Abstract
Interindividual variability in outcomes across individuals poses great challenges for the application of noninvasive brain stimulation in psychological research. Here, we examined how the effects of high-frequency transcranial random-noise stimulation (tRNS) on sustained attention varied as a function of a well-studied electrocortical marker: spontaneous theta:beta ratio. Seventy-two participants received sham, 1-mA, and 2-mA tRNS in a double-blind, crossover manner while they performed a sustained-attention task. Receiving 1-mA tRNS was associated with improved sustained attention, whereas the effect of 2-mA tRNS was similar to the effect of sham tRNS. Furthermore, individuals’ baseline theta:beta ratio moderated the effects of 1-mA tRNS and provided explanatory power beyond baseline behavioral performance. The tRNS-related effects on sustained attention were also accompanied by reductions in theta:beta ratio. These findings impart novel insights into mechanisms underlying tRNS effects and emphasize how designing studies that link variability in cognitive outcomes to variability in neurophysiology can improve inferential power in neurocognitive research.
Noninvasive brain stimulation (NIBS) is a valuable tool for assessing how experimentally induced changes in neural processes affect behavior. However, there have been increasing concerns about reported variability in response patterns across individuals. Although there is abundant evidence of physiological factors influencing interindividual variability (Harty, Sella, & Cohen Kadosh, 2017; Li, Uehara, & Hanakawa, 2015), remarkably little work has been explicitly directed at identifying baseline markers that could identify individuals who are more likely to be sensitive to NIBS. Recent investigations have highlighted how off-line electroencephalography (EEG) recordings acquired prior to NIBS interventions could be particularly viable in this regard (see Thut et al., 2017). The present study had the dual aims of examining the impact of a relatively novel NIBS technique known as high-frequency transcranial random-noise stimulation (tRNS) on sustained attention and evaluating the potential for baseline levels of an EEG marker—spontaneous theta:beta ratio—to inform variability in response patterns across individuals.
Theta:beta ratio is one of the most studied physiological markers in relation to normal variation in cognitive functioning. Particularly consistent associations have been documented between theta:beta ratio and performance on tasks that demand top-down attention (Angelidis, van der Does, Schakel, & Putman, 2016; O’Connell et al., 2007; Putman, van Peer, Maimari, & van der Werff, 2010). A prevailing interpretation of these findings is that greater theta, relative to beta, power reflects poorer top-down cortical regulation of subcortical processes (e.g., Angelidis et al., 2016). Theta:beta ratio has also repeatedly been found to be higher in clinical groups with sustained attention deficits (Arns, Conners, & Kraemer, 2013), albeit developmental changes in EEG power may undermine its reliability and predictive value in pediatric groups (e.g., Saad, Kohn, Clarke, Lagopoulos, & Hermens, 2015). Furthermore, elevated baseline theta:beta ratio has been associated with a favorable response to stimulant medications and neurofeedback protocols tailored to improve top-down regulation of attention (Arns et al., 2013). Together, these findings highlight the potential for theta:beta ratio to be informative with regard to differences in the ability to regulate top-down attention and the extent to which individuals are likely to benefit from interventions that target the associated neural systems.
During tRNS, alternating current is delivered at frequencies and intensities that vary in a randomized manner within specified ranges. The effect of tRNS, at least when applied within the 0.75-mA to 2-mA range, is believed to be excitatory because of the fast-oscillating electrical fields putatively depolarizing neurons irrespective of the current polarity (Fertonani & Miniussi, 2017; Terney, Chaieb, Moliadze, Antal, & Paulus, 2008; but see Parkin, Bhandari, Glen, & Walsh, 2019). Studies have demonstrated the potential for tRNS to modulate a range of capacities from motor (Terney et al., 2008) and sensory (van der Groen & Wenderoth, 2016), to cognitive abilities such as arithmetic learning (Snowball et al., 2013), selective attention (Shalev, De Wandel, Dockree, Demeyere, & Chechlacz, 2018), adaptive reasoning (Brem et al., 2018), and procedural learning (Frank, Harty, Kluge, & Cohen Kadosh, 2018).
Here, we examined the impact of sham, 1-mA, and 2-mA tRNS applied over key nodes of the sustained-attention system, right dorsolateral prefrontal cortex and right inferior parietal lobule (Posner & Petersen, 1990; Singh-Curry & Husain, 2009), using a double-blind, within-subjects, randomized design. Previous research with both tRNS (van der Groen & Wenderoth, 2016) and other NIBS approaches (e.g., Benwell, Learmonth, Miniussi, Harvey, & Thut, 2015) has suggested that greater stimulation intensity does not necessarily produce greater benefits, so we anticipated that the overall relationship between tRNS-induced gains and tRNS intensity would not necessarily be linear. We also examined the potential for theta:beta ratio to predict objective sustained-attention performance, subjective appraisal of attentiveness in everyday life, and—of foremost interest—the extent to which individuals would gain from tRNS. We predicted that individuals with relatively high baseline theta:beta ratio, compared with individuals with relatively low baseline theta:beta ratio, would be more likely to benefit from tRNS.
