Current source reconstructing and magnetic imaging of cardiac electrical activity during P-wave

Zhou Da-Fang; Jiang Shi-Qin; Zhao Chen; Peter van Leeuwen

doi:10.7498/aps.68.20190005

Abstract

The current source reconstruction and magnetic imaging is a new technique to non-invasively obtain spatial information regarding cardiac electrical activity using magnetocardiogram (MCG) signals measured by the superconducting quantum interference device (SQUID) on the human thorax surface. Using MCG signals to reconstruct distributed current sources needs to solve the inverse problem of magnetic field. The beamforming is a type of spatial filter method that has been used for distributed source reconstruction and source imaging in electroencephalogram (EEG) and magnetoencephalogram (MEG). In this paper, the dipole moment of distributed current source is estimated with corresponding each spatial filter based on the cardiac source field model. The purpose is to enhance the intensity contrast of the dipole moment of distributed current sources in distributed source spatial spectrum estimation with beamforming, so that the reconstructed-pseudo sources beyond the heart can be removed for imaging cardiac electric activity well. A new beamforming method of improving intensity contrast (IIC) of distributed source spatial spectrum estimation is developed for imaging cardiac electric activity in P-wave, due to cardiac magnetic signals in P-wave lower than that of the peak value of R-wave, which has a relatively low signal-to-noise ratio (SNR). For enhancing the accuracy of current source reconstruction in P-wave, the IIC divided into two steps: firstly, to introduce the lead-field matrix, which represents the measurement sensor-array sensitivity to magnetic field current sources, into a weight matrix of the spatial filter for making the output estimation of the filter more sensitive to the current sourcedistribution, so as to improve the intensity contrast of the reconstructed distributed sources.Secondly, by setting a threshold of source intensity from experience, to extract the reconstructed source with locally-maximal dipole strength at each time for eliminating the relatively weak pseudo sources in other locations, so as to enhance the accuracy of current source reconstruction during P-wave. In this paper, the IIC and three other methods, including minimum variance beamforming (MVB), suppressing spatial filter output noise-power gain (SONG) and trust region reflective (TRR), are compared by using the theoretical analysis and simulation experiments of MCG current source reconstruction during P-wave. The results show that the IIC has higher intensity contrast of the single source spatial spectrum estimation, and possesses better accuracy of the current source reconstruction. The 61-channel MCG signals of two healthy subjects and their imaging of cardiac electrical activity during P-wave also are analyzed. The result shows that the IIC is better than the other three methods. It is indicated that two healthy subjects have stronger electrical activity in the atrium than that in the ventricle at Ppeak time, also that the electrical activity has the direction feature when the right-atrium is depolarized during P-wave. In summary, the IIC is useful for imaging the cardiac electrical activity. However, it is needed to carry out a further research on patients with local myocardial ischemia and left or right coronary artery stenosis, and to establish the evaluation index for imaging of cardiac electrical activity in such patients.

Keywords:

Authors and contacts

1.
College of Electronics and Information Engineering, Tongji University, Shanghai 201804, China
2.
Faculty of Health, University of Witten/Herdecke, Witten D-58448, Germany

Corresponding author: Jiang Shi-Qin, sqjiang@tongji.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 60771030), the National High Technology Research and Development Program of China (Grant No. 2008AA02Z308), the Shanghai Foundation for Development of Science and Technology, China (Grant No. 08JC1421800), the Open Project of State Key Laboratory of Function Materials for Information, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, China (Grant No. SKL2013010), and the Open Project of Key Laboratory of Medical Image Computing and Computer Assisted Intervention of Shanghai, Shanghai Medical College of Fudan University, China (Grant No. 13DZ2272200-2)

