6.3  Inverse measure

All information to this point has shown a stable and consistent behavior of the high frequency band during behavioral failures identified by the visual test.  These consistently observed trends form the basis of the detection algorithm developed in this work.  This detection algorithm will only use frequency activity above 80Hz for three primary reasons.  First, although lower frequency bands from the middle of the alpha band and higher react during failures by losing energy, the activity (as it pertains to this test) tends to be very unstable with large energy fluctuations that require significant smoothing, thereby decreasing their responsiveness to behavioral changes.  The low frequency band information is more inconsistent than the high frequency bands both in terms of observed changes and variations among test subjects.  Third, by limiting the algorithm to only use frequencies above 80Hz, we can demonstrate the ability of the high frequency bands to track the evolution of drowsiness without confusing the analysis by introducing the traditional low frequency bands which have already been thoroughly studied and reported to be inaccurate correlaters with "drowsiness" in the literature.

In order to use the high frequency bands as the basis of an analytic measure, there are several modifications which need to be made to increase the usefulness of the high frequency information.  In particular, these changes are:

• Amplify the energy changes that correlate with drowsiness.
• Reduce the large amplitude fluctuations caused by artifact and peaks.
• Expand the range between good performance and failure.
• Map decreases in energy to an increased measure of drowsiness.

Although there are many functions which satisfy the above requirements (any mapping where decreased energy is transformed to increased output), a simple function that has good performance is to invert the total energy in each frequency bin over time.  The inverse function amplifies the small changes in signal energy, nonlinearly expands the range between good performance and failure, and drives the large amplitude spikes toward zero.  These changes now shift the natural scale of the measure from the higher amplitude "alert" levels to the lower amplitude "drowsy" levels which require a higher level sensitivity for tracking.  Inverting the energy only appears to work in the high frequency bands and does not perform well on energy in the traditional frequency range due to the large fluctuations and inconsistent correlations with the behavior to be classified and detected.

By inverting the energy in the frequency bands shown in Figure 6.2.5 (and Figure 6.2.4), Figure 6.3.1 results.  The output activity is now the inverse of the actual behavior, that is, the energy in each frequency band increases with drowsiness instead of decreasing.  Because the smallest components become the largest and the large amplitude spikes are driven toward zero, there is no further need to rescale the ordinate (energy in the spectrogram) so that the important features of the energy shifts are visible.  The effect of the changes in the high frequency content of the EEG  that we are interested in capturing now naturally follow a suitable scale.  Artifact and spikes increase energy in the segments and drive the output of the frequency bands toward zero (which still indicates alertness).  For any energy-based measure of this type, spikes and other artifact will drive the measure toward one of the two extremes of the scale.  In our case, artifact drives the output toward alertness and this should not present any significant problems because we have observed that as subjects are approaching failures due to extreme drowsiness, they produce much less artifact before and during failures than during periods of normal behavior.  This behavior can work in our favor by naturally lowering the probability of missed detections caused by artifact that would otherwise obscure the measure.  In contrast, the low frequency (traditional) bands of delta and theta activity (and those cases where alpha bursts are being tracked) correlates with drowsiness and sleep by the presence of energy and not its disappearance, therefore, the presence of artifact could produce false positive indications of drowsiness during "normal" alert periods, while the frequencies being used in the proposed measure react with the disappearance of energy and are not prone to these particular false alarms.  Although artifact increases the sensitivity of the high frequency energy to missed detections, there is a natural decrease in artifact during drowsiness because artifact is most commonly induced by movement and activity (talking, moving, etc.) which is more of an indication of waking behavior than extreme sleep.

 

Figure 6.3.1  Inverse high frequency energy band tracking

Activity of inverse energy bands (fluctuations, swing, etc.)

Limiting the bandwidth of each frequency bin to 41.5Hz shows how different portions of the high frequency band react during drowsiness.  Because of the individual characteristics of the various frequency bins, the output falls on different scales.  By combining all of the individual frequency bands as shown in Figure 6.3.1 onto a single 3-dimensional surface shaded by amplitude, we are able to display all of the frequency bands on a single scale to highlight differences in amplitude between the various frequency bands.  In Figure 6.3.2, all ten frequency bands are displayed on the surface (corresponding to bins 0-9 of Figure 6.3.1).  Linear interpolation between the individual bands is used to produce a continuous surface which eliminates the visual discontinuities that would normally exist between bands.  Just as observed during the analysis given in chapter 5, the lowest frequency bands contain the most energy, which is now realized as the lowest amplitudes of the inverse bands.  The total energy in each band decreases as frequency increases.

 

Figure 6.3.2  Inverse high frequency energy bands

In Figure 6.3.2 we see that all frequency bands respond to the failure by an increase in amplitude of the inverse measure.  The highest frequency bands achieve the highest output levels both during failures and under normal conditions.  The higher frequency bands have been shown to react sooner than the lowest frequencies in this range during the onset of a failure.  All frequency bands return to normal levels after the failure subsides and normal performance resumes.

Because the highest frequency bands have the highest overall levels, fluctuations in this energy are most visible for these bands.  Although all of the frequency bands show fluctuations, it appears that proper combination of these frequency bands may result in a reduction of the fluctuations and an overall smoothing and stabilization of the measure.

In the examples which follow both the inverse of the high frequency bands and the 3-dimensional surface plots generated from the individual bands are shown.

 

Figure 6.3.3  Inverse high frequency energy band tracking

 

Figure 6.3.4  Inverse high frequency energy bands

 

Figure 6.3.5  Inverse high frequency energy band tracking

Figure 6.3.6  Inverse high frequency energy bands

 

Figure 6.3.7  Inverse high frequency energy band tracking

Figure 6.3.8  Inverse high frequency energy bands

In each of the above examples, the high frequency activity was consistent with failures and by this stage there seems to be no doubt as to the usefulness of the high frequency information in correlating with drowsiness.  As clearly indicated, the high frequency inverse-bands increase during the failure portions and immediately return to normal levels after the failure has subsided.  In all cases the transition into the failure is a gradual process relative to the exit transitions.  In all of these examples the subject was allowed to naturally progress into the failure, but was awakened abruptly from the failure either by their head falling to the side or by an operator speaking to them for the purpose of continuing the test.

As observed, the general trend and behavior of the high frequency bands are obvious, next a computational framework is defined which uses the high frequency information and produces a one-dimensional output corresponding to the levels of drowsiness as indicated by test performance.  After formally defining the structure of the measure, a specific set of parameters are determined, and the measure is examined under various conditions to gauge performance.

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