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For non-invasive imaging of cardiac electrical activity using magnetocardiogram (MCG) data measured on human body surface, a key problem that needs to be solved is to enhance the spatial resolution of reconstructing distributed current source dipole moment strength in MCG imaging. In this paper, a beamforming method of suppressing spatial filter output noise-power gain (SONG) is proposed based on the minimum variance beamforming (MVB). The purpose is to improve the resolution of the distributed source dipole moment strength reconstruction, i.e., the ability to resolve the source for distributed current source spatial spectrum estimation, in order to enhance the resolution of the cardiac electrical activity magnetic imaging. The method offers a new spatial filter weight matrix by using a low-trace positively-semidefinite matrix that will affect the spatial filter output power, on the premise that the influence of noise spatial spectrum of spatial filter on the estimation of current source spatial spectrum has been constrained by the noise spatial spectrum intensity normalization. The positively-semidefinite matrix is specially constructed to satisfy the condition that the eigenvalue is not greater than 1 and the trace of the matrix is lower than its order, so that it can be used to constrain the spatial filter output noise-power gain for improving the robustness to noise of the source spatial spectrum estimation. In addition, a classical model of the horizontally layered conductor is used as the heart-torso model to calculate the lead-field matrix that needs to be used in source spatial spectrum estimation. The results obtained in this study are as follows. For validating the proposed method, a theoretical analysis and simulation tests of the current source reconstruction are performed, where the SONG and MVB methods are compared and a parameter of the signal-to-noise ratio is considered according to the realistic MCG data. In this paper we also give the cardiac electrical activity imaging of 36-channel cardiac magnetic field data of single-cycle from two healthy people, where a heart profile from the magnetic resonance imaging is used as a reference and adjusted to the MCG measurement system. The results show that the SONG method has ability to better resolve the current source and can observe the significant electrophysiological characteristics such as the strong electrical activity in the ventricles of the healthy people at the time of Rpeak. In summary, our proposed method can improve the visual effect of the cardiac electrical activity imaging, when the signal-to-noise ratio of the single-cycle cardiac magnetic signal is not lower than 10 dB. Therefore, this method of measuring the non-invasively imaging cardiac electrical activity is a promising one and helpful for relevant medical research and applications.
[1] van Veen B, van Drongelen W, Yuchtman M, Suzuki A 1997 IEEE Trans. Biomed. Eng. 44 867
[2] Sekihara K, Nagarajan S S 2005 Modeling and Imaging of Bioelectrical Activity: Principles and Applications (New York: Kluwer Academic/Plenum Publishers) p213
[3] Gross J, Ioannides A A 1999 Phys. Med. Biol. 44 2081
[4] Sekihara K, Sahani M, Nagarajan S S 2005 NeuroImage 25 1056
[5] Brookes M J, Vrba J, Robinson S E, Stevenson C M, Peters A M, Barnes G R, Hillebrand A, Morris P G 2008 NeuroImage 39 1788
[6] Kumihashi I, Sekihara K 2010 IEEE Trans. Biomed. Eng. 57 1358
[7] Ha T, Kim K, Lim S, Yu K K, Kwon H 2015 IEEE Trans. Biomed. Eng. 62 60
[8] Kobayashi K, Uchikawa Y, Nakai K, Yoshizawa M 2004 IEEE Trans. Magn. 40 2970
[9] Kim K, Lee Y, Kwon H, Kim J, Bae J 2006 Comput. Biol. Med. 36 253
[10] Kim K, Kim D, Shim E, Lee Y, Kwon H, Park Y 2007 Proceedings of the Joint Meeting of the 6th International Symposium on Noninvasive Functional Source Imaging of the Brain and Heart the International Conference on Functional Biomedical Imaging Hangzhou, China, October 1214, 2007 p316
