www.elsevier.com/locate/ynimg NeuroImage 25 (2004) 539 – 553
Validation of SOBI components from high-density EEG Akaysha C. Tang,a,b,c,* Matthew T. Sutherland,a and Christopher J. McKinneya a
Department of Psychology, University of New Mexico, Logan Hall, Albuquerque, NM 87131, USA Department of Neuroscience, University of New Mexico, Albuquerque, NM 87131, USA c Department of Computer Science, University of New Mexico, Albuquerque, NM 87131, USA b
Received 29 June 2004; revised 8 October 2004; accepted 22 November 2004 Available online 27 January 2005 Second-order blind identification (SOBI) is a blind source separation (BSS) algorithm that can be used to decompose mixtures of signals into a set of components or putative recovered sources. Previously, SOBI, as well as other BSS algorithms, has been applied to magnetoencephalography (MEG) and electroencephalography (EEG) data. These BSS algorithms have been shown to recover components that appear to be physiologically and neuroanatomically interpretable. While some proponents of these algorithms suggest that fundamental discoveries about the human brain might be made through the application of these techniques, validation of BSS components has not yet received sufficient attention. Here we present two experiments for validating SOBI-recovered components. The first takes advantage of the fact that noise sources associated with individual sensors can be objectively validated independently from the SOBI process. The second utilizes the fact that the time course and location of primary somatosensory (SI) cortex activation by median nerve stimulation have been extensively characterized using converging imaging methods. In this paper, using both known noise sources and highly constrained and well-characterized neuronal sources, we provide validation for SOBI decomposition of high-density EEG data. We show that SOBI is able to (1) recover known noise sources that were either spontaneously occurring or artificially induced; (2) recover neuronal sources activated by median nerve stimulation that were spatially and temporally consistent with estimates obtained from previous EEG, MEG, and fMRI studies; (3) improve the signal-to-noise ratio (SNR) of somatosensory-evoked potentials (SEPs); and (4) reduce the level of subjectivity involved in the source localization process. D 2004 Elsevier Inc. All rights reserved. Keywords: Blind source separation (BSS); Second-order blind identification (SOBI); Independent component analysis (ICA); Electroencephalography (EEG); Source modeling; Equivalent current dipole (ECD); Event-related potentials (ERP); Median nerve; Somatosensory; Source localization
* Corresponding author. Department of Psychology, University of New Mexico, Logan Hall, Albuquerque, NM 87131, USA. Fax: +1 505 277 1394. E-mail address:
[email protected] (A.C. Tang). Available online on ScienceDirect (www.sciencedirect.com). 1053-8119/$ - see front matter D 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.neuroimage.2004.11.027
Introduction Electroencephalography (EEG) and magnetoencephalography (MEG) are noninvasive tools that offer millisecond temporal resolution for the study of neural mechanisms underlying mental phenomena. Both EEG and MEG signals recorded at the scalp are mixtures of signals from multiple intra- and extracranial sources, thus such sensor signals do not necessarily reflect brain activity immediately below the sensors. To extract underlying sources of interest from such mixtures, blind source separation (BSS) algorithms (Hyvarinen et al., 2001; Jutten and Herault, 1991) have been increasingly applied to EEG and MEG data (Jung et al., 2001; Stone, 2002; Tang and Pearlmutter, 2003; Vigario and Oja, 2000; Vigario et al., 2000) collected during a range of sensory and motor activation tasks, including signals recorded during activation of visual (Makeig et al., 1999a,b, 2002; Tang et al., 2000, 2002a,b), auditory (Cao et al., 2002; Makeig et al., 1997; Tang et al., 2000, 2002a,b; Vigario et al., 2000; Wubbeler et al., 2000), somatosensory (Sutherland et al., 2004; Tang et al., 2000, 2002a,b; Vigario et al., 2000; Wang et al., 2004), and motor systems (Mackert et al., 2001), and during the performance of complex real world tasks (Tang et al., 2003). Several advantages of using BSS as a preprocessing tool for analyzing EEG and MEG data have been demonstrated. First, more effective artifact removal than that offered by conventional approaches can be achieved (Barbati et al., 2004; Culpepper and Keller, 2003; Ikeda and Toyama, 2000; Iriarte et al., 2003; Joyce et al., 2004; Jung et al., 2000a,b; Kobayashi et al., 2001; Tang et al., 2000, 2002b; Tong et al., 2001; Vigario, 1997). Second, weak or highly variable neuronal activations that were otherwise undetectable can be recovered (Tang et al., 2002b). Third, higher effective signal-to-noise ratios (SNRs) can be achieved at the level of single trial to allow for increased single-trial response onset time detection (Loring et al., 2004; Tang et al., 2002a) and for improved single-trial event-related potential (ERP) classification (Wang et al., 2004). Fourth, neuronal sources with slow DC changes in their activations can be recovered (Mackert et al., 2001; Wubbeler et al., 2000). Fifth, synchronization and desynchronization at specific brain locations can be more effectively studied (Makeig et al., 2004). Most recently, we have
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shown that by using BSS, single-trial ERPs from visual and frontal cortices can be extracted from EEG collected during video game play where continuous free eye movement was permitted (Tang et al., 2003). Despite these promising findings made over the last decade, some reported in highly visible journals, BSS algorithms have not been adopted by the EEG or MEG communities as part of routine analysis. Aside from the normal delays one might expect for new methods to become a part of routine analysis, what hinders the wide use of BSS algorithms appears to be a perceived lack of attempts to validate BSSrecovered putative sources prior to their interpretations. While some BSS algorithms have been applied to simulated EEG and MEG data (Cao et al., 2002; Makeig et al., 2000), in this paper we considered alternative ways for validating BSS-recovered putative sources. The main obstacle for satisfactory validation is that the nature of neuronal activation recorded at the scalp by EEG or MEG is inherently unknown. Even with intracranial recordings, it is difficult and impractical to precisely position electrodes to capture the center of neuronal activations among functionally unique brain regions. The aim of the present study was to determine whether the putative sources recovered by a BSS algorithm adequately approximated the true sources. We do so by providing objective spatial and temporal validation of BSS components recovered using second-order blind identification (SOBI) (Belouchrani et al., 1993, 1997; Cardoso and Souloumiac, 1996). First, we took advantage of the presence of known sources such as 60-Hz line noise and artificially induced noise to provide objective validation. Secondly, because primary somatosensory (SI) cortex activation by median nerve stimulation has been well characterized both spatially and temporally (for reviews, see Allison et al., 1991; Hari and Forss, 1999; Kakigi et al., 2000; McLaughlin and Kelly, 1993), we further used SI activations as known sources to validate the SOBI decomposition process. Through this validation process, we provide a step by step description of the application of SOBI to high-density EEG with sufficient details to allow new users of SOBI to replicate the analysis process. We demonstrate that the SNRs of somatosensoryevoked potentials (SEPs) associated with the SOBI-recovered SI components were significantly larger than the SNRs measured at the EEG sensors. Spatially we show how the location of the recovered putative sources can be determined using a dipole modeling method. We demonstrate that SOBI-aided source localization does not require the step of generating an averaged eventrelated potential (ERP) and significantly reduces the subjectivity involved in the source modeling process. We also expand our previous work by demonstrating that SOBI is not only useful for analyzing data of relatively poor SNR obtained under unfavorable experimental conditions but can also further improve SNR even when data are collected under relatively optimal experimental conditions.
