非均匀电磁介质中的等效源重构

赵晨; 蒋式勤; 石明伟; 朱俊杰

doi:10.7498/aps.63.078702

摘要

本文提出了一种用于等效源重构的磁场极值信号法. 并通过给定不同的电流偶极子作为信号源，仿真研究了多腔体心脏磁场模型及非均匀介质情况下等效源重构的精度. 分析了体电导对心脏磁场的影响，以及磁场极值信号反映的体电导作用. 文中将该方法与其他四种源估计方法：磁场梯度极值法、Nelder-Mead单纯形算法、信赖域反射算法和粒子群优化算法作了比较. 分析了这些方法的源重构精度和计算所需时间. 结果表明，这种针对非均匀介质情况提出的心脏磁场逆问题求解方法有一定的实用价值.

关键词:

心磁图 /
逆问题 /
心脏模型 /
体电导

Abstract

In this paper, a method that uses magnetic extreme signals for equivalent source reconstruction is presented. Through simulation of specific current dipoles given as the sources of magnetic field signals, the feasibility of a multi-chamber heart model is investigated and the accuracy analysis of equivalent source reconstruction in inhomogeneous media is conducted. The magnitude of the magnetic extreme signals is indicative of the influence of volume conductor on the cardiac magnetic field is analyzed. The method is compared with other four methods which are the method of magnetic gradient extreme signals, the Nelder-Mead algorithm, the trust region reflective algorithm, and the particle swarm optimization algorithm against the criteria in terms of accuracy of source reconstruction and computation time of the algorithm. Results show that the method is practically useful for solving inverse cardiac magnetic field problems.

Keywords:

作者及机构信息

1.
同济大学, 电子与信息工程学院, 上海 201804

基金项目: 国家自然科学基金（批准号：60771030）、国家高技术研究发展计划（批准号：2008AA02Z308）、上海市重点基础研究发展计划（批准号：08JC1421800）、上海市重点学科建设项目（批准号：B004）、和信息功能材料国家重点实验室（中国科学院上海微系统与信息技术研究所）开放课题和上海市医学图像处理与计算机辅助手术重点实验室开放课题（批准号：13DZ2272200-2）资助的课题.

Authors and contacts

1.
School of Electronics and Information Engineering, Tongji University, Shanghai 201804, China

Funds: Project supported in part 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 Science and Technology Development Foundation, China (Grant No 08JC1421800), the Shanghai Leading Academic Discipline Project (Grant No B004), the Open Project of State Key Laboratory of Function Materials for Information (Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences), and the Key Laboratory of Medical Imaging Computing and Computer Assisted Intervention of Shanghai (Grant No. 13DZ2272200-2).

参考文献

[1]	Bruder H, Killmann R, Moshage W, Weismuller P, Achenbach S, Bommel F 1994 Phys. Med. Biol. 39 655
[2]	Sekihara K, Nagarajan S S, Poeppel D, Marantz A, Miyashita Y 2001 IEEE Trans. Biomed. Eng. 48 760
[3]	Kim K, Lee Y H, Kwon H, Kim J M, Bae J H 2006 Comput. Biol. Med. 36 253
[4]	Im U Bin, Kwon S S, Kim K, Lee Y H, Park Y K, Youn C H, Shim E B 2008 Prog. Biophys. Mol. Biol. 96 339
[5]	Jazbinšek V, Kosch O, Steinhoff U, Trontelj Z, Trahms L 2001 Biomed. Tech. Eng. 46 141
[6]	Wang Q, Ma P, Lu H, Tang X Z, Hua N, Tang F K 2009 Chin. Phys. B 18 5566
[7]	Bing L, Wang W Y, Wang Y L, Jiang S Q 2013 Acta Phys. Sin. 62 118703 (in Chinese)[邴璐, 王伟远, 王永良, 蒋式勤2013 物理学报62 118703]
[8]	Wang W Y, Zhao C, Lin Y Z, Zhang S L, Xie X M, Jiang S Q 2013 Acta Phys. Sin. 62 148703 (in Chinese)[王伟远, 赵晨, 林玉章, 张树林, 谢晓明, 蒋式勤2013 物理学报 62 148703]
[9]	Zhu J J, Jiang S Q, Wang W Y, Zhao C, Wu Y H, Luo M, Quan W W 2013 Chinese Phys. B (in press)
[10]	Purcell C J, Stroink G 1991 IEEE Trans. Biomed. Eng. 38 82
[11]	Nenonen J, Purcell C J, Horacek B M, Stroink G, Katila T 1991 IEEE Trans. Biomed. Eng. 38 658
[12]	Ramon C, Casem M 1999 Phys. Med. Biol. 44 2551
[13]	Haueisen J, Schreiber J, Brauer H, Knosche T R 2002 IEEE Trans. Magn. 38 1045
[14]	He B, Li G, Zhang X 2003 IEEE Trans. Biomed. Eng. 50 1190
[15]	Shou G, Xia L, Jiang M, Dou J 2011 IEEE Trans. Magn. 47 2224
[16]	Zhu J J, Jiang S Q, Wang W Y, Zhao C, Wang Y L, Li W S, Quan W W 2014 Acta Phys. Sin. 63 058703 (in Chinese) [朱俊杰, 蒋式勤, 王伟远, 赵晨, 王永良, 李文生, 权薇薇2014 物理学报63 058703]
[17]	Nelder J A, Mead R 1965 Comput. J. 7 308
[18]	Gllmar D, Haueisen J, Reichenbach J R 2010 Neuroimage 51 145
[19]	Kennedy J, Eberhart R 1995 Proceedings of ICNN’95-International Conference on Neural Networks (Vol. 4) Perth, Australia, November 27, 1995–December 1, 1996 p1942
[20]	Ahirwal M K, Kumar A, Singh G K 2013 Swarm Evol. Comput. 300 1
[21]	Shirvany Y, Edelvik F, Jakobsson S, Hedström A, Persson M 2013 Appl. Soft Comput. 13 2515
[22]	Coleman T F, Li Y 1996 SIAM J. Optim. 6 418
[23]	Irimia A 2005 J. Phys. A. Math. Gen. 38 8123
[24]	Bcker H M, Beucker R, Rupp A 2008 SIAM J. Sci. Comput. 30 2905
[25]	Czapski P, Ramon C, Haueisen J, Huntsman L L, Nowak H, Bardy G H, Leder U, Yongmin K, Kim Y 1998 Biomed. Eng. IEEE Trans. 45 1313
[26]	Jiang S, Shi M 2011 2011 8th International Symposium on Noninvasive Functional Source Imaging of the Brain and Heart and the 2011 8th International Conference on Bioelectromagnetism Banff, Canada, May 13–16, 2011 p35
[27]	Zhao C, Zhang W, Jiang S 2012 2012 International Conference on Biomedical Engineering and Biotechnology Macao, China, May 28–30, 2012 p897
[28]	Sarvas J 1987 Phys. Med. Biol. 32 11