Method
Sample-size calculation and participants
Given that, to the best of our knowledge, this is the first study to employ a within-subjects design to examine the effects of tRNS on high-level cognition, it was not possible to do a precise a priori sample-size calculation. However, previous research involving the application of tRNS to frontal and parietal regions (Cappelletti et al., 2013; Snowball et al., 2013) using between-groups designs has revealed large effect sizes (Cohen’s ds > 1). Assuming that these effect sizes could be inflated (Button et al., 2013), we used G*Power software (Faul, Erdfelder, Lang, & Buchner, 2007) to determine what sample size we would need to have 80% power to detect a small effect (Cohen’s d = 0.2) at an alpha level of .05. This calculation suggested that a sample of 42 participants would be sufficient to detect even a small effect of tRNS on performance. But given that we were additionally interested in examining individual differences in tRNS effects based on variability in theta:beta ratio, we elected to collect data on a larger sample of 72 participants.
These 72 participants were 33 females and 39 males between the ages of 19 and 35 years (M = 25.1, 95% confidence interval, or CI = [24.0, 26.1]). Exclusion criteria for participation were left-handedness, visual impairment, history of fainting, history of neurological or psychiatric illness, neurological insult, drug or alcohol abuse, and reporting current use of antipsychotic or antidepressant medications. All participants were asked to refrain from consuming more than 1 unit of alcohol in the 24 hr preceding each testing session. All participants provided written consent, and all aspects of the study were approved by the University of Oxford Medical Sciences Interdivisional Research Ethics Committee.
Procedure overview
An overview of the study procedure is schematically depicted in Figure 1. Participants were required to attend three testing sessions on 3 consecutive days. At the beginning of their first session, they completed a self-report measure of attentiveness in daily life—the Cognitive Failures Questionnaire (Broadbent, Cooper, FitzGerald, & Parkes, 1982; see the description in the Supplemental Material available online). This was administered only once, as it measures traitlike characteristics that are relatively stable over time (Bridger, Johnsen, & Brasher, 2013). During the first session, participants were also introduced to the continuous-monitoring task (described below) and completed a practice block consisting of 14 targets while the experimenter observed their performance and provided verbal feedback. For the subsequent two sessions, they were offered the opportunity to complete the practice block again, but the vast majority declined. Finally, to compare the relative impact of sham, 1-mA, and 2-mA tRNS, we assigned each participant to a different stimulation condition at each session. The order in which they received each stimulation condition across the three sessions was assigned in a double-blind and fully randomized manner. In an effort to control for the known influence of circadian rhythms on cortical excitability, we scheduled the testing sessions for each participant at the same time each day.

Schematics illustrating the experimental procedure, continuous-monitoring task, and electrode placement. The experiment consisted of a high-frequency transcranial random-noise stimulation (tRNS) preceded and followed by measurements of resting electroencephalography (EEG). Participants completed a continuous-monitoring task during each phase of the experiment. The graph (b) illustrates how stimulus contrast varied throughout each trial of the continuous-monitoring task. EEG was monitored using (c) electrodes placed over right dorsolateral prefrontal cortex (F4) and right inferior parietal lobule (P4) according to the international 10-20 EEG system.
Apart from the above, participants completed the same experimental procedure on each day. Before, during, and after the delivery of tRNS on each day, participants performed a continuous-monitoring task devised by O’Connell, Dockree, and Kelly (2012). In an effort to guard against the possibility that the monotony of the experimental procedure would affect participants’ motivation to perform their best on each block of the task, we informed participants on each day of testing that they had the opportunity to win an extra £25 based on their performance. Specifically, they were informed that 1 of their 36 task blocks from across the three sessions would be randomly selected and compared with the blocks of 9 (i.e., 72/8) other participants who participated directly before or after them. The participant whose block was found to have the fastest response time (RT) and highest accuracy would be awarded £25. The experimenter emphasized to participants that randomly selecting a block in this manner meant that they should not be discouraged about their potential to win if they felt they had performed short of their best on any individual block.
Questionnaire measures
All participants completed questionnaires to assess attentiveness in daily life, subjective fatigue, and perceived sensations. Details about these questionnaire measures can be found in the Supplemental Material.
Continuous-monitoring task
The continuous-monitoring task we employed (O’Connell et al., 2012) is tailored to evaluate what is widely considered the defining property of sustained attention: the ability to reliably detect rarely and unpredictably occurring signals over prolonged periods of time (Dockree et al., 2017; Sarter, Givens, & Bruno, 2001). Participants are instructed to continuously monitor a flickering (21.25 Hz) annular-pattern stimulus for intermittent targets, which are defined by linear contrast changes from 65% to 35% over 1.6 s (see Fig. 1b). See the Supplemental Material for further details about the stimuli used in this task.
