Wave intensity analysis of left ventricular filling: application of windkessel theory

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

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

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

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

PKC independent inhibition of voltage gated calcium channels by volatile anesthetics in freshly isolated vascular myocytes from the aorta

In this study we used barium currents through voltage gated L-type calcium channels (recorded in freshly isolated cells with a conventional patch-clamp technique) to elucidate the cellular action mechanism for volatile anesthetics. It was found that halothane and isoflurane inhibited (dose-dependently and voltage independently) Ba2+ currents through voltage gated Ca2+ channels. Half maximal inhibitions occurred at 0.64 ± 0.07 mM and 0.86 ± 0.1 mM. The Hill slope value was 2 for both volatile anesthetics, suggesting the presence of more than one interaction site. Current inhibition by volatile anesthetics was prominent over the whole voltage range without changes in the peak of the current voltage relationship. Intracellular infusion of the GDPβS (100 μM) together with staurosporine (200 nM) did not prevent the inhibitory effect of volatile anesthetics. Unlike pharmacological Ca2+ channel blockers, volatile anesthetics blocked Ca2+ channel currents at resting membrane potentials. In other words, halothane and isoflurane induced an 'initial block'. After the first 4-7 control pulses, the cells were left unstimulated and anesthetics were applied. The first depolarization after the pause evoked a Ca2+ channel current whose amplitude was reduced to 41 ± 3.4% and to 57 ± 4.2% of control values. In an analysis of the steady-state inactivation curve for voltage dependence, volatile anesthetics induced a negative shift of the 50% inactivation of the calcium channels. By contrast, the steepness factor characterizing the voltage sensitivity of the channels was unaffected. Unitary L-type Ca2+ channels blockade occurred under cell-attached configuration, suggesting a possible action of volatile anesthetics from within the intracellular space or from the part of the channel inside the lipid bilayer.

Clinical benefits of integrating cardiac and vascular models

INTRODUCTION

Recent advances in computational methods and medical imaging techniques have enabled non-invasive exploration of cardiovascular pathologies, from cardiac level to complex arterial networks. The potential of cardiac and vascular modeling in guiding and monitoring therapies could be further extended through the integration of the two systems.

AREAS COVERED

This review includes advances in methods for cardiac electromechanics and vascular flow simulations. The results of a literature search depicting the state of the art in cardiac and vascular modeling are reviewed. The paper goes on to address the benefits and challenges of combined cardiovascular modeling, highlighting the relevance of specific cardiovascular features and implementation. Various alternative approaches and insights on future directions are presented and analyzed with respect to their applicability to clinical practice.

EXPERT OPINION

The article has emerged from the exploration of currently available cardiac and vascular mathematical tools and their corresponding clinical application. The summarized analysis suggests that future efforts should be aimed at developing more accurate and patient-specific mathematical models integrating cardiac and vascular functions to enhance the knowledge of cardiovascular pathologies.

Mathematical multi-scale model of the cardiovascular system including mitral valve dynamics. Application to ischemic mitral insufficiency

Background

Valve dysfunction is a common cardiovascular pathology. Despite significant clinical research, there is little formal study of how valve dysfunction affects overall circulatory dynamics. Validated models would offer the ability to better understand these dynamics and thus optimize diagnosis, as well as surgical and other interventions.

Methods

A cardiovascular and circulatory system (CVS) model has already been validated in silico, and in several animal model studies. It accounts for valve dynamics using Heaviside functions to simulate a physiologically accurate "open on pressure, close on flow" law. However, it does not consider real-time valve opening dynamics and therefore does not fully capture valve dysfunction, particularly where the dysfunction involves partial closure. This research describes an updated version of this previous closed-loop CVS model that includes the progressive opening of the mitral valve, and is defined over the full cardiac cycle.

Results

Simulations of the cardiovascular system with healthy mitral valve are performed, and, the global hemodynamic behaviour is studied compared with previously validated results. The error between resulting pressure-volume (PV) loops of already validated CVS model and the new CVS model that includes the progressive opening of the mitral valve is assessed and remains within typical measurement error and variability. Simulations of ischemic mitral insufficiency are also performed. Pressure-Volume loops, transmitral flow evolution and mitral valve aperture area evolution follow reported measurements in shape, amplitude and trends.

Conclusions

The resulting cardiovascular system model including mitral valve dynamics provides a foundation for clinical validation and the study of valvular dysfunction in vivo. The overall models and results could readily be generalised to other cardiac valves.

