Computational Study of Thermal Changes during the Non-invasive

Neuro-electrostimulation of the Nerve Structures in the Human Neck

Modelling Using Finite Element Method

Vladimir Kublanov

, Mikhail Babich

, Anton Dolganov

, Fedor Kornilov

and Anna Sajler

Research Medical and Biological Engeneering Centre of Hight Technologies, Ural Federal University, Mira, 19, 620002,

Yekaterinburg, Russian Federation

N. N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Sofia

Kovalevskaya, 16, 620990, Yekaterinburg, Russian Federation

Ural State Medical University, Department of Human Anatomy, Repina, 3, 620028, Yekaterinburg, Russian Federation

Keywords: FEM Modelling, Neuro-electrostimulation, Human Neck, SYMPATHOCOR-01 Device.

Abstract: In the article methodology of FEM stimulation of thermal effects, caused by neck-region neuro-

electrostimulation was shown. Algorithm of the voxel model conversion to the 3-D objects represented as the

complex of the STL-files was described. The evaluation of the temperature in the biological tissues is based

on the association of the partial thermal changes, caused by the harmonics components of the pulsed neuro-

electrostimulation signal. Features of the thermal changes in the neck region were considered for the neuro-

electrostimulation by means of the current pulse field formed in the "SYMPATHOCOR-01" device. Results

have shown that for modulation frequencies in range 45-55 Hz, duration of the partial pulses 25-30 us, current

pulse amplitude less than 13 mA, the neuro-electrostimulation does not cause thermal changes higher

than 0.1 K.

1 INTRODUCTION

Non-invasive portable neuro-electrostimulation

devices are widely used in the contemporary medical

practice. These devices use low-frequency pulse

signals with single polarity for the stimulation. These

devices are used to treat patients with exogenously-

organic diseases of the central nervous system,

anxiety and depressive disorders, atrophic diseases of

the nervous system, and diseases accompanied by

cognitive, sensory, motor and autonomic disorders.

The peripheral nervous system is usually used as the

target for devices exposure. Among the variety of the

non-invasive devices, the multi-electrode systems are

the most promising. The effectiveness of the multi-

electrode systems arises from the spatial distribution

of current pulses in the stimulation zone.

The “SYMPATHOCOR-01” is an example of

such multi-electrode systems. Methods of the

“SYMPATHOCOR-01” device clinical application

implements the methodology of dynamic correction

of the activity of the sympathetic nervous system

(DCASNS) and provide correction of the autonomic

balance, determined by the ratio of activity of the

sympathetic and parasympathetic divisions of the

autonomic nervous system (ANS). The

“SYMPATHOCOR-01” device is included in the

State Registry of medical devices in Russia

(registration certificates №FSR 2007/00757 from

28.09.2007), and instructions for its use were

approved in August 1999, by head of the State control

of the Quality, Efficiency, and Safety of Medicines

and Medical Equipment Department of the Russian

Ministry of Health (Kublanov, 2008a).

During the neuro-electrostimulation procedure

via the “SYMPATHOCOR-01” device, Joule heating

of electric currents cause local heating zones.

Excessive heating of the biological tissues may

change normal functioning in the local zones or cause

thermal damage of tissue.

There is many papers that study heating processes

of biological tissues during electrostimulation.

However, as heating processes cannot be investigated

invivo, these processes are assessed by numerical

solving of the Pennes equation (Bergman and

Incropera, 2011) or by physical experiments (Su et

Kublanov V., Babich M., Dolganov A., Kornilov F. and Sajler A.

Computational Study of Thermal Changes during the Non-invasive Neuro-electrostimulation of the Nerve Structures in the Human Neck - Modelling Using Finite Element Method.

DOI: 10.5220/0006174702830290

al., 2014). Yet implementation of physical

experiments can be difficult.

Biological objects have a complex geometry.

