Normalization of end-systolic pressure-volume relation and Emax of different sized hearts

A shift of the ventricular end-systolic pressure-volume (P-V) relation and a change in its slope Emax reasonably reflect a change in contractility in a given ventricle. However, comparison of Emax's of different sized hearts may be difficult without an appropriate normalization. We attempted to normalize Emax of different sized hearts to the force-length (F-L) relation of unit mass of myocardium in the ventricular wall. We formulated the end-systolic P-V relation as (end-systolic pressure) = Emax (end-systolic volume Vi - Vd), where Vd = volume axis intercept of the end-systolic P-V relation line. As a first step, both thick wall sphere and cylinder models of the ventricle with a wall volume of Vm were used. Circumferential F-L relation of unit myocardium in different ventricular wall layers were formulated as functions of Emax, Vd, and Vm. We found that as long as the product of Emax and Vd remains constant, the F-L relation in the midwall layer and the average F-L relation in the wall remain relatively unchanged regardless of wide changes in Vm and Vi. The elevation of the F-L relation curve, which represents myocardial contractility, was found to change in proportion to Emax Vd, largely independent of Vm and Vi, or the size of the ventricle.