The Rules of Pulsatile Neurostimulation

Electrical stimulation of neural responses is used both scientifically in brain mapping studies and in many clinical applications such as cochlear, vestibular, and retinal implants. Due to safety considerations, stimulation of the nervous system is restricted to short biphasic pulses. Despite decades of research and development, neural implants are far from optimal in their ability to restore function and lead to varying improvements in patients. In this study, we provide an explanation for how pulsatile stimulation affects individual neurons and therefore leads to variability in restoration of neural responses. The explanation is grounded in the physiological response of channels in the axon and represented with mathematical rules that predict firing rate as a function of pulse rate, pulse amplitude, and spontaneous activity. We validate these rules by showing that they predict recorded vestibular afferent responses in macaques and discuss their implications for designing clinical stimulation paradigms and electrical stimulation-based experiments. Introduction Electrical stimulation is ubiquitous in modern treatments for neurological disorders and studies of neural function. It has a longstanding and intertwined history with the field of neuroscience, starting from the first studies showing neurons could be activated by electrical stimulation. In the present, electrical microstimulation remains a prominent way to understand neural function and connectivity at local and interregional levels of the nervous system. Clinically, it is not only relied on for brain mapping to inform treatments; usages have expanded to neural prostheses for restoration of perception and treating neuropsychiatric disorders. The main driver of safety standards has been developing paradigms suitable for long-term, implantable devices, which led to the restriction of current delivery to biphasic, charged-balanced pulses that prevent electrochemical reactions at the electrode interface and neural damage. Resultantly, electrical stimulation has become synonymous with this form of pulsatile stimulation across applications. Implantable pulse generators have been used in neural implants since the 1950s to treat impairments including hearing, visual, and balance and movement disorders. These devices use changes in pulse rate and amplitude to modulate local neural activity to replace natural function. While the list of clinically viable prostheses based on this technology is rapidly growing, their ability to restore encoding of the full range of information remains limited. Even in the cochlear implant, which has been continually improved since the initial introduction in 1957, speech perception is restored, but pitch perception, which is encoded in finetiming of firing rates, is at a deficit, likely leading to lack of music appreciation and tonal language perception. Many explanations have been proposed for limitations in restored function for the each sensory prostheses, such as noise reduction in the front-end processing in cochlear implants 16 , pathological neural rewiring of the retina , or central nervous system adaptation to vestibular stimulation18. These findings imply that present stimulation paradigms do not restore the natural local responses and, in turn, raise significant questions about the validity of using either microstimulation or cortico-cortical evoked responses to understand natural local and interregional connectivity and function. Here we argue that a common element associated with the inability to optimize the clinical systems may be the complexity and unpredictability of evoked neural activity in response to stimulation pulse trains. While substantial experimental evidence exists for pulsatile effect on neurons, a systematic theory of how pulse rate and pulse amplitude affect neurons of varying spontaneous activity has not been established. What is established, however, is that pulses produce complex effects at the axon (e.g., facilitation and blocking of future pulses), and spontaneous activity significantly impacts the induced firing rate in response to pulses. In this study, we perform a systematic investigation of the relationship between pulse rate (pr), pulse amplitude (I), and spontaneous rate (S) in a biophysical model of a vestibular afferent, where baseline spontaneous firing has been shown to impact pulsatile stimulation. We use a computational model to determine the physiological underpinnings these non-linear effects on firing rate and describe them with equations related to measurable and controllable quantities: fr = φ(pr, I, S). We further validate this framework with experimental observations of vestibular afferents obtained in non-human primates in response to vestibular canal stimulation with pulse trains of different amplitudes and rates. We determine whether these non-linearities can be corrected for algorithmically in neural implants and conclude by discussing their implications for interpreting electrical stimulation studies.