Aim: Growth and remodeling (G&R) in soft tissue can be triggered when perturbing its mechanical homeostatic state. Experimentally, it has been observed that load-bearing constituents such as collagen and cardiomyocytes are deposited with a preferred pre-stretch in the tissue, which guarantees biological equilibrium. While to achieve mechanical equilibrium as well, we need to estimate the correct elastin prestretches. We have developed an algorithm that numerically determines elastin pre-stretch in the cardiac tissue.
Methodology: As a test case, we considered an idealized left ventricle. We assumed that the geometry is acquired from medical images representing an in vivo configuration (x_ivo). The tissue was assumed to be comprised of elastin, collagen, and myocytes. Next, we assigned the biologically relevant orientation of myocytes and collagen fibers and prescribed experimentally derived stretches to those constituents, thereby achieving their stress contribution. The only unknown to be determined was elastin pre-stretch to achieve a biological and mechanical equilibrium against the applied in vivo pressure (= 120 mmHg). Using finite-element analysis, we iteratively estimated the stress-free configuration of elastin (SFCE) in such a way that the deformation field achieved by applying the pressure and stresses from collagen and myocytes on the SFCE would yield a deformed geometry (x_elastin,estimated) which matches x_ivo within a reasonable tolerance (10-3 mm) and satisfy the in vivo biological and mechanical equilibrium for all constituents.
Results: Our algorithm was able to estimate the SFCE of an idealized LV hexahedral mesh (900 elements, 1284 nodes) in 8 iterations (computation time: 20.3s), yielding a final residual ||x_elastin,estimated - x_ivo|| of 4.0·10-4 mm.
Conclusions: Our method provides a practical framework for determining a prestressed configuration of cardiac configurations that satisfy mechanical and biological equilibrium, enabling further implementation for mechanistic G&R studies. Next steps include anatomical mesh validation and benchmarking with other pre-stress algorithms.