Entropy

[JA20061004: Entropy]

Definition of entropy

Entropy in thermodynamics = the state of a gaseous or fluid system and the distribution probability of molecules

Entropy in information theroy by Shannon = a measure of information comparised in a given amount of signal

Shannon entropy

Shannon entropy measures the predictability of future amplitude values of the EEG based on the probability distribution of amplitude values already observed in the signal.

Awake state vs anaesthesia

Probability density functions are histograms of amplitude values vs the number of sample EEG signals at each value

In awake state, the probability density function curve is skewed

In anaesthesia, the probability density function curve is more flat and uniform

Deficiency

Conceptually, there is no normalisation
--> Absolute value varies considerably between individuals

Therefore,

Cannot be used to measure depth of clinical anaesthesia between patients

Spectral entropy

EEG signals are first subjected to Fast Fourier transformation to identify sinusoidal components
--> A power spectrum is calculated

Then,

Shannon function is applied to the power spectrum to assign each frequency present a specific value

Thus,

Spectral entropy = the sum of these values

Awake state vs anaesthesia

An anaesthetised person has more regular and orderly EEG

--> Power spectrum has more similar frequencies

--> When Shannon function is applied, spectral entropy number is low

M-Entropy

Spectral entropy is used in M-Entropy module of the S/5 Anaesthesia monitor by GE Healthcare Finland

Sampling rate is 400Hz

State entropy and response entropy

EEG vs EMG

EEG signals taken by frontal electrodes includes a significant electromyographic (EMG) component (which originate from facial muscle activity)

Lower frequencies (<32Hz) contains predominantly EEG signals

At higher frequencies, EEG power decreases exponentially

EMG has a wide noise-like spectrum and dominates at frequencies > 32Hz

State entropy (SE)

State entropy is calculated over the EEG-dominant part of the spectrum
* 0.8 - 32 Hz
* Should reflect the cortical state of the patient
* Range of SE = 0 - 91

Response entropy (RE)

Response entropy is calculated over a frequency range from 0.8 to 47Hz
* Includes both EEG and EMG dominant spectrum
* Range of RE = 0 - 100

Inadequent analgesia
--> Increased EMG
--> Increased RE (relative to SE)

Thus,

RE should be an indirect measure of analgesia adequacy

SE and RE

When EMG power = 0
--> RE = SE

When EMG power > 0
--> RE > SE

Recommended range

Recommended range for both RE and SE = 40-60

Clinical studies

• RE indicates emergence from anaesthesia 11 seconds earlier than SE
• During anaesthesia with propofol and remifentanil, BIS is comparable to spectral entropy (SE and RE), but more specific
• BIS, SE and RE are not valid when anaesthetics is by ketamine (increase of value despite deeper hypnosis) and by nitrous oxide (unchanged value despite deeper hypnosis)