BackgroundUnperturbed tumor growth kinetics is one of the more studied cancer topics; however, it is poorly understood. Mathematical modeling is a useful tool to elucidate new mechanisms involved in tumor growth kinetics, which can be relevant to understand cancer genesis and select the most suitable treatment.MethodsThe classical Kolmogorov-Johnson-Mehl-Avrami as well as the modified Kolmogorov-Johnson-Mehl-Avrami models to describe unperturbed fibrosarcoma Sa-37 tumor growth are used and compared with the Gompertz modified and Logistic models. Viable tumor cells (1×105) are inoculated to 28 BALB/c male mice.ResultsModified Gompertz, Logistic, Kolmogorov-Johnson-Mehl-Avrami classical and modified Kolmogorov-Johnson-Mehl-Avrami models fit well to the experimental data and agree with one another. A jump in the time behaviors of the instantaneous slopes of classical and modified Kolmogorov-Johnson-Mehl-Avrami models and high values of these instantaneous slopes at very early stages of tumor growth kinetics are observed.ConclusionsThe modified Kolmogorov-Johnson-Mehl-Avrami equation can be used to describe unperturbed fibrosarcoma Sa-37 tumor growth. It reveals that diffusion-controlled nucleation/growth and impingement mechanisms are involved in tumor growth kinetics. On the other hand, tumor development kinetics reveals dynamical structural transformations rather than a pure growth curve. Tumor fractal property prevails during entire TGK.

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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.

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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