using applanation tonometry and doppler ultrasound, respectively, in 1037 healthy humans collected randomly from the Asklepios population, aged 35 to 55 years old. Different fitting techniques to the diastolic decay of the measured arterial pressure were used to determine the asymptotic pressure decay, which in turn was used to determine the reservoir pressure waveform. The corresponding wave speed was determined using the PU-loop method, and wave intensity parameters were calculated and compared. Different fitting methods resulted in significant changes in the shape of the reservoir pressure waveform; however, its peak and time integral remained constant in this study. Although peak and integral of excess pressure, velocity components and wave intensity changed significantly with changing the diastolic decay fitting method, wave speed was not substantially modified. We conclude that wave speed, peak reservoir pressure and its time integral are independent of the diastolic pressure decay fitting techniques examined in this study. Therefore, these parameters are considered more reliable diagnostic indicators than excess pressure and velocity which are more sensitive to fitting techniques.

Phylogenic Determinants of Cardiovascular Frailty, Focus on Hemodynamics and Arterial Smooth Muscle Cells

The evolution of the circulatory system from invertebrates to mammals has involved the passage from an open system to a closed in-parallel system via a closed in-series system, accompanying the increasing complexity and efficiency of life’s biological functions. The archaic heart enables pulsatile motion waves of hemolymph in invertebrates, and the in-series circulation in fish occurs with only an endothelium, whereas mural smooth muscle cells appear later. The present review focuses on evolution of the circulatory system. In particular, we address how and why this evolution took place from a closed, flowing, longitudinal conductance at low pressure to a flowing, highly pressurized and bifurcating arterial compartment. However, although arterial pressure was the latest acquired hemodynamic variable, the general teleonomy of the evolution of species is the differentiation of individual organ function, supported by specific fueling allowing and favoring partial metabolic autonomy. This was achieved via the establishment of an active contractile tone in resistance arteries, which permitted the regulation of blood supply to specific organ activities via its localized function-dependent inhibition (active vasodilation). The global resistance to viscous blood flow is the peripheral increase in frictional forces caused by the tonic change in arterial and arteriolar radius, which backscatter as systemic arterial blood pressure. Consequently, the arterial pressure gradient from circulating blood to the adventitial interstitium generates the unidirectional outward radial advective conductance of plasma solutes across the wall of conductance arteries. This hemodynamic evolution was accompanied by important changes in arterial wall structure, supported by smooth muscle cell functional plasticity, including contractility, matrix synthesis and proliferation, endocytosis and phagocytosis, etc. These adaptive phenotypic shifts are due to epigenetic regulation, mainly related to mechanotransduction. These paradigms actively participate in cardio-arterial pathologies such as atheroma, valve disease, heart failure, aneurysms, hypertension, and physiological aging.

Quantification of Pulsed Operation of Rotary Left Ventricular Assist Devices with Wave Intensity Analysis

The current generation of left ventricular assist devices (LVADs) provides continuous flow and has the capacity to reduce aortic pulsatility, which may be related to a range of complications associated with these devices. Pulsed LVAD operation using speed modulation presents a mechanism to restore aortic pulsatility and potentially mitigate complications. We sought to investigate the interaction of axial and centrifugal LVADs with the LV and quantify the effects of continuous and pulsed LVAD operations on LV generated wave patterns under different physiologic conditions using wave intensity analysis (WIA) method. The axial LVAD created greater wave intensity associated with LV relaxation. In both LVADs, there were only minor and variable differences between the continuous and pulsed operations. The response to physiologic stress was preserved with LVAD implantation as wave intensity increased marginally with volume loading and significantly with infusion of norepinephrine. Our findings and a new approach of investigating aortic wave patterns based on WIA are expected to provide useful clinical insights to determine the ideal operation of LVADs.

Associations of Reservoir-Excess Pressure Parameters Derived From Central and Peripheral Arteries With Kidney Function

BACKGROUND

Central artery reservoir-excess pressure parameters are clinically important but impractical to record directly. However, diastolic waveform morphology is consistent across central and peripheral arteries. Therefore, peripheral artery reservoir-excess pressure parameters related to diastolic waveform morphology may be representative of central parameters and share clinically important associations with end-organ damage. This has never been determined and was the aim of this study.

