Excitatory and Inhibitory Cable Properties Controls the Transient Amplification of Electrical Stimulation

Abstract

Neuromodulation therapies such as deep brain stimulation have shown some clinical success in treating Parkinson's, epilepsy, essential tremor, and many other conditions. However, these devices primarily target the subcortex and treat a small subset of neurological disorders. To address these limitations, we investigate cortical stimulation as an alternative, focusing on the biophysical and network-level mechanisms that shape the brain's responses to electrical input.

This thesis investigates how excitatory and inhibitory cable properties influence the transient amplification resulting from electrical stimulation in the cortex. Cortical stimulation remains poorly understood, and debates persist about the biological processes involved in direct electrical stimulation. To better understand these responses, we developed a mathematical model grounded in the biophysical properties of neurons, combining axonal cable theory to emulate experimentally observed cortical phenomena.

We begin by analyzing recruitment through cable theory, and we derive a relationship between the intensity threshold and the axon diameter. Experimental studies (Micheva, Kristina D., et al., 2016) show that inhibitory axons in the cortex are larger in diameter compared to excitatory ones, resulting in a bias toward inhibitory recruitment. However, to promote excitatory recruitment, we assume that inhibitory axons, particularly those with larger diameters, are myelinated. Since myelinated axons require higher stimulus intensities to be activated, this assumption raises the activation threshold for inhibition, while favouring excitation. Therefore, the axonal cable properties in our model suggest that excitation is more readily recruited than inhibition.

Next, we develop the mean-field model, which begins with a network of intercommunicating excitatory and inhibitory neurons. We introduce two stimulation paradigms: the activation model, which focuses on the recruitment of antidromic axons and somas to initiate the input into our field model, and the depolarization model, which assumes direct electrical stimulation of neurons, leading them to depolarize in response to external extracellular voltage.

We find that both models elicit the same cortical responses from electrical stimulation. With fine-tuned parameters, both models exhibit transient amplification due to the excitatory-inhibitory imbalance in activation.

The cable properties of axons allow for the recruitment of excitatory and inhibitory neurons during electrical stimulation. The recruitment imbalance results in different network-level responses. In particular, our model demonstrates that these imbalances can lead to transient amplification, resulting in early excitatory activation followed by lagging inhibition that restores the network.