**3. Results**

#### *3.1. Participants' Clinical Assessment*

We used the R language and standard packages for the statistical analyses [56] and for each variable we report the values *m*, (*M* ± *SEM*), corresponding to the median (*m*) and mean (*M*) ± standard error of the mean (*SEM*). Participant's age for controls and ADHD was 22 years old (22.3 ± 0.51) and 21 years old (22.1 ± 0.71), respectively. The female-to-male gender ratio was 17:20 and 7:21 in controls and ADHD, respectively. The 2 × 2 contingency table showed no difference of gender ratio between the groups, *χ*<sup>2</sup>(1, 65) = 2.17, *p* > 0.05.

A two-way analysis of variance, (*group*: controls, ADHD) × (*gender*: female, male), was run to assess ADHD symptoms. This analysis showed that normalized *T*-score values for CAARS-S:SV were always significantly higher for ADHD patients, such that it yielded a significant main effect for *group*, *F*(1, 61) = 35.98, *p* < 0.001 for DSM-IV Inattentive Symptoms and *F*(1, 61) = 21.65, *p* < 0.001 for the ADHD index. ADHD reported also higher values for ASRS than controls with a significant *group* effect, *F*(1, 61) = 11.19, *p* = 0.001. The main effect of *gender* was always non-significant, F(1, 61) = 0.26, *p* > 0.05, *F*(1, 61) = 2.18, *p* > 0.05 and *F*(1, 61) = 0.004, *p* > 0.05, for DSM-IV inattentive symptoms, ADHD index, and ASRS, respectively. The interaction effect was also non-significant *F*(1, 61) = 0.59, *p* > 0.05, *F*(1, 61) = 1.94, *p* > 0.05 and *F*(1, 61) = 1.12, *p* > 0.05, for DSM-IV inattentive symptoms, ADHD index, and ASRS, respectively. In our previous paper [41] we have extensively analyzed and discussed the fact that there is a general agreemen<sup>t</sup> in the literature that there is no clear gender effect in young adult ADHD behavioral expression. For this reason we will not analyze further gender effects in this study, whose focus is the effect of the level of difficulty of the WM training protocol on the evoked brain activity.

#### *3.2. Working Memory Performance*

The effect of WM training was assessed by comparing the performance between the post- and pre-training sessions for the level *n* of difficulty achieved during the Dual *n*-Back task, the normalized score for the WAIS-IV digit span and the percentiles for the total score of the Corsi Block-Tapping Task (Table 1). A three-way analysis of variance, (group: controls, ADHD) × (WMT: pre-training, post-training) × (training level: baseline, adaptive) was carried out with a *F*(1, 122) *F*-statistics for all main and interaction effects because all factors had two levels.

The ANOVA for the dual *n*-back task yielded a significant interaction between factors WMT and training level. A one-way analysis of variance for the pre-training and post-training sessions separately yielded a significant effect of the kind of training protocol (*F*(1, 63) = 7.70, *p* < 0.01, and *F*(1, 63) = 19.35, *p* < 0.001, respectively) on the average *n*-back level achieved by the participants. Another one-way analysis of variance for the baseline or the adaptive training protocol separately yielded a significant effect of the WM training (*F*(1, 62) = 15.20, *p* < 0.001, and *F*(1, 64) = 94.25, *p* < 0.001, respectively). This can be interpreted as some bias effect due to the initial random assignment of the participants to either the baseline or the adaptive training protocol. Table 1 shows that before WM training, the participants assigned to the baseline training protocol performed better than those assigned to the adaptive protocol (on average 2.20 ± 0.12 vs. 1.90 ± 0.06 and 2.10 ± 0.13 vs. 1.84 ± 0.11 for controls and ADHD, respectively). Despite this bias, the outcome of WM training was such that after being trained with the adaptive protocol both groups showed a better performance than being trained with the baseline protocol (on average 3.80 ± 0.23 vs. 2.91 ± 0.17 and 3.55 ± 0.29 vs. 2.52 ± 0.16 for controls and ADHD, respectively). This means that a one-month training of working memory had an effect on the outcome of the dual *n*-back task and that a training by the adaptive

protocol produced a larger effect than baseline. Hence, the simple main effects on training level and WMT were truly significant by themselves, irrespective of the group of participants.

