Finite element stress analysis of left ventricular mechanics in the beating dog heart

A three-dimensional finite element model was used to explore whether or not transmural distributions of end-diastolic and end-systolic fiber stress are uniform from the apex to the base of the canine left ventricular wall. An elastance model for active fiber stress was incorporated in an axisymmetric model that accurately represented the geometry and fiber angle distribution of the anterior free wall. The nonlinear constitutive equation for the resting myocardium was transversely isotropic with respect to the local fiber axis. Transmural distributions of end-diastolic fiber stress became increasingly nonuniform from midventricle toward the apex or the base. At a typical diastolic left ventricular pressure (1 kPa), the differences between largest and smallest fiber stresses were only 0.5 kPa near midventricle, compared with 4.6 kPa at the apex, and 3.3 kPa at the base. Transmural fiber stress differences at end-systole (14 kPa) were relatively small in regions from the base to the midventricle (13–22 kPa), but were larger between midventricle and the apex (30–43 kPa). All six three-dimensional end-diastolic strain components were within or very close to one standard deviation of published measurements through the midanterior left ventricular free wall of the passive canine heart [Omens et al., Am. J. Physiol.261, H918–H928 (1991)]. End-systolic in-plane normal and shear strains also agreed closely with published experimental measurements in the beating dog heart [Waldman et al., Circ. Res.63, 550–562 (1988)]. The results indicate that, unlike in the midventricle region that has been studied most fully, there may be significant regional nonhomogeneity of fiber stress in the normal left ventricle associated with regional variations in shape and fiber angle.