Abstract—Transcutaneous Electrical Stimulation (TES) has

been used widely to recover motor functions to neurologically

impaired individuals by artificially activating skeletal muscles

using superficial electrodes. Some stimulation schemes try to use

the conductivity change due to frequency to improve the

effectiveness of TES like interferential and Russian stimulation.

However, interferential and Russian current do not improve the

effectiveness to activate a muscle in experimental studies. In this

study, the effect of the frequency in the impedance change is

investigated to determine the variation in nerve activation. In

this regard, we develop a 3D multi-scale (skin, fat, muscle, and

nerve) model coupled with a mammalian nerve of the thigh using

a finite element method. The motor threshold is calculated to

obtain the necessary intensity stimulus to initiate nerve

activation to observe the influence of the frequency in the

electrical properties of the tissues and nerve activation. As a

result, an increase in the frequency does not translate into a

better energy transmission.

I. INTRODUCTION

Transcutaneous Electrical Stimulation (TES) has been used widely to recover motor functions to neurologically impaired individuals by artificially activating skeletal muscles using superficial electrodes [1,2].

The effect of TES depends greatly on stimulation parameters, electrical and mechanical properties of the bio-tissues, which are subject to the influence of individual difference, daily physiological condition, morphological change due to muscle contraction and motion of the musculoskeletal system. Nevertheless, in clinical practice, the setting of TES is empirically based on trial-and-error-based approaches.

Some stimulation schemes try to take advantage of the conductivity change due to the frequency to improve the effectiveness of TES like interferential and Russian stimulation [3].

Interferential stimulators produce 2 independent kilohertz-frequency AC currents of constant intensity applied by 2 separate pairs of electrodes, which are positioned diagonally opposed to produce an interference effect in the central region of intersection of the currents. It will cause a difference in frequency (beat) to occur in the muscle which will then cause the muscle to contract. The premise is that

these high frequencies will not stimulate skin sensory nerves and therefore there will be less pain.

Russian stimulation also uses high frequency stimulation. The signal is modulated at low frequencies, typically 40 Hz. It is argued that this modulated frequency will traverse the skin without causing pain or discomfort and stimulate muscle. Premodulated is similar to Russian current, but its current intensity is modulated: it increases and decreases at a regular frequency [4].

As reported by [3], interferential and Russian waveform are somewhat more comfortable than square wave stimulation. However, to achieve the same force of muscle contraction of square stimulation, Russian and interferential stimulation required substantially higher currents because of the poor transfer of functional energy into the muscle. The results of the experiments showed that sine wave stimulation produced significantly greater muscle strength and less pain than square wave, Russian or interferential stimulation at that same current. The most painful stimulation was square wave. Strength production was greatest with sine wave and least with Russian and interferential.

It is clear that interferential and Russian current do not improve the effectiveness to activate a muscle. However the reason is not clear. In this study, the effect of the frequency in the impedance is studied to determine the effect of decreasing the impedance on the nerve. In consequence, the effect of using high frequency stimulus to decrease the impedance will be investigated.

In this regard, we develop a 3D multi-scale (skin, fat, muscle, and nerve) model of the thigh using a finite element method to study the effect of the electrical properties of the tissues in the nerve activation.

II. METHOD

A two-step method is adopted in a 3D multi-scale model of the thigh using a finite element method coupled with a mammalian nerve.

First step, computation of the voltage distribution within the tissues (Ve), equation 1. Second step, prediction of nerve activity employing a compartment model [5] of a mammalian nerve [6].

(1)

Effect of the Electrical Properties of the Tissues in the Nerve

Activation Using Transcutaneous Electrical Stimulation

Jose D. Gomez-Tames, Jose Gonzale, Wenwei Yu

Medical System Engineering Department

Chiba University

Chiba, Japan

Figure 2. Compartment model of the myelinated fiber. Nodes are modeled as active membranes (CRRSS model). Internodes are

represented by single compartments with constant membrane conductance.

Figure 1. 3D multi-scale model of the thigh representing the

different tissues.

where conductivity σ and relative permittivity ε of different tissues are presented in table 1. The frequency values corresponds to the frequency range for Russian and interferential stimulation systems.

TABLE I. PARAMETERS OF THE TISSUES AND DIMENSIONS [7,8]

Layer

Conductivity

(10-4S/m)

Relative

Permittivity

(104S/m)

Dimension

100 Hz 2,500 Hz Frequency

independent

Electrode 33.33 33.33 1.0X10-4 Square

(12.25 cm2)

Skin 2 2 0.1136 1.5 mm

(radial)

Fat 406.40 424.20 15.15 6 mm

(radial)

Muscle

Transversal 760.00 800.00 932.9

50.6 mm

(radial)

Muscle

Longitudinal 2,667.00 3,316.00 932.9

50.6 mm

(radial)

Bone

Cortical 200.60 202.6 0.5853

6.0 mm

(radial)

Bone

Marrow 1013 1020 7.246

7.6 mm

(radial)

Compartment models helps to explain the influences of applied electric or magnetic fields in representative target neurons. McNeal [5] developed a compartment model for myelinated nerve fiber and its subthreshold response to

external point source stimulation. He represented the myelinated nerve by an equivalent circuit for the Ranvier node and assumed that the myelin sheath was a perfect insulator. In this work, an electrical network for the myelinated nerve is employed, but the myelin sheath is modeled as a passive circuit (figure 2).