METHODS

Intra-arterial blood pressure (BP) waveforms were measured sequentially at the aorta, brachial, and radial arteries among 220 individuals (aged 61 ± 10 years, 68% male). Customized software was used to derive reservoir-excess pressure parameters at each arterial site (reservoir and excess pressure, systolic and diastolic rate constants) and clinical relevance was determined by association with estimated glomerular filtration rate (eGFR).

RESULTS

Between the aorta and brachial artery, the mean difference in the diastolic rate constant and reservoir pressure integral was -0.162 S-1 (P = 0.08) and -0.772 mm Hg s (P = 0.23), respectively. The diastolic rate constant had the strongest and most consistent associations with eGFR across aortic and brachial sites (β = -0.20, P = 0.02; β = -0.20, P = 0.03, respectively; adjusted for traditional cardiovascular risk factors). Aortic, but not brachial peak reservoir pressure was associated with eGFR in adjusted models (aortic β = -0.48, P = 0.02).

CONCLUSIONS

The diastolic rate constant is the most consistent reservoir-excess pressure parameter, in both its absolute values and associations with kidney dysfunction, when derived from the aorta and brachial artery. Thus, the diastolic rate constant could be utilized in the clinical setting to improve BP risk stratification.

Clinically applicable model-based method, for physiologically accurate flow waveform and stroke volume estimation

BACKGROUND AND OBJECTIVES

Cardiovascular dysfunction can be more effectively monitored and treated, with accurate, continuous, stroke volume (SV) and/or cardiac output (CO) measurements. Since direct measurements of SV/CO are highly invasive, clinical measures are often discrete, or if continuous, can require recalibration with a discrete SV measurement after hemodynamic instability. This study presents a clinically applicable, non-additionally invasive, physiological model-based, SV and CO measurement method, which does not require recalibration during or after hemodynamic instability.

METHODS AND RESULTS

The model's ability to predict flow profiles and SV is assessed in an animal trial, using endotoxin to induce sepsis in 5 pigs. Mean percentage error between beat-to-beat SV measured from an aortic flow probe and estimated by the model was -2%, while 90% of estimations fell within -24.2% and +27.9% error. Error between estimated and measured changes in mean SV following interventions was less than 30% for 4 out of the 5 pigs. Correlations between model estimated and probe measured flow, for each pig and hemodynamic interventions, was r² = 0.58 - 0.96, with 21 of the 25 pig intervention stages having r²  >  0.80.

CONCLUSION

The results demonstrate the model accurately estimates and tracks changes in flow profiles and resulting SV, without requiring model recalibration.

Determinants of Increased Central Excess Pressure in Dialysis: Role of Dialysis Modality and Arteriovenous Fistula

BACKGROUND

Arterial reservoir-wave analysis (RWA)-a new model of arterial hemodynamics-separates arterial wave into reservoir pressure (RP) and excess pressure (XSP). The XSP integral (XSPI) has been associated with increased risk of clinical outcomes. The objectives of the present study were to examine the determinants of XSPI in a mixed cohort of hemodialysis (HD) and peritoneal dialysis (PD) patients, to examine whether dialysis modality and the presence of an arteriovenous fistula (AVF) are associated with increased XSPI.

METHOD

In a cross-sectional study, 290 subjects (232 HD and 130 with AVF) underwent carotid artery tonometry (calibrated with brachial diastolic and mean blood pressure). The XSPI was calculated through RWA using pressure-only algorithms. Logistic regression was used for determinants of XSPI above median. Through forward conditional linear regression, we examined whether treatment by HD or the presence of AVF is associated with higher XSPI.

RESULTS

Patients with XSPI above median were older, had a higher prevalence of diabetes and cardiovascular disease, had a higher body mass index, and were more likely to be on HD. After adjustment for confounders, HD was associated with a higher risk of higher XSPI (odds ratio = 2.39, 95% confidence interval: 1.16-4.98). In a forward conditional linear regression analysis, HD was associated with higher XSPI (standardized coefficient: 0.126, P = 0.012), but on incorporation of AVF into the model, AVF was associated with higher XSPI (standardized coefficient: 0.130, P = 0.008) and HD was excluded as a predictor.

CONCLUSION

This study suggests that higher XSPI in HD patients is related to the presence of AVF.

