In many electroporation applications mass transport in biological tissue is of primary concern. This paper presents a theoretical advancement in the field and gives some examples of model use in electroporation applications. The study focuses on post-treatment solute diffusion. We use a dual-porosity approach to describe solute diffusion in electroporated biological tissue. The cellular membrane presents a hindrance to solute transport into the extracellular space and is modeled as electroporation-dependent porosity, assigned to the intracellular space (the finite rate of mass transfer within an individual cell is not accounted for, for reasons that we elaborate on). The second porosity is that of the extracellular space, through which solute vacates a block of tissue. The model can be used to study extraction out of or introduction of solutes into tissue, and we give three examples of application, a full account of model construction, validation with experiments, and a parametrical analysis. To facilitate easy implementation and experimentation by the reader, the complete derivation of the analytical solution for a simplified example is presented. Validation is done by comparing model results to experimentally-obtained data; we modeled kinetics of sucrose extraction by diffusion from sugar beet tissue in laboratory-scale experiments. The parametrical analysis demonstrates the importance of selected physicochemical and geometrical properties of the system, illustrating possible outcomes of applying the model to different electroporation applications. The proposed model is a new platform that supports rapid extension by state-of-the-art models of electroporation phenomena, developed as latest achievements in the field of electroporation.
Keywords: Analytical solution of PDE; Diffusion; Electroporation; Mass transfer; Mathematical modeling; Solute extraction.
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