Introducing the reduced membrane voltage Vn = Vi,n - Ve,n - Vrest leads to the following system of differential equations for calculating the time-courses of Vn in every compartment.

(2)

where cm is the membrane capacitance and R the intra-axonal resistance between the centers of two adjacent compartments.

Then, it is necessary to compute Iion,n to solve the membrane voltage. In the case of the internodes, they are considered as passive membranes and are assumed to have a constant membrane conductance Gm,n. In contrast, the Ranvier nodes present non-linear activity; therefore, additional differential equations are included (CRRSS model).

CRRSS model (Chiu-Ritchie-Rogart-Stagg-Swenney) [9,10], which describes the nonlinear gating mechanism of ion channels across the unmyelinated neuronal membrane, was used to calculated Iion,n at the Ranvier nodes. The model incorporates sodium and leakage currents but disregards potassium channels as they were found to be less important in the excitation process of myelinated mammalian nerves.

A. Parameters

A variable cathodic square stimulus is employed to obtain the motor threshold. The resolution of the stimulus intensity is 10 µA. Two square electrodes of 12.25 cm

2 of area and

inter-electrode distance of 6 cm are chosen for this study, which corresponds to a typical clinical application. The frequency under study are 100 Hz and 2.5 kHz to cover traditional stimulation and high frequency stimulation (e.g. Russian stimulation). The location of the nerve fiber is 4.2 mm under the muscle surface which is bellow the electrodes.

Figure 3. Motor threshold. (a) The nerve is activated when an electrical

stimulation of 33.4 mA is applied. (b) There is no nerve activity when the

intensity of the electrical stimulation is reduced to 33.395 mA

B. Evaluation Indexes

Motor threshold is the nerve activation at the lowest stimulation intensity. One myelinated fiber is placed under the electrode to investigate its motor threshold. The cathodic stimulation current was increased until the transmembrane potential exceeded a threshold of 80 mV, i.e., and action potential propagation is elicited using the CRRSS model.

III. SIMULATION

The motor threshold is computed adjusting the conductivity of the model layers to values that corresponds to 100 Hz and 2.5 kHz to determine whether or not the frequency plays an important role in the Russian and interferential stimulation, figure 3. Additionally, the effect of conductivity change due to frequency is examined on only the muscle or skin-fat-bone layer.

The increase of the frequency from 100 Hz to 2.5 kHz decreases the impedance 0.18%. However, the motor threshold at 2.5 kHz increases 20.33% respect to 100 Hz, table 2.

Furthermore, the contribution of skin-fat-bone and muscle are inspected. The motor threshold increase due to the muscle layer (19.73%) is larger than skin-fat-bone layer (2.13%). Thus, conductivity variation of the muscle layer is dominant compared with the conductivity.

TABLE II. MOTOR THRESHOLD. THE CONDUCTIVITIES OF THE LAYERS

CORRESPONDS TO FREQUENCIES OF 100 HZ AND 2.5 KHZ [7]

Frequency

(Hz)

Layers under

inspection

Impedance

(kΩ)

Motor

Threshold

(mA)

100 All 16,482 33.40

2500

All 16,452 40.19

Skin, fat, and bone 16,453 34.11

Muscle 16,426 39.99

IV. DISCUSSION

The effect of conductivity change due to frequency is

examined to determine whether or not the frequency played an

important role in high frequency stimulation. As a result, a

frequency increase does not improve activation at deeper

locations.

The motor threshold is computed adjusting the conductivity

of the model layers to values that corresponds to 100 Hz and

2.5 kHz. Additionally, the effect of conductivity change due to

frequency is examined on only the muscle or skin-fat-bone

layer.

The increase of the frequency from 100 Hz to 2.5 KHz

reduced the impedance, as expected. Consequently, the

volume conductor's impedance decreases 0.18%. However,

the motor threshold at 2.5 kHz increases 20.33% respect to

100 Hz. Therefore, the frequency increase does not benefit the

effectiveness of a stimulation scheme that uses higher

frequency for TES applications. It also agrees with other

results that indicate no advantage in force production of

Russian or interferential stimulation over other stimulations

(square and sine wave), as state in [11,12].

Furthermore, the contribution of skin-fat-bone and muscle

are inspected. The motor threshold increase due to the muscle

layer (19.73%) is larger than skin-fat-bone layer (2.13%).

Thus, conductivity variation of the muscle layer is dominant

compared with the conductivity variation of skin-fat-bone

under the inspected frequencies.

The reason why an increase of the conductivity of the

muscle do not cause less stimulus intensity to achieve motor

threshold is that the longitudinal conductivity of the muscle

changes at a major proportion than transversal conductivity at

low frequency (less than 10 kHz), which means that the

conditions for deeper activation are no achieved.

V. CONCLUSION

A frequency increase from 100 Hz to 2.5 KHz did not

improve the activation at deeper location. The reason is that

the longitudinal conductivity of the muscle changed at a major

proportion than transversal conductivity at low frequency

(less than 10 kHz), which means that the conditions for deeper

activation were not achieved. Additionally, conductivity

variation of the muscle layer was dominant compared with the

conductivity variation of skin-fat-bone under the inspected

frequencies.

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