Using the conventional Haberkorn approach, it is evaluated the recombination of the radical pair (RP) singlet spin state to study theoretically the cytoprotective effect of an extremely-low-frequency electromagnetic field (ELF-EMF) on early stages of hepatic cancer chemically induced in rats. The proposal is that ELF-EMF modulates the interconversion rate of singlet and triplet spin states of the RP populations modifying the products from the metabolization of carcinogens. Previously, we found that the daily treatment with ELF-EMF 120 Hz inhibited the number and area of preneoplastic lesions in chemical carcinogenesis. The singlet spin population is evaluated diagonalizing the spin density matrix through the Lanczos method in a radical pair mechanism (RPM). Using four values of the interchange energy, we have studied the variations over the singlet population. The low magnetic field effect as a test of the influence over the enzymatic chemical reaction is evaluated calculating the quantum yield. Through a bootstrap technique the range is found for the singlet decay rate for the process. Applying the quantum measurements concept, we addressed the impact toward hepatic cells. The result contributes to improving our understanding of the chemical carcinogenesis process affected by charged particles that damage the DNA.

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.

BackgroundElectrotherapy 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.MethodsThe 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.ResultsThe 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.ConclusionThe 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.

BackgroundRecently, extremely low frequency electromagnetic fields (ELF-EMF) have been studied with great interest due to their possible effects on human health. In this study, we evaluated the effect of 4.5 mT - 120 Hz ELF-EMF on the development of preneoplastic lesions in experimental hepatocarcinogenesis.MethodsMale Fischer-344 rats were subjected to the modified resistant hepatocyte model and were exposed to 4.5 mT - 120 Hz ELF-EMF. The effects of the ELF-EMF on hepatocarcinogenesis, apoptosis, proliferation and cell cycle progression were evaluated by histochemical, TUNEL assay, caspase 3 levels, immunohistochemical and western blot analyses.ResultsThe application of the ELF-EMF resulted in a decrease of more than 50% of the number and the area of γ-glutamyl transpeptidase-positive preneoplastic lesions (P = 0.01 and P = 0.03, respectively) and glutathione S-transferase placental expression (P = 0.01). The number of TUNEL-positive cells and the cleaved caspase 3 levels were unaffected; however, the proliferating cell nuclear antigen, Ki-67, and cyclin D1 expression decreased significantly (P ≤ 0.03), as compared to the sham-exposure group.ConclusionThe application of 4.5 mT - 120 Hz ELF-EMF inhibits preneoplastic lesions chemically induced in the rat liver through the reduction of cell proliferation, without altering the apoptosis process.