Methods Subjects Four right-handed subjects (two males), aged between 20 and 25 years, volunteered to participate in the present study. All subjects were free of any history of neurological or psychological disorders. The experimental procedures were conducted in
accordance with the Human Research Review Committee at the University of New Mexico. Stimuli Constant current square-wave pulses were delivered transcutaneously to the median nerve at the wrist using a pulse generator (S88) and a photoelectric stimulus isolation unit (Model SIU7) from Grass Instrument (Astro-Med, Inc. West Warwich, RI). Stimulation intensity was adjusted slightly below motor threshold to selectively activate somatosensory cortex while minimizing activation of motor cortex (Spiegel et al., 1999) as well as to minimize nonspecific somatosensory activation associated with finger movement. Stimulus duration was 0.25 ms and intensity ranged from 4.5 to 8.5 mA (M = 6.5 mA). The perceived intensities of left and right stimulation were reported to be similar by the subjects. Subjects were instructed to keep their eyes closed during stimulation. Unilateral (L: left; R: right) and bilateral (B) stimuli were delivered intermixed and pseudorandomly with no more than three consecutive identical stimulations. Bilateral stimulation was used to generate temporally overlapping activation in both hemispheres, thus providing a challenge for the source separation of left and right SI activation. The number of stimuli per condition was 400 for two subjects, 200 and 150 for the remaining two. The intertrial intervals (ITIs) were uniformly distributed, ranging from 0.75 to 1.25 (for the two subjects with 400 trials), 1.25 to 1.75 (for the subject with 200 trials), and 1 to 2 s (for the subject with 150 trials) with increments of 0.05, 0.05, and 0.1 s, respectively. These variations allowed us to determine whether source separation results were dependent upon particular stimulation parameters1. Stimulation lasted less than 20 min. No behavioral responses were required. Data acquisition EEG signals were recorded in an electrically shielded room from the whole head with a 128-channel EEG system (SymAmps, Neuroscan, El Paso, TX) using tin electrodes mounted in a custom-made cap (ElectroCap International, Eaton, OH). The sensor (electrode) locations are indicated in Fig. 1C. The signals were continuously sampled at 1000 Hz and bandpass filtered between 0.1 and 200 Hz. All channels were referenced to the nose and impedances were maintained below 10 kV. Electrode and landmark positions (nasion, left and right pre-auriculars) were digitized (Fastrack, Polhemus Inc., Colchester, VT) and used for subsequent source localization. In conventional sensor-based data analysis, the continuous EEG signals from each sensor are typically epoched, baseline corrected, possibly filtered, and averaged. Data length is typically reduced after rejecting epochs containing visually identified artifacts. Here, the SOBI BSS algorithm was applied directly to the continuous EEG data as it had been collected without epoching, artifact rejection, baseline correction, filtering, removal of bad channels, or signal averaging, similar to previous applications of SOBI to MEG data (Tang et al., 2002a,b).
1 SOBI analysis did not indicate noticeable differences produced by these different block sizes or ITIs.
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SOBI decomposiotn of EEG SOBI decomposes n-channel continuous EEG data into n SOBI components, each of which corresponds to a recovered putative source2 that contributes to the scalp EEG signal. Each SOBI-recovered putative source has a time course of activation and an associated sensor space projection that specifies the effect of that putative source, in isolation, on each of the n electrodes. Let x(t) represent n-dimensional vectors that correspond to the n continuous time series from the n EEG channels. Then x i (t) corresponds to the continuous sensor readings from the ith EEG channel. Because various underlying sources are summed via volume conduction to give rise to the scalp EEG, each of the x i (t) can be assumed to be an instantaneous linear mixture of n unknown components or sources s i (t), via the unknown n n mixing matrix A3, xðt Þ ¼ Asðt Þ SOBI uses the EEG measurement x(t) and nothing else to generate an n n unmixing matrix W that approximates A1, and the vector of the estimated component or putative source values sˆ (t) = Wx(t). The time courses of the components are given by sˆ (t) and sensor projections of the components are given by the estimated ˆ = W1. The time course of the ith component is mixing matrix A given by sˆ i (t). The sensor space projection for the ith component is ˆ , which indicates the effect of that given by the ith column of A component, in isolation, on all sensors. SOBI exploits the time coherence of the source signals to decompose the mixture of sources. SOBI finds W by minimizing the sum-squared cross-correlations between one component at time t and another component at time t + s, across a set of time delays (ss) (for details, see Cardoso and Souloumiac, 1996; Belouchrani et al., 1997; Tang et al., 2002b appendix). Because such crosscorrelations are sensitive to the temporal characteristics within the time series, temporal information contained in the continuous EEG data affects the results of source separation. As such, detailed temporal characteristics in the ongoing activity of the underlying brain sources can provide useful information for source separation. This feature of SOBI contrasts with the insensitivity of InfoMax independent component analysis (ICA) (Bell and Sejnowski, 1995) and fICA (Hyvarinen and Oja, 1997) in that the latter two algorithms are insensitive to the shuffling of data points. The following set of time delays ss (in ms) was used in the present study and chosen to cover a reasonably wide interval without extending beyond the support of the autocorrelation function: sf1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 12; 14; 16; 18; 20 25; 30; 35; 40; 45; 50; 55; 60; 65; 70; 80; 90; 95; 100 120; 140; 160; 180; 200; 220; 240; 260; 280; 300g: Similar sets of ss have previously been used to effectively isolate various task-related neuronal components as well as various artifacts from MEG data (Tang et al., 2002a,b). By using multiple 2 We use the phrase brecovered putative sourceQ and bcomponentQ interchangeably. 3 In the formulation of the BSS problem, the mixing matrix A is an m n matrix. However, for simplicity, A is often assumed to be a square matrix (Hyvarinen and Oja, 2000). In the particular implementation of SOBI used in this manuscript, a square n n mixing matrix was assumed.
