Behavior analysis and the ERPs recordings of numerical comparison and mental subtraction

The subjects were instructed to complete two tasks, consisting of two runs each. They were presented with a pair of sequenced digital numbers (S1 > S2) and required to assess whether S2 was identical to S1 in Task 1. Subsequently, the participants were requested to examine whether the difference between S1 and S2 (S1-S2) was equal to 3 in Task 2 (Fig. 1a). Overall, the following five conditions were evaluated: “S1 = S2”, “S1 ≠ S2”, “S1-S2 = 0”, “S1-S2 = 3” and “S1-S2 ≠ 3/0”. The statistics for the behavioral data showed that the accuracy in the five conditions were 97.50% (97.50, 100), 96.25% (95.00, 100), 100.00% (97.56, 100.00), 94.87% (87.18, 99.36) and 95.00% (92.50, 100), respectively (Wilcoxon matched-pairs signed rank test; Fig. 1b-upper panel). The RTs, which were the intervals between the onset of S2 and the time when the answer key was pressed, were 472.1 ± 16.99 ms, 561.30 ± 20.53 ms, 600.10 ± 23.10 ms, 654.10 ± 23.65 ms and 720.50 ± 20.73 ms, respectively (paired t-test; Fig. 1b-bottom panel). All participants performed the two tasks with a high accuracy, and their RT patterns reflected the most widely replicated behavioral effect in the numeric cognitive arithmetic: the problem size effect (Ashcraft 1992). Specifically, the behavioral data indicated the degree of difficulty across the conditions with an order of “S1 = S2”< “S1 ≠ S2”, “S1-S2 = 0”< “S1-S2 = 3”< “S1-S2 ≠ 3/0”. The correlation analysis suggested no significant correlations between the participants’ sex or age and the behavioral data, respectively (Supplemental Table 2).

Figure 1

Experimental design and the SEEG recording in the human brain.

A, the illustration of Tasks 1 and 2. The subjects confirmed the answer (“YES” or “NO”) for each task by pressing the right and left buttons of the mouse that had been balanced. In one trial, the paired digit (S1 > S2) that ranged from 11 to 49 were sequentially appeared for 300 ms respectively, with an interval of 200 ms. The interval between two trials was 5 s. Five conditions (“S1=S2”, “S1≠S2”, “S1-S2=0”, “S1-S2=3” and “S1-S2≠3/0”) were contained in two tasks.

B, behavior analysis of five conditions in Task 1 and 2. Upper panel: the accuracies of the five conditions. The data were presented as median ± quartile. A Wilcoxon test was performed to examine the mean correct rate for each of the two conditions. Bottom panel: the reaction times of the five conditions. The data were presented as mean ± SEM. A paired t-test was conducted to assess the mean reaction time for each of the two conditions. * p<0/05, ** p<0.01 and *** p<0.001.

C, the example reconstruction of the depth electrodes into the brain (Patient #15). The surface of the peripheral images (left-top) show the reconstruction of eight electrodes into the brain of Patients #15. The lateral view (right-top), the coronal view (left-bottom) and the top views (right-bottom) of the reconstructed electrode were based on the three-dimensional co-registered MRI.

D, the distribution counts of the 348 SEEG recording sites in the cortex lobes.

E, the average ERPs amplitudes of total 348 electrodes of Task 1 (green line) and 2 (red line), with the shadow as the SEM, respectively. The grey rectangle indicated the durations of S1 and S2. The black bar presented the t-test between Tasks 1 and 2 with p<0.01.

The implanted electrodes were reconstructed through the co-registered preoperative MRI and the postimplantation CT (Fig. 1c). Out of the total 348 recording sites, 157 (45.11%), 77 (22.13%), 46 (13.22%), and 44 sites (12.64%) were located in the temporal, frontal, insular, and parietal lobes, respectively. In addition, 13 sites (3.74%) were within the occipital lobe, and 11 sites (3.16%) in the limbic lobe (Fig. 1d; for detailed information of the subregional distribution, see Supplemental Table 3). The SEEG was segmentally extracted to ERP epochs between the 200-ms pre-S1 and 700-ms post-S2 period (total 1700 ms). The average epochs in five conditions were rearranged based on the lobar distribution of the sites (Supplemental Fig. 2A). The amplitudes of the average epochs of the ERPs showed significant differences during the cognition activities in Tasks 1, Task 2 (Supplemental Fig. 2B-C), and between Task 1 and 2, respectively (Fig. 1e). It is suggested the human brain goes through a discriminative cognition processing during simple numeric comparison and mental subtraction. However, the precise pathway of this distinguished cognition controls should be explored.

