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Comparative evaluation of three elastance-resistance models of left ventricular mechanics
Abstract
Three local elastance-resistance models of the left ventricular
(LV) systolic function are compared starting from LV pressure and aortic
flow curves measured on dogs at different afterloads. All three models,
characterized by different elastance time-behaviors during relaxation,
predict a decrease of the elastance and an increase of resistance for
growing afterloads, in agreement with the force-length-velocity
relationship at the cardiac muscle level. All models predict negative
elastance values at the highest afterload supporting the presence of
hyperactivation. The descriptive test is satisfied only when elastance
increases during relaxation, and this supports the presence of
flow-induced deactivation. In particular, the model characterized by a
linear increase of elastance is clearly preferred. This is also
confirmed by the results of the sensitivity analysis
... In the ventricle, the diastolic period is described by a variable function in which it includes two different terms: relaxation and distensibility. From this, the elastance of ventricles during diastole is modelled by a non-linear function, which represents post-systolic relaxation, and by a constant function for the rest of the diastolic period, which represents the distensibility of the chamber according to expression (10) (Avanzolini et al., 1991): ...
Simulated experience was performed through a computational haemodynamic model, with the implementation of a cardiovascular numerical model in which the dynamics of the transmitral flow is represented. The influence of haemodynamic variables are evaluated upon the calculated Mitral Valve Area (MVA) using the method of Gorlin's formula. By sensitivity analysis of haemodynamic variables, it is found that blood density, cardiac output, length of valvular tunnel, heart rate and compliance are variables influencing the determination of the calculated MVA. In conclusion, the computational haemodynamic model helps to evaluate the isolated influence of haemodynamic parameters on the functional calculated MVA.
A study of pressure generated by the left ventricle after ejection with constant flow for different values of the ejection flow, flow duration, time of flow arrest, and ventricular volume is discussed. It was found that pressure after ejection, normalized with respect to isovolumic pressure, is regenerated according to a model consisting of an elastance, a resistance, a series elastance, and an additional deactivation component. Deactivation is defined as the difference between the value 1 and the plateau value of the normalized pressure after constant flow ejection. It is shown that this plateau value is constant after constant flow ejection until the minimum in isovolumic dP/dt, i.e. during physiological systole. The plateau value is uniquely related to the value of the normalized pressure with a time constant of 10.44+or-0.09 ms which agrees with the series-elastance time constant of 10.35+or-0.26 ms.
Three viscoelastic models of the left-ventricular (LV) pumping function are proposed and compared with the classical elastance-resistance description starting from data measured on dogs: isovolumic pressure at a given preload together with a series of LV pressure and outflow curves with graded aortic occlusions. The comparison criterion takes into account descriptive ability, robustness of the estimates, and their physical interpretation. The analysis confirms the presence of both activation and deactivation phenomena. The dependence of stiffness and resistance on afterload agrees with known myocardial features and supports the local validity of the proposed models.
Left ventricular pressure, P(t), and outflow Q(t), data were collected in anesthetized, open-chest rats and dogs. The data were used in a three-tiered validation procedure to evaluate 14 competing forms of elastance [E(t)]-resistance (R) left ventricle (LV) pump models. Competing models arose from considering two forms of parameterization of E(t), time variation versus no time variation in LV unstretched volume (Vd) and dependence versus no dependence of R on P(t) and isovolumic P(t). A descriptive test based on the normalized root-mean-square errors in the fit to P and, separately, in the fit to Q was used to distinguish between models. The best of the competing models was the one that treated Vd as a function of time and R as a constant. Models of this form fitted the data very well and were said to be descriptively valid. The best of the competing models were then asked to predict the observed responses to changes in afterload, preload, and prior-beat history. The models did not predict these conditions well and failed to pass the test for predictive validity. Additionally, the model parameters were judged not to represent their supposed physical homologs and, thus, failed the test for explanative validity. One cause for E(t)-R model failure was an inadequate representation of events at end systole. This deficiency was apparently due to not accounting for deactivation in the model. Other features may also be needed before a comprehensive LV model can be formulated. Identical conclusions were made from data from the rat and the dog.
A simple model which represents a linear approximation of the pressurel volume/flow relationship extensively used for describing
ventricular mechanics, especially in simulation studies, is developed. In this model, the left ventricle is represented by
a pressure generator in series with viscous and elastic time-varying elements. Despite its simplicity, the model elucidates
the intimate connections between some current approaches for characterising pulsatile ventricular behaviour. A conventional
identification scheme was used to estimate viscous and elastic parameters from data measured in both isolated rabbit hearts
and open-chest dogs. Their variations with preload and afterload are shown to reflect known local characteristics of the inherently
nonlinear cardiac pump, which correspond also to relevant features at muscular level. These results, together with some recent
experimental evidence, substantially support the finding that both viscosity and elastance vary with time in linear proportion
to the isovolumic pressure.
