Biomedical Engineering Reference
In-Depth Information
The amplitude probability distributions {
P
m
(
I
i
)} within
W
(
m, w,
) then are the
ratios of the number of samples falling into bins {
I
i
} to the window size (
w
). Accord-
ingly, the Shannon entropy (
SE
(
m
)) corresponding to the window
W
(
m, w,
Δ
Δ
) will
be
M
=−
=
∑
(
)
()
()
()
m
m
SE m
P
I
log
2
P
I
(3.73)
i
i
i
1
By sliding the window
w
, we eventually obtain the time-dependent entropy
(TDE) of the whole signal. Figure 3.29 demonstrates the general procedure for cal-
culating time-dependent entropy. One of the advantages of TDE is that it can detect
the transient changes in the signals, particularly the spiky components, such as the
seizures in epilepsy or the bursting activities in the EEG signals during the early
recovery stage following hypoxic-ischemic brain injury. When such a seizure-like
signal enters the sliding window, the probability distribution of the signal ampli-
tudes within that window will change and become sharper, resulting in more diver-
sion from the uniform distribution. Therefore, a short transient activity causes a
lower value for the TDE. We demonstrate such a spike-sensitive property of TDE
with the synthesized signal shown in Figure 3.30. Figure 3.30(a) is the simulated sig-
nal consisting of a real EEG signal recorded from a normal anesthetized rat and
three spiky components. The amplitudes of the spikes have been deliberately
rescaled such that one of them was even unnoticeable in the compressed waveforms.
By using a 128-sample sliding window (
w
1), Figures 3.30(b, c) show that
TDE successfully detected the three transient events.
The choices of the parameters, such as windows size (
w
), window lag (
=
128,
Δ=
), parti-
tioning of the probability (
I
i
and
P
i
), and entropic index
q
, directly influence the per-
formance of TDE. Nevertheless, parameter selection should always consider the
rhythmic properties in the signals.
Δ
100
I
1
80
I
2
60
I
3
40
I
4
20
I
5
0
I
6
−
20
I
7
−
40
I
8
−
60
W(1, w,
Δ
I
9
W(2, w,
Δ
−
80
I
10
−
100
0
128
256
384
512
640
768
896
1024
Figure 3.29
Time-dependent entropy estimation paradigm. The 1,024-point signal is partitioned
into 10 disjoint amplitude intervals. The window size is
w
= 128 and it slides every
Δ
= 32 points.
(
From:
[97]. © 2003 Biomedical Engineering Society. Reprinted with permission.)
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