As outlined in Figure 1, participants performed 12 blocks of this task on each day of testing. Each block comprised 25 targets and lasted approximately 4 min. The intertarget interval was randomly assigned to be 4.0, 7.2, or 10.4 s. Participants were instructed to avoid guessing and to press the mouse button with their right index finger as soon as they were certain that the annular pattern was fading.
If participants’ attention were tightly focused on the task goal, we expected RTs to be consistently both fast and accurate. However, if attention were not tightly focused on the task goal, we expected that lapses of attention would occur. Such lapses in attention would likely result in either prepotent responses guiding behavior (and hence the occurrence of fast reflexive RTs; Unsworth, Schrock, & Engle, 2004) or RTs that were much slower than normal (Unsworth, Redick, Lakey, & Young, 2010). Sustained-attention proficiency can accordingly be captured by measuring intraindividual variations in RT (e.g., O’Connell et al., 2008). Since there is typically a strong relationship between standard deviation of RT and overall mean RT, we used each participant’s coefficient of variation (SDRT/MRT; thus controlling for differences in mean RT) as our primary metric of interest on this task.
tRNS
We delivered tRNS through circular electrodes using a StarStim device (Neuroelectrics, Barcelona, Spain). The electrodes were encased in a pair of saline-soaked sponges (25 cm2) and were secured within a Neuroelectrics EEG cap over right dorsolateral prefrontal cortex (F4) and right inferior parietal lobule (P4; see Fig. 1c), according to the international 10-20 EEG system. Before commencing the stimulation, we measured the impedance levels of the tRNS electrodes, and if they exceeded 5 kΩ, additional saline solution was injected onto the surface of the sponges. The 1-mA-tRNS condition consisted of 1-mA peak-to-peak (−0.5 mA to 0.5 mA) high-frequency noise (100–500 Hz, the maximum frequency supported by the StarStim device), with amplitude values that were normally distributed and had a mean of zero. The only factor that varied for the 2-mA-tRNS condition was that the high-frequency noise had peaks of −1 mA and 1 mA as opposed to −0.5 mA and 0.5 mA. For both of these conditions, the stimulation was delivered for 20 min, with a ramping period of 30 s at the onset and offset. The sham-tRNS condition involved 30 s of 1.5-mA tRNS, with a ramping period of 30 s at the onset and offset. This procedure ensured that, in both the active and sham conditions, participants experienced the sensations associated with the onset of transcranial electrical stimulation (e.g., tingling sensation; Gandiga, Hummel, & Cohen, 2006).
Some readers may wonder why we chose 1.5 mA for the sham condition. This decision was motivated by pilot testing suggesting that a sham condition that mounted transiently to 1 mA would be less optimal than a sham condition that mounted transiently to 2 mA for producing the level of sensation akin to the 2-mA-tRNS condition and, similarly, that a sham condition that mounted transiently to 2 mA would be less optimal than a sham condition that mounted transiently to 1 mA for producing the level of sensation akin to the 1-mA-tRNS condition. We accordingly reasoned that there would be less of a discrepancy in the sensations produced during a sham condition that mounted to 1.5 mA and the sensations produced during each of the active conditions.
EEG acquisition and analysis
Continuous EEG data were acquired using the Enobio 20 (Neuroelectrics). The 20 EEG channels were secured to Ag/AgCl-coated electrodes (1 cm2) and were positioned in accordance with the international 10-20 EEG system at the following locations—Fp1, Fpz, Fp2, F3, Fz, Fc1, Fc2, C3, Cz, C4, Cpz, Pz, P3, PO3, PO4, PO7, O1, Oz, O2—and the reference electrodes (common mode sense, driven right leg) were adhered over the right mastoid using Covidien (Dublin, Ireland, H124SG) electrodes. EEG data were sampled at a rate of 500 Hz with 24-bit resolution and transmitted via Bluetooth to Neuroelectrics Instrument Controller (NIC) software on a standard Windows 7 desktop computer. For the resting-state EEG recordings, participants were requested to stare at a fixation cross presented centrally on a uniform black background and endeavor to avoid mental activities as well as eye movements or muscular contractions for the duration of each 4-min recording.
The EEG data were processed in MATLAB (The MathWorks, Natick, MA) using a combination of custom scripts and EEGLAB routines (Delorme & Makeig, 2004). During some EEG recordings, there was transient packet loss—that is, samples failed to record because of miscellaneous sources of interference. The NIC software, by default, imputes the values for these samples by repeating the amplitude values for the preceding successful sample and assigning a marker code (255) to the trigger column so they can be easily identified. All EEG data files for each participant were screened for packet loss in excess of 10%. Nine files were found to have packet loss exceeding this criterion. Given that five and four of these files, respectively, were from just 2 participants, all EEG data from these 2 participants were excluded from the EEG analyses. Packet loss for all other files was low (0–6%). A 40-Hz low-pass filter was then applied to all remaining participants’ files using a fourth-order Butterworth filter. Noisy channels were identified by visual inspection of signal variance and were interpolated using spherical spline interpolation. The EEG data were then rereferenced to an average that excluded electrodes for which there was not an analogous electrode located on the right hemisphere of the scalp because of the placement of the tRNS electrodes (i.e., F3 and P3).
