The results section is divided into four subsections, namely (a) Dataset and experimental analysis, (b) Sequential activities of ACT-R modules & Cortex activation analysis, (c) Effective connectivity analysis among brain scouts, and (d) Statistical analysis of Granger prediction results. A detailed discussion of each section is mentioned below.

Dataset and experimental analysis

An open access dataset Shin et al. (2018) is used to evaluate the proposed model. Therefore, no ethical permission is required for data collection. The dataset contains EEG recordings of twenty-six subjects (9 males and 17 females, average age of 26.1±3.5 years). EEG data were recorded using 30 EEG electrodes according to the international 10-5 electrode placement system (Fp1, Fp2, AFF5h, AFF6h, AFz, F1, F2, FC1, FC2, FC5, FC6, Cz, C3, C4, T7, T8, CP1, CP2, CP5, CP6, Pz, P3, P4, P7, P8, POz, O1, O2, TP9 (reference) and TP10 (ground)). The sampling frequency was 200 Hz. The raw EEG was already filtered (fourth-order of Chebyshev type II) with a passband of \(1-40\) Hz to remove high-frequency noise from the EEG. The fourth-order Chebyshev type II filter provides a sharp transition between the passband and stopband. This characteristic of the Chebyshev type II filter effectively isolates the desired frequency components of the EEG signal from noise, especially when the noise is close to the frequency band of interest. Moreover, the stopband attenuation feature of this filter is useful for filtering out specific noise components, leading to better filtered EEG data Sree et al. (2023).

In the n-back test, participants need to identify the letter/digit presented n stimuli earlier in the sequence. The experimental dataset includes three sessions, each with three series of 0, 2, and 3-back (i.e.; \(n=0,2,3\)) tasks arranged in a counterbalanced order. Participants completed nine series of n-back tasks in total. Each series consisted of a 2s instruction, a 40s task period, and a 20s rest period. During the rest period, a fixation cross was shown. In the task period, a random digit/number appeared in every 2s, with 20 trials per series where the targets appeared with a 30% chance (70% non-targets). Each number was displayed for 0.5s, followed by a fixation cross for the remaining 1.5s. For the 0-back task, participants either pressed the target or non-target button without recalling any earlier digit. For the 2- and 3-back tasks, they pressed the target button if the current number matched the one 2 or 3 positions back, respectively. Participants completed a total of 180 trials (20 trials \(\times\) 3 series \(\times\) 3 sessions) for each n-back task across the three sessions. For computational constraints, randomly two consecutive digits of the task are selected to identify the activation time sequences of different ACT-R modules.

Fig. 2

Activation time sequence diagram of ACT-R modules for EEG-based n-back task. The duration of each digit presentation (with fixation cross) is 2 s. Here, only the first two input digits are considered to illustrate the retrieval operation. For the first stimulus in the trial, the participant presses the button without checking the target letter. Activation time denotes the duration of the ACT-R module’s activation while the subject performs a specific event (i.e., digit encoding, pressing key, etc). After a digit presentation, a fixation cross appears in the rest state

Fig. 3

a Time-wise activation of brain scouts for different workload levels. Top row: 0-back, middle row: 2-back, and last row: 3-back task. The activation time is written at the top of each cortex image. b The scout region in each ACT-R module is marked in a circle. Bright (yellow) and dark (blue) colors represent the high and low brain activations respectively