Therefore, numerical solving of the Pennes equation

is usually performed by the finite element method

(FEM) (Cao et al., 2015). At present time, FEM

modelling does not allow transient simulation of the

pulsed current for frequency dependent

characteristics of biological tissues. Therefore, it is

advisable to produce decomposition of the pulse

currents into Fourier series, to perform modelling of

the harmonic components of the pulsed current, and

to combine partial effects of the harmonic

components.

The aim of the present work is to evaluate the

tissue heating process formed during nero-

electrostimulation of the human neck by the field of

the pulsed current.

2 MATHERIALS AND METHODS

To evaluate the tissue heating process, voxel model

of the human neck was used. In order to simplify the

simulation procedure, it is appropriate to consider a

pulse sequence as a superposition of harmonic

components, determined by Fourier series.

In current work COMSOL Multiphysics

(COMSOL Inc., USA) software was used for solution

of the Pennes bioheat equation for heat transfer.

Before the solution start, human body voxel model

was transformed into the STL-files. Every STL-file

represent particular 3-D biological object. For the

voxel body model transformation, the in-house script

was written in the Python language of with Anaconda

distribution (Continuum analytics, USA).

After solution solving by means of the FEM,

temperatures dependencies on the x, y, z spatial

coordinates have been exported to *.csv files.

Further by means of the in-house script in the

Python language with Anaconda distribution using

the set of *.csv files, maximum thermal changes in

the biological tissues of the human neck in

dependence on amplitude, frequency and duration of

the neuro-electrostimulation impulse signal were

plotted.

2.1 “SYMPATHOCOR-01” Device

Description

In the “SYMPATHOCOR-01” device for neuro-

electrostimulation of the nerve structures, the

spatially distributed rotating field of the current

pulses is formed. The field is created between two

multi-electrode arrays, located on the left and right

sides of the neck. The central electrode of each multi-

electrode array serve as anode, and is placed on the

projection of the cervical ganglia of the ANS. The

other electrodes in the multi-electrode array are

partial cathodes provide spatial patterns of the filed.

Partial current pulses, flowing from the anode of

one electrode array to partial cathodes of another

electrode array, form resulting current pulse filed.

Each of the partial pulses have an amplitude and

duration in the following ranges:

 the pulse amplitude varies from 0 to 15 mA;

 duration of each pulse ranges from 15 to 60 us.

Current pulse filed is modulated by frequency,

that ranges from 5 to 150 Hz. In that case for a single

period of the field formation, from 1 to 13 partial

current pulses can be generated. Each pulse follows

the previous one consequently.

The process of the thermal changes formation as

the result of the neuro-electrostimulation is formed by

set of partial current pulses, flowing between the

anode and the partial cathodes. Therefore, for

simulation formation of the current pulse field as the

superposition of the processes, caused by the

transition of the partial currents pulses between

anodes and one partial cathode.

The partial current pulses used in the

“SYMPATHOCOR-01” device has a very small

duty-cycle varying from 75*10E-6 to 9*10E-3.

Therefore 99% of the power is contained in first 2000

harmonics.

Low-frequency monopole pulse sequence of the

signal, formed in the “SYMPATHOCOR-01” device,

as any periodic signal can be decomposed into a

Fourier series as a sum of harmonics.

















cos2π















,

(1)

where: t – time, f(t) – neuro-electrostimulation signal

in time domain, a

– amplitude of constant part of

signal, n – number of harmonic component of the

signal, a

– amplitude of n-th harmonic component of

the signal, T – period of signal repetition, θ

– phase

of n-th harmonic component of the signal.

On the other hand, according to the Parseval's

theorem, the average power of the signal is the sum

of the power spectral densities of the components,

which does not depend on their phases (Arfken et al.,

2011).









,

(2)

where: P – average power of the signal, P

– average

power of n-th harmonic component of the signal.

According to the Newton’s law of cooling, power

is directly proportional to the thermal difference

between body and its surroundings.











∆,

)

where: Q – thermal energy, h – heat transfer

coefficient, A – heat transfer source area, ΔT – thermal

difference between the body and its surroundings

(Bergman et al., 2011).

