Subband Spectral Complexity Distance for Cortical Health
Evaluation and Monitoring in Ischemic Brain Injury
R. R. Gharieb, M. Hathi and N. Thakor
ABSTRACT- A quantitative electroencephalogram (qEEG)
index for the evaluation and monitoring of cortical health in
ischemic brain injury is presented. The proposed qEEG index,
called the subbands spectral complexity distance (SSCD),
measures the distance between a vector of subbands spectral
complexities computed from the investigated EEG and a one
computed from normal EEG. For the computation of the
SSCD, the spontaneous power spectral density of the EEG
signal is estimated using the time-varying autoregressive (TVAR) model, decomposed into subbands and the spectral
complexity of each subband is computed. Results of evaluating
human EEG data are presented to show the usefulness of the
proposed SSCD index. It is shown that the index increases
during the time-segments of ischemic brain injury while
decreases during the normal and recovery segments. This can
be explained by the fact that the ischemic brain injury may
increase the irregularity of the EEG signal and therefore the
power spectral density becomes more complex with ischemic
brain injury.
1
INTRODUCTION
C
ARDIAC arrest affects about 200,000 to 375,000
patients annually in the USA and it is therefore a
common
problem
[1].
After
cardiopulmonary
resuscitation from cardiac arrest, brain damage due to
hypoxic-ischemic encephalopathy is considered one of the
leading causes of morbidity and mortality. Intensive care
requires tracking the electrical brain activity post cardiac
arrest in order for clinicians to be ready for
neuroprotective intervention. The electroencephalogram
(EEG) is a noninvasive indication for the brain electrical
activity. Since injury causes death of many thousands of
brain cells, this results in change in the EEG signal
amplitude, power spectrum and complexity. For the
evaluation of the cortical health during ischemic brain
injury and recovery based on EEG signal, various
quantitative measures, such as temporal amplitude-based
entropy, time-varying spectral distance and Itakura
Manuscript received by June 20, 2010. This work has been carried
out at Infinite Biomedical Technologies LLC, Baltimore, USA, during
the tenure of Prof. Gharieb as a Senior Scientist.
R. R. Gharieb is with the Faculty of Engineering, Assiut University,
Egypt. E-mail: rrgahrieb@ieee.org, rrgharieb@gmail.com.
M. Hathi is with Infinite Biomedical Technologies LLC, Baltimore,
USA.
N. Thakor is with the Department of biomedical Engineering, Johns
Hopkins School of Medicine, Baltimore, USA.
distance have been used [4]-[8]. The spectral distance
expresses the sum of square-differences between the
spectral lines of the baseline (normal) EEG and the
injury-related one [13]. The spectral distance then reflects
the similarity/dissimilarity of the spectral lines, their
values and corresponding frequencies with respect to the
baseline EEG signal. For the computation of the power
spectrum, a time-varying autoregressive (TV-AR)
modeling is often employed [4], [11], [12], [13]. The
amplitude-based entropy has been used as a measure of
the information contents of the EEG signal [4], [5], [7],
[8]. This is implemented by treating the EEG amplitude as
a random variable within a sliding window; then the
probability distribution function and time-dependent
entropy have been computed. As known, the amplitude is
very sensitive to additive noise.
In this paper, a spectral complexity distance (SSCD) is
proposed for quantitatively measuring and monitoring the
ischemic brain injury post cardiac arrest. The proposed
distance evaluates how far the subband spectral
complexities of the investigated EEG signal are from
those of the normal EEG signal. In Section 2 we presents
description of the computation of the proposed spectral
complexity distance, a brief review for the TV-AR
modeling and a brief description for the employed human
real-world EEG data. Section 3 presents the results of
applying the proposed SSSCD to 4 real-world EEG data
of human subjects. Finally in Section 4, the conclusions
are drawn.
