Comparison of arterial waves derived by classical wave separation and wave intensity analysis in a model of aortic coarctation

Relationship between Pulmonary Regurgitation and Ventriculo-Arterial Interactions in Patients with Post-Early Repair of Tetralogy of Fallot: Insights from Wave-Intensity Analysis

This study aimed to investigate the effect of pulmonary regurgitation (PR) on left ventricular ventriculo-arterial (VA) coupling in patients with repaired tetralogy of Fallot (ToF). It was hypothesised that increasing PR severity results in a smaller forward compression wave (FCW) peak in the aortic wave intensity, because of right-to-left ventricular interactions. The use of cardiovascular magnetic resonance (CMR)-derived wave-intensity analysis provided a non-invasive comparison between patients with varying PR degrees. A total of n = 201 patients were studied and both hemodynamic and wave-intensity data were compared. Wave-intensity peaks and areas of the forward compression and forward expansion waves were calculated as surrogates of ventricular function. Any extent of PR resulted in a significant reduction in the FCW peak. A correlation was found between aortic distensibility and the FCW peak, suggesting unfavourable (VA) coupling in patients that also present stiffer ascending aortas. Data suggest that VA coupling is affected by increased impedance.

Arterial pressure pulse wave separation analysis using a multi-gaussian decomposition model

OBJECTIVE

Methods for separating the forward-backward components from blood pulse waves rely on simultaneously measured pressure and flow velocity from a target artery site. Modelling approaches for flow velocity simplify the wave separation analysis (WSA), providing a methodological and instrumentational advantage over the former; however, current methods are limited to the aortic site. In this work, a multi-Gaussian decomposition (MGD) modelled WSA (MGDWSA) is developed for a non-aortic site asuch as the carotid artery. While the model is an adaptation of the existing wave separation theory, it does not rely on the information of measured or modelled flow velocity.

APPROACH

The proposed model decomposes the arterial pressure waveform using weighted and shifted multi-Gaussians, which are then uniquely combined to yield the forward (PF(t)) and backward (PB(t)) pressure wave. A study using the database of healthy (virtual) subjects was used to evaluate the performance of MGDWSA at the carotid artery and was compared against reference flow-based WSA methods.

MAIN RESULTS

The MGD modelled pressure waveform yielded a root-mean-square error (RMSE) < 0.35 mmHg. Reliable forward-backward components with a group average RMSE < 2.5 mmHg for PF(t) and PB(t) were obtained. When compared with the reference counterparts, the pulse pressures (ΔPF and ΔPB), as well as reflection quantification indices, showed a statistically significant strong correlation (r > 0.96, p < 0.0001) and (r > 0.83, p < 0.0001) respectively, with an insignificant (p > 0.05) bias.

SIGNIFICANCE

This study reports WSA for carotid pressure waveforms without assumptions on flow conditions. The proposed method has the potential to adapt and widen the vascular health assessment techniques incorporating pulse wave dynamics.

A review study of fetal circulatory models to develop a digital twin of a fetus in a perinatal life support system

BACKGROUND

Preterm birth is the main cause of neonatal deaths with increasing mortality and morbidity rates with decreasing GA at time of birth. Currently, premature infants are treated in neonatal intensive care units to support further development. However, the organs of, especially, extremely premature infants (born before 28 weeks of GA) are not mature enough to function optimally outside the womb. This is seen as the main cause of the high morbidity and mortality rates in this group. A liquid-filled incubator, a so-called PLS system, could potentially improve these numbers for extremely premature infants, since this system is designed to mimic the environment of the natural womb. To support the development and implementation of such a complex system and to interpret vital signals of the fetus during a PLS system operation, a digital twin is proposed. This mathematical model is connected with a manikin representing the digital and physical twin of the real-life PLS system. Before developing a digital twin of a fetus in a PLS system, its functional and technical requirements are defined and existing mathematical models are evaluated.

