Modelling motor cortex stimulation for chronic pain control: Electrical potential field, activating functions and responses of simple nerve fibre models

Abstract

This computer modelling study on motor cortex stimulation (MCS) introduced a motor cortex model, developed to calculate the imposed electrical potential field characteristics and the initial response of simple fibre models to stimulation of the precentral gyrus by an epidural electrode, as applied in the treatment of chronic, intractable pain. The model consisted of two parts: a three-dimensional volume conductor based on tissue conductivities and human anatomical data, in which the stimulation-induced potential field was computed, and myelinated nerve fibre models allowing the calculation of their response to this field. A simple afferent fibre branch and three simple efferent fibres leaving the cortex at different positions in the precentral gyrus were implemented. It was shown that the thickness of the cerebrospinal fluid (CSF) layer between the dura mater and the cortex below the stimulating electrode substantially affected the distribution of the electrical potential field in the precentral gyrus and thus the threshold stimulus for motor responses and the therapeutic stimulation amplitude. When the CSF thickness was increased from 0 to 2.5 mm, the load impedance decreased by 28%, and the stimulation amplitude increased by 6.6 V for each millimetre of CSF. Owing to the large anode-cathode distance (10 mm centre-to-centre) in MCS, the cathodal fields in mono- and bipolar stimulation were almost identical. Calculation of activating functions and fibre responses showed that only nerve fibres with a directional component parallel to the electrode surface were excitable by a cathode, whereas fibres perpendicular to the electrode surface were excitable under an anode.

A model for transcutaneous current stimulation: simulations and experiments

“…neglecting capacitive effects) to describe the volume conductor, and linear nerve models to describe nerve activation. Up to now non-linear nerve models, which can describe more facets of nerve activation [45], were mainly used for implantable systems [31,49,47], epidural stimulation [18], or motor cortex stimulation [33], where the exciting electrodes are small and close to the nerve (near-field). To address if these nerve models can also be used to model TES (far-field), we have developed a TES model that comprises a volume conductor and different non-linear nerve models.…”

Targeted Subcortical Nerve Recruitment by Controlling the Waveform of Electrical Stimulation for MRI-guided Surgical Ablation

“…We slightly modi ed a 3D volume conductor model of a part of the human head described in prior studies [4,9,10], which is based on the anisotropic properties of the human brain. The model comprises the skull, dura mater, cerebrospinal uid (CSF), gray matter, and white matter ( Fig.…”

“…However, the authors who originally developed the nerve ber model assumed the diameters of the bers to be over 5 μm [13], and no description was found for bers thinner than 5 μm. Thus, we assumed the following equations for bers thinner than 5 μm by extrapolating the de ned range: Layers II-IV 1.4 0.36 [4,9] Layers V-VI 2.1 0.36 [4,9] White matter 12 0.083 (perpendicular to the ber), 0.6 (parallel to the ber) [4,9] Advanced Biomedical Engineering. Vol.…”

Selective stimulation of the subthalamic nucleus

“…During bipolar stimulation, one of the remaining electrode contacts was used as a reference. Like Manola et al (Manola et al 2005), we set the conductance of the dura mater to a value that gives an impedance matching to the mean empirical value of ~1000 ohm during bipolar stimulation. This resulted in a conductance of 0.055 S/m, which is in between the values of 0.065 S/m proposed by Manola et al (Manola et al 2005) and 0.03 S/m used by Struijk et al (Struijk et al 1993).…”

“…We propose a modelling approach using a finite element volume conduction model in combination with an axon model, similar to previously developed models for MCS (Manola et al 2005;Silva et al 2008;Wongsarnpigoon and Grill 2008;Wongsarnpigoon and Grill 2012) Basket cell axons, which have inhibitory properties, are mainly located in layer III and V; PT type pyramidal axons, being excitatory and composing the hyperdirect pathway, originate from deep layer V (Reiner et al 2003); IT type pyramidal axons, which are also excitatory and compose the direct and indirect pathway. Their soma's are located in layer III, superficial and deep layer V (Reiner et al 2003) (those located in deep layer V are not considered, since their relatively small diameter makes them less excitable than PT type axons at similar locations).…”