Research Article
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Year 2023, , 105 - 119, 21.12.2023
https://doi.org/10.33187/jmsm.1126660

Abstract

References

  • [1] F. Bray, M. Laversanne, E. Weiderpass, I. Soerjomataram, The ever-increasing importance of cancer as a leading cause of premature death worldwide, Cancer, 127 (16) (2021), 3029-3030.
  • [2] W. Organization, Global Health Estimates 2019: deaths by cause, age, sex, by country and by region 2000–2019, WHO, (2020).
  • [3] H. Sung, J. Ferlay, R. Siegel, M. Laversanne, I. Soerjomataram, A. Jemal, F. Bray, Global cancer statistics 2020: GLOBOCAN estimates of incidence and mortality worldwide for 36 cancers in 185 countries, CA: A Can. J. Clinc., 71 (3) (2021), 209-249 .
  • [4] M. Lu, X. Xiao, G. Liu, H. Lu, Microwave breast tumor localization using wavelet feature extraction and genetic algorithm-neural network, Med. Phys., 48 (10) (2021), 6080-6093.
  • [5] E. Bond, X. Li, S. Hagness, B. Van Veen, Microwave imaging via space-time beamforming for early detection of breast cancer, IEEE Trans. Anten. Prop., 51 (8) (2003), 1690-1705.
  • [6] M. Lazebnik, M. Okoniewski, J. Booske, S. Hagness, Highly accurate Debye models for normal and malignant breast tissue dielectric properties at microwave frequencies, IEEE Mic. Wirel. Comp. Lett., 17 (12) (2007), 822-824.
  • [7] N. Nikolova, Microwave imaging for breast cancer, IEEE Mic. Mag., 12 (7) (2011), 78-94.
  • [8] R. Conceicao, J. Mohr, M. OHalloran, (Eds.), An Introduction to Microwave Imaging for Breast Cancer Detection, Basel, Switzerland, Springer International Publishing, 2016.
  • [9] S. Kwon, S. Lee, Recent advances in microwave imaging for breast cancer detection, Internat. J. Biomed. Imaging, (2016), 1-26.
  • [10] S. Davis, B. Van Veen, S. Hagness, F Kelcz, Breast tumor characterization based on ultrawideband microwave backscatter, IEEE Trans. Biomed. Engrg., 55 (1) (2007), 237-246.
  • [11] M. Zhao, J. Shea, S. Hagness, D. Weide, B. Van Veen, T. Varghese, Numerical study of microwave scattering in breast tissue via coupled dielectric and elastic contrasts, IEEE Anten. Wirer. Prop. Lett., 7 (2008), 247-250.
  • [12] E. Zastrow, S. Davis, M. Lazebnik, F. Kelcz, B. Van Veen, S. Hagness, Development of anatomically realistic numerical breast phantoms with accurate dielectric properties for modeling microwave interactions with the human breast, IEEE Trans. Biomed. Eng., 55 (12) (2008), 2792-2800.
  • [13] R. Torrealba-Melendez, J. Olvera-Cervantes, A. Corona-Ch´avez, UWB microwave radar imaging for detection and discrimination of benign and malignant breast tumors using circularly polarized antennas, (IEEE WAMICON 2014), (2014), 1-3.
  • [14] K. Noritake, S. Kidera, Accurate breast surface imaging method with FDTD-based waveform correction for microwave mammography, 2017 International Symposium On Antennas And Propagation (ISAP 2017), (2017), 1-2.
  • [15] A. Fhager, M. Persson, Reconstrunction strategies for microwave imaging of breast; reconstructions constrained to the breast domain, IEEE MTT-S International Microwave Bio Conference (IMBIOC 2017), (2017), 1-3.
  • [16] L. Wang, Microwave sensors for breast cancer detection, Sensors, 18 (2) (2018), 655.
  • [17] H. El Misilmani, T. Naous, S. Al Khatib, K. Kabalan, A survey on antenna designs for breast cancer detection using microwave imaging, IEEE Access, 8 (2020), 102570-102594. [18] M. Ahadi, J. Nourinia, C. Ghobadi, Square monopole antenna application in localization of tumors in three dimensions by confocal microwave imaging for breast cancer detection: experimental measurement, Wirel. Pers. Commun., 116 (2021), 2391-2409.
  • [19] B.Moloney, D. O’Loughlin, S. Abd Elwahab, M. Kerin, Breast cancer detection—A synopsis of conventional modalities and the potential role of microwave imaging, Diagnostics, 10 (2) (2020), 103.
