A Fractional Order Model for Local Electric Fields in Tissues

Abstract

In recent years, electro-chemotherapy and gene electro-transfer have emerged as promising cancer therapies that use locally applied electric fields to facilitate the transport of chemotherapeutic drugs into tumor cells or genes into target cells based on the cell membrane electroporation. It is well known that the local electric field in the tissue depends on the applied voltage on the electrodes, the geometry and position of the electrodes, and on the heterogeneity and geometry of the tissue. So far, the local electric field distribution in tissues was found by solving the classic Laplace equation. However, tissues and tumors have evolving microstructures which affect the distribution of the applied electric field. Inspired by the successful application of fractional order constitutive models of tissues, in our exploratory study we propose a fractional calculus based approach to model the electric field and potential distribution in tissues. The resulting fractional differential equation of Laplace type is solved analytically. Our preliminary results on the local electric field distribution might help to find electrode configurations for optimal treatment outcome.