Prognostic Value of Carotid and Radial Artery Reservoir-Wave Parameters in End-Stage Renal Disease

Background Reservoir-wave approach is an alternative model of arterial hemodynamics based on the assumption that measured arterial pressure is composed of volume-related (reservoir pressure) and wave-related components (excess pressure). However, the clinical utility of reservoir-wave approach remains debatable. Methods and Results In a single-center cohort of 260 dialysis patients, we examined whether carotid and radial reservoir-wave parameters were associated with all-cause and cardiovascular mortality. Central pulse pressure and augmentation index at 75 beats per minute were determined by radial arterial tonometry through generalized transfer function. Carotid and radial reservoir-wave analysis were performed to determine reservoir pressure and excess pressure integral. After a median follow-up of 32 months, 171 (66%) deaths and 88 (34%) cardiovascular deaths occurred. In Cox regression analysis, carotid excess pressure integral was associated with a hazard ratio of 1.33 (95% CI , 1.14-1.54; P<0.001 per 1 SD) for all-cause and 1.45 (95% CI : 1.18-1.75; P<0.001 per 1 SD) for cardiovascular mortality. After adjustments for age, heart rate, sex, clinical characteristics and carotid-femoral pulse wave velocity, carotid excess pressure integral was consistently associated with increased risk of all-cause (hazard ratio per 1 SD, 1.30; 95% CI : 1.08-1.54; P=0.004) and cardiovascular mortality (hazard ratio per 1 SD, 1.31; 95% CI : 1.04-1.63; P=0.019). Conversely, there were no significant associations between radial reservoir-wave parameters, central pulse pressure, augmentation index at 75 beats per minute, pressure forward, pressure backward and reflection magnitude, and all-cause or cardiovascular mortality after adjustment for comorbidities. Conclusions These observations support the clinical value of reservoir-wave approach parameters of large central elastic vessels in end-stage renal disease.

Wave Intensity Analysis of Right Ventricular Function during Pulsed Operation of Rotary Left Ventricular Assist Devices

Changing the speed of left ventricular assist devices (LVADs) cyclically may be useful to restore aortic pulsatility; however, the effects of this pulsation on right ventricular (RV) function are unknown. This study investigates the effects of direct ventricular interaction by quantifying the amount of wave energy created by RV contraction when axial and centrifugal LVADs are used to assist the left ventricle. In 4 anesthetized pigs, pressure and flow were measured in the main pulmonary artery and wave intensity analysis was used to identify and quantify the energy of waves created by the RV. The axial pump depressed the intensity of waves created by RV contraction compared with the centrifugal pump. In both pump designs, there were only minor and variable differences between the continuous and pulsed operation on RV function. The axial pump causes the RV to contract with less energy compared with a centrifugal design. Diminishing the ability of the RV to produce less energy translates to less pressure and flow produced, which may lead to LVAD-induced RV failure. The effects of pulsed LVAD operation on the RV appear to be minimal during acute observation of healthy hearts. Further study is necessary to uncover the effects of other modes of speed modulation with healthy and unhealthy hearts to determine if pulsed operation will benefit patients by reducing LVAD complications.

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.

Arterial reservoir characteristics and central-to-peripheral blood pressure amplification in the human upper limb

BACKGROUND

Arterial reservoir characteristics are related to blood pressure (BP) and independently predict cardiovascular events. It is unknown if arterial reservoir characteristics are modified from the central-to-peripheral large arteries and whether there is a contributory role to BP amplification. The aim of this study was to assess central-to-peripheral changes in arterial reservoir characteristics and determine associations with BP.

METHODS

Reservoir pressure (RP) and excess pressure (XSP) were derived from intra-arterial BP waveforms among 51 participants (aged 63 ± 13 years, 63% men) undergoing clinically indicated cardiac angiography. BP waveforms were recorded in the ascending aorta, brachial (mid-humerus) and radial (wrist) arteries via catheter pull-back.

RESULTS

There was no significant difference in RP between arterial sites (54 ± 15, 53 ± 15 and 52 ± 17 mmHg for the aorta, brachial and radial artery, respectively; P = 0.68). Conversely, XSP increased stepwise from the aorta to the brachial and radial arteries (24 ± 11, 42 ± 14 and 53 ± 16 mmHg; P < 0.001), as did SBP (134 ± 18, 141 ± 16 and 146 ± 19 mmHg; P = 0.004). There were highly significant associations between RP and SBP at all arterial sites (r = 0.821, 0.649 and 0.708; P < 0.001 for all), but the strength of associations between peak XSP and SBP increased significantly from the aorta to the radial artery (r = 0.121 and 0.508; z = 3.04; P = 0.004).

