Bassukas I D
Institut für Medizinische Strahlenkunde, University of Würzburg, Germany.
Cell Prolif. 1994 Apr;27(4):201-11. doi: 10.1111/j.1365-2184.1994.tb01417.x.
The method of the recursion formula of the Gompertz function (Bassukas & Maurer-Schultze 1988) has been applied to analyse tumour growth data taken from the literature; namely the growth perturbation of transplantable mammary tumours in sialoadenectomized mice with or without subsequent epidermal growth factor substitution (results on two mouse strains, C3H or SHN, have been reported; Inui, Tsubura & Morii 1989). The recursion formula of the Gompertz function fits growth curves to all seven sets of data well (P > 0.05 for lack of fit test). The growth pattern of the tumours in the unperturbed hosts is Gompertzian and does not change if tumours are transplanted in sialoadenectomized mice, although the starting specific growth rate decreases in C3H mice. However, if sialoadenectomy is carried out after tumour inoculation, a complex alteration of the tumour growth evolves: tumour growth does not simply decelerate but it also shifts from the conventional Gompertzian to an exponential or even 'hyperexponential' growth pattern, i.e. with an accelerating specific growth rate. Some theoretical mechanisms of this alteration, as well as the differences between the present Gompertzian analysis and a previously published Verhulstian analysis of part of the same data (Leith, Harrigan & Michelson 1991), are discussed. It is concluded that the quantitative analysis of tumour growth patterns by the method of the difference equation of the Gompertz function presently applied may substantially contribute to the improvement of the interpretation of perturbations of tumour growth--irrespective of their genesis. In contrast to the application of some a priori fixed growth function, e.g. the Verhulstian one, the present method can quantitatively interpret different growth patterns and their classification on the basis of linear regression analysis.
已应用Gompertz函数递归公式的方法（Bassukas和Maurer-Schultze，1988年）来分析取自文献的肿瘤生长数据；即唾液腺切除小鼠中可移植乳腺肿瘤的生长扰动，有无后续表皮生长因子替代（已报道了两种小鼠品系C3H或SHN的结果；Inui、Tsubura和Morii，1989年）。Gompertz函数的递归公式能很好地拟合所有七组数据的生长曲线（拟合优度检验P>0.05）。未受扰动宿主中肿瘤的生长模式符合Gompertz模型，且在唾液腺切除小鼠中移植肿瘤时该模式不变，尽管C3H小鼠的起始比生长速率降低。然而，如果在接种肿瘤后进行唾液腺切除，则肿瘤生长会发生复杂变化：肿瘤生长不仅简单减速，还会从传统的Gompertz模式转变为指数甚至“超指数”生长模式，即比生长速率加速。本文讨论了这种变化的一些理论机制，以及当前Gompertz分析与先前发表的对部分相同数据的Verhulst分析（Leith、Harrigan和Michelson，1991年）之间的差异。得出的结论是，目前应用的Gompertz函数差分方程方法对肿瘤生长模式进行定量分析，可能会极大地有助于改进对肿瘤生长扰动的解释——无论其起源如何。与应用某些先验固定生长函数（如Verhulst函数）不同，当前方法可基于线性回归分析对不同生长模式及其分类进行定量解释。
