Lemon G, King J R
School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, UK.
J Math Biol. 2007 Oct;55(4):449-80. doi: 10.1007/s00285-007-0091-9. Epub 2007 May 12.
This paper analyses travelling-wave behaviour in a recently-formulated multiphase model for the growth of biological tissue that comprises motile cells and water inside a porous scaffold. The model arises in the context of tissue engineering, and its purpose is to study how cells migrate and proliferate inside porous biomaterials. In suitable limits, tissue growth in the model is shown to occur in the form of travelling waves that can propagate either forwards or backwards, depending on the values of the parameters. In the case where the drag force between the scaffold and the cells is non-zero, the growth of the aggregate can be analysed in terms of the propagation of a constant-speed wavefront in a semi-infinite domain. A numerical (shooting) method is described for calculating the wave speed, and detailed results for how the speed varies with respect to the parameters are given. In the case where the drag force is zero, the size of the aggregate is shown either to grow or to shrink exponentially with time. These results may be of importance in determining the experimental factors that control tissue invasiveness in scaffolds thereby allowing greater control over engineered tissue growth.
本文分析了一种最近提出的用于生物组织生长的多相模型中的行波行为，该模型包含多孔支架内的运动细胞和水。该模型产生于组织工程背景下，其目的是研究细胞如何在多孔生物材料内部迁移和增殖。在适当的条件下，模型中的组织生长表现为行波形式，行波可以向前或向后传播，这取决于参数的值。在支架与细胞之间的阻力不为零的情况下，可以根据半无限域中恒速波前的传播来分析聚集体的生长。描述了一种用于计算波速的数值（打靶）方法，并给出了波速如何随参数变化的详细结果。在阻力为零的情况下，聚集体的大小显示出随时间呈指数增长或收缩。这些结果对于确定控制支架中组织侵袭性的实验因素可能具有重要意义，从而可以更好地控制工程组织的生长。
