The relationship between ERP components and EEG spatial complexity in a visual Go/Nogo task

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1 J Neurophysiol 117: , First published October 26, 2016; doi: /jn RESEARCH ARTICLE Higher Neural Functions and Behavior The relationship between ERP components and EEG spatial complexity in a visual Go/Nogo task Huibin Jia, 1 Huayun Li, 1,2 and Dongchuan Yu 1 1 Key Laboratory of Child Development and Learning Science (Ministry of Education), Research Center for Learning Science, Southeast University, Nanjing, China; and 2 Centre for Vision Research, Department of Psychology, York University, Toronto, Canada Submitted 12 May 2016; accepted in final form 20 October 2016 Jia H, Li H, Yu D. The relationship between ERP components and EEG spatial complexity in a visual Go/Nogo task. J Neurophysiol 117: , First published October 26, 2016; doi: /jn The ERP components and variations of spatial complexity or functional connectivity are two distinct dimensions of neurophysiological events in the visual Go/Nogo task. Extensive studies have been conducted on these two distinct dimensions; however, no study has investigated whether these two neurophysiological events are linked to each other in the visual Go/Nogo task. The relationship between spatial complexity of electroencephalographic (EEG) data, quantified by the measure omega complexity, and eventrelated potential (ERP) components in a visual Go/Nogo task was studied. We found that with the increase of spatial complexity level, the latencies of N1 and N2 component were shortened and the amplitudes of N1, N2, and P3 components were decreased. The anterior Go/Nogo N2 effect and the Go/Nogo P3 effect were also found to be decreased with the increase of EEG spatial complexity. In addition, the reaction times in high spatial complexity trials were significantly shorter than those of medium and low spatial complexity trials when the time interval used to estimate the EEG spatial complexity was extended to 0 1,000 ms after stimulus onset. These results suggest that high spatial complexity may be associated with faster cognitive processing and smaller postsynaptic potentials that occur simultaneously in large numbers of cortical pyramidal cells of certain brain regions. The EEG spatial complexity is closely related with demands of certain cognitive processes and the neural processing efficiency of human brain. NEW & NOTEWORTHY The reaction times, the latencies/amplitudes of event-related potential (ERP) components, the Go/Nogo N2 effect, and the Go/Nogo P3 effect are linked to the electroencephalographic (EEG) spatial complexity level. The EEG spatial complexity is closely related to demands of certain cognitive processes and could reflect the neural processing efficiency of human brain. Obtaining the single-trial ERP features through single-trial spatial complexity may be a more efficient approach than traditional methods. spatial complexity; visual Go/Nogo task; event-related potentials IN THE FIELD OF COGNITIVE NEUROSCIENCE, the Go/Nogo experimental paradigm, typically in conjunction with event-related potentials (ERPs) and functional magnetic resonance imaging (fmri), has been widely used to investigate how the human Address for reprint requests and other correspondence: D. Yu, Liwenzheng Bldg., Rm. 323, Southeast Univ., 2 Sipailou, Xuanwu District, Nanjing , China ( dcyu@seu.edu.cn). cognitive system suppresses inappropriate processing of nontarget information (Bokura et al. 2001; Brown et al. 2015). In this paradigm, two kinds of visual or auditory stimuli were presented to the participants randomly. The participants were asked to generate an overt response (e.g., press or release a button) or covert response (e.g., count the number) to one of the stimuli (i.e., the go stimulus) and withhold the response to the other stimulus (i.e., the no-go stimulus) (Burle et al. 2004; Smith et al. 2008). Researchers have consistently found several ERP components in the visual Go/Nogo task, such as the visual P1, visual N1, N2, and P3 (Gajewski and Falkenstein 2013; Kopp et al. 1996; Lavric et al. 2004; Vogel and Luck 2000). The visual P1 and N1 components are associated with visual stimulus processing and are part of the visual evoked potentials (VEPs). The visual P1 has maximum amplitude over the lateral occipital areas, whereas the visual N1 is widely distributed over the entire scalp, maximally over the frontal or posterior regions (Mangun 1995; Mangun and Hillyard 1991). Both components can be modulated by selective attention and the visual discrimination difficulty (Luck et al. 2000; Mangun and Hillyard 1991; Vogel and Luck 2000). The N2 component in the visual Go/Nogo task, usually named N2b, peaks around ms poststimulus and is usually largest over anterior or frontocentral scalp sites (Folstein and Van Petten 2008). This component can be clearly seen in the ERP waveforms of both the go condition and the no-go condition; however, the no-go N2 is consistently discovered to be more negative compared with the go N2, which is referred to as the Go/Nogo N2 effect (Gajewski and Falkenstein 2013). Source localization revealed that the Go/Nogo N2 effect is generated in the anterior cingulate cortex (ACC) and the ventral prefrontal cortex (vpfc) (Lavric et al. 2004). Previous neuroimaging studies stated that the ACC is involved in error detection and conflict monitoring (Braver et al. 2001) and that vpfc is associated with response inhibition (Morita et al. 2004). Taking these findings together with previous ERP studies that focused on the functional significance of N2 component, the Go/Nogo N2 effect was hypothesized to reflect the conflict monitoring and inhibition of the prepotent response in the no-go condition (Jeremy et al. 2014). Research on the P3 component supports the idea that it consists of two subcomponents with distinct functional signif /17 Copyright 2017 the American Physiological Society 275

