A simple and accurate FDTD based technique to determine equivalent complex permittivity of the multi-layered human tissue in MICS band

This paper proposes a methodology to determine the equivalent electrical properties of multilayered human tissue using the Finite Difference Time Domain (FDTD) method for dispersive media. In addition, the impact of fat layer thickness on the equivalent dielectric properties has also been critically analyzed.

Original Article

A simple and accurate FDTD based technique to determine equivalent

complex permittivity of the multi-layered human tissue in MICS band

Mir Mohsina Rahmana,1,*, G.M Rathera

a Department of Electronics and Communication Engineering, National Institute of Technology Srinagar, Hazratbal Srinagar, 190006, Jammu and Kashmir,

India

a r t i c l e i n f o

Article history:

Received 6 December 2019

Received in revised form

8 February 2020

Accepted 16 February 2020

Available online 26 February 2020

Keywords:

FDTD

NRW

MICS

Phantom

a b s t r a c t

This paper proposes a methodology to determine the equivalent electrical properties of multilayered human tissue using the Finite Difference Time Domain (FDTD) method for dispersive media In addition, the impact of fat layer thickness on the equivalent dielectric properties has also been critically analyzed The effect of moisture content present in the skin layer has also been studied The main advantage of the proposed method is that it can be used for any thickness and any number of layers of human tissue The multilayer reflection and transmission coefficients of the human tissue are first calculated using the FDTD method and then the permittivity and conductivity are extracted using the Nicholson Ross Weir (NRW) Method The results are validated analytically using the concept of transmission line analogy for plane wave propagation The tool used is MATLAB In this paper, a three-layered software model of the human chest for pacemaker applications has been analyzed in the Medical Implants Communication Service band (MICS) At the frequency of 403.5 MHz in the MICS band, the equivalent permittivity of 3 layered human tissue is approximately 43 and its conductivity is 0.41 s=m Moreover, the effective permittivity, conductivity and tan delta loss decrease with the increase in fat layer thickness These results form the basis for the development of phantom mixtures used for designing, testing and eval-uation of implantable antenna and SAR measurements The choice of using FDTD is because it is a very powerful tool for creating a numerical mixture

© 2020 The Authors Publishing services by Elsevier B.V on behalf of Vietnam National University, Hanoi This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)

1 Introduction

Medical implantable devices support and improve the quality of

life, playing a vital role in modern health care The possibilities of

wireless communication with implantable devices open up many

interesting outcomes This communication is achieved byfitting a

miniature radio transceiver in the implantable medical device that

requires proper testing before surgical implantation in the patient's

body [1,2] It is important to note that the test and evaluation of

these implantable devices should be carried out in an environment

that closely resembles the human body Such an environment can

be replicated using software or can be realized in the physical form

called “Phantom” [3e6] Similarly, in order to study the Surface

Absorption Rate (SAR) or the power absorbed by the tissues while using mobile phones or wearable antennas, such an environment is required In the development of a complete phantom, the equiva-lent electrical properties of the human body part involved in the specific medical application, have to be determined, as a first step [7,8] Moreover, the thickness of the fat layer varies from person to person and also with time for a particular person Therefore, the alteration of dielectric properties due to varying fat thickness needs

to be studied in order to design and test implantable transmitters that are either impervious to such variations or have an appropriate margin to operate within all varying conditions

In the literature, several methods have been described for the numerical analysis of the electrical properties of human tissue The problem is approached by numerically solving Maxwell's equations

in either differential or integral form These methods fall into two categories: time domain and frequency domain Among the fre-quency domain techniques, the most successful is the Method of Moments (MOM) [9,10] However, MOM requires large memory and computation time The computer storage required is of the order ofð3NÞ2and the computation time required is of the order of

* Corresponding author.

E-mail addresses: mohsina_57phd15@nitsri.net (M.M Rahman),

gulammohdrather@yahoo.co.in (G.M Rather).

Peer review under responsibility of Vietnam National University, Hanoi.

