**1. Introduction**

### **1.1 EEG and epilepsy**

Epileptic seizures usually do not emerge during the consultation. The diagnosis of epilepsy begins with a conversation with the individual and those who witnessed the seizures. [1] An electroencephalogram (EEG) is also used for the diagnosis of epilepsy. The gold standard for diagnosis of epilepsy is simultaneous ictal EEG recording with video, but this method is not applicable for many patients. The presence of epileptic paroxysmal abnormalities can help with the diagnosis. If a non-expert makes the diagnosis based on EEG findings alone rather than seizure symptoms, misinterpretation of the EEG findings may increase the false-positive diagnosis of epilepsy. Many physicians anticipate that EEG diagnosis for epilepsy will become possible with technological advances, even when no EEG abnormalities are present. EEG is useful not only for diagnosis, but also for monitoring during the course of treatment. [2] Psychiatric disorders occur more frequently as comorbidities in patients with epilepsy [3], and they can affect quality of life. [4]

#### **1.2 EEG and nonlinearity**

EEG is characterized by its nonlinearity. [5] Nonlinear dynamics is a concept that includes chaos. Therefore, the adaptation of nonlinear EEG analysis is more useful than that of linear EEG analysis. [6] In nonlinear dynamics, the time series data of EEG can be transformed into a reconstructed state space, which is calculated according to the embedded theorem [7, 8], and the dynamic attractors can be reconstructed. The reconstruction enables us to estimate nonlinear statistics such as fractal dimension and bifurcation structure. The attractor here is a set of trajectories where all of the nearest trajectories converge. [9] CD [9–11], which is a kind of fractal dimension, is a dimension that is occupied by the attractor in phase space. The method of Grassberger et al. is often used. [10] The lyapunov exponent is the degree of exponential separation between orbits, and measures the extent by which nearby points on an attractor diverge or converge with respect to each other while moving along any trajectory of the attractor. [9, 12] If the largest lyapunov exponent is greater than zero, this shows the presence of deterministic chaos. If the lyapunov exponent is less than or equal to zero, this shows a periodic or quasiperiodic motion, respectively. Furthermore, to show the nonlinearity of EEG, generation of surrogate data with linear characteristics and demonstration of a significant difference between them are necessary. In addition, nonlinear analysis is possible with the assumption that EEG exhibits weak stationarity, that the mean and the variance are normally distributed in the evaluated interval, and that no noise is present. [13]

#### **1.3 Epilepsy and nonlinear EEG analysis**

Many studies on the nonlinear analysis of EEG and epilepsy have been reported, including reviews concerning ictal EEG detection and machine leaning approaches. [14–16] Ideally, interictal EEG with no paroxysmal abnormalities should be used to diagnose epilepsy and comorbid psychiatric disorders by using computerized analysis rather than expert observation and interpretation.

#### **1.4 Objectives in this review**

Therefore, in the present review, we investigated the reports on the nonlinear analysis of EEG between normal and epileptic groups, focusing on the diagnosis of epilepsy and comorbid psychiatric disorders.

### **2. Methods**

#### **2.1 Public data set in Andrzejak 2001**

A literature search of Scopus and PubMed was performed. In addition, we identified other relevant literature. We selected only about English language reports that compared normal and epilepsy groups. Many reports used data from Andrzejak 2001. [17] They prepared and used five different data sets, A-E, which each contain 100 single channels from EEG segments of 23.6-sec duration. These segments were

*Is EEG a Useful Examination Tool for Diagnosis of Epilepsy and Comorbid Psychiatric Disorders? DOI: http://dx.doi.org/10.5772/intechopen.94352*

selected and extracted from continuous multichannel EEG recordings after visual inspection for artifacts, e.g., due to muscle activity or eye movements. Set A and set B consisted of EEGs from five healthy volunteers with eyes open and closed, respectively. Set C and set D consisted of EEGs from five patients in the epileptogenic zone (set D) and from the hippocampal formation of the opposite hemisphere of set D (set C). Set E contains ictal activity. Set A and set B were recorded extracranially, whereas set C, set D, and set E were recorded intracranially.

