脑电磁源定位算法研究及其在初级听觉皮层定位中的应用
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摘要
脑电图/脑磁图具有无创性和精确到毫秒的时间分辨率等特性而成为一项重要的研究脑神经活动的工具。时空脑电源成像技术MUSIC和Beamformers具有三个特点:一充分利用数据的时间特征;二避免陷入单时刻偶极子拟合优化过程中的局部极小值;三能够获得源的时间过程,获得广泛关注和应用。然而,由于他们都是基于数据相关矩阵的二阶统计量的方法,哪么就隐含了一个约束条件:源之间的时间过程应该是独立的或者不相关的。在实践中,这两种方法对高度相关源比较敏感,会导致较大偏差或者定位失败。而且,对于Beamformers,源之间的相关会导致重建波形畸变。
为了解决这个问题,我们通过改进经典的方法,提出了自己的方法来改善或者解决这些问题。本论文的主要创新点如下:
1.设计特别的变换矩阵,把原始的记录变换到新的数据空间。在变换过程中,压制掉相干干扰源区的活动,从而移除它对定位的影响。在新的数据空间应用经典的时空定位方法将会得到相干源的正确定位。
2.相干干扰源区压制的方法有一个缺点,当源在区域的边缘时,定位误差较大。我们提出了加权源区压制的方法,可以自适应地压制相干干扰源,极大地提高了这种情况下的定位性能。
3.对于Beamformers,由于源间的相关,将导致重建的波形发生较大的畸变。我们提出一种迭代Beamformers来改善性能。这种方法通过点源压制的方法,移除源间的相互影响,可以合理精确地重建相关源的时间过程。
4.经典的时空源定位方法有两个弱点:不能定位高度相关源,尤其距离较近;强源附近的弱源定位有困难,尤其是能量差很大的情况。我们提出了基于噪声不变性的方法NOISE,可以解决这个问题。NOISE可以在合理的噪声下,定位高度相关和/或距离较近的源,对于能量相差大的源也能定位。
我们也通过模拟测试和真实数据测试,证明了以上四种方法的有效性。
MEG/EEG are noninvasive brain imaging techniques providing millisecond time resolution, thereby becoming an important tool for investigating brain neuronal activities. Commonly used spatio-temporal brain source imaging techniques, MUSIC (Multiple Signal Classification) and beamfomers, have three main advantages: utilizing information about spatio-temporal characteristics of the measured data; avoiding being trapped in local minima usually encountered in least squares dipole-searching algorithms; being able to retrieve source time courses, and thus attracted much attention and were widely applied. However, since they are based on the second order statisctics of the data correlation matrix, an implicit assumption is introduced: the time courses between sources are uncorrelated. In practice, due to sensitiveness against high correlation between sources, MUSIC and beamformer in such cases are prone to large bias, even fail to localize coherent sources. Furthermore, for beamformers, correlations between sources will result in significiant distortion for retrieved time courses.
To solve such problems, we proposed the following methods:
1. Coherent source Localization In Space Transformed (LIST). Transform original measured data into new data space by designing specific transformation matrix. The transformation matrix is designed for suppressing the activations from coherent interferring source region, and thus, remove the influence on the subsequent spatio-temporal source localization. Employing concentional MUSIC or beamformers to the new data space will result in correct coherent source localization.
2. weighted coherent source region based beamformers for coherent source localization. a disadvantage of the method-coherent interferring source region suppression-is that, when suppressed source is located close to the bound of the suppression region, it is much more likely to large bias. We proposed the weighted source region suppression strategy. such improvement may adaptively suppress coherent interfering sources, thereby largely reducing localization bias for this case.
3. Iterative beamformer for the waveform reconstruction of correlated brain sources. Due to correlation between sources, beamformers will reconstuct source waveforms with significiant distortion. We proposed a kind of iterative beamformers to improve the reconstruction performance. The method removes the influence of correlation between sources by point source suppression and is able to reasonably accurately reconstruct time courses of coherent sources.
4. NOise Invariant based MEG/EEG Source Estimation (NOISE). Conventional spatio-temporal source localization methods have two main shortcomings: failing to localize highly correlated sources, especially for closely spaced ones; having difficulty identifying weak sources in the vicinity of strong ones, especially in the case of large amplitude difference between sources. The proposed NOISE can largely improve performance in such cases. NOISE can localize highly correlated and/or closely spaced sources under appropriate SNR. For the sources with large amplitude difference, NOISE clearly outperforms MUSIC and beamformers.
All the above methods were validated by simualtion data test and real data.
