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

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

doi:10.1016/j.matcom.2007.06.004

Cited by 23 publications

(64 citation statements)

References 12 publications

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“…This result is in contrast with the fact that these two kinetic parameters are constant during all TGK, as we assume in this paper and as reported previously by our group [17] and other authors [1,23]. Additionally, the TV dependence of FDTV indicates that, V i may have important implications in DEC planning, if we take into account the fact that the tumor is more sensitive to DEC than healthy tissue [7][8][9][10][11][12][13][14][15][18][19][20][21], the Steel equation [22], and the results of Smith et al [34].…”

Section: Unperturbed Fibrosarcoma Sa-37 Tgkcontrasting

confidence: 93%

“…In this case, τ is a time delay , is constant during TGK. In this case, the MGE coincides with the conventional Gompertz equation [1,17,22,23].…”

Section: Reconstruction Of Reg-i For Fibrosarcoma Sa-37 Tgkmentioning

confidence: 57%

“…These results have been theoretically corroborated through the use of a modified Gompertz equation (MGE), which has a good prediction capability to describe both unperturbed and DECperturbed TGK [17].…”

Section: Introductionmentioning

confidence: 77%

“…The actual idea behind in vitro and in vivo studies is to treat the tumor and then to observe its evolution, which is not known to priori [7][8][9][10][11][12][13][14][15][18][19][20][21]. However, the existence of V d establishes that fibrosarcoma Sa-37 tumors have a DEC threshold for which the tumor is completely destroyed, as demonstrated experimentally and theoretically for Ehrlich and fibrosarcoma Sa-37 tumors [14,17], in agreement with other studies [9,10,18,21,33]. This is possible if we establish an explicit dependence of V d as a function of the parameters of Equation 7, the host type, and the ET parameters (dosage and exposure time of DEC, electrode array, and times that DEC is repeated).…”

Section: Dec-treated Fibrosarcoma Sa-37 Tgk For Tg3mentioning

confidence: 99%

“…As a result an optimal electrode distribution has not been determined for ET, nor has the dose-response relationship been established. For this reason, we pay special attention to these two factors [16,17].…”

Section: Introductionmentioning

confidence: 99%

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Modified Gompertz Equation for Electrotherapy Murine Tumor Growth Kinetics: Predictions and New Hypotheses

Cabrales¹,

Nava²,

Aguilera³

et al. 2015

IFMBE Proceedings

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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.

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Section: Unperturbed Fibrosarcoma Sa-37 Tgkcontrasting

confidence: 93%

“…In this case, τ is a time delay , is constant during TGK. In this case, the MGE coincides with the conventional Gompertz equation [1,17,22,23].…”

Section: Reconstruction Of Reg-i For Fibrosarcoma Sa-37 Tgkmentioning

confidence: 57%

Section: Introductionmentioning

confidence: 77%

Section: Dec-treated Fibrosarcoma Sa-37 Tgk For Tg3mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Modified Gompertz Equation for Electrotherapy Murine Tumor Growth Kinetics: Predictions and New Hypotheses

Cabrales¹,

Nava²,

Aguilera³

et al. 2015

IFMBE Proceedings

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3D Stationary electric current density in a spherical tumor treated with low direct current: An analytical solution

Jiménez

Pupo

Cabrales

et al. 2010

Bioelectromagnetics

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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.

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Dose‐response study for the highly aggressive and metastatic primary F3II mammary carcinoma under direct current

González

Morales

Cabrales

et al. 2018

Bioelectromagnetics

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Electrochemical treatment has been suggested as an effective alternative to local cancer therapy. Nevertheless, its effectiveness decreases when highly aggressive primary tumors are treated. The aim of this research was to understand the growth kinetics of the highly aggressive and metastatic primary F3II tumor growing in male and female BALB/c/Cenp mice under electrochemical treatment. Different amounts of electric charge (6, 9, and 18 C) were used. Two electrodes were inserted into the base, perpendicular to the tumor's long axis, keeping about 1 cm distance between them. Results have shown that the F3II tumor is highly sensitive to direct current. The overall effectiveness (complete response + partial response) of this physical agent was ≥75.0% and observed in 59.3% (16/27) of treated F3II tumors. Complete remission of treated tumors was observed in 22.2% (6/27). An unexpected result was the death of 11 direct current-treated animals (eight females and three males). It is concluded that direct current may be addressed to significantly affect highly aggressive and metastatic primary tumor growth kinetics, including the tumor complete response. Bioelectromagnetics. 39:460-475, 2018. © 2018 Wiley Periodicals, Inc.

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

Cited by 23 publications

References 12 publications

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

3D Stationary electric current density in a spherical tumor treated with low direct current: An analytical solution

Dose‐response study for the highly aggressive and metastatic primary F3II mammary carcinoma under direct current

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