volume | PIER Journals

Abstract

This paper introduces a novel finite element boundary integral approach for magnetic resonance electrical properties tomography (MR-EPT) with an inhomogeneous background which improves imaging quality by utilizing inhomogeneous background inversion and allows for a flexible selection of areas for fine reconstruction, thereby saving resources and quickly obtaining the most important information. In the proposed approach, a fictitious inhomogeneous background is initialized, followed by a preliminary reconstruction conducted across the entire field of view (FOV) through a few iterations. This fictitious inhomogeneous background aims to enhance the quality of reconstruction, surpassing that achieved through inversion in a homogeneous background. The proposed method is significantly suitable to the prevailing refinement mechanism, where the refinement area identified from the preliminary reconstruction image is embedded in an inhomogeneous background. This method combines the advantages of the computational efficiency of local methods and the noise robustness of global methods. Numerical examples have validated that the inversion with a fictitious inhomogeneous background yields a superior reconstruction quality. The subsequent narrowing of the inversion area results in a more focused inversion process, significantly reducing reconstruction time.

1. Zhang, Xiaotong, Jiaen Liu, and Bin He, "Magnetic-resonance-based electrical properties tomography: A review," IEEE Reviews in Biomedical Engineering, Vol. 7, 87-96, 2014.
doi:10.1109/rbme.2013.2297206

2. Liu, Jiaen, Yicun Wang, Ulrich Katscher, and Bin He, "Electrical properties tomography based on B1 maps in MRI: Principles, applications, and challenges," IEEE Transactions on Biomedical Engineering, Vol. 64, No. 11, 2515-2530, Nov. 2017.
doi:10.1109/tbme.2017.2725140

3. Leijsen, Reijer, Wyger Brink, Cornelis van den Berg, Andrew Webb, and Rob Remis, "Electrical properties tomography: A methodological review," Diagnostics, Vol. 11, No. 2, 176, Jan. 2021.
doi:10.3390/diagnostics11020176

4. Borsic, A., I. Perreard, A. Mahara, and R. J. Halter, "An inverse problems approach to MR-EPT image reconstruction," IEEE Transactions on Medical Imaging, Vol. 35, No. 1, 244-256, Jan. 2016.
doi:10.1109/tmi.2015.2466082

5. Katscher, Ulrich and Cornelius A. T. van den Berg, "Electric properties tomography: Biochemical, physical and technical background, evaluation and clinical applications," NMR in Biomedicine, Vol. 30, No. 8, e3729, 2017.
doi:10.1002/nbm.3729

6. Hosseini, Seyyed Mohammd and Amir Ahmad Shishegar, "Mapping MRI intensity to the dielectric properties of body tissues using microwave imaging," IEEE Transactions on Antennas and Propagation, Vol. 71, No. 8, 6744-6752, 2023.
doi:10.1109/tap.2023.3281071

7. Haacke, E. M., L. S. Petropoulos, E. W. Nilges, and D. H. Wu, "Extraction of conductivity and permittivity using magnetic resonance imaging," Physics in Medicine & Biology, Vol. 36, No. 6, 723, 1991.
doi:10.1088/0031-9155/36/6/002

8. Wen, Han, "Noninvasive quantitative mapping of conductivity and dielectric distributions using RF wave propagation effects in high-field MRI," Medical Imaging 2003: Physics of Medical Imaging, Vol. 5030, 471-477, San Diego, California, United States, Jun. 2003.
doi:10.1117/12.480000

9. Voigt, Tobias, Ulrich Katscher, and Olaf Doessel, "Quantitative conductivity and permittivity imaging of the human brain using electric properties tomography," Magnetic Resonance in Medicine, Vol. 66, No. 2, 456-466, 2011.
doi:10.1002/mrm.22832

