The modulus of fibroblast-populated collagen gels is not determined by final collagen and cell concentration: Experiments and an inclusion-based model

The fibroblast-populated collagen lattice is an attractive model tissue for in vitro studies of cell behavior and as the basis for bioartificial tissues. In spite of its simplicity - containing only collagen and cells - the system is surprisingly difficult to describe mechanically because of the ability of the cells to remodel the matrix, including compaction at short times and synthesis and/or degradation (and cell proliferation) at longer times. The objectives of this work were to measure the equilibrium modulus of fibroblastpopulated gels with different collagen and cell concentrations, and to use that characterization as the basis for a theoretical model that could be used to predict gel mechanics based on conditions. Although many observations were as expected (e.g., the gel compacts more when there are more cells in it, and the gel is stiffer when there is more collagen in it), an unexpected result arose: the final modulus of the gel was not dependent solely on the final composition. Even if it compacted more than a gel that was originally at a high collagen concentration, a gel that started at a low collagen concentration remained less stiff than the higher-concentration gel. In light of these results and experimental studies by others, we propose a model in which the gel compaction is not homogeneous but consists instead of extreme densification near the cells in an otherwise unchanged matrix. By treating the dense regions as spherical inclusions, we used classical composite material theory to develop an expression for the modulus of a compacted gel based on the initial collagen density and the final inclusion (i.e., cell) density. The new model fit the data for moderately compacted gels well but broke down, as expected, for larger volume fractions at which the underlying model assumptions did not apply.