Measurements of changes in left ventricular volume, strain, and twist during isovolumic relaxation using MRI

Left ventricular (LV) active relaxation begins before aortic valve closure and is largely completed during isovolumic relaxation (IVR), before mitral valve opening. During IVR, despite closed mitral and aortic valves, indirect assessments of LV volume have suggested volume increases during this period. The aim of this study is to measure LV volume throughout IVR and to determine the sources of any volume changes. For 10 healthy individuals (26.0 ± 3.8 yr), magnetic resonance imaging was used to measure time courses of LV volume, principal myocardial strains (circumferential, longitudinal, radial), and LV twist. Mitral leaflet motion was observed using echocardiography. During IVR, LV volume measurements showed an apparent increase of 4.6 ± 1.5 ml (5.0 ± 2.0% of the early filling volume change), the LV untwisted by 4.5 ± 1.9° (36.6 ± 18.0% of peak systolic twist), and changes in circumferential, longitudinal, and radial strains were +0.87 ± 0.64%, +0.93 ± 0.57%, and −1.46 ± 1.66% (4.2 ± 3.3%, 5.9 ± 3.3%, and 5.3 ± 7.5% of peak systolic strains), respectively. The apparent changes in volume correlated ( P < 0.01) with changes in circumferential, longitudinal, and radial strains ( r = 0.86, 0.69, and −0.37, respectively) and untwisting ( r = 0.83). The closed mitral valve leaflets were observed to descend into the LV throughout IVR in all subjects in apical four- and three-chamber and parasternal long-axis views by 6.0 ± 3.3, 5.1 ± 2.4, and 2.1 ± 5.0 mm, respectively. In conclusion, LV relaxation during IVR is associated with changes in principal strains and untwisting, which are all correlated with an apparent increase in LV volume. Since closed mitral and aortic valves ensure true isovolumic conditions, the apparent volume change likely reflects expansion of the LV myocardium and the inward bowing of the closed mitral leaflets toward the LV interior.

Quantitative analysis of exercise-induced enhancement of early- and late-systolic retrograde coronary blood flow

Coronary blood flow (CBF) is reduced and transiently reversed during systole via cardiac contraction. Cardiac contractility, coronary tone, and arterial pressure each influence systolic CBF (CBF(SYS)), particularly by modulating the retrograde component of CBF(SYS). The effect of concurrent changes in these factors on CBF(SYS) during dynamic exercise has not been examined. Using chronically instrumented swine, we hypothesized that dynamic exercise enhances retrograde CBF(SYS). Phasic CBF was examined at rest and during treadmill exercise [2-5 miles/h (mph)]. Absolute values of mean CBF over the cardiac cycle (CBF(CYCLE)) as well as mean CBF in diastole (CBF(DIAS)) and mean CBF(SYS) were increased by exercise, while relative CBF(DIAS) and CBF(SYS) expressed as percentage of mean CBF(CYCLE) were principally unchanged. Early retrograde CBF(SYS) was present at rest and increased in magnitude (-33 +/- 4 ml/min) and as a percent of CBF(CYCLE) (-0.6 +/- 0.1%) at 5 mph. This reversal was transient, comprising 3.7 +/- 0.3% of cardiac cycle duration at 5 mph. Our results also reveal that moderately intense exercise (>3 mph) induced a second CBF reversal in late systole before aortic valve closure. At 5 mph, late retrograde CBF(SYS) amounted to -53 +/- 11 ml/min (-3.1 +/- 0.7% of CBF(CYCLE)) while occupying 11.1 +/- 0.3% of cardiac cycle duration. Wave-intensity analysis revealed that the second flow reversal coincided with an enhanced aortic forward-going decompression wave (vs. rest). Therefore, our data demonstrate a predictable increase in early-systolic CBF reversal during exercise and additionally that exercise induces a late-systolic CBF reversal related to the hemodynamic effects of left ventricular relaxation that is not predictable using current models of phasic CBF.

The compression and expansion waves of the forward and backward flows: an in-vitro arterial model

Although the propagation of arterial waves of forward flows has been studied before, that of backward flows has not been thoroughly investigated. The aim of this research is to investigate the propagation of the compression and expansion waves of backward flows in terms of wave speed and dissipation, in flexible tubes. The aim is also to compare the propagation of these waves with those of forward flows. A piston pump generated a flow waveform in the shape of approximately half-sinusoid, in flexible tubes (12 mm and 16 mm diameter). The pump produced flow in either the forward or the backward direction by moving the piston forward, in a 'pushing action' or backward, in a 'pulling action', using a graphite brushes d.c. motor. Pressure and flow were measured at intervals of 5 cm along each tube and wave speed was determined using the PU-loop method. The simultaneous measurements of diameter were also taken at the same position of the pressure and flow in the 16 mm tube. Wave intensity analysis was used to determine the magnitude of the pressure and velocity waveforms and wave intensity in the forward and backward directions. Under the same initial experimental conditions, wave speed was higher during the pulling action (backward flow) than during the pushing action (forward flow). The amplitudes of pressure and velocity in the pulling action were significantly higher than those in the pushing action. The tube diameter was approximately 20 per cent smaller in the pulling action than in the pushing action in the 16 mm tube. The compression and expansion waves resulting from the pushing and pulling actions dissipated exponentially along the travelling distance, and their dissipation was greater in the smaller than in the larger tubes. Local wave speed in flexible tubes is flow direction- and wave nature-dependent and is greater with expansion than with compression waves. Wave dissipation has an inverse relationship with the vessel diameter, and dissipation of the expansion wave of the pulling action was greater than that of the pushing action.