Potential distribution and nerve fiber responses in transcutaneous lumbosacralspinal cord stimulation

S.M. Danner1,2,∗, U.S. Hofstoetter1, M. Krenn1, W. Mayr1, F. Rattay2 and K. Minassian1

1 Center for Medical Physics and Biomedical Engineering, Medical University of Vienna, Vienna, Austria2 Institute for Analysis and Scientific Computing, Vienna University of Technology, Vienna, Austria

Abstract—Transcutaneous electrical spinal cord stimulationis a non-invasive method to stimulate afferent structures con-nected to the human spinal cord. Here, computer simulationsare presented that aim at shedding light on why distant skinelectrodes selectively activate specific groups of afferent fiberslocalized in the spinal canal and whether other neural structuresare concomitantly stimulated.

The simulation was conducted in two steps: i) A finite elementmodel of the human trunk was applied to calculate the electricpotential generated by electrodes placed over the paravertebralskin and the abdomen. ii) The electric potential evaluated alongthe trajectories of target neural structures was used as the in-put for nerve fiber models and to calculate activating functions.Due to the electrophysiological findings, the responses of largediameter myelinated fibers in the posterior root (PR), anteriorroot (AR) and posterior column (Pcol) of the lumbar spinal cordwere simulated.

The activating functions revealed sites of strong depolariza-tion at the entrance of the PR fibers into the spinal cord and atthe entrances/exits of the PR and AR fibers into/from the spinalcanal. The nerve fiber model confirmed that action potentialswere initiated at these low threshold sites. No such ‘hot-spots’were found for the Pcol fibers. Activation thresholds for the mostpreferentially located fibers of each class were 14.1 V, 22.6 V and45.4 V for the PRs, ARs and Pcols, respectively.

‘Hot-spots’ for extrecellular stimulation appear at axonbends and at transitions through media with different con-ductivities. PRs are the preferential targets, while direct co-activation of Pcol fibers is improbable.

Keywords—Spinal cord stimulation, posterior root-muscle re-flexes, computer simulation, activating function.

I. INTRODUCTION

Stimulation of nervous tissue of and close to the spinalcord has neuromodulatory benefits in upper motor neurondisorders, like reduction of spasticity [1, 2, 3] and modifi-

*Corresponding author (simon.danner@gmail.com).S. Vlad and R. V. Ciupa (eds.). International Conference on Advancementsof Medicine and Health Care through Technology; June 5–7, 2014, Cluj-Napoca, Romania. IFMBE Proceedings Volume 44, 2014, pp 203–208. DOI:10.1007978-3-319-07653-9 41

cation of gait [4, 5]. Further, evoked spinal reflexes can beused in electrophysiological studies [6, 7, 8]. Magnetic orelectrical stimulation are methods to induce electrical fieldsaround the nerve structures of interest. Both can be appliednon-invasively at the skin over the spine. Paraspinal magneticstimulation, following the principles of electromagnetic in-duction, induces circular ionic current flows. The restrictionof a coils placement dorsal to the lumber spinal cord pre-dominantly induces currents oriented parallel to the frontalplane [9]. The common muscle responses are due to stimu-lation of efferent fibers to the muscles, but afferents in thespinal roots can be stimulated as well [10, 11, 12]. Tran-scutaneous electrical stimulation produces a potential dif-ference between the skin electrodes and current flows fromthe anode to the cathode, passing the intermediate anatomi-cal structures. Thus, transcutaneous electrical stimulation en-ables more freedom of steering the current flow than mag-netic stimulation and specifically allows for current flows per-pendicular to the frontal plan [9]. This is achieved by placingelectrodes paraspinally and the centrally over the abdominalsurface or the iliac crest [7, 13, 14, 15], e.g. two round 5cm diameter electrodes placed paraspinally at the level be-tween the T11–T12 spinous processes and two larger rectan-gular electrodes centrally over the abdominal surface. Elec-trophysiological investigations showed that with such elec-trode setup, reflexes can be elicited in the lower limb muscles[7]. These reflexes can be modified by vibration, by apply-ing double stimuli paradigms [7], by performing volitionalmotor tasks [7, 13, 8] and by the stimulation of peripheralnerves [16]. They were shown to be similar to those elicitedby epidural spinal cord stimulation [6] and dubbed as poste-rior root-muscle (PRM) reflexes, according to their initiationand recording sites [7]. Therefore and also due to the latenciesof the recorded compound motor action potentials (CMAPs),it could be deduced that Ia afferents are among the stimulatedstructures. Yet, with differences in the stimulation setup, in-cluding body posture, electrode positions, and polarity of thestimulation, it is possible to co-activate efferent fibers. Yet,it is not clear from the electrophysiological studies whetherother fiber types are co-activated. Computer simulations thataddressed these questions [17, 18, 19] are reviewed here in

