*3.2. Analysis of Realistic EEG in Mental Arithmetic Tasks*

In order to demonstrate the performance of the proposed CBTN method on realistic experimental data, the EEG signals of mental arithmetic tasks-dataset were used to distinguish the difference between the resting and the arithmetic states of the brain [41]. The dataset can be downloaded freely from the website: https://physionet.org/content/eegmat/1.0.0/, accessed on 23 January 2022. Electrodes were placed according to the international 10/20 scheme and the equipment used was the Neurocom monopolar EEG 23-channel system (Ukraine, XAI-MEDICA). The placement of the silver/silver chloride electrodes on the scalp was prefrontal (Fp1 and Fp2), frontal (F3, F4, Fz, F7, and F8), central (C3, C4, and Cz), parietal (P3, P4, and Pz), occipital (O1 and O2), and temporal (T3, T4, T5, and T6), all referenced to an interconnected ear reference electrode. The impedance between the electrodes and the scalp was less than 5 kΩ, and the sampling rate for each channel was 500 Hz. The acquired EEG signals were filtered using a high-pass filter with a cut-off frequency of 0.5 Hz, a low-pass filter with a cut-off frequency of 45 Hz, and a power line notch filter (50 Hz). The EEG data from 36 subjects (9 males and 27 females, aged 16–26 years) met the requirements for analysis, after a visual inspection of the filtered signals by neuroelectrophysiologists to remove data with poor signal quality. Subject 31 was not included because the length of the recordings was different from that of other subjects. The experiments involved mental arithmetic tasks and each experiment trial was divided into three phases: an adaptation

period, a resting state and an arithmetic state. First, the subjects were acclimatized to the experimental conditions for 3 min. Afterwards, the subjects relaxed for 3 min with their eyes closed in the resting state. Finally, the subjects were asked to perform a succession of subtractions in 4 min, each consisting of a four-digit (subtracted number) and two-digit (subtracted number) succession. The two digits were given to the subject verbally and the arithmetic task was not allowed to be performed verbally, but finger movements were allowed. In order to minimize the effect of emotional fluctuations caused by the increased cognitive load of the subjects during intensive cognitive activity on the results of the EEG analysis, the last minute of the resting state and the first minute of the arithmetic state were selected for analysis. Neuroimaging studies showed that the prefrontal and frontal regions were significantly activated during the performance of arithmetic or cognitive tasks [42,43]. Therefore, EEG data collected from seven channels (FP1, FP2, F3, Fz, F4, F7, and F8) in the prefrontal and frontal lobes were used in this study, and the NOTE between any two channels was calculated using the CBTN method to construct an undirected weighted network with the NOTE as the edge weight. Network parameters were extracted from the constructed complex network as a quantitative evaluation indicator of cognitive load. Since the NOTE value is inversely correlated with the coupling strength, in the subsequent analysis, the NOTE values were reversely processed (1 minus the value of NOTE), so that they would adhere to our intuition.

EEG signals were first detrended using the singular value decomposition (SVD) method. Then, the detrended EEG signal was filtered using the harmonic wavelets in the frequency range of 1 to 42 Hz. The obtained resting and arithmetic state EEG signals from seven channels were segmented using a sliding time window with a width of 2000 samples and a moving step of 500 samples. Within each window, the NOTE was estimated between any two of the seven EEG channels using the CBTN method. With the NOTE value as the edge weight, the complex network was constructed and the average clustering coefficient and the global network efficiency of the complex network were calculated. Following the same procedure, all sliding windows were analyzed in turn to obtain the average aggregation coefficient sequence and the global network efficiency sequence of the subject in a state. Since the distribution of the obtained sequences were unknown, the nonparametric permutation test (1000 repeated arrangement sampling) was used to assess the significance between the same sequences in the two states of the subject. The significance level *p* was set to 0.05. As a comparison, the same operation was performed on this subject using the CPE method with an embedding dimension of 5 and a delay time of 8. The results of the significance analysis between the feature sequences for all the 35 subjects under the two method treatments are shown in Table 1. The values bolded in black in Table 1 indicate statistical insignificance between the two states. As can be seen from the results of the analysis in Table 1, the CBTN method is obviously superior to the CPE method.

In order to confirm whether there were group differences in the EEG signals between the resting and arithmetic states, the mean adjacency matrix of each subject was constructed using the CBTN, and the network parameters of the mean adjacency matrix were extracted for each subject. The same procedure was performed using the CPE as comparison. The EEG data within each sliding window were analyzed using the CBTN to build a complex network, and its adjacency matrix was obtained. All adjacency matrices from the same subject under the same state were averaged. The clustering coefficient and the global network efficiency of the average adjacency matrix were used as a feature for each subject. In this way, the feature in the two states was obtained for individual subjects. The results obtained for all subjects are shown in Figure 5. It can be seen that for most subjects, the mean clustering coefficient of the arithmetic state was smaller than that of the resting state and the global efficiency of the arithmetic state was greater than that of the resting state. This means that the network in the prefrontal area was more efficient and had enhanced information processing capacity during the arithmetic state. It also means an increased

cognitive load during the arithmetic state. Figure 6 shows the analysis results of extracting the features of the complex network constructed by the CPE method under two states.


