Modeling Workflow for Study of Functional Electrical Stimulation

in Peripheral Nerves

Fábio Rodrigues

, Marian Bartek

and Paulo Mendes

Centro Algoritmi, University of Minho, Guimarães, Portugal

Dimes/ECTM, Delft University of Technology, Delft, the Netherlands

Keywords: Modeling, Selective Stimulation, Multipolar Cuff Electrode.

Abstract: Urinary dysfunctions are among the most devastating consequences of spinal cord injuries (SCI).

Neurostimulation of intact sacral nerve roots innervating bladder is potentially a good alternative to the

treatments using drugs and catheterization. A finer control over the electrical stimulation of sacral roots can

be an enabling technology for developing advanced neurostimulation matching the patient needs. In this

paper a modeling workflow to study axon behaviour in sacral nerve roots is presented. Simulation results

show that the width and the amplitude of the stimulation electric pulses can be tuned to selectively recruit

axons in sacral roots. A selective recruitment of axons innervating bladder is shown to be possible for pulse

widths above 9 ms.

1 INTRODUCTION

Spinal cord injuries (SCIs) are estimated to affect

330,000 people (with about 11,000 new cases every

year) in Europe (Social and F.A.C, 2002), and about

300,000 in the USA (with also about 12,000 new

cases every year) (National Institute of Neurological

Disorders and Stroke, 2012). Among the most

traumatic consequences of an SCI event are the

urinary dysfunctions (e.g., incontinence) due to

lesions above the level of sacral nerve roots (bundle

of nerves innervating bladder and urethral

sphincter). In the conservative medical approach,

drugs and catheters are used to manage the lower

urinary system in cases of SCIs. However, side

effects of medication and the unwilling of patients to

use catheters have driven research in the pursuit of

electrical devices for neurostimulation of sacral

roots innervating bladder.

Sacral nerve roots have become a preferential

site to elicit bladder voiding by neurostimulation

(Rijkhoff et al., 1997); (Brindley, 1977). The sacral

roots are made out of several sub-units, known as

fascicles. Each fascicle is derived from neural cells

in the spinal cord with certain degree of specificity

for their function (Probst et al., 1997). Somatic and

parasympathetic are the two fiber types present in

the fascicles of sacral roots - the parasympathetic

fibers are the smaller fibers innervating bladder,

while the somatic fibers are the larger fibers

innervating sphincter.

Even there are differences between individuals in

terms of histology of sacral roots, still fascicular

trends in specificity are observed. This fact raises the

potential that a focal stimulation can selectively

stimulate the neural unit (fiber/nerve) for a certain

function, e.g., parasympathetic stimulation for

bladder contraction (Hauck et al., 2009). Hence, the

steering of electric current applied in

neurostimulation of sacral roots can yield a selective

recruitment of parasympathetic fibers resulting in

bladder voiding. The selective control of muscles

activation can be achieved using a multipolar nerve

cuff electrode (Schiefer et al., 2010). In terms of

design and optimization of multipolar electrodes for

functional electrical stimulation (FES) of peripheral

nerves two factors are crucial: 1) anatomical trends

and 2) nerves response. Indeed, modeling nerve

response to a given external stimulation parameters

(e.g. pulse width, pulse amplitude) allows to predict

whether a neuron will or will not be activated. In this

work, axonal response in sacral roots is studied -

axon is the most excitable part of a peripheral nerve.

The hypothesis of this study is that a multipolar cuff

electrode placed proximally on the sacral root with a

fixed number of contacts can selectively stimulate

smaller parasympathetic axons that are preferentially

grouped by specialized fascicles. Stimuli is defined

178

Rodrigues F., Bartek M. and Mendes P..

Modeling Workﬂow for Study of Functional Electrical Stimulation in Peripheral Nerves.

DOI: 10.5220/0004250001780183

In Proceedings of the International Conference on Biomedical Electronics and Devices (BIODEVICES-2013), pages 178-183

ISBN: 978-989-8565-34-1

 2013 SCITEPRESS (Science and Technology Publications, Lda.)

a priori as a simple monopolar, square and cathodic

waveform. Through the use of finite element models

and nonlinear axonal models, the presented study

investigates selectivity for given combinations of

pulse width/pulse amplitude.

2 METHODS

Selective stimulation effect of a multipolar cuff

electrode on sacral roots was investigated using a

modeling workflow based on 3 different software

tools: ANSYS Multiphysics, MATLAB and

NEURON. First, a finite element model (FEM) of a

sacral root together with a multipolar cuff electrode

was developed and implemented in ANSYS

Multiphysics. Steady-state electric potential field

was calculated in ANSYS for several electrode

configurations. The potentials were exported to

MATLAB. In MATLAB, ordered pairs (x, y) were

randomly generated inside a circle with radius of

300 µm and centered at the origin – this circle

defines the contour of the sacral root. Longitudinal

points representing different segments of each axon

were randomly generated. Voltages were

interpolated at each (x, y, z) position representing a

specific anatomical compartment of each axon. As

its output MATLAB returned a matrix of [M x N],

where M is the number of axons inside each fascicle

and N is the number of axon’s segments (nodes of

Ranvier + internodal positions). In NEURON,

electric potential at each axon position is applied as

an extracellular field to an axon model representing

the mammalian motor axon. Each node of Ranvier is

checked for action potential (AP) events indicating

that the extracellular field invoked axonal activation.

