Autism spectrum disorder (ASD) is a complex brain disorder that damages patients’ cognitive and social skills. Previous studies using static functional connectivity analysis from electroencephalogram (EEG) neglected dynamic traits of EEG signal. This study thus combined the dynamic functional connectivity with local graph theory indices to seek for biomarkers to diagnose the ASD. Traditionally, static local graph theory index was calculated using the entire EEG signal, and afterward 6 derivative dynamic graph theory indices were calculated by sliding windows with different width and moving step. For each index above, 95 features could be extracted. Further, they were selected and compared for its classification performance by support vector machine-recurrence feature elimination method. Our results indicated that dynamic graph theory indices in the 3s window width and 50% moving step achieved the best classification performance with average accuracy 0.952, which was better than its static counterpart. The distribution for selected features showed a preference in the frontal lobe and Beta band. Our studies indicated the window width of 3s with 50% moving step could be the appropriate settings for dynamic graph theory analysis, and the distribution tendency for the frontal lobe and Beta band could render researchers’ fresh perspectives into mechanism studies.
Research Article
Diagnosis for autism spectrum disorder based on electroencephalogram dynamic local graph theory indices
https://doi.org/10.21203/rs.3.rs-3331622/v1
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Electroencephalography
Autism Spectrum Disorder
Feature extraction
Dynamic functional connectivity
Graph theory analysis
Machine learning
Autism spectrum disorder (ASD) is a complex brain disease, which tends to cause restricted and repeated behaviors to patients and hinders theirs daily life [1]. ASD was firstly disclosed by Kanner in 1943 featured by social communication deficits and repetitive and unusual sensory-motor behaviors [2]. Although diagnosis and intervention in the early will effectively relieve subsequent sequelae [3], traditional diagnosis methods remains relying on clinical symptom questionnaires without effective neural biomarkers, which may lead to massive cases of misdiagnosis [4, 5]. Considering the diagnosis difficulties from the ambiguous and overlapping symptoms, it is urgent to find out symptom-related biomarkers to assist clinical diagnosis and help shed light on the developing mechanisms for ASD [6].
Previous research has attempted to identify core biomarkers in the aspect of brain functional connectivity. Electronic physiology pointed out that aberrant functional nervous circuits act as a potential trait for ASD [7, 8]. In other words, ASD patients do not undergo normal synaptic pruning during childhood, and will leave too many synaptic connections [9]. It has been proposed that an excess of neurons causes local functional overconnectivity. Although nowadays the most acceptable finding was that ASD patients have a decreased long-range functional connectivity and increased short-range connectivity [10], some studies gave mixed or even contradictory results [11–13]. In the meanwhile, the most previous research concentrated on the static functional connectivity analysis (sFCA). This sort of method treats the EEG signal as a whole to calculate the functional connectivity between different brain regions and assumes that EEG signal is a static one without changes of statistical parameters along the time, which disagrees with the essences of brain electronic signals [14]. Some studies found that there existed distinct dynamic mode in ASD patients [15]. To catch the dynamic traits that cannot be caught by traditional sFCA, a new method called dynamic functional connectivity analysis (dFCA) comes up to explore the dynamic fluctuations of EEG along the time. The most usual method for dFCA is the sliding window scanning, which scans EEG signal by the window with fixed width and moving step. By the scanning of sliding window, the dynamic variability of the brain network could be obtained. Variability could reflect the dynamic reconfiguration between different regions at different time points, which could possibly reflect the flexibility and adaptability of the brain and has been proven to be informative in the diagnosis for several diseases, including ASD [16].
Connectivity matrix is the most common form to describe the global connectivity for a whole brain because of its easy interpretability, but two-region connectivity contains rather little information and cannot take into account the interaction from other regions, and thus is viewed as a low-order index [17]. Currently, many study analyses have been conducted by means of complex network analysis, or graph theory analysis [18, 19], in which connectivity network in a brain can be described by a graph where the EEG channels are treated as the nodes, and the connectivity intensity between assessed EEG channels as the edges, whereby a series of graph theory indices can be calculated. Graph theory analysis of brain networks is particularly appropriate for ASD, because ASD can be considered as a disconnection syndrome [20]. A study found that preschool-aged children underwent changes in some nodes graph theory indices, which were considered to be potential biomarkers for the diagnosis of ASD [21]. Naturally, it is rational to combine the advantages from both dynamic functional connectivity and graph theory analysis to explore ASD from a fresh perspective. Research [22] combined the analysis of dynamic functional connectivity and global graph theory indices, and found that only in the condition of dynamic functional connectivity was there significant classification ability. Nonetheless, some research tended to use global graph theory indices to explore the whole brain variability, and neglect the role of the variability in certain brain regions. Graph theory analysis from [21] indicated that there was no significant difference in global graph theory index between ASD patients and controls, whereas for local graph theory indices, such as node degree, ASD patients had higher node degree in right medial frontal gyrus than controls, which meant some local network connectivity structure underwent changes and cannot be found by global graph theory index. Accordingly, in our research we attempted to combine dynamic functional connectivity with local graph theory indices to further compute its derivative dynamic graph theory indices, compare their diagnosis performance, and determine the most discriminating features for the diagnosis of ASD by machine learning and feature selection methods.
