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

The end-systolic elastance ($E_{es}$) -- 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 $E_{es}$ 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 $E^{model}(t)$. 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 \inserted{published} physiological experiments.