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time delays, the SOBI algorithm has been shown to be more robust than when fewer time delays are used particularly when SNR is relatively poor and when large spectral overlap between sources is present (Belouchrani et al., 1997). For an empirical study of how different combinations of temporal delays affect SOBI separation quality of actual EEG data, see Sutherland et al. (2004). Identification of SOBI-recovered neuronal sources SOBI allows for the decomposition of as many components as there are sensors. Thus, using a 128-channel EEG system, a total of 128 components or putative sources were generated. Of all 128 recovered putative sources, only a subset corresponded to neuronal sources exhibiting time-locked activation to task-related events. The remaining components were assumed to correspond to sources of electrical signals captured by the EEG that were not task related. The first step in identifying the task-related components was to compute various event-triggered averages for each of the 128 components, in this case, somatosensory-evoked potentials (SEPs). For example, in the present somatosensory activation experiment, three stimulation events were presented: left, right, and bilateral median nerve stimulations. Using these three events as triggers, SEPs were generated for all 128 components. If a component showed a stimulus-triggered response that deviated beyond the baseline fluctuations of a prestimulus window (200 ms), it became a candidate for further analysis (typically the 10–12 components with the highest SNR). Next, these temporally defined candidates were further evaluated using spatial criteria. For example, if a component showed focal and confined activation over the region corresponding to the presumed location of SI and the SEP of such a source contained a peak around 20–40 ms after contralateral stimulation, then these components were considered to be potential candidates for the recovered left and right SI activations. Localization of SOBI-recovered sources The sensor space projection of each SOBI-recovered source can be used as input to any localization algorithm for source modeling, such as point-source dipole modeling (e.g., Hamalainen et al., 1993; Scherg, 1990) or distributed-source modeling algorithms (e.g., Ioannides et al., 1990; Komssi et al., 2004; Sarvas, 1987). The sensor signals resulting from just one of the components can ˆ DWx(t) = A ˆ Dsˆ (t), where D is a matrix of be computed as xˆ (t) = A zeros except for ones on the diagonal entries corresponding to the component that is to be retained. Thus, to localize a single component, one computes the sensor space projection for source i xˆ ðiÞ ðt Þ ¼ sˆ i ðt Þaˆ ðiÞ ; ˆ . Because xˆ (i)(t) is at each point in where aˆ (i) is the ith column of A time equal to the unchanging vector aˆ (i), scaled by the selected time course of interest sˆ i (t) (i.e., the continuous time course, a single epoch, or an averaged ERP), source localization algorithms will localize xˆ (i)(t) to the same location no matter what window in time is chosen. While the sensor space projection can be used as input to any source modeling algorithm, in the present study an equivalent current dipole (ECD) fitting method (BESA 5.0, Brain Electrical Source Analysis; MEGIS Software, Munich, Germany) was applied to the sensor space projections of the task-related SOBI components. It is possible that multiple brain regions share very similar time courses of activation through synchronization. In
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such a case, a single SOBI component will be recovered whose time course will reflect the synchronized activity from multiple brain regions. The number of spatially discontinuous brain regions showing a synchronized time course of activation can
be initially estimated by inspecting the scalp current source density (CSD) of the component’s sensor space projection because it offers sharpened spatial resolution of the observed data (Lagerlund, 1999). An example of such a multiple dipole source may be found for SOBI components that reflect activation of bilateral homologous brain structures, such as the left and right SI, which have been shown to contain neurons with bilateral receptive fields in primates (Iwamura, 2000; Iwamura et al., 1994, 2001). In such a case, instead of fitting the source with a single dipole, we recommend the use of a symmetric dipole model that allows for greater degrees of freedom because the ipsilateral dipole can have a range of strength (including zero, which would correspond to a single dipole solution). To obtain a measure of a component’s strength, its sensor space projection is given as input to a specific physical model, in this case, an equivalent dipole model provided by a commercially available software package (BESA). Signal-to-noise ratio (SNR) We compared the SNRs of the averaged SEPs from the SOBIrecovered left and right SI components with those of the bbest sensorsQ from the unprocessed sensor data. SNR was estimated with Scan 4.2 (Neuroscan) using a modified computation from Raz et al. (1988) and Turetsky et al. (1988), and was calculated as the difference between the total power in the data rˆX2 and the noise power rˆN2 (i.e., signal power rˆS2 = rˆ X2 rˆ N2) divided by the noise power, rˆ 2 rˆ 2 rˆ 2 S Nˆ R ¼ 2S ¼ X 2 N rˆ N rˆ N The measurements X j (t) are made at time points (t = 1,. . .,T) in trials/epochs ( j = 1,. . .,J). Total power in the data set was estimated as the sum of each data point squared (where the sum is over all epochs and all time points) divided by the product of the number of time points and the number of epochs minus one, PP 2 x j ðt Þ j t rˆ 2X ¼ T ð J 1Þ and noise power was estimated as the sum of squared deviations of each data point from the average (where the sum is over all epochs and all time points) divided by the product of the number of time points and the number of epochs minus one, 2 P P Xj ðt Þ X¯ ðt Þ t j : rˆ 2N ¼ T ð J 1Þ The bbest sensorsQ were defined as those over SI with the greatest peak SEP response. For SNR calculations, the bbest Fig. 1. Localization of a spontaneously occurring noisy sensor. Sensor space projections of the unprocessed EEG sensor data (A) and a SOBIrecovered component (B) from a single matching 200-ms epoch. The boxed sensor indicates the known (A) and the SOBI-recovered noisy sensor locations (B). (C) The scalp current source density (CSD) maps and the single equivalent current dipole (ECD) solution for the SOBI-recovered noise component, superimposed on the structural MRI of a standard brain, g = 94%.
