Computational and Mathematical Methods in Medicine

Volume 2016, Article ID 2582478, 9 pages

http://dx.doi.org/10.1155/2016/2582478

## Abnormal EEG Complexity and Functional Connectivity of Brain in Patients with Acute Thalamic Ischemic Stroke

^{1}Neural Engineering & Rehabilitation Lab, Department of Biomedical Engineering, College of Precision Instruments and Optoelectronics Engineering, Tianjin University, Tianjin 300072, China^{2}Department of Neurology, Tianjin First Center Hospital, Tianjin 300072, China

Received 23 January 2016; Revised 26 March 2016; Accepted 10 April 2016

Academic Editor: Nadia A. Chuzhanova

Copyright © 2016 Shuang Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Ischemic thalamus stroke has become a serious cardiovascular and cerebral disease in recent years. To date the existing researches mostly concentrated on the power spectral density (PSD) in several frequency bands. In this paper, we investigated the nonlinear features of EEG and brain functional connectivity in patients with acute thalamic ischemic stroke and healthy subjects. Electroencephalography (EEG) in resting condition with eyes closed was recorded for 12 stroke patients and 11 healthy subjects as control group. Lempel-Ziv complexity (LZC), Sample Entropy (SampEn), and brain network using partial directed coherence (PDC) were calculated for feature extraction. Results showed that patients had increased mean LZC and SampEn than the controls, which implied the stroke group has higher EEG complexity. For the brain network, the stroke group displayed a trend of weaker cortical connectivity, which suggests a functional impairment of information transmission in cortical connections in stroke patients. These findings suggest that nonlinear analysis and brain network could provide essential information for better understanding the brain dysfunction in the stroke and assisting monitoring or prognostication of stroke evolution.

#### 1. Introduction

Stroke is a leading cause of disability with a relatively high death ratio around the world, and up to 70% of stroke patients are left with moderate or severe functional impairment [1], placing a heavy physical and mental burden on both the patients and their families. It has been reported that early rehabilitation after stroke can enhance recovery, minimize functional disability, and reduce potential costly long-term care expenditures [1]. Patients with thalamic stroke only show minor changes on physical examination; thus valid and objective early diagnosis becomes extremely necessary.

The rapid development of imaging technology, such as computed tomography (CT), positron emission tomography (PET), magnetic resonance imaging (MRI), and electroencephalography (EEG), gives researchers an access to an embedded knowledge of the brain changes during stroke onset and recovery process [2]. Among these, EEG offers a continuous, real-time, and noninvasive measure of brain function, providing new insights into poststroke cerebral pathophysiology [3–6]. Because of its sensitivity to metabolic and ionic disturbances related to ischemia, it can be a potentially useful tool for acute stroke detection and for monitoring affected tissue [6]. In acute ischemic stroke, the primary injury has typically occurred prior to presentation, but EEG may be able to detect patterns to suggest severity, prognosis, and secondary injury (e.g., reocclusion, edema, or hemorrhagic transformation) [7]. Several parameters have been found correlated with initial stroke severity as measured by the National Institutes of Health Stroke Scale (NIHSS) in both the acute (brain symmetry index) [8, 9] and subacute periods (relative alpha percentage, relative alpha-beta percentage, relative delta-theta percentage, delta/alpha ratio, delta-theta/alpha-beta ratio, and global pairwise derived BSI) [10–12]. In summary, the existing researches mostly concentrated on power spectral density (PSD), and the PSD in various frequency bands has revealed to be a distinguishable indicator [13].

It is well accepted that brain is truly a complex system; therefore nonlinearities and nonlinear measures must be taken into account in its modeling and analysis [14, 15]. It has been reported that nonlinear parameters were more sensitive to both the power spectrum and the temporal amplitude distribution comparing with conventional spectral analysis in many other diseases [16–19]. Consequently, nonlinear analysis of the EEG may shed additional light on analyzing cortical information processing deficits in acute thalamic ischemic stroke. The first nonlinear methods that were used to analyze EEG are the correlation dimension (D2) and the first Lyapunov exponents (L1). D2 was applied by Grassberger and Procaccia in 1983 to quantify the number of independent variables that are necessary to describe the dynamic system. It was used to provide the statistical characteristic of the system. By contrast, L1 was applied by Wolf in 1985 as a dynamic measure to gauge the flexibility of the system [20, 21]. Then several methods of complexity and entropy techniques have dealt with the complexity or irregularity in the ability of the system to create information and showed promising results in detecting EEG abnormalities [14]. On-line use of D2 and L1 in a clinical situation is still impractical, since reliable estimation of them requires a large quantity of data and a long calculation time. Fortunately, the Lempel-Ziv complexity (LZC) measure [22] can act as an alternative tool for EEG analysis, since it is well suited for characterizing the development of spatiotemporal activity patterns in high-dimensionality nonlinear systems, like brain and heart. Moreover, the concept of LZC is simpler to understand and its computation is easier to implement. Entropy is a concept addressing randomness and predictability, with greater entropy often associated with more randomness and less system order [23]. Among these, Sample Entropy (SampEn) [24] has stood out with excellent antinoise and anti-interference performance; moreover, it could predict stable values with shorter data. LZC and SampEn have shown encouraging results in differentiating patients and healthy controls in some mental diseases, such as Alzheimer’s disease [25], Schizophrenia and depression [18], and global Hypoxic-Ischemic brain injury [26].

