A cell-based constitutive relation for bio-artificial tissues

By using a combination of continuum and statistical mechanics we derive an integral constitutive relation for bio-artificial tissue models consisting of a monodisperse population of cells in a uniform collagenous matrix. This constitutive relation quantitatively models the dependence of tissue stress on deformation history, and makes explicit the separate contribution of cells and matrix to the mechanical behavior of the composite tissue. Thus microscopic cell mechanical properties can be deduced via this theory from measurements of macroscopic tissue properties. A central feature of the constitutive relation is the appearance of "anisotropy tensors" that embody the effects of cell orientation on tissue mechanics. The theory assumes that the tissues are stable over the observation time, and does not in its present form allow for cell migration, reorientation, or internal remodeling. We have compared the predictions of the theory to uniaxial relaxation tests on fibroblast-populated collagen matrices (FPMs) and find that the experimental results generally support the theory and yield values of fibroblast contractile force and stiffness roughly an order of magnitude smaller than, and viscosity comparable to, the corresponding properties of active skeletal muscle. The method used here to derive the tissue constitutive equation permits more sophisticated cell models to be used in developing more accurate representations of tissue properties.