New formulation of the Gompertz equation to describe the kinetics of untreated tumors

English version

Autoři: Antonio Rafael Selva Castañeda ^aff001; Erick Ramírez Torres ^aff003; Narciso Antonio Villar Goris ^aff004; Maraelys Morales González ^aff007; Juan Bory Reyes ^aff008; Victoriano Gustavo Sierra González ^aff009; María Schonbek ^aff010; Juan Ignacio Montijano ^aff001; Luis Enrique Bergues Cabrales ^aff001
Působiště autorů: Departamento de Matemática Aplicada, Instituto Universitario de Matemáticas y Aplicaciones, Universidad de Zaragoza, Zaragoza, Spain ^aff001; Departamento de Telecomunicaciones, Facultad de Ingeniería en Telecomunicaciones Informática y Biomédica, Universidad de Oriente, Santiago de Cuba, Cuba ^aff002; Departamento de Biomédica, Facultad de Ingeniería en Telecomunicaciones Informática y Biomédica, Universidad de Oriente, Santiago de Cuba, Cuba ^aff003; Universidad Autónoma de Santo Domingo, Santo Domingo, Dominican Republic ^aff004; Universidad Católica Tecnológica del CIBAO, Ucateci, La Vega, Dominican Republic ^aff005; Departamento de Ciencia e Innovación, Centro Nacional de Electromagnetismo Aplicado, Universidad de Oriente, Santiago de Cuba, Cuba ^aff006; Departamento de Farmacia, Facultad de Ciencias Naturales y Exactas, Universidad de Oriente, Santiago de Cuba, Cuba ^aff007; ESIME-Zacatenco, Instituto Politécnico Nacional, CD-MX, Mexico ^aff008; Grupo de las Industrias Biotecnológica y Farmacéuticas (BioCubaFarma), La Habana, Cuba ^aff009; Department of Mathematics, University of California Santa Cruz, Santa Cruz, CA, United States of America ^aff010
Vyšlo v časopise: PLoS ONE 14(11)
Kategorie: Research Article
prolekare.web.journal.doi_sk: https://doi.org/10.1371/journal.pone.0224978

Souhrn

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.

Klíčová slova:

Apoptosis – Graphs – Histology – Interpolation – Malignant tumors – Angiogenesis – Fractals – Fibrosarcoma

Zdroje

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