2.1 Data derivation
EEG data and diagnosis information were derived from the internal medical record system in Zhongshan Bo’ai Hospital, Zhongshan city, China. The inclusion criteria for the ASD patient group were: (1) diagnosed as autism spectrum disorder according to diagnostic and statistical manual of mental disorders-V (DSM-V) criteria; (2) aged between 1–6 years. Exclusion criteria for the ASD patient were: (1) patients accompanying with history of epilepsy seizures; (2) patients who had suffered from other neurological, developmental diseases or extra-cranial injury. Controls were selected from children who were hospitalized for non-neurological disease, such as diarrhea, in the same age range. Altogether 20 ASD patients and 25 health controls were contained.
2.2 EEG data preprocess
The EEG signals were recorded by Nicolet EEG machine with a sampling rate of 125Hz. Totally 19 channels (Fp1, Fp2, F7, F3, Fz, F4, F8, T3, C3, Cz, C4, T4, T5, P3, Pz, P4, T6, O1, and O2) were placed onto the scalp of the patient according to the international 10–20 montage system with reference channels being Fz, Cz and Pz. The preprocessing steps of EEG were as follows: (1) band-pass filtering between 0.1Hz-45Hz was conducted for EEG signals to eliminate artifacts; (2) independent component analysis (ICA) was performed to remove artifacts derived from eyes and muscle movement; (3) manually removing the bad segments which can not be identified by ICA; (4) the 100s segments that included as few artifacts as possible were selected by experts; (5) finally, EEG were further filtered into 5 frequency subbands, namely Delta (0.5–4 Hz), Theta (4–8 Hz), Alpha-1 (8–10 Hz), Alpha-2 (10–12 Hz), Beta (12–30 Hz). The preprocess mentioned above were conducted by EEGLab toolbox [23] in Matlab v. 2019a.
2.3 Functional connectivity calculation
In our research, Magnitude squared coherence (MSQ), or coherence, was calculated to explore the linear relationship between two signals in the fixed frequency. Assuming that Y (t) and X (t) represent EEG signals in two brain regions or region of interests (ROIs), respectively. Firstly Y (t) and X (t) are converted from time domain to frequency domain using fast Fourier transform:
$$F(f)=\sum\limits_{{t=0}}^{{T - 1}} {x[t]} {e^{ - i2\pi tf}}$$
1
Then, for each frequency point f, power spectral densities Sxx (f) and Syy (f) and their cross power spectral density Sxy (f) are estimated, and finally, the coherence function Kxy (f) at that frequency point f is further calculated as follows:
$${K_{XY}}(f)=\frac{{{S_{xy}}(f)}}{{\sqrt {{S_{xx}}(f){S_{yy}}(f)} }}$$
2
After computation for every pair of ROIs has done, all the results can form a connectivity matrix. Because some low-connectivity pairs of ROIs may be caused by noise, it is crucial to apply a certain threshold to remove these noise-triggered low-connectivity edges. The nail-down for the threshold is a subjective and controversial problem, where a high threshold would result in an oversparse connectivity network while a low one would even form a regular lattice. Considering this, we chose an intermediate threshold of 0.8 (namely preserving top 20% edges of the graph) as previous research did [24] to maintain this subtle balance.
2.4 Static graph theory index calculation
In this paper, node strength was calculated as static graph theory index for each ROIs for its easy interpretability. The calculation formula of the node strength for node i in the graph G is as follows:
$${S_{nodal}}(i)=\sum\limits_{{i \ne j \in G}} {{w_{ij}}}$$
3
Where the wij represents the weight of the edge linking the node j to node i. The value of node strength reflects the importance and the total ability to transfer information of that node in the network.
Each subject could obtain 5 (frequency subband number) × 19 (EEG channel number) = 95 features in node strength index for modeling.
All the node strength were calculated using the “igraph” package in R v. 4.2.2.
2.5 Dynamic graph theory indices calculation
By the application of sliding window, a series of functional connectivity matrix down the time can be acquired, from which subsequent dynamic graph theory indices can be reached. Here the width for window was set in 1s, 3s, 5s, respectively, and the moving step was set to be 50% or 100% of the window width. Here we utilize 6 types of dynamic indices, namely the mean, standard deviation, median, inter-quartile range, kurtosis and skewness of the node strength [25] to describe the dynamic traits along the extracted windows. Like static node strength index, for each of 6 dynamic graph theory indices, 5 (frequency subband number) × 19 (EEG channel number) = 95 features can be calculated for each subject.
2.6 Classification and feature selection by SVM-RFE
Since the number of features was larger than the number of subjects, and in order to rank the importance of features and extract the most important ones to form the optimal feature subset, this study used support vector machine-recursive feature elimination (SVM-RFE) to conduct feature reduction, ranking and classification simultaneously.
SVM-RFE treats support vector machine (SVM) classification performance as the evaluation standard, and is widely used due to its high efficiency [26]. Specifically, it sorts the features by the coefficient size of each feature on the classification hyperplane function in SVM, and repeatedly eliminate a feature which is the least important and remodel. When the recurrence process finishes, the feature subset with the greatest accuracy will be extracted.