2 276 ERP COMPONENTS AND SPATIAL COMPLEXITY icance: one is an anterior or frontocentral distributed component, termed P3a, novelty P3, or Nogo-P3 in different experimental paradigms, and the other is a parietal distributed component that is named P3b, target P3, Go-P3, or classical P3 in different literature (Polich 2007). The former subcomponent often peaks earlier than the latter one (Comerchero and Polich 1999). Through the manipulation of task difficulty in the three-stimulus oddball paradigm, researchers have established that the P3a, novelty P3, and Nogo-P300 are most likely variants of the same ERP component that varies in scalp topography as a function of attentional and task demands (Katayama and Polich 1998). In the visual Go/Nogo tasks, this anteriorly distributed P3 component is often found to be larger in the go condition, compared with that in the no-go condition, which is known as the Go/Nogo P3 effect (Gajewski and Falkenstein 2013). This effect has been assumed to be involved in response inhibition process by researchers (Bokura et al. 2001) and is influenced by the response type (i.e., the Go/Nogo P3 effect was larger when participants were asked to make an overt response compared with when they were asked to make a covert response), which suggests it may represent a separate response-monitoring process (Bruin and Wijers 2002). In addition to this anterior distributed subcomponent, the parietal P3 also could be seen in the ERP waveforms of the visual Go/Nogo task, which is often associated with the identification, evaluation, or categorization of the stimuli and context, and reflects the allocation of cognitive resources in these mental processes (Polich 2007). Its amplitude is associated with the amount of resources invested to the stimulus, and its latency is proportional to the evaluation time (Mccarthy and Donchin 1981). In the visual Go/Nogo task, the parietal Go-P3 amplitude is significantly larger than parietal Nogo-P3 amplitude, which is believed to be related with response commission by some researchers (Kopp et al. 1996; Pfefferbaum et al. 1985). The execution of the visual Go/Nogo task not only evokes certain ERP components (e.g., P1, N1, N2, and P3) and the Go/Nogo effects illustrated above but also induces the alterations of functional connectivity or the synchronization between spatially remote brain regions (Duann and Ide 2009). During the performing of cognitive tasks (e.g., the visual Go/Nogo task), the functional connectivity is changed dynamically, which can be observed between different latencies of a single trial or between different trials (Huster et al. 2014; Rissman et al. 2004; Valencia et al. 2008). A concept closely related to the global functional connectivity level between spatially distributed brain areas is the spatial complexity, which is by definition a global estimate of the number of uncorrelated brain processes active during the data analysis period (Wackermann 1996). When different brain regions are completely synchronized, the spatial complexity is lowest (i.e., exactly one brain process is found). When these spatially remote brain regions are independent between each other, the spatial complexity is highest. Thus the spatial complexity varies inversely with the global functional connectivity level, which fluctuates dynamically during the execution of the visual Go/Nogo task. In summary, the ERP components and variations of spatial complexity or functional connectivity are two distinct dimensions of neurophysiological events in the visual Go/Nogo task. Whereas the former reflects the summation of postsynaptic potentials (PSPs) that occur simultaneously in large numbers of cortical pyramidal cells, which are lined up together perpendicularly with respect to the cortical surface, the latter represents the degree of statistical independence between large-scale spatially remote brain regions or the number of independent neural processes (Olejniczak 2006; Wackermann 1996). Extensive studies have been conducted on these two distinct dimensions (Folstein and Van Petten 2008; Huster et al. 2014; Luck et al. 2000; Saito et al. 1998); however, no study has investigated whether these two neurophysiological events are linked to each other in the visual Go/Nogo task. We studied the relationship between ERP components and spatial complexity in a visual Go/Nogo task. Note that plenty of EEG measures based on deterministic chaos theory or the theory of nonlinear systems (e.g., approximate entropy, Taken s estimator, Lyapunov exponent, and multiscale entropy) have been developed to characterize the physiological complexity of human brain (Bhattacharya 2000; Catarino et al. 2011; Röschke et al. 1997). Research has revealed that these measures are closely associated with neurophysiological disorders (e.g., schizophrenia, depression, autism spectrum disorder, and Alzheimer s disease), emotion states, and attentional processes (Aftanas et al. 1998; Bob et al. 2011; Catarino et al. 2011; Li et al. 2008; Mizuno et al. 2010). On the basis of these findings, researchers found that intrinsic complexity can subserve adaptability in biological systems, and the loss of complexity is closely linked to the cognitive impairments in certain patients (Catarino et al. 2011; Goldberger et al. 2002). However, all these measures mainly focused on the signal complexity of neurophysiological time series in a single channel and failed to assess the spatial complexity of the whole brain. Thus it is interesting to test whether the whole brain spatial complexity is related with the ERP components and behavioral performance in cognitive task, which has already been observed using traditional single-channel complexity measures (Mölle et al. 1999; Molnár 1999; Molnár et al. 1995). In this study, the spatial complexity was quantified using the omega complexity proposed by Wackermann (1996), which is a linear measure that assesses the degree of global synchronization between spatially distributed brain areas. It is defined as