Thus, the total thermal difference between the

body and its surroundings as a result of current pulses

Joule heating can be determined as the sum of the

partial thermal differences between the body and its

surroundings caused by individual harmonic

components.

∆  ∆







)

where: ΔT

– thermal difference between the body

and its surroundings caused by n-th harmonic

component of pulse signal.

Harmonic signals with constant amplitude were

used for simulation. Thermal effect of each harmonic

component was computed proportional to the ratio of

the signal components and simulation components

powers.

∆

















∆



(5)

where: b

– harmonic signal amplitude used in FEM

solution, ΔTm

– thermal difference between the body

and its surroundings obtained after FEM solution for

n-th harmonic component of pulse signal.

Finally, the total thermal difference of biological

tissues caused by the current pulses Joule heating is

determined by the following equation.

∆  













∆







(6)

2.2 Model Preparation

Model Duke from the Virtual Population ViP1

models has been used as the primary model of human

body(Christ et al. 2010). The Duke model provides

reliable information about the anatomy of the entire

human body, obtained with the help of magnetic

resonance imaging and the subsequent segmentation

of the results. This method of constructing the model

provides high accuracy of the simulation results.

The Duke model is a 3-D matrix. Each element

(voxel) of the 3-D matrix stores a value indicating

whether an element belongs to a particular biological

tissue. The model represents 77 types of various

biological tissues. Geometric size of one voxel is 1

mm x 1 mm x 1 mm.

The whole body model has been truncated to the

human’s neck area, in accordance with papers goals.

Truncated 3-D matrix has a size of 201 mm  222

mm  102 mm. Length and width of the truncated

matrix fully include the cross-section of the human

neck. Truncated matrix height is 7 times larger than

the standard electrode used in the

“SYMPATHOCOR-01” device for neuro-

electrostimulation procedures. For these procedures,

circular brass electrodes with 15 mm diameter and 0.2

mm thickness are uses (Kublanov, 2008b).The

boundaries of the model are far away enough from the

electrode application site and have a minimal impact

on the current distribution and the formation of local

heating zones in the neck.

Cross-section of the 3-D human neck model

matrix in the area of the electrodes placement is

shown in Fig 1. At Fig. 1 pixels, representing the

same biological tissue have the same brightness.

Figure 1: Cross-section of the three-dimensional human

neck model.

The COMSOL simulation software has no

possibility of using voxel models of geometric solids.

Therefore, it is necessary to transform a voxel model

to the format of 3-D models of objects, such as STL.

Block diagram of the algorithm for voxel models

to STL format conversion is shown in Fig. 2. This

algorithm has been implemented in Python using the

Anaconda distribution.

Figure 2: Block diagram of an algorithm for voxel models

to STL format conversion.

For COMSOL simulation software it is necessary

that objects do not contain zero thickness geometry.

Therefore, the algorithm includes a step of bringing a

voxel model to well-composed state. Feature of this

step is the increase of the voxel 3D-matrix resolution.

This leads to a significant increase of 3D-matrix

elements and, as the result, significant increase of the

requirements for computational resources. Pre-

decimation of the original 3D matrix model was

carried out for the optimization of computing

resources.

In the first step of the conversion algorithm

decimation (reduction in size) of 3-D voxel model of

the neck by a factor of 3 is executed for each

dimension. Decimation factor should be selected to

be the smallest among all possible values, in a way

that the number of elements obtained in the 3D-

matrix does not cause difficulties in solution of the

FEM model. Decimation procedure consists of the

following steps:

 selection of the cube with the size 3  3  3

voxels in initial 3D-matrix;

 picking of the most common value in the

selected voxel;

 setting the most common value to appropriate

place into decimated matrix.

As a result, the algorithm creates a decimated

matrix comprising (x/3)  (y/3)  (z/3) voxels in each

dimension, where x, y, z the number of voxels in the

initial 3D-matrix. The size of each voxel in the

decimated 3D-matrix is increased to a value of 3 mm

x 3 mm x 3 mm.