detail. Furthermore, their results are extended by a compari-son of two widely used mammalian nerve fiber models.

II. METHODS

To simulate the effect of electrical stimulation on neuraltissue located deeply inside the body, it is customary to ap-ply two simulation steps. First, the generated electrical po-tential in the volume conductor, here the human torso, is sim-ulated by numerically solving partial differential equationsusing the finite element method [20, 19, 21]. This calculationof the electrical potential Φ is based on a reduced form ofMaxwell’s equation and depends from the conductivity σ themedium:

∇ · (σ∇Φ) = 0.

The second step involves using the solution of the previ-ous step, the generated potential of the electrical stimula-tion, along the target nerve fibers, as the input to compart-ment models of neurons, especially axons, or for the activat-ing function [22] in order to assess the effectiveness of theelectrical field in activating these neurons [21]. In the firststep, the excitable neural structures are not part of the simu-lation. The activation function [22] is given by

fn =d∆x

4ρiLcVe,n−1−2Ve,n +Ve,n+1

∆x2 ,

where d is the fiber diameter, ∆x the node-to-node distance,L the node length, ρi the axomplasmatic resistivity, c the ca-pacity, Ve the extracellular potential and n the compartmentindex. Positive values of fn indicate de- and negative valueshyperpolarization. Note that if L = ∆x and ∆x→ 0 then fnbecomes proportional to the second order, spatial derivativeof the extracellular potential along the fiber.

In the simulation of transcutaneous spinal cord stimula-tion the target structures are located deeply inside the body,surrounded by various anatomical structures that possibly in-duce electrical inhomogeneities and anisotropies, which inturn influence the generated electric potential at the regionsof interest. Thus, the simulations [17, 18] included a detailed,yet, stereotypical, model of the gray and white matter of thespinal cord, the cerebrospinal fluid, the vertebrae, paraspinalmuscles, body fat and skin as well as a rough representationof the torso (see figure 1). The electrical parameters of thedistinct tissues were selected from the literature and mea-surements (see [17, 18]). Neumann boundary conditions wereused for the external surface of the skin, the midsagittal sym-metry plane, thus reducing the complexity of the model byhalf, and the bottom and top surfaces of the model. For theelectrodes, Dirichlet boundary conditions were used, where

Fig. 1: Representation of the model geometry (a) and the paths of the sim-ulated axons (marked by arrowheads). (b-c) Sketches of spinal canal crosssections. (d) Cross section of the volume conductor model. (e) Midsagittalsection showing the relation between the spine, spinal cord, intervertebraldiscs and the transcutaneous paravertebral electrode. Model fiber entry andexit levels into the spinal cord are marked with arrows. (f) Sketch of posterior(1) and anterior root fibers (2), joining together at the intervertebral foram-ina (3), and of the posterior columns (4) in relation to the spinal geometry.(g) Computer simulated current flow within a 2 mm layer at the midsagittalplane. The electrodes are illustrated in red (adapted from [17, 18]).

the paraspinal electrodes acted as the active and the abdomi-nal electrodes as the reference electrode. The steady-state so-lutions were calculated using COMSOL.

