Time-varying Elastance Concept Research Articles

The unknown shown by numerical tools: application to right dysfunction

Abstract Funding Acknowledgements Type of funding sources: Public Institution(s). Main funding source(s): Ph.D. Research Grant Introduction. Numerical modelling of cardiovascular flows is emerging as a powerful tool when applied to clinical practice, thanks to its capability of describing hemodynamics non-invasively. Among the different approaches, lumped parameters (0D) models present the advantage of describing the complete circulation at low computational cost, with strong stress on cause-effect relationships between the different functional elements and flow/pressure waveforms. 0D models fully express their potentiality when applied to complex physio-pathological conditions. This work applies such an approach to the right ventricular (RV) dysfunction, modelling the case of an equal systolic and diastolic percentage dysfunction, i.e., 60%. The model highlights how the right dysfunction affects the left performances, despite the unaltered left ventricular (LV) functionality. Purpose. Numerical tools may help clinicians in understanding the characteristic features of physio-pathological conditions, clearly differentiating the contributions of single functional elements. Methods. We develop a 0D model of both left and right circulation, in which heart chambers are simulated with the time-varying elastance concept. Ideal diodes associated with resistances are adopted for the heart valves, and the dissipative effects for the vascular beds and elastic properties for the great vessels are considered. The healthy and the RV dysfunction cases are considered, and, for the pathological condition, we impose a 60% right systolic and diastolic dysfunction. Results. Fig. 1 shows an example of the outputs calculated by our model e.g., the pressure-volume (pV) loops which, in the clinical practice, are obtained with invasive measurements. On the right heart, the simulated dysfunction reduces systolic pressures, augments diastolic pressures and causes an enlargement of the ventricle (Fig. 1a). Interestingly, the pathology reflects also on the LV: the left pV loop exhibits a left/downward shift, despite the unaltered functionality (Fig. 1b). Overall hemodynamic variables reported in Fig. 1c confirm that RV dysfunction causes a deterioration of the global hemodynamics, i.e., CVP increases and, SV and CI decrease. Moreover, RV dysfunction reduces not only the RV performances (EFrv), but the well-functioning LV activities (EFlv) as well. These findings strengthen the arising clinical practice of checking the LV performance to understand when it is necessary to intervene, e.g., in the presence of the Tetralogy of Fallot. Conclusion. Numerical models are powerful tools that can help clinicians in understanding the featuring element of a physio-pathological condition. Here, we have shown that RV dysfunction reduces LV functionalities, thus corroborating the emerging idea that optimal timing for intervention in right diseases requires that also the left side circulation is considered. Abstract Figure. Fig. 1.

Mechano-electric effect and a heart assist device in the synergistic model of cardiac function.

The breakdown of cardiac self-organization leads to heart diseases and failure, the number one cause of death worldwide. Within the traditional time-varying elastance model, cardiac self-organization and breakdown cannot be addressed due to its inability to incorporate the dynamics of various feedback mechanisms consistently. To face this challenge, we recently proposed a paradigm shift from the time-varying elastance concept to a synergistic model of cardiac function by integrating mechanical, electric and chemical activity on micro-scale sarcomere and macro-scale heart. In this paper, by using our synergistic model, we investigate the mechano-electric feedback (MEF) which is the effect of mechanical activities on electric activity-one of the important feedback loops in cardiac function. We show that the (dysfunction of) MEF leads to various forms of heart arrhythmias, for instance, causing the electric activity and left-ventricular volume and pressure to oscillate too fast, too slowly, or erratically through periodic doubling bifurcations or ectopic excitations of incommensurable frequencies. This can result in a pathological condition, reminiscent of dilated cardiomyopathy, where a heart cannot contract or relax properly, with an ineffective cardiac pumping and abnormal electric activities. This pathological condition is then shown to be improved by a heart assist device (an axial rotary pump) since the latter tends to increase the stroke volume and aortic pressure while inhibiting the progression (bifurcation) to such a pathological condition. These results highlight a nontrivial effect of a mechanical pump on the electric activity of the heart.

Synergistic Model of Cardiac Function with a Heart Assist Device.