  • [20] D. Carvalho, A. Aragao, A. Ferrari, B.Sanches, W. Noije, Software-defined radio assessment for microwave imaging breast cancer detection, 2020 IEEE Nordic Circuits and Systems Conference (NorCAS 2020), (2020), 1-6.
  • [21] D. Godinho, J. Felicio, C. Fernandes, R. Conceicao, Experimental evaluation of an axillary microwave imaging system to aid breast cancer staging, IEEE J. Elect., RF Mic. Med. Biology, 6 (1) (2021), 68-76.
  • [22] C. Balanis, Advanced Engineering Electromagnetics, John Wiley and Sons, 2012. [23] İ. Ünal, B. Turetken, U. Bulus, C. Canbay, Analysis of the electromagnetic field scattered by a spherical breast tumour model, 2013 International Symposium On Electromagnetic Theory, (2013), 574-577.
  • [24] A.Taflove, S. Hagness, M. Piket-May, Computational electromagnetics: the finite-difference time-domain method, Elec. Eng. Hand., 3 (15) (2005), 629-670.
  • [25] D. Sullivan, Electromagnetic Simulation Using the FDTD Method, John Wiley and Sons, 2013.
  • [26] K. Kunz, R. Luebbers, The Finite Difference Time Domain Method for Electromagnetics, CRC Press,1993.
  • [27] A. Elsherbeni, V. Demir, The Finite-Difference Time-Domain Method for Electromagnetics with MATLABR Simulations, IET, 2015.
  • [28] T. Namiki, A new FDTD algorithm based on alternating-direction implicit method, IEEE Trans. Mic. Theory Tech., 47 (10) (1999), 2003-2007.
  • [29] T.Namiki, 3-D ADI-FDTD method-unconditionally stable time-domain algorithm for solving full vector Maxwell’s equations, IEEE Trans. Mic. Theory Tech., 48 (10) (2000), 1743-1748.
  • [30] X. Wang, J. Gao, Z. Chen, F. Teixeira, Unconditionally stable one-step leapfrog ADI-FDTD for dispersive media, IEEE Trans. Antenn. Prop., 67 (4) (2019), 2829-2834.
  • [31] D. Y. Heh, E. L. Tan, Unconditionally stable multiple one-dimensional ADI-FDTD method for coupled transmission lines, IEEE Trans. Antenn. Prop., 66 (12) (2018), 7488-7492.
  • [32] E. L. Tan, D. Y. Heh, Multiple 1-D fundamental ADI-FDTD method for coupled transmission lines on mobile devices, IEEE J. Multisc. Multiph. Comp. Tech., 4 (2019) 198-206.
  • [33] B. Zou, S. Liu, L. Zhang, S. Ren, Efficient one-step leapfrog ADI-FDTD for far-field scattering calculation of lossy media, Mic. Opt. Tech. Lett. 62 (5) (2020), 1876-1881.
  • [34] G. Mur, Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations, IEEE Trans. Elec. Comput., 4 (1981), 377-382.
  • [35] J. Berenger, A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys., 114 (2) (1994), 185-200.
  • [36] J. Berenger, Perfectly matched layer for the FDTD solution of wave-structure interaction problems, IEEE Trans. Antenn. Prop., 44 (1) (1996), 110-117.
  • [37] E. Zastrow, S. Davis, M. Lazebnik, F. Kelcz, B. Van Veen, S. Hagness, Development of anatomically realistic numerical breast phantoms with accurate dielectric properties for modeling microwave interactions with the human breast, IEEE Trans. Biomed. Engrg., 55 (12) (2008), 2792-2800.
  • [38] E. Fear, M. Stuchly, Microwave detection of breast cancer, IEEE Trans. Mic. Theory Tech., 48 (11) (2000), 1854-1863.
  • [39] S. Hagness, A. Taflove, J. Bridges, Three-dimensional FDTD analysis of a pulsed microwave confocal system for breast cancer detection: Design of an antenna-array element, IEEE Trans. Antenn. Prop., 47 (5) (1999), 783-791.
  • [40] M. Lazebnik, C. Watkins, S. Hagness, J. Booske, D. Popovic, L. McCartney, M. Okoniewski, M. Lindstrom, T. Breslin, J. Harter, The dielectric properties of normal and malignant breast tissue at microwave frequencies: analysis, conclusions, and implications from the wisconsin/calgary study, 2007 IEEE Antennas And Propagation Society International Symposium (2007), 2172-2175.