METHOD AND DATA
A. Spectral Complexity
The time-varying spectral entropy can be computed by
[2], [3], [4]
v ( n)  

f
H ( f , n) log( H ( f , n)) ,
(1)
where H ( f , n) is the normalized power spectral density,
f is the discrete normalized frequency and n is the timesample number. If the logarithmic base is 2, then spectral
entropy based complexity (simply, spectral complexity)
measure can be obtained as follows:
s ( n)  2 v ( n )
(2)
It is simple to demonstrate that the spectral complexity
(SC) increases with the increase of the randomness, i.e. it
reaches its maximum value when the signal is white
random process. If x(n) is a unity-power white random
process, then the normalized power spectral density is
constant for each f and is equal to 1 / N , where 1/N is the
normalized frequency resolution. The spectral entropy is
equal to log (N) and therefore the SC is equal to N. It is
also simple to prove that the spectral entropy of a single
sinusoid is zero and therefore the SC is equal to 1. If x(n)
consists of three sinusoids of equal amplitudes, the
normalized power spectral density shows three lines each
of amplitude 1/3. The SC is therefore equal to 3.
B. Subband Complexities and Complexity Distance
The normalized power spectral density H ( f , n) is
decomposed into M of either equal- or non equal-width
subbands, i.e.,
H ( f , n)  H 1 ( f , n)  H 2 ( f , n)  ...
 H M ( f , n)
(3)
The ith subband spectral entropy
vi (n) and the ith
subband spectral complexity
si (n) are computed as
implies that the analysis window is overlapped on the
previous one by (W-  ) samples. More details about
Burg’s method and its lattice realization are found in [10],
[12]. After the computation of the TV-AR coefficients in
(7), the power spectral density of the EEG signal x(n)
versus the time-sample n is given by
Hˆ ( f , n)  1 / | A(e j 2 f , n) | 2
D. Data
The SSSCD described in this paper are computed for the
EEG of 4 subjects. Each EEG signal was acquired using
sampling frequency of 256 Hz. The signals were filtered
with a digital bandpass filter between 1 and 70 Hz with a
notch at 60 Hz in order to remove the out-of-EEG-band
noise and the power line interference. Each subject was
later evaluated at discharge using a functional outcome
measure, the Cerebral Performance Category (CPC)
which is of 5 point scale further divided as good and poor
outcome [9], [10]. Table 1 presents the CPC outcomes
that we used.
RESULTS
follows [10]
v i ( n) 

 H i ( f , n) log( H i ( f , n))
f
si ( n)  2 v i ( n )
(4)
(5)
The subbands can be selected to cover the clinical EEG
rhythms. The subband complexities can be converted into
various single measures.
Of these measures, the
complexity distance which measures how far the spectral
complexity of the investigated EEG signal from a baseline
EEG signal. The Euclidian distance as an example is
computed as follows
u(n)  (
where

M
(s m (n)  rm (n)) 2 )1 / 2
m1
rm (n) represent
the
(6)
subband-spectral
complexities of the baseline EEG.
C. TV-AR Power Spectral Model
The EEG signal, x(n), could be modeled as a timevarying autoregressive (TV-AR) process given by [11],
[12].

x(n)  
p
i 1
ai (n) x(n  i)  e(n)
(7)
where p is the AR model order. This implies that x(n) is
generated as the output of the all-poles system
p
[1 / (1  i 1 ai (n) z  i )  1 / A( z , n) ] driven by
the unpredictable (white noise) process e(n). Since the
system coefficients are time-varying, the power spectral
density is time-varying as well. For the computation of
the TV-AR coefficients, Burg’s method is applied to a
sliding window of size W samples. Burg’s method finds
an all-pole model that minimizes the sum of the squares
of both the forward and backward prediction errors [11],
[12]. As time increases by  samples, the sliding window
is moved to the advance by  samples as well. This

(8)
For the computation of the TV-AR coefficients, the
windowed Burg’s method has been used with window
size of 2 sec overlapped by 1 sec. The TV-AR model
order p is chosen 8, generally, the order of such model is
determined by using Akaike criteria [14]. Various model
orders greater than 8 have also been examined and have
shown no significant improvement. The SSCD is
computed using the schematic diagram shown in Fig. 1.
