TY - JOUR
T1 - New formulation of the Gompertz equation to describe the kinetics of untreated tumors
AU - Castañeda, Antonio Rafael Selva
AU - Torres, Erick Ramírez
AU - Goris, Narciso Antonio Villar
AU - González, Maraelys Morales
AU - Reyes, Juan Bory
AU - González, Victoriano Gustavo Sierra
AU - Schonbek, María
AU - Montijano, Juan Ignacio
AU - Cabrales, Luis Enrique Bergues
N1 - Publisher Copyright:
© 2019 Castañeda et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
PY - 2019/11
Y1 - 2019/11
N2 - Background Different equations have been used to describe and understand the growth kinetics of undisturbed malignant solid tumors. The aim of this paper is to propose a new formulation of the Gompertz equation in terms of different parameters of a malignant tumor: the intrinsic growth rate, the deceleration factor, the apoptosis rate, the number of cells corresponding to the tumor latency time, and the fractal dimensions of the tumor and its contour. Methods Furthermore, different formulations of the Gompertz equation are used to fit experimental data of the Ehrlich and fibrosarcoma Sa-37 tumors that grow in male BALB/c/Cenp mice. The parameters of each equation are obtained from these fittings. Results The new formulation of the Gompertz equation reveals that the initial number of cancerous cells in the conventional Gompertz equation is not a constant but a variable that depends nonlinearly on time and the tumor deceleration factor. In turn, this deceleration factor depends on the apoptosis rate of tumor cells and the fractal dimensions of the tumor and its irregular contour. Conclusions It is concluded that this new formulation has two parameters that are directly estimated from the experiment, describes well the growth kinetics of unperturbed Ehrlich and fibrosarcoma Sa-37 tumors, and confirms the fractal origin of the Gompertz formulation and the fractal property of tumors.
AB - Background Different equations have been used to describe and understand the growth kinetics of undisturbed malignant solid tumors. The aim of this paper is to propose a new formulation of the Gompertz equation in terms of different parameters of a malignant tumor: the intrinsic growth rate, the deceleration factor, the apoptosis rate, the number of cells corresponding to the tumor latency time, and the fractal dimensions of the tumor and its contour. Methods Furthermore, different formulations of the Gompertz equation are used to fit experimental data of the Ehrlich and fibrosarcoma Sa-37 tumors that grow in male BALB/c/Cenp mice. The parameters of each equation are obtained from these fittings. Results The new formulation of the Gompertz equation reveals that the initial number of cancerous cells in the conventional Gompertz equation is not a constant but a variable that depends nonlinearly on time and the tumor deceleration factor. In turn, this deceleration factor depends on the apoptosis rate of tumor cells and the fractal dimensions of the tumor and its irregular contour. Conclusions It is concluded that this new formulation has two parameters that are directly estimated from the experiment, describes well the growth kinetics of unperturbed Ehrlich and fibrosarcoma Sa-37 tumors, and confirms the fractal origin of the Gompertz formulation and the fractal property of tumors.
UR - http://www.scopus.com/inward/record.url?scp=85074958109&partnerID=8YFLogxK
U2 - 10.1371/JOURNAL.PONE.0224978
DO - 10.1371/JOURNAL.PONE.0224978
M3 - Artículo
C2 - 31715625
AN - SCOPUS:85074958109
SN - 1932-6203
VL - 14
JO - PLoS ONE
JF - PLoS ONE
IS - 11
M1 - e0224978
ER -