Cross-section of the human neck model after

decimation is shown in Fig. 3. The vertical level of

the image is selected the same as in Fig. 1. At Fig. 3

pixels, representing the same biological tissue have

the same brightness.

Figure 3: Cross-section of the human neck model after

decimation.

Second step of the conversion algorithm is the

addition of the nervus vagus, sympathetic trunk,

nervus hypoglossus, nervus accessories to the

decimated neck model, in accordance with the

anatomic atlas of Netter and Frank (Netter, 2010). In

the original Duke model as well as in the model after

decimation nerve formations in the neck are not

represented. These nerve structures are the targets for

the "SYMPATOKOR-01" neuro-electrostimulation,

and therefore their presence in the model is needed.

At the third step of the conversion algorithm,

decimated voxel 3D-matrix has been improved to a

well-composed state. The criterion for well-

composed state is the absence in the model geometry

of zero thickness between geometric objects,

consisting of a same biological tissue (Gonzalez-Diaz

et al., 2015).

Algorithm of the 3D-matrix improvement to the

well-composed state consists of the following steps:

 interpolation of the 3D-matrix with the

interpolation factor equaled to 3 for each

dimension based on zero-hold method

(Laughton and Warne, 2002);

 search for not well-composed pairs of voxels in

the interpolated 3D-matrix;

 modification of voxels, neighboring with found

not well-composed pairs so that the not well-

composed pair will become well-composed.

Interpolation factor is set to 3 because this is the

minimum value that will not cause a new not well-

composed pairs by removing the old ones. The

advantage of such algorithm is the preservation of the

topology model from changes. Cross-section model

of the well-composed human neck is shown in Fig. 4.

Figure 4: Cross-section model of the well-composed human

neck.

The vertical level of the image is selected the

same as in Fig. 1. At Fig. 4 points, consisting of the

same biological tissue have the same brightness.

After decimation, interpolation, improvement to

well-composed state steps the resulting 3D-matrix

size was 201  222  102 voxels with voxel size 1

mm  1 mm  1 mm. Using a model of this size

allows us to maintain a balance between accuracy and

required computation resources.

The last step of the algorithm is to convert models

in STL format files for further imports into FEM

simulation software. In order to convert voxel models

to STL format, each model is divided into a set of

binary voxel 3D-matrices. Each binary voxel 3D-

matrix for a certain type of biological tissue contains

a non-zero elements in the respective elements of

these biological tissue of the voxel 3D-matrix.

Each binary voxel 3D-matrix is divided into

connected components with connectivity set to 6.

Each connected component is stored in the form of

geometric bodies in separate STL file. The number of

geometrical bodies after saving was 172. The number

of unique types of biological tissue after save was 21.

After saving as a set of STL-files, the model of

human neck was imported into the COMSOL

Multiphisics 5.2a software. After the meshing

procedure, imported geometry model was presented

in the form of 1.5 million tetrahedra.

Figure 5: Appearance of the human neck 3D-model.

Each imported geometric body was set to its

appropriate biological tissue. All in all, the following

types of biological tissues were used: Blood, Bone,

Cerebrospinal Fluid, Connective Tissue, Esophagus,

Fat, Intervertebral disc, Larynx, Mandible, Bone

marrow red, Mucous, Muscle, Nerve, Subcutaneous

adipose tissue (SAT), Spinal Cord, Skin, Tendon

Ligament, Thyroid Gland, Tongue, Trachea,

Vertebrae. For each biological tissue in the model

physical characteristics were set based on IT'IS

Database for thermal and electromagnetic parameters

of biological tissues (Hasgall et al., 2012). The

following physical characteristics were set: electrical

conductivity, relative permittivity, density, heat

capacity, thermal conductivity, blood perfusion rate,

heat generation rate. Values of relative permittivity

and electrical conductivity physical characteristics

were set to be frequency dependent in range from 1

Hz to 100 MHz Therefore, the developed model took

into account the peculiarities of the formation of

thermal effects with the use of pulsed current.

