Efficacy of direct current generated by multiple-electrode arrays on F3II mammary carcinoma: experiment and mathematical modeling

BACKGROUND: The modified Gompertz equation has been proposed to fit experimental data for direct current treated tumors when multiple-straight needle electrodes are individually inserted into the base perpendicular to the tumor long axis. The aim of this work is to evaluate the efficacy of direct current generated by multiple-electrode arrays on F3II mammary carcinoma that grow in the male and female BALB/c/Cenp mice, when multiple-straight needle electrodes and multiple-pairs of electrodes are inserted in the tumor. METHODS: A longitudinal and retrospective preclinical study was carried out. Male and female BALB/c/Cenp mice, the modified Gompertz equation, intensities (2, 6 and 10 mA) and exposure times (10 and 20 min) of direct current, and three geometries of multiple-electrodes (one formed by collinear electrodes and two by pair-electrodes) were used. Tumor volume and mice weight were measured. In addition, the mean tumor doubling time, tumor regression percentage, tumor growth delay, direct current overall effectiveness and mice survival were calculated. RESULTS: The greatest growth retardation, mean doubling time, regression percentage and growth delay of the primary F3II mammary carcinoma in male and female mice were observed when the geometry of multiple-pairs of electrodes was arranged in the tumor at 45, 135, 225 and 325o and the longest exposure time. In addition, highest direct current overall effectiveness (above 66%) was observed for this EChT scheme. CONCLUSIONS: It is concluded that electrochemical therapy may be potentially addressed to highly aggressive and metastic primary F3II murine mammary carcinoma and the modified Gompertz equation may be used to fit data of this direct current treated carcinoma. Additionally, electrochemical therapy effectiveness depends on the exposure time, geometry of multiple-electrodes and ratio between the direct current intensity applied and the polarization current induced in the tumor

Mathematical modeling and forecasting of COVID-19: experience in Santiago de Cuba province

In the province of Santiago de Cuba, Cuba, the COVID-19 epidemic has a limited progression that shows an early small-number peak of infections. Most published mathematical models fit data with high numbers of confirmed cases. In contrast, small numbers of cases make it difficult to predict the course of the epidemic. We present two known models adapted to capture the noisy dynamics of COVID-19 in the Santiago de Cuba province. Parameters of both models were estimated using the approximate-Bayesian-computation framework with dedicated error laws. One parameter of each model was updated on key dates of travel restrictions. Both models approximately predicted the infection peak and the end of the COVID-19 epidemic in Santiago de Cuba. The first model predicted 57 reported cases and 16 unreported cases. Additionally, it estimated six initially exposed persons. The second model forecasted 51 confirmed cases at the end of the epidemic. In conclusion, an opportune epidemiological investigation, along with the low number of initially exposed individuals, might partly explain the favorable evolution of the COVID-19 epidemic in Santiago de Cuba. With the available data, the simplest model predicted the epidemic evolution with greater precision, and the more complex model helped to explain the epidemic phenomenology