Sequential activities of ACT-R modules & cortex activation analysis

All the ACT-R modules are activated at a specific time in the n-back task (from visualizing the input stimuli to pressing the key). ACT-R modules are communicated using their buffer. The activation sequence diagram of ACT-R modules according to the experimental dataset is shown in Fig. 2. In each trial of the n-back dataset, a digit is presented for 2 s (0.5 s for the input letter and 1.5 s for the fixation cross). The diagram shows the activities of different ACT-R modules according to the timings of the two input letters of a single trial. The goal module only holds the current control information for the task, which is checked with the execution of the final production (P3). Therefore, the execution of the goal module occurs almost simultaneously with the P3 (within the same period of P3), so the goal module is excluded from the experimental analysis. The first input letter (7) appears on the computer screen in the sequence diagram, and the first production (P1) is fired to perceive the letter. Next, the visual module encodes that input letter, and after a slight delay, that letter is stored in the imaginal module. The imaginal module works as an intermediate or short-term memory in the ACT-R module. After the presentation of input stimuli, a fixation cross appears for 1.5 s, and at 2 s, the subject presses the key based on target or non-target stimuli. The next input (8) appears on the screen and follows a procedure similar to the first input. By this time, the imaginal module transfers the previous input letter (7) as a chunk to the declarative module. Once the second input letter is encoded & stored, the second production (P2) is fired to fetch the previous letter from the declarative memory. The Goal module holds the present input stimuli, and when the third production (P3) is fired, the Goal module communicates with the procedural module to check whether the present input is the same as the previous letter in the sequence (retrieved from the declarative memory). Finally, based on the matching or non-matching letter of current stimuli with the previous one, the subject presses the key by calling the motor module of ACT-R.

After identifying the ACT-R activation time sequence (refer to Fig. 2), I identify the activation of brain sources for each ACT-R module. The mapping of ACT-R modules and its corresponding brain sources/scouts are identified based on anatomical positions of BA Qin et al. (2007) (refer to Fig. 3b). Initially, the brain scouts for each n-back task are identified using the sLORETA method. To illustrate the ACT-R modules’ operations, I used two consecutive letters in a trial. Execution of other letters follows the same process. The activation of scouts in the cortex surface for the different time durations (interval of 1 s) is presented in Fig. 3. As neural activation is distributed over the cortex surface, scouts and their nearest locations are activated during a specific time. The cortex activation for 0, 2, and 3-back tasks is presented at the top, middle, and bottom rows of Fig. 3a. I start the scout activation after presenting input stimuli (i.e., 1 s). At 1 s, procedural (basal ganglia), visual (fusiform gyrus: BA-37), and imaginal modules are activated to present and process the visual stimulus of the 0-back task. Production 1 (P1) is activated for perceiving the input letter (refer to Fig. 2). At 2 s, the first letter presentation is completed, and the subject presses the button, so the motor module (BA-2,4) is activated. After 2 s, a second letter appears on the screen. From 2 to 3 s, multiple works perform in a sequence: (a) visual perception of the second letter and firing of P1 for processing the letter, (b) storing the second letter in the imaginal module, (c) fetching the previous letter from the declarative/retrieval module (BA-45) after execution of P2, and (d) P3 is fired to find a match between the retrieved letter and current letter. The goal module is communicated with P3 to find the matched or non-matched letter. Finally, at 4 s, the motor module is activated while the subject presses the button.

Effective connectivity analysis among brain scouts

After the scout identification, the time series of each scout corresponding to the ACT-R module is extracted. The time series are extracted for target and non-target stimulus for all workload levels (0,2 and 3-back). Then, the band-pass filter (0-32 Hz) is applied to remove noise from time series data. For simplicity, the scouts’ time series of target stimuli is presented in Fig. 4. Once the time-series extraction is performed, the effective connectivity analysis among scouts is identified through GC and MTE. The activation time series of ACT-R scouts is extracted using the brainstorm software Tadel et al. (2011). The information flow among ACT-R modules through GC and MTE methods is presented in the subsequent subsections.

Fig. 4

Scouts’ time series of n-back task: a 0-back, b 2-back, and c 3-back. Each stimuli time duration is 2 s (0.5 s for digit and 1.5 s for fixation cross.)

