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Edited by: Plamen Ch. Ivanov, Boston University, United States

Reviewed by: Marina De Tommaso, University of Bari Aldo Moro, Italy; Paul Bogdan, University of Southern California, Los Angeles, United States; Rudolf Marcel Füchslin, Zurich University of Applied Sciences, Switzerland

This article was submitted to Fractal and Network Physiology, a section of the journal Frontiers in Physiology

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

Epilepsy is one of the most common disorders of the brain. Clinically, to corroborate an epileptic seizure-like symptom and to find the seizure localization, electroencephalogram (EEG) data are often visually examined by a clinical doctor to detect the presence of epileptiform discharges. Epileptiform discharges are transient waveforms lasting for several tens to hundreds of milliseconds and are mainly divided into seven types. It is important to develop systematic approaches to accurately distinguish these waveforms from normal control ones. This is a difficult task if one wishes to develop first principle rather than black-box based approaches, since clinically used scalp EEGs usually contain a lot of noise and artifacts. To solve this problem, we analyzed 640 multi-channel EEG segments, each 4

Epilepsy is a chronic neurological disease characterized by the paroxysmal seizures that affects people of all ages (Li et al.,

There are a variety of ways to represent EEG. Among the simplest and most popular are to compute the amplitude values (Toet et al.,

To develop accurate fundamental principle-based instead of black-box based approaches to automatically detect epileptiform discharges, it is critical to comprehensively account for all the major features in the EEG that distinguish epileptiform discharges from normal ones. Based on this rationale, we will consider the long range correlation properties of EEG, together with the Signal Range and the relative energy in the alpha wave band of an EEG signal. The long range correlation properties are characterized by the Hurst parameter

The human brain is comprised of numerous neurons that form a complicated network (Bashan et al.,

The remainder of the paper is organized as follows. In section 2, we briefly describe the EEG data and analysis methods. In section 3, we present results of our analysis. In section 4, we summarize our findings.

The EEG data analyzed in this study were from the First Affiliated Hospital to Guangxi Medical University. The studies involving human participants were reviewed and approved by the ethics committee of the First Affiliated Hospital to Guangxi Medical University. The participants provided their written informed consent to participate in this study. Fifty-nine epilepsy patients underwent a 3 h video-EEG monitoring with 19-channel EEG recording with electrodes placed on the scalp under the international 10–20 system at 256 Hz sampling rate. The electrode impedances were kept below 10

All epileptiform discharges were annotated by an experienced clinical neurophysiologist based on the average montage with an analog bandwidth of 0.1 ~ 70

Spike: The spikes are the most basic paroxysmal EEG activity, with a duration of 20~70

Sharp: A sharp wave is similar to the spike, and its time limit is 70~200

Spike and slow wave complex: An epileptiform pattern consisting of a spike and an associated slow wave following the spike, which can be clearly distinguished from the background activity; may be single or multiple (Kane et al.,

Sharp and slow wave complex: An epileptiform pattern consisting of a sharp wave and an associated slow wave following the sharp wave, which can be clearly distinguished from the background activity; may be single or multiple (Kane et al.,

Polyspike complex: A sequence of two or more spikes.

Polyspike and slow wave complex: An epileptiform pattern consisting of two or more spikes associated with one or more slow waves.

Spike rhythm: refers to a widespread 10~25

Typical waveforms of the 7 major epileptiform EEG, where

Recall that a few epileptiform discharge waveforms were considered to simultaneously belong to more than 1 of the 7 different epileptiform discharges. Because of this, further considering the differences among the seven epileptiform discharges becomes impossible and is not pursued here.

Often EEG epileptic discharges are associated with a larger amplitude than the normal control EEG. This motivates us to compute a simple statistic, which we call Signal Range, to quantify this effect. It is computed as follows:

where

In clinical applications, the brain wave is often categorized into five bands: delta (0.5~3

AFA utilizes an adaptive detrending algorithm to extract globally smooth trend signals from the data for a given time scale and then analyzes the scaling of the residuals to the fit as a function of the time scale (Hu et al.,

Suppose starting from a stationary incremental process

where

After we get the global trend

The above equation means by calculating the variance of the residual between the original random walk process and the fitted global trend under a varying window _{2} _{2}

To illustrate the procedures described, we have shown in _{2} _{2}

Illustration of estimation of the Hurst exponent using AFA:

Brain activities involve spatial-temporal coordinated dynamics of numerous neurons in different regions of the brain, i.e., involve numerous functional brain networks. To better characterize the synergistic effects among the brain networks, it is important to construct brain networks based on multi-channel EEG signals. For this purpose, we consider networks with nodes being the 19 electrodes. Between any two of the nodes, we consider the difference between the two associated EEG signals. This is illustrated in

A 19 × 19 table consisting of the difference of the EEG signals between two electrodes.

