The Dynamics of Error Processing in the Human Brain as Reflected by High-Gamma Activity in Noninvasive and Intracranial EEG

Error detection in motor behavior is a fundamental cognitive function heavily relying on cortical information processing. Neural activity in the high-gamma frequency band (HGB) closely reflects such local cortical processing, but little is known about its role in error processing, particularly in the healthy human brain. Here we characterize the error-related response of the human brain based on data obtained with noninvasive EEG optimized for HGB mapping in 31 healthy subjects (15 females, 16 males), and additional intracranial EEG data from 9 epilepsy patients (4 females, 5 males). Our findings reveal a comprehensive picture of the global and local dynamics of error-related HGB activity in the human brain. On the global level as reflected in the noninvasive EEG, the error-related response started with an early component dominated by anterior brain regions, followed by a shift to parietal regions, and a subsequent phase characterized by sustained parietal HGB activity. This phase lasted for more than 1 s after the error onset. On the local level reflected in the intracranial EEG, a cascade of both transient and sustained error-related responses involved an even more extended network, spanning beyond frontal and parietal regions to the insula and the hippocampus. HGB mapping appeared especially well suited to investigate late, sustained components of the error response, possibly linked to downstream functional stages such as error-related learning and behavioral adaptation. Our findings establish the basic spatio-temporal properties of HGB activity as a neural correlate of error processing, complementing traditional error-related potential studies. Significance Statement There is great interest to understand how the human brain reacts to errors in goal-directed behavior. An important index of cortical and subcortical information processing is fast oscillatory brain activity, particularly in the high-gamma band (above 50 Hz). Here we show that it is possible to detect signatures of errors in event-related high-gamma responses with noninvasive techniques, characterize these responses comprehensively, and validate the EEG procedure for the detection of such signals. In addition, we demonstrate the added value of intracranial recordings pinpointing the fine-grained spatio-temporal patterns in error-related brain networks. We anticipate that the optimized noninvasive EEG techniques as described here will be helpful in many areas of cognitive neuroscience where fast oscillatory brain activity is of interest.

both transient and sustained error-related responses involved an even more extended 48 network, spanning beyond frontal and parietal regions to the insula and the 49 hippocampus. HGB mapping appeared especially well suited to investigate late, 50 sustained components of the error response, possibly linked to downstream functional 51 stages such as error-related learning and behavioral adaptation. Our findings establish 52 the basic spatio-temporal properties of HGB activity as a neural correlate of error 53 processing, complementing traditional error-related potential studies. 54

