The recursion formula of the Gompertz function: a simple method for the estimation and comparison of tumor growth curves.

Abstract

A method for analysing tumor growth curves is presented based on regression analysis of the linear relationship between the logarithm of the tumor size at a certain time and of that at a constant time interval earlier. By measuring the tumor size at constant time intervals the Gompertzian growth curve can be transformed into a straight line. This permits both the calculation of best fit Gompertzian curves and the comparison of different growth curves simply based on linear regression analysis. Since this new method includes exponential growth as a special case, it enables a quantitative discrimination between exponential and Gompertzian growth. Furthermore, this method permits the calculation of best fit Gompertz functions based upon individual measurements of tumor collectives without a common time scale (i.e., spontaneous tumors). As an example, it is demonstrated that the growth curves of the transplantable mouse adenocarcinoma EO 771 do not depend on the number of tumor cells inoculated.