2. OVERVIEW
There is a
great
importance
of the EEG
as a non-
One of them
invasive
is Epilepsy.
diagnostic
tool in a
wealth of
neurological
disorders,
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3. The segmentation
procedure assumes
that the second
These transients are order signal
of great diagnostic characteristics after
values and are reaching a new state
characteristic of remain constant for
EEGs of epileptic at least a couple of
patients. seconds.
It is therefore badly affected
by the occurrence of short-
time non- stationaries i.e.
transients, which are
typically 100 ms or less in
duration.
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6. An example of above is in below figre, whiich
shows an EEG of the burst suppression type.
Observe that the suppression period is
interrupted by a sharp wave(event 1) and
subsequently followed by a burst (event 2).
The linear prediction filter adapted within the
suppression period.
The corresponding SEM fig. above clearly
exhibits sharp jumps as the transient enters
and leaves the moving window of 2 s length as
indicated by the arrows 3 & 4(Fig. 4.15b).
Then this would lead to a meaningless
segmentation at event 3. The reason for this
behavior is seen when examining the
prediction error(fig. 4.15 c). Page 6
7. The transient leads to isolated high values of
the prediction error.
Consequently, a constant high value of the
power term SEM results as long as the
transient is contained in the moving window.
There is a clear & simple technique to remedy
this situation.
We may limit the instantaneous power by clipping the
prediction error at a threshold Ɵ, i.e set Ɵ is indicated by the
dashed line in Fig. 4.15c. Fig 4.15d is the SEM as calculated
from the clipped prediction error, the jumps are no longer
present and threshold is reached at event 2 as desired.
The signal reconstructed form the clipped
prediction error is shown in Fig. 4.15e.
Within the suppression segment, only the
transient is reduced in power. The rest of the
signal is unaffected.
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8. After we have seen how we may remove the undesirable influence of a
transient on the segmentation process the natural question, if we may turn the
argument around, is does eq. 4.105 yield a reasonable definition for transient
behavior? Generally speaking transients are not deterministic signals. The
sharp waves have to be seen in their proper context. The sharp waves in the
burst phase of Fig. 4.15a are not regarded as such by the electro-
encephalographer for the simple reason that they are not isolated. Instead, the
“burst” is thought to reflect a new state of the brain, which we formalize by
calling it a quasi-stationary segment.
Recall the prediction error is a measure of the unexpectedness of the current
value of the signal, unexpected with regard to the type of activity in the
adaptation window. In this way the prediction error is indeed a good indicator for
non-stationary behavior.
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9. (n-1) +
(n-1)
=
It will be sensitive to steep slopes & large amplitudes provided the wavelength
(n) + is different from those encountered during adaptation. In this way clipping the
prediction error provides us with the desired splitting of the signal into a quasi-
stationary part (below threshold) and local non-stationaries(above threshold).
However, experience has shown that criterion given by Eq. 4.105 with a
threshold setting suitable for segmantation is far too sensitive for transient
detection. EEG spikes generally have a duration of 50-100 ms. As a reasonable
method for the elimination o ffalse alarm caused by random fluctuations in the
prediction error it is the elimination of false alarm caused by random
fluctuations in the prediction error power with this time constant. Accordingly,
the following heuristic criterion is adopted as suggested in [1], i.e.
= (n-1)+
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10. From those, e(k)’s for which │e(k)│≥ Ɵ. Then, if > theta cap with yet
another threshold theta cap the triple {s(n-1), s(n), s(n+1)} of the signal
values iss called a Spike and classified as a transient.
Note that segmentation without transient elimination leads to meaningless
results. If the background activity changes and the linear prediction filter
does not adapt to the new signal structure it may happen that
subsequently the total signal is classified as a transient as shown in fig.
4.15b. If no segmentation and correspondingly no new adaptation takes
place at event 2, the whole burst phase would appear as a concatenation
of sharp waves.
While this is certainly not the best method from a theoretical view point(as
this prediction filter is neither in frequency nor in phase with the (optimum)
matched filter for the sharp waves), nevertheless it has the advantage of
not consuming any additional computation time.
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11. For a demonstration of the detection of spikes in real life situations using the
above procedure we refer to the example discussed in [1] and given in detail in
Fig. 4.16.
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12. OVERALL PERFORMANCE
The only real way to find out would be to construct the entire algorithm
which takes the EEG as input & produces a diagnosis, say healthy or
sick, as output and then compare it with that given by the neurophysiologist.
Nevertheless, we give an example, the most interesting, from a clinical
stand point that demonstrates the effectiveness of the proposed method on
four channels of an EEG with paroxysmal potentials[1] as shown in Fig.
4.17. Note how well the spike and wave patterns are separately segmented
and observe that the most pronounced individual spikes are detected
simultaneously in all the channels. Also the train of rhythmical delta waves
in channels 1 and 3 are clearly identified.
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14. Another way of judging the perormance is to reconstruct the original EEG
signal using the ( ) coefficients of the prediction error filter(Wiener
filter), for each one of them. The O/P( of each of these filters), when excited
by computer generated white noise, must mimic the original EEG segment
while ignoring the phase relationship. The resemblance to the original EEG
is a measure of performance of the proposed method.
Fig. 4.18 shows how a simulated EEG siganl has been obtained by using
the above concept and its comparison with the original signal.
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16. This brings to a close of our discussion on how one is not only able to
recognize and classify EEG waveforms but also detect paraoxysms,
i.e. transients associated with abnormalities.
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