Time-domain representation of ventricular-arterial coupling as a windkessel and wave system

Impact of pulmonary endarterectomy on pulmonary arterial wave propagation and reservoir function

High wave speed and large wave reflection in the pulmonary artery have previously been reported in patients with chronic thromboembolic pulmonary hypertension (CTEPH). We assessed the impact of pulmonary endarterectomy (PEA) on pulmonary arterial wave propagation and reservoir function in patients with CTEPH. Right heart catheterization was performed using a combined pressure and Doppler flow sensor-tipped guidewire to obtain simultaneous pressure and flow velocity measurements in the pulmonary artery in eight patients with CTEPH before and 3 mo after PEA. Wave intensity and reservoir-excess pressure analyses were then performed. Following PEA, mean pulmonary arterial pressure (PAPm; ∼49 vs. ∼32 mmHg), pulmonary vascular resistance (PVR; ∼11.1 vs. ∼5.1 Wood units), and wave speed (∼16.5 vs. ∼8.1 m/s), i.e., local arterial stiffness, markedly decreased. The changes in the intensity of the reflected arterial wave and wave reflection index (pre: ∼28%; post: ∼22%) were small, and patients post-PEA with and without residual pulmonary hypertension (i.e., PAPm ≥ 25 mmHg) had similar wave reflection index (∼20 vs. ∼23%). The reservoir and excess pressure decreased post-PEA, and the changes were associated with improved right ventricular afterload, function, and size. In conclusion, although PVR and arterial stiffness decreased substantially following PEA, large wave reflection persisted, even in patients without residual pulmonary hypertension, indicating lack of improvement in vascular impedance mismatch. This may continue to affect the optimal ventriculoarterial interaction, and further studies are warranted to determine whether this contributes to persistent symptoms in some patients.NEW & NOTEWORTHY We performed wave intensity analysis in the pulmonary artery in patients with chronic thromboembolic pulmonary hypertension before and 3 mo after pulmonary endarterectomy. Despite substantial reduction in pulmonary arterial pressures, vascular resistance, and arterial stiffness, large pulmonary arterial wave reflection persisted 3 mo postsurgery, even in patients without residual pulmonary hypertension, suggestive of lack of improvement in vascular impedance mismatch.

Windkessel Measures Derived From Pressure Waveforms Only: The Framingham Heart Study

Background

Waveform parameters derived from pressure‐only Windkessel models are related to cardiovascular disease risk and could be useful for understanding arterial system function. However, prior reports varied in their adjustment for potential confounders.

Methods and Results

Carotid tonometry waveform data from 2539 participants (mean age 63±11 years, 58% women) of the Framingham Heart Study were used to derive Windkessel measures using pressure and assuming a linear model with fixed diastolic time constant (τ_dias) and variable asymptotic pressure (P_inf, median 54.5; 25th, 75th percentiles: 38.4, 64.9 mm Hg) or nonlinear model with inverse pressure‐dependent τ_dias and fixed P_inf (20 mm Hg). During follow‐up (median 15.1 years), 459 (18%) participants had a first cardiovascular disease event. In proportional hazards models adjusted for age, sex, total cholesterol, high‐density lipoprotein cholesterol, smoking, antihypertensive medication use, diabetes mellitus, and physician‐acquired systolic blood pressure, only the systolic time constant (τ_sys) derived from the nonlinear model was related to risk for cardiovascular disease events (hazard ratio=0.91 per 1 SD, 95% CI=0.84–0.99, P=0.04). When heart rate was added to the model, τ_sys (hazard ratio=0.92, CI=0.84–1.00, P=0.04) and reservoir pressure amplitude (hazard ratio=1.14, CI=1.01–1.28, P=0.04) were related to events. In contrast, measures derived from the linear model were not related to events in models that adjusted for risk factors including systolic blood pressure (P>0.31) and heart rate (P>0.19).

Conclusions

Our results suggest that pressure‐only Windkessel measures derived by using a nonlinear model may provide incremental risk stratification, although associations were modest and further validation is required.

