Dynamical regimes of excitable cells under pulsed electric fields: From excitation to electroporation
Nanosecond pulse electric fields (nsPEFs) are an established treatment modality for cancer and have emerged as a potential approach for deep brain stimulation and cardiac defibrillation. The concerns in these two applications are at odds. While pulsed-field electroporation applications aim to minimise excitation of surrounding neurons, therapies based on neuronal stimulation demand minimal electroporation of neurons. Although nsPEFs offer various advantages, such as minimising power input and suppressing electrode reactions, they require strong electric fields to reach both the excitation and electroporation thresholds, so maintaining a safety gap between the two is crucial. Because these coupled processes unfold on time scales ranging from nanoseconds to milliseconds and cannot be resolved simultaneously in experiments, a computational approach is used. This study examines the interplay between excitation and electroporation within the Hodgkin-Huxley (HH) framework for a planar two-bilayer model coupled with the Asymptotic Smoluchowski Equation for electroporation, and solves for transmembrane potentials (TMPs), pore statistics and pore size evolution. The model can predict the role of electroporation in modulating neuronal responses and qualitatively explain key experimental observations in the literature. These include excitation with a single action potential (SAP), repetitive spiking (RS), and depolarisation block (DB), and are explained here with detailed mechanisms, including the subtle effects of strong electric fields and electroporating currents on ion-channel dynamics. Importantly, our work establishes a parameter space for strength-duration curves in regimes of safe excitation without electroporation, and vice versa. For a neuron with an equivalent RC time constant of 10 ns, pulses shorter than about 20 ns electroporate the membrane before they excite it, and the safety factor falls below 5% for 1-ns pulses. The work also expands into s and ms pulses, and delves into possible regimes that could lead to neuronal inviability due to irreversible electroporation or excessive fractional pore area.