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References

[1]	Cohen D, Edelsack E A, Zimmerman J E 1970 Appl. Phys. Lett. 16 278 Google Scholar
[2]	Van Leeuwen P, Hailer B, Lange S, Klein A, Geue D, Seybold K, Poplutz C, Grönemeyer D 2008 Phys. Med. Biol. 53 2291 Google Scholar
[3]	Zhang S L, Wang Y L, Wang H W, Jiang S Q, Xie X M 2009 Phys. Med. Biol. 54 4793 Google Scholar
[4]	Chen T, Zhao C, Jiang S Q, van Leeuwen P, Gronemeyer D 2014 Sci. Bull. 59 1123 Google Scholar
[5]	李明, 张朝祥, 张树林, 陈威, 鲁丽, 王毅, 孔祥燕 2017 低温 39 4 Li M, Zhang C Y, Zhang S L, Chen W, Lu L, Wang Y, Kong X Y 2017 Chin. J. Low Temp. Phys. 39 4
[6]	Zhao C, Jiang S Q, Wu Y H, Zhu J J, Zhou D F, Hailer B, Gronemeyer D, van Leeuwen P 2017 IEEE J. Biomed. Health 22 495
[7]	Tao R, Zhang S L, Huang X, Tao M F, Ma J, Ma S X, Zhang C X, Zhang T X, Tang F K, Lu J P, Shen C X, Xie X M 2018 IEEE Trans. Biomed. Eng. 66 1658
[8]	Zhang S L, Zhang G F, Wang Y L, Zeng J, Qiu Y, Liu M, Kong X Y, Xie X M 2013 Sci. Bull. 58 2917 Google Scholar
[9]	Tripp J H 1983 Biomagnetism: An Interdisciplinary Approach (New York: Springer) p101
[10]	Sarvas J 1987 Phys. Med. Biol. 32 11 Google Scholar
[11]	Sekihara K, Nagarajan S S, Poeppel D, Marantz A 2002 IEEE Trans. Biomed. Eng. 49 1534 Google Scholar
[12]	Sekihara K, Sahani M, Nagarajan S S 2005 NeuroImage 25 1056 Google Scholar
[13]	Sekihara K, Nagarajan S S 2005 Modeling and Imaging of Bioelectrical Activity: Principles and Applications (New York: Kluwer Academic/Plenum Publishers) p213
[14]	Van Veen B, Van Drongelen W, Yuchtman M, Suzuki A 1997 IEEE Trans. Biomed. Eng. 44 867 Google Scholar
[15]	Gramfort A, Strohmeier D, Haueison J, Hämäläinen M S, Kowalski M 2013 NeuroImage 70 410 Google Scholar
[16]	王伟远, 蒋式勤, 周大方, 朱嘉辰, 闫玉蕊, 权薇薇 2014 63 248701 Google Scholar Wang W Y, Jiang S Q, Zhou D F, Zhu J C, Yan Y R, Quan W W 2014 Acta Phys. Sin. 63 248701 Google Scholar
[17]	Ha T, Kim K, Lim S, Yu K K, Kwon H 2015 IEEE Trans. Biomed. Eng. 62 60 Google Scholar
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[19]	Kobayashi K, Uchikawa Y, Nakai K, Yoshizawa M 2004 IEEE Trans. Magn. 40 2970 Google Scholar
[20]	Kim K, Lee Y, Kwon H, Kim J, Bae J 2006 Comput. Biol. Med. 36 253 Google Scholar
[21]	Zhu J J, Jiang S Q, Wang W Y, Zhao C, Wu Y H, Luo M, Quan W W 2014 Chin. Phys. B 23 048702 Google Scholar
[22]	Chen M, Jiang S, Bing L, Zhao C, Hailer B, Grönemeyer D, Van Leeuwen P 2015 Sci. Bull. 60 1235 Google Scholar
[23]	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 Google Scholar
[24]	Kumihashi I, Sekihara K 2010 IEEE Trans. Biomed. Eng. 57 1358 Google Scholar
[25]	Nakai K, Kawazoe K, Izumoto H, Tsuboi J, Oshima Y, Oka T, Yoshioka K, Shozushima M, Suwabe A, Itoh M, Kobayashi K, Shimizu T, Yoshizawa M 2005 Int. J. Cardiovasc Imaging 21 555 Google Scholar
[26]	Nakai K, Izumoto H, Kawazoe K, Tsuboi J, Fukuhiro Y, Oka T, Yoshioka K, Shozushima M, Itoh M, Suwabe A, Yoshizawa M 2006 Int. J. Cardiovasc Imaging 22 573 Google Scholar
[27]	周大方, 张树林, 蒋式勤 2018 67 158702 Google Scholar Zhou D F, Zhang S L, Jiang S Q 2018 Acta Phys. Sin. 67 158702 Google Scholar
[28]	Gross J, Ioannides A A 1999 Phys. Med. Biol. 44 2081 Google Scholar
[29]	Horn R A, Johnson C R 2013 Matrix Analysis (New York: Cambridge University Press) p49, p139, p231
[30]	Coleman T F, Li Y 1993 SIAM J. Optim. 6 418
[31]	Coleman T F, Li Y 1994 Math. Program. 67 189 Google Scholar
[32]	赵晨, 蒋式勤, 石明伟, 朱俊杰 2014 63 078702 Google Scholar Zhao C, Jiang S Q, Shi M W, Zhu J J 2014 Acta Phys. Sin. 63 078702 Google Scholar
[33]	Malmivuo J, Plonsey R 1995 Bioelectromagnetism: Principles and Applications of Bioelectric and Biomagnetic Fields (New York: Oxford University Press) p165
[34]	Durrer D, Van Dam R T, Freud G E, Janse M J, Meijler F L, Arzbaecher R C 1970 Circulation 41 899 Google Scholar