66
Error processing is a fundamental brain function. A breakthrough in research on error 67 processing in the human brain was the independent discovery of the "error-related 68 negativity" (ERN) (Gehring et al., 1993), or error negativity (Ne) (Falkenstein et al., 1991) 69 in noninvasive electroencephalography (EEG). The ERN/Ne is a negative deflection 70 above the fronto-central midline, peaking shortly after the electromyogram (EMG) onset 71 of an erroneous response, followed by the error positivity (Pe) (Falkenstein et al., 1991) 72 with parietal maximum. ERN/Ne and Pe are often assumed to reflect sequential 73 functional aspects of error processing, including precursors of error detection such as 74 conflict monitoring and explicit error detection itself. In contrast to the ERN/Ne, the Pe 75 was linked to conscious error processing (Nieuwenhuis et al., 2001). Moreover, the Pe 76 might reflect evidence strength during error detection and could thus provide input to 77 further downstream stages, e.g., to the evaluation of the significance of errors and the 78 implementation of behavioral reactions (Steinhauser and Yeung, 2010). 79 To further dissect error-related processing both in healthy subjects and in patients with a 80 broad spectrum of brain disorders ( and we are not aware of any other study using noninvasive EEG recorded from the 88 healthy human brain. 89 However, gamma-band frequencies may be especially important to understand cortical 90 function in general, including error processing. A large body of empirical evidence 91 indicates that high-gamma band (HGB, including the 50-150 Hz range) activity is a 92 spatially and temporally specific index of the underlying, functionally relevant neural 93 networks (Crone et al., 1998(Crone et al., , 2006Brunel and Wang, 2003). Compared to lower 94 frequencies, however, detecting HGB power modulations in noninvasive EEG is 95 challenging for several reasons that are related to the more focal spatial distribution of 96 cortical high-frequency sources (Crone et al., 2006), their much smaller power, 97 (Freeman et al., 2000), and their greater susceptibility to artifacts, such as from muscle 98 activity (Goncharova et al., 2003) or microsaccades. The latter particularly can mimic 99 physiological responses within the HGB range (Yuval-Greenberg et al., 2008). 100 To overcome these problems, we carefully optimized the procedure of EEG acquisition 101 and analysis for the detection of high-frequency EEG modulations, combining high-102 resolution EEG acquisition, optimized electromagnetic shielding, low-noise amplifier 103 systems, as well as high-precision eye tracking simultaneously acquired to the EEG data 104 to tightly control for ocular artifacts. Utilizing this optimized setup, we re-examined a 105 classical paradigm to elicit error responses in a large group (n=35) of healthy subjects. 106 Furthermore, to validate our noninvasive EEG findings, we also ran the same paradigm 107 in patients with intracranially implanted electrodes. 108 Our findings clearly demonstrate that error-related HGB brain responses can be 109 detected in noninvasive EEG recorded from healthy subjects; importantly, we rule out 110 ocular including micro-saccadic effects as an explanation for the observed HGB 111 responses, as well as corroborate our noninvasive observations by intracranial EEG 112 data. For the first time, our findings reveal a clear picture of the global dynamics of the 113 error-related HGB response of the human brain, starting from an early response 114 dominated by anterior brain regions, over a shift to medial parietal regions parallel to the 115 Pe, and finally to a subsequent phase characterized by sustained parietal HGB activity. 116 This phase lasts for more than 1 s after the onset of the error event and constitutes a 117 novel candidate signal of the downstream processes following the classical Pe. 118 Combined investigation of both the classical error-related potentials and of HGB 119 modulations thus promises to shed new light on error processing in the human brain. 120

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Subjects 122 In the noninvasive EEG study, 35 healthy subjects participated; thereof, 4 subjects had 123 to be excluded because of extensive muscular or ocular artifacts. Thus, data of 31 124 subjects (mean age 24.6 years, standard deviation (SD) = 3.1 years, 15 females) were 125 further analyzed. Handedness was assessed according to a modified Edinburgh 126 handedness questionnaire (Oldfield, 1971); 28 subjects were right-handed, 3 were left-127 handed. All stated not to have neurological or psychiatric diseases and not to be under 128 the influence of medication affecting the central nervous system. 129 In the intracranial EEG study, 9 right-handed patients (mean age 27.0 years, SD = 7.7 130 years, 4 females) with pharmacoresistant epilepsy were recruited. They were implanted 131 with intracranial electrodes in Freiburg, Germany, or in Prague, Czech Republic. 132 All subjects and patients gave their written informed consent before participating in the 133 study. The study was approved by the local ethics committees. 134

