Cell contraction forces in scaffolds with varying pore size and cell density

The contractile behavior of cells is relevant in understanding wound healing and scar formation. In tissue engineering, inhibition of the cell contractile response is critical for the regeneration of physiologically normal tissue rather than scar tissue. Previous studies have measured the contractile response of cells in a variety of conditions (e.g. on two-dimensional solid substrates, on free-floating tissue engineering scaffolds and on scaffolds under some constraint in a cell force monitor). Tissue engineering scaffolds behave mechanically like open-cell elastomeric foams: between strains of about 10 and 90%, cells progressively buckle struts in the scaffold. The contractile force required for an individual cell to buckle a strut within a scaffold has been estimated based on the strut dimensions (radius, r, and length, l) and the strut modulus, E(s). Since the buckling force varies, according to Euler's law, with r(4)/l(2), and the relative density of the scaffold varies as (r/l)(2), the cell contractile force associated with strut buckling is expected to vary with the square of the pore size for scaffolds of constant relative density. As the cell density increases, the force per cell to achieve a given strain in the scaffold is expected to decrease. Here we model the contractile response of fibroblasts by analyzing the response of a single tetrakaidecahedron to forces applied to individual struts (simulating cell contractile forces) using finite element analysis. We model tetrakaidecahedra of different strut lengths, corresponding to different scaffold pore sizes, and of varying numbers of loaded struts, corresponding to varying cell densities. We compare our numerical model with the results of free-floating contraction experiments of normal human dermal fibroblasts (NHDF) in collagen-GAG scaffolds of varying pore size and with varying cell densities.