[11] van Leeuwen P, Hailer B, Lange S, Klein A, Geue D, Seybold K, Poplutz C, Grnemeyer D 2008 Phys. Med. Biol. 53 2291
[12] Zhang S L 2011 Ph. D. Dissertation (Shanghai: Graduate University of Chinese Academy of Sciences) (in Chinese) [张树林 2011 博士学位论文 (上海: 中国科学院研究 生院)]
[13] Tripp J H 1983 Biomagnetism: An Interdisciplinary Approach (New York: Springer) p101
[14] Sarvas J 1987 Phys. Med. Biol. 32 11
[15] Wang W Y, Jiang S Q, Zhou D F, Zhu J C, Yan Y R, Quan W W 2014 Acta Phys. Sin. 63 248702 (in Chinese) [王伟远, 蒋式勤, 周大方, 朱嘉辰, 闫玉蕊, 权薇薇 2014 物 理学报 63 248702]
[16] Zhou D F, Jiang S Q, Zhu J C, Zhao C, Yan Y R, Grnemeyer D, van Leeuwen P 2015 Proceedings of the 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society Milan, Italy, August 2529, 2015 p4479
[17] Malmivuo J, Plonsey R 1995 Bioelectromagnetism: Principles and Applications of Bioelectric and Biomagnetic Fields (New York: Oxford University Press) p165
[18] Durrer D, van Dam R T, Freud G E, Janse M J, Meijler F L, Arzbaecher R C 1970 Circulation 41 899
[19] Pesola K, Nenonen J 2000 Proceedings of the 12th International Conference on Biomagnetism Espoo, Finland, August 1317, 2000 p835
[20] Nenonen J, Pesola K, Hnninen H, Lauerma K, Takala P, Mkel T, Mkijrvi M, Knuuti J, Toivonen L, Katila T 2001 J. Electrocardiol. 34 37
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[1] van Veen B, van Drongelen W, Yuchtman M, Suzuki A 1997 IEEE Trans. Biomed. Eng. 44 867
[2] Sekihara K, Nagarajan S S 2005 Modeling and Imaging of Bioelectrical Activity: Principles and Applications (New York: Kluwer Academic/Plenum Publishers) p213
[3] Gross J, Ioannides A A 1999 Phys. Med. Biol. 44 2081
[4] Sekihara K, Sahani M, Nagarajan S S 2005 NeuroImage 25 1056
[5] Brookes M J, Vrba J, Robinson S E, Stevenson C M, Peters A M, Barnes G R, Hillebrand A, Morris P G 2008 NeuroImage 39 1788
[6] Kumihashi I, Sekihara K 2010 IEEE Trans. Biomed. Eng. 57 1358
[7] Ha T, Kim K, Lim S, Yu K K, Kwon H 2015 IEEE Trans. Biomed. Eng. 62 60
[8] Kobayashi K, Uchikawa Y, Nakai K, Yoshizawa M 2004 IEEE Trans. Magn. 40 2970
[9] Kim K, Lee Y, Kwon H, Kim J, Bae J 2006 Comput. Biol. Med. 36 253
[10] Kim K, Kim D, Shim E, Lee Y, Kwon H, Park Y 2007 Proceedings of the Joint Meeting of the 6th International Symposium on Noninvasive Functional Source Imaging of the Brain and Heart the International Conference on Functional Biomedical Imaging Hangzhou, China, October 1214, 2007 p316
[11] van Leeuwen P, Hailer B, Lange S, Klein A, Geue D, Seybold K, Poplutz C, Grnemeyer D 2008 Phys. Med. Biol. 53 2291
[12] Zhang S L 2011 Ph. D. Dissertation (Shanghai: Graduate University of Chinese Academy of Sciences) (in Chinese) [张树林 2011 博士学位论文 (上海: 中国科学院研究 生院)]
[13] Tripp J H 1983 Biomagnetism: An Interdisciplinary Approach (New York: Springer) p101
[14] Sarvas J 1987 Phys. Med. Biol. 32 11
[15] Wang W Y, Jiang S Q, Zhou D F, Zhu J C, Yan Y R, Quan W W 2014 Acta Phys. Sin. 63 248702 (in Chinese) [王伟远, 蒋式勤, 周大方, 朱嘉辰, 闫玉蕊, 权薇薇 2014 物 理学报 63 248702]
[16] Zhou D F, Jiang S Q, Zhu J C, Zhao C, Yan Y R, Grnemeyer D, van Leeuwen P 2015 Proceedings of the 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society Milan, Italy, August 2529, 2015 p4479
[17] Malmivuo J, Plonsey R 1995 Bioelectromagnetism: Principles and Applications of Bioelectric and Biomagnetic Fields (New York: Oxford University Press) p165
[18] Durrer D, van Dam R T, Freud G E, Janse M J, Meijler F L, Arzbaecher R C 1970 Circulation 41 899
[19] Pesola K, Nenonen J 2000 Proceedings of the 12th International Conference on Biomagnetism Espoo, Finland, August 1317, 2000 p835
[20] Nenonen J, Pesola K, Hnninen H, Lauerma K, Takala P, Mkel T, Mkijrvi M, Knuuti J, Toivonen L, Katila T 2001 J. Electrocardiol. 34 37
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