Experimental design 135
To probe error-related processing, we used the Eriksen flanker task (Eriksen and 136 the subjects in the center of a 19-inch monitor (4:3-screen ratio, 60-Hz frame rate) for 142 1 s. After that, one of four stimuli was shown for 100 ms, each with a probability of 0.25. 143 Two of the stimuli were congruent stimuli (LLLLL & RRRRR) and the other two 144 incongruent stimuli (RRLRR & LLRLL). To respond, subjects used their left or right 145 index finger to press the left or right analog shoulder button on a wireless gamepad 146 (Logitech F710, Apples, Switzerland) if the central letter of the stimulus was an "L" or 147 "R", respectively. The deflection threshold of the analog joystick button was set to 10% 148 of its maximal deflection. 149 As proposed by (Herrmann et al., 2004b), we set an individual reaction time limit for 150 each subject. This response time limit was determined as the mean response time in a 151 32-trial training session. Subjects were instructed to respond as fast and as accurately 152 as possible. The subjects were also introduced to a scoring point system, and instructed 153 to get as many points as possible. For each correct response, subjects gained 5 points, 154 and lost 5 points in the event of an erroneous response. By missing the individual 155 reaction time limit, subjects lost 10 points; this stronger penalty was introduced to keep 156 the subject under time pressure, hence inducing errors. In each break after a recording 157 run, the score and performance of the respective run was shown to the subjects along 158 with a comparison to their total performance up to this run. 159 Two seconds after their response, the subjects received an audiovisual feedback 160 according to their performance. If the response was fast enough and correct, the 161 feedback consisted of a smiling face icon and a 1-kHz sine tone, the feedback for an 162 erroneous but fast enough response consisted of a sad face and a 500-Hz sine tone. 163 For responses slower than the individual reaction time limit, a cartoon of a snail was 164 displayed accompanied by a 5-kHz sine tone. The two-second delay was introduced to 165 avoid an influence of the feedback on error-related brain responses. We did not verify 166 the error awareness prior to the feedback directly; however, all subjects reported that 167 they were aware of most errors directly after the motor response. 168 Before the start of each trial, only the fixation dot was shown for 3 s. In the case of 169 healthy subjects, one session consisted of 100 trials, after which the subjects had the 170 possibility to have a break. Each experiment included 10 sessions, so that altogether 171 1000 trials were collected for each subject; on average, the error rate was 22.23 ± 0.11 172 (mean ± SD) %. Recording sessions with epilepsy patients were shorter and included 173 overall fewer trials depending on the condition of the respective patient. On average, 174 patients completed 369 ± 111 trials, thereof 218 ± 74 correct trials and 57 ± 32 error 175 trials, with a total error rate of 20.95 ± 0.11 %.   with 'R' target letter in inset). 2 s after the button press, one of the three types of audiovisual feedback 183 indicated to the subjects whether their response was correct, incorrect, or too slow.

Recording and preprocessing of noninvasive EEG 185
The noninvasive EEG setup was optimized for the measurement of high-frequency 186 responses. We used NeurOne amplifiers (Mega Electronics Ltd., Kuopio, Finland) with a 187 24-bit resolution and low input noise (root mean square < 0.6 μV between 0.16-200 Hz). 188 We recorded 128 EEG channels with the waveguard EEG cap (ANT Neuro, Enschede, 189 Netherlands) at a sampling rate of 5 kHz (AC, 1250-Hz anti-aliasing low-pass filter). The The EEG recordings took place in an electromagnetically shielded cabin ("mrShield" -199 CFW Trading Ltd, Heiden, Switzerland) to reduce electromagnetic artifact 200 contamination. All exchange of information between inside and outside of the cabin was 201 done with fiber optic cables to sustain the shielding. Also, electrical devices inside the 202 cabin, such as EEG amplifier, eye tracker and loudspeakers, were powered by DC 203 batteries to prevent 50-Hz power line artifacts from interfering with the EEG signal. The 204 cabin furthermore dampens sounds and vibrations to protect the subject from external 205