Numerical and subtraction results comparison set the time window of digital subtraction

The procedure of mental subtraction was initiated immediately after the onset of S2. However, during the paradigms, the introduction of the task must have affected the participants’ attention and motivation. This attentional effect would be an interference of the procedure of mental subtraction. Especially in the Task 2, two types of incongruency processing were mixed, including the incongruency processing of visual acquired numbers as the precondition for subtraction (Prado et al. 2011; Gómez-Velázquez et al. 2015), and the incongruency processing of discriminating the results from the enquired ones 3 after mental subtraction.

To extract the core process of mental subtraction, we attempted to set a time frame for the subtraction in the human brain. Thus, a time-lapse reordering was applied to the heatmap of the FDR-corrected p-values, which resulted from the comparison of the SEEG amplitude of each recording site in conditions 1 vs. 2 (“S1 = S2” vs. “S1 ≠ S2”, Fig. 2a), 3 vs. 4 (“S1-S2 = 0” vs. “S1-S2 = 3”, Fig. 2c), and 4 vs. 5 (“S1-S2 = 3” vs. “S1-S2 ≠ 3/0”, Fig. 2e). The comparison represented the differences between two cognitive control activities, which were numeric comparison and digital subtraction with the same introduction, respectively. In “S1 = S2” vs. “S1 ≠ S2”, the comparison only presented the incongruency processing of simple digitals. Since the SEEG amplitudes of the IFG site demonstrated the earliest significant difference at 183.5 ms after the S2 onset (Fig. 2b), the result indicated the initiation timepoint of numeric comparison (183.5 ms after S2 onset, Fig, 2a) and subregion in the brain (IFG, Fig. 2b). In “S1-S2 = 0” vs. “S1-S2 = 3”, the comparison contained the incongruency processing of both digital and subtraction results. Notably, the peak amplitudes of the paracentral lobule (paraCL) site indicated the earliest difference emerged at 228 ms after the S2 onset (Fig. 2d). In “S1-S2 = 3” vs. “S1-S2 ≠ 3/0”, the comparison only presented the incongruency processing of the subtraction results, that is the result-decision after the subtraction operation in the brain. Furthermore, the peak amplitudes of the IFG site primarily showed the earliest difference at 320.5 ms after the S2 onset (Fig. 2f). The result indicated the termination timepoint of subtraction operation (320.5 ms after S2 onset, Fig, 2e) and subregion in the brain (IFG, Fig. 2f). Therefore, the result indicated that the core process of mental subtraction would proceed between the numeric comparison and subtraction results comparison, which was between 183.5 ms and 320.5 ms from the S2 onset.

Figure 2

The incongruent processing of the numerical and subtraction comparison.

A, left panel: the heatmap of the p-value from the nonparametric test of the SEEG amplitude of the recording sites examined in conditions 1 vs. 2 (S1=S2 vs. S1≠S2) after the S2 onset. Each row represented one recording site. The p-values were ordered as the occurrence time when the FDR corrected p<0.05 for individual recording sites. The values of p>0.05 were shown as the background (blue). The shadow rectangle indicated the duration of S2. Right panel: the time lapse of each recording site from the heatmap on the left panel with p<0.05. The different colored bars represented cortical lobes, in which the recording sites were distributed: pink, frontal lobes; blue, parietal lobes; purple, temporal lobes; green, occipital lobes; orange, insular lobes and yellow, limbic lobes. The vertical dotted lines indicated the duration of S2.

B, the average trace of the ERPs of the earliest recoding site with p<0.05 in (A), under the conditions of S1=S2 (grey line) and S1≠S2 (black line). The site, located at the IFG, was indicated as the yellow arrow in the sagittal MRI individually (insertion).