Fp1-Fp1 | Fp1-Fp2 | Fp1-F7 | Fp1-F3 | Fp1-Fz | Fp1-F4 | Fp1-F8 | Fp1-T3 | Fp1-C3 | Fp1-Cz | Fp1-C4 | Fp1-T4 | Fp1-T5 | Fp1-P3 | Fp1-Pz | Fp1-P4 | Fp1-T6 | Fp1-O1 | Fp1-O2 |

Fp2-Fp1 | Fp2-Fp2 | Fp2-F7 | Fp2-F3 | Fp2-Fz | Fp2-F4 | Fp2-F8 | Fp2-T3 | Fp2-C3 | Fp2-Cz | Fp2-C4 | Fp2-T4 | Fp2-T5 | Fp2-P3 | Fp2-Pz | Fp2-P4 | Fp2-T6 | Fp2-O1 | Fp2-O2 |

F7-Fp1 | F7-Fp2 | F7-F7 | F7-F3 | F7-Fz | F7-F4 | F7-F8 | F7-T3 | F7-C3 | F7-Cz | F7-C4 | F7-T4 | F7-T5 | F7-P3 | F7-Pz | F7-P4 | F7-T6 | F7-O1 | F7-O2 |

F3-Fp1 | F3-Fp2 | F3-F7 | F3-F3 | F3-Fz | F3-F4 | F3-F8 | F3-T3 | F3-C3 | F3-Cz | F7-C4 | F3-T4 | F3-T5 | F3-P3 | F3-Pz | F3-P4 | F3-T6 | F3-O1 | F3-O2 |

Fz-Fp1 | Fz-Fp2 | Fz-F7 | Fz-F3 | Fz-Fz | Fz-F4 | Fz-F8 | Fz-T3 | Fz-C3 | Fz-Cz | Fz-C4 | Fz-T4 | Fz-T5 | Fz-P3 | Fz-Pz | Fz-P4 | Fz-T6 | Fz-O1 | Fz-O2 |

F4-Fp1 | F4-Fp2 | F4-F7 | F4-F3 | F4-Fz | F4-F4 | F4-F8 | F4-T3 | F4-C3 | F4-Cz | F4-C4 | F4-T4 | F4-T5 | F4-P3 | F4-Pz | F4-P4 | F4-T6 | F4-O1 | F4-O2 |

F8-Fp1 | F8-Fp2 | F8-F7 | F8-F3 | F8-Fz | F8-F4 | F8-F8 | F8-T3 | F8-C3 | F8-Cz | F8-C4 | F8-T4 | F8-T5 | F8-P3 | F8-Pz | F8-P4 | F8-T6 | F8-O1 | F8-O2 |

T3-Fp1 | T3-Fp2 | T3-F7 | T3-F3 | T3-Fz | T3-F4 | T3-F8 | T3-T3 | T3-C3 | T3-Cz | T3-C4 | T3-T4 | T3-T5 | T3-P3 | T3-Pz | T3-P4 | T3-T6 | T3-O1 | T3-O2 |

C3-Fp1 | C3-Fp2 | C3-F7 | C3-F3 | C3-Fz | C3-F4 | C3-F8 | C3-T3 | C3-C3 | C3-Cz | C3-C4 | C3-T4 | C3-T5 | C3-P3 | C3-Pz | C3-P4 | C3-T6 | C3-O1 | C3-O2 |

Cz-Fp1 | Cz-Fp2 | Cz-F7 | Cz-F3 | Cz-Fz | Cz-F4 | Cz-F8 | Cz-T3 | Cz-C3 | Cz-Cz | Cz-C4 | Cz-T4 | Cz-T5 | Cz-P3 | Cz-Pz | Cz-P4 | Cz-T6 | Cz-O1 | Cz-O2 |

T4-Fp1 | T4-Fp2 | T4-F7 | T4-F3 | T4-Fz | T4-F4 | T4-F8 | T4-T3 | T4-C3 | T4-Cz | T4-C4 | T4-T4 | T4-T5 | T4-P3 | T4-Pz | T4-P4 | T4-T6 | T4-O1 | T4-O2 |

T5-Fp1 | T5-Fp2 | T5-F7 | T5-F3 | T5-Fz | T5-F4 | T5-F8 | T5-T3 | T5-C3 | T5-Cz | T5-C4 | T5-T4 | T5-T5 | T5-P3 | T5-Pz | T5-P4 | T5-T6 | T5-O1 | T5-O2 |