The breakdown of cardiac self-organization leads to heart diseases and failure, the number one cause of death worldwide. The left ventricular pressure–volume relation plays a key role in the diagnosis and treatment of heart diseases. Lumped-parameter models combined with pressure–volume loop analysis are very effective in simulating clinical scenarios with a view to treatment optimization and outcome prediction. Unfortunately, often invoked in this analysis is the traditional, time-varying elastance concept, in which the ratio of the ventricular pressure to its volume is prescribed by a periodic function of time, instead of being calculated consistently according to the change in feedback mechanisms (e.g., the lack or breakdown of self-organization) in heart diseases. Therefore, the application of the time-varying elastance for the analysis of left ventricular assist device (LVAD)–heart interactions has been questioned. We propose a paradigm shift from the time-varying elastance concept to a synergistic model of cardiac function by integrating the mechanical, electric, and chemical activity on microscale sarcomere and macroscale heart levels and investigating the effect of an axial rotary pump on a failing heart. We show that our synergistic model works better than the time-varying elastance model in reproducing LVAD–heart interactions with sufficient accuracy to describe the left ventricular pressure–volume relation.

Minimally invasive estimation of ventricular dead space volume through use of Frank-Starling curves.

This paper develops a means of more easily and less invasively estimating ventricular dead space volume (Vd), an important, but difficult to measure physiological parameter. Vd represents a subject and condition dependent portion of measured ventricular volume that is not actively participating in ventricular function. It is employed in models based on the time varying elastance concept, which see widespread use in haemodynamic studies, and may have direct diagnostic use. The proposed method involves linear extrapolation of a Frank-Starling curve (stroke volume vs end-diastolic volume) and its end-systolic equivalent (stroke volume vs end-systolic volume), developed across normal clinical procedures such as recruitment manoeuvres, to their point of intersection with the y-axis (where stroke volume is 0) to determine Vd. To demonstrate the broad applicability of the method, it was validated across a cohort of six sedated and anaesthetised male Pietrain pigs, encompassing a variety of cardiac states from healthy baseline behaviour to circulatory failure due to septic shock induced by endotoxin infusion. Linear extrapolation of the curves was supported by strong linear correlation coefficients of R = 0.78 and R = 0.80 average for pre- and post- endotoxin infusion respectively, as well as good agreement between the two linearly extrapolated y-intercepts (Vd) for each subject (no more than 7.8% variation). Method validity was further supported by the physiologically reasonable Vd values produced, equivalent to 44.3–53.1% and 49.3–82.6% of baseline end-systolic volume before and after endotoxin infusion respectively. This method has the potential to allow Vd to be estimated without a particularly demanding, specialised protocol in an experimental environment. Further, due to the common use of both mechanical ventilation and recruitment manoeuvres in intensive care, this method, subject to the availability of multi-beat echocardiography, has the potential to allow for estimation of Vd in a clinical environment.

Modeling muscle's nonlinear viscoelastic dynamics.

Muscle's contractile properties are complicated by its viscoelastic properties. Failure of early viscoelastic muscle models led to Hill's force-velocity relation embodied as the contractile element. Adopting a particular force-velocity relation to describe muscle is neither easy, nor unique [1]. Time-varying elastance based models of the left ventricle have been popular since the idea was presented in 1969 [2]. This paper investigates adoption of the time-varying elastance concept to describe the viscoelastic properties of muscle. It will be shown that a time-varying elastance must be extended to a time, length, and velocity dependent elastance. Results show how a generalized force generator description of muscle [3] may be used to realistically model muscle's viscoelasticity.