The WAIS-IV digit span showed no interaction between factors (Table 1), such that all significant simple main effects for factors *group*, *WMT* and *training level* can be considered as independent. This means that ADHD's performance to this digit span sequencing test was poorer than in controls, and that Dual *n*-Back adapative training improved performance to WAIS-IV Digit Span irrespective of the group of participants. On the opposite, no significant effect was found for the visuospatial short-term memory assessed by the Corsi block-tapping task.


**Table 1.** Pre and post-training performance (median, mean, and SEM)to the memory tasks and results of the three-way analysis of variance (ANOVA).

> \*\*: *p* < 0.01; \*\*\*: *p* < 0.001.

#### *3.3. Probabilistic Gambling Task*

The response time during the PGT, measured as indicated in Figure 2, decreased in all groups from the pre- to the post-training session, *F*(1, 122) = 18.65 (*p* < 0.001), thus showing a significant main effect for factor *WMT*, irrespective of the training condition. In addition, Table 2 shows that the response time in controls was shorter than in ADHD, as revealed by the significant main effect of factor *group*. The WT training did not affect the total gains earned by all participants at the Probabilistic Gambling Task, irrespective of the group and the training condition. A Risk index *RI* = (*HIR* − −*LIR*)/(*HIR* + *LIR*) is calculated as a function of *LIR*, corresponding to low valued gambles (i.e., small amounts equal to 0, 4, or 8 points were gambled by the participant), and *HIR*, corresponding to high value gambles (i.e., the participant gambled 12, 16, or 20 points). The index *RI* is centralized such that a risk averse strategy is characteristic by *RI* ≈ −1, a risk neutral attitude by *RI* ≈ 0 and a risky decision-making by *RI* ≈ 1. It is interesting to notice that ANOVA shows the only significant main factor for Risk index is training level (Table 2). A two-way analysis of variance, (*group*: controls, ADHD) × *training level*: baseline, adaptive), was run for the pre- and post-training sessions separately. Before training, the two-way analysis of variance shows that the factor ttraining level was not significant (*F*(1, 61) = 3.37, *p* > 0.05). On the contrary, after training the factor *training level* affected the Risk index (*F*(1, 61) = 5.40, *p* = 0.023). In the baseline training condition, the *RI* increased on average by 0.07 and by 0.04 for controls and ADHD, respectively, from the pre- to the post-training session. This means that a WMT in the baseline condition tended to increase a risk taking attitude in both groups. Conversely, the adaptive training tended to increase a risky decision making in controls but in ADHD it tended to increase risk aversive attitude. However, *t*-test were not significant for each of these comparisons taken separately.


**Table 2.** Pre and post-training performance (median, mean and SEM) during the probabilistic gambling task and results of the three-way analysis of variance (ANOVA).

\*:*p*< 0.05;\*\*:*p*< 0.01;\*\*\*:*p*< 0.001.

#### *3.4. Event Related Potentials Triggered by Gambling Choice*

In controls (*N* = 37), the median number of epochs per participant was equal to 69 (63.8 ± 2.6) and 71 (65.4 ± 2.7) during the pre- and post-training sessions, respectively. In ADHD (*N* = 28), we analyzed 48 (52.6 ± 2.9) and 60 (58.3 ± 2.6) epochs per participant during the pre- and post-training sessions, respectively. A three-way analysis of variance, (group: controls, ADHD) × (WMT: pre-training, post-training) × (*training level*: baseline, adaptive) yielded a significant main *group* effect, *F*(1, 122) = 11.17(*p* < 0.01) for the number of epochs. This is due to the fact that EEG recordings of ADHD are always contaminated by more muscular artefacts than controls. It is important to notice that neither a main effect for the training level, *F*(1, 122) = 0.24(*p* > 0.05), nor for the WMT, *F*(1, 122) = 1.52(*p* > 0.05), was observed, thus validating the ERP analysis as a function of the WM training protocol in both groups of participants. Several positive and negative peaks were identified in the ERP grand averages waveforms in both control and ADHD participants before the training (Figure 3).