Phase-contrast magnetic resonance imaging for analyzing hemodynamic parameters and wall shear stress of pulmonary arteries in patients with pulmonary arterial hypertension

OBJECTIVE

To investigate flow-related parameters in pulmonary arteries of patients with pulmonary arterial hypertension (PAH).

MATERIALS AND METHODS

Eleven PAH patients and twelve control participants were recruited. PAH and controls had similar age and gender distribution. 2D phase-contrast MRI (PC-MRI) was performed in the main, right, and left pulmonary artery (MPA, RPA, and LPA). The flow velocity, wall shear stress (WSS), and oscillatory shear index (OSI) were measured.

RESULTS

PAH patients displayed prolonged acceleration time (T_acce) and increased ratio of flow change to acceleration volume in pulmonary arteries (both P < 0.001). The temporally averaged WSS values of MPA, RPA, and LPA in PAH patients were significantly lower than those of control participants (P < 0.001). The OSI in the pulmonary arteries was higher in PAH patients than control participants (P < 0.05). The ROC analysis indicated the ratio of maximum flow change to acceleration volume, WSS, and T_acce exhibited sufficient sensitivity and specificity to detect patients with PAH. The WSS demonstrated strong correlations with T_acce and the ratio value in the two groups (R² = 0.78-0.96).

CONCLUSIONS

We used a clinically feasible 2D PC-MRI sequence with a reasonable scanning time to compute aforementioned indices. The quantitative parameters provided sufficient information to differentiate PAH patients from control participants.

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.

Doppler indexes of left ventricular systolic and diastolic function in relation to haemodynamic load components in a general population

BACKGROUND

The contribution of central pulsatility to left ventricular (LV) dysfunction might be mediated by the haemodynamic loads of forward (Pf) and backward (Pb) pulse waves. We investigated the relation between echocardiographic indexes of LV function and pulsatile loads derived by wave separation analysis (WSA).

METHODS

In 755 participants, we assessed LV dimensions, transmitral blood flow and mitral annular tissue velocities. We derived central pulse pressure (cPP) from radial tonometric recordings and calculated Pf, Pb and their ratio (reflection magnitude) using an automated, pressure-based WSA algorithm. Despite good quality recordings, WSA failed to derive Pf and Pb in 139 participants (18.4%), in particular in older women with unfavourable haemodynamics. Thus, our analysis included 616 participants (46.1% women; mean age, 49.2 years).

RESULTS

Age and age explained most of the variance in cPP (36.9%), Pf (18.6%), Pb (41.5%) and reflection magnitude (36.7%; P < 0.0001) and altered the direct correlation between Pf and Pb (Pint < 0.0001). Haemodynamic loads were independently associated with sex, BMI, heart rate, mean arterial pressure, history of diabetes and use of antihypertensive drugs. In multivariable-adjusted analyses, transmitral velocities and E/e' ratio increased with higher cPP, Pf and Pb in men and women. We also observed an age-dependent association of LV radial strain with cPP, Pf and Pb.

CONCLUSION

The commercial WSA algorithm holds limited clinical utility given its low feasibility in older participants with unfavourable haemodynamics. LV function indexes were similarly associated with Pf and Pb, favouring the use of the composite cPP for prediction of LV dysfunction.

A review on low-dimensional physics-based models of systemic arteries: application to estimation of central aortic pressure