Nonlinear lymphangion pressure-volume relationship minimizes edema

Lymphangions, the segments of lymphatic vessel between two valves, contract cyclically and actively pump, analogous to cardiac ventricles. Besides having a discernable systole and diastole, lymphangions have a relatively linear end-systolic pressure-volume relationship (with slope E(max)) and a nonlinear end-diastolic pressure-volume relationship (with slope E(min)). To counter increased microvascular filtration (causing increased lymphatic inlet pressure), lymphangions must respond to modest increases in transmural pressure by increasing pumping. To counter venous hypertension (causing increased lymphatic inlet and outlet pressures), lymphangions must respond to potentially large increases in transmural pressure by maintaining lymph flow. We therefore hypothesized that the nonlinear lymphangion pressure-volume relationship allows transition from a transmural pressure-dependent stroke volume to a transmural pressure-independent stroke volume as transmural pressure increases. To test this hypothesis, we applied a mathematical model based on the time-varying elastance concept typically applied to ventricles (the ratio of pressure to volume cycles periodically from a minimum, E(min), to a maximum, E(max)). This model predicted that lymphangions increase stroke volume and stroke work with transmural pressure if E(min) < E(max) at low transmural pressures, but maintain stroke volume and stroke work if E(min)= E(max) at higher transmural pressures. Furthermore, at higher transmural pressures, stroke work is evenly distributed among a chain of lymphangions. Model predictions were tested by comparison to previously reported data. Model predictions were consistent with reported lymphangion properties and pressure-flow relationships of entire lymphatic systems. The nonlinear lymphangion pressure-volume relationship therefore minimizes edema resulting from both increased microvascular filtration and venous hypertension.

Cardiac phase-dependent time normalization reduces load dependence of time-varying elastance

The time-varying elastance concept provides a comprehensive description of the intrinsic mechanical properties of the left ventricle that are assumed to be load independent. Based on pressure-volume measurements obtained with combined pressure conductance catheterization in six open-chest anesthetized sheep, we show that the time to reach end systole (defined as maximal elastance) is progressively prolonged for increasing ventricle pressures, which challenges the original (load-independent) time-varying elastance concept. Therefore, we developed a method that takes into account load dependency by normalization of time course of the four cardiac phases (isovolumic contraction, ejection, isovolumic relaxation, filling) individually. With this normalization, isophase lines are obtained that connect points in pressure-volume loops of different beats at the same relative time in each of the four cardiac phases, instead of isochrones that share points at the same time in a cardiac cycle. The results demonstrate that pressure curves can be predicted with higher accuracy, if elastance curves are estimated using isophase lines instead of using isochrones [root-mean-square error (RMSE): 3.8 +/- 1.0 vs. 14.0 +/- 7.4 mmHg (P < 0.001), and variance accounted for (VAF): 94.8 +/- 1.3 vs. 78.6 +/- 14.8% (P < 0.001)]. Similar results were found when the intercept volume was assumed to be time varying [RMSE: 1.7 +/- 0.3 vs. 13.4 +/- 7.4 mmHg (P < 0.001), and VAF: 97.4 +/- 0.5 vs. 81.8 +/- 15.5% (P < 0.001)]. In conclusion, phase-dependent time normalization reduces cardiac load dependency of timing and increases accuracy in estimating time-varying elastance.

Time-Varying Elastance Concept Applied to the Relation of Carotid Arterial Flow Velocity and Ventricular Area

Time-Varying Elastance Concept Applied to the Relation of Carotid Arterial Flow Velocity and Ventricular Area

Time-Varying Elastance Concept Applied to the Relation of Carotid Arterial Flow Velocity and Ventricular Area

In this study, the relationship V(f)AR, which was obtained from carotid blood-flow velocity (V(f)) and the cross-sectional area (A) of the left ventricle, was used to assess changes in left ventricular (LV) systolic performance as indicated by the LV pressure-volume relationship (PVR) and end-systolic LV elastance (E(es)). The relationship of maximum systolic V(f) as a surrogate for LV pressure and end-systolic LV area as a surrogate for end-systolic LV volume may allow for the estimation of LV elastance and ejection properties. In 25 pigs, internal carotid V(f) was recorded by using continuous-wave Doppler mode. Echocardiographic measurements of A were continuously performed with an automated border detection system and combined with data for V(f) to display V(f)AR as a series of loop diagrams. These were shifted during acute preload reduction, and an index E'(es) was calculated by applying the time varying elastance concept to end-systolic V(f)AR. Simultaneously, E(es) was acquired by conductance catheter and micromanometer techniques. Comparisons of E'(es) and E(es) were made at various contractility levels obtained by the administration of dobutamine, 5 microg/kg/min, and esmolol, 40 to 60 mg, and at various cardiac load levels, obtained by a fluid bolus infusion or administration of a vasoconstrictor. Highly linear elastance curves (r >or= 0.85, p < 0.0001) were derived from both end-systolic V(f)AR and PVR. Correlation of E'(es) and E(es) revealed an almost linear function: E'(es) = 0.052 + 0.11 E(es) (r = 0.98, p < 0.0001). Administration of dobutamine increased E(es) from 5.8 +/- 3.04 mmHg/mL to 10.1 +/- 4.19 mmHg/mL (p < 0.05), and E('es) from 0.68 +/- 0.288 cm(2)/min/mL to 1.24 +/- 0.458 cm(2)/min/mL (p < 0.05). After administration of esmolol, E(es) and E'(es) both dropped significantly by 3.7 +/- 2.4 mmHg/mL and 0.44 +/- 0.15 cm(2)/min/mL, respectively. No load dependency of E'(es) was seen. Bland-Altman analysis revealed that the change in E'(es), which is required to predict a significant change in E(es), should exceed +16.9% or -13.1% of the preceding value. Application of the time-varying elastance concept on the relation of V(f) and LV area allows for the determination of an index E'(es) that may be used to estimate E(es).

