# Discrimination between Ictal and Seizure-Free EEG Signals Using Empirical Mode Decomposition

Authors: Ram Bilas Pachori
Journal: Research Letters in Signal Processing
 (2008)

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## Abstract

A new method for analysis of electroencephalogram (EEG) signals using empirical mode decomposition (EMD) and Fourier-Bessel (FB) expansion has been presented in this paper. The EMD decomposes an EEG signal into a finite set of band-limited signals termed intrinsic mode functions (IMFs). The mean frequency (MF) for each IMF has been computed using FB expansion. The MF measure of the IMFs has been used as a feature in order to identify the difference between ictal and seizure-free intracranial EEG signals. It has been shown that the MF feature of the IMFs has provided statistically significant difference between ictal and seizure-free EEG signals. Simulation results are included to illustrate the effectiveness of the proposed method.


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## Body

## 1. Introduction

Epileptic
seizures are the outcome of the transient and unexpected electrical disturbance
of the brain. The electroencephalogram (EEG) signal has been the most utilized
signal to clinically assess brain activities. The detection of epileptic
seizures in the EEG signals is an important part in the diagnosis of epilepsy
[1].Parameters
extracted from EEG signals are highly useful in diagnostics. Spectral analysis
is a common technique used for the analysis of EEG signals, as it reveals the
frequencies present in the signal. An underlying assumption of the Fourier
transform, however, is that the signal being analyzed is stationary (i.e., the
mean value, variance, and frequency content of the signal do not change over
time).Recently,
nonlinear methods have been proposed to extract new parameters linked to the
electrical activity of the brain. Among these parameters, the Lyapunov exponent
provides clinically useful information about the signal [2]; the correlation
dimension techniques can contain information about the different neurological
states of the brain [3]; the fractal dimension (FD) and entropy measure the
complexity or the degree of disorder of the EEG signal [4, 5], while
correlation integral, the measure sensitive to wide variety of nonlinearities,
used in [6], could be used to characterize the epileptogenic regions of the
brain during the interictal period. However, recent work shows that the EEG
signals exhibit nonstationary behavior [7, 8].In this paper,
a new technique of EEG signal analysis is presented, which is based on the
empirical mode decomposition (EMD) developed specially for nonlinear and
nonstationary time-series analysis [9] and the Fourier-Bessel (FB) expansion
suitable for nonstationary signal representation [10]. The EMD extracts the
local oscillations composing the signal, referred to as the intrinsic mode
functions (IMFs), as well as the residual representing the local trends. The
IMFs can be considered as a set of narrow-band
nonstationary signals. The coefficients of the FB expansion have been
used to compute the mean frequency of the IMFs. The FB coefficients are unique
for a given signal in the same way that Fourier series coefficients are unique
for a given signal. However, unlike the sinusoidal basis functions in the
Fourier transform, the Bessel functions are aperiodic, and decay over time.
These features of the Bessel functions make the FB series expansion suitable
for analysis of nonstationary signals when compared to simple Fourier transform
[11, 12]. The MF measure of the IMFs has been used as a feature in order to discriminate
seizures from seizure-free intervals in intracranial EEG data recordings.


## 2. Empirical Mode Decomposition

Empirical mode
decomposition (EMD) represents any temporal signal into a finite set of
amplitude and frequency modulated (AM-FM) oscillating components which are
bases of the decomposition. The decomposition is an intuitive and adaptive
signal-dependent decomposition. Moreover, the decomposition does not require
any conditions about the stationarity and linearity of the signal. The principle
of the EMD technique is to decompose a signalx(t) automatically into a set of the band-limited
functions Dp(t) named intrinsic mode functions (IMFs) [9].
Each IMF satisfies two basic conditions: (i) in the complete dataset, the
number of extrema and the number of zero-crossings must be the same or differ
at most by one, (ii) at any point, the mean value of the envelope defined by
the local maxima and the envelope defined by the local minima is zero. The
first condition is similar to the narrow-band requirement for a stationary
Gaussian process and the second condition is a local requirement induced from
the global one, and necessary to ensure that the instantaneous frequency will
not have redundant fluctuations as induced by asymmetric waveforms. The EMD
algorithm [13] for the signal x(t) can be summarized as follows.
(1)
Setg1(t)=x(t).(2)
Detect the extrema (both maxima and minima) ofg1(t).(3)
Generate the upper and lower envelopesem(t) and el(t),
respectively, by connecting the maxima and minima separately with cubic spline
interpolation.(4)
Determine the local mean asm(t)=(em(t)+el(t))/2.(5)
IMF should have zero local mean; subtractm(t) from the original signal as g1(t)=g1(t)−m(t).(6)
Decide whetherg1(t) is an IMF or not by checking the two basic
conditions as described above.(7)
Repeat steps (2) to (6) and end when an IMFg1(t) is obtained.
Once the first IMF is derived, define D1(t)=g1(t),
which is the smallest temporal scale in x(t).
To find the rest of the IMF components, generate the residue r1(t) of the data by subtracting D1(t) from the signal as r1(t)=x(t)−D1(t). The sifting process will be continued until the final residue is a constant, a
monotonic function, or a function with only maxima and one minima from which no
more IMFs can be derived. The subsequent basis functions and the residues are
computed as
(1)r1(t)−D2(t)=r2(t),…,rM−1(t)−DM(t)=rM(t),
where rM(t) is the final residue. At the end of the
decomposition, the signal x(t) is represented as
(2)x(t)=∑p=1MDp(t)+rM(t),
where M is the number of IMFs and rM(t) is the final residue.Matlab codes
are available athttp://perso.ens-lyon.fr/patrick.flandrin/emd.html. An example
of the application of EMD on the 23.6 seconds EEG time series is shown in Figure 1.Empirical mode decomposition of the 23.6 seconds EEG signal.
(a)(b)