entropy of the eigenspectrum of the covariance matrix of EEG data (Wackermann 1996) and has been found to be sensitive to different types of cognitive processes, chronological ages, neuroactive substances, and neuropathological variables (Kondakor et al. 1997, 1999, 2005; Saito et al. 1998; Stam et al. 2000). Because performing the visual Go/Nogo task requires the simultaneous activation of multiple brain regions or brain networks (Menon et al. 2001; Steele et al. 2013), higher spatial complexity (i.e., larger number of uncorrelated brain processes) may signify higher neural processing efficiency. If this assumption holds, trials with higher spatial complexity should have faster information processing speed and shorter reaction times (RTs). Moreover, higher neural processing efficiency may be associated with relatively a lower level of neural activity or PSPs of each brain functional area, since a low level of activation is sufficient to complete the task. Thus, in the case of ERP study of the visual Go/Nogo task, we hypothesize that RTs of Go trials with higher spatial complexity may be significantly longer than the trials with relatively lower spatial complexity. In addition, spatial complexity may be inversely proportional to the latencies/amplitudes of certain ERP components (e.g., visual P1, visual N1, N2, and P3 commonly

3 ERP COMPONENTS AND SPATIAL COMPLEXITY 277 observed in the visual Go/Nogo task). Finally, the spatial complexity also may be associated with the magnitudes of Go/Nogo N2 effect and Go/Nogo P3 effect. MATERIAL AND METHODS Participants The behavioral performance and EEG data were collected from 14 healthy right-handed volunteers (7 women) aged from 22 to 46 yr. All participants with normal or corrected-to-normal vision gave their written informed consent and were paid for their participation. The local ethics committee approved the experimental procedures. The data sets used in this study were published in previous studies (Delorme et al. 2002, 2004). The original EEG data sets distributed under the GNU license can be downloaded from the open-access website ( EEG_data.html). Stimuli The stimulus battery used in this study included 1,000 color photographs of complex natural scenes (Corel CD-ROM library), which were purchased by the Centre de Recherche Cerveau et Cognition CNRS laboratory in Toulouse, France (Delorme et al. 2004). Fifty percent of the photographs included animal items (e.g., mammals, birds, fish, arthropods, and reptiles) and were used as the target stimuli, whereas the other 50% of photographs, which did not have any animal items, were used as the nontarget stimuli. There was no a priori information about the size, position, or number of animals in the target stimuli. In these nontarget images, a large range of outdoor and indoor scenes (e.g., natural landscapes, city scenes, food, fruits, vegetables, trees, and flowers) were used. Examples of two kinds of stimuli can be seen in Delorme et al. (2004). All stimuli subtended a vertical visual angle of 4.5 and a horizontal visual angle of 6.5 (Delorme et al. 2004). Design and Procedure The participants were seated in a comfortable chair at about 110 cm from the monitor in a silent, temperature-controlled room and were instructed to keep relaxed throughout the whole experiment (Delorme et al. 2004). The participants performed 10 blocks of the task, with each block consisting of 50 trials with target stimuli and 50 trials with nontarget stimuli. At the beginning of each block, a small dot was presented in the middle of the screen, and participants were instructed to press a touch-sensitive button. Shortly thereafter, one of the selected images, either target stimulus or nontarget stimulus, was displayed in the middle of the screen for 20 ms. Participants were asked to decide whether the presented image contained an animal or not. They should release the button as quickly and accurately as possible within 1,000 ms when they saw a target image (i.e., go trials). If the stimulus is one of the nontarget stimuli, they should keep their finger on the button for at least 1,000 ms (i.e., no-go trials). The interval between the onsets of successive stimuli (i.e., the stimulus onset asynchrony, SOA) was randomized with a range from 1,800 to 2,200 ms. The mean SOA was about 2,000 ms. EEG Data Recording and Preprocessing. EEG data were recorded using a 32-channel SynAmps recording system (sampling rate, 1,000 Hz; physical reference channel, Cz; low-pass frequency, 500 Hz) with a standard EEG cap based on the extended system. All channel impedances were kept lower than 5 K. EEG data were preprocessed using EEGLAB, an open source toolbox running in the MATLAB environment (Delorme and Makeig 2004). EEG data were re-referenced to a common average reference, since Wackermann and Allefeld (2007) demonstrated that this operation could successfully avoid effects of an active reference on the eigenvalue spectrum and, consequently, the value of omega complexity (Wackermann and Allefeld 2007). The EEG data were then low-pass filtered at 30 Hz. Epochs to target/nontarget stimuli were extracted using a time window of 1,100 ms (100-ms prestimulus and 1,000-ms poststimulus) and baseline corrected by demeaning the EEG activity within the prestimulus interval. Epochs contaminated by eye blinks and movements were corrected using an independent component analysis algorithm. The go trials without any reaction or with RTs 1,000 ms and no-go trials with a behavioral response were discarded from the following analysis. Omega Complexity Analysis The omega complexity was developed to provide a single quantitative descriptor that could assess complexity of multichannel brain electric field data through state-space representation (Wackermann and Allefeld 2007). If the multichannel EEG data at each time point are viewed as a momentary map or state, the trajectory of these states over time forms a state-space trajectory in m-dimensional state space (m is the