A negative readiness potential maximal at frontocentral electrodes, or decision preceding negativity (DPN), peaked at 40 ms before the trigger in both groups (Figure 3). After the trigger, we observed a positive wave component peaking at 90 ms in control participants (a P1-like component) corresponding to an early positive frontocentral deflection (Figure 3). Notice that in electrodes Fz and Cz, this P1-like component component was much less visible in ADHD participants, as confirmed by the topographic maps for the interval 70–120 ms, at the top of Figure 3. These topographic maps show also that this early positive component reaches its maximum at central electrodes, slightly lateralized on the left, and that ADHD patients are characterized by a stronger lateralization and a negative amplitude in frontal sites.

**Figure 3.** Grand average event-related potentials (ERPs) recorded before the working memory (WM) training at Fz, Cz and Pz sites triggered at lag 0, corresponding to button-click of the selected gamble, in attention deficit/hyperactivity disorder (ADHD) (*N* = 28, green curves over light green shaded areas) and control participants (*N* = 37, white curves over brown shaded areas) on a millisecond scale. The confidence interval (mean curve ± SEM) is shown by the shaded areas. We identified the decision preceding negativity (DPN), P1-like, N2, P3a, N500, and a late parietal negativity (LPN). Signal amplitude is scaled in microvolts (μV). The topographic maps on the top represent the distribution of the mean amplitude of the signal between 70 and 120 ms (estimated P1-like component) using a color-coded scale in μV.

At all electrode sites, we observed a clear N2/P3 complex with N2 peaking at 180 ms and P3a peaking at about 250 ms. ADHD were characterized by a larger posterior P3 component than controls. The peak-to-peak amplitude between the N2 and P3a ERPs was measured for Pz, Cz and Fz. We ran a three-way ANOVA for factors (*group*: controls, ADHD), (WMT: pre-training, post-training) and (training level: baseline, adaptive) to determine any affect on the peak-to-peak amplitudes. We found no effect (*p* > 0.05) of *group* with statistics *F*(1, 122) = 0.01, *F*(1, 122) = 1.03, and *F*(1, 122) = 0.37 for Pz, Cz and Fz, respectively. We found neither any effect (*p* > 0.05) of WMT with statistics *F*(1, 122) = 0.03, *F*(1, 122) = 0.00, and *F*(1, 122) = 0.05 nor of *training level* with statistics *F*(1, 122) = 3.60, F(1,122)=0.00, and *F*(1, 122) = 0.23, for Pz, Cz and Fz, respectively. In Figure 3 we have also marked the N550 and the late parietal negativity (LPN). This latter component (LPN) is barely visible before training, in particular only in controls at site Pz in Figure 3. After training, LPN is very much affected and for this reason we have marked it already in this figure.

#### *3.5. Effect of WM Training Condition on Differential Topographic Maps*

At first, we compute the topographic head map distribution of the grand-average ERP amplitude (in μV) at post- and pre-training sessions for both subgroups of ADHD and controls, those who were trained in the baseline protocol (i.e., with the fixed level *n* = 1 of the dual *n*-back task), and those with the adaptive protocol. After the ERP onset, corresponding to the choice of the selected gamble with the button-click, we determined five intervals of interest corresponding to the time course of the most relevant components observed in the ERPS. These wave components and their respective intervals were P1-like (70–120 ms), N2 (150–200 ms), P3a (240–290 ms), P3b (350–400 ms), and LPN (800–950 ms). All but LPN corresponded to time windows of 50 ms. The differential head maps were obtained with the topographic map for a specific time interval of the ERP at the post-training session minus the topographic map at the pre-training session for the same interval (Figure 4).

