Mathematical modeling of the thermal effects of irreversible electroporation for in vitro, in vivo, and clinical use: a systematic review

Irreversible electroporation (IRE) is a relatively new ablation method for the treatment of unresectable cancers. Although the main mechanism of IRE is electric permeabilization of cell membranes, the question is to what extent thermal effects of IRE contribute to tissue ablation. This systematic review reviews the mathematical models used to numerically simulate the heat-generating effects of IRE, and uses the obtained data to assess the degree of mild-hyperthermic (temperatures between 40 °C and 50 °C) and thermally ablative (TA) effects (temperatures exceeding 50 °C) caused by IRE within the IRE-treated region (IRE-TR). A systematic search was performed in medical and technical databases for original studies reporting on numerical simulations of IRE. Data on used equations, study design, tissue models, maximum temperature increase, and surface areas of IRE-TR, mild-hyperthermic, and ablative temperatures were extracted. Several identified models, including Laplace equation for calculation of electric field distribution, Pennes Bioheat Equation for heat transfer, and Arrhenius model for thermal damage, were applied on various electrode and tissue models. Median duration of combined mild-hyperthermic and TA effects is 20% of the treatment time. Based on the included studies, mild-hyperthermic temperatures occurred in 30% and temperatures ≥50 °C in 5% of the IRE-TR. Simulation results in this review show that significant mild-hyperthermic effects occur in a large part of the IRE-TR, and direct thermal ablation in comparatively small regions. Future studies should aim to optimize clinical IRE protocols, maintaining a maximum irreversible permeabilized region with minimal TA effects.