Implementation of the Hybrid ADI-FDTD Scheme to Maxwell Equation for Mathematical Modeling of Breast Tumor

Year 2023, , 105 - 119, 21.12.2023
https://doi.org/10.33187/jmsm.1126660

Abstract

Breast cancer is the most common cancer in women, and non-destructive detection of the tumor is vital. The interaction of electromagnetic waves with breast tissue and the behavior of waves after interaction are used to model tumor detection mathematically. The behavior of electromagnetic waves in a medium is described using Maxwell's equations. Electromagnetic waves propagate according to the electrical properties of a medium. Since the electrical properties of tumor tissue are different from those of normal breast tissue, it is assumed that the tumor is a lossy dielectric sphere, and the breast is a lossy dielectric medium. Under this assumption, Maxwell's equations are used to calculate the scattered field from the tumor. The field scattered by the tumor is different from other tissues because their dielectric properties are different. The location and size of the tumor can be determined by utilizing the difference in scattering from the tissues. While the scattering field from the tumor in spherical geometric form is analytically calculated, it is not analytically possible to calculate the scattering field from the tumor in different geometric shapes. In addition to non-destructive detection of the tumor, an efficient numerical method, the finite difference time domain method (FDTD), is used to simulate the field distribution. After the location of the tumor is determined, the Alternating Direction Implicit (ADI) FDTD method, which gives simulation results by dividing the computation domain into smaller sub-intervals, can be used. Scattered fields are calculated analytically in the geometry where the tumor is in the form of a smooth sphere, and in more complex geometry, the field distributions are successfully obtained with the help of MATLAB using FDTD and ADI-FDTD algorithms.