Nonlinear isochrones in murine left ventricular pressure-volume loops: how well does the time-varying elastance concept hold?

The linear time-varying elastance theory is frequently used to describe the change in ventricular stiffness during the cardiac cycle. The concept assumes that all isochrones (i.e., curves that connect pressure-volume data occurring at the same time) are linear and have a common volume intercept. Of specific interest is the steepest isochrone, the end-systolic pressure-volume relationship (ESPVR), of which the slope serves as an index for cardiac contractile function. Pressure-volume measurements, achieved with a combined pressure-conductance catheter in the left ventricle of 13 open-chest anesthetized mice, showed a marked curvilinearity of the isochrones. We therefore analyzed the shape of the isochrones by using six regression algorithms (two linear, two quadratic, and two logarithmic, each with a fixed or time-varying intercept) and discussed the consequences for the elastance concept. Our main observations were 1) the volume intercept varies considerably with time; 2) isochrones are equally well described by using quadratic or logarithmic regression; 3) linear regression with a fixed intercept shows poor correlation (R(2) < 0.75) during isovolumic relaxation and early filling; and 4) logarithmic regression is superior in estimating the fixed volume intercept of the ESPVR. In conclusion, the linear time-varying elastance fails to provide a sufficiently robust model to account for changes in pressure and volume during the cardiac cycle in the mouse ventricle. A new framework accounting for the nonlinear shape of the isochrones needs to be developed.

Modeling of the Coronary Circulatory System

The dynamics of the coronary system is complicated by its dependence on the mechanical properties of the coronary vessels, the anatomical distribution of the vasculature, the biochemical and neurohormonal regulation, and the effect of myocardial contraction. Several types of coronary system models were proposed, focusing on different aspects of coronary system behavior and supported by different animal experiment methodologies. The lumped models were based on well-controlled coronary pressure–flow measurement and simplified assumptions. They are probably most useful for interpreting hemodynamic data measured in modern catheterizaton labs. Anatomical models, with the advancement in morphometric research, coronary angiography, and video densitometry, provided branching pattern, geometric distribution, and distensibility of coronary vessels. Mathematical description based on vascular waterfall theory, intramyocardial pump model, and time varying elastance concept provided some explanation of the interaction between the coronary system and myocardial contraction. More accurate models would include intramyocardial pressure, microcirculatory hemodynamics, coronary flow regulation, and myocardial oxygen supply and consumption. The combination of different models, may lead to a more comprehensive understanding of the coronary system.

Describing the Pumping Heart as a Pressure Source

The pumping heart is described by a new mathematical approach which considers the heart as a pressure source depending on time, volume and flow. This new approach allows a separation between isovolumic (non-ejecting) and ejecting heart properties. The computed results cover most of the features of the human ventricle during normal and altered vascular conditions. It is shown that the time-varying elastance concept is disqualified as an independent description of the heart, it follows from isovolumic heart properties and an ejection effect which consists of positive and negative effects of ventricular blood ejection.

Modeling pressure-flow relations in cardiac muscle in diastole and systole.