10. Ammari, Habib, Hyeuknam Kwon, Yoonseop Lee, Kyungkeun Kang, and Jin Keun Seo, "Magnetic resonance-based reconstruction method of conductivity and permittivity distributions at the Larmor frequency," Inverse Problems, Vol. 31, No. 10, 105001, 2015.
doi:10.1088/0266-5611/31/10/105001

11. Gurler, Necip and Yusuf Ziya Ider, "Gradient‐based electrical conductivity imaging using MR phase," Magnetic Resonance in Medicine, Vol. 77, No. 1, 137-150, Jan. 2017.
doi:10.1002/mrm.26097

12. Wang, Yicun, Pierre-Francois Van de Moortele, and Bin He, "Automated gradient-based electrical properties tomography in the human brain using 7 Tesla MRI," Magnetic Resonance Imaging, Vol. 63, 258-266, Nov. 2019.
doi:10.1016/j.mri.2019.08.003

13. Hafalir, Fatih S., Omer F. Oran, Necip Gurler, and Yusuf Z. Ider, "Convection-reaction equation based magnetic resonance electrical properties tomography (cr-MREPT)," IEEE Transactions on Medical Imaging, Vol. 33, No. 3, 777-793, Mar. 2014.
doi:10.1109/tmi.2013.2296715

14. Yildiz, Gulsah and Yusuf Ziya Ider, "Use of dielectric padding to eliminate low convective field artifact in cr‐MREPT conductivity images," Magnetic Resonance in Medicine, Vol. 81, No. 5, 3168-3184, May 2019.
doi:10.1002/mrm.27648

15. Balidemaj, Edmond, Cornelis A. T. van den Berg, Johan Trinks, Astrid L. H. M. W. van Lier, Aart J. Nederveen, Lukas J. A. Stalpers, Hans Crezee, and Rob F. Remis, "CSI-EPT: A contrast source inversion approach for improved MRI-based electric properties tomography," IEEE Transactions on Medical Imaging, Vol. 34, No. 9, 1788-1796, Sep. 2015.
doi:10.1109/tmi.2015.2404944

16. Leijsen, Reijer L., Wyger M. Brink, Cornelis A. T. Van Den Berg, Andrew G. Webb, and Rob F. Remis, "3-D contrast source inversion-electrical properties tomography," IEEE Transactions on Medical Imaging, Vol. 37, No. 9, 2080-2089, Sep. 2018.
doi:10.1109/tmi.2018.2816125

17. Arduino, Alessandro, Luca Zilberti, Mario Chiampi, and Oriano Bottauscio, "CSI-EPT in presence of RF-shield for MR-coils," IEEE Transactions on Medical Imaging, Vol. 36, No. 7, 1396-1404, Jul. 2017.
doi:10.1109/tmi.2017.2665688

18. Arduino, Alessandro, Oriano Bottauscio, Mario Chiampi, and Luca Zilberti, "Magnetic resonance-based imaging of human electric properties with phaseless contrast source inversion," Inverse Problems, Vol. 34, No. 8, 084002, 2018.
doi:10.1088/1361-6420/aac536

19. Leijsen, Reijer L., Wyger M. Brink, Andrew G. Webb, and Rob F. Remis, "Effects of simulated error-sources on different 3-D CSI-EPT strategies," IEEE Transactions on Computational Imaging, Vol. 7, 713-723, 2021.
doi:10.1109/tci.2021.3094742

20. Serrallés, José E. C., Ilias I. Giannakopoulos, Bei Zhang, Carlotta Ianniello, Martijn A. Cloos, Athanasios G. Polimeridis, Jacob K. White, Daniel K. Sodickson, Luca Daniel, and Riccardo Lattanzi, "Noninvasive estimation of electrical properties from magnetic resonance measurements via global maxwell tomography and match regularization," IEEE Transactions on Biomedical Engineering, Vol. 67, No. 1, 3-15, Jan. 2020.
doi:10.1109/tbme.2019.2907442

