Theoretical model for myocardial trabeculation.

During the morphogenetic process of myocardial trabeculation, most of the cardiac jelly of the initially smooth-walled heart is replaced by sponge-like muscle. The mechanisms that drive and regulate this important process are poorly understood. Using a theoretical model, we examined the possible role that cytoskeletal contraction plays during the initial stages of trabeculation. The myocardium is modeled as a thin viscoelastic membrane consisting of contractile (stress) fibers embedded in an isotropic incompressible matrix, with the interaction of myocardial cells and cardiac jelly fibers providing long-range mechanical effects. The stress fibers are assumed to behave like smooth muscle and to normally operate on the descending limb of their stress-stretch curve. Mechanical instability due to the effectively negative stiffness then leads to the creation of pattern. As a first approximation, computations were carried out for a flat rectangular membrane with stress fibers aligned along a single direction. The computed deformation patterns depend strongly on the magnitude and anisotropy of the long-range effects. Given plausible assumptions about the mechanical properties of the embryonic heart, the model predicts trabecular patterns similar to those observed in the embryo, including the development of circumferential ridges and relatively thin regions ("holes") in the trabecular sheets.