The solution of the finite element model was evaluatedalong fibers in the posterior roots (PR), the anterior roots(AR) and the posterior columns (Pcol). They present myeli-nated nerve fibers with the largest diameters, outside as wellas inside the spinal cord. Since myelinated fibers are easier toexcite electrically than unmyelinated ones and thicker fibershave lower thresholds [23], these fiber classes are the primecandidates for the simulation and only if all three classeswould be easily excitable, additional fiber classes would be

Fig. 2: Stimulation effect evaluated along exemplary target nerve structures. (a) Extracellular potential along the three fiber types studied. The posterior root(PR) and the anterior root (AR) fibers enter and exit the spinal cord, respectively, at the level of the stimulating electrode. The posterior column fiber is locatedmedially and superficially in the posterior white matter. (b) Enlarged view of the box in (a). (c) Activating functions corresponding to (a). (d) Topview of thefiber trajectories and the spinal cord. The excitation thresholds for these fibers calculated by the MRG model were 17.6 V, 51.7 V and 67.4 V for the PR, ARand Pcol, respectively. (adapted from [18]).

necessary to consider. Fibers in the PRs and ARs enter-ing and exiting the spinal cord at different segmental lev-els (see figure 1a,e,f) and Pcol fibers with different depthand mediolateral positions in the white matter were simu-lated using the activating function [22] and two nerve fibermodels, the McIntrye-Richardson-Grill (MRG) [24] and theChiu-Ritchie-Rogart-Stagg-Sweeney (CRRSS) [25, 26] mod-els. Anodic and cathodic monophasic stimulation pulses with1 ms width were applied. Activation thresholds and siteswere calculated for different fiber diameters, depending onthe fiber classes (10.5 µm for Pcol, 14 µm for AR and 16 µmfor PR) [27, 28, 29, 18].

III. RESULTS

The electrical field produced by transcutaneous stimula-tion with –1 V along selected target nerve structures is il-lustrated in figure 2a and b and the simulated current flowcan be seen in figure 1g. The corresponding activating func-tions are depicted in figure 2c and the geometrical relationsin figure 2d. Along the most preferentially located (medialand superficial) Pcol fiber, there are few inhomogeneities of

the potential and also the activating function showed the low-est deviations from 0. The fibers in the PR and AR on theother hand had strong discontinuities in the potential alongthe fiber, specifically at the locations where the fibers en-tered/exited the spinal cord and canal. At these points, alsothe activating functions showed strong deviations from 0. Thestrongest depolarization—as suggested by a positive peak ofthe activating function (cf. figure 2c)—of the PR fiber oc-curred at its entrance into the spinal cord. At the exit of theAR fiber from the spinal cord it was mainly hyperpolarized.At the exits of both fibers from the spinal canal, they werecomparably excitable. Fittingly, the sites of action potentialinitiation of the fiber in the PR was at the node of Ranvierclosest to its entrance into the spinal cord and the one of theAR fiber closest to its exit from the spinal canal. The fiber inthe Pcol was activated at the node of Ranvier closest to thestimulation electrode.

The activation thresholds of PR and AR fibers with differ-ent positions entering and exiting the spinal cord are depictedin table 1. The thresholds were lower for the PR than the ARfibers. Cathodic stimulation was more efficient to stimulatePR fibers. To stimulate AR fibers, anodic and cathodic stim-

Table 1: Excitation threshold (in V) of root fibers

posterior root anterior rootcathodic anodic cathodic anodic

d1 MRG2 S3 MRG S MRG S MRG S

3.9 20.1 97 50.0 272 23.2 110 22.6 1052.6 26.1 101 51.5 324 28.9 103 37.1 1611.3 29.5 129 49.5 230 37.1 147 51.4 2240 17.6 76 65.0 224 51.7 222 67.9 176

-1.3 21.5 99 87.1 307 72.2 333 68.5 356-2.6 14.1 69 110.9 405 82.4 433 67.6 238-3.9 14.4 65 114.1 482 33.9 174 70.9 401

1 d (in cm) denotes the vertical distance of the entry point of the root fibreinto the spinal cord from the centre of the stimulation electrode. The lowestexcitation thresholds are written in bold.

2 MRG: McIntyre-Richardson-Grill model,3 S: Chiu-Ritchie-Rogart-Stagg-Sweeney (CRRSS) model.

ulation were both similarly effective, with a slight advantagefor the anodic case. Furthermore, the stimulation was moreeffective for PR fibers caudal to the stimulation electrode. Forthe AR fibers, the opposite was evident.

