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:10.1007/978-3-642-03882-2_134

Cited by 9 publications

(44 citation statements)

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“…Mean doubling time (DT) of the solid F3II tumor (in days) was estimated for each individual tumor, once it reached its first volume measured. DT was the time required for a solid tumor to reach a twofold increase of its initial volume [Cabrales et al, ; González et al, ].…”

Section: Methodsmentioning

confidence: 99%

“…The modified Gompertz equation (MGE) [Cabrales et al, , ] was used to fit experimental data for individual F3II tumor in each experimental group. MGE was given by

V^{*} (t) = V_{o} e^{(\frac{α^{*}}{β}) ({1 - e}^{- β t})},

where

α^{*} = true[a_{1} (1 - e^{- γ t}) + a_{2} true] α,

with

a_{1} = true(\frac{i}{i_{o}} true) true(2 - \frac{i}{i_{o}} true),

and

a_{2} = true(1 - \frac{i}{i_{o}} true),

where V ( t ) represented the tumor volume at time t after DC treatment.…”

Section: Methodsmentioning

confidence: 99%

“…Disease progression (DP) and non‐change or stable disease (SD) are other tumor responses after the application of any therapy [Xin et al, ; Eisenhauer et al, ]. These aspects may be evaluated by means of an analysis of tumor growth kinetics (TGK) under DC action [Miklavčič et al, ; Ciria et al, ; Cabrales et al, , ].…”

Section: Introductionmentioning

confidence: 99%

“…The analysis of DC‐treated TGK allows simulation of these tumor responses, to know the kinetics and electrical parameters of a tumor growing in a host, to adequately select a therapeutic scheme, among others. These elements are important for planning and personalized therapy [Cabrales et al, , ]. Nevertheless, few studies deal with this analysis of DC‐treated TGK in female and male animals, mainly for highly aggressive and metastatic primary tumors, such as F3II mammary carcinoma.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Methodsmentioning

confidence: 99%

“…The modified Gompertz equation (MGE) [Cabrales et al, , ] was used to fit experimental data for individual F3II tumor in each experimental group. MGE was given by

V^{*} (t) = V_{o} e^{(\frac{α^{*}}{β}) ({1 - e}^{- β t})},

where

α^{*} = true[a_{1} (1 - e^{- γ t}) + a_{2} true] α,

with

a_{1} = true(\frac{i}{i_{o}} true) true(2 - \frac{i}{i_{o}} true),

and

a_{2} = true(1 - \frac{i}{i_{o}} true),

where V ( t ) represented the tumor volume at time t after DC treatment.…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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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“…So we will consider numerical oscillation for Gompertz equation with one delay in this paper. In the past few years, Gompertz equation has been generally used to describe the population dynamics and tumour growth (see [7,8]). In 1825, Benjamin Gompertz proposed the classical Gompertz model [9]…”

Section: Introductionmentioning

confidence: 99%

Numerical Oscillation Analysis for Gompertz Equation with One Delay

Yang¹

2020

Fundamental Journal of Mathematics and Applications

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This paper concerns with the oscillation of numerical solutions of a kind of nonlinear delay differential equation proposed by Benjamin Gompertz, this equation usually be used to describe the population dynamics and tumour growth. We obtained some conditions under which the numerical solutions are oscillatory. The non-oscillatory behaviors of numerical solutions are also analyzed. Numerical examples are given to test our theoretical results.

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Hyperbolastic modeling of tumor growth with a combined treatment of iodoacetate and dimethylsulphoxide

2010

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BackgroundAn understanding of growth dynamics of tumors is important in understanding progression of cancer and designing appropriate treatment strategies. We perform a comparative study of the hyperbolastic growth models with the Weibull and Gompertz models, which are prevalently used in the field of tumor growth.MethodsThe hyperbolastic growth models H1, H2, and H3 are applied to growth of solid Ehrlich carcinoma under several different treatments. These are compared with results from Gompertz and Weibull models for the combined treatment.ResultsThe growth dynamics of the solid Ehrlich carcinoma with the combined treatment are studied using models H1, H2, and H3, and the models are highly accurate in representing the growth. The growth dynamics are also compared with the untreated tumor, the tumor treated with only iodoacetate, and the tumor treated with only dimethylsulfoxide, and the combined treatment.ConclusionsThe hyperbolastic models prove to be effective in representing and analyzing the growth dynamics of the solid Ehrlich carcinoma. These models are more precise than Gompertz and Weibull and show less error for this data set. The precision of H3 allows for its use in a comparative analysis of tumor growth rates between the various treatments.

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

Cited by 9 publications

References 0 publications

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

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

Numerical Oscillation Analysis for Gompertz Equation with One Delay

Hyperbolastic modeling of tumor growth with a combined treatment of iodoacetate and dimethylsulphoxide

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