Recovery of correlated neuronal sources from EEG - Semantic Scholar

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www.elsevier.com/locate/ynimg NeuroImage 28 (2005) 507 – 519

Recovery of correlated neuronal sources from EEG: The good and bad ways of using SOBI Akaysha C. Tang,a,b,* Jing-Yu Liu,c and Matthew T. Sutherland a a

Department of Psychology, University of New Mexico, Albuquerque, NM 87131, USA Department of Neurosciences, University of New Mexico, Albuquerque, NM 87131, USA c Department of Electrical and Computer Engineering, University of New Mexico, Albuquerque, NM 87131, USA b

Received 30 April 2005; revised 3 June 2005; accepted 8 June 2005 Available online 31 August 2005

Second-order blind identification (SOBI) is a blind source separation (BSS) algorithm that has been applied to MEG and EEG data collected during a range of sensory, motor, and cognitive tasks. SOBI can decompose mixtures of electric or magnetic signals by utilizing detailed temporal structures present in the continuously recorded signals. Successful decomposition critically depends on the choice of temporal delay parameters used for computing multiple covariance matrices. Here, we present empirical findings from high-density EEG data (128 channels) to show that SOBI’s ability to recover correlated neuronal sources critically depends on the appropriate use of these temporal delay parameters. Specifically, we applied SOBI to EEG data collected during correlated activation of the left and right primary somatosensory cortices (SI). We show that separation of signals originating from the left and right SI is better achieved by using a large number and a wide range of temporal delays between a few and several hundred milliseconds when compared to results using various subsets of these delays. The paper also offers nonmathematician/engineer users a gentle introduction to the inner workings of SOBI. D 2005 Elsevier Inc. All rights reserved. Keywords: Blind source separation (BSS); Electroencephalography (EEG); Somatosensory evoked potential (SEP); Median nerve stimulation; Primary somatosensory cortex (SI); Independent component analysis (ICA); Second-order blind identification (SOBI)

Introduction Second-order blind identification (SOBI) (Belouchrani et al., 1997) is an emerging signal processing technique that can be used to facilitate source analysis from EEG (Joyce et al.,

* Corresponding author. Department of Psychology, University of New Mexico, Albuquerque, NM 87131, USA. E-mail address: [email protected] (A.C. Tang). URL: http://www.atlab.unm.edu (A.C. Tang). Available online on ScienceDirect (www.sciencedirect.com). 1053-8119/$ - see front matter D 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.neuroimage.2005.06.062

2004; Tang et al., 2005) and MEG data (Tang et al., 2000; 2002a,b; Mackert et al., 2001). This method enables both model-free extraction of electric or magnetic signals associated with neuronal activity at specific brain locations and simultaneous isolation of large-amplitude ocular and sensor artifacts when given continuously recorded EEG or MEG data. Therefore, this method may be particularly useful for cognitive neuroscientists and clinicians who are interested in more than scalp signals which do not map directly to signals arising from functionally specific brain areas. From a practical point of view, SOBI’s performance is robust across subjects (Tang et al., 2005) and across repeated measures over large time intervals (unpublished data). Its use involves significantly reduced subjectivity and increased efficiency in comparison to most commonly adopted source analysis practices (Tang et al., 2005). Finally, SOBI’s assumptions are sufficiently weak such that they can be easily satisfied by brain imagining data (Joyce et al., 2004; Tang et al., 2005). These features of SOBI make feasible its routine use for the analysis and interpretation of EEG and MEG data. SOBI works to minimize the relatedness among the final recovered source signals that make up the mixtures of signals, in this case, the scalp recorded EEG time series. Instead of simply minimizing the instantaneous correlation, i.e., correlation with a fixed temporal delay of zero, SOBI considers cross-correlations at multiple time delays. Therefore, SOBI quantifies the relatedness of the recovered sources by taking into account the fact that one source might influence another immediately or after a certain time delay. In this way, SOBI supports the use of temporal information present in the time series for source separation. At the level of implementation, SOBI minimizes a quantity that is the sum of the squared correlations among all pairs of putative sources and across all temporal delays (excluding autocorrelations). Although considering cross-correlation at multiple temporal delays might seem a trivial departure from minimizing instantaneous correlation, the impact of this idea on source separation is non-trivial particularly when the underlying source signals