CONCLUSION

Arterial reservoir characteristics are modified through the large arteries of the upper limb. Although RP remains relatively constant, XSP increases significantly and is highly related to BP (SBP and pulse pressure) amplification. These data provide a new understanding on arterial reservoir characteristics and large-artery BP physiology.

Fluid mechanics of Windkessel effect

We describe a mechanistic model of Windkessel phenomenon based on the linear dynamics of fluid-structure interactions. The phenomenon has its origin in an old-fashioned fire-fighting equipment where an air chamber serves to transform the intermittent influx from a pump to a more steady stream out of the hose. A similar mechanism exists in the cardiovascular system where blood injected intermittantly from the heart becomes rather smooth after passing through an elastic aorta. In existing haeodynamics literature, this mechanism is explained on the basis of electric circuit analogy with empirical impedances. We present a mechanistic theory based on the principles of fluid/structure interactions. Using a simple one-dimensional model, wave motion in the elastic aorta is coupled to the viscous flow in the rigid peripheral artery. Explicit formulas are derived that exhibit the role of material properties such as the blood density, viscosity, wall elasticity, and radii and lengths of the vessels. The current two-element model in haemodynamics is shown to be the limit of short aorta and low injection frequency and the impedance coefficients are derived theoretically. Numerical results for different aorta lengths and radii are discussed to demonstrate their effects on the time variations of blood pressure, wall shear stress, and discharge. Graphical Abstract A mechanistic analysis of Windkessel Effect is described which confirms theoretically the well-known feature that intermittent influx becomes continuous outflow. The theory depends only on the density and viscosity of the blood, the elasticity and dimensions of the vessel. Empirical impedence parameters are avoided.

Value of Excess Pressure Integral for Predicting 15-Year All-Cause and Cardiovascular Mortalities in End-Stage Renal Disease Patients

BACKGROUND

The excess pressure integral (XSPI), derived from analysis of the arterial pressure curve, may be a significant predictor of cardiovascular events in high-risk patients. We comprehensively investigated the prognostic value of XSPI for predicting long-term mortality in end-stage renal disease patients undergoing regular hemodialysis.

METHODS AND RESULTS

A total of 267 uremic patients (50.2% female; mean age 54.2±14.9 years) receiving regular hemodialysis for more than 6 months were enrolled. Cardiovascular parameters were obtained by echocardiography and applanation tonometry. Calibrated carotid arterial pressure waveforms were analyzed according to the wave-transmission and reservoir-wave theories. Multivariable Cox proportional hazard models were constructed to account for age, sex, diabetes mellitus, albumin, body mass index, and hemodialysis treatment adequacy. Incremental utility of the parameters to risk stratification was assessed by net reclassification improvement. During a median follow-up of 15.3 years, 124 deaths (46.4%) incurred. Baseline XSPI was significantly predictive of all-cause (hazard ratio per 1 SD 1.4, 95% confidence interval 1.15-1.70, P=0.0006) and cardiovascular mortalities (1.47, 1.18-1.84, P=0.0006) after accounting for the covariates. The addition of XSPI to the base prognostic model significantly improved prediction of both all-cause mortality (net reclassification improvement=0.1549, P=0.0012) and cardiovascular mortality (net reclassification improvement=0.1535, P=0.0033). XSPI was superior to carotid-pulse wave velocity, forward and backward wave amplitudes, and left ventricular ejection fraction in consideration of overall independent and incremental prognostics values.

CONCLUSIONS

In end-stage renal disease patients undergoing regular hemodialysis, XSPI was significantly predictive of long-term mortality and demonstrated an incremental value to conventional prognostic factors.

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.

Improved pressure contour analysis for estimating cardiac stroke volume using pulse wave velocity measurement

BACKGROUND

Pressure contour analysis is commonly used to estimate cardiac performance for patients suffering from cardiovascular dysfunction in the intensive care unit. However, the existing techniques for continuous estimation of stroke volume (SV) from pressure measurement can be unreliable during hemodynamic instability, which is inevitable for patients requiring significant treatment. For this reason, pressure contour methods must be improved to capture changes in vascular properties and thus provide accurate conversion from pressure to flow.

