<span class='text_page_counter'>(1)</span><div class='page_container' data-page=1>

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 Rahman

a,1,*

, G.M. Rather

a

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 xxx

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 ( />

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 ofð3NÞ2_{and the computation time required is of the order of}

* Corresponding author.

E-mail addresses: (M.M. Rahman),

(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

/>

</div>
<span class='text_page_counter'>(2)</span><div class='page_container' data-page=2>

ð3NÞ3

, 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 and_{findings 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: section2 gives 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:

f ị ẳ 0

f ị  00

f ị (1)

0

f ị ¼ ε0εrðf Þ (2)

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:

f ị ẳ εrðf Þ 

s

_u

ðf Þ

ε0

(3)

where

s

is 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):

tan

d

ẳ00f ị

0_{f ị} (4)

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

Fig. 1. Three-layer diagram of human chest.

Table 1

Dielectric Properties of Human Tissue at 403.5 MHz.

Tissue Thickness (mm) 403.5 MHz

εr sðs =mÞ

Dry Skin 3 46.706 0.68956
Wet Skin 3 49.842 0.6702

Fat 10 5.5783 0.04117

</div>
<span class='text_page_counter'>(3)</span><div class='page_container' data-page=3>

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;

s

equivalentðf 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!ẳ

s

!E ỵv D
!

vt (5)

D

 E!¼ v B
!

vt (6)

where E!is the electricfield intensity, H!is the magneticfield
in-tensity,

s

is the conductivity of the medium, D!is the magneticflux
density, B!is the electricflux density, respectively given by:

B
!

¼

m

0H

!

(7)

D
!

¼ ε0εr!E (8)

where

m

0is 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 (

D

Z), Taflove [33,38] suggested
the size of the time step (

D

t) to be restricted as:

D

t¼

D

Z
2C0

(9)

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 re_{flections 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 Nỵ 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 the_{N ỵ 1ị}thlayer i.e

ZLNẳ ZNỵ1 (10)

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

ZL_n1¼ Zn



1ỵ Rn exp2j

b

ntnịị

1 Rn exp2j

b

ntnịị



(11)

Where nẳ 2; 3; 4; N; ZL is the wave impedance at each interface,
‘Z’ is the characteristic impedance of the medium,

b

is the
propa-gation constant of the medium,‘t’ is the thickness of the layer and
‘R’ is the reection coefcient given by:

RnẳZLn Zn

ZLnỵ Zn (12)

where nẳ 1; 2:::N: R1will give the equivalent reflection coefficient
of the whole structure. Similarly, for transmission coef_{ficient T, the}
electric field at each interface is calculated from the recursive
relation:

Enẳ En1



1ỵ Rn1

expj

b

ntnị ỵ Rn expj

b

ntnịịị



(13)

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

</div>
<span class='text_page_counter'>(4)</span><div class='page_container' data-page=4>

E_Nỵ1ẳ ENẵ1 þ RN (14)

T¼ENþ1
E1

(15)

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:

G

¼ XHpX2_{ 1} ₍₁₆₎

where,

XẳS211 S211ỵ 1

2S₁₁ (17)

The transmission coefcient, T, is stated as:

Tẳ S11 S11

G

1

G

S11ỵ S11ị

(18)

From the above equations, the complex permittivity and
permeability of the sample can be calculated as:

ẳ

G

1

G

0


1

G

1ỵ

G



(19)

m

ẳ

G

1

G

0


1ỵ

G

1

G



(20)

where,

G

1ẳ log



1
T



d (21)

G

0¼ j2_C

p

f
0

(22)

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 done_{first 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. 4 illustrates 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:

S₁₁f ị ẳEreff ị

Eincf ị

(23)

E_reff ị ẳ Etotalðf Þ  Eincðf Þ (24)
Fig. 3. Planar human chest model.

</div>
<span class='text_page_counter'>(5)</span><div class='page_container' data-page=5>

S₂₁f ị ẳEtransf ị

Eincf ị

(25)

where Etotalf ị 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 electric_{fields for the MICS band are depicted in}

Figs. 5e11.Fig. 5a gives Einci.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 S21 in 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 for_εrequivalent and

s

equivalent, 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 Electricfield without medium (a)Einc, (b) Magnitude of. Einc

</div>
<span class='text_page_counter'>(6)</span><div class='page_container' data-page=6>

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 Electricfield with medium (a)Etrans, (b) Magnitude of. Etrans

Fig. 8. FFT of Transmitted Electricfield with medium (a)Etrans, (b) Magnitude of. Etrans

</div>
<span class='text_page_counter'>(7)</span><div class='page_container' data-page=7>

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 Electricfield with medium (a)Etotal, (b) Magnitude of. Etotal

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

Table 2

S-Parameter comparison using FDTD and Analytical method.

Model FDTD Analytical

S11 S21 S11 S21

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 _s

eqs/m tandloss

</div>
<span class='text_page_counter'>(8)</span><div class='page_container' data-page=8>

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.

