Wave intensity analysis and the development of the reservoir–wave approach

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.

Newly Developed Graft Failure Detected Using Computed Tomography Within 1 Year After Coronary Artery Bypass Grafting Surgery: One Single-Center Experience

Background

Newly developed graft failure negatively affects the short- and long-term outcomes of patients who experience coronary artery bypass grafting (CABG) surgery. This study explored the value of transit time flow measurement (TTFM) parameters for predicting the risk of newly developed graft failure that occurs within 1 year after CABG, as well as investigated the relationship between newly developed graft failure and adverse cardiovascular events.

Methods

A total of 134 patients who underwent CABG and had CT angiography (CTA) data (1 year post-operatively) were divided into two groups: the patient group, in which patients did not have newly developed graft failure, and the occluded group, in which patients developed newly developed graft failure between 1 and 12 months after CABG. The patency rate of grafts in different targets was analyzed. The correlations between graft failure and TTFM parameters and between graft failure and the occurrence of adverse cardiovascular events were investigated.

Results

The overall rate of newly developed graft failure was 7.2%, the venous graft failure was 10.8%, and the arterial graft failure was 0.7%. The occluded group had a higher pulse index (PI) (2.9 vs. 2.4, P = 0.007), a lower mean graft flow (MGF) (20 vs. 25 ml/min, P = 0.028), and a lower diastolic flow fraction (DF) (63.5 vs. 70%, P = 0.019) than the patent group. The cut-off value for predicting newly developed graft failure was PI > 2.75 (P = 0.007), MGF < 23.5 ml/min (P = 0.03), and DF < 65.5% (P = 0.019). Compared with the patent group, the newly developed graft failure group had higher rates of recurrent angina (13.6 vs. 0.9%, P = 0.0014) and revascularization intervention (9.1 vs. 0% P = 0.026). However, there were no differences in death, cardiac death, myocardial infarction, and cerebral infarction after CABG operation between these two groups (P > 0.05).

Conclusions

A high PI and low MGF and DF are risk factors for newly developed graft failure. The patients with newly developed graft failure had higher rates of recurrent angina and revascularization intervention. TTFM parameters may be used to predict the occurrence of newly developed graft failure in patients after CABG surgery.

Modulation of Arterial Stiffness Gradient by Acute Administration of Nitroglycerin

Background: Physiologically, the aorta is less stiff than peripheral conductive arteries, creating an arterial stiffness gradient, protecting microcirculation from high pulsatile pressure. However, the pharmacological manipulation of arterial stiffness gradient has not been thoroughly investigated. We hypothesized that acute administration of nitroglycerin (NTG) may alter the arterial stiffness gradient through a more significant effect on the regional stiffness of medium-sized muscular arteries, as measured by pulse wave velocity (PWV). The aim of this study was to examine the differential impact of NTG on regional stiffness, and arterial stiffness gradient as measured by the aortic-brachial PWV ratio (AB-PWV ratio) and aortic-femoral PWV ratio (AF-PWV ratio).

Methods: In 93 subjects (age: 61 years, men: 67%, chronic kidney disease [CKD]: 41%), aortic, brachial, and femoral stiffnesses were determined by cf-PWV, carotid-radial (cr-PWV), and femoral-dorsalis pedis artery (fp-PWV) PWVs, respectively. The measurements were repeated 5 min after the sublingual administration of NTG (0.4 mg). The AB-PWV and AF-PWV ratios were obtained by dividing cf-PWV by cr-PWV or fp-PWV, respectively. The central pulse wave profile was determined by radial artery tonometry through the generalized transfer function.

Results: At baseline, cf-PWV, cr-PWV, and fp-PWV were 12.12 ± 3.36, 9.51 ± 1.81, and 9.71 ± 1.89 m/s, respectively. After the administration of NTG, there was a significant reduction in cr-PWV of 0.86 ± 1.27 m/s (p < 0.001) and fp-PWV of 1.12 ± 1.74 m/s (p < 0.001), without any significant changes in cf-PWV (p = 0.928), leading to a significant increase in the AB-PWV ratio (1.30 ± 0.39 vs. 1.42 ± 0.46; p = 0.001) and AF-PWV ratio (1.38 ± 0.47 vs. 1.56 ± 0.53; p = 0.001). There was a significant correlation between changes in the AF-PWV ratio and changes in the timing of wave reflection (r = 0.289; p = 0.042) and the amplitude of the heart rate-adjusted augmented pressure (r = − 0.467; p < 0.001).