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sensorQ EEG signals were first lowpass filtered (b40 Hz) with zero-phase shift, epoched with a window of 100, 200 ms around the stimuli, and baseline corrected using a prestimulus window of 100 ms. Similar windows and filtering parameters were used for computing the SNRs for the SOBI components. The epoched sensor data were then further subjected to artifact rejection (b100 AV) (thus giving the bbest sensorsQ an advantage).
Results Validation using known noise sources Noisy sensors are typically considered undesirable. However, naturally occurring, sometimes unavoidable, 60-Hz noise can be used to provide objective validation of the SOBI source separation process because both the spatial and temporal characteristics of such a source can be determined independently from the SOBI process. The location of a noisy sensor containing 60-Hz activity can be determined by viewing the continuous EEG data as routinely practiced in EEG labs. Spectral characteristics of this 60-Hz noise source are known, for example, a peak in the power spectrum around 60 Hz. If the SOBI decomposition process works successfully, the characteristics of a SOBI-recovered 60-Hz noise component should match those of the known 60-Hz noisy sensor. Fig. 1A shows the topography of the sensor space projection from the unprocessed sensor data for a single randomly selected epoch of 200 ms. The presence of a noisy sensor containing 60-Hz activity was apparent at the boxed location. Fig. 1B shows the topography of a SOBI-recovered 60-Hz component with preferential activation at the boxed sensor location that matched the known noisy-sensor location shown in Fig. 1A. The spatial location of the SOBI-recovered component was determined by fitting a single ECD (Fig. 1C) and matched the known location of the noisy sensor determined independently of the SOBI process. Temporally, while both the SOBI-recovered noise component (Fig. 2, blue) and the unprocessed sensor waveforms (Fig. 2, red) contained 60-Hz noise (both shown for the boxed sensor location in Fig. 1), the SOBI-recovered 60-Hz noise source displayed more uniform and constant amplitude throughout the epochs. In contrast, the unprocessed sensor waveforms deviated from a periodic 60-Hz signal, presumably, because it contained a mixture of signals from other intra- and possibly extracranial sources. The relatively constant amplitude of this SOBIrecovered 60-Hz noise component indicated that it adequately captured the 60-Hz line noise in isolation. A comparison of PCA- and SOBI-recovered 60-Hz noise sources
Fig. 2. The SOBI-recovered noise component isolated the 60-Hz noise. For three arbitrarily chosen epochs, the extracted 60-Hz noise waveform from the SOBI-recovered component (blue) is superimposed on the EEG sensor signals (red) that consisted of 60-Hz noise as well as signals from other sources.
For one subject, we compared the performance of principal component analysis (PCA) and SOBI using the spontaneously occurring known 60-Hz noise source for assessment. PCA components derived using singular value decomposition (SVD) were obtained using Scan 4.3 (Neuroscan) and those that contained 60-Hz activity were identified by their sensor space projections and the 60-Hz signal in their time course, similar to the identification of SOBI-recovered 60-Hz sources. For 10 randomly selected epochs, the waveforms (Fig. 3A) and power spectra (Fig. 3B) from the unprocessed sensor data are shown. Because EEG sensors record a
mixture of signals from many intra- and extracranial sources, it was expected that the power spectra of the unprocessed sensor data (Fig. 3B) would indicate activity at several frequencies, both at 60 Hz and in other frequency bands. By comparing the power spectra of the PCA-recovered (Fig. 3C) and SOBI-recovered (Fig. 3D) 60Hz components, it was apparent that while the SOBI component contained relatively pure 60-Hz activity, the PCA-recovered 60-Hz noise component was contaminated by signals in other frequency bands.
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Fig. 3. Successful isolation of the 60-Hz noise source by SOBI, a comparison with PCA. (A) Ten randomly selected epochs of unprocessed EEG sensor data from the known noisy sensor of one subject. (B) Power spectra of the 10 epochs in A. (C) Power spectra of the PCA-recovered 60-Hz noise component (projected at the same sensor as in A). (D) Power spectra of the SOBI-recovered 60-Hz noise component (projected at the same sensor as in A). Notice the power spectra of the SOBI-recovered 60-Hz noise component displayed peaks centered only at 60 Hz, which indicated successful source separation of the 60Hz noise source. In contrast, the power spectra of the PCA-recovered 60-Hz noise component displayed multiple peaks at other frequencies (outside of the grayed area), which indicated the presence of additional source signals.
Validation of SOBI-recovered sources using artificially created noise To take this validation process one step further, we induced temporally overlapping noise into three adjacent EEG sensors during the recording session of one subject. A blunt-tipped needle was briefly inserted into three recording electrodes at three epochs. During epochs 1, 2, and 3, noise was induced, respectively, into one (electrode 60), two (electrodes 60/61), and three electrodes
(60/61/59) simultaneously to produce overlapping activation between the three bnoise sourcesQ. If SOBI decomposed the sensor signals correctly, three separate components should be found, each of which corresponds to one of three electrodes. The time course of these components and their spatial locations should match those of the sensors that are known independently of the SOBI process. Fig. 4 shows that both the time course and spatial location of the SOBI-recovered artificial bnoise sourcesQ (Fig. 4, bottom) matched well to those observed in the unprocessed sensor data (Fig. 4, top).
