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

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

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 thes...

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Published in:BMC cancer Vol. 10; no. 1; p. 589
Main Authors: Cabrales, Luis E Bergues, Nava, Juan J Godina, Aguilera, Andrés Ramírez, Joa, Javier A González, Ciria, Héctor M Camué, González, Maraelys Morales, Salas, Miriam Fariñas, Jarque, Manuel Verdecia, González, Tamara Rubio, Mateus, Miguel A O'Farril, Brooks, Soraida C Acosta, Palencia, Fabiola Suárez, Zamora, Lisset Ortiz, Quevedo, María C Céspedes, Seringe, Sarah Edward, Cuitié, Vladimir Crombet, Cabrales, Idelisa Bergues, González, Gustavo Sierra
Format: Journal Article
Language:English
Published: England BioMed Central 28-10-2010
BioMed Central Ltd
BMC
Subjects:
Animals
Cancer
Cancer therapies
Cell Line, Tumor
Clinical medicine
Electric Stimulation Therapy - methods
Fibrosarcoma - metabolism
Humans
Kinetics
Mathematical models
Mice
Mice, Inbred BALB C
Models, Biological
Models, Statistical
Models, Theoretical
Neoplasms - pathology
Neoplasms - therapy
Ostomy
Phase transitions
Remission Induction
Studies
Time Factors
Tumors
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Summary: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. 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. 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. 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.
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ISSN:1471-2407
1471-2407
DOI:10.1186/1471-2407-10-589