METHOD AND RESULTS

This review summarizes existing 0D and 1D fetal circulatory models that potentially could be (partly) adopted for integration in a digital twin of a fetus in a PLS system based on predefined requirements. The 0D models typically describe hemodynamics and/or oxygen transport during specific events, such as the transition from fetus to neonate. Furthermore, these models can be used to find hemodynamic differences between healthy and pathological physiological states. Rather than giving a global description of an entire cardiovascular system, some studies focus on specific organs or vessels. In order to analyze pressure and flow wave profiles in the cardiovascular system, transmission line or 1D models are used. As for now, these models do not include oxygen transport.

CONCLUSION

This study shows that none of the models identified in literature meet all the requirements relevant for a digital twin of a fetus in a PLS system. Nevertheless, it does show the potential to develop this digital twin by integrating (parts) of models into a single model.

The effect of coarctation degrees on wall shear stress indices

Coarctation of the aorta (CoA) is a congenital tightening of the proximal descending aorta. Flow quantification can be immensely valuable for an early and accurate diagnosis. However, there is a lack of appropriate diagnostic approaches for a variety of cardiovascular diseases, such as CoA. An accurate understanding of the disease depends on measurements of the global haemodynamics (criteria for heart function) and also the local haemodynamics (detailed data on the dynamics of blood flow). Playing a significant role in clinical processes, wall shear stress (WSS) cannot be measured clinically; thus, computation tools are needed to give an insight into this crucial haemodynamic parameter. In the present study, in order to enable the progress of non-invasive approaches that quantify global and local haemodynamics for different CoA severities, innovative computational blueprint simulations that include fluid-solid interaction models are developed. Since there is no clear approach for managing the CoA regarding its severity, this study proposes the use of WSS indices and pressure gradient to better establish a framework for treatment procedures in CoA patients with different severities. This provides a platform for improving CoA therapy on a patient-specific level, in which physicians can perform treatment methods based on WSS indices on top of using a mere experience. Results show how severe CoA affects the aorta in comparison to the milder cases, which can give the medical community valuable information before and after any intervention.

Wave Reflection and Ventriculo-Arterial Coupling in Bicuspid Aortic Valve Patients With Repaired Aortic Coarctation

BACKGROUND

Ventriculo-arterial (VA) coupling in bicuspid aortic valve (BAV) patients can be affected by the global aortopathy characterizing BAV disease and the presence of concomitant congenital lesions such as aortic coarctation (COA). This study aimed to isolate the COA variable and use cardiovascular magnetic resonance (CMR) imaging to perform wave intensity analysis non-invasively to shed light on VA coupling changes in BAV. The primary hypothesis was that BAV patients with COA exhibit unfavorable VA coupling, and the secondary hypothesis was that BAV patients with COA exhibit increased wave speed as a marker of reduced aortic distensibility despite successful surgical correction.

METHODS

Patients were retrospectively identified from a CMR database and divided into two groups: isolated BAV and BAV associated with repaired COA. Aortic and ventricular dimensions, global longitudinal strain (GLS), and ascending aortic flow data and area were collected and used to derive wave intensity from CMR data. The main variables for the analysis included all wave magnitudes (forward compression/expansion waves, FCW and FEW, respectively, and reflected backward compression wave, BCW) and wave speed.

RESULTS

In the comparison of patients with isolated BAV and those with BAV associated with repaired COA (n = 25 in each group), no differences were observed in left ventricular ejection fraction, GLS, or ventricular volumes, whilst significant increases in FCW and FEW magnitude were noted in the BAV and repaired COA group. The FCW inversely correlated with age and aortic size. Whilst the BCW was not significantly different compared with that in patients with/without COA, its magnitude tends to increase with a lower COA index. Patients with repaired COA exhibited higher wave speed velocity. Aortic wave speed (inversely related to distensibility) was not significantly different between the two groups.