METHODS

This paper presents a novel pressure contour method utilizing pulse wave velocity (PWV) measurement to capture vascular properties. A three-element Windkessel model combined with the reservoir-wave concept are used to decompose the pressure contour into components related to storage and flow. The model parameters are identified beat-to-beat from the water-hammer equation using measured PWV, wave component of the pressure, and an estimate of subject-specific aortic dimension. SV is then calculated by converting pressure to flow using identified model parameters. The accuracy of this novel method is investigated using data from porcine experiments (N = 4 Pietrain pigs, 20-24.5 kg), where hemodynamic properties were significantly altered using dobutamine, fluid administration, and mechanical ventilation. In the experiment, left ventricular volume was measured using admittance catheter, and aortic pressure waveforms were measured at two locations, the aortic arch and abdominal aorta.

RESULTS

Bland-Altman analysis comparing gold-standard SV measured by the admittance catheter and estimated SV from the novel method showed average limits of agreement of ±26% across significant hemodynamic alterations. This result shows the method is capable of estimating clinically acceptable absolute SV values according to Critchely and Critchely.

CONCLUSION

The novel pressure contour method presented can accurately estimate and track SV even when hemodynamic properties are significantly altered. Integrating PWV measurements into pressure contour analysis improves identification of beat-to-beat changes in Windkessel model parameters, and thus, provides accurate estimate of blood flow from measured pressure contour. The method has great potential for overcoming weaknesses associated with current pressure contour methods for estimating SV.

Excess Pressure Integral Predicts Long-Term All-Cause Mortality in Stable Heart Failure Patients

BACKGROUND

Excess pressure integral (XSPI) derived from reservoir-excess pressure analysis is proposed as a novel indicator of cardiovascular dysfunction in hypertensives. Our study investigated the prognostic value of XSPI for stable heart failure (HF) patients.

METHODS

In total, 238 subjects (mean age 63 ± 18 years, 111 male), comprising 168 stable HF patients with either reduced (SHF; n = 64) left ventricular (LV) ejection fraction (EF) or isolated diastolic dysfunction (DHF, n = 104), and 70 healthy controls, were enrolled. Tonometry-derived carotid pressure waveforms were analyzed with the reservoir pressure theory. XSPI was calculated by subtracting the reservoir pressure from carotid pressure waveform.

RESULTS

XSPI in SHF and DHF (14.01 ± 5.16 and 13.90 ± 5.05 mm Hg•s) were significantly higher than that in controls (11.01 ± 3.67 mm Hg•s, both P < 0.001). During a median follow-up of 9.9 years, 56 deaths occurred. XSPI was a significant independent predictor of total mortality after adjusting for age, sex, left ventricular ejection fraction (LVEF), glomerular filtration rate (GFR), and N-terminal pro-B-type natriuretic peptide (NT-proBNP) (hazard ratio = 4.37 per 1 SD, 95% confidence interval, 1.31-14.58). In subgroup analysis by different baseline characteristics including age, gender, NT-proBNP, LVEF, and GFR, higher XSPI was consistently associated with greater risk of total mortality.

CONCLUSION

In patients with stable HF, XSPI, a novel maker of cardiovascular dysfunction, was associated with long-term risk of total mortality.

The reservoir-wave approach to characterize pulmonary vascular-right ventricular interactions in humans

Using the reservoir-wave approach (RWA) we previously characterized pulmonary vasculature mechanics in a normal canine model. We found reflected backward-traveling waves that decrease pressure and increase flow in the proximal pulmonary artery (PA). These waves decrease right ventricular (RV) afterload and facilitate RV ejection. With pathological alterations to the pulmonary vasculature, these waves may change and impact RV performance. Our objective in this study was to characterize PA wave reflection and the alterations in RV performance in cardiac patients, using the RWA. PA pressure, Doppler-flow velocity, and pulmonary arterial wedge pressure were measured in 11 patients with exertional dyspnea. The RWA was employed to analyze PA pressure and flow; wave intensity analysis characterized PA waves. Wave-related pressure was partitioned into two components: pressures due to forward-traveling and to backward-traveling waves. RV performance was assessed by examining the work done in raising reservoir pressure and that associated with the wave components of systolic PA pressure. Wave-related work, the mostly nonrecoverable energy expended by the RV to eject blood, tended to vary directly with mean PA pressure. Where PA pressures were lower, there were pressure-decreasing/flow-increasing backward waves that aided RV ejection. Where PA pressures were higher, there were pressure-increasing/flow-decreasing backward waves that impeded RV ejection. Pressure-increasing/flow-decreasing backward waves were responsible for systolic notches in the Doppler flow velocity profiles in patients with the highest PA pressure. Pulmonary hypertension is characterized by reflected waves that impede RV ejection and an increase in wave-related work. The RWA may facilitate the development of therapeutic strategies.

