A micromechanical model for the growth of collagenous tissues under mechanics-mediated collagen deposition and degradation

Abstract

In this study, we developed a micromechanical model for the growth and remodeling of a soft tissue based on the concurrent action of collagen deposition and degradation. We assumed in the model that collagen degradation causes a reduction in the fiber radius, while collagen deposition can increase both the radius and length of the collagen fibers growing under load. The latter arises from the assumption that collagen is deposited in an unstressed state, which increases the reference length of a fiber growing under mechanical load. The rate of collagen deposition and degradation can be stimulated and inhibited, respectively, by the fiber axial strain energy density. From these assumptions, we derived kinetic relationships for the fiber radial and axial growth stretch, and constitutive relations for the stress response and growth and remodeling of the tissues. We applied the model to study the growth of collagen fibers under a static and cyclic force. Cyclic force loading can drive the continual axial growth of collagen fiber, while the axial growth under a constant force eventually halts when an equilibrium state is reached. We then applied the model to investigate the development of stress and strain homeostasis of a spherical collagenous tissue membrane in response to a perturbation in the internal pressure. The model showed that an increase in the pressure produced growth in the tissue radius and thickness, such that the stress response was able to recover the equilibrium membrane stress before the pressure perturbation. Tissues composed of slender, or low-crimp collagen fibers also recovered the equilibrium mechanical stretch level before the perturbation. These results indicated that concurrent mechanics-stimulated collagen deposition and mechanics-inhibited degradation can produce stress homeostasis and for some fiber morphology strain homeostasis without prescribing a target stress or fiber strain.