Ohsumi TOSHIRO K., Flaherty JOSEPH E., Barocas VICTOR H., Adjerid SLIMANE, Aiffa MOHAMMED
Department of Computer Science, Rensselaer Polytechnic Institute, 110 Eighth Street, Troy, NY 12180-3590.
Comput Methods Biomech Biomed Engin. 2000;3(3):215-229. doi: 10.1080/10255840008915266.
The nonlinear partial differential equations of the anisotropic biphasic theory of tissue-equivalent mechanics are solved with axial symmetry by an adaptive finite element system. The adaptive procedure operates within a method-of-lines framework using finite elements in space and backward difference software in time. Spatial meshes are automatically refined, coarsened, and relocated in response to error indications and material deformation. Problems with arbitrarily complex two-dimensional regions may be addressed. With meshes graded in high-error regions, the adaptive solutions have fewer degrees of freedom than solutions with comparable accuracy obtained on fixed quasi-uniform meshes. The adaptive software is used to address problems involving an isometric cell traction assay, where a cylindrical tissue equivalent is adhered at its end to fixed circular platens; a prototypical bioartificial artery; and a novel configuration that is intended as an initial step in a study to determine bioartificial arteries having optimal collagen and cell concentrations.
采用自适应有限元系统，在轴对称条件下求解组织等效力学各向异性双相理论的非线性偏微分方程。自适应过程在一种线方法框架内运行，在空间上使用有限元，在时间上使用向后差分软件。空间网格会根据误差指示和材料变形自动细化、粗化和重新定位。可以处理任意复杂二维区域的问题。在高误差区域进行网格分级后，自适应解的自由度比在固定准均匀网格上获得的具有可比精度的解要少。该自适应软件用于处理涉及等距细胞牵引试验的问题，其中圆柱形组织等效物在其端部粘附到固定的圆形平板上；一个典型的生物人工动脉；以及一种新颖的结构，该结构旨在作为确定具有最佳胶原蛋白和细胞浓度的生物人工动脉的研究的第一步。
