Modeling the instantaneous pressure-volume relation of the left ventricle: a comparison of six models

Simulations are useful to study the heart's ability to generate flow and the interaction between contractility and loading conditions. The left ventricular pressure-volume (PV) relation has been shown to be nonlinear, but it is unknown whether a linear model is accurate enough for simulations. Six models were fitted to the PV-data measured in five sheep and the estimated parameters were used to simulate PV-loops. Simulated and measured PV-loops were compared with the Akaike information criterion (AIC) and the Hamming distance, a measure for geometric shape similarity. The compared models were: a time-varying elastance model with fixed volume intercept (LinFix); a time-varying elastance model with varying volume intercept (LinFree); a Langewouter's pressure-dependent elasticity model (Langew); a sigmoidal model (Sigm); a time-varying elastance model with a systolic flow-dependent resistance (Shroff) and a model with a linear systolic and an exponential diastolic relation (Burkh). Overall, the best model is LinFree (lowest AIC), closely followed by Langew. The remaining models rank: Sigm, Shroff, LinFix and Burkh. If only the shape of the PV-loops is important, all models perform nearly identically (Hamming distance between 20 and 23%). For realistic simulation of the instantaneous PV-relation a linear model suffices.