An ADE-TLM Algorithm for Modeling Wave Propagation in Biological Tissues with Debye Dispersion
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Abstract
In this paper we present a Transmission Line Matrix (TLM) algorithm for the simulation of electromagnetic wave interaction with a Debye dispersive medium. This new formulation is based on the use of the polarization currents in the medium. The auxiliary differential equation (ADE) method is considered to deal with dispersion after the classical discretization. The accuracy and efficiency of this approach were tested on 1D Debye medium by calculating the reflection coefficient on an air-dielectric interface. The potential of the developed algorithm to model the existence of tumors in a human breast is also demonstrated. The obtained results compared with the analytic model show a good agreement. The number of operations needed for each iteration has been reduced, hence the computational time in comparison with time convolution techniques, while maintaining a comparable numerical accuracy.
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References
D. F. Kelley and R. J. Luebbers, "Piecewise linear re-cursive convolution for dispersive media using FDTD",IEEE Transactions on Antennas and Propagation,vol. 44, no. 6, pp. 792-797, Jun. 1996.
M. Feliziani, S. Cruciani, V. De Santis, and F. Maradei, "Fd2td analysis of electromagnetic field propagation in multipole debye media with and with-out convolution", Progress In Electromagnetic Re-search, vol. 42, pp. 181-205, 2012.
V. Demir, A. Z. Elsherbeni, and E. Arvas, "FDTD formulation for dispersive chiral media using the z transform method",IEEE Transactions on Antennas and Propagation, vol. 53, no. 10, pp. 3374-3384, Oct. 2005.
D. M. Sullivan, "Frequency-dependent fdtd methods using Z transforms", IEEE Transactions on Antennas and Propagation, vol. 40, no. 10, pp. 1223- 1230, Oct. 1992.
M. Okoniewski, M. Mrozowski, and M. Stuchly, "Simple treatment of multi-term dispersion in FDTD", IEEE Microwave and Guided Wave Letters, vol. 7, no. 5, pp. 121-123, 1997.
W.-J. Chen and J. Tang, "High-order fdtd with exponential time differencing algorithm for modeling wave propagation in debye dispersive materials", Progress In Electromagnetics Research, vol. 77, pp. 103-107, 2018.
T. Kashiwa and I. Fukai, "A treatment by the FDTD method of the dispersive characteristics associated with electronic polarization",Microwave and Optical Technology Letters, vol. 3, no. 6, pp. 203-205, 1990.
T. Kashiwa, Y. Ohtomo, and I. Fukai," A finite difference time-domain formulation for transient propagation in dispersive media associated with Cole-Cole's circular arc law",Microwave and Optical Technology Letters, vol. 3, no. 12, pp. 416-419, 1990.
P. M. Goorjian and A. Taflove, "Direct time integration of maxwell's equations in nonlinear dispersive media for propagation and scattering of femtosecond electromagnetic solitons", Opt. Lett., vol. 17, no. 3, pp. 180- 182, Feb. 1992.
M. Fujii, M. Tahara, I. Sakagami, W. Freude, and P. Russer, "High-order FDTD and auxiliary differential equation formulation of optical pulse propagation in 2-d kerr and raman nonlinear dispersive media", IEEE Journal of Quantum Electronics, vol. 40, no. 2, pp. 175-182, 2004.
K. Chun, H. Kim, H. Kim, and Y. Chung, "PLRC and ade implementations of drude-critical point dispersive model for the FDTD method", Progress In Electromagnetics Research, vol. 135, pp. 373-390, 2013.
L. R. de Menezes andW. J. Hoefer," Modelling non linear dispersive media in 2D TLM, in 1994 24th European Microwave Conference", IEEE, vol. 2, 1994, pp. 1739-1744.
C. Smartt and C. Christopoulos, "Modelling nonlinear and dispersive propagation problems by using the TLM method",IEE Proceedings- Microwaves, Antennas and Propagation, vol. 145, no. 3, pp. 193-200, 1998.
I. Barba, A. Cabeceira, J. Represa, M. Panizo, and C. Pereira, "Modeling dispersive dielectrics for the 2D TLM method",IEEE microwave and guided wave letters, vol. 6, no. 4, pp. 174-176, 1996.
I. Barba, A. Cabeceira, M. Panizo, and J. Represa," Modelling dispersive dielectrics in TLM method",International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, vol. 14, no. 1, pp. 15-30, 2001.
T. Wuren, T. Takai, M. Fujii, and I. Sakagami, "Effective 2-debye-pole FDTD model of electromagnetic interaction between whole human body and UWB radiation", IEEE Microwave and Wireless Components Letters, vol. 17, no. 7, pp. 483-485, 2007.
F. Krewer, F. Morgan, and M. O'Halloran, "Development of accurate multi-pole debye functions for electromagnetic tissue modelling using a genetic algorithm",Progress In Electromagnetics Research, vol. 43, pp. 137-147, 2013.
