Forty-two participants, consisting of 11 males and 31 females with a mean age of 24 ± 2.62 years, were equally divided into two cohorts. Most of the participants (n = 25) held a bachelor’s degree, while 11 participants had a master’s degree. None of the participants reported any history of psychiatric or neurological disorders, nor had contraindications to tDCS (Antal et al., 2017). Recruitment for this study was conducted on a word-of-mouth basis at a university site. Participants’ ethical treatment was in accordance with the principles stated in the Declaration of Helsinki and was approved by the Ethics Board of the Faculty of Psychotherapy Science and the Faculty of Psychology of Sigmund Freud University (Vienna, Austria; protocol number: JBWXE8CIAVWD788416). Informed consent was obtained from all subjects.

The tDCS current stimulus consisted of 2 mA DC delivered using a BrainSTIM device (E.M.S. s.r.l., Italy) to the Fp1 and Fp2 sites (10–20 EEG system) with 5 × 5 cm² electrodes, resulting in a current density of 0.08 mA/cm². As illustrated in Figure 1, two stimulation polarities and a Sham (no stimulation) condition were adopted: anodal Fp1–cathodal Fp2 (also referred to as Anodal Left/Cathodal Right in the following); cathodal Fp1–anodal Fp2 (Anodal Right/Cathodal Left) (Figure 1). The current stimulus was continuously delivered for 20 min, including two ramping periods of 30 s at both the beginning and the end of stimulation. On the contrary, in the Sham condition, no stimulation was provided, with the exclusion of a sequence of two opposite ramping stimuli, each lasting 15 s, where the current was raised from 0 to 2 mA and immediately lowered from 2 to 0 mA, that was delivered both at the beginning and at the end of a 20 min time window, i.e., the stimulation period of the other conditions.

Each participant underwent testing using the Italian version of the Barratt Impulsiveness Scale-11 (BIS-11) (Fossati et al., 2001) which assesses global, motor (BIS_M), non-planning (BIS_N), and attentional impulsivity (BIS_I). Behavioral impulsivity was assessed through a computerized Go/NoGo task created using PEBL 2.1 software (Mueller and Piper, 2014). The stimuli for this task were the letters “P” and “R” presented randomly in one of four square grids with a blue star in the middle. The stimulus time was 500 ms followed by a blue star for 500 ms, resulting in an interstimulus time of 1,000 ms. The task comprised 480 Go stimuli (80%) and 120 NoGo stimuli (20%), presented in two separate blocks of 300 stimuli each, with a short break between the blocks and the “P” and “R” letters inverted (i.e., “P” become “R” and vice versa) in the second block. On average, the Go/NoGo task required approximately 20 min. For this reason, it was not feasible to administer it during tDCS stimulation. DD was evaluated using a computerized custom-made monetary intertemporal choice task (MICT) developed in jsPsych¹ that determined the subjective value/indifference point for six temporal delays (1, 6, 12, 24, 60, and 120 months) for two maximal reward values: 500 € and 10,000 €, using the adjusting immediate amount procedure described by Holt et al. (2012). Participants had to choose between an immediate but adjusted reward or a maximal but delayed one during each step of the task. Briefly, the test involves making a choice between the full reward (i.e., 500 or 10,000 €) at one of the previously indicated delays (1, 6, 12, 24, 60, and 120 months) or receiving half of that value immediately. Depending on the choice, the immediate reward is increased by half of the difference between its current amount and the maximal one if the subject chooses the delayed reward, or it is reduced by the same amount if the subject chooses the immediate one. This approximation process is repeated for 6 rounds, and at the end, the IP for that specific reward and delay is determined. The reward and delay are presented randomly.

Working memory performance was assessed using a computerized n-Back task created with PEBL 2.1 software (Mueller and Piper, 2014). The task consisted of two blocks, 2nback and 3nback, each comprising 32 and 33 letters/items presented at intervals of 1,500 ms. Participants received brief training for each task before starting the experiment.

A double-blind between-subject design was adopted for this study, wherein participants underwent two sessions spaced at least 1 week apart, regardless of their random cohort assignment. During the first session, participants completed the BIS-11 and Go/NoGo tasks. Afterward, they underwent the first tDCS stimulation, which was randomly assigned as either real or sham. Six minutes after the stimulation began, participants were tested with the MICT and n-Back tests in random order. During the second session, participants only underwent the stimulation protocol (real or sham) with the MICT and n-Back tests. For the first cohort of subjects (n = 21), the tDCS anodal electrode was placed over Fp1 while the cathodal electrode over Fp2, whereas for the second cohort (n = 21), the anodal electrode was placed over Fp2 while the cathodal electrode over Fp1.