References

  • [1] F. Bray, M. Laversanne, E. Weiderpass, I. Soerjomataram, The ever-increasing importance of cancer as a leading cause of premature death worldwide, Cancer, 127 (16) (2021), 3029-3030.
  • [2] W. Organization, Global Health Estimates 2019: deaths by cause, age, sex, by country and by region 2000–2019, WHO, (2020).
  • [3] H. Sung, J. Ferlay, R. Siegel, M. Laversanne, I. Soerjomataram, A. Jemal, F. Bray, Global cancer statistics 2020: GLOBOCAN estimates of incidence and mortality worldwide for 36 cancers in 185 countries, CA: A Can. J. Clinc., 71 (3) (2021), 209-249 .
  • [4] M. Lu, X. Xiao, G. Liu, H. Lu, Microwave breast tumor localization using wavelet feature extraction and genetic algorithm-neural network, Med. Phys., 48 (10) (2021), 6080-6093.
  • [5] E. Bond, X. Li, S. Hagness, B. Van Veen, Microwave imaging via space-time beamforming for early detection of breast cancer, IEEE Trans. Anten. Prop., 51 (8) (2003), 1690-1705.
  • [6] M. Lazebnik, M. Okoniewski, J. Booske, S. Hagness, Highly accurate Debye models for normal and malignant breast tissue dielectric properties at microwave frequencies, IEEE Mic. Wirel. Comp. Lett., 17 (12) (2007), 822-824.
  • [7] N. Nikolova, Microwave imaging for breast cancer, IEEE Mic. Mag., 12 (7) (2011), 78-94.
  • [8] R. Conceicao, J. Mohr, M. OHalloran, (Eds.), An Introduction to Microwave Imaging for Breast Cancer Detection, Basel, Switzerland, Springer International Publishing, 2016.
  • [9] S. Kwon, S. Lee, Recent advances in microwave imaging for breast cancer detection, Internat. J. Biomed. Imaging, (2016), 1-26.
  • [10] S. Davis, B. Van Veen, S. Hagness, F Kelcz, Breast tumor characterization based on ultrawideband microwave backscatter, IEEE Trans. Biomed. Engrg., 55 (1) (2007), 237-246.
  • [11] M. Zhao, J. Shea, S. Hagness, D. Weide, B. Van Veen, T. Varghese, Numerical study of microwave scattering in breast tissue via coupled dielectric and elastic contrasts, IEEE Anten. Wirer. Prop. Lett., 7 (2008), 247-250.
  • [12] E. Zastrow, S. Davis, M. Lazebnik, F. Kelcz, B. Van Veen, S. Hagness, Development of anatomically realistic numerical breast phantoms with accurate dielectric properties for modeling microwave interactions with the human breast, IEEE Trans. Biomed. Eng., 55 (12) (2008), 2792-2800.
  • [13] R. Torrealba-Melendez, J. Olvera-Cervantes, A. Corona-Ch´avez, UWB microwave radar imaging for detection and discrimination of benign and malignant breast tumors using circularly polarized antennas, (IEEE WAMICON 2014), (2014), 1-3.
  • [14] K. Noritake, S. Kidera, Accurate breast surface imaging method with FDTD-based waveform correction for microwave mammography, 2017 International Symposium On Antennas And Propagation (ISAP 2017), (2017), 1-2.
  • [15] A. Fhager, M. Persson, Reconstrunction strategies for microwave imaging of breast; reconstructions constrained to the breast domain, IEEE MTT-S International Microwave Bio Conference (IMBIOC 2017), (2017), 1-3.
  • [16] L. Wang, Microwave sensors for breast cancer detection, Sensors, 18 (2) (2018), 655.
  • [17] H. El Misilmani, T. Naous, S. Al Khatib, K. Kabalan, A survey on antenna designs for breast cancer detection using microwave imaging, IEEE Access, 8 (2020), 102570-102594. [18] M. Ahadi, J. Nourinia, C. Ghobadi, Square monopole antenna application in localization of tumors in three dimensions by confocal microwave imaging for breast cancer detection: experimental measurement, Wirel. Pers. Commun., 116 (2021), 2391-2409.
  • [19] B.Moloney, D. O’Loughlin, S. Abd Elwahab, M. Kerin, Breast cancer detection—A synopsis of conventional modalities and the potential role of microwave imaging, Diagnostics, 10 (2) (2020), 103.
  • [20] D. Carvalho, A. Aragao, A. Ferrari, B.Sanches, W. Noije, Software-defined radio assessment for microwave imaging breast cancer detection, 2020 IEEE Nordic Circuits and Systems Conference (NorCAS 2020), (2020), 1-6.
  • [21] D. Godinho, J. Felicio, C. Fernandes, R. Conceicao, Experimental evaluation of an axillary microwave imaging system to aid breast cancer staging, IEEE J. Elect., RF Mic. Med. Biology, 6 (1) (2021), 68-76.
  • [22] C. Balanis, Advanced Engineering Electromagnetics, John Wiley and Sons, 2012. [23] İ. Ünal, B. Turetken, U. Bulus, C. Canbay, Analysis of the electromagnetic field scattered by a spherical breast tumour model, 2013 International Symposium On Electromagnetic Theory, (2013), 574-577.
  • [24] A.Taflove, S. Hagness, M. Piket-May, Computational electromagnetics: the finite-difference time-domain method, Elec. Eng. Hand., 3 (15) (2005), 629-670.
  • [25] D. Sullivan, Electromagnetic Simulation Using the FDTD Method, John Wiley and Sons, 2013.
  • [26] K. Kunz, R. Luebbers, The Finite Difference Time Domain Method for Electromagnetics, CRC Press,1993.
  • [27] A. Elsherbeni, V. Demir, The Finite-Difference Time-Domain Method for Electromagnetics with MATLABR Simulations, IET, 2015.
  • [28] T. Namiki, A new FDTD algorithm based on alternating-direction implicit method, IEEE Trans. Mic. Theory Tech., 47 (10) (1999), 2003-2007.
  • [29] T.Namiki, 3-D ADI-FDTD method-unconditionally stable time-domain algorithm for solving full vector Maxwell’s equations, IEEE Trans. Mic. Theory Tech., 48 (10) (2000), 1743-1748.
  • [30] X. Wang, J. Gao, Z. Chen, F. Teixeira, Unconditionally stable one-step leapfrog ADI-FDTD for dispersive media, IEEE Trans. Antenn. Prop., 67 (4) (2019), 2829-2834.
  • [31] D. Y. Heh, E. L. Tan, Unconditionally stable multiple one-dimensional ADI-FDTD method for coupled transmission lines, IEEE Trans. Antenn. Prop., 66 (12) (2018), 7488-7492.
  • [32] E. L. Tan, D. Y. Heh, Multiple 1-D fundamental ADI-FDTD method for coupled transmission lines on mobile devices, IEEE J. Multisc. Multiph. Comp. Tech., 4 (2019) 198-206.
  • [33] B. Zou, S. Liu, L. Zhang, S. Ren, Efficient one-step leapfrog ADI-FDTD for far-field scattering calculation of lossy media, Mic. Opt. Tech. Lett. 62 (5) (2020), 1876-1881.
  • [34] G. Mur, Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations, IEEE Trans. Elec. Comput., 4 (1981), 377-382.
  • [35] J. Berenger, A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys., 114 (2) (1994), 185-200.
  • [36] J. Berenger, Perfectly matched layer for the FDTD solution of wave-structure interaction problems, IEEE Trans. Antenn. Prop., 44 (1) (1996), 110-117.
  • [37] E. Zastrow, S. Davis, M. Lazebnik, F. Kelcz, B. Van Veen, S. Hagness, Development of anatomically realistic numerical breast phantoms with accurate dielectric properties for modeling microwave interactions with the human breast, IEEE Trans. Biomed. Engrg., 55 (12) (2008), 2792-2800.
  • [38] E. Fear, M. Stuchly, Microwave detection of breast cancer, IEEE Trans. Mic. Theory Tech., 48 (11) (2000), 1854-1863.
  • [39] S. Hagness, A. Taflove, J. Bridges, Three-dimensional FDTD analysis of a pulsed microwave confocal system for breast cancer detection: Design of an antenna-array element, IEEE Trans. Antenn. Prop., 47 (5) (1999), 783-791.
  • [40] M. Lazebnik, C. Watkins, S. Hagness, J. Booske, D. Popovic, L. McCartney, M. Okoniewski, M. Lindstrom, T. Breslin, J. Harter, The dielectric properties of normal and malignant breast tissue at microwave frequencies: analysis, conclusions, and implications from the wisconsin/calgary study, 2007 IEEE Antennas And Propagation Society International Symposium (2007), 2172-2175.
There are 38 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences, Applied Mathematics (Other)
Journal Section Articles
Authors