The resting-state EEG data were segmented into 2-s epochs. Epochs in which any channel exceeded ±100 µV at any time during the epoch were rejected in order to exclude excessive electromyogram, electrooculogram, and other noise transients. One further participant was excluded at this stage because of excessive artifacts (> 50% epoch loss). The clean epochs of the remaining 69 participants were then transformed into the frequency domain via fast Fourier transformation. The number of EEG epochs used for each transformation ranged from 151 to 208 (M = 176.2, 95% CI = [173.9, 178.8]). Frequency data of less than 1.5 Hz were excluded from further analysis to circumvent the inclusion of slow lateral eye movements.
Relative power (µV2) for the theta (4–7.5 Hz) and beta (14–30 Hz) bands was calculated by dividing the absolute power within each frequency band by the absolute power within the 1.5- to 30-Hz range, and resulting values were natural log transformed to normalize the data. Each power estimate was derived separately for frontal (Fz), central (Cz), parietal (Pz), and occipital (Oz) regions. The theta:beta ratio over each of these regions were subsequently calculated.
Following the majority of studies that have examined the relationship between theta:beta ratio and executive functions (see Arns et al., 2013), we report analyses conducted on the theta:beta ratio measured over the central electrode sites. However, we found that a similar pattern of results was also evident for the theta:beta ratio measured over frontal sites, but this was not the case for parietal or occipital sites.
Statistical analysis
We used the Friedman test to compare levels of subjective fatigue at the baseline period of each testing session. Friedman tests, along with follow-up Wilcoxon signed-rank tests, were also used to compare the sensations reported by participants at the end of each testing session.
Our behavioral analyses were centered on our main index of sustained-attention proficiency—the coefficient of variation on the continuous-monitoring task. For information about analyses and results relating to the other performance metrics of the task, see the Supplemental Material. We used a one-way repeated measures analysis of variance (ANOVA) to assess the extent to which the coefficient of variation on the continuous-monitoring task was matched at the baseline period for each testing session. To evaluate the impact of tRNS on the coefficient of variation, we used a repeated measures ANOVA with time (prestimulation, during stimulation, poststimulation) and tRNS condition (sham, 1 mA, 2 mA) as within-subjects factors. The significant interaction was followed up with a planned one-way ANOVA and paired-samples t test. All results are accompanied by effect sizes (η2s), and the error bars on plotted data points in the figures represent within-subjects 95% CIs.
The effects during tRNS (on-line effects) were calculated by subtracting the coefficient of variation measured during tRNS from the coefficient of variation measured before tRNS. The effects after tRNS (off-line effects) were calculated by subtracting the coefficient of variation measured after tRNS from the coefficient of variation measured before tRNS. A partial correlation between the coefficient of variation during tRNS and the coefficient of variation after tRNS, while controlling for the coefficient of variation before tRNS, verified that there was a correspondence between the observed on-line and off-line changes. We used Pearson’s r to test the respective relationships between baseline theta:beta ratio, baseline coefficient of variation, and attentiveness in daily life; to test our hypothesis that the effect of tRNS on the on-line and off-line changes would depend on individuals’ baseline levels of theta:beta ratio; and, consistent with previous work (Angelidis et al., 2016), to examine the retest reliability of baseline theta:beta ratio. We used Spearman’s correlations for instances in which the data were not normally distributed, such as to examine the correspondence between tRNS-related changes in performance and perceived sensations (which were measured on a Likert-type scale).
We used principal component analysis (PCA) to derive a single component of baseline theta:beta ratio with a view to capturing the maximum systematic variance and minimizing the measurement error associated with a single measure of theta:beta ratio. To compare the relative strengths of the correlations between tRNS effects and this PCA component with the single baseline measures of theta:beta ratio, we employed Lee and Preacher’s (2013) approach for comparing correlation strengths between dependent correlations. This approach entails converting the correlation coefficients into z scores and then computing the asymptotic covariance of the estimates (Steiger, 1980) for use in an asymptotic z test to account for the samples being dependent rather than independent.
Finally, we fitted linear mixed-effects models using the lme function from the nlme package in the R programming-language environment (Version 3.3.2; R Core Team, 2011) to compare and quantify the goodness of fit of models with and without baseline theta:beta ratio included as an independent predictor, using a likelihood-ratio test. In each of these models, participant was included as a random intercept.