Conclusion: This study shows that acute administration of NTG reduces PWV of muscular arteries (brachial and femoral) without modifying aortic PWV. This results in an unfavorable profile of AB-PWV and AF-PWV ratios, which could lead to higher pulse pressure transmission into the microcirculation.

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.

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.

The predictive value of intraoperative transit-time flow measurement parameters for early graft failure in different target territories

BACKGROUND

Early graft failure can affect the short- and long-term outcomes of patients undergoing coronary bypass grafting surgery (CABG). The aim of our study was to explore the predictive value of transit-time flow measurement (TTFM) parameters for early graft failure (before discharge) after CABG in different coronary territories and calculate the TTFM cut-off values.

METHODS

We analyzed a total of 761 grafts (360 patients) that were evaluated by intraoperative TTFM and computed tomography angiography prior to discharge. Logistic model was established to detect the parameters of TTFM to predict early graft failure and receiver operating characteristic curve analysis was used to calculate the cut-off values.

RESULTS

The overall early graft failure was 3.5%. The results demonstrated that compared with off-pump CABG, mean graft flow volume was higher (28.0 vs 21.0 mL/min, p = 0.000), but pulse index (PI) (2.3 vs 2.5, p = 0.049) and diastolic flow fraction (DF) (68.0% vs 71.0%, p = 0.001) were lower in on-pump CABGs. DF (73.0% vs 65.5%, p = 0.000) of arterial grafts was higher than that of venous grafts. DF (72.0% vs 62.0%, p = 0.000) in left was higher than that in the right coronary artery territories. The results of multivariate logistic analysis showed that not only in the overall (OR 1.18, 95% CI 1.07-1.30, p = 0.001), but also the left (OR 1.21, 95% CI 1.03-1.41, p = 0.017) and right (OR 1.15, 95% CI 1.03-1.29, p = 0.017) coronary artery target territories, PI was a risk factor for early graft failure and the cut-off value was 3.4, 3.4, and 3.6, respectively. For grafts in left target territories, the results showed that DF (OR 0.94, 95% CI 0.91-0.97, p = 0.000) just in the univariate analysis was a risk factor that affected graft failure.

CONCLUSIONS

The overall early graft failure was about 3.5%. High PI value is a risk factor for early graft failure in not only overall grafts but in grafts of different target territories. DF might be more useful for the quality evaluation of grafts in left than in right target territories.

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.

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.

Ambulatory pulse wave monitoring: current and future. Opinion paper of Russian Experts

The predictive value of vascular biomarkers such as pulse wave velocity (PWV), central arterial pressure (CAP), and augmentation index (AIx), obtained through pulse wave analysis (PWA) in resting conditions, has been documented in a variety of patient groups and populations. There are appropriate recommendations on their clinical use in clinical practice guidelines of various scientific societies. Operator-independent methods are currently available for estimating vascular biomarkers also in ambulatory conditions. The acceptable accuracy and reproducibility of ambulatory PWA makes it be a promising tool for evaluating vascular biomarkers in daily-life conditions. This approach may provide an opportunity to further improve the early cardiovascular screening in subjects at risk. However, there is no sufficient evidence to support the routine clinical use of PWA in ambulatory conditions at the moment. In particular, long-term outcome studies are needed to show the predictive value of ambulatory PWV, CAP and AIx values.

Non-invasive measurement of reservoir pressure parameters from brachial-cuff blood pressure waveforms

