Neonatal Background Electroencephalogram (EEG)

Atomic Decomposition for Measuring the Instantaneous Amplitude and Frequency Content of the Electroencephalogram in Neonates with Encephalopathy

Index Terms-Atomic decomposition, Support vector machine, Time-frequency analysis, Neonatal electroencephalogram, Hypoxic ischaemic encephalopathy .

I. INTRODUCTION

In neonatal intensive care units (NICUs), the background EEG is reviewed by clinicians in order to detect and track the progress of brain injury. Visual inspection is not always ideal as it provides occasional evaluations, is tedious and requires special expertise to interpret the signal which is not available across all NICUs. Automated assessment of the EEG can therefore be advantageous in the NICU. Methods should be robust enough for use in a NICU environment and provide important information to help the clinician in the management of the critically ill neonate.

The background neonatal EEG signal is nonstationary with amplitude and frequency characteristics varying with time. The EEG can be considered, at it simplest, as coloured random noise with amplitude modulation (AM) [1]. The predominant clinically useful information is found in the AM as evidenced by the proliferation of signal representations such as the amplitude-integrated EEG (aEEG) in the NICU. The aEEG can be considered as a visualisation of the AM. Extracting AM and frequency modulation (FM) is an important problem for both analysis and synthesis of EEG signals. It is known that brain rhythms are a manifestation of ensemble neuronal activity; therefore, modulations of neural circuits should directly result in modulations in amplitude (AM) and frequency (FM) of oscillatory field potentials. Several algorithms such as the Hilbert transform (HT) [2], discrete energy separation algorithm [3], extended Kalman filter [4] and phase-locked loops [5] have already been proposed to extract AM and FM components in the case of mono-component signals. However, generalizing these methods to extract AM and FM for signals that contains at various times, multicomponent, stochastic and chaotic behaviour, such as the EEG is not a trivial task. This has inspired the application of methods such as filter banks [6], the phase vocoder algorithm [7] and the HT based asymptotic method using a multicomponent sinusoidal model [8]. These methods tend to use fixed time scales of analysis and fixed smoothing windows which best fit the data under analysis.

In this paper, we propose an alternate method of estimating the AM and FM using AD with a Gabor dictionary. The Gabor dictionary contains a range of atoms over varying duration and frequency. By selecting an overcomplete dictionary of atoms with varying time and frequency domain characteristics we can effectively control the level of smoothing in the time and frequency domains. Several studies have shown the effectiveness of using AD for the analysis of background EEG signals [9], [10], [11], [12]. We investigate the advantages of AD based AM/FM estimation by applying it to the task of classifying EEG of neonates with hypoxic-ischemic encephalopathy (HIE) into several grades [1], [13]. We compare it to alternate methods for estimating AM and FM: HT and marginals of a quadratic time-frequency distribution (QTFD) [1].

II. METHODOLOGY

A. Neonatal EEG Data

One-hour long EEG recordings free of major movement artefacts(amplitude > 250 µV ) from 54 full term neonates with HIE recorded between May 2003-May 2005 was used in this study. Recordings took place at the NICU of Cork University Maternity Hospital (CUMH), Cork, Ireland using the NicoletOne EEG system (Carefusion Neurocare, Wisconsin, USA) with a sampling frequency of 256 Hz. All EEGs were recorded with informed parental consent and under ethical approval of the CUMH and University College Cork and were anonymized at the time of recording. The EEG was recorded within 12h of birth and it was continued for 24-72h to track the development of the HIE [14], [15]. Neonates were not treated with therapeutic hypothermia. The data were annotated using eight EEG channels in bipolar montage: F4-C4, C4-O2, F3-C3, C3-O1, T4-C4, C4-Cz, Cz-C3, and C3-T3. The segments of the EEG recording selected had a constant HIE grade within an hour. The EEG recordings were graded independently by two neonatal EEG experts based on predefined EEG patterns [16]. The neonatal EEG was assigned one of the 4 grades based on the degree of abnormality: grade 1-mild, grade 2 -moderate, grade 3 -major abnormalities and grade 4 -inactive/idle EEG. In total there were 22 grade 1, 14 grade 2, 12 grade 3 and 6 grade 4 EEG recordings. The same dataset had been previously used in [1], [17]. A sample 64s EEG HIE grades is shown in figures 1 and 2, respectively. It can be seen that the EEG with HIE shows different patterns across different HIE grades. Ideally these patterns are very different between HIE grades, however the measurement of the variability of these patterns over one hour of EEG recording plays an important role in HIE-EEG classification.