P3-Fp1 | P3-Fp2 | P3-F7 | P3-F3 | P3-Fz | P3-F4 | P3-F8 | P3-T3 | P3-C3 | P3-Cz | P3-C4 | P3-T4 | P3-T5 | P3-P3 | P3-Pz | P3-P4 | P3-T6 | P3-O1 | P3-O2 |

Pz-Fp1 | Pz-Fp2 | Pz-F7 | Pz-F3 | Pz-Fz | Pz-F4 | Pz-F8 | Pz-T3 | Pz-C3 | Pz-Cz | Pz-C4 | Pz-T4 | Pz-T5 | Pz-P3 | Pz-Pz | Pz-P4 | Pz-T6 | Pz-O1 | Pz-O2 |

P4-Fp1 | P4-Fp2 | P4-F7 | P4-F3 | P4-Fz | P4-F4 | P4-F8 | P4-T3 | P4-C3 | P4-Cz | P4-C4 | P4-T4 | P4-T5 | P4-P3 | P4-Pz | P4-P4 | P4-T6 | P4-O1 | P4-O2 |

T6-Fp1 | T6-Fp2 | T6-F7 | T6-F3 | T6-Fz | T6-F4 | T6-F8 | T6-T3 | T6-C3 | T6-Cz | T6-C4 | T6-T4 | T6-T5 | T6-P3 | T6-Pz | T6-P4 | T6-T6 | T6-O1 | T6-O2 |

O1-Fp1 | O1-Fp2 | O1-F7 | O1-F3 | O1-Fz | O1-F4 | O1-F8 | O1-T3 | O1-C3 | O1-Cz | O1-C4 | O1-T4 | O1-T5 | O1-P3 | O1-Pz | O1-P4 | O1-T6 | O1-O1 | O1-O2 |

O2-Fp1 | O2-Fp2 | O2-F7 | O2-F3 | O2-Fz | O2-F4 | O2-F8 | O2-T3 | O2-C3 | O2-Cz | O2-C4 | O2-T4 | O2-T5 | O2-P3 | O2-Pz | O2-P4 | O2-T6 | O2-O1 | O2-O2 |

SVD is a decomposition method that can be applied to arbitrary matrices. For an

where, _{n×n} and _{m×m} are orthogonal matrices, which are composed of eigenvectors of square matrices, ^{T} and ^{T}_{n×m}, called the singular value matrix, is non-zero only on the main diagonal with the elements there being the square root of the eigenvalues of ^{T} (or ^{T}_{ii} = σ_{i}, ^{T} (or ^{T}

Based on the networks constructed using the three variables, the signal range, the relative energy of the alpha wave component, and the Hurst parameter, and using SVD, we can infer the localization of each type of epileptiform discharges. The approach is as follows. For each network of a subject, after we obtain the SVD, we project each column vector of the network to the singular vector corresponding to the largest singular value. The vector is then retained if the absolute value of the projection coefficient is ≥ 0.5. These vectors allow us to determine which channels of the original data are important. The procedure is applied to each of the three networks of the subject. We assume the common channels indicate the localization of this particular type of epileptiform discharge for that subject. As this localization may vary among subjects, we determine the most likely localization of a particular type of epileptiform discharge for all relevant subjects by requiring that each channel occurs at least with certain probability. Here, we has chosen this probability to be 0.55.

Random forest (RF) is an ensemble-based learning technique for classification (Cutler et al.,

The objective of the RF classifiers used here is to classify which of the two classes an EEG signal belongs to: normal or epileptic discharges. The inputs to the RF classifier are the square of the largest singular values of the three networks (e.g., based on the Signal Range, the energy of the alpha wave component, and Hurst parameters) based on SVD. Following usual practice, we have randomly taken one-third of the total data as testing data and two-thirds of the data for training the model in this paper.

To assess the consistency of the diagnosis by the neurologists and machine classification, we need to compute the classification accuracy. This can be accomplished by computing the receiver operating characteristic (ROC) curve and many statistics derived from the ROC curve. In fact, all these are best understand with the confusion matrix, which is a table with two rows and two columns that reports the number of false positives (FP), false negatives (FN), true positives (TP), and true negatives (TN). From them we can define three major metrics:

Note that the sensitivity is also called true positive rate (TPR) and 1 −

The ROC is a plot of TPR vs. FPR using different threshold values as a sweeping variable. Not suffering from class imbalance, the ROC is a good way to characterize imbalanced data sets. The area below the ROC is called area under curve (AUC). Its value takes from 0 to 1. A value of AUC being 0.5 means the classification model has no predictive ability at all. On the other hand, when the value of AUC reaches 1, it means that the probability density functions of negative and positive classes are completely separated, and the prediction ability is 100%. This is equivalent to the ROC being a unit step function.

