Landry J, Freyer J P, Sutherland R M
Cell Tissue Kinet. 1982 Nov;15(6):585-94. doi: 10.1111/j.1365-2184.1982.tb01065.x.
Based on biological observations and the basic physical properties of tri-dimensional structures, a mathematical expression is derived to relate the growth rate of multicellular spheroids to some easily measurable parameters. This model involves properties both of the individual cells and of the spheroid structure, such as the cell doubling time in monolayer, the rate of cell shedding from the spheroid and the depth of the external rim of cycling cells. The derived growth equation predicts a linear expansion of the spheroid diameter with time. The calculated growth rate for a number of spheroid cell types is in good agreement with experimental data. The model provides a simple and practical view of growth control in spheroids, and is further adapted to include parameters presumably responsible for the growth saturation in large spheroids.
基于生物学观察和三维结构的基本物理特性，推导了一个数学表达式，以将多细胞球体的生长速率与一些易于测量的参数联系起来。该模型涉及单个细胞和球体结构的特性，例如单层细胞的倍增时间、细胞从球体脱落的速率以及循环细胞外缘的深度。推导的生长方程预测球体直径随时间呈线性扩展。对多种球体细胞类型计算出的生长速率与实验数据高度吻合。该模型提供了一个关于球体生长控制的简单实用观点，并进一步进行了调整，以纳入可能导致大球体生长饱和的参数。