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图 1 分布源位置及指定的26个邻域位置, 分别用红色和蓝色表示

Figure 1. The position of the source and 26 specified adjacent positions are shown in red and blue colors, respectively

DownLoad: Full-Size Img PowerPoint

图 2 (a) 水平分层导体. 其中黑色直线表示分层躯干的边界, 黄色椭圆体表示心脏; (b), (c) 测量通道1和61的磁场导联$l_{j,k}^\zeta , \left( {\zeta = X, Y, Z} \right)$曲线. 其中红、绿和蓝色分别表示X, Y和Z方向导联的曲线

Figure 2. (a) The horizontally layered conductor (HLC), where the black line indicates the boundary of HLC, and the yellow spheroid the heart; (b),(c) The X, Y and Z lead-field based plots of channels 1 and 61 are expressed in red, green and blue, respectively

DownLoad: Full-Size Img PowerPoint

图 3 (a) 黑色圆圈○和箭头表示沿直线方向的参考路径1; (b)−(e) 是SNR = 20 dB时, IIC, SONG, MVB和TRR方法的源重建结果. 黑圈中的浅绿色到深绿色表示重建电流源位置随时间的变化

Figure 3. (a) The black circles ○ and arrow indicate the reference path 1 along the straight line; (b)−(e) The results of the current source reconstruction using IIC, SONG, MVB and TRR methods when SNR is 20 dB. The green points at different color levels denote the reconstructed source locations at different times

DownLoad: Full-Size Img PowerPoint

图 4 (a) 黑色圆圈○和箭头表示沿直线方向的参考路径2; (b)−(e) SNR = 20 dB时, IIC,SONG,MVB和TRR方法的源重建结果. 黑圈中的浅绿色到深绿色表示重建电流源位置随时间的变化

Figure 4. (a) The black circles ○ and arrow indicate the reference path 2 along the straight line; (b)−(e) The results of the current source reconstruction using IIC, SONG, MVB and TRR methods when SNR is 20 dB. The green points at different color levels denote the reconstructed source locations at different times

DownLoad: Full-Size Img PowerPoint

图 5 (a), (b) 健康人A与B的单周期61通道心脏磁场信号及其P_peak时刻; (c), (d) 用IIC,SONG与MVB方法得到的2个健康人P_peak时刻源空间谱强度的XY与XZ面等高线图

Figure 5. (a),(b) The 61-channel MCG signals and P_peak time of single-cycle from healthy subjects A and B; (c),(d) The XY and XZ based spatial spectrum intensity contours from subjects A and B at P_peak using IIC, SONG or MVB

DownLoad: Full-Size Img PowerPoint

图 6 (a), (b) 健康人A与B的单周期61通道心脏磁场信号及其P_onset-P_peak段; (c), (d) 用IIC, SONG, MVB和TRR得到的2个健康人的P_onset-P_peak段的心脏电流源重建结果. 圆点中的浅红色到深红色表示重建电流源随时间的位置变化. 绿色箭头表示电活动的方向

Figure 6. (a),(b) 61-channel MCG signal and P_onset-P_peak segment of single-cycle from healthy subjects A and B; (c), (d) The cardiac current sources reconstruction of subjects A and B in P_onset-P_peak segment using IIC, SONG, MVB or TRR. The reconstructed current sources change the color from white to red with time. The green arrow shows the direction of electrical activity

