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

N. A. Villar Goris, A. R. Selva Castañeda, E. E. Ramirez-Torres, J. Bory Reyes, L. Randez, L. E. Bergues Cabrales, J. I. Montijano


The classical and modified equations of Kolmogorov-Johnson-Mehl-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.


Avrami formulations; Gompertz formulations; tumor growth kinetics; fractal dimension

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