Considering the sample set:
$$D=\{ ({x_1},{y_1}),({x_2},{y_2}),...,({x_m},{y_m})\} ,{x_i} \in {R^d},{y_i} \in \{ +1, - 1\}$$
4
The m points to the sample size, xi is a d-dimension vector of features, and y is the label of that sample. SVM seeks to find a hyperplane w to completely classify positive and negative samples, which can be formulated as:
$${w^T}+b=0$$
5
Finally, for the jth feature, the importance of that feature could be calculated as the square of that coefficient in w, namely:
$${c_j}=w_{j}^{2},j=1,2,...,d$$
7
Involving a simple process and comparatively little calculation, the feature ranking and selection process of SVM-RFE proceeds almost simultaneously with model construction, and is a fast heuristic search algorithm.
Here for static node strength and its 6 derivative dynamic graph theory indices, we establish the model with the whole features to obtain the feature importance ranking. At every step of feature-removal recurrence process, leave-one-out cross-validation(LOOCV) was performed using the feature subset, and the average accuracy on the test set was used to select the optimal feature subset. In the meanwhile, sensitivity, specificity, precision, recall and AUC would be calculated as auxiliary measures to evaluate the classification performance. The AUC was calculated as area under the receiver operating characteristic curve, and other 5 measures were calculated as follows:
To reduce the computation consumption and concentrate on nonnegligible features, the size of starting feature subset would only contain the top 30 important features. In each recurrence, the most unimportant feature would be removed until only top 5 important features remained in the subset. The execution of SVM-RFE was based on self-edited code in Matlab v. 2019a, in which the fitcsvm function was used to establish the SVM model, and the parameter remained its default with C equal to 1.0. The whole workflow could refer to Fig. 1.
Figure 1 The work flow of SVM-RFE
3.1 Demographic data analysis
The median age of ASD group and control group were respectively 37.5 months and 32.0 months, and showed no difference by Wilcoxon rank-sum test (P = 0.192). The proportion of male were respectively 20% and 28% for ASD group and control group with no difference by Fisher's exact test (P = 0.730).
3.2 Comparison of classification performance with different window width and moving step
Table 1 unfolds the performance measures for static node strength and its 6 derivative dynamic graph theory indices in the condition of window width of 1s, 3s and 5s and moving step of 50%. Figure 2 demonstrated the changing process of evaluation measures along with the number of features.
Results showed that the average classification accuracy of dynamic graph theory indices under the window widths of 1s and 5s were 0.859 and 0.870, respectively, and inferior to static counterpart 0.933. When in the condition of 3s width, the average accuracy 0.952 outperformed the static counterpart 0.933, and among them, 3 dynamic graph theory indices, namely the mean, median and inter-quartile range of node strength, even achieved the accuracy and AUC equal to 1.000. From the Table 1 and Fig. 2, we can also see that 3s-window-width indices needed average 15.5 features in the optimal feature subset to achieved the best accuracy, which was less than the condition of static (22), 1s-window-width (22.5) and 5s-window-width (17.3).
| Type of Index | Name of Index | Accuracy | Sensitivity | Specificity | Precision | Recall | AUC | Number of features in optimal subset |
|---|---|---|---|---|---|---|---|---|
| Static | Strength | 0.933 | 0.8500 | 1.000 | 1.000 | 0.893 | 0.944 | 22 |
| 1s window width and 50% moving step | Mean | 0.822 | 0.700 | 0.920 | 0.875 | 0.793 | 0.946 | 26 |
| STD | 0.822 | 0.750 | 0.920 | 0.875 | 0.808 | 0.884 | 23 | |
| Median | 0.867 | 0.800 | 0.920 | 0.889 | 0.852 | 0.938 | 18 | |
| IQR | 0.889 | 0.850 | 0.960 | 0.917 | 0.885 | 0.916 | 21 | |
| Kurtosis | 0.800 | 0.650 | 0.920 | 0.867 | 0.767 | 0.910 | 20 | |
| Skewness | 0.956 | 0.900 | 1.000 | 1.000 | 0.926 | 0.992 | 27 | |
| Average | 0.859 | 0.775 | 0.940 | 0.904 | 0.839 | 0.931 | 22.5 | |
| 3s window width and 50% moving step | Mean | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 14 |
| STD | 0.978 | 1.000 | 0.960 | 0.952 | 1.000 | 0.960 | 12 | |
| Median | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 11 | |
| IQR | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 20 | |
| Kurtosis | 0.889 | 0.850 | 1.000 | 1.000 | 0.885 | 0.934 | 20 | |
| Skewness | 0.844 | 0.800 | 1.000 | 1.000 | 0.840 | 0.950 | 16 | |
| Average | 0.952 | 0.942 | 0.993 | 0.992 | 0.954 | 0.974 | 15.5 | |
| 5s window width and 50% moving step | Mean | 0.889 | 0.800 | 0.960 | 0.941 | 0.857 | 0.936 | 17 |
| STD | 0.933 | 1.000 | 0.920 | 0.905 | 1.000 | 0.948 | 22 | |
| Median | 0.867 | 0.800 | 0.960 | 0.934 | 0.852 | 0.922 | 14 | |
| IQR | 0.889 | 0.800 | 1.000 | 1.000 | 0.857 | 0.980 | 29 | |
| Kurtosis | 0.867 | 0.850 | 0.900 | 0.8824 | 0.880 | 0.896 | 11 | |
| Skewness | 0.778 | 0.700 | 0.920 | 0.8571 | 0.778 | 0.870 | 11 | |
| Average | 0.870 | 0.825 | 0.943 | 0.920 | 0.871 | 0.925 | 17.3 |
STD: standard deviation; IQR: inter-quartile range.