2.3 Model Configuration

The electrode system in model is represented by two

cylindrical brass electrodes with 15 mm in diameter

and 10 mm thickness. The conductivity of brass is

much greater than the conductivity of the biological

tissues. Therefore, accurate transmission of the real

electrode geometry to model is not needed. The single

requirement to the model electrode is equality of

model electrode diameter to real electrode diameter

(Kublanov and Babich, 2015).

Appearance of the human neck 3D-model with

placed electrodes is shown in Fig. 5. The electrode

placement on Fig. 5 corresponds to one of the

possible variants of the partial current formation. The

left electrode is used as anode, and the right electrode

is used as cathode. The electrodes are marked in the

image in black.

For the model calculation, frequency stationary

study was used. This study calculates temperature

distribution by the model volume at thermal

equilibrium.

Temperature on boundaries, which were formed

after truncating model to the human’s neck area, was

set to 310 K.

For simulation, the frequency range from 1 Hz to

100 MHz was used. This range includes first 20000

harmonics of the neuro-electrostimulation signal.

Low-frequency components contain significantly

greater amount of energy than high. Therefore, the

frequency range for simulation was set to a

logarithmic scale as follows: (1, 3, 5, 7, 9, 10, 30, 50,

70, 90, 100, 300, 500, 700, 900, 1k, 3k, 5k, 7k 9k,

10k, 30k, 50k, 70k, 90k, 100k 300k, 500k, 700k,

900k, 1M, 3M, 5M, 7M, 9M, 10M, 30M, 50M, 70M,

90M 100M) Hz.

For simulation, amplitude of the harmonic current

components was set to 10 mA. Although it is possible

to conduct simulation with other values of the current.

In addition, we studied model without applied

partial currents. These results were used for the base

of the temperature distribution in human tissues in the

neck in the absence of neuro-electrostimulation

signal.

After computation of the models for all

harmonics, temperatures values depending on the

coordinates x, y, z were exported into *.csv files.

Each frequency corresponds to a separate *.csv file.

2.4 Preparation of Thermal Difference

Results

Python script has been written for the calculation and

analysis of the thermal changes during the neuro-

electrostimulation process on the basis of equation 6,

using the previously exported temperature

distributions, saved in set of * .csv files. This script

performs the following steps:

 import of the *.csv files and convert them to the

form of thermal distribution 3D-matrices;

 calculation of amplitudes and frequencies of

the Fourier series harmonics of the periodic

pulsed signal used for neuro-

electrostimulation;

 3D-matrix calculation of thermal changes for

each harmonic used in simulation;

 interpolation of existing thermal changes 3D-

matrices for decomposed harmonic frequencies

used for neuro-electrostimulation signal;

 summation of 3D-matrix thermal changes for

each decomposed harmonic of neuro-

electrostimulation in accordance with equation

The results of script execution are thermal

changes for the whole model volume depending on

neuro-electrostimulation pulse characteristics was

calculated.

3 RESULTS

The cross-section of the thermal increase distribution

of tissues human neck during neuro-

electrostimulation processes is shown in Fig. 6.

Neuro-electrostimulation pulse characteristics were:

1 mA amplitude, 30 us duration, and 50 Hz

frequency. The vertical level of the image is selected

the same as in Fig. 1.

Figure 6: The cross-section of temperature increase in the

human neck for neuro-electrostimulation current pulse

characteristics 1 mA amplitude, 30 us duration, and 50 Hz

frequency.

According to the image in the Fig. 6, the

maximum temperature increase (0.05 K) is located at

cathode and anode application points. Significant

thermal increase were not observed in the inner

biological tissues of neck area This can explained by

a decrease of the current density with increasing

depth of biological tissue location. One can note that

the maximal thermal increase under the cathode and

the anode are different. That can be explained by the

different thicknesses of the skin in electrode

application points of the Duke model. For human

neck model with a constant thickness of the skin

difference of maximum thermal increase under the

cathode and anode application points will not be

observed.