为了解决这个问题,我们通过改进经典的方法,提出了自己的方法来改善或者解决这些问题。本论文的主要创新点如下:
1.设计特别的变换矩阵,把原始的记录变换到新的数据空间。在变换过程中,压制掉相干干扰源区的活动,从而移除它对定位的影响。在新的数据空间应用经典的时空定位方法将会得到相干源的正确定位。
2.相干干扰源区压制的方法有一个缺点,当源在区域的边缘时,定位误差较大。我们提出了加权源区压制的方法,可以自适应地压制相干干扰源,极大地提高了这种情况下的定位性能。
3.对于Beamformers,由于源间的相关,将导致重建的波形发生较大的畸变。我们提出一种迭代Beamformers来改善性能。这种方法通过点源压制的方法,移除源间的相互影响,可以合理精确地重建相关源的时间过程。
4.经典的时空源定位方法有两个弱点:不能定位高度相关源,尤其距离较近;强源附近的弱源定位有困难,尤其是能量差很大的情况。我们提出了基于噪声不变性的方法NOISE,可以解决这个问题。NOISE可以在合理的噪声下,定位高度相关和/或距离较近的源,对于能量相差大的源也能定位。
我们也通过模拟测试和真实数据测试,证明了以上四种方法的有效性。
MEG/EEG are noninvasive brain imaging techniques providing millisecond time resolution, thereby becoming an important tool for investigating brain neuronal activities. Commonly used spatio-temporal brain source imaging techniques, MUSIC (Multiple Signal Classification) and beamfomers, have three main advantages: utilizing information about spatio-temporal characteristics of the measured data; avoiding being trapped in local minima usually encountered in least squares dipole-searching algorithms; being able to retrieve source time courses, and thus attracted much attention and were widely applied. However, since they are based on the second order statisctics of the data correlation matrix, an implicit assumption is introduced: the time courses between sources are uncorrelated. In practice, due to sensitiveness against high correlation between sources, MUSIC and beamformer in such cases are prone to large bias, even fail to localize coherent sources. Furthermore, for beamformers, correlations between sources will result in significiant distortion for retrieved time courses.
To solve such problems, we proposed the following methods:
1. Coherent source Localization In Space Transformed (LIST). Transform original measured data into new data space by designing specific transformation matrix. The transformation matrix is designed for suppressing the activations from coherent interferring source region, and thus, remove the influence on the subsequent spatio-temporal source localization. Employing concentional MUSIC or beamformers to the new data space will result in correct coherent source localization.
2. weighted coherent source region based beamformers for coherent source localization. a disadvantage of the method-coherent interferring source region suppression-is that, when suppressed source is located close to the bound of the suppression region, it is much more likely to large bias. We proposed the weighted source region suppression strategy. such improvement may adaptively suppress coherent interfering sources, thereby largely reducing localization bias for this case.
3. Iterative beamformer for the waveform reconstruction of correlated brain sources. Due to correlation between sources, beamformers will reconstuct source waveforms with significiant distortion. We proposed a kind of iterative beamformers to improve the reconstruction performance. The method removes the influence of correlation between sources by point source suppression and is able to reasonably accurately reconstruct time courses of coherent sources.
4. NOise Invariant based MEG/EEG Source Estimation (NOISE). Conventional spatio-temporal source localization methods have two main shortcomings: failing to localize highly correlated sources, especially for closely spaced ones; having difficulty identifying weak sources in the vicinity of strong ones, especially in the case of large amplitude difference between sources. The proposed NOISE can largely improve performance in such cases. NOISE can localize highly correlated and/or closely spaced sources under appropriate SNR. For the sources with large amplitude difference, NOISE clearly outperforms MUSIC and beamformers.
All the above methods were validated by simualtion data test and real data.
引文
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[32] Darvas, F., et al., Mapping human brain function with MEG and EEG: methods and validation. Neuroimage, 2004. 23 Suppl 1:S289-99.
[33] Dalal, S.S., K. Sekihara, and S.S. Nagarajan, Modified beamformers for coherent source region suppression. IEEE Trans Biomed Eng, 2006. 53(7):1357-63.
[34] Quraan, M.A. and D. Cheyne, Reconstruction of correlated brain activity with adaptive spatial filters in MEG. Neuroimage, 2009. 49(3):2387-2400.
[35] Popescu, M., et al., Spatio-temporal reconstruction of bilateral auditory steady-state responses using MEG beamformers. IEEE Trans Biomed Eng, 2008. 55(3):1092-102.
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[37] Herdman, A.T., et al., Determination of activation areas in the human auditory cortex by means of synthetic aperture magnetometry. Neuroimage, 2003. 20(2):995-1005.
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[39] Zhang, J. and D. Yao, Improved beamformer with weighted source region suppression for coherent MEG source localization. Biomedical Engineering: Applications, Basis and Communications, 2010. 22(3):239-248.