Figure 2 The changing process of performance measures and ROC curve in 50% moving step and different window width condition.(a–c) Changing process of accuracy along with the number of features under window width of 1s, 3s, and 5s. (d–f) Changing process of AUC along with the number of features under window width of 1s, 3s, and 5s. (g–i) The ROC under the window width of 1s, 3s and 5s. The vertical line means the location where the accuracy peaks
To explore the effect of moving step, the above analysis process was repeated under the condition of 100% moving step, which meant that there was no overlap between two adjacent windows. The results were displayed in the Table 2 and Fig. 3.
The Table 2 showed that the average accuracy of dynamic graph theory indices under 1s and 5s window width were 0.863 and 0.851, respectively, and fairly close to that in 50% moving step condition(0.859 and 0.870, respectively), while the average accuracy under 3s window width were 0.930 and lower than its counterpart in 50% moving step (0.952). Nonetheless, the performance under 3s window width remained the best compared with 1s and 5s window width condition. Similarly, the performance of the mean, median and inter-quartile of node strength in 3s window width were still acceptable (0.933, 0.933 and 0.956, respectively).
| Type of Index | Name of Index | Accuracy | Sensitivity | Specificity | Precision | Recall | AUC | Number of features in optimal subset |
|---|---|---|---|---|---|---|---|---|
| Static | Strength | 0.933 | 0.8500 | 1.000 | 1.000 | 0.893 | 0.944 | 22 |
| 1s window width and 100% moving step | Mean | 0.844 | 0.800 | 0.960 | 0.933 | 0.846 | 0.926 | 15 |
| STD | 0.844 | 0.800 | 0.920 | 0.882 | 0.846 | 0.904 | 20 | |
| Median | 0.888 | 0.850 | 0.960 | 0.941 | 0.884 | 0.934 | 17 | |
| IQR | 0.866 | 0.900 | 0.920 | 0.866 | 0.913 | 0.896 | 15 | |
| Kurtosis | 0.911 | 0.900 | 0.920 | 0.900 | 0.920 | 0.910 | 19 | |
| Skewness | 0.822 | 0.800 | 1.000 | 1.000 | 0.840 | 0.910 | 21 | |
| Average | 0.863 | 0.842 | 0.947 | 0.920 | 0.875 | 0.913 | 17.8 | |
| 3s window width and 100% moving step | Mean | 0.933 | 0.900 | 0.960 | 0.947 | 0.923 | 0.964 | 13 |
| STD | 0.933 | 0.950 | 0.920 | 0.905 | 0.958 | 0.966 | 29 | |
| Median | 0.933 | 0.900 | 0.960 | 0.947 | 0.923 | 0.948 | 29 | |
| IQR | 0.956 | 0.900 | 1.000 | 1.000 | 0.926 | 0.994 | 29 | |
| Kurtosis | 0.911 | 0.800 | 1.000 | 1.000 | 0.862 | 0.990 | 16 | |
| Skewness | 0.911 | 0.900 | 0.960 | 0.944 | 0.920 | 0.955 | 28 | |
| Average | 0.930 | 0.892 | 0.967 | 0.957 | 0.919 | 0.970 | 24.0 | |
| 5s window width and 100% moving step | Mean | 0.866 | 0.800 | 0.960 | 0.933 | 0.851 | 0.866 | 14 |
| STD | 0.844 | 0.700 | 0.960 | 0.933 | 0.800 | 0.844 | 22 | |
| Median | 0.888 | 0.850 | 0.960 | 0.941 | 0.884 | 0.888 | 26 | |
| IQR | 0.933 | 0.900 | 1.000 | 1.000 | 0.920 | 0.933 | 14 | |
| Kurtosis | 0.822 | 0.700 | 0.960 | 0.875 | 0.793 | 0.822 | 11 | |
| Skewness | 0.755 | 0.700 | 0.880 | 0.800 | 0.769 | 0.755 | 8 | |
| Average | 0.851 | 0.775 | 0.953 | 0.913 | 0.836 | 0.851 | 15.8 |
STD: standard deviation; IQR: inter-quartile range.
Figure 3 The changing process of performance measures and ROC curve in 100% moving step and different window width condition. (a–c) Changing process of accuracy along with changing of the number of features under window width of 1s, 3s, and 5s. (d–f) Changing process of AUC along with changing of the number of features under window width of 1s, 3s, and 5s. (g–i) The ROC under the window width of 1s, 3s and 5s. The vertical line means the location where the accuracy peaks.