References

[1] F. Merli,“Implantable Antennas for Biomedical Applications,” Tech. Rep., EPFL,
2011.

[2] R. Alrawashdeh, Implantable Antennas for Biomedical Applications, PhD
thesis, University of Liverpool, 2015.

[3] Y. Hao, A. Brizzi, R. Foster, M. Munoz, A. Pellegrini, T. Yilmaz, Antennas and
propagation for body-centric wireless communications: current status,
applica-tions and future trend, in: 2012 IEEE International Workshop on Electromagnetics:
Applications and Student Innovation Competition, IEEE, 2012, pp. 1e2.
[4] C.K. Looi, Z.N. Chen, Design of a human-head-equivalent phantom for ism

2.4-ghz applications, Microw. Opt. Technol. Lett. 47 (2) (2005) 163e166.
[5] H. Do Choi, K.Y. Cho, J.S. Chae, H.G. Yoon, Method of manufacturing the human

tissue phantoms for evaluation of electromagnetic wave environment, US
Patent 6 (Jan. 30 2001), 181,136.

[6] A. Kraszewski, G. Hartsgrove, A macroscopic model of lungs and a material
simulating their properties at radio and microwave frequencies, J. Microw.
Power Electromagn. Energy 21 (4) (1986) 233e240.

[7] B.B. Beard, W. Kainz, T. Onishi, T. Iyama, S. Watanabe, O. Fujiwara, J. Wang,

G. Bit-Babik, A. Faraone, J. Wiart, et al., Comparisons of computed mobile
phone induced sar in the sam phantom to that in anatomically correct models
of the human head, IEEE Trans. Electromagn C. 48 (2) (2006) 397e407.
[8] G. Hartsgrove, A. Kraszewski, A. Surowiec, Simulated biological materials for

electromagnetic radiation absorption studies, Bioelectromagnetics 8 (1)
(1987) 29e36.

[9] R.F. Harrington, The method of moments in electromagnetics, J. Electromagn.
Waves Appl. 1 (3) (1987) 181e200.

[10] D.M. Sullivan, O.P. Gandhi, A. Taflove, Use of the finite-difference time-domain
method for calculating em absorption in man models, IEEE (Inst. Electr.
Electron. Eng.) Trans. Biomed. Eng. 35 (3) (1988) 179e186.

[11] B.K.P. Scaife, W. Scaife, R. Bennett, J. Calderwood, Complex Permittivity:
Theory and Measurement, English Universities Press, 1971.

[12] W.C. Gibson, The Method of Moments in Electromagnetics, Chapman and
Hall/CRC, 2014.

[13] K.D. Paulsen, X. Jia, J. Sullivan, Finite element computations of specific
ab-sorption rates in anatomically conforming full-body models for hyperthermia
treatment analysis, IEEE Trans. Biomed. Eng. 40 (9) (1993) 933e945.
[14] D. Li, C.D. Sarris, Efficient finite-difference time-domain modeling of driven

periodic structures and related microwave circuit applications, IEEE Trans.
Microw. Theor. Tech. 56 (8) (2008) 1928e1937.

[15] D.M. Sullivan, Electromagnetic Simulation Using the FDTD Method, John

Wiley& Sons, 2013.

[16] K.K. Karkkainen, A.H. Sihvola, K.I. Nikoskinen, Effective permittivity of
mix-tures: numerical validation by the fdtd method, IEEE Trans. Geosci. Rem. Sens.
38 (3) (2000) 1303e1308.

[17] T.-J. Kao, G.J. Saulnier, D. Isaacson, T.L. Szabo, J.C. Newell, A versatile
high-permittivity phantom for eit, IEEE Trans. Biomed. Eng. 55 (11) (2008) 2601e2607.
[18] K.-P. Hwang, A.C. Cangellaris, Effective permittivities for second-order
accu-rate fdtd equations at dielectric interfaces, IEEE Microw. Wireless Compon.
Lett. 11 (4) (2001) 158e160.

[19] J.-J. Hao, L.-J. Lv, L. Ju, X. Xie, Y.-J. Liu, H.-W. Yang, Simulation of microwave
propagation properties in human abdominal tissues on wireless capsule
endoscopy by fdtd, Biomed. Signal Process Contr. 49 (2019) 388e395.
[20] H. Alisoy, S.B. Us, B. Alagoz, An fdtd based numerical analysis of microwave

propagation properties in a skinefat tissue layers, Optik 124 (21) (2013)
5218e5224.

[21] E. Rufus, Z.C. Alex, Fdtd based em modeling and analysis for microwave
im-aging of biological tissues, in: International Conference on Smart Structures
and Systems-Icsss’13, IEEE, 2013, pp. 87e91.

