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Open Access Research article

Modified Gompertz equation for electrotherapy murine tumor growth kinetics: predictions and new hypotheses

Luis E Bergues Cabrales12*, Juan J Godina Nava2, Andrés Ramírez Aguilera3, Javier A González Joa4, Héctor M Camué Ciria1, Maraelys Morales González5, Miriam Fariñas Salas1, Manuel Verdecia Jarque6, Tamara Rubio González7, Miguel A O'Farril Mateus8, Soraida C Acosta Brooks9, Fabiola Suárez Palencia1, Lisset Ortiz Zamora5, María C Céspedes Quevedo8, Sarah Edward Seringe8, Vladimir Crombet Cuitié1, Idelisa Bergues Cabrales4 and Gustavo Sierra González10

Author Affiliations

1 Universidad de Oriente, Centro Nacional de Electromagnetismo Aplicado, Departamento de Bioelectromagnetismo, Grupo de Bioelectricidad, Av. Las Américas s/n. G.P. 4078. Santiago de Cuba 90400, Cuba

2 Departamento de Física, Centro de Investigación y Estudios Avanzados del Instituto Politécnico Nacional, Laboratorio de Estimulación Magnética, Av. Instituto Politécnico Nacional 2508, Col. San Pedro Zacatenco, Ap. Post. 14-740, México, D.F. 07000, México 07360, Distrito Federal, México

3 Universidad de Oriente, Centro de Biofísica Médica, Departamento de Biofísica. Santiago de Cuba 90500, Cuba

4 Universidad de Oriente, Facultad de Ciencias Naturales, Departamento de Física. Calle Patricio Lumumba s/n. Santiago de Cuba 90500, Cuba

5 Universidad de Oriente, Facultad de Ciencias Naturales, Departamento de Farmacia. Patricio Lumumba s/n. Santiago de Cuba 90500, Cuba

6 Hospital Infantil Sur, Servicio de Oncohematología. Santiago de Cuba 90200, Cuba

7 Dirección Municipal de Salud Pública. Servicio de Genética. Santiago de Cuba 90500. Cuba

8 Hospital Oncológico Conrado Benítez, Servicio de Mastología. Santiago de Cuba 90500, Cuba

9 Hospital Provincial Saturnino Lora, Servicio de medicina Interna. Santiago de Cuba 90500, Cuba

10 Instituto Finley. Ave. 27 No. 19805, La Lisa, A.P. 16017 Cod. 11600. La Habana

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BMC Cancer 2010, 10:589  doi:10.1186/1471-2407-10-589

Published: 28 October 2010

Abstract

Background

Electrotherapy effectiveness at different doses has been demonstrated in preclinical and clinical studies; however, several aspects that occur in the tumor growth kinetics before and after treatment have not yet been revealed. Mathematical modeling is a useful instrument that can reveal some of these aspects. The aim of this paper is to describe the complete growth kinetics of unperturbed and perturbed tumors through use of the modified Gompertz equation in order to generate useful insight into the mechanisms that underpin this devastating disease.

Methods

The complete tumor growth kinetics for control and treated groups are obtained by interpolation and extrapolation methods with different time steps, using experimental data of fibrosarcoma Sa-37. In the modified Gompertz equation, a delay time is introduced to describe the tumor's natural history before treatment. Different graphical strategies are used in order to reveal new information in the complete kinetics of this tumor type.

Results

The first stage of complete tumor growth kinetics is highly non linear. The model, at this stage, shows different aspects that agree with those reported theoretically and experimentally. Tumor reversibility and the proportionality between regions before and after electrotherapy are demonstrated. In tumors that reach partial remission, two antagonistic post-treatment processes are induced, whereas in complete remission, two unknown antitumor mechanisms are induced.

Conclusion

The modified Gompertz equation is likely to lead to insights within cancer research. Such insights hold promise for increasing our understanding of tumors as self-organizing systems and, the possible existence of phase transitions in tumor growth kinetics, which, in turn, may have significant impacts both on cancer research and on clinical practice.