More recently, resting-state functional connectivity has a strong genetic component and shows characteristic changes in various psychiatric and neurological disorders [27]. Functional connectivity is assumed to reflect functional interactions between the underlying brain regions and has become very popular in the study of brain mechanisms underlying disturbed cognition diseases such as Alzheimer’s disease and Parkinson’s disease [28–30]. For the stroke, loss of neurons, as well as disturbed synaptic transmission, may lead to abnormal functional interactions between cortical regions.

In this study, we recorded the resting-state EEGs in patients with thalamic ischemic stroke from the acute stage and controls. Nonlinear analysis and functional connectivity were firstly employed to discriminate between the strokes and controls, providing a new insight into the brain changes in the stroke patients. LZC, SampEn, and partial directed coherence (PDC), which are important but always overlooked methods in stroke studies, were used to calculate the EEG features in order to seek and determine the proper and distinguishable way in the diagnosis of acute thalamic ischemic stroke disease.

The remainder of this paper is structured as follows. Section 2 describes the experimental methodology and systematically details signal processing methods. Contrastive analysis on EEG features between strokes and controls is addressed in Section 3. At last, the discussion and conclusion are stated in Sections 4 and 5, respectively.

#### 2. Materials and Methods

##### 2.1. Subjects

From December 2012 to January 2015, 12 patients (7 females and 5 males; mean age of 65 years) with ischemic thalamic stroke took part in the study, with 11 healthy subjects (4 females and 7 males; mean age of 53 years) as controls. Independent-samples -test were performed on ages between two groups, and there were no statistical differences (, df = 12.828, and ). The clinical data were acquired in Tianjin First Central Hospital. Inclusion criteria of the patients consisted of a focal ischemic lesion of the thalamus and a symptom of hand numbness. Exclusion criteria were a history of substance abuse, additional neurological or psychiatric disorders, and current psychoactive drug treatment. All the patients had been examined from the acute stage (<7 days).

##### 2.2. EEG Recording

EEG was recorded with the Netlink 40 developed by the Bio-logic company. The 10–20 system of electrode placement was used with electrodes placed at Fp1, Fp2, F3, F4, F7, F8, Fz, T3, T4, T5, T6, A1, A2, C3, C4, Cz, P3, P4, Pz, O1, O2, and Oz. The sampling rate was 256 Hz and impedance was kept below 10 k′Ω. The EEG was recorded in the resting condition with eyes closed. The raw EEG data were exported into MATLAB (The MathWorks, Natick, MA, USA) for further analysis.

##### 2.3. Calculation of EEG Features

###### 2.3.1. Preprocessing

Prior to further analysis, a preprocessing stage of the EEG signals is required. Five-minute data without apparent artifacts (such as blinks, EMG, and visible drift) were selected manually from each patient’s EEG recording. All channels were rereferenced to bilateral mastoid, band pass filtered at 1–45 Hz. EEG data were then split into five-second, nonoverlapping epochs in the following step of feature extraction. 60 epochs of artefact-free EEG data per participant was obtained finally.

###### 2.3.2. Lempel-Ziv Complexity (LZC)

An algorithmic complexity measurement introduced by Lempel and Ziv [22] is a measure reflecting the rate of new pattern generation along given sequence of symbols. In other words, it characterizes the structure or, as the name implicates, the complexity of the signal whether the signal is predictable (has simple structure) or nonpredictable (has complex, random structure) [31]. Applications of Lempel-Ziv complexity (LZC) to EEG signals include assessment of the depth of anesthesia [32] and sedation [31] and analysis of the background activity in Alzheimer’s disease [33].