C, left panel: the heatmap of the p-value from the nonparametric test of the SEEG amplitude of the recording sites examined in conditions 3 vs. 4 (S1-S2=0 vs. S1-S2=3) after the S2 onset. Each row represented one recording site. The p-values were ordered as the occurrence time when the FDR corrected p<0.05 for individual recording sites. The values of p>0.05 were shown as the background (blue). The shadow rectangle indicated the duration of S2. Right panel: the time lapse of each recording site from the heatmap on the left panel, with p<0.05. The different colored bars represented the cortical lobes, in which the recording sites were distributed: pink, frontal lobes; blue, parietal lobes; purple, temporal lobes; green, occipital lobes; orange, insular lobes and yellow, limbic lobes. The vertical dotted lines indicated the duration of S2.

D, the average trace of the ERPs of the earliest recoding site with p<0.05 in (C), under the conditions of S1-S2=0 (light blue line) and S1-S2=3 (dark blue line). The site, situated at the paraCL, was indicated as the yellow arrow in the sagittal MRI individually (insertion).

E, left panel: the heatmap of the p-value from the nonparametric test of the SEEG amplitude of the recording sites examined in condition 4 vs. 5 (S1-S2=3 vs. S1-S2≠3/0) after the S2 onset. Each row represented one recording site. The p-values were ordered as the occurrence time when the FDR corrected p<0.05 for the individual recording sites. The values of p>0.05 were displayed as the background (blue). The shadow rectangle indicated the duration of S2. Right panel: the time lapse of each recording sites from the heatmap on the left panel, with p<0.05. The different colored bars represented cortical lobes, in which the recording sites were distributed: pink, frontal lobes; blue, parietal lobes; purple, temporal lobes; green, occipital lobes; orange, insular lobes and yellow, limbic lobes. The vertical dotted lines indicated the duration of S2.

F, the average trace of the ERPs of the earliest recoding site with p<0.05 in (E), under the conditions of S1-S2=3 (blue line) and S1-S2≠3/0 (orange line). The site, located at the IFG, was indicated as the yellow arrow in the sagittal MRI individually (insertion).

Temporal-spatial comparison of numerical comparison and subtraction

To explore the temporal-spatial progressing of mental subtraction, the ERPs amplitudes of each recording site were compared between Tasks 1 and 2. The FDR-corrected p-value (p < 0.05 lasting over 50 ms) was also reordered in a time lapse (Fig. 3a). The chronological sites distributed in the brain lobes, within which the frontal, temporal, and insular lobes emerged distinct amplitudes of the ERPs between numeric comparison and subtraction early after 200 ms of the S1 onset (Fig. 3b). Furthermore, the majority of the sites had reacted at the differences between tasks since 100 ms after the S2 onset.

Figure 3

The comparison of numerical comparison and subtraction.

A, the heatmap of p-value from the nonparametric test of the SEEG amplitude of 348 recording sites examined in Tasks 1 (numerical comparison) vs. 2 (digital subtraction). Each row represented one recording site. The shadow rectangles indicated the durations of S1 and S2, respectively. The p values were ordered as the occurrence time when the FDR corrected p<0.05 (continuous for 50 ms) for individual recording sites. The values with p>0.05 were shown as the background (blue).

B, the distribution counts of the recording sites at different time periods after the S1 onset in (A). The interval time was 100 ms. The shadow rectangles signified the duration of S1 and S2, respectively. The different colored bars represented cortical lobes, in which the recording sites were distributed: pink, frontal lobes; blue, parietal lobes; purple, temporal lobes; green, occipital lobes; orange, insular lobes; and yellow, limbic lobes.

C, the example the ERPs traces of the recording sites distributed in the paraCL, IFG, MFG, AI, PI, and paraHG. The ERPs amplitudes were significantly different between Tasks 1 (green line) and 2 (red line) during S1 and S2 (p<0.05 continuous for 50 ms), with the shadow as the SEM, respectively. The location of each region was shown in the brain template: pink, frontal lobes; purple, temporal lobes; and orange, insular lobes. The vertical dotted lines indicated the duration of S1 and S2.

