Relation between left ventricular cavity pressure and volume and systolic fiber stress and strain in the wall

Pumping power as delivered by the heart is generated by the cells in the myocardial wall. In the present model study global left-ventricular pump function as expressed in terms of cavity pressure and volume is related to local wall tissue function as expressed in terms of myocardial fiber stress and strain. On the basis of earlier studies in our laboratory, it may be concluded that in the normal left ventricle muscle fiber stress and strain are homogeneously distributed. So, fiber stress and strain may be approximated by single values, being valid for the whole wall. When assuming rotational symmetry and homogeneity of mechanical load in the wall, the dimensionless ratio of muscle fiber stress (sigma f) to left-ventricular pressure (Plv) appears to depend mainly on the dimensionless ratio of cavity volume (Vlv) to wall volume (Vw) and is quite independent of other geometric parameters. A good (+/- 10%) and simple approximation of this relation is sigma f/Plv = 1 + 3 Vlv/Vw. Natural fiber strain is defined by ef = In (lf/lf,ref), where lf,ref indicates fiber length (lf) in a reference situation. Using the principle of conservation of energy for a change in ef, it holds delta ef = (1/3)delta In (1 + 3Vlv/Vw).