Fig. 2 shows the spectral complexity of 6 equal-width
subbands of the EEG recorded from the normal subject
and the one with severe injury. Subbands can be adjusted
to cover the EEG wave rhythms. Results of other subjects
were omitted for the paper space limitation. It is obvious
that there are valuable changes in the subband
complexities of the subject having CPC of grade 5 in
comparison with the normal subject.
TABLE 1:
THE PITTSBURG-GLASGOW CEREBRAL PERFORMANCE CATEGORIES
Grades
1
2
3
4
5
Cerebral Performance Category
(CPC)
Conscious and alert with
normal function or slight
disability
GOOD
Conscious and alert with
moderate disability
Conscious and alert with
severe disability
Comatose or persistent
POOR
vegetative state
Brain death or death from
other causes
Fig. 3 shows a bar plot of the spectral complexities of
the 6 subbands of the EEG of the four subjects. Fig. 4
shows the ongoing SSCD of the four EEG subjects and
the normal subject. It is obvious that the online SSCD
changes with ischemic brain injury grade. The SSCD of
the normal subject and the one performing good outcomes
are very close. However the SSCD of the subject with
CPC of grade 5 who died after 24 Hours are very far from
the normal subject. It is also obvious that the one with
CPC 5 died after 72 Hours is separated from the subject
with CPC of grade 5 who died after 24 Hours. Therefore
the SSCD could distinguish between the different injury
levels. The spectral complexity distance shows that the
subject with CPC of grade 5 and died after 24 Hours is far
from the normality while the subject with good outcome
is close to the normal one.
CONCLUSIONS
In this paper, a subbands spectral complexity distance
(SSCD) of EEG signal has been proposed as a
quantitative EEG (qEEG) index to evaluate and monitor
ischemic brain injury. The qEEG index has been
formatted as the Euclidean distance between a vector of
subbands spectral complexities computed from the patient
investigated EEG and the one from a control (normative)
subject. The real-time power spectral density is estimated
using the time-varying autoregressive (TV-AR) model
computed by applying Burg’s method to a sliding
window. The SSCD obtained from EEG data recorded
from four human subjects with ischemic brain injury and
a normative subject has shown the significant usefulness
of the approach. It has been noticed that the SSCD value
increases with the increase of the grade of the cortical
injury. The subject with brain injury and good outcomes
provides a very close distance from the normal subject.
ACKNOWLEDGMENT
The data presented in this paper were collected by our
collaborators at the Johns Hopkins Medical Institution.
They have collected these data as part of an NIH funded
SBIR Phase II project, where they monitored patients
suffering from in-hospital or out-of-hospital cardiac arrest
in the Cardiac Care Unit of the Johns Hopkins Hospital.
TVAR-Power Spectral
Estimation and
Normalization
EEG
1
| A(e j 2 f , n) |2
REFERENCES
[1] M. Thel and C. O'Connor, "Cardiopulmonary resuscitation:
historical perspective to recent investigations," Am Heart J, vol. 137,
pp. 39-48, 1999.
[2] C. E. Shannon, A mathematical theory of communication,” Bell
System Technical Journal, vol. 27, pp.279-423, 623-656, July Oct.
1948.
[3] H. Misra, S. Ikbal, S. Sivadas and H. Bourlard, “Multi-resolution
spectral entropy feature for robust ASR,” Proc. ICASSP, March
2005, pp. 253-256.
[4] R. R. Gharieb and N. V. Thakor, “Neurological EEG Monitors: A
review,” Encyclopedia of Medical Devices and Instrumentation,
Second Edition, edited by John G. Webster Copyright 2006 John
Wiley & Sons, Inc.
[5] R. R. Gharieb, “Self and mutual information for the diagnosis of
Alzheimer’s disease,” JES, Assiut University, Vol. 33, No. 3, pp.
887-896, 2005.