The physiological processes and mechanisms of an arterial system are complex and subtle. Physics-based models have been proven to be a very useful tool to simulate actual physiological behavior of the arteries. The current physics-based models include high-dimensional models (2D and 3D models) and low-dimensional models (0D, 1D and tube-load models). High-dimensional models can describe the local hemodynamic information of arteries in detail. With regard to an exact model of the whole arterial system, a high-dimensional model is computationally impracticable since the complex geometry, viscosity or elastic properties and complex vectorial output need to be provided. For low-dimensional models, the structure, centerline and viscosity or elastic properties only need to be provided. Therefore, low-dimensional modeling with lower computational costs might be a more applicable approach to represent hemodynamic properties of the entire arterial system and these three types of low-dimensional models have been extensively used in the study of cardiovascular dynamics. In recent decades, application of physics-based models to estimate central aortic pressure has attracted increasing interest. However, to our best knowledge, there has been few review paper about reconstruction of central aortic pressure using these physics-based models. In this paper, three types of low-dimensional physical models (0D, 1D and tube-load models) of systemic arteries are reviewed, the application of three types of models on estimation of central aortic pressure is taken as an example to discuss their advantages and disadvantages, and the proper choice of models for specific researches and applications are advised.

Comparison of invasive and non-invasive aortic wave intensity and wave power analyses in sheep

OBJECTIVE

Wave intensity (WI) and wave power (WP) analyses are powerful approaches for assessing ventricular-vascular interactions and arterial dynamics using invasive and non-invasive methods. However, in vivo comparison of these methods for large arteries is lacking. This study assessed agreement, correlation and relative changes in wave size in invasive and non-invasive aortic WI/WP analyses, and associated sources of error.

APPROACH

The proximal descending thoracic aorta (DTA) of nine wethers was instrumented with a micromanometer and perivascular transit-time flow probe to measure high-fidelity blood pressure (P) and flow (Q) for invasive WI/WP analyses at baseline and during haemodynamic perturbations produced by cardiac pacing, distal DTA constriction and dobutamine-induced inotropic stimulation. In 212 experimental runs, concurrent echocardiographic DTA diameter and velocity (U) data were acquired for non-invasive WI/WP analyses, with measurement of forward compression wave (FCW), backward compression wave (BCW) and forward decompression wave (FDW) cumulative intensity (CI), cumulative power (CP) and wave-related pressure changes (ΔP).

MAIN RESULTS

Although agreement between invasive and non-invasive FCW, BCW and FDW CI/CP measures was variable (bias  -84% to  +7%), correlation was good (R  =  0.66-0.84), with lower bias and higher correlation for ΔP variables and similar relative changes in FCW and BCW CI/ΔP during haemodynamic perturbations. Main error sources were overestimation of invasive U due to assumed fixed vessel diameter, inaccuracies in non-invasive Q, and non-invasive underestimation of peak P/U and Q rates of change.

SIGNIFICANCE

Despite variable agreement, non-invasive CI/CP indices correlate well with invasive measurements, and detect relative changes in major waves induced by haemodynamic perturbations.

A hybrid Windkessel-Womersley model for blood flow in arteries

A hybrid Windkessel-Womersley (WK-W) coupled mathematical model for the study of pulsatile blood flow in the arterial system is proposed in this article. The model consists of the Windkessel-type proximal and distal compartments connected by a tube to represent the aorta. The blood flow in the aorta is described by the Womersley solution of the simplified Navier-Stokes equations. In addition, we defined a 6-elements Windkessel model (WK6) in which the blood flow in the connecting tube is modeled by the one-dimensional unsteady Bernoulli equation. Both models have been applied and validated using several aortic pressure and flow rate data acquired from different species such as, humans, dogs and pigs. The results have shown that, both models were able to accurately reconstruct arterial input impedance, however, only the WK-W model was able to calculate the radial distribution of the axial velocity in the aorta and consequently the model predicts the time-varying wall shear stress, and frictional pressure drop during the cardiac cycle more accurately. Additionally, the hybrid WK-W model has the capability to predict the pulsed wave velocity, which is also not possible to obtain when using the classical Windkessel models. Moreover, the values of WK-W model parameters have found to fall in the physiologically realistic range of values, therefore it seems that this hybrid model shows a great potential to be used in clinical practice, as well as in the basic cardiovascular mechanics research.

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.