To compare the classification ability between 6 dynamic graph theory indices, Table 3 and Fig. 4 generalized the overall classification ability measures across all conditions. It can be seen from the Table 3 and Fig. 4 that the IQR index performed the best by peaking in all measures, after that the median index took the second position.
| Dynamic Feature | Accuracy | Sensitivity | Specificity | Precision | Recall | AUC | Number of features in optimal subset |
|---|---|---|---|---|---|---|---|
| Mean | 0.892 ± 0.065 | 0.833 ± 0.103 | 0.960 ± 0.025 | 0.938 ± 0.040 | 0.878 ± 0.073 | 0.940 ± 0.044 | 16.5 ± 4.8 |
| STD | 0.892 ± 0.064 | 0.867 ± 0.133 | 0.933 ± 0.021 | 0.909 ± 0.029 | 0.902 ± 0.095 | 0.918 ± 0.049 | 21.3 ± 5.5 |
| Median | 0.907 ± 0.051 | 0.867 ± 0.072 | 0.960 ± 0.025 | 0.942 ± 0.035 | 0.899 ± 0.056 | 0.938 ± 0.037 | 19.2 ± 7.0 |
| IQR | 0.922 ± 0.050 | 0.892 ± 0.066 | 0.980 ± 0.033 | 0.964 ± 0.058 | 0.917 ± 0.048 | 0.953 ± 0.044 | 21.3 ± 6.5 |
| Kurtosis | 0.867 ± 0.047 | 0.792 ± 0.097 | 0.950 ± 0.043 | 0.921 ± 0.062 | 0.851 ± 0.059 | 0.910 ± 0.055 | 16.2 ± 4.3 |
| Skewness | 0.844 ± 0.077 | 0.800 ± 0.089 | 0.960 ± 0.050 | 0.934 ± 0.086 | 0.846 ± 0.067 | 0.905 ± 0.085 | 18.5 ± 8.3 |
STD: standard deviation; IQR: inter-quartile range.
Figure 4 The radar plot of overall performance measures across all conditions for 6 dynamic graph theory indices
3.3 Feature ranking, selection and visualization
Considering that it took the best performance for dynamic graph theory indices under the window width of 3s and moving step of 50%, we explored further by looking into the feature rankings and the distribution of scalp regions and frequency subbands for selected features. Table 4 described the feature rankings and relevant weights for 6 dynamic graph theory indices under the window width of 3s and moving step of 50%, and Fig. 5 projected the feature weights into a 3D brain model using projection coordinate develop by Okamoto et al [27]. The generation of 3D brain model was support by Matlab toolbox BrainNet Viewer [28]. In the Fig. 5, the color of the sphere pointed to the frequency subband and the volume meant the weight. It can be seen from the Table 4 and Fig. 5 that the majority of top positions were occupied by the features in Beta and Alpha2 frequency bands, which meant features in the high frequency subbands contributed more to the classification of ASD patients.
Table 5 gave the proportion distribution of selected features in five frequency subbands across 6 dynamic graph theory indices. It suggested that features from Beta subband took the dominant position with unweighted proportion 28.283% and weighted proportion 40.739%.
Similarly, we explored the distribution of selected features in five scalp regions, namely frontal (Fp1, Fp2, F7, F3, Fz, F4, F8), central (C3, Cz, C4), parietal (P3, Pz, P4, P7, P8), temporal (T4, T5) and occipital (O1, and O2). It could be seen that the selected features from frontal region had the greatest unweighted proportion (36.364%) and weighted proportion (46.153%). Considering that each region has different number of channels and will affect the proportion distribution, we further calculated the relative importance for scalp region, which is calculated by dividing channel proportion (k/19, k is the number of channels in the region). For example, the unweighted relative importance for frontal region was 0.364 divided by 7/19 and equal to 0.987. It can be seen from the Table 5 that the weighted relative importance of features from frontal lobe remained the greatest (1.253) even correcting the proportion of channels.
