Estimation of time-varying systolic properties of left ventricular mechanics

Late-systolic pumping properties of the left ventricle. Deviation from elastance-resistance behavior

Elastance-resistance [E(t)-R] representations of the left ventricle (LV) were evaluated for their ability to reproduce instantaneous pressure [P(t)] and outflow [Q(t)]. Experiments were performed in open-chest rats. P(t) and Q(t) were measured during steady-state ejecting beats and during a beat in which the aorta was suddenly clamped. The degree of clamping varied from partial to total occlusion. The total occlusion beat was considered an isovolumic beat that generated an isovolumic pressure [Piso(t)] with a characteristic time to maximal Piso(t) [Tpisomax]. In ejecting beats, 34% of stroke volume was delivered after Tpisomax. P(t) and Q(t) from the steady-state ejecting beats and Piso(t) from the clamped beat were then used to estimate parameters of an E(t)-R model. Components of P(t) and Q(t) not accounted for by E(t)-R were identified and termed extra-pressure [Pext(t)] and extra-outflow [Qext(t)]. Pext(t) and Qext(t) were near-zero valued until Tpisomax; then they became systematically positive and finally negative valued after end ejection. During partial aortic occlusion, P(t) was elevated and Q(t) was reduced. However, the time of ejection was extended, and the fraction of stroke volume delivered after Tpisomax increased as P(t) was made higher. Partial occlusion also prolonged the positive phase of Pext(t) and Qext(t). Elements possessing "active" and "deactive" properties were added to the E(t)-R model in an attempt to account for Pext(t) and Qext(t) during partial occlusion. Optional forms of these elements were considered. These expanded E(t)-R models were fitted to basal ejecting data and then asked to predict data from a partial occlusion beat. All expanded models failed to adequately predict the partial occlusion pressure and/or outflow. It was concluded that 1) late ejection was quantitatively important to LV pumping, 2) behavior during late ejection was inconsistent with E(t)-R, and 3) ad hoc modification of E(t)-R models was not likely to yield LV pumping models that could satisfactorily reproduce instantaneous P(t) and Q(t) behavior over the entire ejection period.

Three-element model for total systemic circulation: emphasis on the accuracy of parameter estimates

In this study, the accuracy achievable in the parameter estimates of a three-element linear model for the systemic vascular bed is considered. The model neglects inertial effects and includes only three elements representing arterial compliance, peripheral resistance and venous compliance, in agreement with recent sensitivity investigations. Parameter estimation starts from arterial and right atrial pressure signals generated by a closed-loop simulator of the cardiovascular circulation and corrupted with normal noise to account for measurement errors. In this way, the influences of a wide variety of circulatory conditions were investigated. The results achieved give evidence that arterial compliance is generally well estimated, while venous compliance is more variable, particularly at high peripheral resistance when measured signals appear to be less sensitive to this parameter. However, presence of cardiac disease, such as heart failure and valvular stenosis has minimal influence on compliance estimates. These results suggest that this simple model can be conveniently applied even under noisy conditions.

Model selection for ventricular mechanics: a sensitivity analysis approach

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.