Author(s)

R. M. Shoucri

Abstract

Numerical evaluation of two methods to calculate slope and intercept of endsystolic pressure-volume relation (ESPVR) in the left ventricle is presented. The mathematical formalism is based on results previously published in which the active force of the myocardium (also called isovolumic pressure Piso) is introduced in the formalism describing the pressure-volume relation (PVR) in the left ventricle. The numerical calculation is simple and can be easily implemented in routine clinical work, only the ventricular pressure Pm near endsystole needs to be estimated. A thick-walled cylindrical model contracting symmetrically is assumed for the left ventricle. Keywords: ventricular elastance, end-systolic pressure-volume relation, pressure-volume relation in the ventricles, peak isovolumic pressure, active force of the myocardium. 1 Introduction In previous studies the author has stressed the importance of introducing the active force of the myocardium (also called isovolumic pressure Piso by physiologists) in the formalism describing the pressure-volume relation (PVR) in the ventricles [1–5]. The mathematical formalism developed was used to calculate the stress in the myocardium by using linear elasticity [5] and large elastic deformation [1–4], in this formalism the active force of the myocardium is modelled as force/unit volume of the myocardium generated by the cardiac muscle (see fig. 1). In this study a relation derived in [2] is used to calculate the non-linear end-systolic pressure-volume relation (ESPVR). It is shown that this mathematical relation can be used to calculate in a non-invasive way the

Keywords

ventricular elastance, end-systolic pressure-volume relation, pressure-volume relation in the ventricles, peak isovolumic pressure, active force of the myocardium