Developing quantitative models for contraction at wound edges using finite element analysis

Abstract

Finite element analysis was applied to develop a quantitative tool for studying contraction at wound edges. Two models showing contraction at the edges of a cylindrical liver wound were employed. The first model assumed that contractile cells applied forces to the wound only at the top and bottom surfaces of the liver; the second model assumed that the contractile forces occurred along the entire wound surface. Assumptions based on prior studies on skin wound contraction where used to obtain the magnitude and direction of the contractile forces applied to the wound edges and the material properties of the models. The magnitudes of deformations in all three planar coordinates were obtained, and mathematical expressions describing the deformation gradients viewed at the edges were derived. The deformations on Model B where found to be three orders of magnitude larger than those on Model A. The deformations in Model A were found to change exponentially with respect to the y- and z-axis, while the deformations in Model B fit 2nd-degree polynomials with respect to both the y- and z-axis. Displacements with respect to the x-axis were zero in both models. The applications of these quantitative models to current studies on contraction and scaffold fabrication were discussed.