Electroporation has become an important tool for drug delivery such as gene therapy. The technique uses electric pulses to create transient pores in the cell membrane. To ensure proper uptake of targeted molecules, it is essential to create sufficiently large pores, which remain open long enough. In this work, we explore evolution of the pores using dynamical analysis and control of electroporation based on a simplified two-dimensional model. A detailed bifurcation analysis reveals the existence of saddle-node bifurcations, which induce hysteresis into the system dynamics. The bifurcation analysis also sheds light on the relation between the applied voltage and the pore radius. Based on the dynamics and bifurcation analysis, we design a feedback control algorithm that is able to achieve any desired pore size. Numerical examples demonstrate the control strategy is robust. The control algorithm will improve the operation of electroporation in drug delivery.
Corrigendum to “Advanced Topics in Modeling, Bifurcation Analysis, and Control Theory of Complex Systems”