Recall that among the 640 EEG data sets analyzed here, 69, 82, 174, 72, 64, 77, and 2 data sets are for spike, sharp, spike and slow wave complex, sharp and slow wave complex, polyspike complex, polyspike and slow wave complex, and spike rhythm, respectively, and 100 are for normal controls.

Comparison of epileptiform discharges and normal EEG:

Same as

To complement the Signal Range, let us examine the long range correlations captured by the Hurst parameter

Scatter plots using features Signal Range and the Hurst parameter

To compute the classification accuracy based on the Signal Range and the Hurst parameter, we have employed the RF classifier. We have randomly taken two-thirds of the data as the training data and the remaining one-third of the total data as the testing data. The class distribution of the samples in the training and testing data set is summarized in

Class distribution of the samples in the training and test data sets.

Normal controls | 66 | 34 | 100 |

Epileptiform discharges | 360 | 180 | 540 |

Total | 426 | 214 | 640 |

Confusion Matrix for the testing data of 180 epileptiform discharges and 34 normal controls: Method One uses Signal Range and

Method one | Epileptiform discharges | 175 | 5 |

Healthy controls | 6 | 28 | |

Method two | Epileptiform discharges | 178 | 2 |

Healthy controls | 1 | 33 |

Classification performance measures.

Signal range and Hurst | 97.22 | 82.35 | 94.86 |

The network based on Signal Range, alpha band energy, and |
98.89 | 97.06 | 98.60 |

The ROC curve for the testing data. The red and blue curves show respectively the ROC based on methods using Signal Range and

To improve the accuracy of classification, we have developed a brain network based approach. Specifically, three separate networks are constructed, based on the Signal Range, the energy of the alpha wave component, and

Typical PSD curves for epileptiform discharges and normal EEG showing that the relative energy of the alpha wave component for epileptiform discharges is often larger for that of normal EEGs.

Heat maps illustrating the three types of networks described in section 2:

Scatter plots using features from networks based on the Hurst parameter and the Signal Range, where

Again, let us input the square of the first singular values of the networks based on the Signal Range, the energy of the alpha wave component, and the

We have tried to infer the localizations of each type of epileptiform discharges based on the approach described in section 2.6, whose essence is to equate the sub-network representing the localization of each type of epileptiform discharge to the nodes which generate the most likely alpha band energy, signal range, and the Hurst parameter of that type of epileptiform discharge. The result is shown in

The localization of the epileptiform discharges.

Spike | |

Spike and slow wave complex | |

Sharp | |

Sharp and slow wave complex | |

Polyspike complex | |

Polyspike and slow wave complex | |

Spike rhythm |

Finally, we have compared our results with that of Anh-Dao et al. (

In this paper, we have proposed two approaches for distinguishing epileptiform discharges from normal EEGs, with the aim of being able to use them widely in a clinical setting. Our first method is based on Signal Range and the Hurst parameter. Every component of our method can be readily understood and implemented based on first principles. Although simple, the approach already achieves a high detection accuracy of 94.86%. To improve the accuracy of detection, our second method employs the notion of network, with the hope of capturing the functioning of human brain network to some degree. Specifically, our approach involves three types of networks, one based on the Signal Range, the second based on the energy of the alpha wave component of EEG, and the third based on the Hurst parameter. Each of the networks is analyzed by SVD, and the square of the first singular value is utilized to construct features to distinguish epileptiform discharges from normal controls. This network based approach, while still fully first principle based and readily understandable, achieves a very high accuracy of 98.60%. This accuracy is higher than a recent approach proposed by Anh-Dao et al. (

We have also designed a network-based approach to infer the localizations of each type of epileptiform discharges based on the networks constructed using the three variables, the signal range, the relative energy of the alpha wave component, and the Hurst parameter. The essence of the approach is to equate the sub-network representing the localization of each type of epileptiform discharge to the nodes which generate the most likely alpha band energy, signal range, and the Hurst parameter of that type of epileptiform discharge. We have found that while the channels

It is worth noting that the epileptiform discharges analyzed here were provided in two batches: in the first batch, which was about 2/3 of the data analyzed here, the accuracy was similar to that reported here. Then more epileptiform data were given to us by clinical doctors to examine whether the accuracy remained as high. It was yes. Nevertheless, the data analyzed here were still quite limited. It would be interesting and important to further validate the proposed approaches with more data in different clinical sets.

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

The studies involving human participants were reviewed and approved by the ethics committee of the First Affiliated Hospital to Guangxi Medical University. The participants provided their written informed consent to participate in this study.

QL performed most of the experimental work. ZZ assisted in data analysis. QH and YW provided the data needed for this experiment and engaged in many analysis and discussions. BX engaged in many discussions. JG conceived the study, provided overall supervision for the study and directed all phases of the study and including writing of the manuscript. All authors read and approved the final manuscript.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.