# Variation Trends of Fractal Dimension in Epileptic EEG Signals
## 3 Results and Discussion  
All 109 groups of 800-s EEG signals were analyzed by using Higuchi and RSE algorithms. The double logarithmic plots were shown in Figure 2, including the typical curves of raw and denoised signal with Higuchi and RSE-f1 algorithm. The typical EEG signals from raw and denoised data with seizure onset and the corresponding \(D_{\mathrm{c}}\) values were shown in Figure 3. The results of the raw data of CHB14_04 and CHB24_01 could be observed in Figure 3a,b, respectively. In the seizure status, \(D_{\mathrm{c}}\) was increased in CHB14_04 but decreased in CHB24_01. However, all \(D_{\mathrm{c}}\) were increased in the seizure status after denoising, as shown in Figure 3c,d. It should be noted that the variation of \(D_{\mathrm{c}}\) values between seizure and normal statuses obtained by using Higuchi algorithm was the least obvious, while that of RSE-f2 sc algorithm was the most obvious, enabling the effective distinguishing of different status based on \(D_{\mathrm{c}}\) values. The more obvious variation of RSE-f2 sc algorithm could be attributed to the influence of scaling region interception method. The \(D_{\mathrm{c}}\) values of RSE-f1 sc and RSE-f2 sc could be below 1 in the normal status, which indicate that the non-fractal nature of EEG signals during normal status. In our recent publication [23], it had been demonstrated that only RSE algorithm could quantify the complexity of non-fractal features, and there could be a continuity of \(D_{\mathrm{c}}\) variation across fractal and non-fractal. Figure 1: The calculation flowchart of fractal analysis on epileptic EEG signals. It was generally regarded that the brain activities during seizure status would become more complex. Since \(D_{\rm c}\) reflect the complexity of features such as signals and surfaces, it is not clear how to detect the brain activity in the brain. Figure 3: Typical EEG signals from (**a**) CHB14_04 raw data, (**b**) CHB24_01 raw data, (**c**) CHB14_04 denoised data and (**d**) CHB_01 denoised data with seizure durations (the range between red dotted vertical lines) and the corresponding variations of \(D_{\rm c}\) values, which were calculated by using Higuchi, RSE-f1, RSE-f1 sc, RSE-f2 and RSE-f2 sc algorithms, respectively. Figure 2: Four typical double logarithmic curves of (**a**) raw signal with Higuchi algorithm, (**b**) denoised signal with Higuchi algorithm, (**c**) raw signal with RSE-f1 algorithm, and (**d**) denoised signal with RSE-f1 algorithm. could be inferred that \(D_{\text{c}}\) should be larger during seizure status [23]. However, the two opposite variation trends of \(D_{\text{c}}\) in Figure 3b were different, which were both found in various publications as mentioned above. It was speculated that the influence of noise was the cause for such a difference, thus the \(D_{\text{c}}\) values of the seizure and normal statuses for all EEG signals were compared. The fractal analysis on EEG signals was illustrated in Figure 4, where the 10 subfigures were the mean values of \(D_{\text{c}}\) by using various algorithms from all 109 groups of 800-s raw and denoised EEG signal. As shown in Figure 4, the mean values of \(D_{\text{c}}\) were larger in the seizure status at most groups of both raw and denoised EEG signals, and the trend was more obvious after denoising. To further analyze the influence of denoising on EEG signals based on fractal analysis, all \(D_{\text{c}}\) values in Figure 4 were statistically analyzed. For raw EEG signals, \(D_{\text{c}}\) values were not much different from various algorithms between the seizure and normal statuses, and \(D_{\text{c}}\) values of the seizure status were generally larger. The \(D_{\text{c}}\) values of RSE-f1 were the largest while those of RSE-f2 sc were the lowest, and all \(D_{\text{c}}\) values were above 1, as shown in Figure 5a. After denoising, all \(D_{\text{c}}\) values were reduced for various algorithms. The \(D_{\text{c}}\) values of Higuchi were the largest, and those of RSE-f2 sc were the lowest.