Transcutaneous Spinal Direct Current Stimulation

Modelling the Electric Field Distribution in the Cervical Spinal Cord

S. R. Fernandes

1,2

, R. Salvador

, C. Wenger

, M. de Carvalho

and P. C. Miranda

Institute of Biophysics and Biomedical Engineering (IBEB), Faculdade de Ciências,

Universidade de Lisboa, 1749-016 Lisboa, Portugal

Molecular Medicine Institute (IMM), Faculdade de Medicina, Universidade de Lisboa,

Avenida Professor Egas Moniz, 1649-028, Lisboa, Portugal

1 OBJECTIVES

Following the reports that weak electrical currents can

modulate excitability in cortical areas, Cogiamanian et

al. (2012) proposed that the same approach could be

applied to modulate spinal cord function. Exploratory

studies in humans showed that transcutaneous spinal

direct current stimulation (tsDCS) has

neuromodulatory effects on spinal motor circuitry

(e.g. Bocci et al., 2014). There is currently only one

computational study of the electric field distribution

during tsDCS applied on the thoracic spine region that

has been published, which applies realistic human

models based on high-resolution MRI of healthy

volunteers (Parazzini et al., 2014). There are no known

tsDCS modelling studies on human cervical spine, so

there is a need to develop human realistic models to

solve for the field distribution in cervical spine

stimulation.

The main objective of the present study is to

perform a finite element analysis (FEA) of the electric

field distribution in tsDCS in the cervical spine region,

and refer to cervical spine circuitry that may be

modulated by tsDCS in order to address viability for

clinical application purposes.

2 METHODS

The 34 year-old Duke model, from the Virtual

Population Family v1.x models (Christ et al., 2010),

was used to generate volume meshes for FEA with

MIMICS (v16, http://www.materialise.com/mimics).

From this model, eight tissues were selected: skin, fat

(including subcutaneous adipose tissue), muscle, bone

and vertebrae, intervertebral disks, dura mater,

cerebrospinal fluid (CSF) and spinal cord.

The electrode configuration tested followed the

experimental setup considered in Bocci et al. (2015):

the target electrode was placed over the C6-T1 spinous

processes; the return electrode was placed over the

right deltoid muscle, in a site far from the target. The

electrodes were modelled as 5x7 cm

rectangular

sponges soaked in saline solution (σ =2 S/m (Miranda,

Mekonnen, Salvador and Ruffini, 2013)), with a

thickness of 3 mm thick, between electrode and skin

surfaces. Electric conductivity value of all tissues

were based on data found in literature for DC currents:

skin

= 0.435 S/m; σ

fat

= 0.040 V/m; σ

muscle

= 0.355 S/m

(average between muscle transverse (0.043 S/m) and

muscle longitudinal conductivity (0.667 S/m) values

from Rush, Abildskov and McFee, 1963); σ

vertebrae/bone

= 0.006 S/m; σ

intervertebral disks

= 0.200 S/m; σ

dura mater

0.03 S/m; σ

CSF

= 1.79 S/m; σ

spinal cord

= 0.154 S/m

(Geddes and Baker, 1967; Rush, Abildskov and

McFee, 1963; Haueisen, Ramon, Eiselt, Brauer and

Nowak, 1997; Baumann, Wozny, Kelly and Meno,

1997; Struijk, Holsheimer, Barolat, He and Boom,

1993). COMSOL Multiphysics (version 4.3b,

www.comsol.com) was used to calculate the electric

field distribution using FEA. The current intensity in

the electrodes was set to 2.5 mA, as in previous studies

(Bocci et al., 2014). The boundary conditions were

applied according to Miranda et al. (2013).

3 RESULTS

Figure 1 presents the electric field magnitude

distribution along the spinal cord. Figure 1a) shows

the volume-weighted average along the z axis,

considering slices of the spinal cord with 1 mm

height. This curve has two peaks in the region of the

spinal segments C5-T1 (corresponding to the braquial

plexus), with values of 0.171 V/m (z = [1570;1571]

mm) and 0.186 V/m (z=[1587; 1588] mm). Figure 1b)

shows the electric field magnitude volume

distribution in the spinal cord, where it can be seen

that these and other local maxima in the field

distribution are found in regions where the vertebral

Fernandes, S., Salvador, R., Wenger, C., Carvalho, M. and Miranda, P..

Transcutaneous Spinal Direct Current Stimulation - Modelling the Electric Field Distribution in the Cervical Spinal Cord.

canal is narrowed due to the intrusion of

intervertebral disks or vertebrae body’s edges.