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Validation using SI activation by median nerve stimulation While up to 11 SOBI neuronal components could be reliably identified across multiple subjects4, in the present study, we focused on the recovered SI components because the spatial and temporal characteristics of SI activity have been well characterized and therefore are ideal for validation purposes (for reviews, see Allison et al., 1991; Hari and Forss, 1999; Kakigi et al., 2000; McLaughlin and Kelly, 1993). The recovered left SI (Component 012, C-012, Fig. 5A) showed preferential activation at sensors over the left hemisphere in response to right stimulation while the recovered right SI (Component 016, C-016) (Fig. 5C) showed preferential activation at sensors over the right hemisphere in response to left stimulation. In contrast, the topographies of the SEPs from the unprocessed sensor data displayed more distributed activation (compare Figs. 5A, C with B, D), indicating that the SEPs were a mixture of multiple underlying sources in addition to SI activation. When the sensor space projections of these two components were fitted with a two-symmetric dipole model, we found close correspondence between the observed data (Figs. 6A and B) and the dipole models (Figs. 6C and D), indicated by both the similarity between the respective CSD maps (compare Figs. 6A, B to C, D) and the minimal residual variance, i.e., the amount of variance in the sensor space projection unaccounted for by the dipole model (Figs. 6E and F). The dipole locations for the left and right SOBI-recovered SI components were in the vicinity of the SI region (Figs. 6G and H) and the waveforms of their SEPs showed characteristic SI-evoked responses to contralateral median nerve stimulation (insert, Figs. 5A and C). Across multiple subjects (n = 4), left and right SI activations were reliably recovered by SOBI. The dipole locations, goodness of fit values, and dipole moments for the left and right SOBIrecovered SI components of each subject are shown in Table 1. The standard error of means (SEM) in the estimated xyz coordinates was fairly small (0.9–2.9 mm, Table 1), no greater than the typical source modeling error associated with EEG or even MEG, indicating minimal influence from different noise sources associated with individual subject runs. The goodness of fit values were above 95% for all subjects (left SI: 97.6 F 0.9%; right SI: 97.3 F 0.4%), indicative of the clean isolation of SI activation from other intra- and extracranial sources. The strength of SI activations obtained from the SOBI-recovered left (24.1 F 2.1 nAm) and right (26.3 F 2.5 nAm) SI sources was approximately equal. Most important, the SNRs of the averaged SEPs from the SOBIrecovered SI sources were significantly greater than those from the bbest sensorsQ ( F(1,3) = 274.412, P b 0.001, Fig. 7), consistent with clean isolation of SI-related signals from other signal sources.
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sufficiently well. Specifically, we validated SOBI-recovered sources using known noise sources and using the well-characterized SI response to median nerve stimulation. Through these validation processes, we provided a step by step description of the SOBI decomposition process and the process for the subsequent determination of the spatial locations of SOBIrecovered neuronal sources. We report that (1) SOBI increases the SNR of ERPs; (2) SOBI-aided source localization has high cross-subject reliability; (3) SOBI-aided localization reduces subjectivity in the source localization process; (4) SOBI allows for the localization of neuronal sources without the explicit use of ERPs. It is important to keep in mind that SOBI-recovered putative sources can only approximate the true sources and this study provides examples of how to evaluate whether the approximation is sufficient to allow for any statement about potential neuronal sources underlying various brain functions to be made. Validation of SOBI-recovered sources using known noise sources We showed that one can take advantage of the presence of noisy sensors to obtain objective validation for a subset of SOBIrecovered sources. Specifically, the location of a SOBI-recovered 60-Hz noise component matched the actual location of the noise generator determined independently from the SOBI process by visual inspection of the sensor data. The continuous time course of this SOBI-recovered noise component displayed cleanly isolated 60-Hz activity. Because such noise sources are recovered simultaneously with the neuronal sources via the same source separation process, correct separation of the noise sources provides objective, although partial, validation for the decomposition process. We further demonstrated that artificially induced (thus known) and temporally overlapping noise signals at three EEG sensors in close spatial proximity could be successfully recovered by SOBI. We found that the location of the recovered noisy sensor locations matched the locations of sensors in which noise was artificially created. The time course of the recovered noise sources resembled that of the induced noise, directly measured by the EEG sensor data5. This finding indicates that known noise sources within close spatial proximity (15–20 mm) and with varying degrees of temporal overlap can be successfully recovered by SOBI. Validation using SI activation by median nerve stimulation
This paper offers the first analysis of SOBI-recovered neuronal sources recovered from high-density EEG data. Two ways of validating BSS-recovered putative sources were used to determine whether the recovered sources approximated the true sources
We consider SI activation by median nerve stimulation as an ideal candidate for the purpose of validation for the following reasons. First, the SI region activated by median nerve stimulation is near the cortical surface, thus estimations of source locations are less influenced by errors related to the source modeling process. Second, the location and time course of SI activation by median nerve stimulation have been well characterized via converging imaging methods (Table 2), thus best serving the role of bknownQ sources. Third, in contrast to the incidental somatosensory stimulation induced by mouse button presses (Tang et al., 2002a,b) that offered testing data with low SNR, median nerve
4 Spatial and temporal characterization of all SOBI-recovered components with visible SEPs is beyond the scope of the current study and will be described in future work.
5 Slight differences are expected because the EEG sensor data contained the artificially injected noise as well as other sensor noise and ongoing brain activity.
Discussion
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Fig. 4. Separation of multiple artificially created noise sources. (Top) Location and time course of three temporally overlapping noise sources. Colored boxes indicate the sensor locations where noise was injected. (Bottom) Location and time course of the SOBI-recovered noise components. (Right) Colored boxes indicate the center of activation on the CSD maps for each of the recovered components. Notice the similarity, both spatially and temporally, between the known and SOBI-recovered artificial noise sources. The numbers on the left give the corresponding sensor and component IDs.