Results from simulations in NEURON were

analyzed in MATLAB to determine selectivity. The

modeling workflow to determine selectivity is

schematically shown in Fig. 1.

In the presented design, the multipolar electrode

is made out of 18 electrode contacts (six tripoles)

that were placed in direct contact with the sacral

root. Each tripole is positioned around the sacral root

at positions {30, 90, 150, 210, 270, and 330 deg}.

The stimulating surface of each electrode is 100 µm

x 50 µm (length x width) and its thickness is 2 µm.

Thickness of the electrodes is derived from the

fabrication process which was used to fabricate the

first prototype of a flexible multipolar cuff

(Rodrigues et al., 2012). Figure 2 shows a schematic

of the contact spacing in the multipolar electrode in

its unrolled state. The simulated sacral root was

600 µm in diameter and 16 mm in length (z axis).

Part of the model is shown in Fig. 3. It comprises

sacral root, 18 metal contacts, insulating cuff,

cephalo raquidian fluid and a highly resistive

boundary layer. Geometric and electric properties of

the various elements within the model were reported

previously (Rodrigues et al., 2012). The electrode

contacts are modeled as current sources and a zero

voltage boundary condition is added to the outer

surfaces of the boundary layer. Steady-state

simulations were performed for several electrode

configurations. The two electrode configurations

presented here are shown in Fig. 4 and Fig. 5.

Figure 1: The modeling workflow used to determine

selectivity of multipolar cuff electrode in sacral roots

stimulation.

Figure 2: Schematic of the multipolar electrode in its

unrolled state.

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Figure 3: Parts of the FEM model. Note that the mesh

elements in the sacral root are half width of the electrode.

To shorten the time of modeling iterations it is

favourable to introduce a pulse amplitude factor

(PAF). This factor is multiplied by electric potential

field solution in each axonal position. So, assuming

V=1 as the electric potential at a given

node/internode position of the axon, if PAF = 0.1,

then V=0.1 will be the electric potential solution at

the same coordinate.

Indeed, simulations were run in NEURON for all

combinations of pulse widths (PW) of 0.01, 0.05,

0.1, 0.2, 0.5, 1, 2, 5, 7, 8, 8.33, 8.66, 9, 10 and 11 ms

and pulse amplitude factors of 0.1, 0.2, 0.5 and 1.

Axonal results from NEURON simulations were

analyzed to determine which stimulation case

(electrode configuration vs. PW vs. PAF) produced

the greatest selectivity. Adapted from Choi (Choi et

al., 2001), muscular selectivity, S, was defined as the

fraction of axons activated within all fascicles

innervating a target muscle (the “recruitment

benefit” or “RB”) minus the fraction of axons not

innervating the target muscle that were activated (the

“recruitment cost” or “RC”) – Eq. 1.

Figure 5: Electrode configuration 1C2A: (a) a transverse

cross section under the central row of electrodes; (b) a

longitudinal cross section with tripole at the top (position

90 deg). Cathode drains 1 mA and each anode injects

0.5 mA.

SRBRC





(1)

In the case of targeting bladder muscle to elicit

bladder voiding, S will be higher when

parasympathetic fibers (innervating bladder) will be

recruited in larger ratio (higher RB) than somatic

fibers innervating the sphincter (lower RC).

For the anatomy of sacral root presented in Fig.

6, selectivity for bladder muscle (activation of

parasympathetic fibers in red color) was calculated

for the considered electrode configurations: 1C2A

and 2C6A.

2.1 Anatomical and Physiological

Considerations

2.1.1 Anatomy of Sacral Nerve Roots

Sacral roots have a mixed population of fibers with

diameters ranging from 1 µm (smaller fibers) to

14 µm (larger fibers). In the present study, a ventral

sacral root, known as S3 is selected to analyze the

effect of the multipolar electrode on axonal

selectivity. S3 has a bimodal axon distribution with

peaks at 4 and 14 µm (Anon, 1996). Inside

peripheral nerves (e.g. sacral nerve roots) the sub-

structures giving support to the axons/fibers are

known by fascicles. In the terminology of Hauck

(Hauck et al., 2009), fascicles mostly carrying

parasympathetic fibers are called vegetative fascicles

and fascicles with predominance of somatic fibers

are called somatic fascicles. In our analysis, 21

fascicles were considered, which is in agreement

with the reported number of fascicles in S3 sacral

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Figure 4: Electrode configuration 2C6A: (a) a transverse cross section under the central row of electrodes; (b) a longitudinal

cross section with tripole at the top (position 90 deg) and steering anode at the bottom (position 270 deg); (c) longitudinal

cross section with steering anode at the top (position 30) and tripole in the bottom (position 210 deg). Each cathode drains

1.5 mA and each anode injects 0.5 mA.

nerve root (Hauck et al., 2009). Distribution in

vegetative and somatic fascicles was previously set

and it is represented in Fig. 6. Each somatic fascicle

contains 50 axons of 14 µm in diameter (somatic

axons innervating sphincter) and each vegetative

fascicle has 50 axons of 4 µm in diameter

(parasympathetic axons innervating bladder).

