Non-invasive calculation of non-linear ESPVR: Theoretical study and clinical applications

Mathematical expressions for the pressure-volume relation (PVR) and the non-linear end-systolic pressure-volume relation (ESPVR) in the heart ventricles have been derived by using the theory of large elastic deformation of the myocardium. A rich collection of new parameters can be derived from the formalism describing the ESPVR, volume values can be measured in a non-invasive way and ratios of pressures can be calculated in a non-invasive way. Relations between the ejection fraction EF and the calculated new indexes give new insight into the problem of heart failure with preserved ejection fraction (HFpEF). Applications to clinical data published in the literature show the consistency of the mathematical formalism used.