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

• Published in: PloS one 2019-11, Vol.14 (11), p.e0224978-e0224978
• Main Authors: Castañeda, Antonio Rafael Selva, Torres, Erick Ramírez, Goris, Narciso Antonio Villar, González, Maraelys Morales, Reyes, Juan Bory, González, Victoriano Gustavo Sierra, Schonbek, María, Montijano, Juan Ignacio, Cabrales, Luis Enrique Bergues
• Format: Article
• Language: English
• Subjects: Angiogenesis; Animals; Apoptosis; Biology and Life Sciences; Cancer; Carcinoma, Ehrlich Tumor - pathology; Cell Count; Computer and Information Sciences; Computer Simulation; Contours; Deceleration; Experiments; Fibrosarcoma; Fibrosarcoma - pathology; Fractal geometry; Fractals; Geometry; Growth kinetics; Growth rate; Kinetics; Latency; Mammography; Medical research; Medicine and Health Sciences; Models, Biological; Parameter estimation; Physical Sciences; Researchers; Sarcoma; Shape; Solid tumors; Tumor cells; Tumors
• ISSN: 1932-6203; 1932-6203
• DOI: 10.1371/journal.pone.0224978

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. 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. 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. 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.