Pressure-flow relations were calculated for a symmetrical, maximally dilated, crystalloid-perfused coronary vascular network embedded in cardiac muscle in (static) diastole and (static) systole at two muscle lengths: slack length and 90% of maximal muscle length (Lmax). The calculations are based on the "time-varying elastance concept." That is, the calculations include the mechanical properties of the vascular wall and the (varying) mechanical properties of the myocardial tissue (in cross-fiber direction). We found that, at any given perfusion pressure, coronary flow is smaller in systole than in diastole. Relative reduction in vascular cross-sectional area, which forms the basis of flow impediment, was largest for the smallest arterioles. At a constant perfusion pressure of 62.5 mmHg, the transition from (static) diastole to (static) systole at constant muscle length ("isometric contraction") was calculated to reduce flow by 74% (from 18.9 to 5.0 ml x min(-1) x g(-1)) and by 64% (from 12.6 to 4.6 ml x min(-1) x g(-1)) for the muscle fixed at slack length and 90% of Lmax, respectively. At this perfusion pressure, contraction with 14% shortening (from 90% of Lmax in diastole to slack length in systole) was calculated to reduce flow by 61% (from 12.6 to 5.0 ml x min(-1) x g(-1)). Increasing muscle length from slack length to 90% of Lmax decreases coronary flow by 34% in diastole and by 8% in systole. We conclude that modeling cardiac contraction on the basis of the time-varying elastic properties of the myocardial tissue can explain coronary flow impediment and that contractions, with or without shortening, have a larger effect on coronary flow than changes in muscle length.

End-systolic pressure length relations of stunned right and left ventricles after inotropic stimulation

Regional end-systolic pressure-segment length relationships (ESPSLR) were used to compare the degree of right and left ventricular stunning induced by a 10-min occlusion of the left anterior descending coronary artery and the response to subsequent atrial pacing (50 beats/min above intrinsic heart rate) without and with dobutamine (2 micrograms.kg-1.min-1) in nine anesthetized open-chest pigs. From the ESPSLR, the slope (Ees) (at 100 mmHg for the left and 25 mmHg for the right ventricle) and the total area of the pressure-length relationship (PLA) were determined. From the latter, the distribution into external work (EW) and potential energy (PE) as well as the efficiency of energy transfer (EET = EW/PLA) were calculated. In both the stunned left and right ventricular myocardium Ees and EW were reduced according to the same linear regression equations (delta Ees = 0.7 Ees,baseline - 11.4, r2 = 0.86 and delta EW = 0.4 EWbaseline + 2.3, r2 = 0.67), where Ees,baseline and EWbaseline are Ees and EW at baseline, respectively. EET of the stunned left and right ventricular segments decreased as PLA remained unchanged, due to an increase in PE. EET decreased from 0.84 +/- 0.02 to 0.71 +/- 0.03 (P < 0.05) in the stunned right ventricular segment and from 0.71 +/- 0.02 to 0.44 +/- 0.03 (P < 0.05) in the stunned left ventricular segment. Atrial pacing did not affect EET with respect to stunning levels, whereas the additional infusion of dobutamine restored Ees, EW, and PE and consequently EET to baseline values. In conclusion, the right ventricle is susceptible to stunning. During atrial pacing the EET was lower than expected from the Ees, which could, in agreement with the time-varying elastance concept, be explained by an increase in afterload (a consequence of the decrease in stroke volume). Dobutamine not only increased Ees, EW, and EET but also restored the relationship between Ees and EET in both ventricular stunned segments.

Dobutamine restores the reduced efficiency of energy transfer from total mechanical work to external mechanical work in stunned porcine myocardium.