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A.C. Tang et al. / NeuroImage 28 (2005) 507 – 519

are correlated (Belouchrani et al., 1997), as they are most likely to be in the case of neuronal source signals underlying EEG or MEG. In several previous applications of SOBI to high-density EEG or MEG data, a large number of temporal delays ranging from a few to several hundred milliseconds have been used (Tang et al., 2000, 2002a,b, 2005). With this specific parameter setting, correlated neuromagnetic signals originating from the primary visual and posterior parietal cortices along the dorsal visual pathway can be separated into two components from MEG data (Tang et al., 2002b). Similarly, correlated electrical signals originating from the left and right primary somatosensory (SI) cortices can also be isolated into separate components from EEG data (Tang et al., 2005). While these findings demonstrate that correlated neuronal sources can be separated from the mixture of signals recorded by EEG and MEG using SOBI, it is not clear whether such a wide range of temporal delays as used in previous EEG and MEG studies is necessary for adequate source separation. It is of both theoretical and practical importance to determine whether the dependency of SOBI performance on a wide range and a large number of temporal delays generalizes from nonphysiological data (Belouchrani et al., 1997) to physiological data and whether this dependency transfers from a small data set (Belouchrani et al., 1997) to a large data set. In the case of highdensity EEG data collected from a 128-channel system sampled at 1000 Hz during a 20-min experiment, SOBI would need to compute correlations among all pairs of 128 time series, each containing 1,200,000 samples, for every temporal delay value selected. For such a large data set, it is not apparent whether SOBI performance would transfer well. The present study sets out to address this empirical question.

To evaluate the dependency of SOBI’s ability to separate correlated neuronal sources on the temporal delay parameters, we specifically designed a stimulation sequence consisting of mixed unilateral and bilateral median nerve stimulations which were expected to generate correlated activation between left and right SI cortices during the bilateral stimulation trials and relatively weaker or minimal correlations during unilateral stimulations. We utilized previously validated SOBI components for the left and right SI—which were recovered using a wide range of temporal delays between a few and a few hundred milliseconds (Tang et al., 2005)—as references for evaluating separation quality. Specifically, we determined whether using various subsets of the full range of temporal delays would degrade SOBI performance and quantified these performance degradations relative to previously reported equivalent current dipole (ECD) locations and goodness-of-fit values. Using the recovery of correlated activations from the left and right primary somatosensory cortices as a benchmark task, we show that the ability of SOBI to isolate signals associated with neuronal activations from specific brain regions depends on the appropriate selection of temporal delays. Critically, SOBI failed to separate these two benchmark sources when used in ways that do not utilize SOBI’s unique feature of simultaneously minimizing cross-correlations across a large number and range of temporal delays. An additional goal of the present work is to provide an intuitive description and a direct demonstration of the SOBI process to those readers, who can clearly benefit from using SOBI in their EEG/MEG data analysis but have not yet considered using SOBI due to a lack of translational papers that present the algorithm in a user-friendly format. It is the hope of these authors to fill this gap.

Methods Subjects Four right-handed subjects (2 males), aged between 20 and 25 years, volunteered to participate in this experiment. No subjects reported a history of neurological or psychological disorder. The experimental procedures were conducted in accordance with the Human Research Review Committee at the University of New Mexico. Choice of stimulation protocol We chose a median nerve stimulation protocol consisting of a mixed sequence of left, right, and bilateral stimulations for the following reasons. First, median nerve stimulation has been shown to reliably activate contralateral SI cortex (Allison et al., 1991). Second, the spatial locations and time course of SI activations have been well characterized with converging imaging methods (e.g., Hari and Forss, 1999; Korvenoja et al., 1999; Arthurs and Boniface, 2003; Thees et al., 2003). Third, SOBIrecovered left and right SI components from scalp-recorded high-density EEG have been previously validated (Tang et al., 2005). Finally, the inclusion of the bilateral stimulation condition can conveniently generate correlated activations between the left and right SI. Experimental procedures Subjects were instructed to keep their eyes closed during stimulation and no behavioral responses were required. Three types of trials, unilateral (L: left; and R: right) and bilateral (B) median nerve stimulations, were delivered intermixed and pseudo-randomly at the wrist with no more than three consecutive identical stimulations. The perceived intensities of left and right stimulations were reported to be similar by the subjects. 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 non-specific somatosensory activation associated with finger movement.


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Fig. 1. Multiple cross-correlation matrices before and after SOBI processing. (A) Before SOBI processing: correlation matrices from the EEG sensor time series. Each non-diagonal element, Rxij , is the cross-correlation between sensors i and j at a given temporal delay (s = 1, 5, 30, 50, 80, 140 ms). (B) After SOBI processing, correlation matrices for the component time series. Rsij is the cross-correlation between SOBI components i and j at a given temporal delay. Data shown are for data from a single subject.

