Bidirectional modulation of neuronal excitability via ionic actuation of potassium

Potassium K+ is a fundamental actor in the shaping of action potentials, and its concentration in the extracellular microenvironment represents a crucial modulator of neural excitability. Yet, its employment as a neuromodulation modality is still in its infancy. Recent advances in the technology of ionic actuators are enabling the control of ionic concentrations at the spatiotemporal scales of micrometers and milliseconds, thereby holding the promise of making the control of K+ concentration a key enabling technology for the next generation of neural interfaces. In this regard, a theoretical framework to understand the possibilities and limits offered by such technology is pivotal. To this aim, we exploit the Hodgkin-Huxley modeling framework, augmented to account for the perturbation of extracellular K+ concentration. We leverage methods of bifurcation analysis to investigate which regimes of electrical activity arise in the space of the input variables, namely the extent of ionic actuation and the synaptic current. We show that, depending on the type of target neuron, switchings of the class of excitability may occur in such space. These effects could rule out the possibility of eliciting tonic spiking when the extracellular K+ concentration is assumed as a sole control input. Building upon these findings, we show in simulations how to address the problem of neuromodulation via ionic actuation in a principled fashion. In this respect, we account for a bidirectional scenario, namely from the perspective of both inhibiting and stimulating electrical activity. We then provide a first-order motivation for the switchings of neural excitability in terms of the conductances of the K+-selective channels. Finally, we introduce a Pinsky-Rinzel-like model to investigate the effects of performing the ionic actuation locally at the neural membrane.