CONCLUSION

In the absence of a significant restenosis, VA coupling in patients with BAV and COA is not negatively affected compared to patients with isolated BAV. A reduction in the magnitude of the early systolic FCW was observed in patients who were older and with larger aortic diameters.

Pressure and Flow Relations in the Systemic Arterial Tree Throughout Development From Newborn to Adult

Objective: Distributed models of the arterial tree allow studying the effect of physiological and pathophysiological changes in the vasculature on hemodynamics. For the adult, several models exist; however, a model encompassing the full age range from newborn to adult was until now lacking. Our goal is to describe a complete distributed hemodynamic model for normal development from newborn to adult. Methods: The arterial system was modeled by 121 segments characterized by length, radius, wall thickness, wall stiffness, and wall viscosity. The final segments ended in three-element Windkessels. All parameters were adapted based on body height and weight as a function of age as described in the literature. Results: Pressures and flows are calculated as a function of age at sites along the arterial tree. Central to peripheral transfer functions are given. Our results indicate that peripheral pressure in younger children resembles central pressure. Furthermore, total arterial compliance, inertance and impedance are calculated. Findings indicate that the arterial tree can be simulated by using a three-element Windkessel system. Pulse wave velocity in the aorta was found to increase during development. Conclusions: The arterial system, modeled from newborn to adult bears clinical significance, both for the interpretation of peripheral measured pressure in younger and older children, and for using a Windkessel model to determine flow from pressure measurements.

Myocardial preload alters central pressure augmentation through changes in the forward wave

OBJECTIVE

Augmentation index (AIx) is often used to quantify the contribution of wave reflection to central pulse pressure. Recent studies have challenged this view by showing how contractility-induced changes in the forward pressure wave can markedly impact AIx. We hypothesized that changes in preload will also affect AIx through changes in the forward wave and studied this in two experiments.

METHODS

Noninvasively obtained aortic pressure was used to study central haemodynamics and wave morphology. In the first experiment, we examined the effects of head-up tilt with and without unilateral thigh cuff in 12 young healthy volunteers (mean age 26 years, 50% men). In the second experiment, we examined the effects of active standing in 31 middle-aged patients (mean age 57 years, 65% men) before and after phlebotomy.

RESULTS

Head-up tilt or active standing significantly decreased AIx [-17.7 ± 10.4 percentage point (pp) in the young population, -4.7 ± 12.3 pp in the middle-aged population, both P < 0.05]. The fall in AIx was associated with increases in HR, diastolic pressure and systemic vascular resistance and a decrease in stroke volume (all P < 0.05). Inflation of a unilateral thigh cuff reduced the decrease in AIx by 10.7 pp, whereas 500 ml of blood loss augmented the fall in AIx by 5.9 pp (both P < 0.05). The changes in AIx were related to a preload-induced change in forward pressure wave shape (earlier peaking and steeper downstroke).

CONCLUSION

Next to inotropic and chronotropic effects, preload emerges as another myocardial factor that obscures the relation between wave reflection and AIx.

Reduced Aortic Distensibility is Associated With Higher Aorto-Carotid Wave Transmission and Central Aortic Systolic Pressure in Young Adults After Coarctation Repair

