The equatorial region of the canine left ventricle was modeled as a thick-walled cylinder consisting of an incompressible hyperelastic material with homogeneous exponential properties. The anisotropic properties of the passive myocardium were assumed to be locally transversely isotropic with respect to a fiber axis whose orientation varied linearly across the wall. Simultaneous inflation, extension, and torsion were applied to the cylinder to produce epicardial strains that were measured previously in the potassium-arrested dog heart. Residual stress in the unloaded state was included by considering the stress-free configuration to be a warped cylindrical arc. In the special case of isotropic material properties, torsion and residual stress both significantly reduced the high circumferential stress peaks predicted at the endocardium by previous models. However, a resultant axial force and moment were necessary to cause the observed epicardial deformations. Therefore, the anisotropic material parameters were found that minimized these resultants and allowed the prescribed displacements to occur subject to the known ventricular pressure loads. The global minimum solution of this parameter optimization problem indicated that the stiffness of passive myocardium (defined for a 20 percent equibiaxial extension) would be 2.4 to 6.6 times greater in the fiber direction than in the transverse plane for a broad range of assumed fiber angle distributions and residual stresses. This agrees with the results of biaxial tissue testing. The predicted transmural distributions of fiber stress were relatively flat with slight peaks in the subepicardium, and the fiber strain profiles agreed closely with experimentally observed sarcomere length distributions. The results indicate that torsion, residual stress and material anisotropy associated with the fiber architecture all can act to reduce endocardial stress gradients in the passive left ventricle.

Background-To treat cardiac injuries created by myocardial infarcts, current approaches seek to add cells and/or synthetic extracellular matrices to the damaged ventricle to restore function. Because definitive myocardial regeneration remains undemonstrated, we propose that cardiac changes observed from implanted materials may result from altered mechanisms of the ventricle. Methods and Results-We exploited a validated finite element model of an ovine left ventricle with an anteroapical infarct to examine the short-term effect of injecting material to the left ventricular wall. The model's mesh and regional material properties were modified to simulate expected changes. Three sets of simulations were run: (1) single injection to the anterior border zone; (2) therapeutic multiple border zone injections; and (3) injection of material to the infarct region.Results indicate that additions to the border zone decrease end-systolic fiber stress proportionally to the fractional volume added, with stiffer materials improving this attenuation. As a potential therapy, small changes in wall volume (Ϸ4.5%) reduce elevated border zone fiber stresses from mean end-systole levels of 28.2 kPa (control) to 23.3 kPa (treatment), similar to levels of 22.5 kPA computed in remote regions. In the infarct, injection improves ejection fraction and the stroke volume/end-diastolic volume relationship but has no effect on the stroke volume/end-diastolic pressure relationship. Conclusions-Simulations indicate that the addition of noncontractile material to a damaged left ventricular wall has important effects on cardiac mechanics, with potentially beneficial reduction of elevated myofiber stresses, as well as confounding changes to clinical left ventricular metrics.

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Tagged MRI and finite-element (FE) analysis are valuable tools in analyzing cardiac mechanics. To determine systolic material parameters in three-dimensional stress-strain relationships, we used tagged MRI to validate FE models of left ventricular (LV) aneurysm. Five sheep underwent anteroapical myocardial infarction (25% of LV mass) and 22 wk later underwent tagged MRI. Asymmetric FE models of the LV were formed to in vivo geometry from MRI and included aneurysm material properties measured with biaxial stretching, LV pressure measurements, and myofiber helix angles measured with diffusion tensor MRI. Systolic material parameters were determined that enabled FE models to reproduce midwall, systolic myocardial strains from tagged MRI (630 +/- 187 strain comparisons/animal). When contractile stress equal to 40% of the myofiber stress was added transverse to the muscle fiber, myocardial strain agreement improved by 27% between FE model predictions and experimental measurements (RMS error decreased from 0.074 +/- 0.016 to 0.054 +/- 0.011, P < 0.05). In infarct border zone (BZ), end-systolic midwall stress was elevated in both fiber (24.2 +/- 2.7 to 29.9 +/- 2.4 kPa, P < 0.01) and cross-fiber (5.5 +/- 0.7 to 11.7 +/- 1.3 kPa, P = 0.02) directions relative to noninfarct regions. Contrary to previous hypotheses but consistent with biaxial stretching experiments, active cross-fiber stress development is an integral part of LV systole; FE analysis with only uniaxial contracting stress is insufficient. Stress calculations from these validated models show 24% increase in fiber stress and 115% increase in cross-fiber stress at the BZ relative to remote regions, which may contribute to LV remodeling.