Results
Pre-tRNS baseline measures of behavior and neurophysiology
Participants exhibited similar levels of coefficient of variation at each baseline testing phase, F(2, 142) = 0.027, p = .974, η2 < .01. There were also no differences in self-reported levels of fatigue at each baseline testing phase, χ2(2, N = 72) = 1.15, p = .563, Kendall’s W < .01. These observations provided confidence that tRNS-related effects were being compared with a common baseline for each tRNS condition and accordingly allowed us to exclude the possibility that there were significant carryover effects with respect to either tRNS or practice on the task. Further, individuals who reported more frequent attentional failures in everyday life also exhibited greater coefficients of variation at each pre-tRNS testing phase—before sham tRNS: r(72) = .299, p = .011; before 1-mA tNRS: r(72) = .351, p = .002; before 2-mA tRNS: r(72) = .235, p < .047—supporting the assumption that the coefficient of variation on this continuous-monitoring task provides a valid index of attentional lapses.
In line with the well-documented association between high theta:beta ratio and poorer executive functioning, our results showed a positive correspondence between baseline theta:beta ratio and attentiveness in daily-life scores, all rs(69) > .297, all ps < .05, and between baseline theta:beta ratio and coefficient of variation at each pre-tRNS testing phase, all rs(69) > .324, all ps < .01, irrespective of the day that each was measured. We examine this latter association further in the linear mixed-effects model below.
There was also a strong correspondence between the measures of resting theta:beta ratio at each pre-tRNS testing phase—before sham tRNS and before 1-mA tRNS: r(69) = .885, p < .001; before sham tRNS and before 2-mA tRNS: r(69) = .896, p < .001; before 1-mA tRNS and before 2-mA tRNS: r(69) = .893, p < .001 (see Fig. S1 in the Supplemental Material). Thus, consistent with previous research, our findings showed that there was good retest reliability for resting theta:beta ratio (Angelidis et al., 2016).
tRNS-related effects on coefficients of variation
We found effects of time, F(2, 142) = 4.76, p = .010, η2 = .06; tRNS, F(2, 142) = 3.06, p = .050, η2 = .07; and a Time × tRNS interaction, F(4, 284) = 3.08, p = .017, η p 2 = .04, for coefficients of variation (see Fig. 2). Planned follow-up tests indicated an effect of time for the 1-mA-tRNS condition, F(2, 142) = 11.06, p < .001, η2 = .14, but not for either the sham-tRNS condition or the 2-mA-tRNS condition (all ps > .4, η2 < .02). For the 1-mA-tNRS condition, the effect of time was driven by a reduction from before 1-mA tRNS to after 1-mA tRNS in coefficients of variation (on-line effect), t(71) = 4.17, p < .001, η2 = .19, and a reduction from before 1-mA tRNS to after 1-mA tRNS in coefficients of variation (off-line effect), t(71) = 3.20, p = .002, η2 = .13. A highly similar pattern of effects was observed for SDRT (see the Supplemental Material).

Coefficient of variation for each phase of the experiment, separately for each of the three types of transcranial random-noise stimulation (tRNS; sham, 1 mA, 2 mA). Each data point corresponds to one individual’s coefficient of variation at each time point. Squares indicate means. Asterisks indicate significant differences between phases (**p < .01). Error bars represent within-subjects 95% confidence intervals.
There was no difference between coefficients of variation measured during 1-mA tRNS and after 1-mA tRNS, t(71) = −1.43, p = .158, η2 < .03, and there was a close correspondence between the tRNS-related changes observed at these two time points, partial r = .558, p < .001, controlling for coefficients of variation measured before tRNS.
When we examined the impact of 1-mA tRNS on coefficients of variation with greater temporal resolution, we found that coefficients of variation were significantly lower for all blocks both during tRNS and after tRNS relative to each of the blocks before tRNS (all ps < .05, η2 > .05). Further, there was no difference between any of the blocks during tRNS and after tRNS (all ps > .36, η2 < .02), suggesting that the tRNS-related effects endured in a stable manner. Thus, 20 min of 1-mA tRNS was associated with an improvement in sustained attention, and this was still evident for at least 24 min after the tRNS had terminated. However, the observation that participants were matched on all performance indices at each baseline period of each testing session provided us with a basis for inferring that effects from the tRNS had dissipated within 24 hr, which is not surprising given the relatively brief stimulation period. See the Supplemental Material for an additional analysis conducted to appraise the longevity of the effect.
Theta:beta ratio as a predictor of tRNS-related effects
Of primary relevance, we found that baseline theta:beta ratio was a significant predictor of the changes in sustained attention for the 1-mA-tRNS condition. Again, this association was evident irrespective of the day that theta:beta ratio was measured, for both the on-line effects, all rs(69) > .422, all ps < .001 (see Fig. 3), and the off-line effects, all rs(69) > .469, all ps < .001 (see Fig. 4), supporting its viability as a marker for predicting responsiveness to tRNS.

Scatterplots (with best-fitting regression lines) showing the relationship between baseline theta:beta ratio before each phase of the experiment and the on-line effect of each type of transcranial random-noise stimulation (tRNS) on the coefficient of variation. On-line effects were calculated by subtracting the coefficient of variation measured during tRNS from the coefficient of variation measured before tRNS; positive coefficients of variation thus reflect a reduction in response time variability.