Reservoir pressure parameters [eg, reservoir pressure (RP) and excess pressure (XSP)] are biomarkers derived from blood pressure (BP) waveforms that have been shown to predict cardiovascular events independent of conventional cardiovascular risk markers. However, whether RP and XSP can be derived non-invasively from operator-independent cuff device measured brachial or central BP waveforms has never been examined. This study sought to achieve this by comparison of cuff reservoir pressure parameters with intra-aortic reservoir pressure parameters. 162 participants (aged 61 ± 10 years, 72% male) undergoing coronary angiography had the simultaneous measurement of cuff BP waveforms (via SphygmoCor XCEL, AtCor Medical) and intra-aortic BP waveforms (via fluid-filled catheter). RP and XSP derived from cuff acquired brachial and central BP waveforms were compared with intra-aortic measures. Concordance between brachial-cuff and intra-aortic measurement was moderate-to-good for RP peak (36 ± 11 vs 48 ± 14 mm Hg, P < 0.001; ICC 0.77, 95% CI: 0.71-0.82), and poor-to-moderate for XSP peak (28 ± 10 vs 24 ± 9 mm Hg, P < 0.001; ICC 0.49, 95% CI: 0.35-0.60). Concordance between central-cuff and intra-aortic measurement was moderate-to-good for RP peak (35 ± 9 vs 46 ± 14 mm Hg, P < 0.001; ICC 0.77, 95% CI: 0.70-0.82), but poor for XSP peak (12 ± 3 vs 24 ± 9 mm Hg, P < 0.001; ICC 0.12, 95% CI: -0.13 to 0.31). In conclusion, both brachial-cuff and central-cuff methods can reasonably estimate intra-aortic RP, whereas XSP can only be acceptably derived from brachial-cuff BP waveforms. This should enable widespread application to determine the clinical significance, but there is significant room for refinement of the method.

Wave intensity analysis in the internal carotid artery of hypertensive subjects using phase-contrast MR angiography and preliminary assessment of the effect of vessel morphology on wave dynamics

Objective: Hypertension is associated with reduced cerebral blood flow, but it is not known how this impacts on wave dynamics or potentially relates to arterial morphology. Given the location of the internal carotid artery (ICA) and risks associated with invasive measurements, wave dynamics in this artery have not been extensively assessed in vivo. This study explores the feasibility of studying wave dynamics in the internal carotid artery non-invasively. Approach: Normotensive, uncontrolled and controlled hypertensive participants were recruited (daytime ambulatory blood pressure  <135/85 mmHg and  >135/85 mmHg, respectively; n  =  38). Wave intensity, reservoir pressure and statistical shape analyses were performed on the right ICA and ascending aorta high-resolution phase-contrast magnetic resonance angiography data. Main results: Wave speed in the aorta was significantly lower in normotensive compared to hypertensive participants (6.7  ±  1.8 versus 11.2  ±  6.2 m s⁻¹ for uncontrolled and 11.8  ±  4.6 m s⁻¹ for controlled hypertensives, p  =  0.02), whilst there were no differences in wave speed in the ICA. There were no significant differences between the groups for the wave intensity or reservoir pressure. Interestingly, a significant association between the anatomy of the ICA and wave energy (FCW and size, r²  =  0.12, p  =  0.04) was found. Significance: This study shows it is feasible to study wave dynamics in the ICA non-invasively. Whilst changes in aortic wave speed confirmed an expected increase in arterial stiffness, this was not observed in the ICA. This might suggest a protective mechanism in the cerebral circulation, in conjunction with the effect of vessel tortuosity. Furthermore, it was observed that ICA shape correlated with wave energy but not wave speed.

Living Without a Pulse: The Vascular Implications of Continuous-Flow Left Ventricular Assist Devices

Pulsatility seems to have a teleological role because evolutionary hierarchy favors higher ordered animals with more complex, multichamber circulatory systems that generate higher pulse pressure compared with lower ordered animals. Yet despite years of such natural selection, the modern generation of continuous-flow left ventricular assist devices (CF-LVADs) that have been increasingly used for the last decade have created a unique physiology characterized by a nonpulsatile, nonlaminar blood flow profile with the absence of the usual large elastic artery Windkessel effect during diastole. Although outcomes and durability have improved with CF-LVADs, patients supported with CF-LVADs have a high rate of complications that were not as frequently observed with older pulsatile devices, including gastrointestinal bleeding from arteriovenous malformations, pump thrombosis, and stroke. Given the apparent fundamental biological role of the pulse, the purpose of this review is to describe the normal physiology of ventricular-arterial coupling from pulsatile flow, the effects of heart failure on this physiology and the vasculature, and to examine the effects of nonpulsatile blood flow on the vascular system and potential role in complications seen with CF-LVAD therapy. Understanding these concomitant vascular changes with CF-LVADs may be a key step in improving patient outcomes as modulation of pulsatility and flow characteristics may serve as a novel, yet simple, therapy for reducing 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.

