Control of pore radius regulation for electroporation-based drug delivery

Electroporation uses electric pulses to create transient, nonselective pores in a cell’s membrane, allowing drugs to be delivered into the targeted cells. To ensure proper uptake of drug molecules, it is essential to control the radii of the pores and the time duration, for which the pores remain open. Electroporation is intrinsically a nonlinear dynamic process. A careful analysis of the electroporation dynamics reveals that, under variation of the magnitude of the input voltage, the equilibrium pore radius undergoes a pair of saddle-node bifurcations. As a result, there exists a range of pore radii that is physically unstable and thus cannot be maintained in conventional experiments. The bifurcations and the associated unstable regime impose restrictions on the operation of electroporation, limiting the sizes of deliverable drug particles. To overcome these problems, we design a novel control strategy to stabilize the originally unstable solutions. In contrast to the conventional control algorithms based on local stability analysis, the present control is globally stable. Numerical examples show that the control eliminates the original bifurcations and allows one to achieve a wide range of pore radii. The robustness and effectiveness of the control strategy would potentially enhance the application of electroporation.