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Fig. 5. Sensor space projections of the SEPs in response to contralateral stimulation are shown. (A and C) SOBI-recovered left (C-012) and right (C-016) SI components showed preferential left and right hemispheric activation in response to contralateral stimulation, respectively. Boxes indicate the sensor location where the largest responses were observed (displayed in the inserts). (B and D) Sensor space projections of the SEPs from the unprocessed EEG sensor data. Notice the more diffused activation in the unprocessed sensor data by contralateral stimulation and the noisier SEPs (n = 400 trials).
stimulation offers more reliable and precisely timed delivery of sensory stimulation, thus offering a data set with relatively high SNR. To validate the spatial characteristics of SOBI-recovered SI sources, we considered four criteria. First, SOBI must recover one and only one component whose ECDs are within the region of left or right SI, known to be activated by contralateral median nerve stimulation. Second, the ECD models for these sources
must have at least 95% goodness of fit. Third, no other intra- or extracranial sources should be mixed with the SI sources, i.e., the final ECD solution (accounting for 95% of the observed variance) for the SOBI-recovered SI component must not contain additional ECDs whose locations are outside of SI. Fourth, the estimated ECD locations for SI should show small betweensubject variability because SOBI is expected to isolate SI actiQ vation from other sources of noise associated with a specific subQ
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Fig. 6. Localization of SOBI-recovered left and right SI components from one subject. (A and B) CSD maps of the SOBI-recovered left (C-012) and right (C016) SI components. (C and D) CSD maps generated from an ECD model with the best least-squares fit to the data. (E and F) CSD maps of the model residuals. (G and H) Dipole locations for the SOBI-recovered left and right SI components, respectively, shown against the structural MRI of a standard brain (left is shown on the right).
ject or a specific run of the experiment conducted on a specific day. Our results showed that SOBI recovered one and only one component whose ECDs were within the range of those reported in the fMRI, MEG, and EEG literatures for median nerve stimulation (Arthurs and Boniface, 2003; Backes et al., 2000; Boakye et al., 2000, 2002; Grimm et al., 1998; Jung et al., 2003; Korvenoja et al., 1999; Spiegel et al., 1999; Thees et al., 2003; Wikstrom et al., 1997). All SOBI-recovered SI sources
had goodness of fit values greater than 95% (range: 95.1– 99.2%), indicating that none of the SI sources were signifi cantly contaminated by additional intra- or extracranial sources. Finally, SOBI-recovered SI sources were reliably localized for all subjects with very small cross-subject variability (SEM b 3 mm). To validate the temporal characteristics of the SOBI-recovered SI components, we considere four criteria. First, the waveforms of the averaged SEPs obtained after source separation must be similar
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Table 1 SOBI-recovered left and right SI component locations for all subjects Subject
SOBI Recovered SI Left
1 2 3 4 Mean SEM
Right
x
y
z
g
nAm
x
y
z
g
nAm
37 35 32 43 36.8 2.3
5 4 12 4 6.3 1.9
91 84 95 83 88.3 2.9
95.1 98.4 97.6 99.2 97.6 0.9
25.4 28.0 18.2 24.9 24.1 2.1
37 35 32 35 34.8 1.0
9 8 6 5 7.0 0.9
93 90 88 93 91.0 1.2
98.1 97.1 97.7 96.3 97.3 0.4
29.8 24.2 20.2 30.8 26.3 2.5
Note. Dipole locations (xyz coordinates), goodness of fit (g), and source strength (nAm). Notice the small variability in the dipole locations as well as the goodness of fit across subjects. SEM: standard error of mean.
to SI responses previously observed using EEG and MEG. Second, the SEPs of SOBI-recovered SI sources must show larger response amplitudes to contralateral than to ipsilateral stimulation. Third, the ECD strengths of the SOBI-recovered SI sources should be within a reasonable range based on previous estimates made under similar experimental conditions. Fourth, the SNRs of SOBI-recovered SI sources should be higher than the SNRs of the bbest sensorsQ situated immediately above SI. For each subject, among the 128 SOBI-recovered sources, two components (left SI and right SI) with characteristic responses to contralateral stimulation were always observed. The estimated ECD strengths were on the same order of magnitude but at the low end of what has been previously reported in MEG studies of median nerve stimulation that ranged between ~20 and 80 nAm (e.g., Karhu and Tesche, 1999; Mauguiere et al., 1997; Simoes and Hari, 1999; Simoes et al., 2002, 2003; Vanni et al., 1996; Wegner et al., 2000). This is consistent with the fact that the intensity of stimulation used in this study was below instead of being above the threshold at which thumb movement could be elicited as is typically the practice in median nerve activation studies (e.g., Hari et al., 1984; Mauguiere et al., 1997; Thees et al., 2003). Finally, the SNRs of the SOBI-recovered SI SEPs were significantly higher than those obtained using the bbest sensorsQ. Based on the spatial and temporal criteria outlined above, it was clear that SOBI source separation was able to recover known neuronal sources, such as SI activation. The SOBI-recovered SI sources displayed all the properties that would be expected if SOBI correctly isolated signals associated with SI activation by median nerve stimulation.