[6] X. Kong, A. Brambrink, D. F. Hanley and Nitish V. Thakor,
“Quantification of injury-related EEG signal changes using distance
measures,” IEEE Trans. Biomed. Eng., vol. 46, pp. 899-901, July
1999.
[7] A. Bezerianos, S. Tong and N. Thakor, “Time-dependent entropy
estimation of EEG rhythm changes following brain ischemia,”
Annals of Biomedical Engineering, vol. 31, pp. 1-12, 2003.
[8] S. Tong, A. Bezerianos, A. Malhotra, Y. Zhu and N. Thakor,
“Parameterized entropy analysis of EEG following hypoxic-ischemic
brain injury,” Physics Letters A 314, pp. 354-361, 2003.
[9] Cummins, R.O., et al., Recommended guidelines for uniform
reporting of data from out-of- hospital cardiac arrest: Ann Emerge
Med, 20(8): p. 861-74, 1991.
[10] Cummins, R.O., et al., “Recommended guidelines for reviewing,
reporting, and conducting research on in-hospital resuscitation: the
in-hospital: Ann Emerge Med, 1997. 29(5): p. 650-79.
[11] Hayes, M. H.: “Statistical digital signal processing and modeling”,
John Wiley & Sons, INC., (1996).
[12] N. Amir and I. Gath, “Segmentation of EEG during sleeps using
time-varying autoregressive modeling, “Biol. Cybern., 61, pp. 447455, 1989.
[13] Geocadin RG, Ghodadra R, Kimura T, Lei H, Sherman DL,
Hanley DF, et al. A novel quantitative EEG injury measure of
global cerebral ischemia. Clin Neurophysiol;111:1779 _/87, 2000.
[14] Akaike H. A new look at the statistical model identification. IEEE
Trans. Auto. ControlAC-19, 716-723, 1974;.
H1 ( f , n)
Com ple xity
H 2 ( f , n)
Com ple xity
s1 (n)
s2 ( n )
Distance
Computation
H ( f , n)
H M ( f , n)
Com ple xity
SCD
sM (n)
Fig. 1. A schematic diagram for the spectral complexity distance (SSCD) computation approach.
4
3
2
1
0
0 50 100 150200 250
4
3
2
1
0
0 50 100 150200 250
4
3
2
1
0
0 50 100 150200 250
s(n)
0 50 100 150200 250
s(n)
4
3
2
1
0
4
3
2
1
0
0 50 100 150200 250
s(n)
s(n)
s(n)
s(n)
4
3
2
1
0
0 50 100 150200 250
4
3
2
1
0
4
3
2
1
0
4
3
2
1
0
0 50 100 150200 250
0 50 100 150200 250
0 50 100 150200 250
Time nT (sec)
4
3
2
1
0
4
3
2
1
0
4
3
2
1
0
0 50 100 150200 250
0 50 100 150200 250
0 50 100 150200 250
Time nT (sec)
Complex. time-averages
Fig. 2. Real-time subband complexities for 6 subbands of the four EEG examples: a, normal subject; and b, cortical brain injury
subject with CPC of grade 5 (died within 24 H after cardiac arrest).
5
4
3
2
1
0
1
2
3
4
Subject title
Fig. 3. Bar plots of the 6 subbands complexities time-average: title #1, normal subject; #2, ischemic cortical brain injury with good
outcomes (diagnosed later that his cerebral performance category (CPC) is of grade 2); #3, ischemic cortical brain injury subject with
CPC of grade 5 (died within 72 H after cardiac arrest); and #4, ischemic cortical brain injury subject with CPC of grade 5 (died within
24 H after cardiac arrest).
2.5
u(n)
2
1.5
1
0.5
0
0
50
100
150
Time nT (sec)
200
250
Fig. 4. The real-time SSCD of the four EEG examples: , normal subject; , ischemic cortical brain injury subject with good outcome
(CPC is of grade 2); , ischemic cortical brain injury subject with CPC of grade 5 (died within 72 H after cardiac arrest); and ,
ischemic cortical brain injury subject with CPC of grade 5 (died within 24 H after cardiac arrest).