noise. 206
Both control of the experiment as well as data analysis was carried out using Matlab 207 R2014a (The MathWorks Inc., Natick, USA, RRID:SCR_001622). Implementation of the 208 paradigm was done within the Psychophysics Toolbox (Brainard, 1997, 209 RRID:SCR_002881). Synchronization of the EEG data and the experimental paradigm 210 was achieved by using a parallel port to send different trigger pulses for each event from 211 Matlab to the EEG amplifiers. 212 To control the signal quality, a visual inspection of the EEG data was done both 213 continuously during the measurement as well as after the experiment in Brainstorm 214 (Tadel et al., 2011). We searched for EMG artifacts by examining time course and 215 topography of single-trial data. Channels with strong contamination with EMG artifacts 216 were excluded from further analysis in single subjects; on average, we rejected 1.03 ± 217 1.75 (mean ± SD) channels. 218 During signal processing, the EEG data and markers were down-sampled from 5 kHz to 219 1 kHz (time-frequency analysis) or 500 Hz (voltage plots). Channels were re-referenced 220 to their common average. The signal was filtered with a Butterworth high-pass filter of 221 fourth order with a cut-off frequency of 0.5 Hz. 222 The indices of the correct and false responses were extracted and aligned on the 223 response EMG. The time point of the EMG onset was found by applying a threshold 224 based retrospective search on the arm EMG channels. 225

Intracranial EEG recording, localization and preprocessing 226
Recording of intracranial EEG signal was done either with Compumedics amplifiers 227 (Singen, Germany) at the epilepsy center in Freiburg, Germany (2 kHz sampling rate), or 228 with Schwarzer Epas amplifiers (Munich, Germany) and Nicolet EEG C-series amplifiers 229 (Pleasanton, USA) at the epilepsy center of the Motol University Hospital in Prague, 230 Czech Republic (512 Hz sampling rate). The depth electrodes used for recording had 231 platinum-iridium contacts (DIXI Medical, Lyon, France & AD-TECH, Racine, WI, USA). 232 The preprocessing was done as for the noninvasive data, with the difference that the 233 channels were re-referenced bipolarly between the respective neighbors. 234 The stereotactic depth electrodes were localized with the help of their post-implantation 235 MRI or CT artifacts in a normalized and co-registered MRI of each patient as described 236 in Pistohl et al. (2012). After transformation to the MNI coordinate system, 237 cytoarchitectonic probabilistic maps were calculated with the SPM anatomy toolbox 238 (Eickhoff et al., 2005(Eickhoff et al., , 2006(Eickhoff et al., , 2007 to assign the electrodes to specific brain regions. This 239 method accounts for inter-subject differences in brain anatomy and allows the 240 comparison on a group level with high precision . 241 Electrodes positioned inside a seizure onset zone or showing frequent interictal activity, 242 as identified by experienced epileptologists, were excluded from further analysis. Of 885 243 bipolar referenced channels from 9 patients, we removed 76 channels because they 244 could not be assigned to a specific brain region, 53 channels which were positioned 245 inside a seizure onset zone, 59 channels because of frequent interictal activity, and 7 246 channels due to technical problems or position outside the brain. Approximately 20 % of 247 the remaining electrodes were identified as lying within white matter. As a control, we 248 also did the analyses of the intracranial data after splitting white and gray matter 249 electrodes; however, as we found that white matter electrodes, especially those near 250 boundary areas, were able to sample a number of significant effects, and further did not 251 change any findings, we did not exclude these channels from further analysis. 252 Thus, 690 sites were available for further analysis.

Time-frequency analysis 257
Time-resolved spectral power was computed with a multitaper method (Thomson, 1982)  Significance of median power changes within individual conditions was computed with a 295 two-sided sign test. Whenever multiple comparisons were done, we estimated the 296 positive false discovery rate (pFDR) for each p-value (Benjamini and Hochberg, 1995;297 Storey, 2002297 Storey, , 2003. 298

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Here we show for the first-time error-related high-gamma responses in a noninvasive 300 EEG study (with 31 healthy subjects) and additionally compare and corroborate them 301 with intracranial EEG measurements (in 9 patients with pharmacoresistant epilepsy). 302