number of channels). The omega complexity can evaluate the complexity of the state-space trajectory by examining its shape through principal component analysis (PCA) (Wackermann 1996). The single-trial omega complexity of each subject was computed as follows (Stam et al. 2000; Wackermann 1996). First, PCA was conducted on each 32-channel epoch between ms after the onset of stimulus, which yielded 32 principal components and a spectrum of eigenvalues ( ) for each trial. The selection of ms is based on the following reasons: 1) the mean RT across participants is ms, with an SD of ms; and 2) the latencies of ERP components observed in the current study are between ms after stimuli onset. To assess the relative contribution of each principal component to the total variance, the eigenvalues of principal components were then normalized to the unit sum. The normalized eigenvalue of the ith principal component was calculated as ' i i i 1 i, where m is the number of principal components or channels (32 in this ' study), and i and i represent the eigenvalues and the normalized eigenvalues of the ith principal component, respectively (Wackermann 1996). Finally, the single-trial omega complexity, which was defined as the Shannon entropy of normalized eigenvalues ( =) of each trial (Wackermann 1996), was computed using the following equation: m exp ' i (log ' i ). i 1 The omega complexity can be regarded as a measure of spatial complexity of a given EEG set and attains values from the interval 1 to 32 (the number of EEG channels). The lowest value ( 1) means the data consist of exactly one principal component or spatial mode, and a maximum synchronization is found between EEG signals at different scalp locations. The highest value ( 32) indicates the total data variance is uniformly distributed across all 32 principal components, and a maximum spatial complexity is found (Kondakor et al. 1999). For each participant, the EEG epochs of each condition were sorted according to the magnitudes of omega complexity. To test the relationship between ERP components and EEG spatial complexity, the entire set of trials for each subject was divided into three bins (i.e., trials with high spatial complexity, trials with medium spatial complexity, and trials with low spatial complexity) for both go and no-go conditions, respectively. The number of trials was identical in different bins. Finally, the ERP waveforms of three bins (high spatial complexity, medium spatial complexity, and low spatial complexity) were obtained by averaging the corresponding epochs for the go and no-go conditions, respectively. m

4 278 ERP COMPONENTS AND SPATIAL COMPLEXITY Behavioral and ERP Analysis The RTs of go trials with the high, medium, and low spatial complexity were extracted for each participant. A one-way ANOVA was then performed with spatial complexity (high, medium, and low) as an independent variable. Through the inspection of grand-average ERP waveforms of the go condition and the no-go condition, four ERP components were identified, which were P1, N1, N2, and P3 (as shown in Fig. 1). The P1 component was maximum over bilateral occipital region, whereas N1 and N2 were detected mainly over the frontocentral scalp sites. The latencies and peak amplitudes of these components were found within the following time windows: P1 ( ms), N1 ( ms), N2 ( ms), and P3 ( ms). Note that in the raw Nogo ERP data, the P3 amplitude showed persistent negative values over the anterior sites due to the presence of the negative ERP component N2 and the use of an average reference in offline analysis. Thus the P3 amplitudes were measured as the difference between the maximum voltage between ms and the minimum voltage between ms. The latency of P3 component was the time point that a maximum voltage between ms was detected. After this transform, we found that the Go-P3 and Nogo-P3 were maximum over parietal and anterior electrodes, respectively, which was consistent with previous studies. It should be mentioned that the Nogo-P3 could also be clearly seen on parietal sites; however, the Go-P3 was absent in frontal electrodes for most participants. After both the amplitudes/latencies of P1, N1, N2, and anterior/ parietal P3 were measured, three-way repeated-measures ANOVAs were performed on three independent variables, which are condition (go and no-go), spatial complexity (high, medium, and low), and electrode site (electrodes O1, O2, and Oz for P1 component; electrodes F3, Fz, and F4 for N1, N2, and anterior P3 components; and electrodes P3, Pz, and P4 for parietal P3 component). For all the statistical tests above, the Greenhouse-Geisser correction method was applied for all the repeated measures that had more than one degree of freedom. By using the Bonferroni procedure ( 0.05), post hoc comparisons were made to determine the significance of pairwise contrasts. RESULTS Behavioral Results One-way within-subjects ANOVA performed on RTs showed that the main effect of spatial complexity was not significant [F(2, 26) 0.54, P 0.05, 2 p 0.04]. ERP Results The grand-average ERP waveforms for go and high spatial complexity trials (red solid lines), go and medium spatial Fz N1 Cz 0 N2 Pz P3 Oz 0 0 P1 Amplitude (µv) Time (ms) Go & high spatial complexity Go & medium spatial complexity Go & low spatial complexity Nogo & high spatial complexity Nogo & medium spatial complexity Nogo & low spatial complexity -10 Fig. 1. Grand-average ERP waveforms for go and high spatial complexity trials (red solid lines), go and medium spatial complexity trials (green solid lines), go and low spatial complexity trials (blue solid lines), no-go and high spatial complexity trials (red dashed lines), no-go and medium spatial complexity trials (green dashed lines), and no-go and low spatial complexity trials (blue dashed lines) at electrodes Fz, Cz, Pz, and Oz. Through the inspection of grand-average ERP waveforms, 4 ERP components were identified, which were P1 ( ms), N1 ( ms), N2 ( ms), and P3 ( ms).

