Barocas V H, Tranquillo R T
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis 55455, USA.
J Biomech Eng. 1997 Aug;119(3):261-8. doi: 10.1115/1.2796090.
We present a method for solving the governing equations from our anisotropic biphasic theory of tissue-equivalent mechanics (Barocas and Tranquillo, 1997) for axisymmetric problems. A mixed finite element method is used for discretization of the spatial derivatives, and the DASPK subroutine (Brown et al., 1994) is used to solve the resulting differential-algebraic equation system. The preconditioned GMRES algorithm, using a preconditioner based on an extension of Dembo's (1994) adaptation of the Uzawa algorithm for viscous flows, provides an efficient and scaleable solution method, with the finite element method discretization being first-order accurate in space. In the cylindrical isometric cell traction assay, the chosen test problem, a cylindrical tissue equivalent is adherent at either end to fixed circular platens. As the cells exert traction on the collagen fibrils, the force 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, leading to cell alignment along the axis. Our simulations predict that cell contact guidance leads to an increase in the load measured in the assay, but this effect is diminished by the tendency of contact guidance to inhibit radial compaction of the sample, which in turn reduces concentrations and hence the measured load.
我们提出了一种方法，用于求解基于组织等效力学各向异性双相理论（Barocas和Tranquillo，1997年）的轴对称问题的控制方程。采用混合有限元方法对空间导数进行离散化，并使用DASPK子程序（Brown等人，1994年）来求解所得的微分代数方程组。预处理的GMRES算法使用基于Dembo（1994年）对粘性流Uzawa算法的扩展的预处理器，提供了一种高效且可扩展的求解方法，有限元方法离散化在空间上具有一阶精度。在圆柱形等距细胞牵引试验（这是所选择的测试问题）中，圆柱形组织等效物的两端附着在固定的圆形平板上。当细胞对胶原纤维施加牵引力时，测量维持样品长度恒定或负载所需的力。然而，在试验过程中会发生径向压实，使得细胞和网络浓度增加，并且胶原纤维沿圆柱体轴线排列，导致细胞沿轴线排列。我们的模拟预测，细胞接触导向会导致试验中测量的负载增加，但这种效应会因接触导向抑制样品径向压实的趋势而减弱，这反过来又会降低浓度，从而降低测量的负载。
