Gaussian source model based iterative algorithm for EEG source imaging

Estimation of the neural active sources from the scalp electroencephalogram (EEG) is an ill-posed inverse problem. In this paper, we propose a new source model: Gaussian distributed Source Model (GSM), to model the activations in brain. GSM may imitate an Isolated Source Model (ISM) or a Distributed Source Model (DSM) by adopting different supporting range parameter of the Gaussian function. Using GSM, an iterative Gaussian source Imaging Algorithm (GIA) is developed to detect the EEG sources. As GIA dynamically reduces the solution space, the solution may gradually converge to a desired distribution. A comparative evaluation among LORETA, FOCUSS and GIA was conducted for both isolated point sources and distributed sources, the results demonstrate that GIA is more flexible and efficient for various actual sources configurations. Finally, GSM was applied to real recordings obtained from a visual spatial attention task; the corresponding source activation areas of the early component are localized in contralateral occipital cortices, consistent with the retinotopic organization of early visual spatial attention effects.     

A Self-Coherence Enhancement Algorithm and its Application to Enhancing Three-Dimensional Source Estimation from EEGs

In this paper a new algorithm is proposed to enhance the spatial resolution of solutions of the underdetermined EEG inverse problem. Termed the self-coherence enhancement algorithm (SCEA), the present algorithm provides a self-coherence solution, which is a function of the high order self-coherence estimate of an unbiased smooth estimate of the underdetermined EEG inverse solution. The order of the high order self-coherence function is determined by the blurring level of the actual source distribution as represented by a normalized blurring index. The proposed SCEA algorithm may be used to enhance the spatial resolution of an inverse solution obtained by any inverse reconstruction algorithm. Computer simulation studies have been conducted to evaluate the performance of the SCEA and to compare its performance to that of the LORETA and the FOCUSS algorithms. © 2001 Biomedical Engineering Society. PAC01: 8719Nn, 8780-y, 0230Zz     

基于fMRI加权约束的FOCUSS迭代脑电源定位方法及其初步应用

脑电(Electroencephalography, EEG)和功能磁共振(Functional magnetic resonance imaging, fMRI)技术的结合,可以实现两者优势的互补,获得更加合理的源定位结果.本文报道的是一种将fMRI先验信息结合到脑电源定位中的新方法.在该方法中,先利用SPM方法计算获得fMRI的统计映射参数,然后将基于计算获得的统计参数构造的权矩阵结合到FOCUSS的迭代过程中,对脑电的反演提供具有fMRI先验空间位置信息的约束,提高脑电的源空间定位精度,从而获得更加合理的定位结果.通过对一形状知觉实验fMRI和脑电数据的结合定位分析,结果初步证实了改进方法能获得和生理更加一致的结果.     

Evaluation of smoothing in an iterative lp-norm minimization algorithm for surface-based source localization of MEG

The imaging of neural sources of magnetoencephalographic data based on distributed source models requires additional constraints on the source distribution in order to overcome ill-posedness and obtain a plausible solution. The minimum l(p) norm (0 < p < or = 1) constraint is known to be appropriate for reconstructing focal sources distributed in several regions. A well-known recursive method for solving the l(p)-norm minimization problem, for example, is the focal underdetermined system solver (FOCUSS). However, this iterative algorithm tends to give spurious sources when the noise level is high. In this study, we present an algorithm to incorporate a smoothing technique into the FOCUSS algorithm and test different smoothing kernels in a surface-based cortical source space. Simulations with cortical source patches assumed in auditory areas show that the incorporation of the smoothing procedure improves the performance of the FOCUSS algorithm, and that using the geodesic distance for constructing a smoothing kernel is a better choice than using the Euclidean one, particularly when employing a cortical source space. We also apply these methods to a real data set obtained from an auditory experiment and illustrate their applicability to realistic data by presenting the reconstructed source images localized in the superior temporal gyrus.     

