A Numerical Study of Fibrous Tissue Formation of Type I Collagen under Mechanical Stimuli by Reaction - Diffusion Equations with Motion of Fibroblasts

ABSTRACT

When the fibrous structure of collagen in soft tissue is adapted to an external load, its stiffness and topological characteristics are changed to achieve favorable function during the adaptation. Thus, a study of the formation of such fibrous tissue under mechanical stimuli is essential. To investigate the formation by the functional adaptation of fibrous tissue from a mechanical viewpoint, the vector of type I collagen fiber density is first defined by analogy to the dislocation density tensor. Then the mathematical model for the motion of a fibroblast and the reaction-diffusion equations for concentrations of the growth factors secreted from a fibroblast are generalized by considering the effect of mechanical load. After a multi-axial constitutive equation for the fibrous tissue is proposed, a finite element simulation of fibrous tissue formation by type I collagen fibers under mechanical stress is performed.