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Fig. 2. Effects of temporal delay parameters on cross-correlation matrices. (A) Using a full range of temporal delays for source separation: the ‘‘standard set’’ [1..300] ms. (B) Using a minimal number of temporal delays for source separation: Set 1 [1..2]. Data from a second subject are shown. Matrices are the same as in Fig. 1 except the diagonal elements are set to zero to optimally reveal the ‘‘peaks’’ in (B).


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Median nerve was stimulated generated using a pulse generator (S88) and a photoelectric stimulus isolation unit (SIU7) from Grass Instrument (Astro-Med, Inc., West Warwick, RI). The total duration of stimulation was less than 20 min. Stimulus duration was 0.25 ms and intensity ranged from 4.5 to 8.5 mA (M = 6.5 mA). The number of stimuli per stimulus condition was 400 for two subjects, 200 and 150 for the remaining two. The inter-trial intervals (ITI) were uniformly distributed, ranging from 0.75 – 1.25 (for the two subjects with

Fig. 3. Cross-correlations between pairs of SOBI components at all temporal delays used by SOBI (‘‘standard set’’ [1..300]). (A, B, C) SOBI-recovered right (A) and left (B) SI components and a noisy-sensor component (C). Top: scalp current source density (CSD) maps; bottom: equivalent current dipole (EOD) locations superimposed on the structural MRI of a standard brain. (D, E) Cross-correlations as a function of temporal delays. (D) Correlations between the left and right SI components (blue) and between the pair of sensors from the unprocessed EEG data (boxed in panels A and B) with maximum signal amplitude situated immediately above the left and right SI (red). (E) Correlations between the left SI and the noisy-sensor components (blue) and between the pair of sensors from the unprocessed EEG data (boxed in panels B and C) with the maximum signal amplitude situated immediately above the left SI and the noisy sensor (red). Shown for the same subject as in Fig. 2.

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Table 1 SOBI-recovered SIs using the ‘‘standard set’’ of temporal delays ([1..300 ms]) Subject

SOBI-recovered SI Left

Right

Location

1 2 3 4 Mean SEM

x

y

z

Distance to ‘‘standard’’

37 35 32 43 36.8 2.3

5 4 12 4 6.3 1.9

91 84 95 83 88.3 2.9

0.0 0.0 0.0 0.0 0.0 0.0

g

# Additional dipoles

Location x

y

95.1 95.1 97.6 99.2 97.6 0.9

0 0 0 0 0.0 0.0

37 35 32 35 34.8 1.0

9 8 6 5 7.0 0.9

g

z



93 90 88 93 91.0 1.2

0.0 0.0 0.0 0.0 0.0 0.0

98.1 97.1 97.7 96.3 97.3 0.4

0 0 0 0 0.0 0.0

Note. x, y, z, and distance in mm; g: goodness-of-fit in %. # of additional dipoles indicates the number of dipoles in non-SI locations that were needed to account for at least 95% of the variance in the scalp projection. The larger the number is, the poorer the separation quality.

400 trials), 1.25 – 1.75 (for the subject with 200 trials), and 1 – 2 s (for the subject with 150 trials) with increments of 0.05, 0.05, and 0.1 s, respectively.1 EEG data EEG signals were recorded using a 128-channel SynAmps EEG system (NeuroScan, El Paso, TX) with tin electrodes mounted in a custom-made cap (ElectroCap International, Eaton, OH) continuously sampled at 1000 Hz and bandpass filtered between 0.1 and 200 Hz. In conventional data analysis, the continuous EEG data are typically epoched, baseline corrected, filtered, and averaged. Data are typically reduced after rejecting or correcting 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. As was shown in previous applications of SOBI to EEG/MEG data, SOBI performance does not require these conventional pre-processing techniques (Tang et al., 2002b, 2005). SOBI processing SOBI decomposes n-channel continuous EEG data into n SOBI components, each of which corresponds to a recovered putative source that contributes to the scalp EEG signal. Each SOBI component has a time course of activation and an associated sensor space projection that specifies the effect of that putative source on each of the n electrodes. Let x(t) represent n continuous time series from the n EEG channels and xi (t) 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 xi (t) can be assumed to be an instantaneous linear mixture of n unknown sources si (t), via the unknown n n mixing matrix A,2 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 putative sources sˆ(t) = W x(t). The time course of the ith component is given by s i (t). The sensor space projection for the ith component is given by ˆ , where A ˆ = W1. the ith column of A 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 multiple time delays (ss) and across all pairs of components (for detailed description, see: Belouchrani et al., 1997; Tang et al., 2002b appendix; Joyce et al., 2004). Because such cross-correlations are sensitive to the temporal characteristics within the time series, temporal information contained in the continuous EEG data is utilized for source separation. As such, detailed temporal characteristics of the ongoing activity of the underlying brain sources can provide useful information for source separation, even in the absence of evoked responses. This feature of SOBI contrasts with InfoMax 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, i.e., temporal information is not used. Identification of candidate SOBI components for the left and right SI We identified SOBI components that corresponded to the left and right SI according to a similar set of spatial and temporal criteria described previously (Tang et al., 2005). Briefly, using stimulus-triggered averages, i.e., the averaged somatosensory evoked potentials (SEPs), we obtained a subset of components that displayed evoked responses to median nerve stimulation from the 128 total recovered components. This subset was further reduced according to the pattern of activation in the component’s sensor space projection, shown in 1