基于正则化方法的加权最小模估计在脑磁源成像中的应用

脑磁图 ( m agnetoencephalography,MEG)逆问题的研究 ,根据点源和分布源两种源模型 ,可分为偶极子定位和磁源成像两大类求逆方法。采用非参数的分布源模型 ,MEG逆问题转化为一个病态的欠定方程组的求解。本文系统地阐述了结合 Tikhonov正则技术的加权最小模磁源重建方法 ,着重介绍了深度归一化算法、低分辨率脑电磁断层成像技术、局部欠定系统解法、选择性最小模方法 ,此外还从广义的加权最小模估计角度对最大熵重建方法 ,融合其它脑功能成像技术的方法以及最大后验概率估计方法加以解释和分析。不同的磁源成像方法目的都是通过引入合适的约束条件 ,从算法公式本身及神经细胞活动的特性中加以修正 ,减少逆问题的不适定程度 ,因此均可认为是使用正则方法来约束解空间 ,从而获得与测量磁场数据相拟合的并具有神经生理学和解剖学意义下的最合理的解。基于正则化技术的加权最小模估计是 MEG逆问题研究中最早开展、并已被广泛应用的磁源分布图像重建方法 ,本文给出了一个较为完整的理论发展框架     

Properties of Advanced Headmodelling and Source Reconstruction for the Localization of Epileptiform Activity

During the last decade multiple work has been done to determine the sources of epileptiform activity by means of dipole source localization based on recordings of the magnetoencephalogram (MEG) or the electroencephalogram (EEG). The actual available advanced volume conductor models and the multiple source reconstruction by regularization may give new impulse to EEG based source analyses in epilepsy patients. This study demonstrates the principal properties of these techniques. We applied two different EEG source reconstruction techniques within different volume conductor models to localize induced spike activity in a selected patient suffering from medically intractable temporal lobe epilepsy: 1) single moving dipole solution in a 3-shell spherical model versus individual head models (boundary-element-model, BEM, and finite-element-model, FEM); 2) a regularization technique for current density reconstructions using both BEM and FEM. When compared to findings of invasive recordings no adequate source locations were derived from the moving dipole solution in both the 3-shell head model and BEM. In contrast, a high congruence of source reconstruction and invasive determination of the focus was obtained using the regularization techniques in both BEM and FEM, indicating the high spatial accuracy of this technique in individual head models.     

Spectral Evaluation of the Electroencephalogram: Power and Variability in Chronic Schizophrenics and Control Subjects

Selected EEG parameters were evaluated for their ability to discriminate between a group of 30 chronic schizophrenic and 30 control Ss. For each S 150 random EEG segments were collected. The results confirmed that the coefficient of variation of the absolute EEG potential recorded from the occiput is significantly (φ <.03) smaller in schizophrenics than in controls. The power density spectrum was calculated for each EEG segment. β power was significantly higher in patients, markedly so in the β₂ band (34–54 Hz). The possibility of muscle contamination was considered. Coefficients of variation were calculated for the power in EEG frequency bands for each S. The most significant discriminator between schizophrenics and controls, considered to be artifact free, was the coefficient of variation of β₁ (18–32 Hz) recorded from an anterior-posterior electrode pair at the vertex (p <.0005). Included in the evaluations were: ordering of the EEG segments by delta band power, as an index of arousal; subject age; exposure to medication; and severity of illness.     

Lead-field Bases for Electroencephalography Source Imaging

In recent years, significant progress has been made in the area of electroencephalography (EEG) source imaging. Source localization on simple spherical models has become increasingly efficient, with consistently reported accuracy of within 5 mm. In contrast, source localization on realistic head models remains slow, with subcentimeter accuracy being the exception rather than the norm. A primary reason for this discrepancy is that most source imaging techniques are based on lead fields. While the lead field for simplified geometries can be easily computed analytically, an efficient method for computing realistic domain lead fields has, until now, remained elusive. In this paper, we propose two efficient methods for computing realistic EEG lead-field bases: the first is element oriented and the second is node oriented. We compare these two bases, discuss how they can be used to apply recent source imaging methods to realistic models, and report timings for constructing the bases. © 2000 Biomedical Engineering Society. PAC00: 8719Nn, 8780Tq     

基于偶极子特征优化的情绪重评同步EEG-fMRI源定位研究

为研究情绪重评时的大脑皮层源活动,针对情绪重评实验范式下采集的15例健康人同步EEG-fMRI数据,首先提出一种新颖的基于偶极子特征优化的融合源定位方法:根据fMRI加权最小范数估计源定位结果,采用20 ms EEG滑动时间窗,提取每个时窗内的偶极子空间融合特征,将其作为动态融合先验进行加权最小范数估计溯源;随后将该结...     