5 ERP COMPONENTS AND SPATIAL COMPLEXITY 279 complexity trials (green solid lines), go and low spatial complexity trials (blue solid lines), no-go and high spatial complexity trials (red dashed lines), no-go and medium spatial complexity trials (green dashed lines), and no-go and low spatial complexity trials (blue dashed lines) at electrodes Fz, Cz, Pz, and Oz can be seen in Fig. 1. Latency. First, for the latency of the visual P1 component, the three-way repeated-measures ANOVA revealed that the main effects of condition, spatial complexity, and electrode site as well as the interaction effects were not significant (all F 1). However, the main effect of spatial complexity for visual N1 latency was significant [F(2, 26) 6.54, P 0.01, p ]. Further analysis showed that the visual N1 latency of high spatial complexity trials was significantly shorter than that of the low spatial complexity trials. Second, for N2 latency, the main effect of condition was significant [F(1, 13) 7.20, P 0.05, p ]. The Go-N2 latency was significantly longer than that of the Nogo-N2. In addition, the main effect of spatial complexity was also significant [F(2, 26) 6.47, P 0.01, p ]. Post hoc tests showed that the N2 latency of the high spatial complexity trials was significantly shorter than that of the low spatial complexity trials. Finally, the main effect of condition was significant for parietal P3 latency [F(1, 13) 18.09, P 0.01, p ]. Also, the latency of parietal Go-P3 was significantly longer than that of the parietal Nogo-P3. No other significant main effects or interaction effects were revealed for anterior or parietal P3 component (all F 1). Amplitude. First, similar to the P1 latency, we did not find any significant main effects or interaction effects for P1 amplitude (all F 1). For N1 component, the main effect of spatial complexity was significant [F(2, 26) 5.33, P 0.05, p ]. The N1 amplitude of the low spatial complexity trials was larger than that of the high spatial complexity trials. Second, for N2 amplitude, the main effects of condition, spatial complexity, and electrode site were significant [F(1, 13) 15.74, P 0.01, p ; F(2, 26) 17.51, P 0.01, p ; and F(2, 26) 6.19, P 0.01, p , respectively]. Post hoc tests showed that the N2 amplitude of the low spatial complexity trials was larger than that of the high spatial complexity trials and medium spatial complexity trials, and the N2 amplitude was found to be largest on electrode Fz. In addition, the Nogo-N2 amplitude was significantly larger than the Go-N2 amplitude. Among the interaction effects, the interaction between condition and spatial complexity was significant for N2 amplitude [F(2, 26) 3.81, P 0.05, p ]. The simple effect analysis suggested that the Go/Nogo N2 effect in the low complexity trials was larger than that in the high complexity trials. Finally, the main effects of condition, spatial complexity, and electrode site were significant for the amplitude of parietal P3 component [F(1, 13) 28.46, P 0.01, p ; F(2, 26) 17.98, P 0.01, p ; and F(2, 26) 11.65, P 0.01, p , respectively]. Post hoc tests showed that the parietal Go-P3 amplitude was significantly larger than that of the parietal Nogo-P3, and the parietal P3 amplitude of the low complexity trials was larger than that of the high complexity trials and that of the medium complexity trials. In addition, we found that the parietal P3 was maximum over electrode Pz. No other significant effect or interaction effects were found (all F 1). The three-way repeated-measures ANOVA on P300 amplitudes in anterior electrodes revealed that the main effects of condition, spatial complexity, and electrode site were significant [F(1, 13) 26.08, P 0.01, p ; F(2, 26) 20.01, P 0.01, p ; and F(2, 26) 5.15, P 0.05, p , respectively]. The anterior Nogo-P3 amplitude was significantly larger than that of the anterior Go-P3, and the anterior P3 amplitude of the low complexity trials was larger than that of the high complexity trials and that of the medium complexity trials. The anterior P3 was maximum over electrode Fz. More importantly, the interaction between condition and spatial complexity was significant [F(2, 26) 16.03, P 0.01, p ]. Further analysis suggested that the Go/Nogo P3 effect in the low complexity trials was larger than that in the high complexity trials and that in the medium complexity trials. In addition, we also tested whether the spatial complexity level was significantly different between the go condition and the no-go condition, using condition (go and no-go) and spatial complexity (high, medium and low) as independent variables. In this statistical comparison, the dependent variable is omega complexity. No doubt, the main effect of spatial complexity was significant. However, the main effect of condition was not significant [F(1, 13) 3.75, P 0.05, p ], which indicated that the EEG spatial complexity in go trials was not significantly different from that in no-go trials. DISCUSSION In this study, by employing the standard visual Go/Nogo task, two classical ERP effects were found, which were the anterior Go/Nogo N2 effect and Go/Nogo P3 effect. Furthermore, the data analysis demonstrated that the spatial complexity of EEG data during task execution of the visual Go/Nogo task was related to the latencies and amplitudes of certain ERP components (e.g., N1, N2, and P3). More importantly, we found that the spatial complexity level was linked