Does the collagen network contribute to normal systolic left ventricular wall thickening? A theoretical study in continuum mechanics

Studies in mammalian hearts shown that left ventricular wall thickening is an important mechanism for normal systolic ejection, and that during contraction the myocardium develops a significant stress in the muscular cross-fiber direction. We suggested that the collagen network surrounding the muscular fibers could account for these two mechanical behaviors. To test this hypothesis, we developed a mathematical model for a large deformation response of an active, incompressible, hyperelastic and transversely isotropic cardiac tissue, in which we included a coupling effect between the connective tissue and the muscular fibers. The three-dimensional constitutive law containing this internal pseudo-active kinematic constraint is derived and applied to obtain solutions for the cases of a free contraction, uniaxial and equibiaxial extensions of a rectangular sample assuming negligible body forces and inertia effects. This model may explain the contribution of the collagen network to the two following mechanics: (i) the normal systolic wall thickening, and (ii) the developed pseudo-active tension in the cross-fiber direction.