Mathematical Models Describing Chinese Hamster Ovary Cell Death Due to Electroporation In Vitro

Electroporation is a phenomenon used in the treatment of tumors by electrochemotherapy, non-thermal ablation with irreversible electroporation, and gene therapy. When treating patients, either predefined or variable electrode geometry is used. Optimal pulse parameters are predetermined for predefined electrode geometry, while they must be calculated for each specific case for variable electrode geometry. The position and number of electrodes are also determined for each patient. It is currently assumed that above a certain experimentally determined value of electric field, all cells are permeabilized/destroyed and under it they are unaffected. In this paper, mathematical models of survival in which the probability of cell death is continuously distributed from 0 to 100 % are proposed and evaluated. Experiments were performed on cell suspensions using electrical parameters similar to standard electrochemotherapy and irreversible electroporation parameters. The proportion of surviving cells was determined using clonogenic assay for assessing the ability of a cell to grow into a colony. Various mathematical models (first-order kinetics, Hülsheger, Peleg-Fermi, Weibull, logistic, adapted Gompertz, Geeraerd) were fitted to experimental data using a non-linear least-squares method. The fit was evaluated by calculating goodness of fit and by observing the trend of values of models' parameters. The most appropriate models of cell survival as a function of treatment time were the adapted Gompertz and the Geeraerd models and, as a function of the electric field, the logistic, adapted Gompertz and Peleg-Fermi models. The next steps to be performed are validation of the most appropriate models on tissues and determination of the models' predictive power.