A laminated shell model for the infarcted left ventricle

Experimental studies have shown that a region of partial dysfunction occurs in non-infarcted heart muscle near the edge of a myocardial infarction, where both blood flow and contractile function are compromised. Most data also indicate that the “border zone” for flow is much narrower than that for function. The factors responsible for these effects, which may lead to further infarction or other complications, are not completely understood. Thus, to study the mechanics of this problem, we present an ellipsoidal shell model for the infarcted left ventricle. The analysis of the model is based on a nonlinear shell theory that includes the effects of large axi-symmetric deformation (with torsion), thick-shell effects, anisotropy, muscle activation, and residual stress. The governing equations are solved with a modified integrating matrix technique. We study both acute and chronic apical infarcts, which are represented by relatively soft and hard passive regions, respectively. Comparing theoretical and experimental pressure—volume relations and wall strains indicates that the model describes the mechanical behavior of the normal and ischemic left ventricle reasonably well. The model predicts significantly elevated end-systolic stresses inside an acute infarct, which may contribute to the complication of infarct expansion. Near the edge of the infarct, the results show that a relatively narrow bending boundary layer occurs within a much wider membrane boundary layer, suggesting that these layers correspond to the perfusion and functional border zones, respectively. The stiffer chronic infarct alleviates the stress concentrations in the border zone. Thus, treatment strategies should consider the relative differences in properties between the infarcted and noninfarcted regions.