Single-trial time–frequency analysis of electrocortical signals: Baseline correction and beyond
Introduction
Sensory, motor and cognitive events not only evoke time-locked and phase-locked changes of ongoing electrocortical signal (e.g., event-related potentials; ERPs and event-related fields; ERFs) (Luck, 2005), but also induce time-locked and non-phase-locked modulations of ongoing oscillatory activity (Neuper and Klimesch, 2006, Pfurtscheller and Lopes da Silva, 1999). These non-phase-locked modulations consist of decreases (event-related desynchronization, ERD) and increases (event-related synchronization, ERS) of oscillatory activity, usually confined to a specific frequency band (Pfurtscheller and Aranibar, 1977, Pfurtscheller and Lopes da Silva, 1999). The functional significance of ERD and ERS varies greatly according to their temporal, spectral, and spatial characteristics (Ohara et al., 2004). For example, ERD in the α band (8–12 Hz) has been hypothesized to reflect cortical activation, whereas ERS in the same frequency band has been interpreted as a reflection of cortical inhibition (Pfurtscheller and Lopes da Silva, 1999). ERD and ERS are extensively used to investigate sensorimotor processes and cognitive tasks, as well as to discriminate neurological disorders and psychometric variables (Fries, 2009, Gross et al., 2007, Neuper and Klimesch, 2006, Pfurtscheller, 1992, Pfurtscheller et al., 1998, Ploner et al., 2006, Schnitzler and Gross, 2005, Singer, 1993).
To measure ERD and ERS, single-trial electrocortical responses in the time domain are usually transformed in time–frequency distributions (TFDs) (Makeig, 1993), which represent signal power as a function of time and frequency, using various time–frequency decomposition methods, such as windowed Fourier transform and continuous wavelet transform (Mouraux and Iannetti, 2008, Zhang et al., 2012). The resulting single-trial TFDs are usually expressed relative to a pre-stimulus reference interval, to highlight stimulus-induced changes in oscillation magnitude (Grandchamp and Delorme, 2011). Such baseline-correction procedure is used because it allows identifying sometimes subtle stimulus-induced changes of ongoing oscillatory power. It is typically achieved using one of two alternative approaches: (1) subtraction, which assumes that ERD and ERS are added onto or subtracted from the existing pre-stimulus power at each frequency, and (2) percentage (i.e., subtraction and division), which assumes that ERD and ERS are proportionally decreased or increased with respect to the magnitude of existing pre-stimulus oscillatory power (Grandchamp and Delorme, 2011, Pfurtscheller and Aranibar, 1977). In both approaches the baseline correction can be performed on TFDs at single-trial, single-subject, or group level (Grandchamp and Delorme, 2011, Mouraux and Iannetti, 2008, Zhang et al., 2012). In any of those cases it is important to consider the effect of trial-to-trial (or subject-to-subject) fluctuations in the magnitude of pre-stimulus oscillatory activity on the ERD/ERS estimates. Particularly in the percentage approach, which consists in dividing the difference between post-stimulus and pre-stimulus amplitudes by the pre-stimulus amplitude, variations in pre-stimulus amplitude can have a very strong effect on the ERD/ERS estimates. Indeed, if the pre-stimulus amplitude is close to zero, even a very minor increase in amplitude will yield a spuriously high percentage increase. Considering that both pre- and post-stimulus amplitudes are always positive, the distribution of percentage estimates across trials (or subjects) will be highly asymmetrical, with a long tail of extremely high percentage values. Therefore, averaging such percentage values across trials (or subjects) will not provide a meaningful summary measure of ERD/ERS.
Across-trial variability in both pre- and post-stimulus amplitudes may reflect important factors such as changes in the sensory input and time-dependent habituation (Iannetti et al., 2008, Ohara et al., 2004, Stancak et al., 2003), as well as fluctuations in vigilance and expectation (Del Percio et al., 2006, Mu et al., 2008, Ploner et al., 2006). Thus, it is also crucial to dissect the contributions of pre- and post-stimulus power to the variability of ERD/ERS, especially when the trial-to-trial variability of pre-stimulus activity is significant and physiologically relevant (Addante et al., 2011, Salari et al., 2012, van Dijk et al., 2008, Wyart and Tallon-Baudry, 2009). Specifically, when investigating the trial-to-trial relationship between ERD/ERS and behavior variables (e.g., reaction times or intensity of perception), it is important to explore whether such relationship is determined by pre- or post-stimulus electrocortical activity, or both.