1 Present Address: Department of ECE, National Institute of Technology Srinagar,

Hazratbal Srinagar, 190006, Jammu and Kashmir, India.

Contents lists available atScienceDirect Journal of Science: Advanced Materials and Devices

j o u r n a l h o m e p a g e : w w w e l s e v i e r c o m / l o c a t e / j s a m d

https://doi.org/10.1016/j.jsamd.2020.02.004

2468-2179/© 2020 The Authors Publishing services by Elsevier B.V on behalf of Vietnam National University, Hanoi This is an open access article under the CC BY license

Journal of Science: Advanced Materials and Devices 5 (2020) 134e141

, where N is the number of cells [11,12] Numerically efficient

algorithms have been developed, but the best possible reduction of

time requirements that could be acquired is Nlog2N, which is still a

large value The time-domain approaches include the Finite

Element Method (FEM) [13] and the Finite Difference Time Domain

method (FDTD) [14] As compared to MOM, the storage and

computational time requirements in FDTD increase linearly rather

than geometrically with respect to N [15] Thus, FDTD presents an

attractive alternative for such applications Moreover, at MICS

fre-quencies FDTD is an effective tool for analyzing wave propagation

in confined spaces The fidelity of the simulations with respect to

the actual measurements is good [16,17] FDTD is also a very

powerful tool when studying the dielectric properties of mixtures

[16,18] Extensive research has been conducted to study the

elec-trical properties of the human body, but there is a lack of complete

methodology to calculate the equivalent dielectric properties of

multi-layered human tissue In ref [19], the simulated human

abdominal tissue for capsule endoscopy using FDTD has been

proposed But the authors have discussed only electricfield

dis-tribution of the tissues involved and no information about the

equivalent dielectric properties of the abdominal tissue has been

presented Similarly, the authors in ref [20] have simulated a

three-layer human tissue using the FDTD method and have studied SAR

changes on the interface of the three layers The authors in ref [21]

have simulated a malignant tissue in a phantom and used FDTD to

study the resolution of microwave imaging for breast cancer Their

study andfindings have mainly limited the scope of their research

to electric field distributions and SAR measurements only This

work has attempted to bridge this gap

In this paper, the tissue modelled is the human chest for

pace-maker applications The pacepace-maker is most often placed

subcuta-neously between the fat and pectoral muscles under the collar

bone So, the human chest in this application can be well

approx-imated by a three-layer planar model consisting of muscle, fat and

skin as shown inFig 1 The equivalent electrical properties of the

modelled human chest tissue are determined in this paper for an

average male adult in the MICS band, but the methodology is good

for any number of layers of human tissue

The remaining part of the paper is divided into the following

sections: section2gives a brief explanation about the dielectric

properties of biological materials; section3describes the proposed

methodology while section4contains the results Lastly, section5

gives the conclusion of the paper

2 Dielectric properties of human tissue

When RF waves fall on the surface of a material, only a part of it

gets absorbed into the material The rest of the energy is reflected

back while some of it is transmitted These categories of energy

have been defined in terms of the dielectric properties of the

material [22] The dielectric properties of a material are a measure

of how electromagnetic waves interact with its constituent ele-ments and are obtained from their measured complex permittivity [23,24] The real part of this complex quantity is the relative permittivity which is the measure of energy stored in the material while its imaginary part gives the dielectric loss factor, a measure of the dissipated electrical energy This complex quantity is fre-quency-dependent and is given by:

εðf Þ ¼ ε0

ðf Þ  ε00

ε0

ε0is the permittivity of free space,εris the relative permittivity and represents the energy stored in the medium,ε00 is the out of phase loss factor representing the dissipation or loss of energy within the medium Equation(1)can be re-written as:

εðf Þ ¼ εrðf Þ sðf Þ

uε0

(3)

where sis the electrical conductivity and u is the angular fre-quency of the field Moreover, the dielectric loss factor can be parametrized in terms of the loss tangent given by equation(4): tand¼ε00ðf Þ