Cathodic and anodic excitation thresholds of PR and ARfibers were computed using the MRG and CRRSS model.The MRG model resulted in considerably lower thresholdsfor any of the calculated target fibers and both stimulationmodes (table 1) as compared to the CRRSS model. Thethresholds were 23.2% ± 4.6% (mean ± SD) of the valuesderived by the CRRSS model. The range varied from 15.9%to 38.6%. The straight Pcol fiber that had a threshold of 67.4V according to the MRG model, and an excitation thresholdof even 611 V when evaluated with the CRRSS model.

Pcol fibers were easiest excitable at their most medial andsuperficial location in the white matter (67.4 V). This is alsothe location where the fiber was closest to the paraspinalelectrodes and the potential was highest. The influence ofan increase in fibre diameter for the medially and most su-perficial located fibre was also investigated. With the diam-eter increased to 16 µm, same as assumed for the posteriorroot fibers, the excitation threshold of the posterior columnfibre decreased to 40.1 V. The activation threshold was alsodecreased by introducing collaterals. A single collateral, at-tached to the node of Ranvier that was the action potentialinitiation site reduced the threshold to 59.6 V. Additional ninecollaterals attached to the neighboring nodes above and be-low reduced the activating threshold to 45.4 V, which is stillapprox. 3 times the threshold of the most excitable PR fiber.

Transcutaneous was compared to epidural stimulation (seefigure 3). With former stimulation the root fibers were alwaysactivated at either one of the ‘hot-spot’ sites, i.e. their points

Fig. 3: Stimulation effect of transcutaneous and epidural electrodes locatedat levels of and rostral to the posterior root fibers (left). The two low-threshold sites can be seen in case of transcutaneous stimulation. Dependingon the distance of the electrode to these sites, either one is the site of actionpotential initiation. In case of epidural stimulation, the electrode placed nearthe fiber introduced strong, local deflections of the potential distribution andthe activating function at the level of the contacts of the electrode. Whereas,the electrode located rostral to the fiber introduced an electric potential andactivating function along the fiber similar to those in case of transcutaneousstimulation. Arrows indicate the site where the spikes were initiated at thethreshold intensity. Right: Sketch of anatomically determined low-thresholdsites (‘hot-spots’; adapted from [19]).

of entry/exit into/from the spinal cord and canal, while in thecase of epidural stimulation, action potentials were initiatedusually close to the cathode. Yet, if the cathode of the epiduralelectrode was located rostral to the target fibers, the actionpotential initiation sites were at the entrances of the PR fibersinto the spinal cord.

IV. DISCUSSION

The reviewed modeling studies elaborated the direct ef-fects of transcutaneous spinal cord stimulation on sensorystructures and motor fibers within lumbar spinal roots as wellas fibers within the posterior white matter of the human lum-bar spinal cord. The MRG model was applied to calculate re-alistic, relatively low excitation thresholds. In fact, the thresh-olds were about four times lower than the results computedby the CRRSS model. Large diameter posterior root affer-ent fibers had the lowest excitation threshold followed by an-terior root efferent fibers. Excitation thresholds of fibers inthe posterior columns were relatively high even when cal-culated with the MRG model. For the most preferential po-sition (superficial and medial) and features (large diametersand presence of collaterals), their thresholds were still threetimes higher than the thresholds of posterior root fibers.

‘Hot-spots’, sites with low activation thresholds, were

identified at the entry point of posterior rootlets into the spinalcord, at the entry/exit point of the posterior and anterior rootsinto/from the spinal canal and at the branching points ofthe collaterals from the posterior column fibers. These ‘hot-spots’ were given rise to by the electrical properties of thesurrounding tissues and the trajectory of the nerve fibers, thuscaused by the anatomy [17, 19]. Transitions of nerve fibers, asseen from the cathodic electrode, between a highly conduct-ing (here the cerebrospinal fluid) into a relatively lower con-ducting medium (here the white matter) cause a large positivepeak of the second-order spatial derivative of the potentialalong the nerve fiber [22]. Thus, the threshold is significantlylowered. Depending on the electrode position relative to thenerve fiber one of the ‘hot-spots’ has the lowest threshold(cf. figure 3). The anterior root fibers only have one ‘hot-spot’at their exit from the spinal canal, and thus more rostrally lo-cated fibers have lower thresholds, since for those fibers, the‘hot-spot’ is closer to the stimulation electrodes. This is alsocorroborated by preliminary experimental results, where M-wave components in the recorded CMAPs were more oftenidentified in quadriceps than in triceps surae [14, 30].