Error-related voltage and spectral power modulations in noninvasive EEG 303
In the following, we show an overview of the dynamics and topography of voltage and 304 spectral power modulations, as averaged over the 31 healthy subjects included in this 305 study, in correct responses (Fig. 2), erroneous responses (Fig. 3) as well as the 306 difference between the two conditions, i.e., error-related activity (Fig. 4). The spectral 307 power responses are shown up to 300 Hz in the time interval from 0.7 s before until 1.5 308 s after the response. For these and all comparable topographical results, the positive 309 false discovery rate was calculated across 128 channels, 24 frequency bands, and 61 310 time points (1 s before response onset until 2 s after response onset in steps of 50 ms). 311 Error-related HGB activity had its maximum approximately between 60 and 90 Hz (Fig.  312 2-4, yellow background), or more narrowly located between 70 and 80 Hz (Fig. 2-4, blue 313 background). Based on these observations, we decided to use these frequency ranges 314 for a closer inspection of HGB responses in the following analyses 315

335
Comparing error and correct conditions, significant differences became evident. While 336 there was lower power at parietal channels in the delta band (< 4 Hz) during and after 337 errors, fronto-central channels exhibited an error-related power increase in the delta and 338 the theta band (4-8 Hz). In the alpha band (8-12 Hz), a spatially more widespread power 339 increase during and shortly after the erroneous response occurred, followed by an Simultaneously with the late LGB increase, a second (with the ERN/Ne being the first) 345 significant negative voltage deflection was seen at central channels. 346 Crucial to the present study, in the high-gamma band (HGB, > 50 Hz), a significant 347 error-related power increase occurred at fronto-central channels shortly after the 348 response onset, and shifted to more central and parietal areas over the course of a few 349 hundred milliseconds, where the error-vs-correct relative HGB power stayed significantly 350 increased until up to 1.5 s after the response. Similar high-gamma increases were 351 observed in errors both after incongruent and congruent stimuli classes (data not 352 shown). After an initial HGB power increase, there was a significant midline power 353 decrease in correct responses after 800 ms until at least 1.5 s (Fig. 2). This power 354 decrease was not observed after erroneous response (Fig. 3) 355

Effects of eye movements on high-gamma signals 399
During the experiments, a great number of miniature eye movements were recorded for 400 each subject. After discarding those events near blinks, on average 6300 ± 2500 (mean 401 ± SD) microsaccades were recorded per subject. To examine the spectral power 402 modulations related to this class of eye movements more closely, we also examined 403 EEG data aligned to the onset of the microsaccades. Fig. 7 shows the group median of 404 those trials. Both at fronto-polar and parieto-central EEG channels, there was a broad-405 band gamma increase during microsaccade (and saccade, data not shown) onset. This 406 increase was prominent from 25 to 120 Hz. In lower frequency bands, e.g., in the delta 407 band, we observed a power decrease, which continued until 500 to 600 ms after the 408 microsaccade onset.

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Next, in each subject we matched the correct and error condition to have the same 417 amount of microsaccades and saccades within each time-frequency bin of the EEG data 418 after the multitaper analysis. To examine the effect of this measure on the results, we 419 compared the error-related high-gamma activity in matched and unmatched data 420 (Fig. 8). 421

428
After the matching, the distribution of electrodes with significant changes in the high-429 gamma band was only minimally altered, and the overall pattern remained the same. 430 There were only very few significant differences between the original and the matched 431 data. We conclude the error-related effects cannot be attributed to the occurrence of 432 saccades and microsaccades. 433

Error-related high-gamma activity: frontal vs. parietal regions 434
We further wished to compare error-related high-gamma activity at frontal and parietal 435 regions as the two major foci of the HGB response. To this aim, we averaged HGB 436 activity in a frontal and a parietal region of interest (ROI). 437   Error-related HGB power in the frontal ROI reached its maximum around 150 to 200 ms 448 after response EMG response onset. The same frequency band in the parietal ROI 449 showed a later peak at 600 to 700 ms. The HGB power in the parietal ROI was 450 significantly increased until up to 1.3 s after the EMG response onset. In the time around 451 the EMG onset, error-related HGB activity in the frontal ROI was significantly (sign test, 452 p<0.01) stronger than in parietal regions. 453