Figure 1: a) Volume-weighted average electric field

magnitude distribution along the z axis; b) Electric field

magnitude volume distribution colour plot in the spinal

cord, including a background representation of anatomical

structures, the target electrode (in red) and the position of

the brachial plexus spinal segments C5-T1 (in orange).

Figure 2: Contour plots of the electric field magnitude

(V/m) in the spinal cord in two axial slices: a) z=1588 mm;

b) z=1571 mm. The anatomic orientation and the colour

scale (in V/m) are presented on the right.

Figure 2 presents two contour plots of the electric

field distribution in the spinal cord at the level of the

two highest peaks in fig. 1a). In Figure 2a), the

maximum values reach 0.26 V/m and are located in

the anterolateral region of the spinal cord, with an

asymmetric distribution with a larger maximum

magnitude region on the right. This could be due to

the position of the return electrode, influencing the

electric field lines direction. Figure 2b) presents a

more symmetric distribution, with maximum field

magnitude values on the posterolateral region of the

spinal cord, reaching a maximum of 0.23 V/m. The

fact that Figure 1a) presents an average distribution

accounts for the difference in maximum value peaks

when comparing with Figure 2.

Values of the ratio between the magnitudes of the

normal and tangential components to the spinal cord

surface as function of position along the z axis are

presented in Figure 3. The values calculated span

between 1.5 and 20.2, which means that the tangential

component is higher than the normal component,

resulting in an electric field direction preferentially

tangential to the spinal cord.

Figure 3: Ratio between the magnitudes of the tangential

and normal components of the electric field along the z axis

in the spinal cord. The red horizontal line corresponds to a

ratio of 1 (equal magnitude of both components). The

region of the segments C5-T1 is marked in the plot area in

grey.

4 DISCUSSION

In modelling studies of tDCS, based on the

stimulation conditions applied to the motor cortex in

clinical studies with neuromodulatory effects

reported, electric field magnitudes of 0.15 V/m and

above were registered (Miranda et al. 2013). In the

present study, the electric field magnitude distribution

presented values above 0.15 V/m in the upper region

of the spinal segments C5-T1. As this region is related

to upper limb function (braquial plexus), this may

indicate that the values reached can be sufficient for

neuromodulatory effects on upper limb neurological

functions. Figure 2a) presents maximum values in the

anterolateral region of the spinal cord. This region is

related with sensory ascending tracts, responsible for

proprioception (spinocerebellar tracts), traditional

senses (spinothatamic tracts), and motor

subconscious descending tracts that regulate balance,

muscle tone, eye, hand and upper limb position. In

Figure 2b), the maximum values are located mainly

on the posterolateral region, related to tracts that

regulate conscious (posterior and lateral costicospinal

tracts) and subconscious (rubrospinal tracts) control

of skeletal muscles. These results are in agreement

with exploratory clinical tsDCS studies, that show

modulation of nociceptive ascending pathways and

spinal motor circuitry, depending on electrode

polarity, when stimulating thoracic and cervical spine

regions (Cogiamanian et al., 2012; Hubli, Dietz,

Schrafl-Altermatt and Bollinger, 2013; Bocci et al.,

2014). In particular, cervical cathodal tsDCS had an

increasing effect in motor unit recruitment and

decreased peripheral silent period in respect to sham

and anodal conditions (Bocci et al., 2014).

In the present study, the electric field in the spinal

cord had a larger tangential electric field component

along the spinal cord. As the electric field is directly

proportional to the current density, this may be in

agreement to the results of the modelling study by

Parazzini et al. (2014), in which the current density

direction in the spinal cord was mostly longitudinal

during thoracic tsDCS.

One shortcoming of the present model is the low

number of tissues, considering only the ones closer to

the target electrode. A more complete model could

reveal more about spreading effects on the electric

field. Also, the muscle conductivity value was taken

as an average between transverse and longitudinal

values in the literature, so anisotropic data could be

valuable in future studies. In spite of these limitations,

the results are in agreement with previous modelling

and experimental results.

Cervical tsDCS is a promising non-invasive

clinical tool for neuronal circuitry modulation in the

cervical spinal cord. It could address neuronal

dysfunctions like spasticity, present in many

neurologic diseases (e.g. amyotrophic lateral

sclerosis). Defining accurate models that predict the

physical effects of tsDCS on spinal neurons could be

a powerful tool to develop clinical applications more

focused on the specific neurologic patient needs.

ACKNOWLEDGEMENTS

This research was supported in part by the

Foundation for Science and Technology (FCT),

Portugal. S. R. Fernandes was supported by a FCT

grant, reference SFRH/BD/100254/2014. C. Wenger

was supported by Novocure.

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