Effects of carotid pressure waveforms on the results of wave separation, wave intensity and reservoir pressure analysis

OBJECTIVE

Recently great attention has been paid to innovative cardiovascular biomarkers obtained from wave separation (WS), wave intensity (WI) and reservoir-wave (RW) theories. All these approaches share a requirement for pressure information. The aim of this study was to evaluate differences in WS-, WI- and RW-derived parameters obtained achieving pressure waveforms in different ways.

APPROACH

Twenty-two individuals (49  ±  17 years, 59% males) were examined. Common carotid blood flow waveforms were obtained from pulsed-wave Doppler images. Carotid pressure waveforms were achieved in four different ways: (1) with applanation tonometry, used as a reference method; (2) linear scaling from an ultrasound (US)-derived diameter curve; (3) exponential scaling from a US-derived diameter curve; and (4) linear scaling from an accelerometric-derived diameter signal. For each case, the reflection magnitude (RM) and index (RI) were obtained from the WS. The amplitude of the first positive peak (W ₁), of the second positive peak (W ₂) and of the negative peak (W _b) were calculated from the WI, while the maximum of the reservoir (maxP_r) and the excess (maxP_ex) pressure were achieved from the RW.

MAIN RESULTS

According to the intra-class coefficient values, the agreement between the standard method and all the others was excellent for the RM (linear: 0.82; exponential: 0.83; accelerometric: 0.86), RI (linear: 0.84; exponential: 0.85; accelerometric: 0.87), maxP_r (linear: 0.97; exponential: 0.96; accelerometric: 0.97) and maxP_ex (linear: 0.85; exponential: 0.87; accelerometric: 0.89), while only a fair/good level was reached for W ₁ (linear: 0.67; exponential: 0.77; accelerometric: 0.52), W ₂ (linear: 0.52; exponential: 0.69; accelerometric: 0.83) and W _b (linear: 0.60; exponential: 0.44; accelerometric: 0.50).

SIGNIFICANCE

Measuring carotid pressure waveforms with different approaches does not influence the cardiovascular parameters obtained by WS and RW; those derived by WI are affected by the carotid pressure curve employed.

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.

The meaning of blood pressure

Measurement of arterial pressure is one of the most basic elements of patient management. Arterial pressure is determined by the volume ejected by the heart into the arteries, the elastance of the walls of the arteries, and the rate at which the blood flows out of the arteries. This review will discuss the three forces that determine the pressure in a vessel: elastic, kinetic, and gravitational energy. Emphasis will be placed on the importance of the distribution of arterial resistances, the elastance of the walls of the large vessels, and critical closing pressures in small arteries and arterioles. Regulation of arterial pressure occurs through changes in cardiac output and changes in vascular resistance, but these two controlled variables can sometimes be in conflict.

Aortic reservoir function of Japanese female pearl divers

Female pearl divers in Japan, called " Ama," engage in repeated breath-hold free-diving maneuvers for collecting pearls, seaweeds, and shellfish in the cold sea. We previously reported that they have lower systemic arterial stiffness than age-matched sedentary peers. As a follow-up study, we evaluated their segmental arterial stiffness and aortic reservoir function. A total of 120 non-medicated women living in the same fishing villages (mean age: 65 ± 11 yr), including 88 Ama and 32 age-matched sedentary peers, were studied. Pulse wave velocity from the heart to the brachial artery (hbPWV; partly reflecting proximal aortic stiffness) and between the brachial artery and the ankle (baPWV; reflecting stiffness of abdominal aorta and leg arteries) were measured. Aortic hemodynamic variables were estimated from applanation tonometry carotid arterial pressure waveforms via general transfer function. Carotid artery impedance was calculated from blood flow velocity and blood pressure of contralateral common carotid arteries. baPWV was not different between the groups ( P = 0.117), whereas hbPWV was significantly lower in pearl divers than sedentary peers ( P = 0.004). Additionally, Ama had significantly lower aortic reservoir pressure integral ( P = 0.029) and carotid artery impedance modulus in frequency ranges from 0.78 to 4.0 Hz ( P = 0.011~0.019) than in sedentary peers. Collectively, these findings indicate that lifelong female pearl divers have superior reservoir function in central elastic arteries (e.g., the proximal aorta and carotid artery) in comparison with age-matched sedentary women living in the same fishing village. NEW & NOTEWORTHY We previously reported that lifelong female pearl divers in Japan, called " Ama," have lower systemic arterial stiffness than age-matched sedentary peers. As a follow-up study, we evaluated their segmental arterial stiffness and aortic reservoir function. In comparison with age-matched sedentary women living in the same fishing village, Ama demonstrated significantly lower arterial stiffness in more proximal and elastic arterial segments and superior reservoir function in central elastic arteries.

