A mathematical model of drug dynamics in an electroporated tissue

Abstract

In order to overcome the obstruction of cell membranes in the path of drug delivery to diseased cells, the applications of electric pulses of adequate potency are designated as electroporation. In the present study, a mathematical model of drug delivery into the electroporated tissue is advocated, which deals with both reversibly and irreversibly electroporated cells. This mathematical formulation is manifested through a set of differential equations, which are solved analytically, and numerically, according to the complexity, with a pertinent set of initial and boundary conditions. The time-dependent mass transfer coefficient in terms of pores is used to find the drug concentrations through reversibly and irreversibly electroporated cells as well as extracellular space. The effects of permeability of drug, electric field and pulse period on drug concentrations in extracellular and intracellular regions are discussed. The threshold value of an electric field ($ E > 100 $ V cm$ ^{-1} $) to initiate drug uptake is identified in this study. Special emphasis is also put on two cases of electroporation, drug dynamics during ongoing electroporation and drug dynamics after the electric pulse period is over. Furthermore, all the simulated results and graphical portrayals are discussed in detail to have a transparent vision in comprehending the underlying physical and physiological phenomena. This model could be useful to various clinical experiments for drug delivery in the targeted tissue by controlling the model parameters depending on the tissue condition.

Keywords

• electroporation
• drug delivery
• reversibly and irreversibly electroporated cells
• cell membrane
• electric pulse