Stimulation of fibers in the posterior columns can be ex-pected only at relatively high stimulation intensities, aroundthree times the threshold of posterior root fibers. This isdue to the relatively few inhomogeneities introduced into theelectrical field surrounding the posterior column fibers, whichwould influence the excitability of the nerve fibers [22, 21].By contrast, the electrical field produced by epidural stimula-tion is focused on its own, producing large values in the acti-vating function, even in straight fibers inside a medium withhomogenous electrical properties. Thus, direct stimulation offibers in the posterior column is more likely with epiduralthan with transcutaneous stimulation [31, 32].

The thresholds calculated by the CRRSS model were re-ported to be 2–3 times higher than the thresholds of the cor-responding clinical effects [33, 34]. Independently, the MRGmodel has been shown to reproduce threshold values of tran-scutaneous electrical stimulation more realistically [35]. In-deed, threshold values reported by Ladenbauer et al. [17]were overestimated and could be reduced here by applyingthe MRG model (see table 1) on average to about a fourthof the CRRSS model. Applying the MRG model, thresholdsof posterior root afferents are now closer to the thresholdsof reflex responses to transcutaneous spinal cord stimulationin lower limb muscles. These PRM reflexes were elicited si-multaneously in the key muscles of thighs and lower legs ata common threshold of 28.6 ± 6.3 V in a group of eight in-dividuals with an intact nervous system [7]. The seeminglyunderestimation (14 V threshold for posterior root activationhere) can be explained by differences between the threshold

of activating the lowest threshold Ia afferents and generat-ing appropriate temporal and spatial synaptic summation foreliciting a reflex. A synchronous volley of action potentialsis needed to activate a motoneuron. Also note that the rela-tionship between the excitation thresholds calculated by theCRRSS and the MRG model is not trivial and cannot be ap-proximated with a common constant factor.

Only the steady-state solution was calculated with the fi-nite element model, neglecting capacitive, which might causea depth dependent filtering of the applied electrical signal,thus altering the pulse shapes acting on the nerve fibers. Sincethe pulse shapes strongly influence the effectiveness of thestimulation, specifically if the pulse duration is relatively long[36], the thresholds and their relationships might be affected.Furthermore, the stereotyped and simplified geometry is notsufficient for the investigation of more complex phenomena,like the influence of the body or (rostro-caudal) electrode po-sitions on the activation thresholds. A more detailed modelincluding the sacrum and properties of the individual ver-tebrae including their relative positions would be necessary.These shortcomings will be addressed in future work.

V. CONCLUSION

The computer simulations demonstrated that the activationof specific neural structures by transcutaneous spinal cordstimulation is predominantly due to the electrical propertiesof the anatomy that introduce inhomogeneities into the elec-trical field, which otherwise would be rather diffuse. The sim-ulation results support that posterior root fibers have the low-est thresholds followed by anterior root fibers. Thresholds ofposterior column fibers are still not effectively reduced by theintroduction of multiple collaterals, their direct activation isunlikely. The finding of the rather high thresholds of poste-rior column fibers grants important information for the po-tential of direct stimulation of other intraspinal neural struc-tures. Posterior column fibers superficially located within thewhite matter with large diameters and multiple collateralscan be assumed to be the intraspinal neural structures withthe lowest thresholds. Thus, excitation of other white mat-ter tracts would require even higher stimulus intensities anddirect electrical activation of grey matter structures can beexcluded with applicable stimulus intensities.

CONFLICT OF INTEREST

The authors declare that they have no conflict of interest.

ACKNOWLEDGEMENTS

Wings for Life Spinal Cord Research Foundation, WFL-AT-007/11; Vienna Science and Technology Fund, LS11-057.

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