Scatterplots (with best-fitting regression lines) showing the relationship between baseline theta:beta ratio before each phase of the experiment and the off-line effect of each type of transcranial random-noise stimulation (tRNS) on the coefficient of variation. Off-line effects were calculated by subtracting the coefficient of variation measured after tRNS from the coefficient of variation measured before tRNS; positive coefficients of variation thus reflect a reduction in response time variability.
A PCA component of theta:beta ratio, derived from the three measures of resting theta:beta ratio at each pre-tRNS testing phase, also predicted the observed on-line effects, r(69) = .480, p < .001, and off-line effects, r(69) = .484, p < .001. However, asymptotic z tests indicated that the predictive power of this PCA component was not greater than that of any of the single measures of theta:beta ratio for predicting either on-line effects (all ps > .6) or off-line effects (all ps > .6). This observation further substantiates the potential utility and feasibility of acquiring a single measure of theta:beta ratio to predict tRNS-related gains.
These results were replicated when we fitted the linear mixed-effects model. Of primary relevance for the present study, we observed three-way interactions among tRNS condition, theta:beta ratio, and time. These interactions were driven by theta:beta ratio’s influence on how individuals responded to the 1-mA-tRNS condition at both the during- and poststimulation time periods, relative to the prestimulation time period, and relative to the sham-tRNS and 2-mA-tRNS conditions (see Table S1 in the Supplemental Material). Figure 5 illustrates the coefficients of variation predicted by this model at high (+1 SD), mean, and low (–1 SD) levels of theta:beta ratio at each time point within each stimulation condition. The observation that baseline theta:beta ratio and baseline coefficient of variation were reliably correlated on each day of testing, all rs(69) > .324, all ps < .01, calls into question whether the observed variability in tRNS-related effects on sustained attention could be attributable to individuals with poorer baseline performance simply having more room to improve. However, we confirmed that the goodness of fit of the model that included baseline coefficient of variation was poorer at explaining the data than the model that included both baseline coefficient of variation and baseline theta:beta ratio, χ2 = 34.22, p < .001 (see Table S1). Thus, the electrocortical marker, theta:beta ratio, provides significant explanatory power over and beyond baseline behavioral performance.

Predictions from the linear mixed-effects model: coefficient of variation for each phase of the experiment and each level of theta:beta ratio, separately for each of the three types of transcranial random-noise stimulation (tRNS; sham, 1 mA, 2 mA). Following the suggestion of Aiken, West, and Reno (1991) for plotting three-way interactions that involve continuous variables, we plotted regression lines for 1 standard deviation above the mean (high), the mean, and 1 standard deviation below the mean (low) of baseline theta:beta ratio. Error bars represent 95% prediction intervals.
We additionally verified whether other individual difference factors, such as age and gender—which have been linked to transcranial-electrical-stimulation outcomes in previous research (e.g., Fertonani & Miniussi, 2017)—provided any explanatory power beyond baseline performance. Neither gender, χ2 = 5.46, p = .793 (see Table S2 in the Supplemental Material) nor age, χ2 = 5.46, p = .793; see Table S2 in the Supplemental Material) improved the fit of the model.
tRNS-related effects on theta:beta ratio
Next, we examined whether the tRNS-related gains in sustained attention were reflected at the electrophysiological level, as indexed by a reduction in theta:beta ratio. We observed a Time × tRNS interaction for theta:beta ratio, F(2, 136) = 5.93, p = .003, η p 2 = .08. As in the behavioral results, this interaction reflected a reduction from before tRNS to after tRNS in theta:beta ratio that was specific to the 1-mA-tRNS condition, t(69) = 2.14, p = .036, η2 = .07 (see Fig. 6). Greater tRNS-induced reductions in theta:beta ratio were, in turn, associated with greater reductions in coefficient of variation—on-line effect: r(69) = .460, p < .001; off-line effect: r(69) = .422, p < .001—for the 1-mA-tRNS condition, providing further support for the intimate relationship between this index of sustained attention and theta:beta ratio.

Theta:beta ratio for the pre- and poststimulation phases of the experiment, separately for each of the three types of transcranial random-noise stimulation (tRNS; sham, 1 mA, 2 mA). Each data point corresponds to one individual’s theta:beta ratio at each time point. Squares indicate means. The asterisk indicates a significant difference between phases (*p < .05). Error bars represent within-subjects 95% confidence intervals.