to the magnitudes of the Go/Nogo N2 effect and Go/Nogo P3 effect. Relationship Between Spatial Complexity and RT One-way within-subjects ANOVA performed on RT showed that the main effect of spatial complexity was not significant, which was not consistent with our hypotheses. Note that the spatial complexity was calculated using the EEG data between ms after the onset of stimulus. However, when the time interval used to estimate the spatial complexity was extended to 0 1,000 ms, the main effect of spatial complexity was found to be significant for RT [F(2, 26) 3.45, P 0.05, 2 p 0.21]. The RTs in high spatial complexity trials were significantly shorter than those of medium and low spatial complexity trials. However, the main effects of N1 latency and amplitude were not significant when this long temporal interval (0 1,000 ms) was used. As has been shown in previous research, considerable cortical areas are activated in the visual Go/Nogo tasks, including regions related with visual processing (e.g., middle/inferior occipital gyrus and fusiform gyrus), conflict monitoring (e.g., anterior cingulate cortex), response inhibition and commission (e.g., right inferior prefrontal cortices, right middle/inferior

6 280 ERP COMPONENTS AND SPATIAL COMPLEXITY frontal gyrus, right inferior parietal regions, and presupplementary motor area) (Horn et al. 2003; Menon et al. 2001; Simmonds et al. 2008). During these different processing stages of the visual Go/Nogo task, distinct brain structures are activated dynamically, and the functional connectivity patterns between different brain regions are also distinct in different temporal windows, which indicates that the spatial complexities of EEG data are different in distinct temporal windows. Thus the behavioral results shown above suggest that the RTs are closely linked to the spatial complexity of the later temporal windows of each trial and are not relevant to the spatial complexity of the earlier temporal windows (i.e., ms). In addition, these findings support our view that spatial complexity varies inversely with the information processing speed and RTs, and may signify the neural processing efficiency. Linkage Between Spatial Complexity and ERP Waveforms First, the visual P1, visual N1, N2, and P3 components could be detected in the ERP waveforms of the current study. In addition, the Go/Nogo N2 effect and Go/Nogo P3 effect were detected on anterior electrodes (i.e., the N2 and P3 components on anterior electrodes were associated with larger amplitude in no-go trials than in go trials), which has been found in a considerable corpus of studies (Bokura et al. 2001; Gajewski and Falkenstein 2013). The Nogo-P3 was found to be more anteriorly distributed than the Go-P3 in our study, which was consistent with findings of previous studies (Gajewski and Falkenstein 2013; Lavric et al. 2004). Also, the parietal Go-P3 amplitude was significantly larger than the parietal Nogo-P3 amplitude, which was thought to be related to response commission (Kopp et al. 1996; Pfefferbaum et al. 1985). As for the latency of ERP components, we found that the anterior N2 and parietal P3 latencies were significantly longer in the go condition compared the no-go condition. Many researchers have reported the distinction in latency between Go-P3 and Nogo-P3 and have shown that the latency of the Nogo-P3 is longer than that of the Go-P3 (Jodo and Inoue 1990). However, Jodo and Inoue (1990) found that the temporal relation between Go-P3 and Nogo-P3 can be reversed by practice. This is consistent with results of the present study, since participants completed 10 blocks of Go/Nogo task with 100 trials in each block. Second, we found that the spatial complexity of EEG data was linked to the latencies of N1 and N2 and the amplitudes of N1, N2, and anterior/parietal P3. In trials with high spatial complexity, the latencies of N1 and N2 components were shortened, and the amplitudes of N1, N2, and anterior/parietal P3 components were decreased, compared with those trials with relatively lower spatial complexity. The omega complexity, which is a linear measure that quantifies the concept spatial complexity, has been proved to be an effective biological index that could discriminate cognitive states and neurological disorders (Kondakor et al. 1997; Saito et al. 1998). Higher omega complexity suggests that the number of independent electrical processing is larger and the global degree of synchronization between spatially distributed brain areas is lower (Kondakor et al. 2005). The amplitudes and latencies of visual N1, N2, and P3 components were found to be enhanced with the increase in visual discrimination difficulty, the demands of conflict monitoring, and the difficulty of the evaluation or categorization processes, respectively (Pfefferbaum et al. 1985; Polich 2007; Vogel and Luck 2000). Thus the variations of ERP component latencies/amplitudes observed in this study suggest that higher spatial complexity may signify higher neural processing efficiency in the visual Go/Nogo task. Finally, in line with the decrease of N2 and P3 amplitudes in high spatial complexity trials, the anterior Go/Nogo N2 effect and the Go/Nogo P3 effect were also found to be decreased in trials with high spatial complexity. On the other hand, the interaction effect between condition and spatial complexity was not detected for parietal P3, which further confirmed the