Does the Collagen Network Contribute to Normal Systolic Left Ventricular Wall Thickening? A Theoretical Study in Continuum Mechanics

Abstract

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.