Prognostic significance of mechanical biomarkers derived from pulse wave analysis for predicting long-term cardiovascular mortality in two population-based cohorts

BACKGROUND

Numerous mechanical biomarkers derived from pulse wave analysis (PWA) have been proposed to predict cardiovascular outcomes. However, whether these biomarkers carry independent prognostic value and clinical utility beyond traditional cardiovascular risk factors hasn't been systematically evaluated. We aimed to investigate the additive utility of PWA-derived biomarkers in two independent population-based cohorts.

METHODS

PWA on central arterial pressure waveforms obtained from subjects without a prior history of cardiovascular diseases of two studies was conducted based on the wave transmission and reservoir-wave theory: firstly in the Kinmen study (1272 individuals, a median follow-up of 19.8years); and then in the Cardiovascular Disease Risk Factors Two-Township Study (2221 individuals, median follow-up of 10years). The incremental value of the biomarkers was evaluated by net reclassification index (NRI).

RESULTS

In multivariate Cox analyses accounting for age, gender, body mass index, systolic blood pressure, fasting glucose, high-density- and low-density-lipoprotein cholesterol, and smoking, only systolic (SC) and diastolic rate constant (DC) of reservoir pressure could independently and consistently predict cardiovascular mortality in both cohorts and the combined cohort (SC: hazard ratio 1.18 [95% confidence interval 1.08-1.28, p<0.001; DC: 1.18 [1.09-1.28], p<0.001]. Risk prediction estimates in traditional risk prediction models were significantly more accurate when incorporating peak of reservoir pressure (NRI=0.049, p=0.0361), SC (NRI=0.043, p=0.0236) and DC (NRI=0.054, p=0.047).

CONCLUSIONS

Of all PWA-derived biomarkers, SC and DC were consistently identified as valuable parameters for incremental cardiovascular risk prediction in two large prospective cohorts.

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.

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.

Assessment and prognosis of peripheral artery measures of vascular function

The endothelium plays a crucial role in the regulation of vascular homeostasis. Our understanding of its role in health and disease has increased dramatically since the pivotal discovery of nitric oxide more than 30 years ago. Clinical researchers utilized emerging technologies to study the vasodilator properties of the endothelium in both the coronary and peripheral circulation. Early studies established the methodologies and were able to demonstrate attenuated endothelium-dependent vasodilation in response to atherosclerosis and its risk factors. A variety of interventions can modulate endothelial function. More recent studies have established that some of these measures are independent predictors of cardiovascular outcomes. As such, peripheral measures of endothelial function are now established surrogate markers of vascular risk and have become important markers for clinical research. In this review, we will discuss a variety of measures of peripheral artery function to assess both conduit and resistance vessel function in humans.

Effects of Thoratec pulsatile ventricular assist device timing on the abdominal aortic wave intensity pattern

Arterial waves are seen as possible independent mediators of cardiovascular risks, and the wave intensity analysis (WIA) has therefore been proposed as a method for patient selection for ventricular assist device (VAD) implantation. Interpreting measured wave intensity (WI) is challenging, and complexity is increased by the implantation of a VAD. The waves generated by the VAD interact with the waves generated by the native heart, and this interaction varies with changing VAD settings. Eight sheep were implanted with a pulsatile VAD (PVAD) through ventriculoaortic cannulation. The start of PVAD ejection was synchronized to the native R wave and delayed between 0 and 90% of the cardiac cycle in 10% steps or phase shifts (PS). Pressure and velocity signals were registered, with the use of a combined Doppler and pressure wire positioned in the abdominal aorta, and used to calculate the WI. Depending on the PS, different wave interference phenomena occurred. Maximum unloading of the left ventricle (LV) coincided with constructive interference and maximum blood flow pulsatility, and maximum loading of the LV coincided with destructive interference and minimum blood flow pulsatility. We believe that noninvasive WIA could potentially be used clinically to assess the mechanical load of the LV and to monitor the peripheral hemodynamics such as blood flow pulsatility and risk of intestinal bleeding.

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.