A three-dimensional collagen-fiber network model of the extracellular matrix for the simulation of the mechanical behaviors and micro structures.

The extracellular matrix (ECM) provides structural and biochemical support to cells and tissues, which is a critical factor for modulating cell dynamic behavior and intercellular communication. In order to further understand the mechanisms of the interactive relationship between cell and the ECM, we developed a three-dimensional (3D) collagen-fiber network model to simulate the micro structure and mechanical behaviors of the ECM and studied the stress-strain relationship as well as the deformation of the ECM under tension. In the model, the collagen-fiber network consists of abundant random distributed collagen fibers and some crosslinks, in which each fiber is modeled as an elastic beam and a crosslink is modeled as a linear spring with tensile limit, it means crosslinks will fail while the tensile forces exceed the limit of spring. With the given parameters of the beam and the spring, the simulated tensile stress-strain relation of the ECM highly matches the experimental results including damaged and failed behaviors. Moreover, by applying the maximal inscribed sphere method, we measured the size distribution of pores in the fiber network and learned the variation of the distribution with deformation. We also defined the alignment of the collagen-fibers to depict the orientation of fibers in the ECM quantitatively. By the study of changes of the alignment and the damaged crosslinks against the tensile strain, this paper reveals the comprehensive mechanisms of four stages of 'toe', 'linear', 'damage' and 'failure' in the tensile stress-strain relation of the ECM which can provide further insight in the study of cell-ECM interaction.