volume | PIER Journals

Abstract

In this paper, an auxiliary differential equation (ADE) transmission line method (TLM) is proposed for broadband modeling of electromagnetic (EM) wave propagation in biological tissues with the Cole-Cole dispersion Model. The fractional derivative problem is surmounted by assuming a linear behavior of the polarization current when the time discretization is short enough. The polarization current density is approached using Lagrange extrapolation polynomial, and the fractional derivation is obtained according to Riemann definition of a fractional α-order derivative. Reflection coefficients at an air/muscle and air/fat tissues interfaces simulated in a 1-D domain are found in good agreement with those obtained from the analytic model over a broad frequency range, demonstrating the validity of the proposed approach.

1. Martellosio, A., M. Pasian, M. Bozzi, L. Perregrini, A. Mazzanti, F. Svelto, P. E. Summers, G. Renne, and M. Bellomi, "0.5–50 GHz dielectric characterisation of breast cancer tissues," Electronics Letters, Vol. 51, No. 13, 974-975, 2015.
doi:10.1049/el.2015.1199

2. Gavazzi, S., P. Limone, G. De Rosa, F. Molinari, and G. Vecchi, "Comparison of microwave dielectric properties of human normal, benign and malignant thyroid tissues obtained from surgeries: A preliminary study," Biomedical Physics & Engineering Express, Vol. 4, No. 4, 047 003, 2018.
doi:10.1088/2057-1976/aa9f77

3. Ruvio, G., J. Eaton-Evans, A. Shahzad, and M. O’Halloran, "Numerical evaluation of microwave thermal ablation to treat small adrenocortical masses," International Journal of RF and Microwave Computer-Aided Engineering, Vol. 28, No. 3, e21236, 2018.
doi:10.1002/mmce.21236

4. Ley, S., S. Schilling, O. Fiser, J. Vrba, J. Sachs, and M. Helbig, "Ultra-wideband temperature dependent dielectric spectroscopy of porcine tissue and blood in the microwave frequency range," Sensors, Vol. 19, No. 7, 1707, 2019.
doi:10.3390/s19071707

5. Chakarothai, J., K. Wake, and S. Watanabe, "Convergence of a single-frequency FDTD solution in numerical dosimetry," IEEE Transactions on Microwave Theory and Techniques, Vol. 64, No. 3, 707-714, 2016.

6. Debye, P., "Part i. Dielectric constant. energy absorption in dielectrics with polar molecules," Transactions of the Faraday Society, Vol. 30, 679-684, 1934.
doi:10.1039/tf9343000679

7. Cole, K. S. and R. H. Cole, "Dispersion and absorption in dielectrics i. Alternating current characteristics," The Journal of Chemical Physics, Vol. 9, No. 4, 341-351, 1941.
doi:10.1063/1.1750906

8. Rekanos, I. T. and T. V. Yioultsis, "Approximation of Gr¨unwald-Letnikov fractional derivative for FDTD modeling of Cole-Cole media," IEEE Transactions on Magnetics, Vol. 50, No. 2, 181-184, 2014.
doi:10.1109/TMAG.2013.2281998

9. Guo, B., J. Li, and H. Zmuda, "A new FDTD formulation for wave propagation in biological media with Cole-Cole model," IEEE Microwave and Wireless Components Letters, Vol. 16, No. 12, 633-635, 2006.
doi:10.1109/LMWC.2006.885583

10. Rekanos, I. T. and T. G. Papadopoulos, "An auxiliary differential equation method for FDTD modeling of wave propagation in Cole-Cole dispersive media," IEEE Transactions on Antennas and Propagation, Vol. 58, No. 11, 3666-3674, 2010.
doi:10.1109/TAP.2010.2071365

11. Barba, I., A. C. L. 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, 15-30, 2001.
doi:10.1002/1099-1204(200101/02)14:1<15::AID-JNM393>3.0.CO;2-J

12. Mounirh, K., 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 M, Vol. 64, 157-166, 2018.
doi:10.2528/PIERM17110103

13. Samko, S. G., A. A. Kilbas, O. I. Marichev, et al. Fractional Integrals and Derivatives, Vol. 1993, Gordon and Breach Science Publishers, Yverdon Yverdon-les-Bains, Switzerland, 1993.

14. "Chapter 8: Techniques in the fractional calculus," The Fractional Calculus, Ser. Mathematics in Science and Engineering, K. B. Oldham and J. Spanier (eds.), Vol. 111, 133–160, Elsevier, 1974.

15. Engheta, N., "On the role of fractional calculus in electromagnetic theory," IEEE Antennas and Propagation Magazine, Vol. 39, No. 4, 35-46, Aug. 1997.
doi:10.1109/74.632994

16. Engheta, N., "On fractional calculus and fractional multipoles in electromagnetism," IEEE Transactions on Antennas and Propagation, Vol. 44, No. 4, 554-566, Apr. 1996.
doi:10.1109/8.489308

17. Wharmby, A. W. and R. L. Bagley, "The application of the fractional calculus model for dispersion and absorption in dielectrics in terahertz waves," International Journal of Engineering Science, Vol. 93, 1-12, 2015.
doi:10.1016/j.ijengsci.2015.04.002

18. Jin, H. and R. Vahldieck, "Direct derivations of TLM symmetrical condensed node and hybrid symmetrical condensed node from Maxwell’s equations using centered differencing and averaging," IEEE Transactions on Microwave Theory and Techniques, Vol. 42, No. 12, 2554-2561, Dec. 1994.
doi:10.1109/22.339796

19. Christopoulos, C., The Transmission-Line Modeling (TLM) Method in Electromagnetics, Morgan & Claypool, 2006.

20. Cabeceira, A. C. L., I. Barba, A. Grande, and J. Represa, "A 2D-TLM model for electromagnetic wave propagation in chiral media," Microwave and Optical Technology Letters, Vol. 46, No. 2, 180-182, 2005.
doi:10.1002/mop.20937

21. Yaich, M. I. 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, 1605-1608, Nov. 2002.
doi:10.1109/TAP.2002.803963

22. Yaich, M. I., 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," 2018 6th International Conference on Multimedia Computing and Systems (ICMCS), 1-5, May 2018.

23. Taflove, A. and S. C. Hagness, Computational Electrodynamics: The Finite-difference Time-domain Method, Artech House, 2005.

24. Juntunen, J. S. and T. D. Tsiboukis, "Reduction of numerical dispersion in fdtd method through artificial anisotropy," IEEE Transactions on Microwave Theory and Techniques, Vol. 48, No. 4, 582-588, 2000.
doi:10.1109/22.842030

25. Chakrabarti, A., et al. "Derivation of the errors involved in interpolation and their application to numerical quadrature formulae," Journal of Computational and Applied Mathematics, Vol. 92, No. 1, 59-68, 1998.
doi:10.1016/S0377-0427(98)00045-4

Dr. Mohammed Kanjaa

Dr. Khalid Mounirh

Dr. Soufiane El Adraoui

Dr. Otman El Mrabet

Prof. Mohsine Khalladi