A Numerical Study of Fibrous Tissue Formation of Type I Collagen under Mechanical Stimuli by Reaction - Diffusion Equations with Motion of Fibroblasts~!2008-03-31~!2008-05-29~!2008-06-12~!

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.