Evaluation of Algorithms for Intracranial EEG (iEEG) Source Imaging of Extended Sources: Feasibility of Using iEEG Source Imaging for Localizing Epileptogenic Zones in Secondary Generalized Epilepsy

Precise identification of epileptogenic zones in patients with intractable drug-resistant epilepsy is critical for successful epilepsy surgery. Numerous source-imaging algorithms for localizing epileptogenic zones based on scalp electroencephalography (EEG) and magnetoencephalography (MEG) have been developed and validated in simulation and experimental studies. Recently, intracranial EEG (iEEG)-based imaging of epileptogenic sources has attracted interest as a promising tool for presurgical evaluation of epilepsy; however, most iEEG studies have focused on localization of epileptogenic zones in focal epilepsy. In the present study, we investigated whether iEEG source imaging is a useful supplementary tool for identifying extended epileptogenic sources in secondary generalized epilepsy such as Lennox-Gastaut syndrome (LGS). To this end, we applied four different cortical source imaging algorithms, namely minimum norm estimation (MNE), low-resolution electromagnetic tomography (LORETA), standardized LORETA (sLORETA), and L _p -norm estimation (p = 1.5, referred to as Lp1.5), to artificial iEEG datasets generated assuming various source sizes and locations. We also applied these four algorithms to clinical ictal iEEG recordings acquired from a pediatric patient with LGS. Interestingly, the traditional MNE algorithm outperformed the other imaging algorithms in most of our experiments, particularly in cases when larger-sized sources were activated. Although sLORETA outperformed both LORETA and Lp1.5, its performance was not as good as that of MNE. Compared to the other algorithms, the performance of Lp1.5 decayed most rapidly as the source size increased. Our findings suggest that iEEG source imaging using MNE is a promising auxiliary tool for the identification of epileptogenic zones in secondary generalized epilepsy. We anticipate that our results will provide useful guidelines for selection of an appropriate imaging algorithm for iEEG source imaging studies.     

Multi-Resolution FOCUSS: A Source Imaging Technique Applied to MEG Data

Summary: A variety of techniques are available for imaging magnetoencephalographic (MEG) data to the corresponding cortical structures. Each performs a functional optimization that includes mathematical and physical restrictions on source activity. Unlike other imaging techniques, MR-FOCUSS (Multi-Resolution FOCal Underdetermined System Solution) utilizes a wavelet statistical operator that allows spatial resolution to be chosen appropriately for focal or extended sources. Control of focal imaging properties is achieved by specifying P in an l_P norm distribution template used to construct the wavelets. In addition, incorporation of a multi-resolution wavelet operator desensitizes the mathematical algorithm to noise, (regularization). Like the FOCUSS imaging technique, an initial estimate of cortical activity is recursively enhanced to obtain the final high resolution imaging results. Studies of model MEG data representing all regions of a realistic cortical model are performed to quantify MR-FOCUSS imaging properties. These modeled data studies included single and multiple dipole sources as well as an extended source model. Thus, MR-FOCUSS is found to be very effective for imaging language processing for pre-surgical planning and provides a high-resolution method to image sequential activation of multiple correlated sources involved in language processing. This research Including the development of the MR-FOCUSS imaging technique and software implementation was supported by NIH/NINDS Grant R01 NS30914.     

The Effect of Predictability on Evoked Response Enhancement in Intramodal Selective Attention

We investigated the relationship between the attention enhancement of the visual average evoked response (AER) and the S's ability to predict the presentation of the attended stimulus. Twelve students were presented with sequences of two distinct visual stimuli while DC EEG and electro-oculogram (EOG) were simultaneously recorded. Stimuli were either regularly alternated (predictable) or randomly intermixed (nonpredictable). Verbal instructions directed S's attention and push button response to either one or both of the two stimuli. Interstimulus interval was held constant to permit computer averaging of the AER and the contingent negative variation. Selective attention enhanced the late positive component of the AER equally in the two conditions of predictability. Thus, it seems that the AER enhancement with intramodal selective attention does not depend on the S's ability to predict the presentation of the attended stimulus or to differentially arouse prior to its presentation. In the high predictability condition, the baseline EEG potential fluctuated with attention such that the AERs to the attended stimuli were negative relative to those to the ignored stimuli.     