**Figure 4.** Differential head maps of the topographical distribution of the Grand-Average ERP amplitude (in μV) at post- minus pre-training sessions for ADHD and controls trained either by the baseline or adaptive protocol of the dual *n*-back task. ERPs were triggered by the choice of the selected gamble with the button-click. Differential head maps using a color-coded scale in μV are plotted for the five major ERP time windows. The red squares correspond to those head maps with significant Bonferroni-corrected *p*-values in the given time window, computed from paired t-tests on the individual average signals (see Figure 5).

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Before the training, no difference was observed between averaged ERPs of either group assigned to adaptive and baseline training protocol. The most significant differential head maps were selected by applying a paired *t*-test with Bonferroni correction for the number of electrodes. We set a criterion of at least three electrode sites with a significant difference (*p* < 0.05) during the very same time window within the interval of the selected wave component to define such significant differential head maps. The P1-like component was particularly affected in ADHD after the adapative training protocol (Figure 4, red square at first raw). Figure 5a shows that this component was increased in a significant way at frontocentral electrodes (F3, *p* < 0.05; Fz, *p* < 0.05; FCz, *p* < 0.01). In this panel, notice that at site F4 the P1-like amplitude after training was also more positive than in the pre-training session, but the criterion of significance for the Bonferroni *t*-test correction was not reached. The grand average ERPS at site Cz is reported (Figure 5a) as a benchmark for a non-significant neighboring channel.

**Figure 5.** Grand average ERPs, triggered (at lag 0 ms) by the button-click at the time of the selection of the amount to gamble, recorded *before working memory training* (blue curves and shaded areas). The confidence interval (mean curve ± SEM) is shown by the shaded areas. The vertical scale represents the amplitude of the signal in μV and the lag is scaled in milliseconds. (**a**). Grand average ERPs at sites F3, F4, Fz, FCz and Cz sites (blue marks in the head map) for ADHD participants recorded after training with the adaptive level protocol (red curves and shaded areas) for the dual *n*-back task. Green ticks show the significant Bonferroni-corrected 1 − *p* values computed from paired *t*-test on individual average ERP signal with significance *p* < 0.05 (\*\*) and *p* < 0.01 (\*\*\*). The panel at the top, shows a head map with the significant sites after Bonferroni correction (red areas around F3, Fz and FCz), at a latency of 100 ms (dashed green vertical line), corresponding to the P1-like component discussed in the text. (**b**). Grand average ERPs at sites P1, P2, P5, Pz, POz, and Cz sites (blue marks in the head map) for controls recorded after training with the baseline level protocol (orange curves and shaded areas), i.e., after the dual 1-back task. In this figure, the head map on the top shows the significant sites (in red areas around P1, P2, P5, CP3 and POz) at a latency of 912 ms (dashed green vertical line), corresponding to the slow negative wave component associated with the expectation of the gambling outcome.

In the interval 150–200 ms, no training protocol produced any major effect on N2 head maps, neither for controls nor for ADHD. Notice that the differential head maps at P3a and P3b were very similar to each other in any of the subgroups. In controls, the maps showed increases in amplitudes at posterior sites, in particular, after adaptive training. Although these differences were

significant for one or another channel, the criterion of three channels simultaneously significant for the paired *t*-test with Bonferroni correction was not reached. The late parietal negativity (LPN) was little affected in ADHD, but the differences in controls were large and mainly distributed over the parietal areas. In controls, Figure 5b shows that baseline training affected the ERPs already appear at wave components P3a and P3b, then disappeared at about 400 ms after the trigger onset. The maximal level of significance was observed at a lag near 900 ms, corresponding to LPN, where we observed significant Bonferroni-corrected *p* values at five posterior electrode sites (CP3, *p* < 0.05; P1, *p* < 0.01; P2, *p* < 0.01; P5, *p* < 0.05; POz, *p* < 0.05) (Figure 4, red square at last raw). A similar but less significant effect was observed in controls after training with the adaptive dual *n*-back task.