Background The long-term prognosis of patients with repaired aortic coarctation is characterized by high rates of cardiovascular and cerebrovascular disease related to hypertension, the basis of which remains unclear. To define potential underlying mechanisms, we investigated aortic and carotid arterial biomechanics and wave dynamics, and determinants of aortic systolic blood pressure, in young adults after coarctation repair. Methods and Results Aortic arch and carotid biomechanics, wave intensity and wave power, and central aortic blood pressure, were derived from echocardiography and brachial blood pressure in 43 young adults after coarctation repair and 42 controls. Coarctation subjects had higher brachial and central systolic blood pressure ( P=0.04), while aortic compliance was lower and characteristic impedance (Zc) higher. Although carotid intima-media thickness was higher ( P<0.001), carotid biomechanics were no different. Carotid forward compression wave power was higher and was negatively correlated with aortic compliance ( R2=0.42, P<0.001) and distensibility ( R2=0.37, P=0.001) in coarctation subjects. Aortic wave power and wave reflection indices were no different in control and coarctation patients, but coarctation patients with elevated aortic Zc had greater aorto-carotid transmission of forward compression wave power ( P=0.006). Aortic distensibility was the only independent predictor of central aortic systolic blood pressure on multivariable analysis. Conclusions Young adults following coarctation repair had a less compliant aorta, but no change in carotid biomechanics. Reduced aortic distensibility was related to greater transmission of aortic forward wave energy into the carotid artery and higher central aortic systolic blood pressure. These findings suggest that reduced aortic distensibility may contribute to later cardiovascular and cerebrovascular disease after coarctation repair.

Ultrasound simulation model incorporating incident and reflected wave propagations along a common carotid artery

An ultrasound simulation model incorporating incident and reflected wave propagations is proposed to provide a realistic data source for validation of transit time (TT)-based local pulse wave velocity (PWV) estimation algorithms. First, the incident wave (IW) and reflected wave (RW) at a certain position over a common carotid artery (CCA) are estimated. Then, the propagating pulse waves (PWs) along the CCA are modelled with the synthesizations of the estimated IWs and RWs, whose occurrences are delayed in opposite sequences according to a preset PWV. In ultrasound simulation, a geometric model of a CCA is built, and the dynamic scatterer models are constructed by moving the scatterer positions according to the synthesized PWs. The RF signals are generated using Field II. To characterize the PW propagations of different arterial stiffnesses consistent with clinical ones in the model, 30 healthy subjects from young, middle-aged, and elderly groups are recruited for extractions of IWs and RWs. To quantitatively verify the effectiveness of the simulation model, the normalized root-mean-squared errors (NRMSEs) are used to compare the estimated and preset PWs, time delays (TDs), and PWVs. Results show that for the three age groups, the estimated PWs, TDs, and PWVs conform to the preset ones with the mean NRMSEs of 0.92%, 18.47%, and 8.55%, respectively. Moreover, the model can characterize the effect of the wave reflection on the local PW propagation as its clinical manifestation. Therefore, the proposed model can be effective as a data source for the validation of TT-based local PWV estimation algorithms, particularly the effects of RWs on the estimation performance.

Abnormal Wave Reflections and Left Ventricular Hypertrophy Late After Coarctation of the Aorta Repair

Patients with repaired coarctation of the aorta are thought to have increased afterload due to abnormalities in vessel structure and function. We have developed a novel cardiovascular magnetic resonance protocol that allows assessment of central hemodynamics, including central aortic systolic blood pressure, resistance, total arterial compliance, pulse wave velocity, and wave reflections. The main study aims were to (1) characterize group differences in central aortic systolic blood pressure and peripheral systolic blood pressure, (2) comprehensively evaluate afterload (including wave reflections) in the 2 groups, and (3) identify possible biomarkers among covariates associated with elevated left ventricular mass (LVM). Fifty adult patients with repaired coarctation and 25 age- and sex-matched controls were recruited. Ascending aorta area and flow waveforms were obtained using a high temporal-resolution spiral phase-contrast cardiovascular magnetic resonance flow sequence. These data were used to derive central hemodynamics and to perform wave intensity analysis noninvasively. Covariates associated with LVM were assessed using multivariable linear regression analysis. There were no significant group differences (P≥0.1) in brachial systolic, mean, or diastolic BP. However central aortic systolic blood pressure was significantly higher in patients compared with controls (113 versus 107 mm Hg, P=0.002). Patients had reduced total arterial compliance, increased pulse wave velocity, and larger backward compression waves compared with controls. LVM index was significantly higher in patients than controls (72 versus 59 g/m², P<0.0005). The magnitude of the backward compression waves was independently associated with variation in LVM (P=0.01). Using a novel, noninvasive hemodynamic assessment, we have shown abnormal conduit vessel function after coarctation of the aorta repair, including abnormal wave reflections that are associated with elevated LVM.

