Ejection Fraction and ESPVR. A study from a theoretical perspective

A formula derived by using large elastic deformation for the contraction of the myocardium is used to describe the pressure-volume relation (PVR) in the heart left ventricle, it is also used to calculate a mathematical expression for the non-linear end-systolic pressure-volume relation (ESPVR) in the left ventricle. An important feature of the mathematical formalism used is the inclusion of the isovolumic pressure Piso (equal active pressure generated by the myocardium) in the formalism describing the PVR. Relations between the ejection fraction (EF) and parameters describing the non-linear ESPVR are presented. It is shown that the non-linear ESPVR offers a rich collection of parameters that can be used to study the performance of the ventricles, like the areas under the ESPVR (units of energy) or the ordinates of the ESPVR (units of pressure), slopes and intercepts of the curves involved. The mathematical procedure can be easily implemented in a non-invasive way in routine clinical work when ratios of variables are calculated, it necessitates only the non-invasive measurement of the dimensions of the ventricles. Applications to clinical data published in the literature are presented, and they give results that show the consistency of the mathematical formalism used. The implications of the results of this research work on the study of the problem of heart failure with normal or preserved ejection fraction (HFpEF) are discussed.