Santiago de Cuba, Cuba
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Jimenez R.P.,Federal University of São Carlos | Jimenez R.P.,University of the East of Cuba | Pupo A.E.B.,University of the East of Cuba | Cabrales J.M.B.,San Jorge University | And 8 more authors.
Bioelectromagnetics | Year: 2011

Electrotherapy with direct current delivered through implanted electrodes is used for local control of solid tumors in both preclinical and clinical studies. The aim of this research is to develop a solution method for obtaining a three-dimensional analytical expression for potential and electric current density as functions of direct electric current intensity, differences in conductivities between the tumor and the surrounding healthy tissue, and length, number and polarity of electrodes. The influence of these parameters on electric current density in both media is analyzed. The results show that the electric current density in the tumor is higher than that in the surrounding healthy tissue for any value of these parameters. The conclusion is that the solution method presented in this study is of practical interest because it provides, in a few minutes, a convenient way to visualize in 3D the electric current densities generated by a radial electrode array by means of the adequate selection of direct current intensity, length, number, and polarity of electrodes, and the difference in conductivity between the solid tumor and its surrounding healthy tissue. Bioelectromagnetics 32:120-130, 2011. © 2010 Wiley-Liss, Inc.


Cabrales L.,University of the East of Cuba | Nava J.,CINVESTAV | Aguilera A.R.,University of the East of Cuba | Ciria H.,University of the East of Cuba | And 12 more authors.
IFMBE Proceedings | Year: 2015

Effectiveness of low-level direct electric current for different doses has been demonstrated in vitro and in vivo studies (animals and patients); however, several aspects that occur in the tumor growth kinetic before and after treatment have not been revealed. Mathematical modeling is a useful instrument to reveal some of these aspects, which cannot be measured or observed because of the low accuracy and resolution of the current techniques. The aim is to modify the Gom- pertz equation to describe the growth kinetics of the solid tumors treated with direct current and to generate useful insight into the mechanisms that underpin this devasting disease. Modified Gompertz equation is modified and fits the experimental data of unperturbed and perturbed fibrosarcoma Sa-37 tumor. Interpolation and extrapolation methods are used. Different graphical strategies are used in order to reveal news information on growth kinetic. The results evidence that in experimental group where partial response is observed, an absolute minimum volume is revealed from which first derivate of tumor volume reaches its minimum. This absolute minimum value has very important therapeutic implications. Also, the existence of a volume for which always tumors are completely destroyed is revealed. The complete tumor reversibility is demonstrated. It is also revealed the existence of two antagonistic processes in the tumor that reaches partial remission; however, in the tumor that reaches complete remission three antitumor mechanisms occur during tumor destruction. In conclusion, 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, the possible existence of phase transitions in tumor growth kinetic, which in turn may have significant impact both on cancer research and on clinical practice. © Springer International Publishing Switzerland 2015.


Ciria H.M.C.,University of the East of Cuba | Cabrales L.E.B.,University of the East of Cuba | Cabrales L.E.B.,National Polytechnic Institute of Mexico | Aguilera A.R.,University of the East of Cuba | And 16 more authors.
Mathematics and Computers in Simulation | Year: 2012

Evaluation of the distance between the electrodes, voltage applied to them, and number of electrodes in tumor growth kinetics is very useful for effective tumor destruction when electrotherapy is used. However, a study of this type has not yet been proposed. The aim of this paper is to simulate the influence of such parameters and the point-point electrode configuration on the tumor growth kinetics through a Modified Gompertz Equation. The results show a good agreement between the simulations performed in this study and the experimental results reported by our group and other authors. A critical distance between electrodes and a threshold ratio between the applied electric field and that distributed in the tumor are revealed, for which higher electrotherapy antitumor effectiveness is reached. In conclusion, electrotherapy antitumor effectiveness not only depends on the distance between the electrodes, voltage applied to them, and number of electrodes, but also on the ratio between the applied electric field and that distributed in the tumor. In addition, the results of these simulations may be used to help physicians choose the most appropriate treatment for patients with malignant solid tumors, as we have implemented in a current clinical trial. © 2012 IMACS. Published by Elsevier B.V. All rights reserved.


Cabrales L.E.B.,University of the East of Cuba | Cabrales L.E.B.,National Polytechnic Institute of Mexico | Nava J.J.G.,National Polytechnic Institute of Mexico | Aguilera A.R.,University of the East of Cuba | And 15 more authors.
BMC Cancer | Year: 2010

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. © 2010 Cabrales et al; licensee BioMed Central Ltd.

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