Confirmation in Intracranial EEG Measurements 454
Intracranial EEG measurements in 9 patients yielded a multitude of error-related 455 changes. For comparability, we concentrated the analysis of error-related high-gamma 456 activity in intracranial EEG to the 60-90 Hz band, as the frequency of interest in 457 noninvasive EEG. An overview of the electrode locations of all 9 patients and sites with 458 significant changes in this range is shown in Fig. 10    gyrus and the insula (Fig. 10 D,F). Secondly, responses with a transient, broadband 477 gamma increase, e.g., in the middle frontal gyrus, the lingual gyrus or the inferior 478 temporal gyrus (Fig. 10 E,H,I). Thirdly, responses with a broad-band gamma increase 479 and with a long duration of around 2 s, e.g., in the middle temporal gyrus (Fig. 10 G). 480 More significant HGB modulations were located in the right hemisphere; however, it is to 481 note that our sample consisted of more electrodes in the right hemisphere (443 sites 482 after bipolar re-referencing & channel rejection) compared to the left hemisphere (247 483 sites). Across the 9 patients, we observed an average error rate of 21.09 ± 0.11 (mean ± 484 SD) % with the left hand, and 20.81 ± 0.10 % with the right hand; there was no 485 significant difference with p=0.46 (paired one-sided t-test). 486 To get an overview of the significance of single-channel observations, we calculated the 487 ratio of significant responses within 19 regions of interest (Table 1). 488

489
For 19 ROIs, the percentages of channels with significant (pFDR<0.05) 60-90 Hz HGB error-related power 490 modulations, averaged across the time window from 0 s to 0.6 s after the response (FDR-corrected over 491 all channels, as in Fig. 10), are listed together with the total number of channels (n) included per area. We further compared error-related spectral power modulations of nearby intracranial 497 EEG and scalp EEG electrodes in the range of the motor cortex (Fig. 11).

508
Both in scalp EEG at central positions and intracranial EEG in the precentral gyrus, 509 significant error-related power modulations were observed in the delta, theta, alpha, 510 beta, and high-gamma band. In these examples, the spectral patterns of nearby 511 intracranial and noninvasive EEG channels were very similar at both group and single-512 subject level (Fig. 11). In intracranial EEG, the high-gamma activity had the strongest 513 error-related power modulation, while in noninvasive measurements, the lower 514 frequency bands showed a greater difference between correct and error responses. 515

Fine-grained dynamics of error-related activity in intracranial EEG 516
For a closer look at the spatio-temporal progression of error-related activity across the 517 brain, we analyzed the time course of error-related low-and high-spectral power 518 modulations in the intracranially recorded data of all 9 patients (Fig. 12). 519

526
It is apparent that low and high frequencies, as well as power increases and decreases, 527 differed in their spatial distribution over time. Subareas in frontal, temporal, and parietal 528 brain regions were activated at various time points before, during and after the error 529 response. Error-related increases in the high-gamma range (Fig. 12 A) especially 530 exhibited a temporal development that started at frontal surface und deep areas, 531 including the ACC, and then advanced to both parietal and temporal regions of the 532 brain. Notably, increased error-related HGB activity in hippocampal areas peaked 0.3 s 533 after the response, while decreased hippocampal HGB activity (Fig. 12 B) occurred -0.4 534 to -0.2 s before the response and again 0.8 to 1.0 s after the response. Overall, 535 intracranial EEG portrays a consistent but much more complex picture of error 536 processing compared to noninvasive data. In the present study, we examined error processing in the human brain as reflected in 553 HGB activity, based on measurements using noninvasive and intracranial EEG. In both, 554 we found significant error-related modulations of high-gamma power. Noninvasive 128-555 channel EEG in an electromagnetically shielded cabin enabled us to reveal the global 556 topography and dynamics of event-related potentials and spectral power modulations, 557 while we used intracranial EEG to validate the noninvasive findings, and additionally to 558 probe local fine-grained activity patterns. 559

