End-systolic Pressure-Volume Relation, Ejection Fraction, and Heart Failure: Theoretical Aspect and Clinical Applications.

A mathematical formalism describing the nonlinear end-systolic pressure-volume relation (ESPVR) is used to derive new indexes that can be used to assess the performance of the heart left ventricle by using the areas under the ESPVR (units of energy), the ordinates of the ESPVR (units of pressure), or from slopes of the curvilinear ESPVR. New relations between the ejection fraction (EF) and the parameters describing the ESPVR give some insight into the problem of heart failure (HF) with normal or preserved ejection fraction. Relations between percentage occurrence of HF and indexes derived from the ESPVR are also discussed.

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.

Criteria for study of heart failure derived from ESPVR.

In this study, the end-systolic pressure-volume relation (ESPVR) is used to derive new criteria that can help understand the problem of heart failure with normal or preserved ejection fraction (HFpEF). It is shown that the ejection fraction (EF) is just one index of several indexes that can be derived from the parameters describing the ESPVR and related areas under ESPVR.

ESPVR, ejection fraction and heart failure.

The problem of heart failure with preserved ejection fraction (HFpEF) has recently received much attention. In this study we discuss some relations that connect ejection fraction EF to the parameters describing the end-systolic pressure-volume relation (ESPVR). It is shown that the study of the relation between EF and ESPVR can give some understanding of the problem of HFpEF.

The calculation of the intramyocardial stress.

A mathematical approach is given by which the intramyocardial stress sigma induced in the passive medium of the myocardium is expressed as the sum of the stress (sigma)p induced in the passive medium by the left ventricular pressure P and the external pressure Po, and the stress(sigma)d induced in the passive medium by the active force generated by the muscular fibers of the myocardium. Relations between sigma = (sigma)p + (sigma)d, the left ventricular elastance E and the residual volume Vd are also derived. Applications to experimental data are given and clinical implications of the results are discussed.