施引文献

[1]	Bruder H, Killmann R, Moshage W, Weismuller P, Achenbach S, Bommel F 1994 Phys. Med. Biol. 39 655
[2]	Sekihara K, Nagarajan S S, Poeppel D, Marantz A, Miyashita Y 2001 IEEE Trans. Biomed. Eng. 48 760
[3]	Kim K, Lee Y H, Kwon H, Kim J M, Bae J H 2006 Comput. Biol. Med. 36 253
[4]	Im U Bin, Kwon S S, Kim K, Lee Y H, Park Y K, Youn C H, Shim E B 2008 Prog. Biophys. Mol. Biol. 96 339
[5]	Jazbinšek V, Kosch O, Steinhoff U, Trontelj Z, Trahms L 2001 Biomed. Tech. Eng. 46 141
[6]	Wang Q, Ma P, Lu H, Tang X Z, Hua N, Tang F K 2009 Chin. Phys. B 18 5566
[7]	Bing L, Wang W Y, Wang Y L, Jiang S Q 2013 Acta Phys. Sin. 62 118703 (in Chinese)[邴璐, 王伟远, 王永良, 蒋式勤2013 物理学报62 118703]
[8]	Wang W Y, Zhao C, Lin Y Z, Zhang S L, Xie X M, Jiang S Q 2013 Acta Phys. Sin. 62 148703 (in Chinese)[王伟远, 赵晨, 林玉章, 张树林, 谢晓明, 蒋式勤2013 物理学报 62 148703]
[9]	Zhu J J, Jiang S Q, Wang W Y, Zhao C, Wu Y H, Luo M, Quan W W 2013 Chinese Phys. B (in press)
[10]	Purcell C J, Stroink G 1991 IEEE Trans. Biomed. Eng. 38 82
[11]	Nenonen J, Purcell C J, Horacek B M, Stroink G, Katila T 1991 IEEE Trans. Biomed. Eng. 38 658
[12]	Ramon C, Casem M 1999 Phys. Med. Biol. 44 2551
[13]	Haueisen J, Schreiber J, Brauer H, Knosche T R 2002 IEEE Trans. Magn. 38 1045
[14]	He B, Li G, Zhang X 2003 IEEE Trans. Biomed. Eng. 50 1190
[15]	Shou G, Xia L, Jiang M, Dou J 2011 IEEE Trans. Magn. 47 2224
[16]	Zhu J J, Jiang S Q, Wang W Y, Zhao C, Wang Y L, Li W S, Quan W W 2014 Acta Phys. Sin. 63 058703 (in Chinese) [朱俊杰, 蒋式勤, 王伟远, 赵晨, 王永良, 李文生, 权薇薇2014 物理学报63 058703]
[17]	Nelder J A, Mead R 1965 Comput. J. 7 308
[18]	Gllmar D, Haueisen J, Reichenbach J R 2010 Neuroimage 51 145
[19]	Kennedy J, Eberhart R 1995 Proceedings of ICNN’95-International Conference on Neural Networks (Vol. 4) Perth, Australia, November 27, 1995–December 1, 1996 p1942
[20]	Ahirwal M K, Kumar A, Singh G K 2013 Swarm Evol. Comput. 300 1
[21]	Shirvany Y, Edelvik F, Jakobsson S, Hedström A, Persson M 2013 Appl. Soft Comput. 13 2515
[22]	Coleman T F, Li Y 1996 SIAM J. Optim. 6 418
[23]	Irimia A 2005 J. Phys. A. Math. Gen. 38 8123
[24]	Bcker H M, Beucker R, Rupp A 2008 SIAM J. Sci. Comput. 30 2905
[25]	Czapski P, Ramon C, Haueisen J, Huntsman L L, Nowak H, Bardy G H, Leder U, Yongmin K, Kim Y 1998 Biomed. Eng. IEEE Trans. 45 1313
[26]	Jiang S, Shi M 2011 2011 8th International Symposium on Noninvasive Functional Source Imaging of the Brain and Heart and the 2011 8th International Conference on Bioelectromagnetism Banff, Canada, May 13–16, 2011 p35
[27]	Zhao C, Zhang W, Jiang S 2012 2012 International Conference on Biomedical Engineering and Biotechnology Macao, China, May 28–30, 2012 p897
[28]	Sarvas J 1987 Phys. Med. Biol. 32 11

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