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

Wave intensity analysis provides detailed insights into factors influencing hemodynamics. However, wave intensity is not a conserved quantity, so it is sensitive to diameter variations and is not distributed among branches of a junction. Moreover, the fundamental relation between waves and hydraulic power is unclear. We, therefore, propose an alternative to wave intensity called “wave power,” calculated via incremental changes in pressure and flow (dPdQ) and a novel time-domain separation of hydraulic pressure power and kinetic power into forward and backward wave-related components (ΠP± and ΠQ±). Wave power has several useful properties: 1) it is obtained directly from flow measurements, without requiring further calculation of velocity; 2) it is a quasi-conserved quantity that may be used to study the relative distribution of waves at junctions; and 3) it has the units of power (Watts). We also uncover a simple relationship between wave power and changes in ΠP± and show that wave reflection reduces transmitted power. Absolute values of ΠP± represent wave potential, a recently introduced concept that unifies steady and pulsatile aspects of hemodynamics. We show that wave potential represents the hydraulic energy potential stored in a compliant pressurized vessel, with spatial gradients producing waves that transfer this energy. These techniques and principles are verified numerically and also experimentally with pressure/flow measurements in all branches of a central bifurcation in sheep, under a wide range of hemodynamic conditions. The proposed “wave power analysis,” encompassing wave power, wave potential, and wave separation of hydraulic power provides a potent time-domain approach for analyzing hemodynamics.

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

BACKGROUND

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

METHOD AND RESULTS

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

CONCLUSION

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

The role of aortic compliance in determination of coarctation severity: Lumped parameter modeling, in vitro study and clinical evaluation

Early detection and accurate estimation of the extent of coarctation of the aorta (COA) is critical to long-term outcome. Peak-to-peak trans-coarctation pressure gradient (PKdP) higher than 20mmHg is an indication for interventional/surgical repair. Patients with COA have reduced proximal and distal aortic compliances. A comprehensive study investigating the effects of variations of proximal COA and systemic compliances on PKdP, and consequently on the COA severity evaluation has never been done. This study evaluates the effect of aortic compliance on diagnostic accuracy of PKdP. Lumped parameter modeling and in vitro experiments were performed for COA severities of 50%, 75% and 90% by area. Modeling and in vitro results were validated against retrospective clinical data of PKdP, measured in 54 patients with COA. Modeling and in vitro. PKdP increases with reduced proximal COA compliance (+36%, +38% and +53% for COA severities of 50%, 75% and 90%, respectively; p<0.05), but decreases with reduced systemic compliance (-62%, -41% and -36% for COA severities of 50%, 75% and 90%, respectively; p<0.01). Clinical study. PKdP has a modest correlation with COA severity (R=0.29). The main determinants of PKdP are COA severity, stroke volume index and systemic compliance. Systemic compliance was found to be as influential as COA severity in PKdP determination (R=0.30 vs. R =0.34). In conclusion, PKdP is highly influenced by both stroke volume index and arterial compliance. Low values of PKdP cannot be used to exclude the severe COA presence since COA severity may be masked by reduced systemic compliance and/or low flow conditions.

Differential impact of local stiffening and narrowing on hemodynamics in repaired aortic coarctation: an FSI study

