Lemon G, King J R
School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK.
Math Med Biol. 2007 Mar;24(1):57-83. doi: 10.1093/imammb/dql020. Epub 2006 Oct 3.
This paper contains analysis of a recently formulated multiphase model for the growth of biological tissue that comprises motile cells and water inside a rigid scaffold material. The model is extended here to include a term describing cell proliferation which is mediated by the supply of a diffusible nutrient and to include the case where the scaffold porosity varies in space. Numerical solutions of the model equations are presented for different values of the parameters. Comparison is drawn between the different types of growth that arise when using static or dynamic methods for seeding the scaffold with cells. Analytical solutions are presented for the limiting cases in which the coefficient of drag between the cells and the scaffold is very large or zero. In the limit of large time, solutions reveal preferential tissue growth in the vicinity of the scaffold edge due to depletion of nutrient by the cells, consistent with experimental results. However, it is shown that reducing the coefficient of drag between the scaffold and the cells overcomes the effects of nutrient depletion by increasing cell mobility, thereby leading to improved uniformity of the cell distribution within the scaffold.
本文包含对最近提出的一种生物组织生长多相模型的分析，该模型包含运动细胞和刚性支架材料内的水。在此扩展该模型，纳入一个描述由可扩散营养物质供应介导的细胞增殖的项，并考虑支架孔隙率在空间中变化的情况。针对不同参数值给出了模型方程的数值解。比较了使用静态或动态方法在支架上接种细胞时出现的不同类型的生长情况。给出了细胞与支架之间的阻力系数非常大或为零时极限情况的解析解。在长时间极限下，解表明由于细胞消耗营养物质，支架边缘附近出现优先组织生长，这与实验结果一致。然而，结果表明，通过增加细胞流动性，降低支架与细胞之间的阻力系数可克服营养物质消耗的影响，从而提高支架内细胞分布的均匀性。