## 3. Mean Frequency Computation Using  Fourier-Bessel Expansion

The zero-order
Fourier-Bessel series expansion of a signalx(t) considered over some arbitrary interval (0,a) is expressed as
in [10]
(3)x(t)=∑m=1QCmJ0(λmat),
where λm,m=1,2,3,… are the ascending-order positive roots of J0(λ)=0, and J0((λm/a)t) are the zero-order Bessel functions. The
sequence of Bessel functions {J0((λm/a)t)} forms an orthogonal set on the interval 0≤t≤a with respect to the weight t, that is,
(4)∫0atJ0(λmat)J0(λnat)dt=0,form≠n.
Using the orthogonality of the set {J0((λm/a)t)},
the FB coefficients Cm are computed by using the following
equation
(5)Cm=2∫0atx(t)J0((λm/a)t)dta2[J1(λm)]2,
with 1≤m≤Q,
where Q is the order of the FB expansion and, J1(λm) are the first-order Bessel functions. The FB
expansion order Q must be known a priori. The interval between
successive zero-crossings of the Bessel function J0(λ) increases slowly with time and approaches π in the limit. If order Q is unknown, then in order to cover full signal
bandwidth, the half of the sampling frequency, Q, must be equal to the length of the signal.It should be
noted that the FB series coefficientsCm are unique for a given signal, similarly as
the Fourier series coefficients are unique for a given signal. However, unlike
the sinusoidal basis functions in the Fourier series, the Bessel functions
decay over time. This feature of the Bessel functions makes the FB series
expansion suitable for nonstationary signals.The mean frequency is calculated as in [14]
(6)fmean=∑m=1QfmEm∑m=1QEm,
where
(7)Em=Cm2a22[J1(λm)]2=(energyatorderm),fm=λm2πa=(frequencyatorderm).
The selection
of the optimum window size a is required for a good resolution. A larger
window provides a finer resolution in frequency, which also means that a
greater number of FB coefficients will be needed to cover the same signal
bandwidth. The mean frequency of the IMFs was computed using FB expansion. Mean
frequency represents the centroid of the spectrum, and thus characterizes the
frequency components of the intrinsic mode functions of the EEG signal.


## 4. Results and Discussion

The use of EMD before calculating mean frequency was
necessary owing to the nonstationary and nonlinear nature of the EEG signals.
Mean frequency (MF) estimation was performed using the Fourier-Bessel expansion
method.In this section, the MF estimate of the IMFs has
been considered as a feature in discriminating EEG
patterns in intracranial EEG data recordings. For this purpose, EEG recordings
having seizure-free intervals and seizures
are considered. The EEG dataset which is available online in [15] is used. In
this section, a short description is given and please refer to [15] for further
detail. The dataset includes single channel EEG data from healthy and epileptic
subjects. The data has five subsets denoted as A, B, C, D, and E, each
containing 100 single-channel recordings, each recording of 23.6 seconds in duration. The subsets A and B have been
acquired using surface EEG recordings of five healthy volunteers with eyes open
and closed, respectively. The signals in two sets have been measured in
seizure-free intervals from five patients in epileptic zone (subset D) and from
hyppocampal formation of opposite hemisphere of the brain (subset C). Finally,
the subset E contains seizure activity selected from all recording sites
exhibiting ictal activity. The subsets A and B have been recorded
extracranially. The sampling frequency of the data is 173.61 Hz. From the
dataset, the subsets C, D, and E have been selected
because these have been acquired intracranially. The subsets C and D are
combined to form one class and subset E forms the other class.The MF values
have been estimated for both the classes using intrinsic mode functions. The
value of MF is small in seizure intervals when compared with that for
seizure-free intervals. The class discriminating ability of MF feature is
quantified using Kruskal-Wallis statistical test. The MF values are
significantly different among the two classes of EEG signals(p<0.01).
The results are shown in Figure 2 for the first four intrinsic mode functions.
The result suggests that MFs are effective for discriminating seizure from
seizure-free intervals for intracranial EEG recordings.Comparison of mean frequency estimation for
seizure-free and seizure intervals for different intrinsic mode functions
(IMFs): IMF1(p=0),
IMF2 (p=0),
IMF3 (p=0),
and IMF4 (p=2.6921×10−12).
(a)(b)(c)(d)The use of
empirical mode decomposition in the present study was justified on the basis of
the lack of stationarity in EEG signals. In this way, the entire signal could
be analysed simultaneously, at least for a given frequency band. However,
although EMD does decompose a signal into different frequency bands (IMFs), the
interpretation of the results derived from these IMFs is problematic. Unlike
other methods such as wavelets, the number of bands (IMF) is dependent on the
frequency content of the signal being analysed, with the number of IMF varying
for each signal. Such a property is problematic, as the IMFs used for
comparison might relate to different frequency bands. For instance, IMF4 for
two subjects might be the fourth of four IMFs for one subject, but the fourth
of eight IMFs for another. In such an example, the former would represent the
low-frequency components in the signal, while the latter would represent
frequency components from the middle of the spectrum.


## 5. Conclusion

The use of EMD to decompose signals into IMFs is a
promising method. However, caution should be exercised when interpreting
results from individual IMFs. It would be of interest to develop a method to
standardise the comparison of individual or summed IMFs, in order to better
compare seizure and seizure-free intervals in the EEG signals.To establish
the clinical use for the proposed technique, it is necessary to test on
out-of-sample datasets. It may require the collection of a very large database
of recordings of sufficient duration (many hours).



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