conclusion that the Nogo-P3 and Go-P3 effects, largest on electrodes Pz and Fz, respectively, have distinct neutral generators and may index distinct functional processes in the visual Go/Nogo task (Bruin and Wijers 2002; Pfefferbaum et al. 1985; Smith et al. 2008). Researchers have indicated that the Go/Nogo N2 effect may have two functional components with separate neural generators, one related to response inhibition (the ventral prefrontal cortex, vpfc) and another associated with conflict monitoring and error detection (the anterior cingulate cortex, ACC) (Gajewski and Falkenstein 2013). On the other hand, the anterior Go/Nogo P3 effect has been linked to more modality-independent inhibition processes than the Go/Nogo N2 effect (Bruin and Wijers 2002). Thus the decrease of Go/Nogo N2 effect and P3 effect in high spatial complexity trials suggests that the demands of conflict monitoring and response inhibition are lower in trials with high spatial complexity (i.e., trials with more independent electrical sources and a lower level of synchronization between distinct brain areas), which further verifies our hypothesis that high spatial complexity is associated with a relatively lower level of neural activation or PSPs of each brain functional area and higher neural processing efficiency. In addition, the EEG spatial complexity in go trials was not significantly different from that in no-go trials, as reported above, which suggested that the Go/Nogo effects found in our study were not caused by the EEG spatial complexity. Functional Significance of EEG Spatial Complexity on Human Physiology Biological systems (e.g., the human brain) are complex at multiple levels of temporal and spatial scales and consist of interconnected feedback loops. The investigation of withinindividual brain signal complexity or variability may provide some insight into the relationship between physiological complexity and cognitive performance. Compared with the traditional EEG analysis measures (e.g., spectral power, coherence, and nonlinear analysis), the spatial complexity of EEG data, quantified by the omega complexity in the current study, could assess the number of independent electrophysiological sources and the degree of global synchronization between spatially distributed brain areas. In this study, we found that spatial complexity was associated with information processing speed, reflected by the RT and ERP component latency, and with the magnitude of PSPs of certain brain regions, reflected by the amplitudes of ERP components and Go/Nogo effects. To conduct the visual Go/Nogo experiment, plenty of brain regions are activated, including regions related with visual processing, conflict monitoring, response inhibition, and commission; thus it seems reasonable that the higher the spatial

7 ERP COMPONENTS AND SPATIAL COMPLEXITY 281 complexity, the higher the information processing speed. Low spatial complexity means that some of these functional brain regions are not activated, which could hamper the information processing in the task. Moreover, because the human nervous system works in an economical and efficient manner, the trials with higher spatial complexity may have a relatively lower neural activation level, reflected by the amplitudes of ERP components and Go/Nogo effects in the current study, since a low level of activation is sufficient to complete the task. Further studies using other experimental paradigms (e.g., the Stroop task, the stop-signal task, and the visual search task) and neuroimaging modalities (e.g., the local field potential, fmri) are needed to determine whether the results found in this study reflect a general principle of human neural processing. The significance of this research is as follows. First, spatial complexity of the EEG data during task execution varies with the information processing speed and reflects the neural processing efficiency of human brain. Moreover, the EEG spatial complexity varies inversely with the neural activation level of task-related brain regions in the visual Go/Nogo task. Second, the therapeutic interventions of certain psychophysiological disorders could modulate the latencies and amplitudes of certain ERP components (Keage et al. 2008); thus in future studies researchers could quantify the effects of therapeutic interventions using the spatial complexity. Third, the spatial complexity may be very useful in the single-trial ERP analysis. Although the spatial complexity can be easily calculated on the single-trial level, the ERP waveforms are typically obtained through the across-trial averaging procedure, which could enhance the signal-to-noise ratio of ERP waveforms (Hu et al. 2011; Mouraux and Iannetti 2008; Murray et al. 2008). If we could establish the functional relationship between ERP components and spatial complexity, we could obtain the single-trial ERP features through single-trial spatial complexity, which may be a more efficient approach than traditional methods. However, a prominent limitation of this study needs to be mentioned. The spatial complexity is computed using the EEG data of ms after stimulus onset. Quantifying the spatial complexity using the corresponding time window of each ERP component may provide a more direct relationship between spatial complexity and ERP components (e.g., assessing the relationship between the N2 component and the EEG spatial complexity calculated