B. Methods of AM/FM Estimation

There are several existing AM/FM estimation methods. Among them, the Hilbert transform (HT) and QTFDs are commonly used methods. Likewise, with the help of additional processing steps AD can be also be used to estimate AM/FM from the selected atoms in the decomposition dictionary.

1) Proposed method: AD uses a time-frequency redundant dictionary to optimally represent a given signal. A dictionary is a collection of elementary signals or atoms (g) such that D = {g(n; λ)λ∈Λ}, where Λ is the set of time-frequency parameters used to build gλ, and can be used for signal representation. The atoms in the dictionary are obtained through the transformations of the fundamental atom gλ(t). AD techniques provide a signal representation (or approximation) as a superposition of atoms selected from the dictionary as

There are several AD techniques available which includes: Matching Pursuit (MP) [18], Orthogonal Matching Pursuit (OMP) [19] and Basis Pursuit (BP) [20]. MP is a greedy algorithm that uses a maximum inner product criteria to select atoms in the dictionary iteratively to reach the desired level of signal approximation. BP utilizes linear programming to minimize the L1-norm which attempts to minimize the number of atoms used to approximate a signal at a given level.

OMP is an iterative, greedy algorithm that calculates the locally optimum signal approximation at each iteration. At every iteration, an optimal approximation is obtained from the linear combination of selected atoms from the dictionary with obtain AM and FM estimates as [1],

where D is the overcomplete dictionary (N ≤ M) with each column representing an atom of length N, N is the length (samples) of the signal, M is the number of atoms in the dictionary (M ≥ N) and γ ∈ RM-1 is the set of sparse coefficients selected by the decomposition algorithm [22].

The performance of the OMP algorithm depends mainly on the choice of the decomposition dictionary. Several dictionaries have been proposed in the literature that can be used with AD including wavelets [24], wavelet packets [25], chirplets [26], Fourier dictionary [27], Gabor dictionaries [28], [29] and so on. We used a Gabor dictionary (time-frequency dictionary) consisting of translated (α), scaled (s) and modulated (β) versions of a Gaussian window [28].

where G[n, q] is the kernel of the QTFD and ρ[n, m] is an N – N matrix. In this work we used the smoothed Wigner-Ville distribution [30] where G[n, q] is a 2D Hamming window of duration Ht seconds and bandwidth of Hf Hz. The AM and FM can be approximated from ρQT F D in a similar manner to (7).

3) Hilbert transform (HT) method: The HT is a popularly used tool in the field of neuroscience that provides an automatic method for separating the signal spectrum into AM and FM components [30]. Given an input signal x[n], the AM and FM can be obtained as,

Here n =0, 1, ··· ,N − 1 and λ =[α, s, β] ∈ Λ are the time-frequency parameters, the time duration of the EEG epoch is 64 s, the sampling frequency is 64Hz and N = 4096. Each atom is normalized to contain unit energy. We used an overcomplete complex Gabor dictionary: D ∈ CN-M (where each column is an atom) based on a limited set of 8 subdictionaries with atom parameters chosen from the dyadic sequence of integers: s =2q, 0 ≤ q ≤ L, N =2L , α ∈{2, 4, 8, 16, 32, 64, 128, 256} and β ∈ {256, 128, 64, 32, 16, 8, 4, 2}. We did not use the full range of possible values for α and β, in order to limit the resolution of AM and FM estimates to practical values. A TFD of the signal can then be approximated as, where h(n; λk) is the analytic associate of g(n; λk). This TFD representation is free of cross-term artifacts and is nonnegative. The range of atom duration and bandwidth in each subdictionary controls the potential bandwidth for the AM and FM estimate. However, marginals and energy conservation will not be satisfied, only approximated [30]. From (5) we can where z[n] is the analytic associate of the signal x[n], and w[n, n] is 2D Hamming window of duration Ht and bandwidth Hf seconds. This provides non-negative AM and FM esti-