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.

Effects of exercise intensity and cardiorespiratory fitness on the acute response of arterial stiffness to exercise in older adults

PURPOSE

Increased arterial stiffness is observed with ageing and in individuals with low cardiorespiratory fitness ([Formula: see text]O_2peak), and associated with cardiovascular risk. Following an exercise bout, transient arterial stiffness reductions offer short-term benefit, but may depend on exercise intensity. This study assessed the effects of exercise intensity on post-exercise arterial stiffness in older adults with varying fitness levels.

METHODS

Fifty-one older adults (72 ± 5 years) were stratified into fitness tertiles ([Formula: see text]O_2peak: low-, 22.3 ± 3.1; mid-, 27.5 ± 2.4 and high-fit 36.3 ± 6.5 mL kg^-1 min^-1). In a randomised order, participants underwent control (no-exercise), moderate-intensity continuous exercise (40% of peak power output; PPO), and higher-intensity interval exercise (70% of PPO) protocols. Pulse wave velocity (PWV), augmentation index (AIx75) and reflection magnitude (RM) were assessed at rest and during 90 min of recovery following each protocol.

RESULTS

After control, delta PWV increased over time (P < 0.001) and delta RM was unchanged. After higher-intensity interval exercise, delta PWV (P < 0.001) and delta RM (P < 0.001) were lower to control in all fitness groups. After moderate-intensity continuous exercise, delta PWV was not different from control in low-fit adults (P = 0.057), but was lower in the mid- and higher-fit older adults. Post-exercise AIx75 was higher to control in all fitness groups (P = 0.001).

CONCLUSIONS

In older adults, PWV increases during seated rest and this response is attenuated after higher-intensity interval exercise, regardless of fitness level. This attenuation was also observed after moderate-intensity continuous exercise in adults with higher, but not lower fitness levels. Submaximal exercise reveals differences in the arterial stiffness responses between older adults with higher and lower cardiorespiratory fitness.

Stroke Volume estimation using aortic pressure measurements and aortic cross sectional area: Proof of concept

Accurate Stroke Volume (SV) monitoring is essential for patient with cardiovascular dysfunction patients. However, direct SV measurements are not clinically feasible due to the highly invasive nature of measurement devices. Current devices for indirect monitoring of SV are shown to be inaccurate during sudden hemodynamic changes. This paper presents a novel SV estimation using readily available aortic pressure measurements and aortic cross sectional area, using data from a porcine experiment where medical interventions such as fluid replacement, dobutamine infusions, and recruitment maneuvers induced SV changes in a pig with circulatory shock. Measurement of left ventricular volume, proximal aortic pressure, and descending aortic pressure waveforms were made simultaneously during the experiment. From measured data, proximal aortic pressure was separated into reservoir and excess pressures. Beat-to-beat aortic characteristic impedance values were calculated using both aortic pressure measurements and an estimate of the aortic cross sectional area. SV was estimated using the calculated aortic characteristic impedance and excess component of the proximal aorta. The median difference between directly measured SV and estimated SV was -1.4ml with 95% limit of agreement +/- 6.6ml. This method demonstrates that SV can be accurately captured beat-to-beat during sudden changes in hemodynamic state. This novel SV estimation could enable improved cardiac and circulatory treatment in the critical care environment by titrating treatment to the effect on SV.