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[42] Sekihara, K., et al., Application of an MEG eigenspace beamformer to reconstructing spatio temporal activities of neural sources. Human Brain Mapping, 2002. 15(4):199-215.
[43] Sekihara, K., et al., Reconstructing spatio-temporal activities of neural sources using an MEG vector beamformer technique. IEEE Trans Biomed Eng, 2001. 48(7):760-771.
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[45] Herdman, A., et al., Determination of activation areas in the human auditory cortex by means of synthetic aperture magnetometry. Neuroimage, 2003. 20(2):995-1005.
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[47] Rodriguez-Rivera, A., et al., MEG and EEG Source Localization in Beamspace. IEEE Transactions on Biomedical Engineering, 2006. 53(3):430-441.
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[2]尧德中,脑功能探测的电学理论与方法. 2003:科学出版社.
[3] Michel, C.M., et al., EEG source imaging. Clin Neurophysiol, 2004. 115(10):2195-222.
[4] Haueisen, J., et al., Influence of tissue resistivities on neuromagnetic fields and electric potentials studied with a finite element model of the head. IEEE Transactions on Biomedical Engineering, 2002. 44(8):727-735.
[5] Fuchs, M., et al., An improved boundary element method for realistic volume-conductor modeling. Biomedical Engineering, IEEE Transactions on, 2002. 45(8):980-997.
[6] Yao, D., High-resolution EEG mapping: an equivalent charge-layer approach. Phys Med Biol, 2003. 48:1997.
[7] Yao, J. and J. Dewald, Evaluation of different cortical source localization methods using simulated and experimental EEG data. Neuroimage, 2005. 25(2):369-382.
[8] H?m?l?inen, M.S. and R.J. Ilmoniemi, Interpreting measured magnetic fields of the brain: estimates of current distributions, in Tech. Rep. TKKF-A559. 1984, Helsinki University of Technology.
[9] Dale, A.M., et al., Dynamic Statistical Parametric Mapping:: Combining fMRI and MEG for High-Resolution Imaging of Cortical Activity. Neuroimage, 2000. 26(1):55-67.
[10] Gorodnitsky, I.F. and B.D. Rao, Sparse signal reconstruction from limited data using FOCUSS: A re-weighted minimum norm algorithm. IEEE Transactions on Signal Processing, 1997. 45(3):600-616.
[11] Pascual-Marqui, R.D., Standardized low-resolution brain electromagnetic tomography (sLORETA): technical details. Methods Find Exp Clin Pharmacol, 2002. 24 Suppl D:5-12.
[12] Yao, D., The Laplacian weighted minimum norm estimate of three dimensional equivalent charge distribution in the brain, in Proc. IEEE/EMBS Conf. 1998, IEEE. p. 2108-2111.
[13] Xu, P., et al., Equivalent charge source model based iterative maximum neighbor weight for sparse EEG source localization. Annals of biomedical engineering, 2008. 36(12):2051-2067.
[14] Yao, D. and B. He, A self-coherence enhancement algorithm and its application to enhancing three-dimensional source estimation from EEGs. Ann. Biomed.Eng., 2001. 29(11):1019-1027.
[15] Xu, P., et al., Lp Norm Iterative Sparse Solution for EEG Source Localization. IEEE Trans Biomed Eng, 2007. 54(3):400-409.
[16] Xu, P., et al., Neuroelectric source imaging using 3SCO: A space coding algorithm based on particle swarm optimization and l0 norm constraint. NeuroImage, 2010. 51(1):183-205.
[17] Lei, X., et al., fMRI Functional Networks for EEG Source Imaging. Human Brain Mapping:In press.
[18] Sekihara, K., M. Sahani, and S.S. Nagarajan, Localization bias and spatial resolution of adaptive and non-adaptive spatial filters for MEG source reconstruction. Neuroimage, 2005. 25(4):1056-1067.
[19] Schmidt, R.O., Multiple emitter location and signal parameter estimation. IEEE Transactions on Antennas and Propagation, 1986. AP-34(3):276-280.
[20] Mosher, J.C., P.S. Lewis, and R.M. Leahy, Multiple dipole modeling and localization from spatio-temporal MEGdata. IEEE Trans Biomed Eng, 1992. 39(6):541-557.
[21] Mosher, J.C. and R.M. Leahy, Recursive MUSIC: a framework for EEG and MEG source localization. IEEE Trans Biomed Eng, 1998. 45(11):1342-54.
[22] Mosher, J.C. and R.M. Leahy, Source localization using recursively applied and projected (RAP) MUSIC. IEEE Transactions on Signal Processing, 1999. 47(2):332-340.
