Numerical modeling in electroporation-based biomedical applications

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Abstract
Background. Numerous experiments have to be performed before a biomedical application is put to practical use in clinical environment. As a complementary work to in vitro, in vivo and medical experiments, we can use analytical and numerical models to represent, as realistically as possible, real biological phenomena of, in our case, electroporation. In this way we can evaluate different electrical parameters in advance, such as pulse amplitude, duration, number of pulses, or different electrode geometries. Such numerical models can contribute significantly to the understanding of an experiment and treatment planning as well as to the design of new electroporation devices and electrodes. Methods. We used commercially available modeling software, based on finite element method. We constructed a model of a subcutaneous tumor during electrochemotherapy (EMAS) and a model of skin during gene electrotransfer (COMSOL Multiphysics). Tissue-electrode geometries, pulse parameters and current-voltage measurements from in vivo experiments were used to develop and validate the models. Results. To describe adequately our in vivo observations, a tissue conductivity increase during electroporation was included in our numerical models. The output currents of the models were compared to the currents and the voltages measured during in vivo experiments and a good agreement was obtained. Also, when comparing the voltages needed for a successful electropermeabilization as suggested by the models, to voltages applied in experiments and achieving a successful electrochemotherapy or in vivo gene electrotransfer, good agreement can be observed. Conclusions. Modeling of electric current and electric field distribution during cell and tissue electroporation proves to be helpful in describing different aspects of the process and allowing us to design electrodes and electroporation protocols as a part of treatment planning.