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.

Next-generation, personalised, model-based critical care medicine: a state-of-the art review of in silico virtual patient models, methods, and cohorts, and how to validation them

Critical care, like many healthcare areas, is under a dual assault from significantly increasing demographic and economic pressures. Intensive care unit (ICU) patients are highly variable in response to treatment, and increasingly aging populations mean ICUs are under increasing demand and their cohorts are increasingly ill. Equally, patient expectations are growing, while the economic ability to deliver care to all is declining. Better, more productive care is thus the big challenge. One means to that end is personalised care designed to manage the significant inter- and intra-patient variability that makes the ICU patient difficult. Thus, moving from current "one size fits all" protocolised care to adaptive, model-based "one method fits all" personalised care could deliver the required step change in the quality, and simultaneously the productivity and cost, of care. Computer models of human physiology are a unique tool to personalise care, as they can couple clinical data with mathematical methods to create subject-specific models and virtual patients to design new, personalised and more optimal protocols, as well as to guide care in real-time. They rely on identifying time varying patient-specific parameters in the model that capture inter- and intra-patient variability, the difference between patients and the evolution of patient condition. Properly validated, virtual patients represent the real patients, and can be used in silico to test different protocols or interventions, or in real-time to guide care. Hence, the underlying models and methods create the foundation for next generation care, as well as a tool for safely and rapidly developing personalised treatment protocols over large virtual cohorts using virtual trials. This review examines the models and methods used to create virtual patients. Specifically, it presents the models types and structures used and the data required. It then covers how to validate the resulting virtual patients and trials, and how these virtual trials can help design and optimise clinical trial. Links between these models and higher order, more complex physiome models are also discussed. In each section, it explores the progress reported up to date, especially on core ICU therapies in glycemic, circulatory and mechanical ventilation management, where high cost and frequency of occurrence provide a significant opportunity for model-based methods to have measurable clinical and economic impact. The outcomes are readily generalised to other areas of medical care.

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.

Identifying Hemodynamic Determinants of Pulse Pressure: A Combined Numerical and Physiological Approach

We examined the ability of a simple reduced model comprising a proximal characteristic impedance linked to a Windkessel element to accurately predict central pulse pressure (PP) from aortic blood flow, verified that parameters of the model corresponded to physical properties, and applied the model to examine PP dependence on cardiac and vascular properties. PP obtained from the reduced model was compared with theoretical values obtained in silico and measured values in vivo. Theoretical values were obtained using a distributed multisegment model in a population of virtual (computed) subjects in which cardiovascular properties were varied over the pathophysiological range. In vivo measurements were in normotensive subjects during modulation of physiology with vasoactive drugs and in hypertensive subjects. Central PP derived from the reduced model agreed with theoretical values (mean difference±SD, -0.09±1.96 mm Hg) and with measured values (mean differences -1.95±3.74 and -1.18±3.67 mm Hg for normotensive and hypertensive subjects, respectively). Parameters extracted from the reduced model agreed closely with theoretical and measured physical properties. Central PP was seen to be determined mainly by total arterial compliance (inversely associated with central arterial stiffness) and ventricular dynamics: the blood volume ejected by the ventricle into the aorta up to time of peak pressure and blood flow into the aorta (corresponding to the rate of ventricular ejection) up to this time point. Increased flow and volume accounted for 20.1 mm Hg (52%) of the 39.0 mm Hg difference in PP between the upper and lower tertiles of the hypertensive subjects.