Figure 6: Sacral nerve roots anatomy considered in the

presented study.

2.1.2 Physiology of the Axon

Myelinated axons are modeled using an active

electrical network to simulate the dynamics of each

node of Ranvier and of internodal sections of the

axon (McIntyre et al., 2002). A simulation procedure

was developed in NEURON to integrate the

NEURON’s open source axon model of McIntyre

(McIntyre et al., 2002). Axonal excitation is

generated by extracellular potentials (potentials

generated outside node of Ranvier and outside

myelinated internodes). These potentials are

assumed to be unaffected by the fiber response and

thus determined only by the stimulus electrodes and

the conductivity of the extracellular space.

Axon model from McIntyre is shown in Fig. 7.

This model used 10 segments between successive

nodes with an explicit representation of the myelin

attachment segment (MYSA), paranode main

segment (FLUT), and internode segment (STIN)

regions of the fiber. Extracellular potentials

interpolated in MATLAB and exported to NEURON

were assigned to these compartments.

Figure 7: Multi-compartment axon model. Axon and

nodes of Ranvier are at the top. Physiological

compartments are in the bottom. Figure adapted from

McIntyre (McIntyre et al., 2002).

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3 RESULTS

In NEURON, action potentials (APs) were used as a

measure to evaluate if the axon has fired for a given

combination of “electrode configuration / PW /

PAF”. It was assumed that if each axon has

registered more than 11 APs (1 AP / 1 node of

Ranvier), axon activation would be assumed. An

example of an action potential registered in

NEURON is plotted in Fig. 8.

Figure 8: Plot of action potential from NEURON.

Selectivity results are shown in Fig. 9. For each

electrode configuration – 1C2A and 2C6A –

selectivity index is plotted for 4 different pulse

amplitude factors (PAF), along the different pulse

widths (PWs).

In case of 1C2A, the activation of any fiber

(parasympathetic or somatic) only occurs for

PW>9 ms. A hypothesis can be that because of the

limitation of electric current (1 mA @ PAF=1), the

pulse width required to inject a sufficient charge is

high. For PW>9 ms, the selectivity shifts from 0 to

1. This means that all the parasympathetic fibers

(4 µm in diameter) were activated and none of the

somatic fibers (14 µm) was. As suggested by

McIntyre (McIntyre et al., 2002), the smaller

diameter fibers have longer chronaxies (i.e. smaller

fibers may need longer time to be electrically

stimulated) than the larger diameter ones. This can

explain the observation that after a 9 ms long pulse,

only the 4 µm fibers are depolarized (i.e. only the

parasympathetic fibers register an action potential).

In case of 2C6A, there is also complete

selectivity (S=1) for PW>9 ms. However, for lower

PWs intermediate selectivity values are registered.

These intermediate values of selectivity were due to

the activation of smaller parasympathetic as well as

to the activation of larger somatic. As it could be

expect, for larger input current levels (3 mA for

2C6A) it is possible to lower the pulse width

required for activation (activation was registered for

PW = 5 ms).

Lowering pulse width is a trade-off. If on the one

side, the lowering of pulse width also lowers the

required power to achieve axonal stimulation; on the

other side, it matches the chronaxie values for larger

somatic fibers, which contributes to lower the

selectivity.

Figure 9: Selectivity for electrode configurations – 1C2A

and 2C6A. Selectivity varies between -1 and 1.

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Figure 10 shows the complete selectivity of axons

for PW > 9 ms. One can observe that only the

smaller parasympathetic fibers are active.

Figure 10: Activated axons for PW > 9 ms.

4 CONCLUSIONS

In this work design and testing of a multipolar cuff

electrode for peripheral nerve is presented. For that

purpose, a modeling workflow to study selectivity in

sacral nerve roots was implemented using ANSYS

Multiphysics, MATLAB and NEURON. Anatomical

studies were used to define a representative

distribution of fascicles in the sacral root. These

anatomical features were used to carry a study on the

effect of a multipolar cuff electrode on selective

stimulation of different fiber diameters. For pulse

widths higher than 9 ms, the selectivity is maximum

(most probably because of a “chronaxie effect”).

However to lower the need for electric power in the

electrical stimulation of sacral roots, further studies

have to be done in order to achieve selectivity for

lower pulse widths – e.g. increasing number of

electrode contacts, increasing number of rows of

electrodes in order to “reshape” the external

stimulation potential on each axon.

Modeling workflow showed to be effective for

the element size used in ANSYS. However, further

simulations are required for finer meshes in order to

study on effectiveness and stability of the workflow.

For that, a real anatomic mesh derived from a

histological cross section of the sacral roots will be

used.

ACKNOWLEDGEMENTS

This work was supported by the Portuguese

Foundation for Science and Technology

(SFRH/BD/62608/2009).

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