[23] Borgiotti, G. and L. Kaplan, Superresolution of uncorrelated interference sources by using adaptive array techniques. IEEE Trans. Antennas Propag., 1979. 27(6):842-845.
[24] Van Veen, B.D., et al., Localization of brain electrical activity via linearly constrained minimum variance spatial filtering. IEEE Trans Biomed Eng, 1997. 44(9):867-80.
[25] Robinson, S.E. and D.F. Rose, Current source image estimation by spatially filtered MEG. Biomagnetism:Clin. Aspects, 1992:761–765.
[26] Zhang, J., et al., Multivariate Correlation Coefficient Decomposition and Its Application to Visual Evoked Potentials, in 27th IEEE Annual International Conference of the Engineering in Medicine and Biology Society. 2005: Shanghai, China.
[27]张军鹏,尧德中, and崔园,多变量相关系数分解及其在脑电相干源成像中的应用.中国生物医学工程学报, 2006. 25(001):6-9.
[28]张军鹏,尧德中, and崔园.一种分析相关脑电活动的新方法. in中国生物医学工程进展——2007中国生物医学工程联合学术年会论文集(上册). 2007.中国西安.
[29] Zhang, J., et al., Multivariate coherence decomposition: a simulation study, in 27th IEEE Annual International Conference of the Engineering in Medicine and Biology Society. 2005: Shanghai, China. p. 1518-1520.
[30] Zhang, J. and D. Yao. Iterative Beamformers for Waveform Reconstruction of the Correlated Neural Sources. in The 2nd IEEE Workshop on Communication among Neuroscience, Cognition and Information Technology. 2010. Chengdu, China.
[31] Zhang, J. and D. Yao. Localization of Brain Electrical Activity by A Combination of Beamforming and Independent Component Analysis. in The 2nd IEEE Workshop on Communication among Neuroscience, Cognition and Information Technology. 2010. Chengdu, China.
[32] Darvas, F., et al., Mapping human brain function with MEG and EEG: methods and validation. Neuroimage, 2004. 23 Suppl 1:S289-99.
[33] Dalal, S.S., K. Sekihara, and S.S. Nagarajan, Modified beamformers for coherent source region suppression. IEEE Trans Biomed Eng, 2006. 53(7):1357-63.
[34] Quraan, M.A. and D. Cheyne, Reconstruction of correlated brain activity with adaptive spatial filters in MEG. Neuroimage, 2009. 49(3):2387-2400.
[35] Popescu, M., et al., Spatio-temporal reconstruction of bilateral auditory steady-state responses using MEG beamformers. IEEE Trans Biomed Eng, 2008. 55(3):1092-102.
[36] Brookes, M.J., et al., Beamformer reconstruction of correlated sources using a modified source model. Neuroimage, 2007. 34(4):1454-1465.
[37] Herdman, A.T., et al., Determination of activation areas in the human auditory cortex by means of synthetic aperture magnetometry. Neuroimage, 2003. 20(2):995-1005.
[38] Huang, M.X., et al., Commonalities and differences among vectorized beamformers in electromagnetic source imaging. Brain topography, 2004. 16(3):139-158.
[39] Zhang, J. and D. Yao, Improved beamformer with weighted source region suppression for coherent MEG source localization. Biomedical Engineering: Applications, Basis and Communications, 2010. 22(3):239-248.
[40] Pascual-Marqui, R., C. Michel, and D. Lehmann, Low resolution electromagnetic tomography: a new method for localizing electrical activity in the brain. International Journal of Psychophysiology, 1994. 18(1):49-65.
[41] Sekihara, K., M. Sahani, and S. Nagarajan, Localization bias and spatial resolution of adaptive and non-adaptive spatial filters for MEG source reconstruction. Neuroimage, 2005. 25(4):1056-1067.
[42] Sekihara, K., et al., Application of an MEG eigenspace beamformer to reconstructing spatio temporal activities of neural sources. Human Brain Mapping, 2002. 15(4):199-215.
[43] Sekihara, K., et al., Reconstructing spatio-temporal activities of neural sources using an MEG vector beamformer technique. IEEE Trans Biomed Eng, 2001. 48(7):760-771.
[44] Pekkonen, E., et al., Age-related functional differences between auditory cortices: a whole-head MEG study. Neuroreport, 1995. 6(13):1803.
[45] Herdman, A., et al., Determination of activation areas in the human auditory cortex by means of synthetic aperture magnetometry. Neuroimage, 2003. 20(2):995-1005.
[46] Gross, J. and A. Ioannides, Linear transformations of data space in MEG. Phys Med Biol, 1999. 44:2081.
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