SOBI increases the SNR of ERPs even in favorable SNR situations Previously, we have shown that SOBI can significantly improve the detection of neuronal activity under conditions of poor SNR (Tang et al., 2002a,b). Compared to the more variable SEPs due to incidental somatosensory stimulation during button presses (Tang et al., 2002a,b), the precise timing and repetitive delivery of median nerve stimulation used here were expected to yield higher SNRs for the evoked potentials. It was not clear at all when the SNR is already high whether SOBI would further increase SNR. It may be the case that SOBI can only offer an advantage when SNR is low and when SNR is already relatively high, a ceiling effect may be encountered. The present results indicate that even for data characterized by relatively high SNRs, SOBI was able to further increase the SNRs of the averaged SEPs when compared to those obtained using the bbest sensorsQ, thus broadening the impact of SOBI application. Together with our previous findings in which SOBI was applied to low SNR data (Tang et al., 2002a,b), this result indicates that SOBI can be an effective and useful preprocessing tool when applied to either high or low SNR data. Table 2 Summary of estimated SI locations from the fMRI, MEG, and EEG literature SI locations Study
Method
Side
x
y
z
Wikstrom et al. (1997)
MEG MEG EEG fMRI MEG fMRI fMRI fMRI fMRI fMRI fMRI fMRI EEG EEG fMRI EEG
L R L L L L L L L R L L L R R R
35 37 39 40 35 43 43 38 40 48 32 40 37 45 44 45 32 48
10 12 1 0 9 5 1 3 5 4 1 1 0 1 0 4 5 12
97 96 82 78 95 98 85 96 87 86 93 96 85 89 88 87 78 98
Grimm et al. (1998) Korvenoja et al. (1999) Spiegel et al. (1999) Backes et al. (2000) Boakye et al. (2000) Boakye et al. (2002) Arthurs and Boniface (2003) Jung et al. (2003) Theese et al. (2003) Min Max
Fig. 7. SEPs of the SOBI-recovered SI components had significantly higher SNRs than the SEPs from the unprocessed sensor data (*P b 0.001).
Note. For comparison, the xyz coordinates of the reported SI locations, when given in Talairach coordinates by the original studies, were converted into Cartesian coordinates using BESA 5.0.
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The localization of the SOBI-recovered SI sources demonstrates several advantages that are not available to a majority of ERP researchers. The first is that SOBI reduces subjectivity inherent in the process of source localization. Because SOBI components, as well as components recovered from other BSS algorithms such as fICA (Hyvarinen and Oja, 1997) and Infomax (Bell and Sejnowski, 1995), have a fixed sensor space projection, the spatial location of a SOBI component is time invariant. Consequently, using SOBI components’ sensor space projections as inputs to source localization algorithms allows one to remove a major source of subjectivity, the selection of a point in time, for source modeling. In contrast, when localizing using scalp ERPs without SOBI source separation, dipole solutions can change dramatically in time because at different points in time the mixing of signal sources changes. Because high levels of subjectivity can have significant impact on the consistency of source localization results obtained by different investigators, the application of SOBI may result in more consistent findings and improve the ease and efficiency of training new researchers.
epileptic spikes, which can propagate rapidly across the cortex, could be viewed as a nonstationary, traveling source (Baillet et al., 2003; Scherg and Ebersole, 1994; Scherg et al., 1999). Thus, one could argue that the assumption of stationarity is violated. However, spike propagation can also be cast as multiple stationary sources activated in a particular temporal order, thus eliminating the need of introducing the concept of moving sources. Within the context of validating the SOBI algorithm, it needs to be pointed out that the performance of SOBI when applied to EEG data collected during epileptic seizure/spiking activity is currently unknown. Furthermore, the appropriate selection of time delays for decomposing epilepsy data with SOBI remains an open question. In regards to assumption (d), when high-density recording systems are used for EEG or MEG (e.g., N128 channels), the number of sources can be considered to be rather small in comparison to the number of channels available because in a typical EEG or MEG experiment no more than a few dozen functionally distinct neuronal sources show task-related activity (e.g., Makeig et al., 1997, 2002; Tang et al., 2002a,b). Unless an extremely large number of noise sources with relatively large signal power are present, assumption (d) can be easily met under normal recoding sessions.
SOBI allows for ERP-less source localization
The independence assumption
Unlike conventional source localization that starts with identifying peaks in the waveform of an averaged ERP, the location of SOBI-recovered sources is determined by their fixed sensor space projections, which are derived from the separation matrix W. Thus, factors, such as large trial to trial variability in single-trial ERPs, which can make averaged ERPs small, become irrelevant for determining the spatial location of sources. This ERP-less source location offers two advantages: (1) source localization from EEG can be performed with individual subject data as easily and efficiently as it can be done with grand mean data from several subjects; (2) source localization can be performed not only on averaged and single-trial ERP data but also on the ongoing EEG data when no stimulation or subject responses are present (i.e., when a subject is at rest). The first advantage makes the practice of grand averaging unnecessary within the context of source localization and the second advantage makes it possible to characterize baseline sources of brain activity from the resting EEG. Future studies are needed to investigate SOBI decomposition of resting EEG data.