D, the example the ERPs traces of the recording sites distributed in the preCG, postCG, SG, AG, cuneus gyrus, fusiform gyrus, ITG, MTG, STG and CG. The ERPs amplitudes were significantly different between Tasks 1 (green line as the average and shadow as the SEM) and 2 (red line as the average and shadow as the SEM) only during S2 (p<0.05 continuous for 50 ms), while there was no significant change during S1. The location of each region has been shown in the brain template: pink, frontal lobes; blue, parietal lobes; purple, temporal lobes; and yellow, limbic lobes. The recording sites, with the ERPs amplitudes were significantly different between Tasks 1 and 2 after 182 ms of the S2 onset, were indicated with a star. The vertical dotted lines indicated the durations of S1 and S2.

Among these aforementioned sites, those distributed in the paraCL, IFG and MFG of the frontal lobes, the anterior insula (AI) and posterior insula (PI) lobes, and the temporal parahippocampous (paraHG), demonstrated the different amplitudes of the ERPs between two tasks before S2 and during S2 (Fig. 3c). This might indicate that more than subtraction, these regions would be involved in other cognitive activities. However, the sites distributed in the frontal preCG, the cingulate gyrus (CG) in the limbic lobe, the postCG, SG, and AG of the parietal lobes, the occipital cuneus gyrus, the fusiform gyrus, the inferior temporal gyrus (ITG), MTG, and STG of the temporal lobes were presented differences between Tasks 1 and 2 during S2 (Fig. 3d). The sites in the parietal lobes emerged with a large proportion during S2 than before it. These results suggested that the parietal region could play a critical role in mental subtraction in the human brain. Further, diverse brain regions participated in the consecutive procedures of cognitive control, respectively. Especially, recordings from five sites in the SG, one site in the AG, two sites in the fusiform, four sites in the MTG, and two sites in the CG within the parietal-cingulate-temporal cortices initiated the differences after 183 ms of the S2 onset that might be considered as an origin of subtraction based on the aforementioned results. Therefore, the mechanism of discriminating numeric comparison and subtraction in the core regions, including the SG, AG, fusiform, MTG, and CG, ought to be clear.

Gamma band activities undertake digital subtraction chronologically

Brain oscillations at different frequency bands, even the high-gamma-band, have been shown to play a key role in various cognitive tasks, including memory, executive control, and attention to internal processing or the external environment (Klimesch 1999; Kawasaki et al. 2010; Gaona et al. 2011; Kucewicz et al. 2014; Akiyama et al. 2017). Therefore, further exploration of the local network in the frequency domain would provide relevant information regarding the neural mechanism of mental subtraction. The power spectra normalized to each frequency in the five core regions, including the SG, AG, fusiform, MTG and CG, spanning across 3–200 Hz were compared between numeric comparison (Task 1) and subtraction (Task 2) (Fig. 4a). The permutation tests were applied to the power spectra in response to subtraction and numeric comparison. This identified clusters with significant event-related differences once after the S1 onset for the two tasks (p.cluster < 0.05, Fig. 4b). The sparse clusters in the high gamma range (> 90 Hz) during S2 were found in all of the five core regions. However, the analysis of high gamma activities (known as the high frequency oscillations, HFOs) showed that there were sparse HFOs during recordings of Task 1 and 2, respectively. And there was no significant difference of the HFOs rate between two tasks (Supplemental Fig. 3). Notably in fusiform, the alpha band activities with a long latency (9–14 Hz, 68 ms before S2 to 263 ms after S2) and early emerging beta band activities (17–22 Hz, 60–177 ms of S2 ) demonstrated higher powers in Task 2 than in Task 1. Moreover, in the MTG, there were consistent theta and alpha band activities (for theta, 4–8 Hz, 130 ms before S2 to 462 ms after S2; for alpha, 12–15 Hz, 37 ms before S2 to 320 ms after S2), with a higher power in Task 2 than that in Task 1. The low frequency activities in the two temporal lobes suggested a background of mental subtraction, such as calculating attention and focusing during the two different tasks.

Figure 4

Time-frequency analysis for numerical comparison and subtraction.