21. Eda, Naohiro, Motofumi Fushimi, Keisuke Hasegawa, and Takaaki Nara, "A method for electrical property tomography based on a three-dimensional integral representation of the electric field," IEEE Transactions on Medical Imaging, Vol. 41, No. 6, 1400-1409, Jun. 2022.
doi:10.1109/tmi.2021.3139455

22. Hong, Ronghan, Shengnan Li, Jianhua Zhang, Youyu Zhang, Na Liu, Zhiru Yu, and Qing Huo Liu, "3-D MRI-based electrical properties tomography using the volume integral equation method," IEEE Transactions on Microwave Theory and Techniques, Vol. 65, No. 12, 4802-4811, Dec. 2017.
doi:10.1109/tmtt.2017.2725830

23. Giannakopoulos, Ilias I., José E. C. Serrallés, Luca Daniel, Daniel K. Sodickson, Athanasios G. Polimeridis, Jacob K. White, and Riccardo Lattanzi, "Magnetic-resonance-based electrical property mapping using Global Maxwell Tomography with an 8-channel head coil at 7 Tesla: A simulation study," IEEE Transactions on Biomedical Engineering, Vol. 68, No. 1, 236-246, Jan. 2021.
doi:10.1109/tbme.2020.2991399

24. Georgakis, Ioannis P., Ilias I. Giannakopoulos, Mikhail S. Litsarev, and Athanasios G. Polimeridis, "A fast volume integral equation solver with linear basis functions for the accurate computation of EM fields in MRI," IEEE Transactions on Antennas and Propagation, Vol. 69, No. 7, 4020-4032, Jul. 2021.
doi:10.1109/tap.2020.3044685

25. Van Den Berg, Peter M. and Ralph E. Kleinman, "A contrast source inversion method," Inverse Problems, Vol. 13, No. 6, 1607, 1997.
doi:10.1088/0266-5611/13/6/013

26. Van den Berg, P. and A. Abubakar, "Contrast source inversion method: State of art," Progress In Electromagnetics Research, Vol. 34, 189-218, 2001.
doi:10.2528/pier01061103

27. Nie, Zaiping, Feng Yang, Yanwen Zhao, and Yerong Zhang, "Variational Born iteration method and its applications to hybrid inversion," IEEE Transactions on Geoscience and Remote Sensing, Vol. 38, No. 4, 1709-1715, Jul. 2000.
doi:10.1109/36.851969

28. Inda, Adan Jafet Garcia, Shao Ying Huang, Nevrez İmamoğlu, and Wenwei Yu, "Physics-coupled neural network magnetic resonance electrical property tomography (MREPT) for conductivity reconstruction," IEEE Transactions on Image Processing, Vol. 31, 3463-3478, 2022.
doi:10.1109/tip.2022.3172220

29. Inda, Adan Jafet Garcia, Shao Ying Huang, Nevrez İmamoğlu, Ruian Qin, Tianyi Yang, Tiao Chen, Zilong Yuan, and Wenwei Yu, "Physics informed neural networks (PINN) for low snr magnetic resonance electrical properties tomography (MREPT)," Diagnostics, Vol. 12, No. 11, 2627, Oct. 2022.
doi:10.3390/diagnostics12112627

30. Qin, Ruian, Adan Jafet Garcia Inda, Zhongchao Zhou, Yukihiro Enomoto, Tianyi Yang, Nevrez İmamoğlu, Jose Gomez-Tames, Shaoying Huang, and Wenwei Yu, "REC-NN: A reconstruction error compensation neural network for Magnetic Resonance Electrical Property Tomography (MREPT)," 2023 45th Annual International Conference of the IEEE Engineering in Medicine & Biology Society (EMBC), 1-4, Sydney, Australia, 2023.
doi:10.1109/embc40787.2023.10340423

31. Ruan, Guohui, Zhaonian Wang, Chunyi Liu, Ling Xia, Huafeng Wang, Li Qi, and Wufan Chen, "Magnetic resonance electrical properties tomography based on modified physics-informed neural network and multiconstraints," IEEE Transactions on Medical Imaging, Vol. 43, No. 9, 3263-3278, 2024.
doi:10.1109/tmi.2024.3391651