Perceived sensations
The results of the perceived-sensations questionnaire indicated that perceived sensations differed across the three tRNS conditions, χ2(2, N = 72) = 44.56, p < .001, Kendall’s W = .309. Follow-up analyses indicated that participants reported significantly more sensations for the 2-mA-tRNS condition compared with both the 1-mA-tRNS condition (mean ranks = 14.43 vs. 24.03, respectively; Z = −4.69, p < .001) and the sham-tRNS condition (mean ranks = 14.42 vs. 24.86, respectively; Z = −5.04, p < .001). There was no difference between the 1-mA-tRNS condition and the sham-tRNS condition (mean ranks = 17.78 vs. 23.73, respectively; Z = −1.64, p = .102). More importantly, however, there was no difference across conditions for the question, “How much did these sensations affect your performance?”—χ2(2, N = 72) = 0.86, p < .651, Kendall’s W = .006. There was also no correspondence between the reported sensations and the tRNS-related changes in coefficient of variation for each of the conditions—sham tRNS: rs = .207, p = .081; 1 mA tRNS: rs = .035, p = .773; 2 mA tRNS: rs = .004, p = .972. Thus, although the 2-mA-tRNS condition was associated with greater perceived sensations, we can infer that it is unlikely that these sensations had a significant impact on the observed tRNS-related effects.
Discussion
We had two primary aims in the present study. The first aim was to examine the differential impact of sham, 1-mA, and 2-mA tRNS on sustained attention. The second aim was to appraise the potential of a well-studied electrocortical marker, spontaneous theta:beta ratio, to provide an index of the extent to which individuals are likely to exhibit gains in sustained attention. Our main findings were threefold. First, 1-mA tRNS was associated with improvements in sustained attention, as indexed by reductions in RT variability on a continuous-monitoring paradigm and reductions from before 1-mA tRNS to after 1-mA tRNS in theta:beta ratio. Second, our results substantiate existing evidence that resting theta:beta ratio constitutes a functionally relevant electrocortical marker of top-down attention. Third, the effects of 1-mA, but not 2-mA or sham, tRNS were moderated by individuals’ baseline theta:beta ratio.
Previous findings from both clinical and healthy populations have suggested that theta:beta ratio can predict scores on various measures of high-level cognitive functioning (e.g., O’Connell et al., 2007; Putman et al., 2010). Here, we corroborate this research by showing correspondence between high theta:beta ratio and poorer sustained attention (as indexed by higher RT variability on the continuous-monitoring paradigm), as well as a greater self-reported propensity for attentional failures in everyday life. These relationships were reliably evident across the measures of baseline theta:beta ratio acquired on 3 different days. These findings, in turn, support the assumption that relatively high theta:beta ratio reflects relatively weak top-down cortical-regulation processes that are required during tasks that demand top-down attention.
The observation that theta:beta ratio explained a significant proportion of variability in the tRNS-related gains in sustained attention is also consistent with previous research demonstrating the potential for resting theta:beta ratio to predict gains from pharmacological and neurofeedback interventions tailored to modulate top-down attentional capacities (Arns et al., 2013). Cumulatively, these findings indicate that resting theta:beta ratio may be capable of distinguishing subsets of individuals who are not engaging the cortical network required for sustained attention in an optimal manner.
NIBS research has previously highlighted neural, anatomical, and genetic markers that distinguish responders from nonresponders (Krause & Cohen Kadosh, 2014; Li et al., 2015). But acquiring these physiological assays is often prohibitively expensive. A few studies have also identified behavioral markers that have potential predictive power (e.g., London & Slagter, 2015). However, in order to derive meaningful metrics from behavioral performance, one must typically administer tasks for prolonged durations. In contrast, the predictive value of theta:beta ratio can be readily derived from 4-min recordings of resting EEG activity acquired from just one central or frontal electrode. Theta:beta ratio demonstrated predictive power over and beyond that observed for the baseline behavioral measure, and our data substantiated previous research that has highlighted its excellent intraindividual retest reliability (Angelidis et al., 2016).
The observed sensitivity of individuals with high theta:beta ratio to 1 mA, but not 2 mA, of tRNS supports models that emphasize the state dependency of NIBS (e.g., Miniussi, Harris, & Ruzzoli, 2013) and is consistent with a number of other NIBS studies that have reported nonlinear relationships between stimulation intensity and behavioral performance (e.g., Benwell et al., 2015). One possible nonlinear mechanism that has been invoked to explain such effects is stochastic resonance, or stochastic facilitation (McDonnell & Ward, 2011), in which an appropriate level of noise is added to enhance the output of subthreshold signals in nonlinear systems. Inherent in this perspective is the idea that the signal-enhancing potential of NIBS will depend on both the task-induced state of the targeted region and the level of noise introduced (Fertonani & Miniussi, 2017; Miniussi et al., 2013). Consequently, individuals with high theta:beta ratio may have had task-relevant neurons that were not reaching thresholds for signal transmission and could be potentiated through stochastic facilitation from the random noise introduced for the 1-mA-tRNS condition. On the other hand, for individuals with lower theta:beta ratio, the 1 mA of tRNS conceivably amounted to quantities of noise that interfered with information processing that was already optimal.
