The end-systolic elastance $(Ees)$-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 $Ees$ 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 bio-physical modelling to estimate the whole time-varying elastance curve $E model (t)$. We compare $E model es$ with the two single-beat estimation methods , and the normalised varying elastance curve $E N,model (t)$ with $E N (t)$ from published physiological experiments.