| Mean | STD | Median | IQR | Kurtosis | Skewness | |||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Selected Features (n = 14) | Weight | Selected Features (n = 12) | Weight | Selected Features (n = 11) | Weight | Selected Features (n = 20) | Weight | Selected Features (n = 20) | Weight | Selected Features (n = 16) | Weight | |
| Beta- F3 | 0.338 | Alpha2- P8 | 0.631 | Beta- F3 | 0.320 | Beta- Fp1 | 0.977 | Beta- Fz | 1.841 | Beta- C3 | 0.887 | |
| Alpha1-T7 | 0.268 | Alpha2- Cz | 0.550 | Alpha1- T7 | 0.155 | Beta- P7 | 0.873 | Beta- Fp1 | 1.316 | Theta- F3 | 0.791 | |
| Beta- F4 | 0.202 | Alpha2- P7 | 0.523 | Alpha2-P7 | 0.154 | Beta- C3 | 0.694 | Alpha2- Fp2 | 0.880 | Alpha1- Pz | 0.680 | |
| Alpha1-P7 | 0.159 | Alpha1- F4 | 0.401 | Alpha2- F3 | 0.113 | Beta- O2 | 0.608 | Beta- Fp2 | 0.861 | Beta- Fz | 0.670 | |
| Alpha2-P7 | 0.147 | Alpha2- Fp1 | 0.366 | Alpha1-Cz | 0.111 | Beta- Fz | 0.526 | Beta- P8 | 0.845 | Alpha2- T8 | 0.530 | |
| Alpha2-T7 | 0.134 | Beta- Fz | 0.353 | Beta- Cz | 0.105 | Beta- O1 | 0.480 | Theta- F8 | 0.798 | Theta- Fz | 0.470 | |
| Alpha1-Cz | 0.125 | Theta- P8 | 0.307 | Beta- C3 | 0.089 | Theta- Fz | 0.480 | Beta- P4 | 0.797 | Alpha2-C4 | 0.460 | |
| Alpha2-F3 | 0.116 | Theta- T8 | 0.287 | Alpha2-Cz | 0.087 | Alpha1- F4 | 0.479 | Theta- C3 | 0.744 | Alpha2- Fz | 0.451 | |
| Alpha2-Cz | 0.106 | Alpha2- P3 | 0.284 | Theta- O1 | 0.084 | Alpha2- P7 | 0.379 | Beta- P7 | 0.633 | Theta- F7 | 0.411 | |
| Beta- P7 | 0.103 | Alpha2- C3 | 0.278 | Delta- Cz | 0.083 | Beta- Fp2 | 0.349 | Delta- C3 | 0.567 | Beta-Cz | 0.385 | |
| Alpha2-T8 | 0.094 | Alpha1- T7 | 0.276 | Alpha1-P7 | 0.083 | Alpha2- T8 | 0.339 | Theta- Fz | 0.560 | Alpha2- P4 | 0.381 | |
| Alpha1-T8 | 0.087 | Alpha2- F4 | 0.271 | Delta- Pz | 0.326 | Beta- Cz | 0.536 | Alpha2- F3 | 0.352 | |||
| Theta-Pz | 0.073 | - | - | Alpha2- P3 | 0.325 | Alpha2- Fz | 0.530 | Delta- O2 | 0.344 | |||
| Theta-O1 | 0.071 | - | - | - | - | Alpha1- F3 | 0.323 | Alpha1- Fp1 | 0.512 | Theta- C4 | 0.342 | |
| - | - | - | - | Alpha2- F4 | 0.317 | Theta- C4 | 0.331 | Delta- P8 | 0.334 | |||
| - | - | - | - | - | - | Alpha2- P8 | 0.314 | Alpha2- P4 | 317 | Theta- Pz | 0.302 | |
| - | - | - | - | - | - | Beta- F8 | 0.302 | Alpha2- F4 | 0.302 | |||
| - | - | - | - | - | - | Alpha1- T7 | 0.281 | Beta- C3 | 0.264 | - | - | |
| - | - | - | - | - | - | Alpha2- Fp2 | 0.279 | Beta- F7 | 0.244 | - | - | |
| - | - | - | - | - | - | Alpha2- T7 | 0.252 | Theta- F4 | 0.242 | - | - | |
STD: standard deviation; IQR: inter-quartile range.
Figure 5 The visualization for the weights and distribution of 6 dynamic graph theory indices under 3s window width and 50% moving step. (a) Mean of node strength. (b) Standard deviation of node strength. (c) Median of node strength. (d) Inter-quartile range of node strength. (e) Kurtosis of node strength. (f) Skewness of node strength.
| Scalp region | Proportion (%) | Relative importance | Weighed proportion (%) | Weighed relative importance | Frequency subband | Proportion (%) | Weighed Proportion (%) |
|---|---|---|---|---|---|---|---|
| Parietal lobe | 26.263 | 0.998 | 24.659 | 0.937 | Alpha-1 | 14.141 | 10.124 |
| Frontal lobe | 36.364 | 0.987 | 46.153 | 1.253 | Alpha-2 | 33.333 | 27.298 |
| Temporal lobe | 11.111 | 1.056 | 6.9450 | 0.660 | Beta | 28.283 | 40.739 |
| Occipital lobe | 7.071 | 0.672 | 4.9120 | 0.467 | Delta | 6.061 | 4.899 |
| Central lobe | 19.192 | 1.215 | 17.331 | 1.097 | Theta | 18.182 | 16.939 |
There are many inconsistency or even contradictions in the previous results from static functional connectivity analysis [29]. It has been pointed out that this paradoxical results may stem from the neglect to instantaneous dynamic change in EEG connectivity measuring [30]. One explanation for this discrepancy in dynamic and static analysis could be that the dFCA may capture subtle dynamic information details related to the dynamics of the continuous reconstruction of brain networks, which has been shown to correlate with mental activity and higher-order cognitive performance [31]. Our study combined dynamic functional connectivity analysis with local graph theory indices in order to provide fresh perspectives for ASD and reinforce the interpretability of our study.
4.1 Influence of different window width and moving step to classification performance
We compared the performance of dynamic graph theory indices with traditional static graph theory index in distinguishing ASD patients from healthy children. The results indicated that when the window width and moving step was set to 3s and 50% respectively, dynamic graph theory indices achieved the highest accuracy compared to other settings, and even some of them encouragingly reached 100% accuracy. Some previous research used global graph theory indices to diagnosed ASD and achieved considerable results. Wadhera T and his colleague [32] explored biomarkers from the perspective of hierarchical complex and put forward a new index named weighted hierarchical complexity, and achieved the highest diagnosis accuracy 0.988 for ASD patients by SVM, which was better than the performance of single or the combination of other traditional graph theory indices such as betweenness centrality. Wadhera T and his colleague [33] also used SVM model to classify ASD by combining the effect of two metrics, namely average weighted degree and mutual Information, and obtained the accuracy 0.923. Alotaibi N et al [34] calculated functional connectivity by trial-averaged standard phase-locking value, and further extracted five graph theory indices, namely transitivity, characteristic, path length, global efficiency, radius and diameter, and achieved the accuracy of 0.958. Based on the research above, our study further explored the classification ability of local graph theory and could provide the combination of high classification ability and location of important features.