Fig. 3: Examples of 16s of EEG HIE grade 3 are shown in (a) and (b). The AM estimates of epoch (a) using the proposed AD technique and the Hilbert transform with a Hamming window length of 0.5s and 2s is shown in (c). Similarly, the AM estimates of epoch (b) is given in (d). Note how the AM value is smoothed with the increase in window duration using HT. The main advantage of using AD is its ability to capture sharp transients in the signal which traditional AM/FM estimation methods fail to capture.

mates of the EEG signals; an example showing the difference between AM and FM estimates are shown in figures 3 and 4, Fig. 4: Examples of 16s of EEG HIE grade 3 are shown in (a) and (b). The FM estimates of epoch (a) using the proposed AD technique and the Hilbert transform with a Hamming window length of 0.5s and 2s is shown in (c). Similarly, the FM estimates of epoch (b) is given in (d). Note how the FM values are smoothed with the increase in window duration using HT similar to AM estimates.

respectively. It can be seen that an AM estimate with AD has a higher bandwidth than estimates with the HT irrespective of the smoothing window.

III. EXPERIMENTAL EVALUATION We investigated the performance of AM/FM estimation methods for classifying EEG from neonates with hypoxic ischemic encephalopathy (HIE). The architecture of the proposed AD based background EEG Automatic Grading System (AGS) is shown in figure 5. This is a multichannel system which consists several pre-processing and post-processing steps for extracting time-frequency features and classification.

A. Preprocessing and epoch selection

8 channels of the EEG were filtered using a highpass filter with a cutoff frequency fc (which will be determined in section III-E) and a transition width of 0.5 Hz. Since the EEG activity of interest in neonates is negligible at frequencies over 32 Hz, the EEG was down-sampled to 64 Hz from 256 Hz. The EEG was then segmented into 64 s epochs with a 32 s overlap (50% overlap). The duration of the epoch was selected based on the definition of EEG grade 4 which states an interburst interval (IBI)> 60s [16]. In total, there were 6991 epochs (grade 1 = 2810, grade 2 = 1818, grade 3 = 1607 and grade 4 = 756).

B. Feature extraction

In the feature extraction step, a basic statistical summary (mean, standard deviation, skewness, kurtosis) of the AM and FM estimates obtained from the EEG epoch were estimated and used as key features to characterize the EEG. Each EEG epoch was therefore, represented by 8 features in total. This process was repeated for all 8 channels. Since HIE is assumed to be a global injury in this study, the median feature vector across 8-channels (multichannel feature fusion) was obtained which combines the information across the EEG channels to form a single feature set [1]. The features were normalized using the Box-Cox transformation [31] to have uniform mean and standard deviation. The normalized features were then passed to a multiclass support vector machine (SVM) classifier to obtain the HIE grade.

C. Classification

The SVM is primarily used for two-class classification problems since it is a binary classifier [32]. Several methods of extending the use of the SVM for multiclass problems have been suggested in the literature, which can be grouped into two categories: Category 1: In this category, the whole dataset with all the classes is used simultaneously and solves the multiclass problem directly [32], [33]. The main drawback of these methods is that due to the large number of variables that need to be optimized, they present numerical difficulties and are difficult to implement. Category 2: In this category, the classification is decomposed into a binary classification problem [32] and is commonly used for multiclass classification problems. The methods used in this approach are: one-against-all and oneagainst-one. In both these methods, a binary SVM classifier is constructed separating the datapoints of one class against the other. After testing, each SVM classifier provides a decision value or class for the test datapoint and the label is assigned to the datapoint from the classifier with the highest positive decision value. One-against-all was used in the present study due to reduced computational complexity [34]. The output of the SVM was converted to a probabilistic measure of a HIE grade, bounded within [0,1] via Platt scaling [35] using a sigmoid function as:

where P (w1|x) is the probability of the HIE grade assigned by the classifier for an epoch, f = f(x) is the output of the SVM classifier, A and B are the sigmoid function parameters which are estimated over the training dataset [35].

