Dynamical diversity in conductance-based neuron response to kilohertz electrical stimulation

Neurons are notably rich in structure and functioning, so rather diverse in their response to stimuli. Consequently, the proper characterization of their dynamical response to external signals is a crucial step in understanding stimulation mechanisms. In particular, kilohertz (kHz) neuronal electrical stimulation tends to induce comportment and drives unseen in (more conventional) lower frequency ranges. Here, we investigate neuronal response of conductance-based models to kHz frequencies stimulation in a broad and often unexplored parameter space region. First, we show that the time evolution exhibited by the paradigmatic Hodgkin-Huxley model under kilohertz stimulation is highly diverse, ranging from regular spiking to chaotic dynamics, as well as displaying regions of complete activity suppression. However, to unveil all these features, a certain level of technical caution is required. For example, we demonstrate that common simplifications of sodium dynamics become inaccurate under these frequency regimes. Also, based on suitable markers, we propose a method for mapping the mentioned behaviors on a stimulation parameter space. Second, by extending the study to models of mammalian central nervous system regions, a comprehensive dynamical atlas is obtained. It provides a rather systematic way to typify the response of rapidly forced conductance-based neurons. Thus, the present findings seems to point to an useful scheme for stimulation-based computational neuroscience research at kilohertz frequencies.