DownLoad: Full-Size Img PowerPoint

表 1 参考路径1对应的单源估计误差

Table 1. The error of single source estimation correspond to the reference path 1

参数设置		方法	单源估计误差/cm
MV/m/s	SNR/dB	方法	E	E_X	E_Y	E_Z
$\sqrt 3 $	无噪声	IIC	1.29	0.75	0.75	0.75
		SONG	1.27	0.74	0.74	0.74
		MVB	1.39	0.80	0.80	0.80
		TRR	0.72	0.52	0.24	0.43
	30	IIC	1.37	0.79	0.79	0.79
		SONG	1.73	1.13	0.81	1.04
		MVB	5.76	3.08	3.73	3.12
		TRR	1.50	0.83	0.17	1.24
	20	IIC	1.19	0.68	0.68	0.68
		SONG	1.67	1.17	0.69	0.98
		MVB	6.73	4.04	3.88	3.74
		TRR	2.13	1.17	1.26	1.26

DownLoad: CSV

表 2 参考路径2对应的双电流源估计误差

Table 2. The error of two sources estimation correspond to the reference path 2

参数设置		方法	一条路径的源估计误差/cm				另一路径的源估计误差/cm
MV/m/s	SNR/dB	方法	E	E_X	E_Y	E_Z	E	E_X	E_Y	E_Z
1	无噪声	IIC	1.71	1.07	0.80	1.07	0.82	0	0.82	0
		SONG	1.70	1.07	0.79	1.07	1.05	0.47	0.81	0.47
		MVB	2.73	0.85	2.45	0.84	2.80	1.53	1.66	1.64
		TRR	*	*	*	*	*	*	*	*
	30	IIC	1.73	1.06	0.86	1.06	1.76	1.03	0.80	1.18
		SONG	1.98	1.09	1.26	1.07	2.18	1.33	1.01	1.40
		MVB	5.00	2.47	4.15	1.30	4.93	1.84	3.27	3.20
		TRR	*	*	*	*	*	*	*	*
	20	IIC	1.66	0.96	0.92	1.00	2.44	1.52	1.38	1.32
		SONG	6.51	2.26	6.01	1.04	4.13	2.04	3.01	1.96
		MVB	5.62	2.58	4.84	1.24	5.20	2.05	3.57	3.17
		TRR	*	*	*	*	*	*	*	*