In biological tissues, when an EM signal travels from one tissue type to another, the impedance difference between the two tissue types results in the reflection of some energy, reducing the power

of the signal that travels to the other side of the interface This gives the corresponding reflection and transmission coefficients which in turn can be used to calculate dielectric properties of the tissue Biological tissues respond weakly to magnetic fields, so their permeability is approximated to unity

The electrical properties of different human tissues for an average human male adult that are relevant for medical implants in the MICS band are given inTable 1[25e27] The fat layer thickness has been varied from 5 mm to 25 mm in order to observe its effect

on the equivalent dielectric properties of the tissue The MICS band ranges from 402 to 405 MHz [28] which is already in use by the Meteorological Aids Service (METAIDS), wherein weather balloons transmit data down to earth Therefore, to avoid any interference, the MICS system is specified to be used only indoors [29] The frequency band has been allocated by the European Telecommu-nications Standards Institute (ETSI) [30,31] All the data are from ref [32] and are given for a frequency of 403.5 MHz The proposed methodology used to determine equivalent electrical properties of the human tissue is discussed in detail in the next section

3 Methodology The determination of equivalent electrical properties of a hu-man tissue requires an understanding of the multi-layered

Table 1 Dielectric Properties of Human Tissue at 403.5 MHz.

Tissue Thickness (mm) 403.5 MHz

ε r sðs =mÞ Dry Skin 3 46.706 0.68956 Wet Skin 3 49.842 0.6702

inversion problem considering that biological tissues have

fre-quency dependent dielectric properties and are multi-layered

Therefore, all the layers of human tissue need to be taken into

ac-count while modelling the human body for a specific application In

this paper, a simplified three-layered model of the human chest has

been computationally modelled in two dimensions using the FDTD

method for a transverse magnetic mode This gives multi-layer

transmissionðS21Þ and reflection ðS11Þ coefficients of the layered

human tissue The FDTD results are validated by using basic plane

wave propagation formulae and the concept of transmission line

analogy of wave propagation Then, the equivalent electrical

properties ðεrequivalentðf Þ;sequi valentðf ÞÞ are derived using the NRW

technique Both the FDTD and NRW techniques are implemented in

MATLAB The FDTD programs used are derived from the algorithms

developed by Taflove et al [33] based on the methodfirst proposed

by Yee [34] The NRW method is taken up from the basic paper by

Ross and Weir [35]

3.1 FDTD method

The Finite Difference Time Domain method is a computational

electromagnetic technique proposed by Yee in 1966 [34,36] It is a

powerful method of solving Maxwell's equations in all three

di-mensions and in time Maxwell's equations for dispersive materials

can be written as:

D H!¼s!E

þv D

!

D E!¼ v B

!

where E!

is the electricfield intensity, H!is the magneticfield

in-tensity,sis the conductivity of the medium, D!is the magneticflux

density, B!is the electricflux density, respectively given by:

B

!

¼m0!H

(7) D

!

¼ ε0εr!E

(8) wherem0is the permeability of free space,ε0is the permittivity of

free space,εr is the relative permittivity of the medium In this

paper, Transverse Magnetic mode with E
!x and H

y

! components have been considered The E!and H!fields are placed at a half step

distance around a unit cell and are calculated at alternate half time

steps Thesefield components are updated in the leapfrog scheme

using thefinite difference form of the curl operators on the fields

that surround the component [14,37] This effectively provides

centred difference expressions for both space and time derivatives

These time-domain data is then converted into the

frequency-domain using Fast Fourier Transform (FFT), in order to get the

reflection and transmission coefficients

The problem domain in the FDTD method is illuminated by

several types of plane wave sources The most commonly used is a

Gaussian-shaped pulse, an exponentially decaying sinusoid and a

continuous sinusoidal wave In this paper, a Gaussian pulse is used

as an excitation source Each cell in the problem space is assigned

material-specific electrical properties corresponding to each layer

of the human tissue The thickness of each layer is equal to their

biological thicknesses Moreover, computational stability is

essen-tial in any numerical equation solver because, if not taken care of, it

causes unbounded growth of the computed results To ensure

nu-merical stability, for given cell size (DZ), Taflove [33,38] suggested

the size of the time step (Dt) to be restricted as:

Dt¼DZ

where C0is the velocity of the electromagnetic wave in free space The E!

and H! fields after getting scattered by the multi-layered modelled tissue, if left alone, do not disappear at the edges of the problem space But, they get reflected back into the problem space

as if they are hit by a“wall” defined by the edges of the problem space This problem is avoided by applying a boundary condition at the edges given by the Berenger called Perfect Matching Layer (PML) condition [39] This way thefields at the edges are perfectly absorbed and there are no reflections in the problem space

3.2 Validation of FDTD results using the analytical model The FDTD results have been validated by using basic plane wave propagation formulae and the concept of transmission line analogy

of wave propagation [40,41] Consider a multiple interface problem with Nþ 1 planar regions separated by N interfaces The multilayer problem thus looks likeFig 2 As seen in thefigure, in each layer, there are both transmitted and reflected waves, except for the last layer where no reflection takes place Therefore, the wave imped-ance as seen from the Nth interface is equal to the characteristic impedance of theðN þ 1Þthlayer i.e

The recursive relation for calculating wave impedances at each interface is given by

ZLn1¼ Zn



1þ ðRn expð2jbntnÞÞ

1 ðRn expð2jbntnÞÞ



(11)

Where n¼ 2; 3; 4; …N; ZL is the wave impedance at each interface,

‘Z’ is the characteristic impedance of the medium,bis the propa-gation constant of the medium,‘t’ is the thickness of the layer and

‘R’ is the reflection coefficient given by:

Rn¼ZLn Zn

where n¼ 1; 2:::N: R1will give the equivalent reflection coefficient

of the whole structure Similarly, for transmission coefficient T, the electric field at each interface is calculated from the recursive relation:

En¼ En1



1þ Rn1

expðjbntnÞ þ ðRn expðjbntnÞÞÞ



(13)

where n¼ 2; 3; …N: Therefore, the transmitted electric field and hence the equivalent transmission coefficient is given by:

Fig 2 Graphical illustration of N- Layered dielectric media.

M.M Rahman, G.M Rather / Journal of Science: Advanced Materials and Devices 5 (2020) 134e141 136

ENþ1¼ EN½1 þ RN (14)

T¼ENþ1

where E1is the electricfield strength in the first layer and T is the

equivalent transmission coefficient of the structure These

formu-lations were coded in MATLAB and the results were used to validate

the FDTD results

3.3 NRW technique

The extraction of the complex permittivity from the

trans-mission and reflection coefficients is done using the NRW method

It was developed by Nicholson, Ross and Weir [35,42] In this

technique, the dielectric constant of the material is computed by

using the S-parameters S11and S21acquired from the FDTD

simu-lation as described above The reflection coefficient is expressed as:

G¼ XHpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiX2 1 (16)

where,

X¼S211 S2

11þ 1

The transmission coefficient, T, is stated as:

T¼ S11 S11G

From the above equations, the complex permittivity and

permeability of the sample can be calculated as:

ε ¼G1

G0



1G

1þG



(19)