32. Yin, Weishi, Wenhong Yang, and Hongyu Liu, "A neural network scheme for recovering scattering obstacles with limited phaseless far-field data," Journal of Computational Physics, Vol. 417, 109594, 2020.
doi:10.1016/j.jcp.2020.109594

33. Gao, Yu, Hongyu Liu, Xianchao Wang, and Kai Zhang, "On an artificial neural network for inverse scattering problems," Journal of Computational Physics, Vol. 448, 110771, 2022.
doi:10.1016/j.jcp.2021.110771

34. Chen, Xudong, Computational Methods for Electromagnetic Inverse Scattering, John Wiley Sons Singapore Pte. Ltd., Singapore, 2018.
doi:10.1002/9781119311997

35. Chen, Xudong, "Subspace-based optimization method for inverse scattering problems with an inhomogeneous background medium," Inverse Problems, Vol. 26, No. 7, 074007, 2010.
doi:10.1088/0266-5611/26/7/074007

36. Jin, J.-M., The Finite Element Method in Electromagnetics, John Wiley & Sons, 2015.

37. Zakaria, Amer, Colin Gilmore, and Joe LoVetri, "Finite-element contrast source inversion method for microwave imaging," Inverse Problems, Vol. 26, No. 11, 115010, 2010.
doi:10.1088/0266-5611/26/11/115010

38. Zakaria, Amer and Joe LoVetri, "The finite-element method contrast source inversion algorithm for 2D transverse electric vectorial problems," IEEE Transactions on Antennas and Propagation, Vol. 60, No. 10, 4757-4765, 2012.
doi:10.1109/tap.2012.2207324

39. Zakaria, Amer, Anastasia Baran, and Joe LoVetri, "Estimation and use of prior information in FEM-CSI for biomedical microwave tomography," IEEE Antennas and Wireless Propagation Letters, Vol. 11, 1606-1609, 2013.
doi:10.1109/lawp.2012.2237537

40. Abubakar, Aria, W. Hu, P. M. Van Den Berg, and T. M. Habashy, "A finite-difference contrast source inversion method," Inverse Problems, Vol. 24, No. 6, 065004, 2008.
doi:10.1088/0266-5611/24/6/065004

41. Sacolick, Laura I., Florian Wiesinger, Ileana Hancu, and Mika W. Vogel, "B1 mapping by bloch-siegert shift," Magnetic Resonance in Medicine, Vol. 63, No. 5, 1315-1322, 2010.

42. Yarnykh, Vasily L., "Actual flip-angle imaging in the pulsed steady state: A method for rapid three-dimensional mapping of the transmitted radiofrequency field," Magnetic Resonance in Medicine, Vol. 57, No. 1, 192-200, Jan. 2007.
doi:10.1002/mrm.21120

43. Peterson, A. F., S. L. Ray, and R. Mittra, Computational Methods for Electromagnetics, Vol. 351, IEEE Press, New York, 1998.
doi:10.1109/9780470544303

44. Zubal, I. George, Charles R. Harrell, Eileen O. Smith, Zachary Rattner, Gene Gindi, and Paul B. Hoffer, "Computerized three-dimensional segmented human anatomy," Medical Physics, Vol. 21, No. 2, 299-302, Feb. 1994.
doi:10.1118/1.597290

45. Gabriel, Camelia and Sami Gabriel, "Compilation of the dielectric properties of body tissues at RF and microwave frequencies," Tech. Rep. N.AL/OE-TR-1996-0037, Occupational and Environmental Health Directorate, Radiofrequency Radiation Division, Brooks Air Force Base, Texas, USA, 1996.
doi:10.21236/ada303903

Mr. Yuyue Zhang

Dr. Hariharan Mohanabala Krishnan

Dr. Tiantian Yin

Professor Xudong Chen