Gompertzian re‐evaluation of the growth patterns of transplantable mammary tumours in sialoadenectomized mice

Abstract

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.