Mathematical modeling of tumor growth in mice following low-level direct electric current

  • Authors:

  • Luis Enrique Bergues Cabrales;Andrés Ramírez Aguilera;Rolando Placeres Jiménez;Manuel Verdecia Jarque;Héctor Manuel Camué Ciria;Juan Bory Reyes;Miguel Angel O'Farril Mateus;Fabiola Suárez Palencia;Marisela González Ávila

  • Affiliations:

  • Sección de Bioelectricidad, Departamento de Bioingeniería y Equipos, Centro Nacional de Electromagnetismo Aplicado, Universidad de Oriente, Santiago de Cuba 90400, Cuba;Centro de Biofísica Medica, Universidad de Oriente, Santiago de Cuba 90500, Cuba;Departamento de Física, Facultad de Ciencias Naturales, Santiago de Cuba 90500, Cuba;Hospital Infantil Sur, Santiago de Cuba, Cuba;Sección de Bioelectricidad, Departamento de Bioingeniería y Equipos, Centro Nacional de Electromagnetismo Aplicado, Universidad de Oriente, Santiago de Cuba 90400, Cuba;Departamento de Matemática, Facultad de Matemática y Cibernética, Santiago de Cuba 90500, Cuba;Hospital Oncológico Conrado Benítez, Santiago de Cuba 90500, Cuba;Sección de Bioelectricidad, Departamento de Bioingeniería y Equipos, Centro Nacional de Electromagnetismo Aplicado, Universidad de Oriente, Santiago de Cuba 90400, Cuba;Universidad Politécnica de Pachuca (UPP), Km 20, Carretera Pachuca, Ciudad Sahún, Exhacienda de Santa Bárbara, Municipio de Zempoala, Estado de Hidalgo, Mexico

  • Venue:
  • Mathematics and Computers in Simulation
  • Year:
  • 2008

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Abstract

A modification to the conventional Gompertz equation (named modified Gompertz equation) is introduced to describe the solid tumor growth perturbed with direct electric current. Simulations of this equation are made. Quantitative fitting criteria as goodness-of-fit, handling missing data and prediction capability are considered. Also, parameter estimation accuracy is calculated. A fit of the experimental data of Ehrlich and fibrosarcoma Sa-37 tumor growths treated with different intensities of direct electric current are also made to validate this modified Gompertz equation. The results obtained in this study corroborate that the direct electric current effectiveness depends on (i/i"0) ratio, and also on the duration of the effects of it into the tumor, and of the tumor type. It was concluded that the modified Gompertz equation has a good prediction capability to describe both unperturbed and perturbed tumor growths and it could be used to help physicians choose the most appropriate treatment for patients and animals with malignant solid tumors.