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

doi:10.31349/RevMexFis.66.632

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

Escuela Superior de Ingeniería Mecánica y Eléctrica (ESIME), Unidad Zacatenco

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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.

Original language	English
Pages (from-to)	632-636
Number of pages	5
Journal	Revista Mexicana de Fisica
Volume	66
Issue number	5
DOIs	https://doi.org/10.31349/RevMexFis.66.632
State	Published - Sep 2020

Keywords

Avrami formulations
Gompertz formulations
fractal dimension
tumor growth kinetics

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title = "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.",

keywords = "Avrami formulations, Gompertz formulations, fractal dimension, tumor growth kinetics",

author = "Goris, {N. A.Villar} and {Selva Casta{\~n}eda}, {A. R.} and Ramirez-Torres, {E. E.} and Reyes, {J. Bory} and L. Randez and Cabrales, {L. E.Bergues} and Montijano, {J. I.}",

year = "2020",

month = sep,

doi = "10.31349/RevMexFis.66.632",

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T1 - Correspondence between formulations of Avrami and Gompertz equations for untreated tumor growth kinetics

AU - Goris, N. A.Villar

AU - Selva Castañeda, A. R.

AU - Ramirez-Torres, E. E.

AU - Reyes, J. Bory

AU - Randez, L.

AU - Cabrales, L. E.Bergues

AU - Montijano, J. I.

PY - 2020/9

Y1 - 2020/9

N2 - 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.

AB - 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.

KW - Avrami formulations

KW - Gompertz formulations

KW - fractal dimension

KW - tumor growth kinetics

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JO - Revista Mexicana de Fisica

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

Abstract

Keywords

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