Even after successful treatment of aortic coarctation, a high risk of cardiovascular morbidity and mortality remains. Uncertainty exists on the factors contributing to this increased risk among which are the presence of (1) a residual narrowing leading to an additional resistance and (2) a less distensible zone disturbing the buffer function of the aorta. As the many interfering factors and adaptive physiological mechanisms present in vivo prohibit the study of the isolated impact of these individual factors, a numerical fluid-structure interaction model is developed to predict central hemodynamics in coarctation treatment. The overall impact of a stiffening on the hemodynamics is limited, with a small increase in systolic pressure (up to 8 mmHg) proximal to the stiffening which is amplified with increasing stiffening and length. A residual narrowing, on the other hand, affects the hemodynamics significantly. For a short segment (10 mm), the combination of a stiffening and narrowing (coarctation index 0.5) causes an increase in systolic pressure of 58 mmHg, with 31 mmHg due to narrowing and an additional 27 mmHg due to stiffening. For a longer segment (25 mm), an increase in systolic pressure of 50 mmHg is found, of which only 9 mmHg is due to stiffening.

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.

Novel wave intensity analysis of arterial pulse wave propagation accounting for peripheral reflections

We present a novel analysis of arterial pulse wave propagation that combines traditional wave intensity analysis with identification of Windkessel pressures to account for the effect on the pressure waveform of peripheral wave reflections. Using haemodynamic data measured in vivo in the rabbit or generated numerically in models of human compliant vessels, we show that traditional wave intensity analysis identifies the timing, direction and magnitude of the predominant waves that shape aortic pressure and flow waveforms in systole, but fails to identify the effect of peripheral reflections. These reflections persist for several cardiac cycles and make up most of the pressure waveform, especially in diastole and early systole. Ignoring peripheral reflections leads to an erroneous indication of a reflection-free period in early systole and additional error in the estimates of (i) pulse wave velocity at the ascending aorta given by the PU-loop method (9.5% error) and (ii) transit time to a dominant reflection site calculated from the wave intensity profile (27% error). These errors decreased to 1.3% and 10%, respectively, when accounting for peripheral reflections. Using our new analysis, we investigate the effect of vessel compliance and peripheral resistance on wave intensity, peripheral reflections and reflections originating in previous cardiac cycles.

THE INFLUENCES OF CARDIOVASCULAR PROPERTIES ON SUPRASYSTOLIC BRACHIAL CUFF WAVE STUDIED BY A SIMPLE ARTERIAL-TREE MODEL

It has been found that a pronounced secondary systolic peak appears on the oscillometric wave recorded by a brachial oscillometric cuff as cuff pressure is raised to a suprasystolic level. This finding has accordingly motivated some studies aimed to explore the potential value carried by the cuff wave for assessing arterial stiffness. However, so far, there remain considerable controversies in the literature regarding the cardiovascular properties that dominate the characteristics of the cuff wave. In this context, we developed a simple arterial-tree model and applied it to investigate the respective influence on the cuff wave of various cardiovascular properties and the associated wave interaction phenomena. It was found that (1) neither aortic stiffness nor brachial arterial stiffness can uniquely determine the time lag (Δt) between the first and secondary peaks of the cuff wave, although both of them significantly influence Δt; and (2) the BAIx (an index that characterize the height of the secondary peak relative to the first) is sensitive to most of the investigated cardiovascular properties and physiological conditions, such as arterial stiffness, intensity of wave reflection in the lower body and heart rate, etc. These findings suggest that the reliability of assessing aortic stiffness based solely on the timings and heights of the two peaks is limited. Moreover, we argued that the controversial findings presented in previous model-based studies are likely to be caused by limitations related to the research objectives or computation conditions of the studies.

Initiation of ventricular contraction as reflected in the aortic pressure waveform

Prior to aortic valve opening, aortic pressure is perturbed by ventricular contraction. The onset of this pressure perturbation coincides with the onset of the left ventricular (LV) isovolumic contraction, and hence will be referred to as the start of the arterially detected isovolumic contraction (AIC(start)). In the present study we test the hypothesis that the pressure perturbation indeed has a cardiac origin. In ten Yorkshire-Landrace swine, waveform intensity analysis demonstrated that AIC(start) was followed by a positive intensity wave (0.3 × 10(5) ± 0.3 × 10(5) W (m(2) s(2))(-1)). Timing analysis of LV and aortic pressure waveform showed that AIC(start) was preceded by a LV pressure perturbation (3.8 ± 1.8 ms, p < 0.001). These novel cardiac timing and aortic wave intensity findings reveal the cardiac origin of the pressure perturbation. In 15 Yorkshire-Landrace swine, myocardial motion analysis showed a significantly higher rate of segment shortening during the first part of the LV pressure perturbation. Therefore, both the LV and aortic pressure perturbation are most likely caused by the early phase of myocardial contraction, which also causes mitral valve closure. Consequently, AIC(start) is useful in the determination of the isovolumic contraction period, a well-known marker to quantify cardiac dysfunction.

