Mathematical Modeling of Irreversible Electroporation for Treatment Planning

Abstract

Irreversible Electroporation (IRE) is a new drug-free method to ablate undesirable tissue of particular use in cancer therapy. IRE achieves cell death within the targeted tissue through a series of electric pulses that elevate the transmembrane potentials to an extent that permanently damages the lipid bilayers throughout the treated region. Although the IRE procedure is easy to perform, treatment planning is complicated by the fact that the electric field distribution within the tissue, the greatest single factor controlling the extents of IRE, depends non-trivially on the electrode configuration, pulse parameters and any tissue heterogeneities. To address this difficulty, we instruct on how to properly model IRE and discuss the benefit of modeling in designing treatment protocols. The necessary theoretical basis is introduced and discussed through the detailed analysis of two classic dual-electrode configurations from electrochemotherapy: coaxial disk electrodes and parallel needle electrodes. Dimensionless figures for these cases are also provided that allow cell constants, treated areas, and the details of heating to be determined for a wide range of conditions, for uniform tissues, simply by plugging in the appropriate physical property values and pulse parameters such as electrode spacing, size, and pulse amplitude. Complexities, such as heterogeneous tissues and changes in conductivity due to electroporation, are also discussed. The synthesis of these details can be used directly by surgeons in treatment planning. Irreversible electroporation is a promising new technique to treat cancer in a targeted manner without the use of drugs; however, it does require a detailed understanding of how electric currents flow within biological tissues. By providing the understanding and tools necessary to design an IRE protocol, this study seeks to facilitate the translation of this new and exciting cancer therapy into clinical practice.