Tissue equivalents (TEs), formed by entrapping cells in a collagen gel, are an important model system for studying cell behavior. We have previously (Barocas and Tranquillo in J Biomech Eng 117:161-170, 1997a) developed an anisotropic biphasic theory of TE mechanics, which comprises five coupled partial differential equations describing interaction among cells and collagen fibers in the TE. The model equations, previously solved in one or two dimensions, were solved in three dimensions using an adaptive finite-element platform. The model was applied to three systems: a rectangular isometric cell traction assay, an otherwise- acellular gel containing two islands of cells, and an idealized tissue-engineered cardiac valve leaflet. In the first two cases, published experimental data were available for comparison, and the model results were consistent with the experimental observations. Fibers and cells aligned in the fixed direction in the isometric assay, and a region of strong fiber alignment arose between the two cell islands. For the valve problem, the alignment predicted by the model was generally similar to that observed experimentally, but an asymmetry in the experiment was not captured by the model.
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Acknowledgments This work was supported by the National Science Foundation’s VIGRE Program (grant DMS-9983646) and by the National Institutes of Health (1R01 HL071538-01). Simulations were made possible by a resources grant from the University of Minnesota Supercomputing Institute.