In order to determine whether the relatively high oxygen consumption of stunned myocardium is related to decreased mechanical efficiency, myocardial oxygen consumption (MVO2) and its major determinants were studied in 10 open chest anaesthetised pigs. According to the time varying elastance concept, MVO2 is determined by contractility (Emax) and total mechanical work (PLA), which is the sum of the external work (EW) and potential energy (PE). Mechanical efficiency (EW/MVO2) equals the product of EW/PLA (= efficiency of energy transfer or EET) and PLA/MVO2. Emax is the slope of the end systolic pressure-segment length relationship, determined by gradually clamping the aorta. PLA is the area enclosed by the end systolic pressure-segment length relationship and the pressure-segment length trajectory. EW is the area of the pressure-segment length loop. Systemic haemodynamics, regional segment shortening, and MVO2 were determined at baseline, during stunning (two sequences of 10 min occlusion and 30 min of reperfusion), after a subsequent 50 beats.min-1 increase in heart rate by atrial pacing and additional infusion of 2 micrograms.kg-1.min-1 dobutamine. Stunning decreased segment shortening from 18.2(SEM 1.9)% to 10.2(1.5)%, MVO2 from 4.16(0.27) x 10(-2) to 2.84(0.25) x 10(-2) mumol.beat-1.g-1, and Emax from 47(9) to 23(3) mm Hg.mm-1 (all p < 0.05). PLA decreased by 13(4)%, as EW decreased by 42(6)%, and PE tended to increase. Although EET decreased from 0.58(0.04) to 0.40(0.03) (p < 0.05), there was no decrease in the mechanical efficiency, as an increase in PE caused an increase in PLA/MVO2 which compensated for the decrease in EET. Dobutamine infusion increased Emax and EW per beat to 120(23)% and 67(8)% of baseline, respectively, while MVO2 [4.12(0.53) mumol.beat-1.g-1] and EET [0.57(0.04)] returned to baseline. In stunned myocardium, mechanical efficiency is not decreased despite a decrease in EET. The increase in EET after dobutamine may explain the lack of the excessive increase in MVO2.

Modeling the dynamic interaction between left ventricle and intra-aortic balloon pump

An analog model is developed to characterize how alterations of some intra-aortic balloon pump (IABP) parameters affect the coupling between left ventricle (LV) and aorta. The time-varying elastance concept is applied to modeling both active components (LV and IABP) in the assisted circulation. Pressure and flow waveforms in the system are determined by numerically integrating five simultaneous state equations that represent the system dynamics. Validity of the model is supported by good agreement between model predictions and published data on LV pressure-volume (P-V) loops, end-systolic P-V relations, and hemodynamic consequences of adjusting IABP timing and speed. The model also predicts that increasing balloon volume increases the diastolic aortic pressure augmentation but has a negative effect of increasing LV load. Increasing balloon diameter over length ratio and holding a constant volume increases the diastolic augmentation and decreases the LV demand. Positioning the balloon closer to the heart improves systolic unloading but affects neither diastolic augmentation nor cardiac output. These results suggest that occlusivity is a major determinant of IABP effectiveness and plays a more important role than balloon volume and position.

Mechanisms for left ventricular systolic dysfunction in aortic regurgitation: Importance for predicting the functional response to aortic valve replacement

To test the hypothesis that the combined use of the time-varying distance concept and conventional circumferential stress-shortening relations would elucidate differential mechanisms for left ventricular systolic dysfunction in severe, chronic aortic regurgitation and therefore predict the functional responses to aortic valve replacement, 31 control patients and 37 patients with aortic regurgitation were studied. The studies included micromanometer left ventricular pressure determinations, biplane contrast cineangiograms under control conditions and radionuclide angiograms under control conditions and during methoxamine or nitroprusside infusions with right atrial pacing.The patients with aortic regurgitation were classified into three groups: Group I had normal Emaxand stress-shortening relations, Group II had abnormal Emaxbut normal stress-shortening relations and Group III had abnormal Emaxand stress-shortening relations. The left ventricular end-diastolic and end-systolic volumes showed a progressive increase and the ejection fraction showed a progressive decrease from Group I to III; these values differed from those in the control patients (p < 0.001). In Group I, then was a decrease in left ventricular volumes (p < 0.05) but no significant change in ejection fraction (61 ± 7% versus 63 ± 4%) after aortic valve replacement. In contrast, in Group II, reduction in left ventricular volumes (p < 0.01) was associated with an increase in ejection fraction from 50 ± 8% to 64 ± 11% (p < 0.01). Finally, in Group III, reduction in left ventricular volumes (p < 0.05) was associated with a further decrement in ejection fraction from 35 ± 13% to 30 ± 13%.Group I patients had compensated adequately for chronic volume overload. However, Group II had left ventricular dysfunction that was associated with an increase in the left ventricular volume/mass ratio compared with that in the control patients and Group I (p < 0.05 for both), suggesting inadequate hypertrophy and assumption of spherical geometry. Finally, irreversible myocardial dysfunction had supervened in Group III.In conclusion, a combined analysis of left ventricular chamber performance using the time-varying elastance concept and myocardial performance using conventional circumferential stress-shortening relations provides complementary information that elucidates differential mechanisms for left ventricular systolic dysfunction and therefore predicts the functional response to aortic valve replacement.

