Extension of the anisotropic biphasic theory to large strain and high cell concentrations

The fiber alignment of engineered tissues is an important design criterion for engineered tissues. The fiber alignment can affect the material properties as well as the behavior of the material. The Anisotropic Biphasic Theory (ABT) has been solved previously in two dimensions for axisymmetric problems such as disks and tubes. We solved the ABT in three dimensions for the first time and used the results from the ABT to determine fiber alignments in various tissue equivalent structures. The framework that the ABT was solved in, called Trellis, has the capability of h and r adaptivity allowing accurate solutions with coarse initial meshes. Several cases were studied to validate the method and were then compared to previously published experiments. The effect of complex constraints on the final fiber alignment was studied. The initial geometry has a dramatic effect on the final fiber alignment for such simple shapes as tissue engineered flaps and cruciforms. The constraints on the gel can affect the fiber alignment throughout the gel. In order to model more complex geometries, such as the bioartificial heart valve, an additional boundary condition was added to our three dimensional formulation. A penalty method was used on the force balance of the ABT to mimic a slippery surface found on a Teflon mandrel. The new boundary condition was used to model the bioartificial heart valve; the alignment generated was similar to that found experimentally.; In order to determine high strain and large cell concentration behavior of collagen gels, a series of experiments was developed to determine material properties after incubation. The cell concentration and collagen concentration was varied and the material properties were measured at several different time points. The tensile material properties were found to increase with both collagen and cell concentration. The compaction ratio was found to increase with cell concentration and time, but decrease with collagen concentration. We propose here a heterogeneous compaction model in which the collagen concentration near the cell increases, while the collagen concentration of the bulk matrix stays constant.