Publications / SAND Report

Modeling the coupled mechanics, transport, and growth processes in collagen tissues

Holdych, David J.; Stevens, Mark J.; In 't Veld, Pieter J.

The purpose of this project is to develop tools to model and simulate the processes of self-assembly and growth in biological systems from the molecular to the continuum length scales. The model biological system chosen for the study is the tendon fiber which is composed mainly of Type I collagen fibrils. The macroscopic processes of self-assembly and growth at the fiber scale arise from microscopic processes at the fibrillar and molecular length scales. At these nano-scopic length scales, we employed molecular modeling and simulation method to characterize the mechanical behavior and stability of the collagen triple helix and the collagen fibril. To obtain the physical parameters governing mass transport in the tendon fiber we performed direct numerical simulations of fluid flow and solute transport through an idealized fibrillar microstructure. At the continuum scale, we developed a mixture theory approach for modeling the coupled processes of mechanical deformation, transport, and species inter-conversion involved in growth. In the mixture theory approach, the microstructure of the tissue is represented by the species concentration and transport and material parameters, obtained from fibril and molecular scale calculations, while the mechanical deformation, transport, and growth processes are governed by balance laws and constitutive relations developed within a thermodynamically consistent framework.