#### **2.2 Nonlinearity of the data set**

The objective of the study by Andrzejak 2001 was examination of nonlinearity. They generated 39 surrogate data points from all EEG segments for nonlinear prediction error and CD according to the weak stationarity assumption. Nonlinearity was found except in set A for nonlinear prediction error, but only in set D and set E for CD. They discussed that they cannot rule out the possibility that the surrogate test compared to the surrogate data with linear properties including the weak stationarity may result in a false-positive rejection of nonstationarity, and that the surrogate test has neither high sensitivity nor specificity for nonstationarity in nonlinear dynamics systems. [17] Thuraisingham reexamined the data using MPR complexity and normalized shanon spectral entropy, taking into account the probability distribution function. [18] He carried out a surrogate test using the Amplitude Adjusted Fourier Transform method to generate 1000 surrogate data points for evaluation of entropy and complexity. The degree of nonlinearity was set E > set D > set C > set B > set A. However, when adjusted for the effect of noise, all data showed the same degree of nonlinearity by the above method. Set A showed more nonlinearity than set B, and Thuraisingham concluded that denoising with a wavelet was effective for nonlinearity. In light of these results, we considered all five EEG sets as nonlinear and examined the difference between the normal EEG and interictal EEG among the five EEG sets. There were many studies on the comparison between other sets vs. set E. However, an expert can easily interpret set E as ictal. The diagnosis of epilepsy from interictal EEG with no paroxysmal abnormalities is meaningful for both specialists and non-specialists. Therefore, in this review, in the studies with explicit comparisons with the data set of Andrzejak 2001, A vs. C, A vs. D, AB vs. CD vs. E, A vs. B vs. C vs. D vs. E, B vs. C, B vs. D, A vs. D vs. E, A vs. C vs. E, and AB vs. CD, were examined.

### **3. Results**

#### **3.1 Normal vs. epilepsy**

The development of feature extraction with nonlinear analysis methods and machine learning has been reported in studies of various combinations of classifications on EEG diagnosis of epilepsy. (**Table 1**). [19–79] **Table 2** shows the details of the classification. Sixty studies using the Andrzejak 2001 data set were selected, and two studies between normal and epileptic groups were selected. Although set C (the opposite site of the epileptogenic zone) and set D (the site of the epileptogenic zone) were interictal and intracranial EEG, the results for B vs. C (99.3% accuracy) and B vs. D (99.5% accuracy) by Gupta 2018 [29] and the results for A vs. D (100% accuracy) by Kaya 2015 [45] and 2018 [30] and for A vs. C (99.7% and 99.6% accuracy) by Raghu 2017 [36] and Liu 2020 [21] were reported. The feature extraction methods and the classifiers were different in each study. Nevertheless,


*Is EEG a Useful Examination Tool for Diagnosis of Epilepsy and Comorbid Psychiatric Disorders? DOI: http://dx.doi.org/10.5772/intechopen.94352*



*Accuracy = (TP+ TN)/(TP + FP+ TN+ FN); TP, TN, FP and FN mean true positive, true negative, false positive and false negative, respectively.*

*\* , †, ‡The accuracy corresponds to each feature extraction and classifier with the symbol.*

#### **Table 1.**

*Results for the data of Andrzejak 2001.*


#### **Table 2.**

*The mean (standard deviation) and number of results for each comparison.*

#### *Is EEG a Useful Examination Tool for Diagnosis of Epilepsy and Comorbid Psychiatric Disorders? DOI: http://dx.doi.org/10.5772/intechopen.94352*

these results were clinically interesting and reasonable. Gruszczyńska 2019 (86.8% accuracy) reported that interictal Fp1 EEG and normal Fp1 EEG using the feature extraction of RQA and RP were classified by SVM. [80] No detailed descriptions were provided for the focal side. Jacob 2016 (100% accuracy) reported the classification of interictal EEG and normal EEG. [81] However, no detailed description was provided of EEGs that were artifact free or with no paroxysmal abnormalities.
