Minimally-invasive estimation of patient-specific end-systolic elastance using a biomechanical heart model

The end-systolic elastance (\(E_{\text {es}}\)) – the slope of the end-systolic pressure-volume relationship (ESPVR) at the end of ejection phase – has become a reliable indicator of myocardial functional state. The estimation of \(E_{\text {es}}\) by the original multiple-beat method is invasive, which limits its routine usage. By contrast, non-invasive single-beat estimation methods, based on the assumption of the linearity of ESPVR and the uniqueness of the normalised time-varying elastance curve \(E^N(t)\) across subjects and physiology states, have been applied in a number of clinical studies. It is however known that these two assumptions have a limited validity, as ESPVR can be approximated by a linear function only locally, and \(E^N(t)\) obtained from a multi-subject experiment includes a confidence interval around the mean function. Using datasets of 3 patients undergoing general anaesthesia (each containing aortic flow and pressure measurements at baseline and after introducing a vasopressor noradrenaline), we first study the sensitivity of two single-beat methods—by Sensaki et al. and by Chen et al.—to the uncertainty of \(E^N(t)\). Then, we propose a minimally-invasive method based on a patient-specific biophysical modelling to estimate the whole time-varying elastance curve \(E^{\text {model}}(t)\). We compare \(E^{\text {model}}_{\text {es}}\) with the two single-beat estimation methods, and the normalised varying elastance curve \(E^{N,\text {model}}(t)\) with \(E^{N}(t)\) from published physiological experiments.