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

Authors

  • N. A. Villar Goris
  • A. R. Selva Castañeda
  • E. E. Ramirez-Torres
  • J. Bory Reyes
  • L. Randez
  • L. E. Bergues Cabrales Centro Nacional de Electromagnetismo Aplicado, Universidad de Oriente
  • J. I. Montijano

DOI:

https://doi.org/10.31349/RevMexFis.66.632

Keywords:

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

Abstract

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.

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Published

2020-09-01

How to Cite

[1]
N. A. Villar Goris, “Correspondence between formulations of Avrami and Gompertz equations for untreated tumor growth kinetics”, Rev. Mex. Fís., vol. 66, no. 5 Sept-Oct, pp. 632–636, Sep. 2020.

Issue

Vol. 66 No. 5 Sept-Oct (2020): Revista Mexicana de Física

Section

11 Medical Physics

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Authors retain copyright and grant the Revista Mexicana de Física right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.