Wave propagation and reflection in the canine aorta: analysis using a reservoir-wave approach

BACKGROUND

Our objective was to demonstrate wave propagation and reflection in the canine aorta. Recently we proposed that aortic pressure is the instantaneous sum of wave-related or "excess" pressure and reservoir or windkessel pressure. Accordingly, in this research we calculated reservoir pressure and subtracted it from measured pressure to identify the change in pressure due to forward- or backward-travelling waves.

METHODS

In 8 anesthetized dogs, excess pressures were calculated from pressure and flow measurements at 4 locations along the aorta; wave intensity analysis was employed to identify wavefronts and the type of waves.

RESULTS

We found that forward compression and decompression waves generated by the left ventricle are reflected, first, from a negative or "open-end" reflection site near the renal arteries (32.0 ± 0.8 cm [SEM] from the aortic root) and, second, from a positive site in the femoral arteries (65.3 ± 2.8 cm or 54.9 ± 2.1 cm, based on 2 alternative extrapolation techniques).

CONCLUSIONS

Aortic wave propagation and reflection can be demonstrated clearly and directly by wave intensity analysis after volume-related changes-changes in reservoir or windkessel pressure-in aortic pressure are accounted for.

Theoretical models for coronary vascular biomechanics: progress & challenges

A key aim of the cardiac Physiome Project is to develop theoretical models to simulate the functional behaviour of the heart under physiological and pathophysiological conditions. Heart function is critically dependent on the delivery of an adequate blood supply to the myocardium via the coronary vasculature. Key to this critical function of the coronary vasculature is system dynamics that emerge via the interactions of the numerous constituent components at a range of spatial and temporal scales. Here, we focus on several components for which theoretical approaches can be applied, including vascular structure and mechanics, blood flow and mass transport, flow regulation, angiogenesis and vascular remodelling, and vascular cellular mechanics. For each component, we summarise the current state of the art in model development, and discuss areas requiring further research. We highlight the major challenges associated with integrating the component models to develop a computational tool that can ultimately be used to simulate the responses of the coronary vascular system to changing demands and to diseases and therapies.

Potential and limitations of wave intensity analysis in coronary arteries

Wave intensity analysis (WIA) is beginning to be applied to the coronary circulation both to better understand coronary physiology and as a diagnostic tool. Separation of wave intensity (WI) into forward and backward traveling components requires knowledge of pulse wave velocity at the point of measurement, which at present cannot accurately be determined in human coronary vessels. This prompted us to study the sensitivity of wave separation to variations in wave speed. An estimate of wave speed (SPc) was calculated based on measured distal intracoronary pressure and Doppler velocity in normal and diseased coronary vessels of patients during hyperemia. Changes of the area under separated WI waveforms were determined for a range of wave speeds from 25 to 200% of the calculated value. Variations in wave speed between half to twice the calculated value did not substantially alter separated WI. In conclusion, although SPc lacks accuracy in determining local coronary wave speed it is within limits still applicable for wave separation in coronary WIA.

Forward and backward waves in the arterial system: impedance or wave intensity analysis?

Both impedance analysis and wave intensity analysis are used to separate measured pressure and flow waveforms into their forward and backward components. The separation is sensitive to the characteristic impedance or wave speed determined from the data. In all other aspects, the results are identical.