Twenty-Four-Hour Ambulatory Pulse Wave Analysis in Hypertension Management: Current Evidence and Perspectives

The predictive value of vascular biomarkers such as pulse wave velocity (PWV), central arterial pressure (CAP), and augmentation index (AIx), obtained through pulse wave analysis (PWA) in resting conditions, has been documented in a variety of patient groups and populations. This allowed to make appropriate recommendations in clinical practice guidelines of several scientific societies. Due to advances in technologies, largely operator-independent methods are currently available for estimating vascular biomarkers also in ambulatory conditions, over the 24 h. According to the acceptable accuracy and reproducibility of 24-h ambulatory PWA, it appears to be a promising tool for evaluating vascular biomarkers in daily life conditions. This approach may provide an opportunity to further improve the early cardiovascular screening in subjects at risk. However, concerning the clinical use of PWA over the 24 h in ambulatory conditions at the moment, there is no sufficient evidence to support its routine clinical use. In particular, long-term outcome studies are needed to show the predictive value of 24-h PWV, CAP, and AIx values, provided by these devices, over and beyond peripheral blood pressure, and to answer the many technical and clinical questions still open. To this regard, the VASOTENS Registry, an international observational prospective study recently started, will help providing answers on a large sample of hypertensive patients recruited worldwide.

A Novel Mean-Value Model of the Cardiovascular System Including a Left Ventricular Assist Device

Time-varying elastance models (TVEMs) are often used for simulation studies of the cardiovascular system with a left ventricular assist device (LVAD). Because these models are computationally expensive, they cannot be used for long-term simulation studies. In addition, their equilibria are periodic solutions, which prevent the extraction of a linear time-invariant model that could be used e.g. for the design of a physiological controller. In the current paper, we present a new type of model to overcome these problems: the mean-value model (MVM). The MVM captures the behavior of the cardiovascular system by representative mean values that do not change within the cardiac cycle. For this purpose, each time-varying element is manually converted to its mean-value counterpart. We compare the derived MVM to a similar TVEM in two simulation experiments. In both cases, the MVM is able to fully capture the inter-cycle dynamics of the TVEM. We hope that the new MVM will become a useful tool for researchers working on physiological control algorithms. This paper provides a plant model that enables for the first time the use of tools from classical control theory in the field of physiological LVAD control.

A method to implement the reservoir-wave hypothesis using phase-contrast magnetic resonance imaging

The reservoir-wave hypothesis states that the blood pressure waveform can be usefully divided into a “reservoir pressure” related to the global compliance and resistance of the arterial system, and an “excess pressure” that depends on local conditions. The formulation of the reservoir-wave hypothesis applied to the area waveform is shown, and the analysis is applied to area and velocity data from high-resolution phase-contrast cardiovascular magnetic resonance (CMR) imaging. A validation study shows the success of the principle, with the method producing largely robust and physically reasonable parameters, and the linear relationship between flow and wave pressure seen in the traditional pressure formulation is retained. The method was successfully tested on a cohort of 20 subjects (age range: 20–74 years; 17 males).

This paper:

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Demonstrates the feasibility of deriving reservoir data non-invasively from CMR.

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Includes a validation cohort (CMR data).

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Suggests clinical applications of the method.

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.

Arterial Stiffness: Going a Step Beyond

Interest in arterial stiffness has been fueled by the scientific and clinical implications of its "vicious cycle" relationship with aging and systolic blood pressure. In physical terms, stiffness is the slope of the relationship between an artery's distending pressure and its cross-sectional area or volume. Pulse wave velocity (PWV, in m/s), the most common arterial stiffness indicator, is usually measured by the foot-to-foot time and distance method and is proportional to [stiffness × area (or volume)]1/2 at a given pressure. Its intrinsic pressure dependency and other flaws in current PWV methods limit its utility. In contrast, the arterial stiffness-arterial pressure relationship is near-linear, with a slope β, the exponent of the curvilinear arterial pressure-arterial volume relationship. The concept of arterial stiffening is related to β and describes a more functionally relevant aspect of arterial behavior: the change in stiffness for a given change in pressure. Arterial stiffening can be estimated from the variability of within-individual BP measurements (24-h ambulatory, home BP, or BP measured at different arm heights) and can be expressed as the pulse stiffening ratio (PSR) = [systolic stiffness]/[diastolic stiffness] or the ambulatory arterial stiffness index (AASI or its symmetric form, sAASI). High arterial stiffness (PWV) and stiffening (β, stiffness index, cardio-ankle vascular index, AASI, and PSR) are associated with increased cardiovascular disease risk, but it remains unclear whether these indicators are useful in improving medical care quality; the standard of care remains stringent BP control.