D. Postprocessing

Majority voting is used here to obtain the final grade of a given sequence vector obtained from the multiclass SVM. In the first step, the output of the ith SVM model is stored in a vector Si. The majority voting of these vectors (Si) is performed to obtain the best grade from each SVM classifier in a vector SCL. Later, in the second step, the output of the best performing SVM classifier is assigned as the final grade to the HIE-EEG. This process of majority voting for a 4-class classification problem is illustrated in figure 6.

E. Training and Testing

From the Gabor dictionary, 4 different subdictionaries were generated: D1 = D, D2 (short duration atoms) = D(:, 1: 3N), D3 (narrowband atoms) = D(:, 5N +1 : 8N) and D4 (mid range atoms) = D(:, 2N +1 : 8N). For each subdictionary, a Leave One Out (LOO) cross validation was used to estimate the overall performance of the proposed AGS since it provides nearly an unbiased performance estimate of the proposed system [36]. In each iteration of the LOO, we used data from 53 EEG recordings as training and the one remaining patients data for testing. Approximately 530 minutes of data from 53 neonates (10 min of randomly selected data from each neonate) was used to train the SVM model to reduce the computational time. A nested LOO cross validation was used on the training set to obtain optimal SVM classifier model parameters. Several parameters given in Table I were searched within the training process using nested LOO cross-validation. The parameters that provided highest classification accuracy over the training set were selected. The AGS trained with the optimal parameters was then tested on the EEG data from the remaining (left out) neonate and the accuracy was obtained. This process was repeated until the recording from each neonate had been used once for testing. The overall mean accuracy across 54 iterations is then reported.

Fig. 6: Illustration of the majority voting system for assigning an overall HIE grade.

IV. RESULTS

The performance of the proposed methods in terms of epoch classification (i.e number of epochs correctly classified in different HIE-EEG groups) was obtained. Table II shows the optimal parameters which provided the highest accuracy for all three methods. The results of the AGS using different methods is shown in Table III. The overall accuracy of the proposed AGS system for classifying long-term HIE EEG using AD, QTFD and HT methods were 82% (44/54), 82% (44/54) and 87% (47/54), respectively. The AD based method outperformed other methods by 2% for the case of epoch by epoch classification but had poorer performance in the neonate by neonate HIE grading classification.

Table III also provides the accuracy obtained for individual patients. It can be seen that the proposed AGS can classify grade 3 and grade 4 efficiently (>90%) but the performance reduced in the case of grade 1 and grade 2 with grade 2 being the most difficult to classify. This was due to the indiscriminatory characteristics/morphology of the EEG signal present in grades 1 and 2 (see figure 1).

Misclassified recordings using AD method were further

analysed and it was observed that the misclassification were due to the presnce of abnormal EEG patterns such as runs of sharp waves, asymmetry and asynchrony. An example of the presence of a sharp wave in grade 2 EEG is shown in figure 7. These sharp waves were not isolated and were present throughout the recording. Examples for the presence of asymmetry and asynchrony are shown in figures 8 and 9 respectively. Due to the presence of these abnormalities in the EEG recording, the AGS decision was downgraded. It is difficult to determine the presence of these abnormalities as they appear intermittently. The incorporation of the methods to detect these abnormalities has a potential to improve the performance of the proposed AGS.

The remaining misclassifications were caused by the presence of long periods of EEG artefacts, however the artefact-free periods were correctly classified by the AGS. Overall, 33% of the EEG recordings were misclassified in which the majority of misclassified epochs were marked as containing some form of artefacts. More than 50% of the data in three misclassified EEG recordings were corrupted with artefacts which significantly influenced the decision during the majority voting. An example of a long duration artefact is shown in figure 10. An example of the AGS output for a misclassified recording is shown in figure 11.

