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.

Journal of Science: Advanced Materials and Devices (2020) 134e141 Contents lists available at ScienceDirect Journal of Science: Advanced Materials and Devices journal homepage: www.elsevier.com/locate/jsamd 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 a b s t r a c t Article history: Received December 2019 Received in revised form February 2020 Accepted 16 February 2020 Available online 26 February 2020 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 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 evaluation 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/) Keywords: FDTD NRW MICS Phantom 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 by fitting 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 * 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 Present Address: Department of ECE, National Institute of Technology Srinagar, Hazratbal Srinagar, 190006, Jammu and Kashmir, India 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 equivalent 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 frequency 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 of ð3NÞ2 and the computation time required is of the order of 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 (http://creativecommons.org/licenses/by/4.0/) M.M Rahman, G.M Rather / Journal of Science: Advanced Materials and Devices (2020) 134e141 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 Nlog2 N, 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 frequencies 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 electrical 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 electric field distribution 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 threelayer 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 pacemaker applications The pacemaker is most often placed subcutaneously between the fat and pectoral muscles under the collar bone So, the human chest in this application can be well approximated by a three-layer planar model consisting of muscle, fat and skin as shown in Fig 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: section gives a brief explanation about the dielectric properties of biological materials; section describes the proposed methodology while section contains the results Lastly, section gives the conclusion of the paper 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 135 material [22] The dielectric properties of a material are a measure of how electromagnetic waves interact with its constituent elements 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 frequency-dependent and is given by: 00 f ị ẳ f ị f ị (1) f ị ẳ ε0 εr ðf Þ (2) ε0 is the permittivity of free space, εr is 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 εr ðf Þ À sðf Þ uε0 (3) where s is the electrical conductivity and u is the angular frequency of the field Moreover, the dielectric loss factor can be parametrized in terms of the loss tangent given by equation (4): tan d ẳ 00 f ị ðf Þ (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 in Table [25e27] The fat layer thickness has been varied from 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 Telecommunications 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 Methodology The determination of equivalent electrical properties of a human tissue requires an understanding of the multi-layered Table Dielectric Properties of Human Tissue at 403.5 MHz Fig Three-layer diagram of human chest Tissue Thickness (mm) 403.5 MHz εr sðs =mÞ Dry Skin Wet Skin Fat Muscle 3 10 20 46.706 49.842 5.5783 57.1 0.68956 0.6702 0.04117 0.79721 136 M.M Rahman, G.M Rather / Journal of Science: Advanced Materials and Devices (2020) 134e141 inversion problem considering that biological tissues have frequency dependent dielectric properties and are multi-layered Therefore, all the layers of human tissue need to be taken into account 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 transmission ðS21 Þ and reflection ðS11 Þ 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 ðεrequivalent ðf Þ; sequivalent ðf 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 method first 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 dimensions and in time Maxwell's equations for dispersive materials can be written as: ! ! D H ẳ sE ỵ ! ! vB D E ¼ À vt ! vD vt (5) (6) ! ! where E is the electric field intensity, H is the magnetic field in! tensity, s is the conductivity of the medium, D is the magnetic flux ! density, B is the electric flux density, respectively given by: ! ! B ¼ m0 H (7) ! ! D ¼ ε0 εr E (8) where m0 is the permeability of free space, ε0 is the permittivity of free space, εr is the relative permittivity of the medium In this ƒ! ƒ! paper, Transverse Magnetic mode with Ex and Hy 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 These field components are updated in the leapfrog scheme using the finite 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 frequencydomain 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 essential in any numerical equation solver because, if not taken care of, it causes unbounded growth of the computed results To ensure numerical stability, for given cell size (DZ), Taflove [33,38] suggested the size of the time step (Dt) to be restricted as: Dt ¼ DZ 2C0 (9) where C0 is 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, 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 the fields 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 N ỵ planar regions separated by N interfaces The multilayer problem thus looks like Fig As seen in the figure, in each layer, there are both transmitted and reflected waves, except for the last layer where no reflection takes place Therefore, the wave impedance as seen from the Nth interface is equal to the characteristic impedance of the N ỵ 1ịth layer i.e ZLN ẳ ZNỵ1 (10) The recursive relation for calculating wave impedances at each interface is given by ZLnÀ1 ¼ Zn   ỵ Rn exp2jbn tn ịị À ðRn  expðÀ2jbn tn ÞÞ (11) Where n ¼ 2; 3; 4; …N; ZL is the wave impedance at each interface, ‘Z’ is the characteristic impedance of the medium, b is the propagation constant of the medium, ‘t’ is the thickness of the layer and ‘R’ is the reflection coefficient given by: Rn ¼ ZLn À Zn ZLn þ Zn (12) where n ¼ 1; 2:::N: R1 will 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:  En ¼ EnÀ1  ỵ Rn1 expjbn tn ị ỵ Rn expjbn tn ịịị (13) where n ẳ 2; 3; N: Therefore, the transmitted electric field and hence the equivalent transmission coefficient is given by: Fig Graphical illustration of N- Layered dielectric media M.M Rahman, G.M Rather / Journal of Science: Advanced Materials and Devices (2020) 134e141 ENỵ1 ẳ EN ẵ1 ỵ RN ENỵ1 E1 Tẳ (14) (15) where E1 is the electric field strength in the first layer and T is the equivalent transmission coefficient of the structure These formulations 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 transmission 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 S11 and S21 acquired from the FDTD simulation as described above The reflection coefficient is expressed as: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi G ¼ XH X À (16) where, X¼ S211 S211 ỵ 2S11 (17) The transmission coefcient, T, is stated as: T¼ 137 S11 À S11 À G GS11 ỵ S11 ị (18) From the above equations, the complex permittivity and permeability of the sample can be calculated as:  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 dispersive 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 are finely 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 instability as already discussed in equation (9) The thicknesses of different layers are equal to their biological thicknesses for an average male human adult Fig 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 electric fields at specified positions in the FDTD sample space using Fast Fourier Transform (FFT) as:  ε¼ G1 À G G0 ỵ G mẳ G1 ỵ G G0 À G  Fig Planar human chest model Eref ðf Þ Einc ðf Þ (19) S11 ðf Þ ¼ (20) Eref ðf Þ ¼ Etotal ðf Þ À Einc ðf Þ (23)  (24) where,   G1 ¼ log G0 ¼ j T d 2pf C0 (21) (22) where C0 is the velocity of the electromagnetic wave in free space, d is the thickness of the sample and f is the frequency of operation 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 frequencydependent 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 in Fig Fig Permittivity (ε) (solid line) and conductivity (s) (dotted line) of the layer slab (Fat, muscle and skin) in the simulation space 138 M.M Rahman, G.M Rather / Journal of Science: Advanced Materials and Devices (2020) 134e141 Fig Incident Electric field without medium (a)Einc , (b) Magnitude of Einc S21 f ị ẳ Etrans ðf Þ Einc ðf Þ (25) where Etotal ðf Þ is the total electric field incident with the medium, Etrans ðf Þ is the transmitted electric field, Einc ðf Þ is the incident electric field without a medium (i.e only free space) and Eref ðf Þ is the reflected electric field The time and frequency domain representation of these electric fields for the MICS band are depicted in Figs 5e11 Fig 5a gives Einc i.e the incident electric field without medium, the magnitude of which is illustrated in Fig 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 Einc and 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, while Fig 8a and b give its frequency-domain representation in the presence of the medium Similarly, Fig 9a and b demonstrate the time domain electric field and its magnitude incident in the presence of the medium i.e the human layered tissue, respectively This gives the total electric field incident on the medium (Etotal ) The FFT of the same is given by Fig 10a and b The reflected wave is then calculated from equation (24) and its FFT and absolute value are given in Fig 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 in Table 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 section 3.2 The results for the same are also depicted in Table 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 in Table Furthermore, the values for εrequivalent and sequivalent , as calculated from equations (2) and (3) are also provided in the same table The equivalent relative 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 in Table The dielectric loss factor of the same is 0.6 After calculating the equivalent dielectric properties of Fig FFT of Incident Electric field without medium (a)Einc , (b) Magnitude of Einc M.M Rahman, G.M Rather / Journal of Science: Advanced Materials and Devices (2020) 134e141 139 Fig Transmitted Electric field with medium (a)Etrans , (b) Magnitude of Etrans Fig FFT of Transmitted Electric field with medium (a)Etrans , (b) Magnitude of Etrans the human chest, the thickness of the fat layer is varied The procedure followed is the same as above The resultant values are given in Table 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 The ε 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 conductivity 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 Incident Electric field with medium (a)Etotal , (b) Magnitude of Etotal 140 M.M Rahman, G.M Rather / Journal of Science: Advanced Materials and Devices (2020) 134e141 Fig 10 FFT of Incident Electric field with medium (a)Etotal , (b) Magnitude of Etotal Fig 11 FFT of the reflected wave (a)Eref , (b) Magnitude of Eref Table S-Parameter comparison using FDTD and Analytical method Model FDTD Analytical S11 S21 rS11r 0.87 0.76 Dermatological feature Dry skin Wet skin :S11 176.4 À175.3 S11 rS21r 0.216 0.089 :S21 À86 140 S21 :S11 0.95 0.79 rS11r 178.3 À177.1 rS21r 0.29 0.092 :S21 À85 142 Table 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 ε 10 15 20 25 0.882 0.87 0.876 0.871 0.862 178.3 177.8 177.5 177.21 177.02 0.208 0.216 0.224 0.233 0.241 À79.3 ¡84.78 À90.75 À97.57 À105.21 47.99 42.56 38.75 35.825 33.424 25.217 18.07 12.604 7.684 3.342 00 seq s/m tan d loss 0.565 0.405 0.282 0.1723 0.0749 0.525 0.424 0.325 0.2144 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 medical devices In addition, phantoms are also used for investigating 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 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- M.M Rahman, G.M Rather / Journal of Science: Advanced Materials and Devices (2020) 134e141 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 electrical 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 permitivitty 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, applications 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 2.4ghz 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 (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 (1) (1987) 29e36 [9] R.F Harrington, The method of moments in electromagnetics, J Electromagn Waves Appl (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 absorption 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 141 [16] K.K Karkkainen, A.H Sihvola, K.I Nikoskinen, Effective permittivity of mixtures: 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 highpermittivity phantom for eit, IEEE Trans Biomed Eng 55 (11) (2008) 2601e2607 [18] K.-P Hwang, A.C Cangellaris, Effective permittivities for second-order accurate 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 imaging 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 materials: a critical review, Crit Rev Biomed Eng 17 (1) (1989) 25e104 [23] R Pethig, Dielectric and electrical properties of biological materials, J Bioelectr (2) (1985) viieix [24] W Tinga, S.O Nelson, Dielectric properties of materials for microwave processingetabulated, J Microw Power (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 (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 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 propagation, IEEE Microw Guid Wave Lett (2) (1999) 54e56 [39] D.M Sullivan, A simplified pml for use with the fdtd method, IEEE Microw Guid Wave Lett (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 [47] U.S Inan, R.A Marshall, Numerical Electromagnetics: The FDTD Method, Cambridge University Press, 2011  ... magnitudes and phases of S11 and S21 in the MICS band (402e405) MHz) are calculated from equations (23) and (25) and are illustrated in Table This frequency band is so small that all the S-parameters... 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... 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,