A mathematical model of pressure and flow waveforms in the aortic root

The differences in the pressure and flow waveforms in the aortic root have not been explained so far in a satisfactory mathematical way. It is a generally accepted idea that the existence of the reflected wave causes the differences in shapes of pressure and flow. In this paper, a mathematical model is proposed that explains the blood pressure and flow waveforms based on changes in left ventricular volume during blood ejection into the aorta. According to the model, a change in volume of the left ventricle during contraction can be mathematically presented with solutions of differential equations that describe the behavior of a second-order system. The proposed mathematical equations of pressure and flow waveforms are derived from left ventricular volume change and basic equations of fluid dynamics. The position of the reflected wave depends on the age and elasticity of arteries, and has an effect on the flow and pressure waveforms. The model is in acceptable agreement with the experimental data available.

Hemodynamics

A review is presented of the physical principles governing the distribution of blood flow and blood pressure in the vascular system. The main factors involved are the pulsatile driving pressure generated by the heart, the flow characteristics of blood, and the geometric structure and mechanical properties of the vessels. The relationship between driving pressure and flow in a given vessel can be understood by considering the viscous and inertial forces acting on the blood. Depending on the vessel diameter and other physical parameters, a wide variety of flow phenomena can occur. In large arteries, the propagation of the pressure pulse depends on the elastic properties of the artery walls. In the microcirculation, the fact that blood is a suspension of cells strongly influences its flow properties and leads to a nonuniform distribution of hematocrit among microvessels. The forces acting on vessel walls include shear stress resulting from blood flow and circumferential stress resulting from blood pressure. Biological responses to these forces are important in the control of blood flow and the structural remodeling of vessels, and also play a role in major disease processes including hypertension and atherosclerosis. Consideration of hemodynamics is essential for a comprehensive understanding of the functioning of the circulatory system.

Percutaneous Coronary Intervention Enhances Accelerative Wave Intensity in Coronary Arteries

Background

The systolic forward travelling compression wave (sFCW) and diastolic backward travelling decompression waves (dBEW) predominantly accelerate coronary blood flow. The effect of a coronary stenosis on the intensity of these waves in the distal vessel is unknown. We investigated the relationship between established physiological indices of hyperemic coronary flow and the intensity of the two major accelerative coronary waves identified by Coronary Wave Intensity analysis (CWIA).

Methodology / Principal Findings

Simultaneous intracoronary pressure and velocity measurement was performed during adenosine induced hyperemia in 17 patients with pressure / Doppler flow wires positioned distal to the target lesion. CWI profiles were generated from this data. Fractional Flow Reserve (FFR) and Coronary Flow Velocity Reserve (CFVR) were calculated concurrently. The intensity of the dBEW was significantly correlated with FFR (R = -0.70, P = 0.003) and CFVR (R = -0.73, P = 0.001). The intensity of the sFCW was also significantly correlated with baseline FFR (R = 0.71, p = 0.002) and CFVR (R = 0.59, P = 0.01). Stenting of the target lesion resulted in a median 178% (interquartile range 55–280%) (P<0.0001) increase in sFCW intensity and a median 117% (interquartile range 27–509%) (P = 0.001) increase in dBEW intensity. The increase in accelerative wave intensity following PCI was proportionate to the baseline FFR and CFVR, such that stenting of lesions associated with the greatest flow limitation (lowest FFR and CFVR) resulted in the largest increases in wave intensity.

Conclusions

Increasing ischemia severity is associated with proportionate reductions in cumulative intensity of both major accelerative coronary waves. Impaired diastolic microvascular decompression may represent a novel, important pathophysiologic mechanism driving the reduction in coronary blood flow in the setting of an epicardial stenosis.

