Basic Step of Spectral Entropy Computations

The core of the algorithm is the concept of entropy As defined in information theory by Shannon and Weaver (1949).

In spectral entropy analysis, this concept is applied to the power spectrum of a signal according to the following steps:

Let's take a simple example where three Pieces of signals corresponding to different Entropy values are shown.

In this simple example, we consider simple Pieces of signal with 8 spectral components, of which N=7 frequency components are considered.

The perfect sine wave includes only one nonzero spectral component, which is normalized to 1 in step 1.

In the Shannon mapping in step2, both spectrum values 1 and 0 contribute a value of 0.Thus in step3, corresponding entropy = 0.

Some amount of white noise is superimposed on top of the sine Wave. After norma1izaUon (step 1), the spectrum includes one high component corresponding to the frequency of the sine wave and smaller nonzero components.

In the Shannon mapping (step2), both types of components Contribute nonzero values to the entropy of the signal, corresponding to a total entropy = 0.12 + 6 * 0.08 = 0.60 (step 3).

The sine wave has disappeared, and there is only white noise left. After normalization (step 1), the noise contributes to N=7 components that are equal to Q(f) = 1l7. These are transformed to values (1/7)log(7) by the Shannon mapping (step 2).

Finally, summation of these components and normalization By 1/log(7) give an entropy value = 7*(1/7)log(7)/log(7) = 1 (step 3). White noise has maximal entropy = 1.

Entropy During Burst Suppression

When burst suppression sets in, the part of the signal that contains suppressed EEG is interpreted as a perfectly regular signal with zero entropy, where as the entropy associated with the bursts is computed according to the techniques described previously.

The burst suppression ratio (BSR) is independently Indicated on the monitor screen.

Advanced Frequency Analysis

An EEG signal consists of a wide selection of frequencies, ranging from slow delta (from 0.5 Hz) up to frequencies on the order of 50 Hz. To optimize between time and frequency resolution, the Entropy module utilizes time-frequency-balanced spectral entropy analysis which apples a set of time windows ranging from less than 2 to 60 seconds. The lengths are optimized for each particular frequency component. In this way, the information is extracted from the signal as fast as possible.

The State Entropy (SE) is computed over the frequency range from 0.8 Hz to 32 Hz. This corresponds to the EEG-dominant part of the spectrum, and SE therefore primarily reflects the cortical state of the patient. The Response Entropy RE) is computed over a frequency range from 0.8 Hz to 47 Hz, containing also the high frontal EMG-dominated frequencies.

The figure shows a schematic drawing of the composite spectrum of EEG and FEMG signals during anesthesia on a logarithmic scale.

The Response Entropy RE (red curve) has been scaled to range between 0 and 100, while the State Entropy SE (black curve) ranges from 0 to 91.

The difference between RE and SE corresponds to the contribution from frequencies between 32 and 47 Hz. These higher frequency components are evaluated with a time window of less than 2 seconds, providing immediate indication of FEMG activation.