A total of 261 adults (143 ADHD persisters, 24 remitters, and 94 controls) participated in the experiment, twelve participants were excluded because they did not follow the instructions. Analyzed data were collected from 162 ADHD (141 persisters and 21 remitters) adults (ages 18-39 years old) diagnosed at Peking University; 87 normal healthy controls recruited through campus advertisements also participated in the study (Table 1). ADHD participants fulfilled a diagnosis of adult ADHD through Conners’ Adult ADHD Diagnostic Interview based on the Diagnostic and Statistical Manual of Mental Disorders. All ADHD participants were medication naive. Another current psychopathology was assessed with the Structured Clinical Interview for DSM-IV Axis I Disorders (SCID). Control participants were recruited from local universities and communities, and interviewed to ensure an absence of past or current ADHD. The ADHD Rating Scale (ADHD-RS), Conners’ Adult ADHD Rating Scale–Self-Report Screening Version, and SCID were applied for assessing all participants. All the control participants had no current or previous psychiatric disorders. All participants were of Chinese Han descent.

Participants were seated in a comfortable chair in a dimly lit, electrically shielded room with a low level of environmental noise. Scalp EEG data were recorded continuously with a 128-channel EEG net (Electrical Geodesic Inc., EGI). After they became familiar with the environment, participants were told to close their eyes and stay relaxed and still for 6-10 min (average of 8.84 min), and to do nothing else. Scalp EEG data were recorded at a sampling rate of 1,000 Hz. All electrode impedances were kept under 50 kΩ. Data were referenced to electrode CZ originally and then referenced to a frontal channel near FZ. The stereotypical artifacts, such as eye blinks, eye movements, and muscle tension, were separately removed using the artifact rejection method based on the blind source separation algorithm, Independent Component Analysis (ICA) (Delorme and Makeig, 2004; Li et al., 2019; Zhao et al., 2020). On average, there are four ICs were selected to remove.

Data processing was performed in MATLAB¹ with custom scripts. The original continuous data were high-pass filtered at 0.5 Hz and low-pass at 40 Hz. Both the high-pass and low-pass filters were zero-phased FIR filters (third order Butterworth filter) which filter the data both forward and backward to ensure phase delays introduced by each filter are nullified. The dickey-Fuller test was used to test the stationary property of the data. Power spectra of the EEG signals were calculated using multi-taper methods with 5 tapers. Each epoch lasted 10 s, enabling a precise spectrum with a resolution of 0.1 Hz.

The Three Gaussian Model is the summation of a baseline and three gaussian functions which represent three component sources in the alpha band for all 128 channels (Figures 1, 2). It is described as follows:

where S(i,h,f) is the i-th source function in h-th electrode of the signal depending on the frequency f, W_i is the weight of each source, μⁱ and σⁱ are peak frequency and bandwidth of the i-th source. To evaluate the fitting performance, we calculated the fitting index as follows, the value of which indicated the percentage variance that can be explained by the model. This method has been used in describing gamma-band activity (Han et al., 2020, 2021a,b,c; Wang et al., 2021).

We used the Jarque-Bera test for the normality of the data. The non-parametric ANOVA test (Kruskal-Walis H test) was employed first to test whether the difference exists for the power (baseline and components) among three groups (ADHD persister, remitter, and control), and then the Mann–Whitney U test with Bonferroni correction was used as the post-hoc to check the difference between pairs of groups.

To see the EEG power in the alpha range more clearly on each electrode, with fine frequency resolution (0.1 Hz), two or even three frequency peaks were visible on many electrodes from temporal (Figure 2 first column), parietal (Figure 2 second column) to occipital (Figure 2 third column) lobe. Based on carefully scrutinizing our data (N = 249), we found that it was typical that there were three frequency components in the narrow range of the alpha band (low alpha (LA), medium alpha (MA), and high alpha (HA)). Their range was defined based on the value orders of their peak frequencies fitted by the descriptive model. Low alpha was defined as the alpha with the lowest peak frequency (LA: mean = 8.42 ± 0.94 Hz), and the high alpha was defined as the alpha with the highest peak frequency (HA: mean = 11.81 ± 0.84 Hz); the medium alpha was defined as the one between LA and HA (MA: mean = 10.15 ± 0.76 Hz).

Based on the observation in our database, we hypothesized that for each individual subject, the EEG power in the resting state in the alpha range on all 128 electrodes could be modeled by the sum of three frequency components. In more detail, the EEG power in the alpha range was a weighted sum of three frequency components and a baseline (Figure 1 dashed line). The frequency profiles of the three components were all modeled as Gaussian functions, and the frequency profile of the baseline was modeled as a function decreasing monotonically in frequency (see more details in the Materials and methods section for model and model fitting). The three oscillatory components were LA, MA, and HA, with different peaking frequencies (LA: mean = 8.42 ± 0.94 Hz; MA: mean = 10.15 ± 0.76 Hz; HA: mean = 11.81 ± 0.84 Hz) (Figure 3). We found that the EEG power could be reconstructed very well by this model. Across the whole dataset, the model explained 99.29% variance of the normalized data (99.27, 99.31, and 99.35% in groups of ADHD persister, control, and ADHD remitter, respectively).