Following this line of reasoning, we can plausibly attribute the null effect for the 2-mA-tRNS condition to this level of tRNS, on average, giving rise to excessive and maladaptive levels of noise, irrespective of whether task-relevant neurons were below threshold or above threshold. This effect is consistent with the suggestion that the neuronal response begins to saturate as the dose increases beyond the optimal point (Miniussi et al., 2013). However, it should be acknowledged that other possible phenomena could underlie the nonlinear effects. For instance, increases in the intensity of the injected current could change the spatial specificity of the current for the 2-mA tRNS condition (Batsikadze, Moliadze, Paulus, Kuo, & Nitsche, 2013). It is conceivable that this could lead to the stimulation of extraneous brain regions that may not be optimal for task performance.
Although this experiment served primarily as a proof of concept, our approach could have important implications for both basic and translational research. From a basic research perspective, these findings emphasize the importance of being mindful of how the data we acquire and analyze as psychologists are from diverse, multifaceted, and dynamic entities that will exhibit both intra- and interindividual differences in response to experimental manipulations. Designing experiments in a manner that can identify for whom experimental manipulations are effective could greatly improve the inferential power and transparency of research.
From a translational perspective, these findings align with the premise of the precision-medicine initiative, namely, that individual variability in physiology leads to inevitable heterogeneity in treatment response. This initiative has gained widespread traction because of the massive challenges in both resources and ethics that accompany response heterogeneity. Our data indicate that acquiring theoretically relevant electrophysiological markers as part of screening protocols may be a feasible means for determining a priori whether individuals are likely to benefit from interventions. In the present experiment, we examined only the extent to which theta:beta ratio was informative with regard to tRNS-related gains in sustained attention. However, given that elevated theta:beta ratio putatively reflects suboptimal engagement of cortical regions required for top-down attention, and that it has been linked to poor performance on several other high-level cognitive functions, there is a basis for exploring whether theta:beta ratio could be informative for predicting tRNS-related gains for other cognitive functions. Furthermore, prior research examining the relationship between theta:beta ratio and responsiveness to neurofeedback protocols and stimulant medications (Arns et al., 2013) suggests that the predictive value of theta:beta ratio may extend to a range of different interventions that are tailored to increase functioning in high-level cortical regions.
In the present experiment, we observed that the tRNS-related gains in sustained attention for the 1-mA-tRNS condition were maintained for up to 24 min beyond the termination of the stimulation, but these gains had dissipated within 24 hr. The transience of the effects is not surprising given previous research suggesting that prolonged gains from NIBS likely necessitates multiple sessions concurrent to challenging and adaptive cognitive training (Cappelletti et al., 2013; Elmasry, Loo, & Martin, 2015). Future work in this area will also need to appraise the real-world feasibility of prolonged or repeated sessions of tRNS, with appropriate consideration of potential habituation or tolerance effects. In this context, the random nature of the input with tRNS could hold an alluring advantage over pharmacological agents (e.g., Dockree et al., 2017) or even alternative NIBS interventions that rely on direct current.
Finally, our findings corroborate an already large body of evidence and theory emphasizing the importance of right frontal and parietal regions for sustained attention. It should be acknowledged, however, that sustained attention deficits are frequently accompanied by changes in neural functioning across a wide range of other brain areas (see Fortenbaugh, DeGutis, & Esterman, 2017). While the focus of the present investigation was to assess the effect of right frontoparietal tRNS as a function of dose and individual differences in theta:beta ratio, it will be of value for future work to determine the regional specificity of the current flow with the present electrode montage and establish whether similar improvements are also observed when the tRNS electrodes are placed over other cortical regions that are commonly implicated in sustained attention. Examining the extent to which these findings generalize to the heterogeneous clinical populations that are known to exhibit sustained attention deficits should also be a priority for future investigations.
Supplemental Material
HartySupplementalMaterial_rev – Supplemental material for Suboptimal Engagement of High-Level Cortical Regions Predicts Random-Noise-Related Gains in Sustained Attention
Supplemental material, HartySupplementalMaterial_rev for Suboptimal Engagement of High-Level Cortical Regions Predicts Random-Noise-Related Gains in Sustained Attention by Siobhán Harty and Roi Cohen Kadosh in Psychological Science
Footnotes
Acknowledgements
We are very grateful to Margherita Nulli for her help with recruitment and data collection. We also thank the participants who generously gave their time to participate in this study.
Action Editor
Philippe G. Schyns served as action editor for this article.
Author Contributions
S. Harty and R. Cohen Kadosh conceived and designed the study. S. Harty collected and analyzed the data and drafted the manuscript. R. Cohen Kadosh provided critical revisions. Both authors approved the final version of the manuscript for submission.
Declaration of Conflicting Interests
R. Cohen Kadosh serves on the scientific advisory boards of Neuroelectrics, Inc., and Innosphere, Inc. S. Harty declares no conflicts of interest.
Funding
This work was supported by grants from the James S. McDonnell Foundation 21st Century Science Initiative in Understanding Human Cognition and the European Research Council (Learning & Achievement; 338065) to R. Cohen Kadosh.
Open Practices
Data and materials for this study have not been made publicly available, and the design and analysis plans were not preregistered.
References
Supplementary Material
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