Cortical neuron activation induced by electromagnetic stimulation: a quantitative analysis via modelling and simulation

Abstract

Previous simulation works concerned with the mechanism of non-invasive neuromodulation has isolated many of the factors that can influence stimulation potency, but an inclusive account of the interplay between these factors on realistic neurons is still lacking. To give a comprehensive investigation on the stimulation-evoked neuronal activation, we developed a simulation scheme which incorporates highly detailed physiological and morphological properties of pyramidal cells. The model was implemented on a multitude of neurons; their thresholds and corresponding activation points with respect to various field directions and pulse waveforms were recorded. The results showed that the simulated thresholds had a minor anisotropy and reached minimum when the field direction was parallel to the dendritic-somatic axis; the layer 5 pyramidal cells always had lower thresholds but substantial variances were also observed within layers; reducing pulse length could magnify the threshold values as well as the variance; tortuosity and arborization of axonal segments could obstruct action potential initiation. The dependence of the initiation sites on both the orientation and the duration of the stimulus implies that the cellular excitability might represent the result of the competition between various firing-capable axonal components, each with a unique susceptibility determined by the local geometry. Moreover, the measurements obtained in simulation intimately resemble recordings in physiological and clinical studies, which seems to suggest that, with minimum simplification of the neuron model, the cable theory-based simulation approach can have sufficient verisimilitude to give quantitatively accurate evaluation of cell activities in response to the externally applied field.

A multi-scale computational model of the effects of TMS on motor cortex

“…However, these attempts had various limitations. First, in early studies no anatomical information on large-scale brain morphology was applied 23– 25 . Rather than constructing a finite element head model, these studies applied a uniform electric field to the neuronal model.…”

“…Thus, while we lengthened PNs to fit the cortex, the uncertainties regarding morphology of neurons was not fully studied. Wu et al (2016) incorporated a multitude of PNs with various stimuli 25 and Salvador et al (2010) constructed various types of neural structures including pyramidal neurons, interneurons, and association fibers 29 ; they found that the excitability can be shaped by field orientation, pulse wave form, and diameter of neurons. In addition, changes in the electrical properties, such as membrane properties and ion channels had the largest influence on neuronal excitability 25 .…”

“…Wu et al (2016) incorporated a multitude of PNs with various stimuli 25 and Salvador et al (2010) constructed various types of neural structures including pyramidal neurons, interneurons, and association fibers 29 ; they found that the excitability can be shaped by field orientation, pulse wave form, and diameter of neurons. In addition, changes in the electrical properties, such as membrane properties and ion channels had the largest influence on neuronal excitability 25 . However, despite the uncertainty with regard to properties of PNs, we produced results matching both experimental studies and other computational studies 23, 25 that incorporated the same models of PNs.…”

“…The membrane potentials induced by stimulation were approximated by adding an external current source I ext to the cable model 2, 21, 22, 24, 25 :…”

“…In early computational models, straight axonal fibers were considered numerically and the response of neurons induced by the external field was modeled by means of the cable equation 21, 22 . Later models investigated the role of cell morphology using multi-compartmental modeling 23– 25 . The responses of cortical neurons vary depending on not only the neuronal morphology but also orientation relative to the induced electric field and stimulus amplitude 6, 26, 27 .…”