DownLoad: CSV

map

[1]	Cohen D, Edelsack E A, Zimmerman J E 1970 Appl. Phys. Lett. 16 278 Google Scholar
[2]	Van Leeuwen P, Hailer B, Lange S, Klein A, Geue D, Seybold K, Poplutz C, Grönemeyer D 2008 Phys. Med. Biol. 53 2291 Google Scholar
[3]	Zhang S L, Wang Y L, Wang H W, Jiang S Q, Xie X M 2009 Phys. Med. Biol. 54 4793 Google Scholar
[4]	Chen T, Zhao C, Jiang S Q, van Leeuwen P, Gronemeyer D 2014 Sci. Bull. 59 1123 Google Scholar
[5]	李明, 张朝祥, 张树林, 陈威, 鲁丽, 王毅, 孔祥燕 2017 低温 39 4 Li M, Zhang C Y, Zhang S L, Chen W, Lu L, Wang Y, Kong X Y 2017 Chin. J. Low Temp. Phys. 39 4
[6]	Zhao C, Jiang S Q, Wu Y H, Zhu J J, Zhou D F, Hailer B, Gronemeyer D, van Leeuwen P 2017 IEEE J. Biomed. Health 22 495
[7]	Tao R, Zhang S L, Huang X, Tao M F, Ma J, Ma S X, Zhang C X, Zhang T X, Tang F K, Lu J P, Shen C X, Xie X M 2018 IEEE Trans. Biomed. Eng. 66 1658
[8]	Zhang S L, Zhang G F, Wang Y L, Zeng J, Qiu Y, Liu M, Kong X Y, Xie X M 2013 Sci. Bull. 58 2917 Google Scholar
[9]	Tripp J H 1983 Biomagnetism: An Interdisciplinary Approach (New York: Springer) p101
[10]	Sarvas J 1987 Phys. Med. Biol. 32 11 Google Scholar
[11]	Sekihara K, Nagarajan S S, Poeppel D, Marantz A 2002 IEEE Trans. Biomed. Eng. 49 1534 Google Scholar
[12]	Sekihara K, Sahani M, Nagarajan S S 2005 NeuroImage 25 1056 Google Scholar
[13]	Sekihara K, Nagarajan S S 2005 Modeling and Imaging of Bioelectrical Activity: Principles and Applications (New York: Kluwer Academic/Plenum Publishers) p213
[14]	Van Veen B, Van Drongelen W, Yuchtman M, Suzuki A 1997 IEEE Trans. Biomed. Eng. 44 867 Google Scholar
[15]	Gramfort A, Strohmeier D, Haueison J, Hämäläinen M S, Kowalski M 2013 NeuroImage 70 410 Google Scholar
[16]	王伟远, 蒋式勤, 周大方, 朱嘉辰, 闫玉蕊, 权薇薇 2014 63 248701 Google Scholar Wang W Y, Jiang S Q, Zhou D F, Zhu J C, Yan Y R, Quan W W 2014 Acta Phys. Sin. 63 248701 Google Scholar
[17]	Ha T, Kim K, Lim S, Yu K K, Kwon H 2015 IEEE Trans. Biomed. Eng. 62 60 Google Scholar
[18]	Nenonen J, Pesola K, Hänninen H, Lauerma K, Takala P, Mäkelä T, Mäkijärvi M, Knuuti J, Toivonen L, Katila T 2001 J. Electrocardiol. 34 37 Google Scholar
[19]	Kobayashi K, Uchikawa Y, Nakai K, Yoshizawa M 2004 IEEE Trans. Magn. 40 2970 Google Scholar
[20]	Kim K, Lee Y, Kwon H, Kim J, Bae J 2006 Comput. Biol. Med. 36 253 Google Scholar
[21]	Zhu J J, Jiang S Q, Wang W Y, Zhao C, Wu Y H, Luo M, Quan W W 2014 Chin. Phys. B 23 048702 Google Scholar
[22]	Chen M, Jiang S, Bing L, Zhao C, Hailer B, Grönemeyer D, Van Leeuwen P 2015 Sci. Bull. 60 1235 Google Scholar
[23]	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 Google Scholar
[24]	Kumihashi I, Sekihara K 2010 IEEE Trans. Biomed. Eng. 57 1358 Google Scholar
[25]	Nakai K, Kawazoe K, Izumoto H, Tsuboi J, Oshima Y, Oka T, Yoshioka K, Shozushima M, Suwabe A, Itoh M, Kobayashi K, Shimizu T, Yoshizawa M 2005 Int. J. Cardiovasc Imaging 21 555 Google Scholar
[26]	Nakai K, Izumoto H, Kawazoe K, Tsuboi J, Fukuhiro Y, Oka T, Yoshioka K, Shozushima M, Itoh M, Suwabe A, Yoshizawa M 2006 Int. J. Cardiovasc Imaging 22 573 Google Scholar
[27]	周大方, 张树林, 蒋式勤 2018 67 158702 Google Scholar Zhou D F, Zhang S L, Jiang S Q 2018 Acta Phys. Sin. 67 158702 Google Scholar
[28]	Gross J, Ioannides A A 1999 Phys. Med. Biol. 44 2081 Google Scholar
[29]	Horn R A, Johnson C R 2013 Matrix Analysis (New York: Cambridge University Press) p49, p139, p231
[30]	Coleman T F, Li Y 1993 SIAM J. Optim. 6 418
[31]	Coleman T F, Li Y 1994 Math. Program. 67 189 Google Scholar
[32]	赵晨, 蒋式勤, 石明伟, 朱俊杰 2014 63 078702 Google Scholar Zhao C, Jiang S Q, Shi M W, Zhu J J 2014 Acta Phys. Sin. 63 078702 Google Scholar
[33]	Malmivuo J, Plonsey R 1995 Bioelectromagnetism: Principles and Applications of Bioelectric and Biomagnetic Fields (New York: Oxford University Press) p165
[34]	Durrer D, Van Dam R T, Freud G E, Janse M J, Meijler F L, Arzbaecher R C 1970 Circulation 41 899 Google Scholar

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