The independence assumption is often discussed within the context of independent component analysis (ICA). Although SOBI does not require statistical independence, some degree of unrelatedness among the sources is required for source separation. Because the words bindependenceQ and bunrelatednessQ mean something similar colloquially, they are often confusing to neurophysiologists who are interested in using BSS methods. One of the most accessible discussions to date can be found in a recent application of SOBI for EEG ocular artifact removal (Joyce et al., 2004). As summarized by Joyce et al. (2004), various BSS and ICA algorithms differ in how each method measures independence or unrelatedness among the components. ICA algorithms, such as InfoMax ICA (Bell and Sejnowski, 1995) or fICA (Hyvarinen and Oja, 1997), assume that the components are statistically independent at each time point and use higher-order spatial moments of the data for source separation. In contrast, SOBI considers the temporal relationship (cross-correlations) between components at multiple time delays (second-order statistics). SOBI tries to minimize the sum-squared correlations across all time delays, making it possible to separate temporally correlated sources (Belouchrani et al., 1993, 1997). Correlation among neuronal sources arises from the fact that certain brain regions may share common inputs and provide inputs to each other. On the other hand, independence of the source signals from distinct neuronal populations can arise from the fact that functionally unique brain regions consist of different populations of neurons with different local network connectivity, different laminar organization, different receptor distribution for neurotransmitters and neuromodulators, different cell packing density, different cell size, and cell types (Peters and Jones, 1997). Consider the hypothetical case of visual areas V1 and V2/ V3, which are known to have reciprocal connections and share common inputs. When a large number of time lags or temporal delays are used by SOBI, only at one or a few particularly temporal delays that are close to the synaptic delay times between V1 and V2/V3 will the cross-correlations be large, while at all other delays, they will be small. Thus, SOBI’s attempt to minimize the sum-
SOBI reduces subjectivity in source localization
Common assumptions shared by BSS algorithms BSS algorithms typically make the following assumptions: (a) the mixing of source signals at the sensors is instantaneous; (b) the mixing is linear; (c) both the mixing and sources are stationary; (d) the number of sources is less than or equal to the number of sensors; (e) some degree of unrelatedness among the sources. The linear and instantaneous mixing of EEG and MEG source signals (assumption a and b) are direct consequences of Maxwell’s equations (Vigario et al., 2000). For EEG, because sensor locations are fixed relative to the head, stationary mixing (assumption c) implies that sources do not move relative to the sensors and are stationary within the brain. This assumption seems reasonable given that specific populations of neurons that generate source signals do not move. This assumption has also been previously used by other non-BSS models for source analysis (Mosher et al., 1992; Scherg and Von Cramon, 1985; Scherg and von Cramon, 1986). Nevertheless,
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squared cross-correlations at many delays will not necessarily result in the grouping of V1 and V2/V3 activity into one component. In fact, when using a large number of time delays, SOBI was able to separate these two early visual sources along the dorsal stream (Tang et al., 2002b). Advantages of SOBI Although mathematicians and engineers continue to devise new algorithms with improved performance, EEG and MEG users might wonder whether it is worthwhile to learn about yet another algorithm. While many properties of SOBI have been presented in previous publications, implications for the analysis of neuronal source activations using EEG have not been sufficiently emphasized. Joyce et al. (2004) called attention to some key advantages offered by SOBI over other ICA-type algorithms within the context of EEG artifact removal; here we suggest that similar arguments be extended to include the isolation and analysis of neuronal source activations. First, unlike ICA, SOBI is capable of separating correlated source signals (Belouchrani et al., 1997). Given the extensive feed-forward and feedback connections between functionally distinct cortical areas, some degree of correlated activity is expected. Theoretically, SOBI is therefore better suited to separate signals from these distinct regions. Second, instead of only instantaneous decorrelation (where s = 0), SOBI minimizes cross-correlations using multiple time delays (Belouchrani et al., 1993, 1997; Muller et al., 2004; Ziehe and Muller, 1998). Thus, temporal structure in ongoing brain activity can be used to separate signals from functionally distinct brain regions. Such temporal information is not used by ICA algorithms. Third, SOBI uses second-order statistics averaged across time to derive components. Therefore, the components are less sensitive to errors caused by random noise (Belouchrani et al., 1997; Tang and Pearlmutter, 2003; Tang et al., 2002b) than those derived by ICA that use higher (fourth)-order instantaneous statistics that are sensitive to outliers. This point is particularly relevant to EEG data that are typically contaminated by various artifacts that are either one-of-a-kind artifacts (e.g., muscle activity) or that are spatially stereotyped and occur repeatedly (e.g., eye blink). In fact, it has been suggested that it is b. . .best to train ICA on carefully pruned dcleanT data epochs. . .Q (Delorme and Makeig, 2004, p. 20). Using SOBI, such precleaning is not necessary. Fourth, while ICA is unable to separate more than one Gaussian or near-Gaussian source (Hyvarinen and Oja, 2000), SOBI can separate Gaussian sources without making assumptions about the number of such sources in the data. Fifth, SOBI uses second-order statistics that can be estimated reliably with fewer data points than that needed by ICA. Therefore, overall SOBI is a promising algorithm for the analysis of EEG and MEG data, deserving to be carefully validated and studied for its own sake. We hope to increase the awareness of the EEG community to this alternative algorithm and to stimulate future work that compares and contrasts different ways of decomposing EEG data. Summary Over the last decade, several papers have described applications of BSS algorithms to EEG and MEG data. While most have focused on artifact removal, some have described the spatial and temporal characteristics of recovered components that resemble the expected spatial and temporal characteristics of source signals from
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different functional brain areas. While some reported new phenomena based on these components, validation efforts have been limited to testing using synthetic data. This paper introduces a few novel approaches and findings to the EEG community. First, we presented the SOBI algorithm, which has many superior properties in comparison to ICA algorithms, to the EEG community and provided the first validation of SOBI neuronal sources from high-density EEG. Second, we directly demonstrated that SOBI preprocessing can significantly increase SNR when compared to the SNR obtained from the bbest sensorsQ. This builds on findings made in our previous application of SOBI to MEG data, in which we inferred that SOBI must have increased the effective SNR because with SOBI preprocessing, single-trial response onset detection increased while false detection was reduced (Tang et al., 2002a). Third, we introduced new ways of providing validation, alternative to testing the algorithm by generating synthetic data. We binjectedQ known temporally overlapping noise into EEG sensors to allow for objective validation, and we designated primary somatosensory cortex activation as a well established, thus, quasi bknownQ neuronal sources and used it for validation. Fourth, we developed a set of spatial and temporal criteria for validation that are beyond showing one or two examples for qualitative statement. Fifth, we provided a step-bystep procedure for determining the location of brain activations that were captured by SOBI components. This procedure allows the researcher to bypass the problem of decomposing, subjectively, a complex spatial topography into its multiple, temporally varying and spatially overlapping constituents. This procedure also allows the researcher to bypass the step of generating an averaged ERP prior to source modeling. To our knowledge, such a systematic procedure, the intuition behind it, and its practical consequences have not been thoroughly presented in the ICA or BSS literature.
Acknowledgments We thank Drs. Lucas Parra, Paul Sajda, Clifford Saron, and Steven Sands for critical comments on earlier versions of the manuscript. This work was funded by grants from DARPA Augmented Cognition Program (ONR: N00014-02-1-0348) and the Mind Institute (#2021) to A.C.T.
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