**Table 1.** Results of nonparametric permutation tests for each subject's feature sequences in the resting and arithmetic states (1000 repeated arrangement sampling, significant level *p =* 0.05).

ACE (average clustering coefficients), GNE (global network efficiency). Non significant results are shown in bold.

In order to verify whether there was significant difference between the two states at the group level, the results was statistically analyzed using a paired sample *t*-test. The significance level was set at *p* = 0.05, and statistical analysis was performed on IBM SPSS25.0. The results of the statistical analysis showed that there was a significant difference in the mean clustering coefficients (*p* = 0.0013) and in the global network efficiency (*p* = 0.0017) between the two states using the CBTN method (Figure 5). The results of the statistical analysis also showed that there was a significant difference in the mean clustering coefficients (*p* = 0.0056) and in the global network efficiency (*p* = 0.0061) between the two states using the CPE method. Although both methods can distinguish between the two states, the CBTN analysis was significantly better than the CPE analysis. This suggests that a complex network based on the CBTN using electrodes in the prefrontal and frontal lobe can distinguish well between the two cognitive states, demonstrating the validity of the CBTN method in practical applications.

**Figure 5.** The average clustering coefficient (**a**) and global network efficiency (**b**) of the average adjacency matrix constructed by the CBTN method for each subject.

**Figure 6.** The average clustering coefficient (**a**) and global network efficiency (**b**) of the average adjacency matrix constructed by the CPE method for each subject.

#### **4. Discussion**

The aim of this study is to construct a complex network using multichannel EEG signals to enable the assessment of cognitive load. The method of constructing the network directly affects the reliability of the assessment. In the process of using CPE suitable for the analysis of short time series to construct complex networks, it was found that the CPE method suffered from the lack of differentiation ability caused by considering only the probability distribution of symbols and ignoring the transition relationship between symbols in the temporal domain. In addition, as a nonlinear analysis method, the choice of parameters in the CPE had a large impact on the analysis results. In order to alleviate these issues, the CBTN is proposed to measure the coupling relationship between two time series from the perspective of cross-transition networks. The innovation of the CBTN is that it combines the advantages of the transition network and the bubble entropy on the basis of the principle of CPE. The introduction of the transition network solved the problem of ignoring the transition relationship between symbols in the CPE method. The symbolization method with reference to bubble entropy made the analysis result less affected by the embedding dimension. The effectiveness of the method was verified via a comparison with the CPE method on the unidirectional coupled Henon model. Firstly, the results show that the CBTN method could achieve satisfactory results when the signal

length reached 2000 samples, although this was slightly larger than that needed in the CPE method. This finding suggests that the CBTN is equally suitable for the analysis of short time series. Secondly, in the experiment study, the result tended to be stable for any coupling strength as long as the embedding dimension of the CBTN was greater than 10. This result indicates that the CBTN method is less affected by the coupling strength. Last, under weak coupling conditions, the CPE method failed to achieve the right results, while the CBTN could still obtain reliable results, indicating that the CBTN was able to uncover the weak coupling relationships between time series. These three properties ensure that the complex network constructed by the CBTN method outperformed the CPE in its ability to analyze cognitive load using EEG datasets. The results of the above analysis clearly demonstrate that the proposed method shows several advantages.

1. This method involves few parameters in use, and the value setting of the parameters has little influence on the analysis results.

2. The cross-transition network allows the method to be more sensitive to weak changes in the information interaction between two time series and is more suitable for analysis in weakly coupled conditions.

3. The normalization measures in the definition of node-wise out-link entropy minimize the impact of intersubject variation on the analysis results.

4. The implementation of the algorithm only involves the ranking of numbers and the probability distribution statistics of symbols, which is easy to be processed and implemented by a computer.

Although the study showed promising results, the limitation of this work should be considered. Firstly, the adjacency matrix of the cross-transition network was a static representation of information interaction between two time series in a period of time. This means that the method was explicitly time-dependent. The analysis of excessively long time series may have caused a reduction in the variation in the adjacency matrix, making identification less effective. This needs further study. Secondly, when using EEG datasets for cognitive load assessment, the electrodes used for analysis were determined subjectively only based on the findings of the neuroimaging, ignoring other aspects of the selection factors. As pointed out in the literature [44], in practical application, the practicality of electrode installation and the comfort of subjects should also be considered. Thirdly, the phase space reconstruction of the time series only considered the influence of the embedded dimension as a variable on the analysis results, and the time delay was set to 1 according to the bubble entropy. In the next research work, the comprehensive impact on the analysis results when these two parameters are variables will be studied in depth.