These variations were for other puposes in the study from which the data were originally collected. The general BSS problem requires A to be an n m matrix, with n m (n: number of mixtures; m: number of sources). In most algorithmic derivations, an equal number of sources and sensors are assumed (Vigario and Oja, 2000). 2


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Table 2 SOBI-recovered SIs using a subset of temporal delays (Set 1: [1..2 ms]) Subject

SOBI-recovered SI Left

Right

Location

1 2 3 4 Mean SEM

x

y

z


39 41 37 29* 36.5 2.6

1 15* 16* 1 7.8 4.5

85 85 83 90 85.8 1.5

7.5 12.6 13.6 16.4 12.5 1.9

g


Location x

y

58.9 81.3 69.1 76.3 71.4 4.9

6 4 4 7 5.3 0.8

31 32 32 46 35.1 3.5

1 5 10 19* 8.9 3.9

g

z



93 87 90 69* 84.8 5.4

10.0 5.2 4.8 29.7 12.4 5.9

71.9 83.2 61.7 48.8 66.4 7.3

5 2 6 6 4.8 0.5

* Coordinate values for SI locations that were outside of the range of previously reported values from multiple imaging modalities.

scalp current source density (CSD) maps. These maps were computed from the scalp potential maps as the second spatial derivative of the voltage distribution and are better at revealing visually the underlying generators than the potential maps (Lagerlund, 1999). To be a candidate for left or right SI, the sensor space projection must show the characteristic pattern of activation. The prototype spatial pattern for SI components were taken from previously validated SOBI SI components, generated using a full range of temporal delays (see below). The components whose spatial pattern best matched to the prototype SI and showed SEPs became the candidate SOBI-recovered SI. In the present study, this pattern matching was performed by visual inspection which in practice was unambiguous, although automated pattern matching can be developed in principle. The sensor space projections of the two candidate components, the left and right SI components, were then used as inputs to BESA 5.0 (Brain Electrical Source Analysis; MEGIS Software, Munich, Germany) to determine whether the components’ sensor space projection could be modeled adequately by dipoles in the vicinity of the SI regions alone or whether additional dipoles were needed to account for an adequate proportion of the variance in the component’s sensor space projection (in this case, a 95% criterion was adopted). If additional non-SI dipoles were needed, the components were considered to be a mixture of multiple sources, thus in such a case, the quality of SOBI decomposition was considered to be poor. Choice of temporal delays for joint diagonalization We generated several sets of temporal delays to evaluate the dependency of SOBI performance on the choice of these parameters. The following set of temporal delays is referred to as the ‘‘standard set’’, covering a wide interval without extending beyond the support of the autocorrelation function3 (in ms): sa f1;2;3;4;5;6;7;8;9;10;12;14;16;18;20; 25;30;35;40;45;50;55;60;65;70;75;80;85;90;95;100;120;140;160;180;200;220;240;260;280;300g: These delays have previously been used to effectively isolate task-related neuronal components as well as various artifacts from EEG and MEG data, including components corresponding to left and right SI activations (Tang et al., 2002a,b, 2005). Four subsets were generated:

& & & &

Subset 1, [1..2]: s Z {1, 2} Subset 2, [1..20]: s Z {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 20} Subset 3, [1..100]: s Z {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100} Subset 4, [25..300]: s Z {25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 120, 140, 160, 180, 200, 220, 240, 260, 280, 300}.

Set 1 was selected to evaluate whether left and right SI activation could be isolated when the use of temporal delays was virtually discarded, i.e., when instantaneous correlations between components were minimized (equivalent to a principal component analysis). Here, due to the specifics of implementation, temporal delays of 1 and 2 ms were used to approximate results from a separation using a single delay value of 0 ms. Set 2 was selected to determine whether covering delays up to an average of typical synaptic delays was sufficient to generate good separation. Set 3 was selected to determine whether adding longer delays would improve separation results. Set 4 was selected to determine whether short temporal delays (