A, time-frequency representations of the power response relative to Tasks 2 and 1 of the earliest recording sites, with discriminable ERPs amplitudes of Task 2 from 1, distributed at the SG, CG, fusiform gyrus, MTG, and AG, respectively. The black lines underneath the heatmap indicated durations of S1 and S2, respectively.

B, time-frequency representation of the power response difference between Tasks 2 and 1 of the five regions in (A), showing significant decreased (blue) or increased (red) activity. Significant clusters (FDR corrected p<0.05, non-parametric permutation test) have been encircled with a solid black line.

C, normalized power of the activities at the identified frequency band (gamma or beta/gamma) of five regions in (A) over time, respectively. Significant differences between Tasks 1 (blue line as the mean and shadow as the SEM) and 2 (orange line as the mean and shadow as the SEM) have been marked by a shadowed bar (p<0.05, t-test). The arrowed line indicated the duration of S2.

D, The average spectral power relative to the baseline activity in the identified time period and frequency band for Tasks 1 (blue) and 2 (orange) in (C) (p<0.05, t-test).

Besides the high gamma and low theta/alpha band, the clusters in gamma or beta/gamma ranges in the five regions presented a chronological order (Fig. 4c): in the SG, the gamma activities in the range of 28–37 Hz at a short latency (133–231 ms of S2 onset) indicated a higher power in Task 1 than in Task 2; in the CG, the gamma activities in the range of 56–66 Hz at a short latency (178–203 ms of S2 onset) showed a greater power in Task 1 than that in Task 2; in the fusiform gyrus, the beta/gamma activities in the range of 24–31 Hz at a latency of 185–231 ms demonstrated a higher power in Task 2 than that in Task 1; in the MTG, the gamma activities in the range of 30–41 Hz at a latency of 189–268 ms showed a greater power in Task 2 than that in Task 1; and in the AG, the gamma activities in the range of 37–42 Hz at a latency of 322–355 ms showed a greater power in Task 2 than that in Task 1 (Fig. 4d).

The power of the activities at the identified frequency band produced differences between numeric comparison and subtraction sequentially. This raised the question as to whether those clusters at a short latency reflects a modulation of oscillations. To address this query, we examined the ERPs latency of the sites, the amplitude of which showed differences during 183–322 ms of the S2 onset. The latency of the sites indicated differences in the following order (early to late): the MTG, SG, CG, fusiform, and AG (Fig. 3d). These analyses demonstrated that the gamma or beta/gamma power in the five regions might not be driven by the phase-locked ERP activities. Therefore, we referred to those chronological frequency power changes between Tasks 1 and 2 as activities rather than oscillations.

To verified the intrinsic effects among aforementioned five regions, a Spearman correlation was conducted in the power at the typical frequency band and time duration. The correlation networks indicated that effective correlations among five regions existed in Task 1 and 2, however, there were not effective connection between the MTG and CG, and the MTG and fusiform in Task 1, while as the connections existed in Task 2 (Fig. 5). Notably, most of correlations, such as the AG-CG, the AG-fusiform, the AG-MTG, the SG-CG, the SG-fusiform, the SG-MTG, and the CG-MTG in Task 1 were opposite to those in Task 2. Exceptionally, the correlation of the AG-SG, the CG-fusiform, and the fusiform-MTG showed the consistently negative correlation in Task 1 and 2. The results provided a possibility that the gamma band activities in the SG, CG, fusiform, MTG, and AG might follow a causal relationship to mediated subtraction process, with a distinguished network connections from that in simple numeric comparison.

Figure 5

Correlation of five core regions in numerical comparison and subtraction.Chord diagrams of correlations among the typical gamma band power of the core regions, including SG, CG, fusiform, MTG, and AG, in Task 1 and 2, respectively. The Spearman correlation were applied in each two regions among SG (power of 28?37 Hz, during 133?163 ms), CG (power of 56?66 Hz, during 178?208 ms), fusiform (power of 24?31 Hz, during 185?315ms), MTG (power of 30?41 Hz, during 189?219 ms), and AG (power of 37?42 Hz, during 322?352 ms), respectively. The average correlation coefficient during the initiated 30 ms of five regions were plotted, with the red and blue link indicated the positive and negative correlation, respectively.