m¼G1

G0



1þG

1G



(20) where,

G1¼ log



1

T



G0¼ j2pf

where C0is the velocity of the electromagnetic wave in free space,

d is the thickness of the sample and f is the frequency of operation

4 Implementation details and results

In this section, the implementation of the above-proposed

method and the corresponding results are discussed The human

body consists of multiple layers of tissue with diverse

frequency-dependent dielectric properties A model representing the body

for some application should account for all these layers For

reasonable analytical calculations, these layers can be simplified to

rectangular slabs [43,44] A simplified model of human chest tissue

can be well approximated by a three-layer planar model consisting

of muscle, fat and skin [45] The problem can be visualized as

shown inFig 3

At‘S’, the excitation source is placed which is a Gaussian pulse and the corresponding reflection and transmission coefficients are calculated using the one-dimensional FDTD equations for disper-sive media The simulation was donefirst for free space and then in the presence of the medium i.e human tissue layers The unit cell size is 0:33mm and the frequency resolution is 0.5 MHz, which is imperative for the very narrow frequency range of the MICS band The choice of the unit cell size is made such that all the geometrical details of the multilayered structure arefinely resolved in the MICS band while not increasing the computational space and time too much [46,47] This, in turn,fixes the unit time step to avoid insta-bility as already discussed in equation (9) The thicknesses of different layers are equal to their biological thicknesses for an average male human adult.Fig 4illustrates the permittivity and conductivity of the three-layer slab (Fat, Muscle and Skin) in the simulation space against their thickness A single simulation is run

as long as is needed to sufficiently dissipate the energy launched into the computational space The S11 and S21 parameters are determined by calculating the frequency domain electric fields from time-domain electricfields at specified positions in the FDTD sample space using Fast Fourier Transform (FFT) as:

S11ðf Þ ¼Erefðf Þ

Erefðf Þ ¼ Etotalðf Þ  Eincðf Þ (24)

Fig 3 Planar human chest model.

Fig 4 Permittivity (ε) (solid line) and conductivity (s) (dotted line) of the 3 layer slab (Fat, muscle and skin) in the simulation space.

S21ðf Þ ¼Etransðf Þ

where Etotalðf Þ is the total electric field incident with the medium,

Etransðf Þ is the transmitted electric field, Eincðf Þ is the incident

electricfield without a medium (i.e only free space) and Erefðf Þ is

the reflected electric field The time and frequency domain

repre-sentation of these electricfields for the MICS band are depicted in

Figs 5e11.Fig 5a gives Einc i.e the incident electricfield without

medium, the magnitude of which is illustrated inFig 5b Since the

source is Gaussian, the electric field is finally reduced to some

ripples as the source stops transmitting.Fig 6a and b give the Fast

Fourier Transform of Eincand its magnitude, respectively The plots

are presented in a narrower time frame for better visualization.Fig

7a and b depict the transmitted wave (Etrans) with respect to time,

whileFig 8a and b give its frequency-domain representation in the

presence of the medium Similarly,Fig 9a and b demonstrate the

time domain electricfield and its magnitude incident in the

pres-ence of the medium i.e the human layered tissue, respectively This

gives the total electricfield incident on the medium (Etotal) The FFT

of the same is given byFig 10a and b The reflected wave is then

calculated from equation(24)and its FFT and absolute value are

given inFig 11a and b, respectively

The magnitudes and phases of S11 and S21in the MICS band

(402e405) MHz) are calculated from equations(23) and (25) and

are illustrated inTable 2 This frequency band is so small that all the S-parameters show an almost constant behaviour, hence a single entry in the table As can be seen from the table, there is a clear difference in the results of the three-layer system for dry and wet skins This implies that the moisture content of the skin appreciably alters the equivalent electrical properties of the layered human tissue These FDTD results have been validated analytically by using the concepts of transmission line analogy of wave propagation and impedance transformation as discussed in section3.2 The results for the same are also depicted inTable 2 The two results favourably agree with each other The slight difference in the results is due to the fact that the analytical model takes only far-field into account while FDTD takes both near and far-field into consideration The S parameters of the human tissue, thus determined in the MICS band, are used to calculate the dielectric constant of the concerned medium using the NRW technique The NRW technique was formulated in MATLAB and corresponding results for the complex permittivity,ε are presented inTable 3 Furthermore, the values forεr equi valent andsequivalent, as calculated from equations(2)

and (3) are also provided in the same table The equivalent rela-tive permittivity and conductivity of the layered human tissue for

an average male adult consisting of muscle, fat and skin is approximately equal to 43 and 0.41 S=m at 403.5 MHz MICS band, respectively, as shown inTable 3 The dielectric loss factor of the same is 0.6 After calculating the equivalent dielectric properties of