A. J. Fitzgerald, E. Pickwell-MacPherson, and V. P.Wallace," Use of finite difference time domain simulations and Debye theory for modelling the terahertz reflection response of normal and tumour breast tissue", PLoS One, vol. 9, no. 7, e99291, 2014.
A. Fhager, M. Gustafsson, and S. Nordebo," Image reconstruction in microwave tomography using a dielectric Debye model",IEEE Transactions on Biomedical Engineering, vol. 59, no. 1, pp. 156-166, 2012.
A. A. Khamzin, R. Nigmatullin, and I. I. Popov, "Microscopic model of a non-debye dielectric relaxation: The Cole-Cole law and its generalization", Theoretical and Mathematical Physics, vol. 173, no. 2, pp. 1604-1619, 2012.
H. H. Abdullah, H. Elsadek, H. ElDeeb, and N.Bagherzadeh," Fractional derivatives based scheme for fdtd modeling of n-th-order Cole-Cole dispersive media", IEEE Antennas and Wireless Propagation Letters, vol. 11, pp. 281-284, 2012.
I. T. Rekanos and T. V. Yioultsis, "Approximation of gruÌ'Lnwald-letnikov fractional derivative for fdtd modeling of Cole-Cole media",IEEE Transactions on magnetics, vol. 50, no. 2, pp. 181-184, 2014.
M. Lazebnik, M. Okoniewski, J. H. Booske, and S. C. Hagness, "Highly accurate debye models for normal and malignant breast tissue dielectric properties at microwave frequencies",IEEE microwave and wireless components letters, vol. 17, no. 12, pp. 822-824, 2007.
P. Debye, Chemical catalog in. New York, 1929.
M. I. Yaich and M. Khalladi, "The far-zone scattering calculation of frequency-dependent materials objects using the TLM method", IEEE Transactions on Antennas and Propagation, vol. 50, no. 11, pp. 1605-1608, Nov. 2002.
R. M. Hill, L. A. Dissado, "Debye and non Debye relaxation",Journal of Physics C: Solid State Physics, vol. 18, no. 19, pp. 3829-3836, Jul. 1985.
C. Kyungwon, K. Huioon,K. Hyounggyu, C. Youngjoo,"PLRC and ADE implementations of Drude-critical point dispersive model for the FDTD method"Progress In Electromagnetics Research, vol 135, pp. 373-390, 2013.
H. B. Lim, N. T. T. Nhung, E.-P. Li, and N. D. Thang, "Confocal microwave imaging for breast cancer detection: Delay-multiply-and-sum image reconstruction algorithm", IEEE Transactions on Biomedical Engineering, vol. 55, no. 6, pp. 1697-1704, 2008.
D. Byrne, M. O'Halloran, M. Glavin, and E. Jones, "Data independent radar beamforming algorithms for breast cancer detection", Progress In Electromag- netics Research, vol. 107, pp. 331-348, 2010.
S. Kobayashi, Y. Tanaka, Y. Baba, T. Tsuboi, and S. Okabe," Computation of lightning electromag- netic pulses using a hybrid constrained interpolation profile and transmission line modeling method", IEEE Transactions on Electromagnetic Compatibility, vol. 59, no. 6, pp 1958-1966, Dec. 2017.
K. Mounirh, S. El Adraoui, Y. Ekdiha, M. Iben Yaich, and M. Khalladi, "Modeling of dispersive chiral media using the ADE-TLM method",Progress In Electromagnetics Research, vol. 64, pp. 157-166, 2018.
M. I. Yaich, M .Kanjaa, S. E.Adraoui, K. Mounirh, and M. Khalladi, "An unsplit formulation of the 3D-PML absorbing boundary conditions for TLM method in time domain", in 2018 6th International Conference on Multimedia Computing and Systems (ICMCS) , pp. 1-5, May 2018.
M. P.Robinson,I. D. Flintoft, L. Dawson,J. Clegg ,J. G. Truscott , X.Zhu, Application of resonant cavity perturbation to in vivo segmental hydration measurement. Measurement Science and Technology, 21(1), 015804, 2009.
D. C. Garrett and E. C. Fear, "Feasibility Study of Hydration Monitoring Using Microwaves-Part 1: A Model of Microwave Property ChangesWith Dehydration," in IEEE Journal of Electromagnetics, RF and Microwaves in Medicine and Biology, vol. 3, no. 4, pp. 292-299, Dec. 2019.
E. C. Fear, X. Li, S. C. Hagness, and M. A. Stuchly, "Confocal microwave imaging for breast cancer detection: Localization of tumors in three dimensions", IEEE Transactions on Biomedical Engineering, vol. 49, no. 8, pp. 812-822, Aug. 2002.