For DD analysis, indifference points (IPs) from each subject/session obtained with the MICT were used to fit, for each subject, two hyperbolic function IP = A/(1 + k ⋅ Delay) (Mazur, 1987), one when A = 10,000 € and the other one 500 € depending on subtask and Delay = 1, 6, 12, 24, 60, and 120 months. By analyzing the test execution times, we observed that subjects took an average of 231.7 ± 64.9 s (mean ± std). Then, we use the non-linear least-mean squares method to get estimates of the devaluation coefficient k (with unit 1/days), while the areas under the curve (AuC) were calculated and normalized following the procedure described by Myerson et al. (2001): the delay was expressed as a proportion of the maximum delay, while the subjective value was expressed as a proportion of the nominal amount, i.e., the subjective value divided by the actual, delayed amount. We fitted multiple linear mixed-effect models (LMEs) to our data, including the logarithm of k and the AuC as dependent variables and different fixed and random effect factors as detailed in the results section, followed by ANOVA or Kenward–Roger tests on the fitted models. The normality of AuC and log(k) distributions, as well as of the LME residuals, were evaluated graphically using qqplots and histograms. All measures obtained from tests in all stimulation conditions were evaluated for the presence of significant correlation using Pearson’s correlation coefficients, corrected using Holm–Bonferroni method. To compare the scores of n-Back performances, Wilcoxon signed-rank tests were conducted. All the analyses were carried out using custom algorithms developed in MATLAB (Mathworks) or R.²

The main aim of this study was to evaluate if OFC neural activity is critically involved in the expression of DD observed with intertemporal choice tasks. To this aim, we opted for testing the effects of tDCS delivered over the OFC on DD performance. Since focusing tDCS stimulation on this brain area is challenging, we evaluated several possible electrode configurations starting from those already adopted by other investigators. Both electric field and electric potential distributions were simulated using the ROAST³ MATLAB package (Huang et al., 2019). Finally, we opted for a custom configuration aiming at bilateral interhemispheric stimulation of OFC. For our configuration, electrodes are placed on Fp1 and Fp2 sites and both current directions were tested in separate subjects (see methods for details): putative electric potential profiles for the two polarities are shown in Figure 1, over the cortical surface as well as over three horizontal brain sections including subcortical regions. As it can be appreciated by looking at the colormaps, sensible stimulation intensities are reached over the medial and lateral portions of the OFC of both hemispheres (with reversed voltage polarities); at the same time, the spread of stimulation is noticeably reduced over the DLPFC and ventromedial prefrontal cortexes, while the frontopolar cortex is inevitably involved (Figure 1).

We then recruited two cohorts of healthy subjects for testing the effects of the two stimulus configurations (compared to the sham condition) on their performance in the MICT and the n-Back tasks (see the section “2. Materials and methods”).

Figure 2 shows the indifference points at varying delays which were obtained with the MICT under Sham (blue) vs. Real (red) stimulation: a clear trend can be appreciated where IPs are increased by both stimulation polarities (Anodal Left, Figures 2A, B; Anodal Right, Figures 2C, D), for both maximal reward levels (10,000 €, Figures 2A, C; 500 €, Figures 2B, D), thus indicating a reduction of delay discounting by OFC tDCS stimulation. To evaluate if such an effect was significant, we used two different measures of DD, the devaluation coefficient k from the hyperbolic fitting of IPs and the AuC (see the section “2. Materials and methods”). Due to the skewness of k distributions, we log-transformed this coefficient as suggested previously (Holt et al., 2012). Values of k and AuC are separately shown in Figure 2 for the two stimulation polarities (Anodal Left, Figures 2E, F; Anodal Right, Figures 2G, H), while pooled data are shown in Figures 2I, J. An average trend can be observed where AuC is increased by the stimulation while log(k) is reduced, thus indicating a possible reduction of discounting exerted by tDCS. Two different LME models were fitted to these data, according to the following formulas (Wilkinson notation):

And

Where y is the response variable (log(k) or AuC). Among the fixed effect factors evaluated, Real indicates whether stimulation is Real or Sham, Polarity indicates the polarity of stimulation, Reward indicates the maximal reward of the MICT, i.e., if the curve were calculated when the delayed reward was € 10,000 or € 500 (all interactions terms have been included for these three factors), while BIS-11, Nback2, and Nback3 indicate the performances in the related tasks. Test Order and Stimulation Order indicate the task presentation order and effect of session order, respectively. Finally, a random effect of the subject was included.