Error-related low-frequency responses in noninvasive EEG 560
Our findings generally reproduced the spectral power modulations in the delta, theta, For example, we observed an error-related delta band pattern characterized by the co-566 occurrence of increased and decreased power in anterior and posterior regions, 567 respectively (Fig. 4,6). In the high-beta and low-gamma band (20 -40 Hz), we observed 568 an error-related power increase in a late time window, starting 800 ms after the 569 response (Fig. 4,6). Interestingly, around 1000 ms after response onset, a second (with 570 the ERN/Ne being the first) smaller but significant (p<0.01) negative deflection in the 571 error-related potential occurred at midline EEG channels (Fig. 4, bottom row) which thus 572 might be termed "Ne1000". The maximal low-gamma band response occurred at roughly 573 the same time with a focus on midline channels. Together, these examples illustrate that 574 an optimized EEG procedure applied to a suitably large group of subjects can reveal a 575 range of additional significant features of the error-related response that may be useful 576 to consider in future studies. 577 578

Error-related high-frequency responses in noninvasive EEG 579
Both in group results and single subjects, we found significant error-related HGB power 580 increases. Although high-gamma activity was seen in both correct and erroneous trials, 581 it was significantly stronger in the erroneous trials. The error-related high-gamma 582 response presented itself as an early fronto-central power increase, followed by a shift to 583 parieto-central areas, where the HGB power after errors was significantly larger than 584 than after correct responses over an extended period (up to 1.5 s, see Fig. 4,9). 585 Importantly, the spatio-temporal dynamics differed clearly from those of theta, alpha, 586 beta, and low-gamma responses, and high-gamma response were not correlated to 587 ERN/Ne and Pe amplitudes across subjects, pointing to a unique functional role. 588 We controlled thoroughly for ocular artifacts in our noninvasive EEG experiments. 589 Firstly, by using high-resolution binocular eye tracking, we were able to exactly match Secondly, the topography of microsaccade-related HGB effects showed a qualitatively 594 different spatial pattern compared to the error-related HGB responses (Fig. 7, 8). Thus, 595 we conclude that our error-related HGB responses cannot be explained as ocular 596

artifacts. 597
Further, we also think that it is highly unlikely that our error-related HGB responses 598 reflect EMG contamination. First, the error-related HGB power did not exhibit the rather 599 flat, broadband power increase typical of EMG contamination (Goncharova et al., 2003), 600 but rather a strong maximum between 60 and 90 Hz. Second, the spatial distribution of 601 the high-gamma increase with the maximum over the midline differed from that to be 602 expected for EMG, which has its emphasis on peripheral electrodes close to the 603 muscles (Goncharova et al., 2003;Whitham et al., 2007). 604