In the field of dynamic functional connectivity analysis, the setting for window width remains a controversial issue, and it majorly depends on subjective choice from researchers. Previous dynamic functional connectivity studies proved that a too short window width would increase the risk of introducing artifacts and reduce the frequency resolution, while window with a too wide width tended to mask the information of dynamic transient shifting [14]. The fact that the highest accuracy was achieved by 3s window width in this study accorded with the theory above for achieving a fabulous balance between frequency resolution and the ability to capture variability. When moving step was set to 100%, the performance o3f 3s-window-width dynamic graph theory indices slightly decreased, but its performance was still superior to 1s and 5s settings, which could be another evidence for selecting 3s as window width.
We also found that the number of features in the optimal subset was the least for 3-window-width and 50%-moving-step dynamic graph theory indices, which is another advantage in terms of over-fitting. It is thought that over-fitting is prone to occur when the number of features is larger than the number of subject [35]. Even though support vector machine adopts regularization techniques to avoid the over-fitting problem to some extent, however, even SVM does benefit from feature reduction, which was proved by experimental results from Guyon et al [26]. To sum up, setting the window width as 3s can achieve the highest classification performance while requiring the least number of features, which offered advises for the choice of the window width and moving step when conducting dynamic functional connectivity analysis in the future.
4.2 Internal comparison between dynamic graph theory indices
Considering that by the 3s window width and 50% moving step was the best performance achieved, in this condition we further compared the performance of 6 dynamic graph theory indices. We found that the inter-quartile range peaked in all performance measures, and the which supported the applicability for dynamic variability index to diagnosis ASD patients. Previous study found that ASD patients showed anomalous dynamic variability even in the station of rest [36]. Dynamic variability pointed to the instability of information transfer inside and between different regions, and reflect the model reconfiguration in the brain. A study found that significant difference was only found in terms of dynamic variability index but not static functional connectivity [37]. Abnormal variability may interfere with the information transfer between crucial brain regions, impair some necessary social function, and thus may contain specific temporal information about ASD [38]. Nonetheless, previous study mainly used the standard deviation as the index to measure dynamic variability, our study found that non-parametric index, namely inter-quartile range, outperformed the parametric standard deviation index. This may reflect the applicability of non-parametric index to describe the dynamic variability in the situation of dynamic local graph theory index.
4.3 Preference of feature distribution at frontal lobe
The distribution analysis of selected features in scalp region indicated an obvious dominance for the frontal region. Many previous studies have found abnormal functional connectivity in the default mode network (DMN) in ASD patients [39–41], where medial prefrontal cortex (mPFC) took the important role for social cognition process. Results from Chen et al suggested that ASD patients had a more stable mPFC-insula coupling, or a less variability, than control group. Chen et al pointed out that when there is no external input, the saliance network (SN), where the insula was a core region, suppresses executive function by increasing its functional coupling to the DMN to maintain an internal-focused state. Nonetheless, SN would spontaneously change the network configurations to monitor possible external changes. Accordingly, ASD patients may have an over-activity of the DMN and thus a more stable mPFC-insula connection, which could explain why ASD patients exhibit more internally-directed cognition and respond less to the external environment [39]. Time variability reflects the tendency for an ROI to be reconfigured to or its functional integration flexibility with different neural systems, and variability in the frontal may be a potential biomarker for the diagnosis of ASD, which was experimentally supported by our results.
4.4 The preference of feature distribution at beta frequency subband
Results from frequency subband distribution also indicated a Beta preference. Coherence of Beta frequency is thought to be associated with attentional and cognitive processes [42]. Beta signal tends to occur predominantly in frontal and central regions and is associated with positive thinking and mindsets [43]. Bolsma and colleagues found that children with ASD have connectivity reduction in 51 ROIs pairs, especially in the Beta frequency. Further, in the Beta band they found significant decreases in whole-brain average connectivity strength and clustering coefficient in ASD patients in the Beta band [44]. Study has shown that reduced ability to recruit Beta band synchronization in large-scale networks may contribute to widespread cognitive difficulties in ASD [45].
4.5 Limitations of this study
Our study has some limitations. Firstly, the 19-chnanel EEG was used, and too few channels led to inability to conduct source reconstruction to locate the EEG signals at cortex level. To refine this, future studies are suggested to use EEG recording instrument with higher spatial resolution, in order to acquire convergence evidence between functional magnetic resonance imaging and EEG. Secondly, the potential to elucidate the mechanisms of ASD were subject to data type of cross-section. Future studies are expected to include longitudinal follow-up EEG to summarize the information from development track to reach better classification performance and provide a new perspective for the assessment of disease progression.
