Gauss continuous wavelet transforms (CWT) were calculated as follows:

(1)$$CWTf(\mathrm{a},\mathrm{b})={\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}f(t)\cdot \overline{{\psi }_{ab}(t)}𝑑t$$

${\psi }_{ab}$ is the family of wavelet analysis functions, which can be obtained by translating the wavelet function (Eqn. 1) by b units and telescoping the transformation by a units:

(2)$${\psi }_{ab}(t)=\frac{1}{\sqrt{a}}\psi \left(\frac{t-b}{a}\right)$$

The schematic diagram of a continuous wavelet transform, as shown in Fig. 1. Table 3 gives the scale and frequency correspondence.

Fig. 1.

Schematic diagram of continuous wavelet transform.

The CWT method was used to decompose the EEG signals. Formulae were the same as Eqns. 1,2. Wavelets of the 11th and 17th scales in the JME seizure period were extracted. The phase of the 17th scale EEG signal was used as the reference. The highest wave amplitude of the 11th scale EEG signal was extracted at different phase angles to observe the PAC relationship of the two scales during a seizure.

After decomposing the raw EEG data using CWT, the EEG signal at a given scale was extracted and the correlations between different leads at the same scale were analyzed using a correlation analysis method calculated as follows:

(3)$${\mathrm{C}}_{\mathrm{m},\mathrm{n}}({\mathrm{a}}_1,{\mathrm{a}}_2)=\frac{{\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}{\mathrm{W}}_{\mathrm{m}}({\mathrm{a}}_1,\mathrm{t}){\mathrm{W}}_{\mathrm{n}}({\mathrm{a}}_2,\mathrm{t})\mathrm{dt}}{\sqrt{{\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}{\left[{\mathrm{W}}_{\mathrm{m}}({\mathrm{a}}_1,\mathrm{t})\right]}^2\mathrm{dt}{\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}{\left[{\mathrm{W}}_{\mathrm{n}}({\mathrm{a}}_2,\mathrm{t})\right]}^2\mathrm{dt}}}$$

Where m and n represent different EEG leads, a${}_{\mathrm{1}}$ and a${}_{\mathrm{2}}$ represent different scales of EEG and the coefficient of correlation between different leads was calculated from Eqn. 3 and represented the degree of correlation between two leads at a given scale.

Characteristics of the EEG signal that can be extracted from the analysis are as follows:

(a) The raw EEG waveform at a particular scale, enables observation and comparison of the characteristics of simultaneous waveform changes between different leads.

(b) The time-frequency and structural characteristics of EEG signals at different scales on a given lead allows observation and comparison of the interrelation between different scales of EEG.

(c) The coefficients of the correlation between different leads of the EEG at a particular scale can be measured, representing the degree of correlation between two leads at the particular scale, while the dynamic evolution over time can be observed for a given time period.

The 11th scale EEG information during seizure was extracted and the waveform, wave amplitude, phase and other characteristics observed (Fig. 10a). The 11th scale EEG signal of JME subjects in the first two seconds before seizure tended to be similar in waveform and consistent in phase, but lower in amplitude. At seizure onset, the waveform amplitude suddenly increased and there was a mild phase difference from the anterior to the posterior head lead. Following the seizure, the 11th scale EEG gradually returned to its original state.

Fig. 10.

Waveform of 11th scale for ictal EEG of (a) JME subjects and (b) normal controls. Note: U, Wavelet coefficients.

Overall wave amplitude was lower in the normal control group, with no fixed correlation in different leads between the wave amplitude and phase (Fig. 10b).

Characteristics of the EEG waveform in the different leads were then investigated at the 17th scale. Results are given in Fig. 11, demonstrating that the wave amplitude increased and decreased at approximately one second before and after the seizure, forming two wave peaks. The wave amplitude dropped sharply, followed by a sharp rise during the seizure, forming a wave valley. The waveform of the 17th scale EEG signal in the normal control group was lower in overall amplitude, with a smoother increase and decrease at the same time.

Fig. 11.

Waveform of 17th scale for ictal EEG of JME subjects and normal controls. Note: U, Wavelet coefficients.

Seizure was segmented into one second intervals and the coefficient of correlation was calculated between different leads (Fig. 13). Two seconds prior to the seizure, the range of leads with a significant positive correlation in the anterior head gradually increased and the correlation between the posterior and anterior head leads gradually changed from no correlation to a mild positive correlation. The correlation increased significantly during the one to two seconds of the seizure. In the subsequent one to two seconds after a seizure, the range of leads with significantly higher correlations gradually decreased. Additionally, the coefficient of correlation gradually decreased and returned to preictal magnitude.

Fig. 13.

Dynamic evolution of correlation coefficients between the leads at the 11th scale for ictal EEG of JME subjects. Note: Lead 1–Lead 16 correspond to FP1–T6. (a) 2 s before seizure. (b) 1 s before seizure. (c) The first second of the seizure. (d) The 2 s of the seizure. (e) 1 s after seizure. (f) 2 s after seizure. R, Correlation coefficients.

Fig. 14 shows the dynamics of the correlation at the 17th scale. The process of change is similar to that for the 11th scale.

Fig. 14.

Dynamic evolution of correlation coefficients between the leads at the 17th scale for ictal EEG of JME subjects. Note: Lead 1–Lead 16 correspond to FP1–T6. (a) 2 s before seizure. (b) 1 s before seizure. (c) The first second of the seizure. (d) The 2 s of the seizure. (e) 1 s after seizure. (f) 2 s after seizure. R, Correlation coefficients.

Results reported in the previous subsection suggest that the correlations in the anterior head were the earliest to exhibit synchronization. The FP1 lead was chosen as the reference lead. In this study, the EEG in JME subjects were segmented into one second blocks to observe the change of correlation in different periods. The preictal period of JME subjects was characterized by disruption of the negative correlation between the anterior and posterior head leads and the gradual expansion of the range of leads with a positive correlation. Additionally, a further increase was observed in the coefficients of leads with a positive correlation during this period. The post-seizure period was characterized by both a gradual decrease in the range of leads with positive correlations and a gradual decrease in the coefficients of correlation. Results revealed a gradual recovery of the negative correlation between the anterior and posterior parts of the head. The extent of involvement of each lead was not the same throughout the seizure. Fig. 15 shows the dynamic evolution of correlation coefficients between FP1 and the other lead at the 11th scale for ictal EEG of JME subjects.

Fig. 15.

Dynamic evolution of correlation coefficients between FP1 and the other lead at the 11th scale for ictal EEG of JME subjects.

As shown in Fig. 16. A comparison of the interictal period and normal controls revealed that the interictal coefficient of correlation was higher in FP2, F4, and F8. The preictal correlation was higher in FP2, F3, and F8 in JME subjects than in the normal controls. It is shows that significantly higher correlation coefficients were found during seizure compared with controls for all leads except F7 and T5. The postictal correlations were stronger in FP2, F3, F4, and F8 in the JME subjects compared with normal controls.

Fig. 16.

Comparison of the 11th scale EEG FP1 lead with other leads at different periods in JME subjects and normal controls. Note: (a) Interictal vs. normal controls. (b) Preictal vs. normal controls. (c) Ictal vs. normal controls. (d) Postictal vs. normal controls. ✳(Red start): p 0.001; ✳(Yellow start): p 0.01; ✳(Green start): p 0.05; R, Correlation coefficients.