The calculation algorithm of LZC for the sequence of symbols of length is defined as follows. A block of length () is a subsequence of consecutive symbols, (). The first block, , is set equal to the first symbol of the sequence ; that is, . Next is defined to be the following consecutive block of minimal length such that it does not occur in the sequence . Therefore, by continuing this recursive procedure until the last symbol of is reached it is possible to obtain the decomposition of into minimal blocksThe complexity Ca of is defined as the number of blocks in the decomposition, where is the number of possible different symbols in . The normalized complexity, , is defined as

Prior to applying the above described algorithm the signal has to be converted into a sequence of symbols, which can be done as follows. Depending on the number of different symbols *α*, thresholds have to be selected within the signal range, , where and are the minimum and maximum values of the signal , respectively. For instance, if , that is, two symbols, “0” and “1” are used, there is only one threshold and by comparing the samples of with this threshold the signal is converted into the sequence of symbols: if then ; otherwise . For larger , the conversion procedure is analogous. Here, the median voltage was considered as the threshold.

LZC values were also calculated in different frequency bands, including delta (1–4 Hz), theta (4–8 Hz), alpha (8–13 Hz), and beta (13–30 Hz).

###### 2.3.3. Sample Entropy (SampEn)

The name of SampEn refers to the applicability to time series data sampled from a continuous process [24]. SampEn does not use a templatewise approach when estimating conditional probabilities. It only requires that one template find a match of length and then computes the logarithm of a probability associated with the time series as a whole. It is well known that entropy is a measure of the rate of information generation; a larger SampEn presents lower self-resemblance and a higher rate of information generation of the signal. Mathematically, to compute SampEn we follow the steps explained as below.

Given a signal , where is the total number of data points, SampEn algorithm [34] can be summarized as follows.

(1) Form a set of vectors defined by

(2) Define the distance between vectors and as the maximum absolute difference between their respective scalar components:

(3) For a given , count the number of (,), denote as , such that , that is, is the number of , . Then, for ,

(4) Define as

(5) Similarly, calculate as times the number of (,), such that the distance between and is less than or equal to :

Set as

Thus, is the probability that two sequences will match for points, whereas is the probability that two sequences will match for points.

(6) Finally, define

Which is estimated by the statistic

As can be seen in the equations described above, and are the two parameters that must be specified for the calculation of SampEn. Pincus and Goldberger [35] have suggested that be set between 0.1 and 0.25 times standard deviation of the signal and be set equal to 1 or 2. In this work, we set , . SampEn values were also calculated in different frequency bands, including delta (1–4 Hz), theta (4–8 Hz), alpha (8–13 Hz), and beta (13–30 Hz).

###### 2.3.4. Partial Directed Coherence

The functional connectivity was estimated with partial directed coherence (PDC) [36]. PDC is based on the concept of partial coherence, a technique that quantifies the directed interdependence of Granger causality between any two signals in a multivariate set. A detailed description of PDC along with an illustrative example is given by Baccalá and Sameshima [37]. Hence, the mean values within 1–45 Hz band, referred as mPDC hereafter, were first compared with the threshold. Then, significant greater () causal interdependence formed an ( in this study) matrix , where each element contains the value of the mPDC from the channel to . To display clearly, the weighted digraph is converted into a binary one by applying a threshold. For example, when exceeds a threshold value, an edge is considered to exist from the node to node . Here, a surrogate data approach was used to obtain the threshold. A 10 s epoch was randomly selected at each channel, and there was no time overlap between two of those 20 channels. Then surrogate were calculate based on these time-mismatched epochs. This procedure was repeated 10 times. Mean value of the surrogate was considered as the threshold, which equaled 0.225.

#### 3. Results

##### 3.1. LZC Analysis in Stroke and Control Groups

The mean values of the LZC are shown for stoke and control groups in Figure 1. The controls showed lower LZC than the strokes at almost all electrodes. A larger LZC means a greater occurrence chance of new sequence patterns; thus the stroke group had a higher EEG complexity. An independent-samples -test, following the normal distribution test, was performed (). Significant statistical differences were found at channels Fp2, F7, F3, F8, T3, C3, P3, T5, and P4. It should be noted that similar distributions could be observed in both groups. Investigating all the electrodes, we could find higher LZCs at the temporal areas (T4, P4, F4, and C4) in both groups while lower values at prefrontal (Fp1, Fp2) and occipital (O2, Oz) areas. Furthermore, LZC values were also calculated in different EEG frequency bands including delta, theta, alpha, and beta bands, as depicted in Figure 2. It could be observed that the stroke group had higher LZC in theta and beta bands but lower values in delta and alpha bands at all channels. The independent-samples -test showed that both groups significantly differed from each other () at channels P4 and O2 in delta band, T3, C3, C4, T5, Pz, and O2 in theta band, Fp1, Fp2, Fz, Cz, C4, T6, O1, and O2 in alpha band, and Fp2, F7, F3, F8, Cz, P3, and T5 in beta band.