Coronary oscillatory flow amplitude is more affected by perfusion pressure than ventricular pressure

In this study on the isolated, maximally vasodilated, blood-perfused cat heart we investigated the relation between left ventricular developed pressure (delta Piv) and coronary oscillatory flow amplitude (diastolic minus systolic flow, delta F) at different levels of constant perfusion pressure (Pp). We hypothesized that the effect of cardiac contraction on the phasic flow results from the changing elastic properties of cardiac muscle. The coronary vessel compartment can, as can the left ventricular lumen compartment, be described by a time-varying elastance. This concept predicts that the effect of left ventricular pressure on delta F is small, whereas the effect of Pp is considerable. Both the waterfall model and the intramyocardial pump model predict the inverse. The relation between delta Piv and delta F at a Pp of 10 kPa is delta F = (4.71 +/- 3.08).delta Piv + 337 +/- 75 (slope in ml.min-1.100 g-1.kPa-1 and intercept in ml.min-1.100 g-1; n = 7); the relation between (constant levels of) Pp and delta F at a constant delta Piv of 10 kPa is delta F = 51.Pp + 211 (slope in ml.min-1.100 g-1.kPa-1 and intercept in ml.min-1.100 g-1; n = 6). The differences in slope are best predicted by the time-varying elastance concept.

Active cross-bridge model Reproduction of the myocardial force-length-time relation and the left ventricular pressure-length-time relation in systole.

A mathematical model has been derived to describe cardiac contraction. This model assumes (1) a linear end-systolic force-length relation for the intact left ventricular (LV) myocardium with proportionality constant Ec, and (2) that the rate of increase in the number of active cross-bridges is proportional to the number of cross-bridges capable of being activated at that moment with a proportionality constant Ka. Quantitative evaluation of this model was performed using parameter values measured in the normal human LV. The model predictions agreed well with many earlier experimental data concerning the myocardial force-time relation, myocardial force-velocity-length relation, systolic time interval-afterload relation, time-varying elastance concept, several LV end-systolic relations, and LV dP/dtmax-end-diastolic volume relation. Moreover, two important basic properties of contractile proteins, i.e., the maximal force-generating capacity and the rate of activation of cross-bridges, were evaluated in the model from the values of Ec and Ka, respectively. Although no definitive biological proof has yet been provided for the assumptions, this model might mathematically integrate the myocardial and ventricular dynamics over the entire systole and then provides a new method for evaluation of the human LV systolic function from two basic properties of active cross-bridges.

Varying elastance concept may explain coronary systolic flow impediment.

We measured phasic arterial coronary inflow in the blood-perfused isolated cat heart (n = 5) with a balloon in the left ventricle under well-defined conditions, i.e., constant perfusion pressure, constant vasomotor tone (maximal vasodilation), and heart rate. The normalized amplitude (A) between systolic flow (Fs) and diastolic flow (Fd) [A = (Fd - Fs)/Fd] was related to systolic left ventricular pressure (Ps, range 1.6-17 kPa, 1 kPa = 7.5 mmHg) for different isovolumic beats obtained by changes in balloon volume and for low load isobarically ejecting beats (pressure 0.2 kPa). The data were fitted to A = a + bPs with a = 0.70 +/- 0.15 (SD) and b = 0.005 +/- 0.005 kPa-1. This relation indicates a very weak effect of left ventricular systolic pressure on normalized flow amplitude. Thus the hypothesis that left ventricular pressure is the sole determinant impeding coronary flow could not be confirmed. However, our data could be explained on basis of the time-varying elastance concept (H. Suga, K. Sagawa, and A. A. Shoukas. Circ. Res. 32: 314-322, 1973). The intravascular and luminal (cavity) compartments both are assumed to be subject to a time-varying elastance. The time-varying luminal elastance is similar for isovolumic and isobaric beats. We assume that the elastance of the vascular compartment also behaves the same for these beats, and therefore coronary flow is affected similarly.(ABSTRACT TRUNCATED AT 250 WORDS)