[22] K.R. Foster, H.P. Schwan, Dielectric properties of tissues and biological
ma-terials: a critical review, Crit. Rev. Biomed. Eng. 17 (1) (1989) 25e104.
[23] R. Pethig, Dielectric and electrical properties of biological materials,

J. Bioelectr. 4 (2) (1985) viieix.

[24] W. Tinga, S.O. Nelson, Dielectric properties of materials for microwave
proc-essingetabulated, J. Microw. Power 8 (1) (1973) 23e65.

[25] C. Gabriel, S. Gabriel, y.E. Corthout, The dielectric properties of biological
tissues: I. literature survey, Phys. Med. Biol. 41 (11) (1996) 2231.

[26] S. Gabriel, R. Lau, C. Gabriel, The dielectric properties of biological tissues: ii.
measurements in the frequency range 10 hz to 20 ghz, Phys. Med. Biol. 41 (11)
(1996) 2251.

[27] S. Gabriel, R. Lau, C. Gabriel, The dielectric properties of biological tissues: iii.
parametric models for the dielectric spectrum of tissues, Phys. Med. Biol. 41
(11) (1996) 2271.

[28] M.N. Islam, M.R. Yuce, Review of medical implant communication system
(mics) band and network, Ict Express 2 (4) (2016) 188e194.

[29] P.D. Bradley, An ultra low power, high performance medical implant
communication system (mics) transceiver for implantable devices, in: 2006
IEEE Biomedical Circuits and Systems Conference, IEEE, 2006, pp. 158e161.
[30] N.F. Virtualization, European Telecommunications Standards Institute (Etsi),

Industry Specification Group (ISG), 2013.

[31] European Telecommunications Standards Institute, Electromagnetic
Compatibility and Radio Spectrum Matters (ERM);Short Range Devices, SRD,
2005, p. 4. V1.1.1.

[32] C. Gabriel,“Compilation of the Dielectric Properties of Body Tissues at Rf and
Microwave frequencies.,” Tech. Rep, KING’S COLL LONDON (UNITED

KINGDOM) DEPT OF PHYSICS, 1996.

[33] A. Taflove, M.E. Brodwin, Numerical solution of steady-state electromagnetic
scattering problems using the time-dependent maxwell's equations, IEEE
Trans. Microw. Theor. Tech. 23 (8) (1975) 623e630.

[34] K. Yee, Numerical solution of initial boundary value problems involving maxwell's
equations in isotropic media, IEEE Trans. Antenn. Propag. 14 (3) (1966) 302e307.
[35] A. Nicolson, Measurement of the intrinsic properties of materials by time

domain techniques, IEEE Trans. Instrum. Meas. 17 (1968) 392e402.
[36] D.M. Sullivan, Frequency-dependent fdtd methods using z transforms, IEEE

Trans. Antenn. Propag. 40 (10) (1992) 1223e1230.

[37] Y.-J. Zhou, X. Zhou, T.-J. Cui, R. Qiang, J. Chen, Efficient simulations of periodic
structures with oblique incidence using direct spectral fdtd method, Progress
In Electromagnetics Research 17 (2011) 101e111.

[38] J.B. Schneider, C.L. Wagner, Fdtd dispersion revisited: faster-than-light
prop-agation, IEEE Microw. Guid. Wave Lett. 9 (2) (1999) 54e56.

[39] D.M. Sullivan, A simplified pml for use with the fdtd method, IEEE Microw.
Guid. Wave Lett. 6 (2) (1996) 97.

[40] C.A. Balanis, Advanced Engineering Electromagnetics, John Wiley& Sons, 1999.
[41] J.W.T.D.S. Ramo, Fields and Waves in Communication Electronics, John Wiley

& Sons, 1994.

[42] E.J. Rothwell, J.L. Frasch, S.M. Ellison, P. Chahal, R.O. Ouedraogo, Analysis of the
nicolson-ross-weir method for characterizing the electromagnetic properties
of engineered materials, Prog. Electromagn. Res. 157 (2016) 31e47.
[43] A. Surowiec, S. Stuchly, L. Eidus, A. Swarup, In vitro dielectric properties of

human tissues at radiofrequencies, Phys. Med. Biol. 32 (5) (1987) 615.
[44] H. Permana, Q. Fang, S.-Y. Lee, A microstrip antenna designed for implantable

body sensor network, in: 2013 1st International Conference on Orange
Technologies (ICOT), IEEE, 2013, pp. 103e106.

[45] A.J. Johansson, Wireless Communication with Medical Implants: Antennas
and Propagation, PhD thesis, Lund University, 2004.

[46] J.-M. Jin, Theory and Computation of Electromagnetic Fields, John Wiley&
Sons, 2011.

</div>

<!--links-->
<a href=' /><a href=' />

Tài liệu University Oars Being a Critical Enquiry Into the After Health of the Men Who Rowed in the Oxford and Cambridge Boat-Race, from the Year 1829 to 1869, Based on the Personal Experience of the Rowers Themselves pdf

• 419
• 542
• 0