Information flow analysis using GC

The GC analysis between two scouts is estimated using bi-variate autoregressive models (BVAR) and time windows (i.e., the segment of the scout’s activation data). The BVAR model’s order is selected using the Bayesian information criterion using the Source Information Flow Toolbox (SIFT) Delorme et al. (2011). From SIFT, the optimal model’s order for the experiment is set as seven. The GC is computed based on the time series data of scouts. As transient connectivity is lost with a large time window, a shorter time window (i.e., 2 ms) is used to estimate the GC efficiently Cohen (2014). Moreover, using a short time window in GC analysis offers several significant advantages, particularly in enhancing temporal resolution. First, it allows for the detection of rapid and transient interactions between variables that may be missed with longer windows. This higher temporal granularity enables researchers to capture detailed dynamics and finer-scale causal relationships Cohen (2014). The GC is calculated for this time segment sequentially for the entire scout time series data of 4 s. Finally, the GC analysis for all such time segments is merged to find the final effective connectivity between the two scouts. The result of GC between different scouts across all the workload levels is presented in Fig. 5a–l. The direction of GC between two scouts (A\(\rightarrow\)B) also refers to the information flow between those scouts. The direction of information flow using GC is also validated through the statistical analysis (refer to Table 2). Here, the GC analysis are performed for target (Fig. 5) and non-target stimuli (Fig. 6) of 2-back and 3-back tasks (as 0-back task only includes fixation cross). The Imaginal module of ACT-R works as a working memory that stores the information and is manipulated during problem-solving Peebles (2019), so I used the GC analysis from Imaginal to other ACT-R modules and vice-versa. The main aim of the paper is to check the information flow between different ACT-R modules (e.g.; scouts) during different events of n-back tasks such as: the presentation of stimuli of n-back task (imaginal-visual modules, vice-versa), information processing/recall (imaginal-procedural/retrieval, vice-versa), and button press event (imaginal-motor, vice-versa). So I used the GC analysis from Imaginal to other modules. In the 0-back task, visual to-imaginal ACT-R scout activation is observed during stimulus presentation (\(0.5-1\) s) (Fig. 5a). Information flow from procedural to imaginal ACT-R scout is observed during stimulus presentation (Fig. 5d). For the target stimuli of 2 and 3-back tasks, a high peak in GC value is observed between visual and imaginal ACT-R scout immediately after the appearance of visual stimuli (Fig. 5e and i). A larger GC value leads to better information flow between brain scouts. For all the 2 and 3-back tasks, information flow is observed from the procedural to the imaginal ACT-R scout (Fig. 5h and l) for the execution of a set of productions (P1, P2, and P3 in Fig. 2). For the execution of P2 and P3, there is an information flow in both directions between the imaginal and retrieval ACT-R scouts for storing the current letter into short-term memory (imaginal buffer) and recalling past n letters from short-term memory (Fig. 5g and k). For all n-back tasks, causal effects are observed from the motor to imaginal ACT-R scout (Fig. 5f and j) at 2 s, when the subject presses the button. In the case of non-target stimuli, I found similar GC flow in visual and imaginal ACT-R scouts (Fig. 6a and e). Information flow between the imaginal and retrieval ACT-R scouts and vice-versa is also observed to check whether the current letter is target or not (Fig. 6c and g). Information flow from procedural to the imaginal ACT-R scout is observed for 2-back and 3-back tasks for executing the productions (Fig. 6d and h).

Fig. 5

Effective connectivity (GC) analysis among activation time series of ACT-R scouts for target stimuli (a–l). GC analysis is divided into 0-back (a–d), 2-back (e–h), and 3-back (i–l) tasks. The time segment for computing Granger prediction is 2ms. The order of the BVAR model is 7. Abbreviations in legends of images are as follows: imaginal (Imag), retrieval (Retr), motor (Mot), procedural (Proc) and visual (Vis)

Fig. 6

Effective connectivity (GC) analysis among ACT-R scouts for non-target stimuli. GC plots are divided into two workload states 2-back(a–d) and 3-back(e–h). The parameters (time segment of GC prediction and BVAR model order) remain the same as Fig. 5

Information flow analysis using MTE

The non-linear effective connectivity analysis is performed using MTE. The MTE computation is performed using the IDTxl tool Wollstadt et al. (2018), where the transfer entropy is depicted between a set of significant sources and the target. Here, the MTE connectivity is performed through the time series of scalp electrodes. The MTE connectivity analysis is performed using the “IDTxl" tool Wollstadt et al. (2018), where the input dimension is no of process/channels and no of samples. Therefore, the scalp electrodes for scouts are required for MTE analysis. The scalp electrodes for each ACT-R module are selected in such a way so that they are validated through BA’s/nearest BA’s anatomical location Qin et al. (2007). The ACT-R module and EEG electrode with the nearest BA location are shown in Table 1.Footnote 1 The results of MTE connectivity graphs among different ACT-R modules are shown in Fig. 7. All MTE graphs are demonstrated based on the activation time of the presentation of two stimuli (i.e., 4 s).