Pulse wave travel distance as a novel marker of ventricular-arterial coupling

Each stroke volume ejected by the heart is distributed along the arterial system as a pressure waveform. How far the front of the pressure waveform travels within the arterial system depends both on the pulse wave velocity (PWV) and the ejection time (ET). We tested the hypothesis that ET and PWV are coupled together, in order to produce a pulse wave travel distance (PWTD = PWV × ET) which would match the distance from the heart to the most distant site in the arterial system. The study was conducted in 11 healthy volunteers. We recorded lead II of the ECG along with pulse plethysmography at ear, finger and toe. The ET at the ear and pulse arrival time to each peripheral site were extracted. We then calculated PWV followed by PWTD for each location. Taken into account the individual subject variability PWTD_Toe in the supine position was 153 cm (95% CI 146-160 cm). It was not different from arterial pathway distance from the heart to the toe (D _Toe 153 cm). The PWTD_Finger and PWTD_Ear were longer than the distance from the heart to the finger and ear irrespective of body position. ET_Ear and PWV_Toe appear to be coupled in healthy subjects to produce a PWTD that is roughly equivalent to the arterial pathway distance to the toe. We propose that PWTD should be evaluated further to test its potential as a noninvasive parameter of ventricular-arterial coupling in subjects with cardiovascular diseases.

Fitness Is Independently Associated with Central Hemodynamics in Metabolic Syndrome

PURPOSE

Fit individuals with metabolic syndrome (MetS) have lower mortality risk compared with less fit counterparts, despite the presence of obesity as a component of the syndrome. To understand the importance of fitness in treating this condition, we examined the association of fitness and fatness with central hemodynamic indices that are known independent predictors of cardiovascular events.

METHODS

Sixty-eight individuals with MetS participated in this cross-sectional study. Central hemodynamics is calculated from radial applanation tonometry and comprised aortic reservoir pressure, backward pressure wave (Pb), reflection magnitude (RM), and augmentation index at 75 bpm (AIx75). Cardiorespiratory fitness (CRF) and body fat percentage (BF%) were determined via indirect calorimetry during maximal exercise testing and dual-energy x-ray absorptiometry, respectively.

RESULTS

CRF was inversely associated with aortic reservoir pressure (r = -0.29, P = 0.02), Pb (r = -0.42, P < 0.001), RM (r = -0.48, P < 0.001), and AIx75 (r = -0.65, P < 0.001). BF% was also correlated with AIx75 (r = 0.37, P < 0.05) and RM (r = 0.36, P < 0.005) but at a weaker association compared with CRF. Multiple regression analysis revealed CRF as a predictor of aortic reservoir pressure (β = -0.52, P = <0.01), Pb (β = -0.41, P < 0.03), and AIx75 (β = -0.45, P = 0.01), independent of BF% and other confounding factors.

CONCLUSIONS

CRF predicts central hemodynamics independent of BF% and other confounding factors. This suggests that CRF improvement may be a higher priority when compared with fat loss for lowering the risk of cardiovascular mortality in MetS individuals.

Pulmonary artery wave propagation and reservoir function in conscious man: impact of pulmonary vascular disease, respiration and dynamic stress tests

KEY POINTS

Wave travel plays an important role in cardiovascular physiology. However, many aspects of pulmonary arterial wave behaviour remain unclear. Wave intensity and reservoir-excess pressure analyses were applied in the pulmonary artery in subjects with and without pulmonary hypertension during spontaneous respiration and dynamic stress tests. Arterial wave energy decreased during expiration and Valsalva manoeuvre due to decreased ventricular preload. Wave energy also decreased during handgrip exercise due to increased heart rate. In pulmonary hypertension patients, the asymptotic pressure at which the microvascular flow ceases, the reservoir pressure related to arterial compliance and the excess pressure caused by waves increased. The reservoir and excess pressures decreased during Valsalva manoeuvre but remained unchanged during handgrip exercise. This study provides insights into the influence of pulmonary vascular disease, spontaneous respiration and dynamic stress tests on pulmonary artery wave propagation and reservoir function.