Error-related high-gamma responses in intracranial EEG 605
Error-related intracranial high-gamma activity was found at multiple locations in the 606 brain, showing much larger amplitudes than the extracranial counterparts. These areas 607 overlapped strongly with areas where intracranial error-related potentials and HGB 608 increases were previously reported (Brázdil et al., 2005;Bastin et al., 2017). In addition 609 to gamma increases, we also observed responses with a decreased relative high- Furthermore, as illustrated by Fig. 12, intracranial and scalp EEG channels placed 616 above central brain regions showed coinciding time-frequency patterns in their error-617 related responses (see Fig. 12). Together, these observations lend additional support to 618 the validity of our noninvasive data. One limitation of such a comparison is, of course, 619 that not all areas can be observed in noninvasive EEG recordings. While we assume 620 signals from the hippocampus and insular cortex to be virtually undetectable in 621 noninvasive EEG, signals from cingular areas might be recordable from the surface (Ball 622 et al., 1999). Generally, the superficial regions of the cortex areas can be expected to 623 have a greater influence on the scalp EEG than subcortical areas (Nunez et al., 1997). 624 The time course of intracranial activations (Fig. 13) confirmed that frontal regions were 625 activated rather early, while parietal (as well as temporal) areas became active later, in 626 line with a downstream role in error processing. Intracranial data also clearly showed 627 that, expectedly, cortical error processing is more complex than what can be observed in 628 noninvasive EEG. Hippocampal high-gamma was significantly decreased prior to the 629 actual error, and increased after the error. This could signify an interaction of error and 630 memory systems, consistent with a role of gamma in memory functions (Howard et al., 631 2003;Jensen et al., 2007;Sederberg et al., 2007;Kucewicz et al., 2014Kucewicz et al., , 2017. 632 Furthermore, Fig. 13 also demonstrates that lower HGB power in pre-, postcentral, and 633 supramarginal gyri as well as the insular cortex may precede errors. One explanation for 634 that could be that high-gamma power could indicate a pre-activation or "readiness" of a 635 brain area. and Wang, 2003). 662 Another network mechanism that can give rise to gamma oscillations relies on the 663 feedback loop between excitatory (E) and inhibitory (I) neurons (Wilson and Cowan, 664 1972), requiring a strong coupling from E to I and from I to E (reviewed in Buzsáki and 665 Wang, 2012). The resulting oscillations in spiking network models are typically in the 666 lower gamma range (Brunel and Wang, 2003). This mechanism has also been 667 employed in a non-linear rate model to explain the dependence of gamma oscillation 668 frequency on the stimulus size in visual cortex, exploiting the modulation of the intra-669 cortical E-I feedback loop through the neuronal non-linearity (Kang et al., 2010). Notably, 670 the gamma frequency peak around 80 Hz observed in our data shows a similarity to the 671 gamma frequency profiles predicted by the model by Brunel (2000, Fig. 9 A). 672 Also, more realistic networks comprised of several layers (Potjans and Diesmann, 2014) 673 are able to generate an oscillation in the same frequency range: A mean-field analysis 674 shows that the network mechanism is here a subcircuit comprised of excitatory and 675 inhibitory neurons in layers 2/3 and 4 (Bos et al., 2016). The mathematical analysis of 676 these networks also exposes why the power of the oscillation is strongly influenced by 677 the tonic drive to the network, predominantly to layer 4. An error-related signal changing 678 the tonic drive to the local oscillation-generating network may thus be a candidate 679 mechanism behind the observed modulations in the power spectra. Such a mechanism 680 would predict a co-modulation of the multi-unit firing rate with the increase of gamma targeted the criterion which participants used to decide whether or not to report errors, 705 has linked the Pe to the strength of accumulated error-related evidence (Steinhauser 706 and Yeung, 2010). Late, sustained parietal high-gamma activity could thus reflect 707 processes downstream to error evidence accumulations, such as behavioral adjustment 708 and motor learning. This speculation could be tested in future studies utilizing EEG-709 based HGB mapping as described in our present study. 710

Conclusion & Outlook 711
The fact that error-related HGB signals are detectable with noninvasive EEG opens up a 712 much wider avenue of research than would be feasible with intracranial recordings electrodes is confined to a much smaller group of patients undergoing pre-neurosurgical 720 evaluation, in most cases for the treatment of focal pharmacoresistant epilepsy. Our 721 findings however clearly highlight the unique value of these intracranial recordings. For 722 example, they allow assessment of brain structures that are difficult or even impossible 723 to probe electrophysiological noninvasively, such as insular cortex and the hippocampal 724

formation. 725
Our findings could help understanding the mechanisms behind human error processing. 726 Further, they could also help in the decoding of errors from single-trial EEG using 727 machine learning algorithms to improve the performance of brain-machine interfacing 728  Table 2: Excerpt of studies about error-related spectral power modulations in EEG & MEG.

1007
As frequency band definitions were not consistent amongst the publications, the respective definition is 1008 stated within parentheses.