using EEG data of ms). The reasons for this relatively longer temporal window are as follows. First, with data points that are too brief, the omega complexity, which was used to estimate the concept spatial complexity, is underestimated because there are not enough data points to provide a representative portrait of the EEG trajectory. Second, because the latency, amplitude, and morphology of ERP components are changed dynamically across trials, providing a constant time window for each component is unreasonable (Hu et al. 2011). Limitations of the Present Study Although this study revealed that the spatial complexity of EEG data during the execution of the visual Go/Nogo task was closely related to the RTs and certain ERP components and showed that the spatial complexity could reflect the information processing speed and neural processing efficiency of human brain, several limitations need to be mentioned. First, the spatial complexity was calculated using the EEG data between ms after stimulus onset. The choice of ms is based on the mean RT across subjects and the latencies of ERP components. However, use of this constant interval for all trials would overestimate the information processing time of trials with RTs smaller than 500 ms and underestimate that of trials with RTs larger than 500 ms. Defining the time interval of computing spatial complexity according to the RT of each trial should produce more reasonable results. For example, if the RT of a certain trial is 400 ms, the time interval of this trial can be ms, considering individuals may engage in a process of response-monitoring that lasts at least 200 ms (Welford 1959, 1967). However, this will make it very difficult to study the relationship between the spatial complexity and ERP components in the no-go condition, since RTs are not available in no-go trials. Moreover, the omega complexity, which is used to quantify the concept spatial complexity, is sensitive to the interval length. It has been shown that there is a positive correlation between omega complexity and interval length when the interval length is shorter than 1 s (Michel et al. 2009; Wackermann 2005). Thus adjusting the time interval according to a single-trial RT will cause confusion. Second, we cannot completely rule out the speed-accuracy trade-off, because the accuracy rates are not available in the original data sets. However, the mean accuracy rate was extremely high in this visual Go/Nogo task (i.e., 93.1%) (Delorme et al. 2004), which may suggest that the speed-accuracy trade-off did not exist in the original data to some extent. Third, the statistical methods used in the current study are somewhat archaic. In addition, they depend on the critical assumption of trial-by-trial state independence, which does not hold in real-world situations (e.g., the ubiquitous slowing of responses after the go trials) (Verbruggen and Logan 2008). In a future study, the behavioral data could be analyzed with more sophisticated methods, such as time series analysis and cumulative distributional analysis (Cheyne et al. 2009; Steinborn and Huestegge 2016). Conclusion The relationship between the spatial complexity of EEG data during task execution and ERP components in a visual Go/ Nogo task was studied. The present study has revealed several important findings. First, if the time interval used to estimate the spatial complexity was extended from ms to 0 1,000 ms, the RTs in high spatial complexity trials were significantly shorter than those of medium and low spatial complexity trials. Moreover, the N1 and N2 latencies of the high complexity trials were significantly shorter than those of the low complexity trials. These results support the hypothesis that the trials with higher spatial complexity have faster information processing speed, and thus the spatial complexity of EEG data could reflect the neural processing efficiency of human brain. Second, the amplitudes of N1, N2, and P3 components were reduced in trials with high EEG spatial complexity. The Go/Nogo N2 effect and Go/Nogo P3 effect were also reduced with increasing spatial complexity. Thus the EEG spatial complexity varies inversely with neural activation level or PSPs of task-related brain regions in the visual Go/ Nogo task, which may reflect the human nervous system working in an economical manner. Above all, the present study

8 282 ERP COMPONENTS AND SPATIAL COMPLEXITY reveals that the spatial complexity of event-related EEG data during the Go/Nogo task is closely associated with the RTs, the latencies/amplitudes of certain ERP components, and the Go/ Nogo effects commonly observed in the visual Go/Nogo task, which may be due to the fact that EEG spatial complexity is closely related to demands of certain cognitive processes and the neural processing efficiency of human brain. GRANTS The work was supported by the Natural Science Foundation of China under Grants , , and and by the Open Research Fund of the State Key Laboratory of Cognitive Neuroscience and Learning under Grant CNLYB1308. DISCLOSURES No conflicts of interest, financial or otherwise, are declared by the authors. AUTHOR CONTRIBUTIONS H.J. analyzed data; H.J., H.L., and D.Y. interpreted results of experiments; H.J. prepared figures; H.J. and H.L. drafted manuscript; D.Y. edited and revised manuscript; D.Y. approved final version of manuscript. 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