Association Between Fibulin-1 and Aortic Augmentation Index in Male Patients with Peripheral Arterial Disease

BACKGROUND

Fibulin-1 (FBLN-1), a newly identified biomarker for vascular stiffness in type 2 diabetes, may participate in the pathophysiological processes leading to progression of arterial stiffness in atherosclerosis. In the present study, the relationship between FBLN-1 and arterial stiffness was examined in patients with atherosclerosis and in healthy subjects.

METHODS

Thirty-eight patients with peripheral arterial disease (PAD) (age 62.4 ± 9.0 years), 38 patients with coronary artery disease (CAD) (age 64.0 ± 9.5 years), and 30 apparently healthy controls (age 61.1 ± 6.4 years) were studied. Serum FBLN-1, oxidized low density lipoprotein (oxLDL), resistin and plasminogen activator inhibitor-1 (PAI-1) levels were measured using the enzyme linked immunosorbent assay method. The technique of applanation tonometry was used for non-invasive pulse wave analysis and pulse wave velocity assessments.

RESULTS

The levels of FBLN-1 (PAD = 9.4 [4.9-17.8] vs. CAD = 7.1 [4.8-11.8] vs. controls = 5.6 [4.1-8.4] μg/mL; p = .005), carotid-femoral pulse wave velocity (cf-PWV) (9.8 ± 2.2 vs. 9.5 ± 2.2 vs. 8.3 ± 2.2 m/s; p = .023) and the heart rate corrected augmentation index (AIx@75) (29.4 ± 7.2 vs. 19.2 ± 7.2 vs. 15.4 ± 7.1%; p < .001), differed among the three groups. A correlation between FBLN-1 and AIx@75 was observed only in patients with PAD (rho = 0.37, p = .021). The relationship retained statistical significance in a multiple regression model after adjustment for potential confounders.

CONCLUSIONS

An independent association was demonstrated between serum FBLN-1 and AIx@75 in the PAD group. Thus, the findings suggest that FBLN-1 may play a role in arterial stiffening in patients with atherosclerosis.

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.

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.

A computational study of pressure wave reflections in the pulmonary arteries

Experiments using wave intensity analysis suggest that the pulmonary circulation in sheep and dogs is characterized by negative or open-end type wave reflections, that reduce the systolic pressure. Since the pulmonary physiology is similar in most mammals, including humans, we test and verify this hypothesis by using a subject specific one-dimensional model of the human pulmonary circulation and a conventional wave intensity analysis. Using the simulated pressure and velocity, we also analyse the performance of the P-U loop and sum of squares techniques for estimating the local pulse wave velocity in the pulmonary arteries, and then analyse the effects of these methods on linear wave separation in the main pulmonary artery. P-U loops are found to provide much better estimates than the sum of squares technique at proximal locations, but both techniques accumulate progressive error at distal locations away from heart, particularly near junctions. The pulse wave velocity estimated using the sum of squares method also gives rise to an artificial early systolic backward compression wave. Finally, we study the influence of three types of pulmonary hypertension viz. pulmonary arterial hypertension, chronic thromboembolic pulmonary hypertension and pulmonary hypertension associated with hypoxic lung disease. Simulating these conditions by changing the relevant parameters in the model and then applying the wave intensity analysis, we observe that for each group the early systolic backward decompression wave reflected from proximal junctions is maintained, whilst the initial forward compression and the late systolic backward compression waves amplify with increasing pathology and contribute significantly to increases in systolic pressure.

Central aortic reservoir-wave analysis improves prediction of cardiovascular events in elderly hypertensives

