A FINITE-ELEMENT SOLUTION FOR THE ANISOTROPIC BIPHASIC THEORY OF TISSUE-EQUIVALENT MECHANICS - THE EFFECT OF CONTACT GUIDANCE ON ISOMETRIC CELL TRACTION MEASUREMENT

We present a method for solving the governing equations from our aniso tropic biphasic theory of tissue-equivalent tissue-equivalent mechanic s (Barocas and Tranquillo, 1997) for axisymmetric problems. A mixed fi nite element method is used for discretization of the spatial derivati ves, and the DASPK subroutine (Brown et al., 1994) is used to solve th e resulting differential-algebraic equation system. The preconditioned GMRES algorithm, using a preconditioner based on an extension of Demb o's ( 1994) adaptation of the Uzawa algorithm for viscous flows, provi des an efficient and scaleable solution method, with the finite elemen t method discretization being first-order accurate in space. In the cy lindrical isometric cell traction assay, the chosen test problem, a cy lindrical tissue equivalent is adherent at either end to fixed circula r platens. As the cells exert traction on the collagen fibrils, the fo rce required to maintain constant sample length, or load, is measured. However, radial compaction occurs during the course of the assay, so that the cell and network concentrations increase and collagen fibrils become aligned along the axis of the cylinder, lending to cell alignm ent along the axis. Our simulations predict that cell contact guidance leads to an increase in the load measured in the assay, but this effe ct is diminished by the tendency of contact guidance to inhibit radial compaction of the sample, which in turn reduces concentrations and he nce the measured lend.