Optimal methods of estimating the AM and FM components of biological signals is an important problem. In this paper, we presented a novel method to estimate AM and FM components from a EEG signal using AD based on the atoms selected from a Gabor dictionary. Although several methods exists to estimate AM/FM measures, the potential of AD to obtain these measures had not yet been explored. The time-frequency representation (TFR) derived from the AD is cross-term free, which results in a clear and easy-to-understand time-frequency distribution of the energy density. However, this is obtained at the cost of higher computational complexity and the loss of desirable properties of the TFR.

We tested three methods to estimate the AM and FM components for use with an automatic grading system for neonatal HIE. It was observed that the proposed AD method improved the recognition of short EEG epochs (64 seconds) but did not improve the classification of long EEG epochs (1 hour) using post-processing for overall HIE grading. This suggests that AM/FM estimates obtained directly from the atoms selected by the AD during decomposition of EEG signal can be useful in short duration classification problems such as seizure detection [12], [37]. The highest accuracy of the AGS using SVM for grading neonate by neonate HIEEEG was obtained using the HT method with 87% (47/54). Using the same set of TF features extracted from the HIEEEG signal using HT method and a simple multi-class linear discriminant classifier, an accuracy of 77.8% was reported in [1]. This suggests that by using an advanced classifier, the performance of the AGS can be improved. The classification accuracy of the AGS in this study was similar to the accuracy obtained in [17] where an accuracy of 87% was reported using the same dataset. However, these results were obtained using 55 generic features when compared to 8 features obtained from the AM/FM estimation in this study. We show that 8 features of the AM/FM provide state-of-the-art performance. This compares favorably with more sophisticated methods which use more complex analysis [17], [37].

The presented AD based AM/FM estimation showed promising results in neonatal HIE-EEG epoch classification, however there are certain opportunities to improve the performance of the proposed AGS. The choice of the decomposition dictionary is an important factor for AD. The Gabor dictionary was used in this study as variables relating in the time and frequency domain are explicit in its definition. There may be a more optimal dictionary for neonatal EEG classification. Since there is no well defined pattern in background EEG, it is difficult to design a model based dictionary for HIE classification. However, with the help of several dictionary learning algorithms the atoms in the dictionary could be trained to be coherent with specific HIE grades and AM/FM can then be obtained from these trained dictionaries to grade HIE-EEG [29]. The OMP selected different atoms for different HIE grades which suggest that there may well be optimal atoms involved in the separation of each EEG class.

Further analysis of the results showed that the performance of the AGS for grading HIE-EEG using AD was sensitive to artefacts. Detection of the short duration physiologically variable neonatal EEG artefacts is a challenging problem, in particular for the analysis and grading of HIE-EEG. It can be seen from figure 11 that the presence of artefacts has a great influence on the AGS decision using AD. Even though the presence of these artefacts had no influence on the decision of the AGS on most of the EEG recordings due to post-processing and majority voting in the Hilbert transform method, the incorporation of an artefact detector to detect these long duration EEG artefacts could improve the performance of the OMP based AGS by removing the artefacts from the misclassified data. In addition, the proposed AGS does not detect certain short duration abnormalities present in the EEG such as asymmetry, asynchrony and runs of sharp waves. Addition of parallel detectors to detect such abnormalities has the potential to improve the performance of the proposed AGS significantly. The proposed AD based AM/FM estimation method has potential use for other analyses of background EEG such as from preterm neonates in which the background EEG is more discontinuous with a wider variety of bursting activity, so here better control over AM/IF may be useful [38].

VI. CONCLUSION

An AD-based method for estimating AM and FM components of the neonatal EEG signal has been presented. The proposed methodology was tested for grading EEG in neonates with HIE and may be used in many other signal classification applications. The experimental results show promising performance in classifying short duration neonatal HIE EEG epochs when compared to state-of-the-art methods. To extract AM/FM features accurately from the background EEG signal, an adaptive method that can decompose the signal with good time-frequency localization and resolution is necessary and AD is an excellent choice for this purpose. The idea of using AD for estimating AM/FM measures seems promising and we will investigate it further to improve the performance of the AGS for long duration neonatal HIE-EEG grading.