4.6 Conclusion
In summary, our study demonstrated that the in the condition of 3s-window width and 50% moving step, the dynamic local graph theory indices provided the best classification performance and needed less features in the optimal feature subset. In the meanwhile, the results from feature selection process showed an obvious dominance for frontal lobe and Beta band, which could help explain the inner mechanisms of ASD from a dynamic perspective.
Ethics approval and consent to participate This work involved human subjects or animals in its research. Approval of all ethical and experimental procedures and protocols was granted by the Ethics Committee of School of Public Health, Sun Yat-sen University under Approval 2021- No.081, and performed in line with the Declaration of Helsinki. Informed consent was obtained from all subjects involved in the study.
Consent for publication Not applicable.
Data Availability Data related to the current study are available from the corresponding author on reasonable request.
Competing Interests The authors declare no competing interests.
Funding This research was funded by the Guangdong Basic and Applied Basic Research Foundation under Grand No. 2022A1515011237 and No. 2023A1515011951.
Author contribution Zhang Jinxin and Luo Hao were responsible for conceptualization; Luo Hao was responsible for methodology; Luo Hao performed formal analysis and investigation; Luo Hao wrote the original draft; Zhang Jinxin, Yang Shuo, Zhang Nanxiang, Huang Leen, Ge Yingfeng, Chen Ang and Zhu Jianping were responsible for review and editing; Chen Ang and Zhu Jianping provided resources. The algorithm concept and design of this paper were contributed by all authors. All authors also participated in the experimental evaluation. Finally, all authors read and approved the final manuscript.
Acknowledgments The authors would like to thank the participants of the Department of Pediatrics and the Department of Science and Education of Zhongshan Bo’ai Hospital (Zhongshan, China) for supporting the data collection of this study.
Authors' information
Hao Luo received the Bachelor’s degree in preventive medicine from China Medical University, Shenyang, Liaoning, China, in 2016, and is currently pursuing the Master’s degree in the Department of Medical Statistics, School of Public Health, Sun Yat-sen University, Guangzhou, Guangdong, China, since 2021. His research interests include time series analysis, medical statistical methods, and machine learning methods applied to the differential diagnosis of diseases.
Shuo Yang received the Bachelor’s degree in preventive medicine from Jining Medical College, Jining, Shandong, China, in 2015, and received the Master’s degree in Epidemiology and Health Statistics from Guangdong Pharmaceutical University, Guangzhou, Guangdong, China, in 2018, and is pursuing the doctorate degree with the Department of Medical Statistics, School of Public Health, Sun Yat-sen University from 2021. His research interests include time series analysis, medical statistical methods, and feature discretion for prediction model.
Nanxiang Zhang received the Bachelor’s degree in preventive medicine from Kunming Medical University, Kunming, Yunnan, China, in 2017. His research interests include mHealth, machine learning, deep learning, mediation analysis, and time series analysis in multivariate statistics.
Leen Huang received the Bachelor’s degree in mathematics from South China Agricultural University, Guangzhou, Guangdong, China, in 2020, and received the master’s degree in Epidemiology and Health Statistics from Sun Yat-sen University, Guangzhou, Guangdong, China, in 2023. Her research interests include time series analysis, medical statistical methods and deep learning applied to the differential diagnosis of diseases.
Yingfeng Ge received the Bachelor’s degree in preventive medicine from Shanghai University of Traditional Chinese Medicine, Shanghai, China, in 2021, and is currently pursuing master’s degree with the Department of Medical Statistics, School of Public Health, Sun Yat-sen University, Guangzhou, Guangdong, China, since 2021. His research interests include time series analysis, medical statistical methods and machine learning method applied to the differential diagnosis of diseases.
Ang Chen received the Bachelor’s degree in preventive medicine from Huazhong University of Science and Technology, Wuhan, Hubei, China, and received the master’s degree in Epidemiology and Health Statistics in the Department of Medical Statistics, School of Public Health, Sun Yat-sen University, Guangzhou, Guangdong, China in 2010. He is working in the Department of Science and Education, Zhongshan Bo’ai Hospital, Zhongshan, China. His research interests is epidemiology of maternal and child health care.
Jianping Zhu received the Bachelor’s degree in preventive medicine from Huazhong University of Science and Technology, Wuhan, China in 1990. She is working in Department of Pediatrics, Zhongshan Bo’ai Hospital, Zhongshan 528400, China as associate chief physician
Jinxin Zhang received the Bachelor’s degree in precision instrument engineering from Tianjin University, Tianjin, China, in 1989, the Master’s degree in medical statistics from Shanxi Medical University, Taiyuan, Shanxi, China, in 1997, and the Ph.D. degree in medical statistics from Air Force Medical University, Xi’an, Shaanxi, in 2000. From 1989 to 2000, he was a Technician and then a Technologist at Second Hospital of Shanxi Medical University. In 2000, he was a Postdoctoral Researcher at Sun Yat-sen University, Guangzhou, Guangdong, China. In 2003, he became a Lecturer at Sun Yat-sen University. Since 2004, he has been an Associate Professor at Sun Yat-sen University and then a Professor at Sun Yat-sen University in 2023. His research interests include research design, time series analysis and statistical prediction.
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No competing interests reported.