Differential Contributions of Blinks and Vertical Eye Movements as Artifacts in EEG Recording

Blinks and vertical eye movements were studied as artifacts of EEG recording. The electro-oculogram (EOG) and vertex vs joined mastoids EEG were recorded in 13 college-aged subjects. Subjects were asked to blink “normally, without excessive effort,” and move their eyes through vertical visual arcs of 5°, 10°, 20°, 30°, and 60°. The ratio EEG/EOG, the fraction of the EOG potential transmitting to the scalp EEG electrode as artifact, was calculated for potentials generated during both blinks and eye movement. Vertical eye movement scalp EEG artifact was a constant percentage of the vertical eye movement EOG across visual arcs of 10° to 60°. Mean percentage eye blink EEG artifact (9.3%) was significantly (p < .001) less than the mean percentage vertical eye movement artifact (13.9%). Thus, blink and vertical eye movement artifact fields are quantitatively different in terms of their transmission to the scalp (C_z) EEG electrode. Subtraction of a single subject specific percentage of the EOG from the EEG would correct for either artifact source, but different subtraction percentages must be used for each.     

Prevalence and Methods of Control of the Cephalic Skin Potential EEG Artifact

Prevalence of the cephalic skin potential (CSP) artifact was studied in 21 Ss during EEG recording of the Contingent Negative Variation (CNV), averaged evoked response (AER), and verbal free association test. Skin potential response and electro-oculogram (EOG) were also recorded. Subdermal pin electrodes and local anesthesia infusion were employed to eliminate the CSP artifact in the EEG. Results indicated that EEG recorded from subdermal pin electrodes or from locally anesthetized scalp was free of CSP artifact. The EEG recorded from subdermal pin electrodes demonstrated spontaneous potential shifts but appeared adequate for EEG recording of the CNV or the AER. Significant CSP artifact was demonstrated in the EEG of 10 of 21 Ss, both evoked by stimuli (10 Ss) and spontaneous (3 Ss). CSP artifact significantly increased CNV amplitude. CSP artifact significantly increased the AER late positive wave (P3) to infrequent tones. Studies of CNV and AER can be confounded by CSP artifact. Above techniques appear promising for recording EEG free of CSP artifact.     

Synthesis of Branched Polymers by Means of Living Anionic Polymerization, 8. Synthesis of Well‐Defined Star‐Branched Polymers by an Iterative Approach Based on Living Anionic Polymerization Using 1,1‐Diphenylethylene Derivatives

The synthesis of well‐defined four‐ and six‐arm star branched polymers in which arms differ either in molecular weight or composition has been achieved via a new iterative approach based on living anionic polymerization using 1,1‐diphenylethylene (DPE) derivatives. Each stage in the iteration involves two reactions: a living functionalization reaction of living anionic polymer with DPE derivatives and an in‐situ reaction of the resulting linked product having two anions with 1‐4‐(4‐bromobutyl)phenyl]‐1‐phenylethylene to introduce two DPE moieties into the polymer. In each living functionalization reaction, a 1.2‐fold excess or more of living anionic polymer relative to DPE moiety was employed to complete the reaction. Asymmetric A₂A′₂ and A₂A′₂A′′₂ star‐branched polystyrenes as well as A₂B₂ and A₂B₂C₂ heteroarm star‐branched polymers were synthesized by repeating the iteration synthetic sequence two and three times, respectively. Since the polymers obtained by each reaction stage were contaminated with their precursor polymers, they were isolated by SEC fractionation. Their high degrees of compositional, molecular weight and architectural homogeneity were confirmed by the analytical results of SEC, SLS, VPO, ¹H NMR and viscosity measurements.     

Equivalent Dipole Source Imaging of Brain Electric Activity by Means of Parametric Projection Filter

In the present study, spatial filters for inverse estimation of an equivalent dipole layer from the scalp-recorded potentials have been explored for their suitability in achieving high-resolution electroencephalogram (EEG) imaging. The performance of the parametric projection filter (PPF), which we propose to use for high-resolution EEG imaging, has been evaluated by computer simulations in the presence of a priori information on noise. An inhomogeneous three-concentric-sphere head model was used in the present simulation study to represent the head volume conductor. An equivalent dipole layer was used to model brain electric sources and estimated from the scalp potentials. Various noise conditions were simulated and the parametric projection filter was compared with standard regularization procedures such as the truncated singular value decomposition (TSVD) and the Tikhonov regularization (TKNV). The present simulation results suggest that the proposed method performs better than that of commonly used inverse regularization techniques, such as the general inverse using the TSVD and the TKNV, when the correlation between the original source distribution and the noise distribution is low, and performs similarly when the correlation is high. A method for determining the optimum regularization parameter, which can be applied to parametric inverse techniques, has also been developed. © 2001 Biomedical Engineering Society. PAC01: 8757Nk, 0230Zz, 8719Nn, 0260Dc     