Fig 5 Incident Electric field without medium (a)E inc , (b) Magnitude of E inc

Fig 6 FFT of Incident Electric field without medium (a)E , (b) Magnitude of E M.M Rahman, G.M Rather / Journal of Science: Advanced Materials and Devices 5 (2020) 134e141 138

the human chest, the thickness of the fat layer is varied The

pro-cedure followed is the same as above The resultant values are given

inTable 3 It can be observed that as the thickness of the fat layer

increases the dielectric permittivity, conductivity, as well as tan

delta loss, decrease This is obvious from the markedly different

properties of the fat tissue as compared to the other tissues Theε of

fat is much less, hence when its thickness increases, it dominates its impact on the total equivalent ε of the three-layered system, thereby decreasing its value Similarly, the tan delta loss and con-ductivity also decrease due to the overall effect of the fat tissue These results form the basis of the development of human phantoms which are extensively used for testing of implantable

Fig 7 Transmitted Electric field with medium (a)E trans , (b) Magnitude of E trans

Fig 8 FFT of Transmitted Electric field with medium (a)E trans , (b) Magnitude of E trans

Fig 9 Incident Electric field with medium (a)E , (b) Magnitude of E

medical devices In addition, phantoms are also used for

investi-gating the effect of electromagnetic radiations from EM sources like

mobile phones, ovens, industrial microwave instruments etc., on

the human body by examining and analysing Surface Absorption

Rate of the human tissue

5 Conclusion This paper proposes a simple and accurate methodology for determining the equivalent electrical properties of multi-layered human tissue The equivalent electrical properties of the

three-Fig 10 FFT of Incident Electric field with medium (a)E total , (b) Magnitude of E total

Fig 11 FFT of the reflected wave (a)E ref , (b) Magnitude of Eref

Table 2

S-Parameter comparison using FDTD and Analytical method.

Dermatological feature rS11r :S11 rS21r :S21 :S11 rS11r rS21r :S21 Dry skin 0.87 176.4 0.216 86 0.95 178.3 0.29 85 Wet skin 0.76 175.3 0.089 140 0.79 177.1 0.092 142

Table 3

Dielectric properties of the three-layered human chest with variable fat thickness at 403.5 MHz MICS band.

Thickness (mm) rS11r :S11 rS21r :S21 ε ε00 seq s/m tandloss

5 0.882 178.3 0.208 79.3 47.99 25.217 0.565 0.525

10 0.87 177.8 0.216 ¡84.78 42.56 18.07 0.405 0.424

15 0.876 177.5 0.224 90.75 38.75 12.604 0.282 0.325

20 0.871 177.21 0.233 97.57 35.825 7.684 0.1723 0.2144

25 0.862 177.02 0.241 105.21 33.424 3.342 0.0749 0.0999 The entry in the bold corresponds to the results for an average human male adult The thickness of fat layer for such a case is taken as 10 mm.

M.M Rahman, G.M Rather / Journal of Science: Advanced Materials and Devices 5 (2020) 134e141 140

layered human chest tissue have been determined The FDTD

method has been used for calculating the transmission and

reflection coefficients which are then used in the NRW algorithm to

find the equivalent dielectric properties of the human tissue The

results are validated analytically using transmission line analogy In

addition, the impact of moisture content in the skin on the

elec-trical properties of the tissue has also been analysed Incorporation

of many layers of tissues offers a more appropriate and more

realistic model of a human chest This methodology is applicable for

any thickness and any number of layers The results are envisaged

to be used as a reference for the development of the phantom It can

also be used for SAR measurements Moreover, the thickness of the

fat layer which varies with time and between individuals influences

the design of implantable transmitters This paper also studies the

effect of varying fat thicknesses on the complex dielectric

permi-tivitty of the human tissue Therefore, the results will be beneficial

for designers to model the transmitters that are insensitive to

varying tissue conditions

Declaration of Competing Interest

The authors declare that they have no known competing

financial interests or personal relationships that could have

appeared to influence the work reported in this paper

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