We further asked whether the powers of alpha components and baseline showed significant differences among ADHD persister, remitter, and normal group by the non-parametric one-way ANOVA test (Kruskal-Walis H test). We found that the power of alpha components was not significantly different among the three groups by one-way ANOVA test (Figure 4; in parietal region, LA: p = 0.11, MA: p = 0.98, HA: p = 0.18; in occipital region, LA: p = 0.18, MA: p = 0.62, HA: p = 0.51). Instead, the baseline power of the three groups showed strong significance among three groups by one-way ANOVA test (Figure 4; in parietal region, LA: p < 0.001, MA: p < 0.001, HA: p < 0.001; in occipital region, LA: p < 0.001, MA: p < 0.001, HA: p < 0.001). In specific multiple comparison, the ADHD persister group is significant smaller than that of remitter (Figure 4; in parietal region, LA: p = 0.0028, MA: p = 0.0034, HA: p = 0.0017; in occipital region, LA: p = 0.047, MA: p = 0.040, HA: p = 0.029) and health control group (Figure 4; in parietal region, LA: p < 0.001, MA: p = 0.0066, HA: p = 0.0074; in occipital region, LA: p = 0.0011, MA: p = 0.0024, HA: p = 0.0014).

There are some possible perspectives on the mechanisms of ADHD remission (Sudre et al., 2018). Some researchers found evidence of a convergence mechanism (Schneider et al., 2010; Shaw et al., 2013; Hoogman et al., 2017; Schulz et al., 2017) that views AD/HD as a neurodevelopment defect and the rectification of early anomalies in brain structure with age contributes to the relief of clinical symptoms (El-Sayed et al., 2003). Others proposed that the neural anomalies of AD/HD leave an indelible mark on the brain that will persist across the lifespan regardless of the clinical effect of AD/HD, and remitters recruit new brain systems that allow effective compensation for AD/HD symptoms (Proal et al., 2011; Francx et al., 2015) which is referred to as the “fixed trait” and compensation mechanism. Our results found that the power of alpha components was not significantly different among the three groups. Instead, the baseline power of the remission group in the high alpha band is significantly smaller than that of persisters and healthy controls. This suggests that ADHD recovery may have a compensatory mechanism.

Our work detected a decreased baseline power in the high alpha band in the ADHD remission group. The previous inconsistent results might be due to a blurring of multiple oscillatory components in the alpha band. We should also notice that for the amplitude of alpha components, there is no significant difference among ADHD persisters, remitters, and normal adults, which may indicate that these alpha components are modulated by some other tasks. Further, dissecting oscillatory components not only increases the sensitivity of specific functions related to alpha but also creates a more precise frequency target for neurofeedback, which has attracted more and more attention recently for the treatment of brain disorders including ADHD.

With the increasing number of studies on alpha oscillation, it has been suggested that there existed two or even three sub-bands of alpha oscillation (Klimesch, 1999; Makeig et al., 2002), which might be related to different cognitive functions. Previous results have shown that the power in these different sub-bands (upper and lower alpha) also differed in tasks requiring visual attention (Ding et al., 2006; Sadaghiani et al., 2010; Liu et al., 2016) and memory (Gruber et al., 2005; Michels et al., 2008; Hanslmayr et al., 2012; Elmer et al., 2015; Barnes et al., 2016), and also in the brain’s network (Murias et al., 2007; Sadaghiani et al., 2012), mental disorders (Stoffers et al., 2007; Poil et al., 2014; Yu et al., 2017), neurofeedback training and resting state (Manshanden et al., 2002; Thorpe et al., 2016). Some animal and human studies also suggested that different cortical regions could generate their own alpha oscillations (Lopes Da Silva et al., 1977; Bollimunta et al., 2008, 2011; Scheering et al., 2016). More specifically, previous works have shown that alpha rhythms could be dissected into two components in scalp EEG (Chiang et al., 2011; Barzegaran et al., 2017; Knyazeva et al., 2018). Our results showed that three components are necessary to reconstruct the power spectrum around the alpha band for most individuals. This suggests that alpha contains at least three distinct and significant oscillatory components in the resting EEG, a result that is consistent with the three sub-bands concept. However, our results also suggest that the way to divide multiple oscillatory components based on fixed frequency bands/ranges with respect to the alpha peak frequency might not be precise; one precise way to divide these components should be based on their oscillatory properties, such as peak frequencies and bandwidths in the power spectrum. The theory of Alpha suppression suggests that many cortical regions can generate alpha rhythm when the main rhythm is inactivated (Palva and Palva, 2007) and electrophysiological studies on animals also showed that multiple cortical regions could generate their own alpha oscillation (Lopes Da Silva et al., 1977; Bollimunta et al., 2008, 2011). Therefore, in theory, we might be able to find multiple alphas in the scalp EEG, but practically, our data suggest that three components are enough to capture alpha at the resting state.

Besides the alpha rhythm in the parieto-occipital lobe, two other rhythms, the mu rhythm and the sensorimotor rhythm (SMR) were also found oscillating in the alpha band (8-13 Hz). The mu rhythm is found in the sensorimotor, motor, and somatosensory cortex (Arroyo et al., 1993; Jones et al., 2010; Liao et al., 2015; Coll et al., 2017). The sensorimotor rhythm (SMR) appears over the sensorimotor cortex (Reichert et al., 2015). Some studies suggested that spectral or topographic properties of the functionally- identified mu rhythm strongly reflect those of upper alpha (Thorpe et al., 2016). Based on previous work on the brain regions that are sources of the EEG (Plattner et al., 2014), our results indicate that low and high alpha is unlikely to be mu and SMR because they are mostly peaking in the parietal lobe, more posterior to sensorimotor, motor and somatosensory cortex. Besides mu and SMR rhythms, alpha oscillation can also be generated by other cortical regions, including multiple areas in the visual cortex (Lopes Da Silva et al., 1977; Bollimunta et al., 2008, 2011).