Maximal thermal increase was considered as the

integral parameter of thermal effects in the entire

volume of biological tissues caused by neuro-

electrostimulation.

Maximal thermal increase in biological tissues of

the human neck using neuro-electrostimulation

dependency on the signal duration and frequency for

the 1 mA pulse amplitude is shown in Fig. 7.

Maximum thermal increase in biological tissues of

the human neck using neuro-electrostimulation

dependency on the signal duration and frequency for

the 15 mA pulse amplitude is shown in Fig. 8.

Figure 7: Maximal thermal increase against frequency, for

different durations, for the 1 mA pulse amplitude.

Figure 8: Maximal thermal increase against frequency, for

different durations, for the 15 mA pulse amplitude.

Fig. 7 and Fig. 8 show that maximal thermal

increase for 1 mA pulse amplitude is 3.5 mK and for

15 mA is 0.7 K. Comparison of the plots, presented

on Fig. 7 and Fig. 8 reveal quadratic dependency of

the maximal temperature on pulse current amplitude.

The thermal increase caused by the neuro-

electrostimulation, becomes stronger, as the pulse

modulation frequency and pulse duration increase.

This can be explained by the fact that the heating of

the tissues magnifies with the increase of the neuro-

electrostimulation duty-cycle.

Let us consider the maximal permissible current

for different stimulation pulse duration and frequency

characteristics with the condition: the maximal

thermal increase in the volume of biological tissue

does not exceed the 0.1 K. The tissue heating less than

0.1 K is considered non-thermal exposure and cannot

cause tissue damage (WHO | Electromagnetic fields

and public health 2016). Plot of the neuro-

electrostimulation current pulse amplitude against

frequency, for different pulse duration, under

condition that the maximum thermal rise in human

tissues of the neck is less than 0.1 K is shown in Fig.

Figure 9: Maximal permissible current against frequency,

for different durations.

According to the Fig. 9 the application of the pulse

current with the frequencies in range 45-55 Hz,

duration 25-30 us and amplitude less than 13 mA, will

not cause significant thermal effects. These pulse

current features are the most frequently used ones for

the neuro-electrostimulation processes. For

application of the pulse current with higher

frequencies, one must reduce duration and amplitude

in order to prevent significant tissue heating.

4 CONCLUSIONS

The current work presented methodology of the FEM

simulation for thermal effects evaluation, caused by

the neck region neuro-electrostimulation. Algorithm

of the voxel model conversion to the 3-D objects

represented as the complex of the STL-files was

described. The evaluation of the temperature in the

biological tissues is based on the association of the

partial thermal changes, caused by the harmonics

components of the pulsed neuro-electrostimulation

signal.

Features of the thermal changes in the neck region

were considered for the neuro-electrostimulation by

means of the current pulse field formed in the

"SYMPATHOCOR-01" device. Results have shown

that for modulation frequencies in range 45-55 Hz,

duration of the partial pulses 25-30 us, current pulse

amplitude less than 13 mA, the neuro-

electrostimulation does not cause thermal changes

higher than 0.1 K.

In our future works, it is planned to carry out

verification of the heat distribution model in the

laboratory. Also in plans, to assess the impact of

deviations of the biological tissue physical

characteristics on the temperature distribution.

The developed methodology of the thermal effects

assessment caused by pulsed current neuro-

electrostimulation in the human neck will allow to

develop guidelines for choosing the parameters of the

current pulses field for each patient, taking into

account his anthropometric characteristics.

The height and body mass index (BMI) will be

used as the anthropometric characteristics of the

patient. It is assumed based on these characteristics, a

doctor will select appropriate model from a set of a

Virtual Population model group and then will produce

linear transformation of the model to meet the

patient’s height and BMI. Then, based on the

calculated model it is suggested to recommend ranges

of stimulation parameters.

ACKNOWLEDGMENTS

The work was supported by Act 211 Government of

the Russian Federation, contract № 02.A03.21.0006.

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