In summary, the correct interpretation of the functional significance of ERD/ERS relies on two important but often neglected conditions: (1) the baseline correction procedure should not introduce biases in the estimated ERD/ERS magnitude, and (2) the contribution of pre- and post-stimulus activity on the trial-to-trial ERD/ERS variability should be correctly dissected and quantified.
Here, we address these points using an electroencephalographic (EEG) dataset collected from a large population of healthy volunteers (n = 96). First, we quantitatively compared the two widely used baseline correction approaches (subtraction and percentage) at three different levels (single-trial, single-subject, and group), and show that the percentage procedure, especially when applied at single-trial level, can yield very misleading results, and largely overestimate ERS and underestimate ERD. Since baseline-corrected TFDs are influenced by the trial-to-trial fluctuations in the magnitude of pre-stimulus EEG activity, the subtraction approach, albeit unbiased, is not adequate to dissect the trial-to-trial relationships between electrocortical (pre- and post-stimulus EEG activity) and behavioral variables. Thus we characterized the trial-to-trial variability in pre-stimulus EEG power, and explored its influence on the post-stimulus EEG activity and baseline-corrected TFDs. Since ERD/ERS capture the mixed variability of pre- and post-stimulus EEG power, it is difficult to determine whether the trial-to-trial relationship between ERD/ERS and behavior variables is contributed by pre-stimulus activity, post-stimulus activity, or both. Therefore, we propose a multivariate linear regression (MVLR) model solved using the partial least squares (PLS) method to dissect the trial-to-trial relationships between electrocortical (pre- and post-stimulus EEG activity) and behavioral variables (e.g., intensity of perception).
Section snippets
Subjects
EEG data were collected from 96 healthy volunteers (51 females) aged 21.6 ± 1.7 years (mean ± SD, range = 17–25 years). All subjects gave their written informed consent and were paid for their participation. The local ethics committee approved the procedures.
Nociceptive stimulation
Radiant-heat stimuli were generated by an infrared neodymium yttrium aluminum perovskite (Nd:YAP) laser with a wavelength of 1.34 μm (Electronical Engineering, Italy). At this wavelength, laser pulses activate directly nociceptive terminals in the
Time–frequency responses without baseline correction
Fig. 1 shows the EEG responses elicited by laser stimulation in 96 subjects, at electrode C4 (contralateral to the stimulation side). The top left panel shows the response in the time domain, characterized by the large N2–P2 biphasic complex (LEPs). Single-subject average waveforms (color-coded) are superimposed. The black waveform represents the group level average. The top right panel shows the group-level average of the TFDs obtained from the single-subject average LEPs. This TFD contains a
Discussion
The present study yielded four main findings. First, performing the baseline correction using the percentage approach introduces a positive bias in the estimation of TFDs, resulting in ERD underestimation and ERS overestimation. In contrast, no bias is introduced when the baseline correction is performed using the subtraction approach. Second, the pre-stimulus EEG power (especially in the α band) varies significantly from trial to trial, following a hyperbolic function of the trial order.
Acknowledgments
LH is supported by the National Natural Science Foundation of China (31200856), Natural Science Foundation Project of CQ CSTC, and Postdoctoral Science Foundation of Chongqing (XM20120034). ZGZ is partially supported by a grant (HKU785913) from the Hong Kong SAR Research Grants Council. GDI is University Research Fellow of The Royal Society. The collaboration between LH and GDI is generously supported by the IASP® Developed–Developing Countries Collaborative Research Grant. AM has received
References (47)
- et al.
Anticipatory electroencephalography alpha rhythm predicts subjective perception of pain intensity
J. Pain
(2006) - et al.
Laser guns and hot plates
Pain
(2005) - et al.
Performance of some variable selection methods when multicollinearity is present
Chemom. Intell. Lab. Syst.
(2005) - et al.
Distraction affects frontal alpha rhythms related to expectancy of pain: an EEG study
Neuroimage
(2006) - et al.
EEGLAB: an open source toolbox for analysis of single-trial EEG dynamics including independent component analysis
J. Neurosci. Methods
(2004) - et al.
A time-varying source connectivity approach to reveal human somatosensory information processing
Neuroimage
(2012) - et al.
Functional features of nociceptive-induced suppression of alpha band electroencephalographic oscillations
J. Pain
(2013) Auditory event-related dynamics of the EEG spectrum and effects of exposure to tones
Electroencephalogr. Clin. Neurophysiol.
(1993)- et al.
Across-trial averaging of event-related EEG responses and beyond
Magn. Reson. Imaging
(2008) - et al.
Non-phase locked electroencephalogram (EEG) responses to CO2 laser skin stimulations may reflect central interactions between A partial partial differential- and C-fibre afferent volleys
Clin. Neurophysiol.
(2003)