Evidence for differential human slow-wave activity regulation across the brain

The regulation of the timing of sleep is thought to be linked to the temporal dynamics of slow‐wave activity [SWA, electroencephalogram (EEG) spectral power in the ～0.75–4.5 Hz range] in the cortical non‐rapid eye movement (NREM) sleep EEG. In the two‐process model of sleep regulation, SWA was used as a direct indication of sleep debt, or Process S. Originally, estimation of the latter was performed in a gross way, by measuring average SWA across NREM–REM sleep cycles, fitting an exponential curve to the values thus obtained and estimating its time constant. In later studies, SWA was assumed to be proportional to the instantaneous decay rate of Process S, rather than taken as a direct reflection of S. Following up on this, we extended the existing model of SWA dynamics in which the effects of intrusions of REM sleep and wakefulness were incorporated. For each subject, a ‘gain constant’ can be estimated that quantifies the efficiency of SWA in dissipating S. As the course of SWA is variable across cortical locations, local differences are likely to exist in the rate of discharge of S, eventually leading to different levels of S in different cortical regions. In this study, we estimate the extent of local differences of SWA regulation on the basis of the extended model of SWA dynamics, for 26 locations on the scalp. We observed higher efficiency of SWA in dissipation of S in frontal EEG derivations, suggesting that SWA regulation has a clear local aspect. This result further suggests that the process involved in (local) SWA regulation cannot be identical to the Process S involved (with Process C) in effectual determination of sleep timing – a single behaviour that cannot vary between locations on the scalp. We therefore propose to distinguish these two representations and characterize the former, purely SWA‐related, as ‘Process Z’, which then is different for different locations on the scalp. To demonstrate those differences, we compare the gain constants derived for the medial EEG derivations (Fz, Cz, Pz, Oz) with each other and with the decay rate derived from SWA values per NREM–REM sleep cycle.     

视听联合刺激的跨感觉通道诱发电位源的分析

运用偶极子源分析方法分析视听单独刺激和联合刺激下脑区的区别和联系.采用64道脑电采集系统,记录了7名被试者在视觉、听觉和视听联合刺激下的脑诱发电位,并分别在初期、早期和晚期时间段对这3种任务做偶极子源分析.通过比较视听联合刺激和视听单独刺激下偶极子源的变化,可以得到视听联合刺激下的源不等于单独视听刺激下的源的简单叠加,从而提示存在视听相互作用的区域.     

基于独立分量分析的拟牛顿方法在脑电多源定位问题中的应用

在时空源模型的基础上，应用基于独立分量分析的拟牛顿方法进行多源的分离及定位，源分离的过程使得多偶极子的定位问题转化成几个单偶极子的定位，此方法的另一个优点是可以获得独立源的数目。计算机仿真表明：基于独立分量分析的拟牛顿方法在定位精度、计算时间及抗噪性能等方面都要优于传统的非线性优化方法。     

Ictal dipole source analysis based on a realistic scalp-skull-brain head model in localizing the epileptogenic zone

The objective of this study is to examine whether dipole modeling based on a realistic scalp-skull-brain head model (SSB/DT) is useful to localize the epileptogenic zone. Eight patients with surgically treated temporal lobe epilepsy were studied. Dipole locations and vector moments of ictal epileptiform activities were calculated by inverse solution methods. Accuracy of dipole locations were assessed by comparing with intracranial EEG. The patterns of ictal epileptiform activities were correlated with the dipole location and vector moment. Dipole locations of the peaks of ictal epileptiform activities estimated by SSB/DT showed good agreement with the epileptogenic foci determined by intracranial EEG. SSB/DT was able to discriminate between medial and lateral temporal epileptogenic foci. Two distinctive types of dipole vector moments, vertical and horizontal were noted. Vertical dipole vector moments corresponded to the medial temporal dipole source and horizontal dipole vector moments were corresponded to the lateral temporal dipole source. Useful clues to differentiate between medial and lateral temporal lobe epilepsy by the visual inspection of scalp EEG were found. SSB/DT is useful tool in the presurgical evaluation of patients with intractable epilepsy.