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

Abstract

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 325^o 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.

Keywords: Array of multiple-electrodes; Electrochemical therapy; Highly aggressive and metastatic primary F3II mammary carcinoma; Modified Gompertz equation; Tumor growth kinetics.

Fig. 1

Schematic representation of different multiple-electrodes arrays inserted in a solid tumor. a Four collinear electrodes with alternating polarities inserted perpendicularly along the largest diameter of the tumor. Electrodes 1 and 3 (positive) and 2 and 4 (negative) were identified (C-I). b Four electrode pairs were arranged in the tumor to 45° (electrode pair 1–2), 135° (electrode pair 3–4), 225° (electrode pair 5–6) and 325° (electrode pair 7–8). Electrodes 1, 4, 5 and 8 were positives whereas electrodes 2, 3, 6 and 7 negatives (C-II). c Four electrode pairs were arranged in the tumor to 0° (electrode pair 1–2), 90° (electrode pair 3–4), 180° (electrode pair 5–6) and 270° (electrode pair 7–8). Electrodes 2, 3, 5 and 8 were positives whereas electrodes 1, 4, 6 and 7 negatives (C-III). Furthermore, the direction of insertion depth along the z-direction and the central plane represented by z = 0 were shown for each geometry of electrode array

Fig. 2

Mean ± mean standard error of corporal weight of the mice BALB/c/Cenp versus days post-inoculation of the tumoral cells F3II. a Males. b Females. The legends of the experimental groups were defined in Methods

Fig. 3

Mean ± mean standard error of the tumor volume against post-inoculation days of F3II tumor cells. a Males BALB/c/Cenp mice (M). b Females BALB/c/Cenp mice (F). Legends of each experimental group were defined in the Experiment subsection

Fig. 4

Survival versus days after inoculation of F3II cells in mice BALB/c/Cenp, by experimental group and gender. a Females. b Males. CG1 (first control group, in which C-I was used but DC was not applied). CG2 (second control group, in which C-II was used but DC was not applied). TG1 (first group treated with 2 mA for 10 min and C-I). TG2 (second group treated with 6 mA for 20 min and C-II). TG3 (third group treated with 2 mA for 10 min and C-III). TG4 (fourth group treated with 2 mA for 10 min and C-II). TG5 (fifth group treated with 6 mA for 10 min and C-II). TG6 (sixth group treated with 10 mA for 10 min and C-II). C-I was formed by four collinear electrodes with alternating polarities inserted perpendicularly along the largest diameter of the tumor (electrodes 1 and 3 were positives whereas electrodes 2 and 4 negatives), as shown in Fig. 1a. C-II were formed by four electrode pairs inserted into the tumor to 45° (electrode pair 1–2), 135° (electrode pair 3–4), 225° (electrode pair 5–6) and 325° (electrode pair 7–8), as shown in Fig. 1b. For C-II, electrodes 1, 4, 5 and 8 were positives whereas electrodes 2, 3, 6 and 7 negatives. C-III were formed by four electrode pairs arranged into the tumor to 0° (electrode pair 1–2), 90° (electrode pair 3–4), 180° (electrode pair 5–6) and 270° (electrode pair 7–8), as shown in Fig. 1c. For C-III, electrodes 2, 3, 5 and 8 were positives whereas electrodes 1, 4, 6 and 7 negatives