Correspondence between formulations of Avrami and Gompertz equations for untreated tumor growth kinetics

Abstract

The classical and modified equations of Kolmogorov-Jormson-Melil-Avrami are compared with the equations of conventional Gompertz and Montijano-Bergues-Bory-Gompertz, in the frame of growth kinetics of tumors. For this, different analytical and numerical criteria are used to demonstrate the similarity between them, in particular the distance of Hausdorff The results show that these equations are similar from the mathematical point of view, and the parameters of the Gompertz equation are explicitly related to those of the Avrami equation. It is concluded that Modified Kolmogorov-Johnson-Mehl-Avrami and Montijano-Bergues-Bory-Gompertz equations can be used to describe the growth kinetics of unperturbed tumors.