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

Producción científica: Contribución a una revista › Artículo › revisión exhaustiva

4 Citas (Scopus)

Resumen

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.

Idioma original	Inglés
Páginas (desde-hasta)	632-636
Número de páginas	5
Publicación	Revista Mexicana de Fisica
Volumen	66
N.º	5
DOI	https://doi.org/10.31349/RevMexFis.66.632
Estado	Publicada - sep. 2020

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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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volume = "66",

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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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U2 - 10.31349/RevMexFis.66.632

DO - 10.31349/RevMexFis.66.632

M3 - Artículo

AN - SCOPUS:85103084342

SN - 0035-001X

VL - 66

SP - 632

EP - 636

JO - Revista Mexicana de Fisica

JF - Revista Mexicana de Fisica

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

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