ABSTRACT

Detailed haemodynamic analysis may provide novel insights into the pulmonary circulation. Therefore, wave intensity and reservoir-excess pressure analyses were applied in the pulmonary artery to characterize changes in wave propagation and reservoir function during spontaneous respiration and dynamic stress tests. Right heart catheterization was performed using a pressure and Doppler flow sensor tipped guidewire to obtain simultaneous pressure and flow velocity measurements in the pulmonary artery in control subjects and patients with pulmonary arterial hypertension (PAH) at rest. In controls, recordings were also obtained during Valsalva manoeuvre and handgrip exercise. The asymptotic pressure at which the flow through the microcirculation ceases, the reservoir pressure related to arterial compliance and the excess pressure caused by arterial waves increased in PAH patients compared to controls. The systolic and diastolic rate constants also increased, while the diastolic time constant decreased. The forward compression wave energy decreased by ∼8% in controls and ∼6% in PAH patients during expiration compared to inspiration, while the wave speed remained unchanged throughout the respiratory cycle. Wave energy decreased during Valsalva manoeuvre (by ∼45%) and handgrip exercise (by ∼27%) with unaffected wave speed. Moreover, the reservoir and excess pressures decreased during Valsalva manoeuvre but remained unaltered during handgrip exercise. In conclusion, reservoir-excess pressure analysis applied to the pulmonary artery revealed distinctive differences between controls and PAH patients. Variations in the ventricular preload and afterload influence pulmonary arterial wave propagation as demonstrated by changes in wave energy during spontaneous respiration and dynamic stress tests.

Longitudinal Changes in Excess Pressure Independently Predict Declining Renal Function Among Healthy Individuals-A Pilot Study

BACKGROUND

Aortic reservoir function independently predicts end-organ damage in cross-sectional analyses. However, longitudinal associations are more important regarding causation, but this has never been examined at rest or in response to light-moderate intensity exercise. The aim of this study was to determine the association between the change in aortic reservoir characteristics, in particular excess pressure integral (Pexcess) at rest and in response to exercise and the change in kidney function among healthy individuals followed over time.

METHODS

Aortic reservoir function (Pexcess and reservoir pressure), aortic stiffness, brachial and central blood pressure (BP), and renal function (estimated glomerular filtration rate [eGFR]) were recorded among 33 healthy individuals (57 ± 9 years; 55% male) at baseline and after an average 3.0 ± 0.3 years.

RESULTS

Over the follow up period, there was a significant increase in resting brachial BP, central BP, Pexcess, and aortic stiffness (P < 0.05 all). The change over time in resting Pexcess (but not aortic stiffness) was significantly related to the change in eGFR (r = -0.38, P = 0.038) and remained independent of age at follow up, change in 24-hour ambulatory systolic BP and body mass index (β = -0.0300, P = 0.043). There was no association between the change in aortic pulse wave velocity and the change eGFR (P = 0.46) nor were there any associations with exercising hemodynamics.

CONCLUSIONS

Pexcess is independently associated with a decline in renal function among healthy people followed over 3 years. These novel findings indicate the need to determine the underlying physiological determinants of aortic reservoir function.

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.

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.

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

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

Roadmap for cardiovascular circulation model

Computational models of many aspects of the mammalian cardiovascular circulation have been developed. Indeed, along with orthopaedics, this area of physiology is one that has attracted much interest from engineers, presumably because the equations governing blood flow in the vascular system are well understood and can be solved with well-established numerical techniques. Unfortunately, there have been only a few attempts to create a comprehensive public domain resource for cardiovascular researchers. In this paper we propose a roadmap for developing an open source cardiovascular circulation model. The model should be registered to the musculo-skeletal system. The computational infrastructure for the cardiovascular model should provide for near real-time computation of blood flow and pressure in all parts of the body. The model should deal with vascular beds in all tissues, and the computational infrastructure for the model should provide links into CellML models of cell function and tissue function. In this work we review the literature associated with 1D blood flow modelling in the cardiovascular system, discuss model encoding standards, software and a model repository. We then describe the coordinate systems used to define the vascular geometry, derive the equations and discuss the implementation of these coupled equations in the open source computational software OpenCMISS. Finally, some preliminary results are presented and plans outlined for the next steps in the development of the model, the computational software and the graphical user interface for accessing the model.

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

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

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.

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.