Several morphological parameters based on the central aortic pressure waveform are proposed as cardiovascular risk markers, yet no study has definitively demonstrated the incremental value of any waveform parameter in addition to currently accepted biomarkers in elderly, hypertensive patients. The reservoir-wave concept combines elements of wave transmission and Windkessel models of arterial pressure generation, defining an excess pressure superimposed on a background reservoir pressure. The utility of pressure rate constants derived from reservoir-wave analysis in prediction of cardiovascular events is unknown. Carotid blood pressure waveforms were measured prerandomization in a subset of 838 patients in the Second Australian National Blood Pressure Study. Reservoir-wave analysis was performed and indices of arterial function, including the systolic and diastolic rate constants, were derived. Survival analysis was performed to determine the association between reservoir-wave parameters and cardiovascular events. The incremental utility of reservoir-wave parameters in addition to the Framingham Risk Score was assessed. Baseline values of the systolic rate constant were independently predictive of clinical outcome (hazard ratio, 0.33; 95% confidence interval, 0.13-0.82; P=0.016 for fatal and nonfatal stroke and myocardial infarction and hazard ratio, 0.38; 95% confidence interval, 0.20-0.74; P=0.004 for the composite end point, including all cardiovascular events). Addition of this parameter to the Framingham Risk Score was associated with an improvement in predictive accuracy for cardiovascular events as assessed by the integrated discrimination improvement and net reclassification improvement indices. This analysis demonstrates that baseline values of the systolic rate constant predict clinical outcomes in elderly patients with hypertension and incrementally improve prognostication of cardiovascular events.

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.

Aortic Reservoir Pressure Corresponds to Cyclic Changes in Aortic Volume

Objective—

Aortic reservoir pressure indices independently predict cardiovascular events and mortality. Despite this, there has never been a study in humans to determine whether the theoretical principles of the mathematically derived aortic reservoir pressure (RP derived ) and excess pressure (XP derived ) model have a real physiological basis. This study aimed to directly measure the aortic reservoir (AR direct ; by cyclic change in aortic volume) and determine its relationship with RP derived , XP derived , and aortic blood pressure (BP).

Approach and Results—

Ascending aortic BP and Doppler flow velocity were recorded via intra-arterial wire in 10 men (aged 62±12 years) during coronary artery bypass surgery. Simultaneous ascending aortic transesophageal echocardiography was used to measure AR direct . Published mathematical formulae were used to determine RP derived and XP derived . AR direct was strongly and linearly related to RP derived during systole ( r =0.988; P <0.001) and diastole ( r =0.985; P <0.001). Peak cross-correlation ( r =0.98) occurred at a phase lag of 0.004 s into the cardiac cycle, suggesting close temporal agreement between waveforms. The relationship between aortic BP and AR direct was qualitatively similar to the cyclic relationship between aortic BP and RP derived , with peak cross-correlations occurring at identical phase lags (AR direct versus aortic BP, r =0.96 at 0.06 s; RP derived versus aortic BP, r =0.98 at 0.06 s).

Conclusions—

RP derived is highly correlated with changes in proximal aortic volume, consistent with its physiological interpretation as corresponding to the instantaneous volume of blood stored in the aorta. Thus, aortic reservoir pressure should be considered in the interpretation of the central BP waveform.

Excess pressure integral predicts cardiovascular events independent of other risk factors in the conduit artery functional evaluation substudy of Anglo-Scandinavian Cardiac Outcomes Trial

Excess pressure integral (XSPI), a new index of surplus work performed by the left ventricle, can be calculated from blood pressure waveforms and may indicate circulatory dysfunction. We investigated whether XSPI predicted future cardiovascular events and target organ damage in treated hypertensive individuals. Radial blood pressure waveforms were acquired by tonometry in 2069 individuals (aged, 63±8 years) in the Conduit Artery Functional Evaluation (CAFE) substudy of the Anglo-Scandinavian Cardiac Outcomes Trial (ASCOT). Measurements of left ventricular mass index (n=862) and common carotid artery intima media thickness (n=923) were also performed. XSPI and the integral of reservoir pressure were lower in people treated with amlodipine±perindopril than in those treated with atenolol±bendroflumethiazide, although brachial systolic blood pressure was similar. A total of 134 cardiovascular events accrued during a median 3.4 years of follow-up; XSPI was a significant predictor of cardiovascular events after adjustment for age and sex, and this relationship was unaffected by adjustment for conventional cardiovascular risk factors or Framingham risk score. XSPI, central systolic blood pressure, central augmentation pressure, central pulse pressure, and integral of reservoir pressure were correlated with left ventricular mass index, but only XSPI, augmentation pressure, and central pulse pressure were associated positively with carotid artery intima media thickness. Associations between left ventricular mass index, XSPI, and integral of reservoir pressure and carotid artery intima media thickness and XSPI were unaffected by multivariable adjustment for other covariates. XSPI is a novel indicator of cardiovascular dysfunction and independently predicts cardiovascular events and targets organ damage in a prospective clinical trial.

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.