Quantitative characterization of left ventricle pump properties has been recognized as being of great significance for both physiological and clinical purposes. Several descriptions have been proposed in the past to this end, where the ventricle is viewed as an isovolumic pressure generator coupled to an internal impedance, considered as either only viscous, only elastic or viscoelastic. Though these models have been used widely, the respective advantages and limits have not been fully elucidated. In this paper, six models for the left ventricular pumping function, of the viscoelastic type, are compared using both simulated and experimental data in a typical parameter estimation approach. Elastic and viscous parameters are estimated starting from ventricular pressure and aortic flow, together with the isovolumic pressure at the same preload. The basis for the comparison is the well-established criterion relating the fit obtained from collected data and the covariance matrix of the parameter estimates. The latter allows evaluation of the so-called indifference region in the parameter space, which is represented by an ellipse if both elastic and viscous elements are present. The properties of the indifference region are synthetically represented by two indices linked to the area and the eccentricity of the ellipse: the first represents the mean accuracy of the parameter estimate, the second gives information about the different sensitivities to variation of single parameters. This comparison, in both simulated and experimental cases, generally leads to preference for a model where elastance and viscosity vary with time in linear proportion to the isovolumically developed ventricular pressure. Appropriate description of the elastic effect reveals it to be very crucial while the viscous effect, though improving the fitting of data, is less critical.
To characterize the mechanical properties of the contracting left ventricle, we studied the changes in left ventricular systolic pressure following step-like perturbations (+/- 3 ml) in ventricular volume, using an isovolumically beating, isolated canine heart preparation. Three mechanical properties (elasticity, resistance, and a deactivation effect) were identified. The elastic property differs from the traditional parallel and series elastic elements; it is a time-varying elasticity that includes active and passive effects of volume changes. Furthermore, it could not be represented by a simple time-varying elasticity, but required a second factor to express the dependence of end-systolic elasticity on the timing of the volume step. This effect was represented by a "volume influence factor," which may arise from length-dependent activation. The resistive property appeared to be related to force-velocity behavior of the myocardium. Each mechanical property reacted characteristically to steady state changes in ventricular filling volume or contractile state produced by dobutamine (2-13 micrograms/min). Our findings indicate that elasticity was the property most sensitive to changes in contractile state; these changes increased peak isovolumetric pressure 54% on average, and raised elastic stiffness 40% above control (which was 5.1 mm Hg/ml). Changes in ventricular filling volume only prolonged, but did not alter, the level of elastic stiffness attained at peak pressure. These results support the view that elasticity--or the end-systolic pressure-volume relationship--serves in a given heart to quantify contractility. The "volume influence factor" was not affected by either filling volume or contractile state. Resistance increased in direct proportion with ventricular pressure, but this linear relation was not altered greatly by changes in contractile state or in ventricular filling volume. At 100 mm Hg, ventricular resistance averaged 0.11 mm Hg/ml per sec. Finally, deactivation was greater the later in systole a volume step was imposed, and this pattern was independent of changes in ventricular filling volume and in contractile state.
A model of the left ventricle is proposed. It consists of a thick-walled cylinder-like cavity, the wall of which contains muscle fibres. Orientation and length of the fibres are functions of their position in the wall. During changes of preload and during ejection the dimensions of the cylinder change in a prescribed way. A sliding filament model in series with a real or apparent elastic element is applied to simulate wall tension from which the pressure in the ventricle results. To test the model and to fit the relevant parameters, experiments on isolated perfused rabbit hearts were carried out. The model could simulate isovolumic and non-isovolumic contractions reasonably well in the case when a series elasticity allowing about 6% fibre shortening was present and a preload dependent activation function was applied. Finally it must be concluded that for an accurate estimation of the parameters, not only pressure development and flow must be recorded, but also certain overall ventricular dimensions.
A numerical model of left ventricular (LV) pump function, incorporating cardiac muscle mechanics and LV geometry, was used to derive a simple linear model of local LV contractile properties. This simplified model views the ventricle as a pressure generator (related to isovolumic contraction) coupled with two time-varying elements: 1) a viscous term (related to the dissipative properties of the myocardium), and 2) an elastic term (related to the tension-length curve of activated fiber and to LV geometry).