Ümmü Şahin Şener 0000-0001-9055-8734

Early Pub Date December 7, 2023
Publication Date December 21, 2023
Submission Date June 6, 2022
Acceptance Date June 9, 2023
Published in Issue Year 2023

Cite

APA Şahin Şener, Ü. (2023). Implementation of the Hybrid ADI-FDTD Scheme to Maxwell Equation for Mathematical Modeling of Breast Tumor. Journal of Mathematical Sciences and Modelling, 6(3), 105-119. https://doi.org/10.33187/jmsm.1126660
AMA Şahin Şener Ü. Implementation of the Hybrid ADI-FDTD Scheme to Maxwell Equation for Mathematical Modeling of Breast Tumor. Journal of Mathematical Sciences and Modelling. December 2023;6(3):105-119. doi:10.33187/jmsm.1126660
Chicago Şahin Şener, Ümmü. “Implementation of the Hybrid ADI-FDTD Scheme to Maxwell Equation for Mathematical Modeling of Breast Tumor”. Journal of Mathematical Sciences and Modelling 6, no. 3 (December 2023): 105-19. https://doi.org/10.33187/jmsm.1126660.
EndNote Şahin Şener Ü (December 1, 2023) Implementation of the Hybrid ADI-FDTD Scheme to Maxwell Equation for Mathematical Modeling of Breast Tumor. Journal of Mathematical Sciences and Modelling 6 3 105–119.
IEEE Ü. Şahin Şener, “Implementation of the Hybrid ADI-FDTD Scheme to Maxwell Equation for Mathematical Modeling of Breast Tumor”, Journal of Mathematical Sciences and Modelling, vol. 6, no. 3, pp. 105–119, 2023, doi: 10.33187/jmsm.1126660.
ISNAD Şahin Şener, Ümmü. “Implementation of the Hybrid ADI-FDTD Scheme to Maxwell Equation for Mathematical Modeling of Breast Tumor”. Journal of Mathematical Sciences and Modelling 6/3 (December 2023), 105-119. https://doi.org/10.33187/jmsm.1126660.
JAMA Şahin Şener Ü. Implementation of the Hybrid ADI-FDTD Scheme to Maxwell Equation for Mathematical Modeling of Breast Tumor. Journal of Mathematical Sciences and Modelling. 2023;6:105–119.
MLA Şahin Şener, Ümmü. “Implementation of the Hybrid ADI-FDTD Scheme to Maxwell Equation for Mathematical Modeling of Breast Tumor”. Journal of Mathematical Sciences and Modelling, vol. 6, no. 3, 2023, pp. 105-19, doi:10.33187/jmsm.1126660.
Vancouver Şahin Şener Ü. Implementation of the Hybrid ADI-FDTD Scheme to Maxwell Equation for Mathematical Modeling of Breast Tumor. Journal of Mathematical Sciences and Modelling. 2023;6(3):105-19.

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