Mathematical models describing cell death due to electroporation

Abstract

Various models have been developed to describe microbial inactivation by pulsed electric field treatment, and they have just recently been used for describing eukaryotic cell death due to irreversible electroporation. In microbial inactivation, the mathematical models of cell death enable the adaptation of the pulse parameters to achieve sufficient microbial reduction at the lowest energy input while preserving flavor and sensitive compounds in the food. For precise prediction, the geometry of the treatment chamber, the fluid flow, the temperature, and the electric field distribution should also be taken into account. In electroporationbased medical treatments, currently, a deterministic critical value of electric field is used to delineate between the destroyed and the unaffected tissue. Consequently, tumor cells which have higher electroporation threshold than the experimentally determined may remain viable and cause incomplete tumor elimination. On the contrary, the more sensitive surrounding tissue could be damaged. Mathematical models of cell death help to achieve sufficient cell death while minimizing the damage to the surrounding vital structures. In this chapter, different models are described which were already used for describing microbial inactivation in liquid foods or eukaryotic cell death (the first order, the Hülsheger, the Peleg-Fermi, the Weibull, the logistic, the Adapted/Modified Gompertz, the Geeraerd, the quadratic, the Peleg-Penchina model). The cell death models have already been used for predicting survival in realistic setups like the treatment chamber in microbial inactivation and different electrode geometries and tissues in irreversible electroporation treatments. In conclusion, cell death models are useful in predicting the treatment outcome. Unfortunately, since the mechanisms of cell death due to electroporation are not yet fully elucidated, the models are empiric. There is no direct connection between the parameters of the models and the biological/electrical parameters. Thus, it is unclear which model is the most appropriate to use. The models have to be optimized for each specific cell type and electric pulses separately. The transferability from the in vitro to the in vivo level is questionable.