For all types of n-back tasks, it can be observed that the visual ACT-R module is mostly activated for stimulus presentation (digit and fixation cross). For the 0-back task (Fig. 7a), the information flow is transferred from visual (EEG channels: P7) to imaginal (EEG channels: P3, P4), procedural (EEG channels: CP5), and motor (EEG channels: C3, C4) ACT-R scouts. For the 2 and 3-back tasks (Fig. 7b–e), information flow is observed from visual (EEG channels: P7) to imaginal (EEG channels: P3/P4), retrieval (EEG channels: F7/F8), and motor (EEG channels: C3/C4) ACT-R scouts. Similar to GC, information flow from visual-to-imaginal ACT-R scouts exists for storing the current stimuli in short-term memory (e.g., imaginal ACT-R module). On the other hand, the connectivity between the imaginal (EEG channels: P4) and retrieval (EEG channels: F8) ACT-R scouts is present for 2 and 3-back tasks for retrieving previous digits from memory. Procedural (EEG channels: CP5) to imaginal (EEG channels: P3) ACT-R scout connectivity is observed for 2 and 3-back tasks during the execution of productions P1, P2, and P3. GC analysis also demonstrates similar findings. However, GC requires the AR model in its backend to execute, whereas MTE does not need any execution model.

Table 1 Mapping between ACT-R module, EEG electrodes, and Brodmann area (BA)Fig. 7

Non-linear causal connectivity analysis using MTE based on channels mentioned in Table 1: a 0-back, b 2-back (target), c 2-back (non-target), d 3-back (target), and e 3-back (non-target). Different colored EEG channels denote different ACT-R modules. The edges represent the MTE values between the two channels

Statistical analysis of granger prediction results

As the Granger prediction depicts the ratio of error variances of two-time series data (predicted from the autoregressive model), the statistical significance between two-time series can be checked using the F-test. For all workload levels, the F-test (Table 2) is performed to find the direction of causality between brain scouts with the significance level of \(p=0.05\). The analysis is performed between the activation time series obtained from brain scouts of each ACT-R module. The following hypothesis needs to be established to find whether the Scout 1 granger causes Scout 2.

\(H_0\): Error Variance (Scout 2) = Error Variance (Scout 1)

\(H_a\): Error Variance (Scout 2) > Error Variance (Scout 1)

If the error variance of two scouts’ time series is the same (i.e., \(H_0\)), then there is no Granger Causality (GC) from Scout 1 to Scout 2. On the other hand, if the error variance of the scout 1-time series is lesser than scout 2, then scout 1 Granger causes scout 2 (\(H_a\)). \(H_0\) is rejected, if the p value of Granger prediction (scout 1\(\rightarrow\) scout 2) < 0.05 (at 5% level of significance). Here, five ACT-R modules are considered, such as scout 1: imaginal, scout 2: visual, scout 3: motor, scout 4: retrieval, and scout 5: procedural in the experiment and perform the F-test to identify the direction of Granger prediction. The prediction validates the direction of effective connectivity between two brain scouts (in terms of ACT-R modules).

Table 2 Statistical result of Granger prediction using F-test.

To maintain a unique common nature across scouts for all subjects, I average the scout time series data across 26 subjects. Then, the statistical test (F-test) is performed on the average time series data of two scouts to find the direction of information flow between scouts (refer to Table 2 ) for both target and non-target stimuli. For 0-back, GC is observed from the visual to the imaginal scout and procedural to the imaginal scout. The causal flow between scouts is represented by the direction of GC. For the 2,3-back tasks, the imaginal module stores previous n-back letters in intermediate memory and send them to the retrieval module as per the demand of the procedural module. Thus, the GC occurs (in both directions) between the imaginal and the retrieval scout for 2-back and 3-back tasks. GC also occurs from the procedural to imaginal ACT-R module for all workload levels to control the tasks. The statistical results of information flow also validate the outcomes of GC analysis.