Comparison of the two models using the Kenward-Roger test showed no significant difference for either log(k) (χ²₄ = 3.6304, p = 0.4583) or AuC (χ²₄ = 5.7006, p = 0.2226), thus excluding a significant contribution of either general impulsivity or WM performance on subject’s DD performance in our conditions. Furthermore, we compared Equation 2 model with a more parsimonious one that did not include factors related to the order of tests and stimulation:

Comparison of the two models using the Kenward-Roger test showed no significant difference for either log(k) (χ²₄ = 7.9083, p = 0.095) or AuC (χ²₄ = 8.4905, p = 0.07517). Based on this, we performed our analyses on the more parsimonious model of equation 3.

Analysis of variance applied to the fitted models revealed a significant effect of tDCS stimulation and maximal reward of the MICT [tDCS: F(1,154) = 13.453, p = 0.0003; Reward: F(1,154) = 44.036, p < 10^–5; Figure 2I]. Interestingly, no significant effect of electrodes configuration (i.e., stimulus polarity, Polarity) was found [for log(k): F(1,38) = 2.1052, p = 0.1547932; for AuC: F(1,38) = 1.9633, p = 0.169071], as well as no significant interaction between pairs of factors. Importantly, the same results were obtained when AuC was set as the response variable [tDCS: F(1,154) = 11.723, p = 0.0008; Reward: F(1,154) = 39.117, p < 10^–5; Figure 2I].

Stimulation of this brain region with two different tDCS configurations revealed a general effect implicating the OFC in this decision-making process. Based on these results, we can conclude that bilateral tDCS focused over the OFC seems to reduce DD in healthy subjects, independently from stimulus polarity. Graphically, it appears that stimulation was more effective for specific delays which is consistent with the notion that intertemporal choice involves different brain circuits depending on the reward delay (Wittmann et al., 2007; Frost and McNaughton, 2017).

The LME analysis presented here contradicts the idea that a clear link exists between impulsive behavior and DD (Moreira and Barbosa, 2019), as none of these variables significantly contributed to the model fitting for either the AuC or log(k). Moreover, all the correlations between the impulsivity traits, BIS-11, and behavioral impulsivity, Go/NoGo, were not significant. On the contrary, as expected, the internal sub-dimension (BIS_M, BIS_N, and BIS_I) are correlated with each other and with the overall score (BIS) (Figure 3). To better evaluate this aspect, as well as the relationship between DD performance and all the other impulsivity measures, we conducted a correlation analysis separately for the three stimulation conditions: Sham, Anodal Left/Cathodal Right, and Anodal Right/Cathodal Left. From these analyses, no significant correlations were found between either impulsivity personality traits (BIS-11) or motor impulsivity (Go/NoGo), both assessed before experiments, and intertemporal choice performance (AuC) measured during any experimental condition (Figure 4). Therefore, we can conclude that DD expression in our condition can be considered as a distinct psychological process that is not merely a manifestation of impulsivity.

As discussed in the introduction, the relationship between WM and DD is controversial (Moro et al., 2023) and WM and DD are typically positively correlated (Wesley and Bickel, 2014). We did not detect a significant contribution of WM performance in fitting LMEs models to either log(k) or AuC data. We also observed no significant correlation between n-Back performance and the AuC of DD in Sham (Figure 5A), in the Anodal Left/Cathodal Right stimulation condition (Figure 5B), or in the Anodal Right/Cathodal Left stimulation condition (Figure 5C): these results confirmed our LME analysis. However, in the Anodal Left/Cathodal Right stimulation condition, we found a significant positive correlation between the n-Back performances (nback2 and nback3: r = 0.59, p = 0.0083, statistical significance corrected with Holm-Bonferroni method; Figure 5B). We also conducted tests to compare correlations using correlation comparison tests (Diedenhofen and Musch, 2015) and found that the correlation in the Anodal Left/Cathodal Right configuration was significantly different from the one obtained in the related Sham condition. More specifically, our results showed a significant difference using Pearson and Filon’s z-test (z = 2.938, p = 0.003). Altogether, such results might reveal a potential specific modulatory action of OFC on WM independently of intertemporal choice processes. To further evaluate this aspect, we tested whether tDCS altered the WM performance as assessed through the n-Back tasks, whose results are shown in Figure 6 for the two stimulation polarities (Anodal Left, Figures 6A, C; Anodal Right, Figures 6B, D). Both 2nback and 3nback performances did not differ significantly between the Real and Sham conditions (Wilcoxon signed-rank test, two-tails, n.s.; Figure 6).