*3.2.2. EEG signal entropy*

Entropy represents the degree of disorder in a system. Ludwig Boltzmann defines entropy as the logarithmic function of the number of microstates corresponding to a macrostate. In 1949, Claude Shanon defines information entropy as being:

$$\mathbf{S} = \sum\_{\mathbb{H}}^{\mathrm{n}} \mathbf{P}(\mathbf{x}) \log \mathbf{P}(\mathbf{x}) \tag{1}$$

The EEG signal entropy calculation is based on the following algorithm:

where [f1, f2] = frequencies between which the EEG signal is analyzed,

40–60 in order to prevent waking up during the intervention [23–25].

xenon anesthesia depth clinical signs correlate well with BIS score values [35].

The algorithm used incorporates spectral analysis, bispectral analysis and burst-suppression activity analysis (BS). Spectral analysis, described above, decomposes the signal based on the amplitude of each frequency, analyzing data individually and ignoring the relationship with other constituents. In the human brain, there are several EEG signal generators. While the patient is awake, the EEG signal is produced by the independently emitted activity of several generators, only slightly synchronized. As the patient falls asleep or is anesthetized,

The EEG signal is acquired at a frequency of 400 Hz, and to analyze it, several epochs (windows) are used, between 0.92 and 60.16 seconds, in order to cover all EEG signal frequencies. The shortest epoch is used to analyze frequencies between 32 and 47 Hz, and the 60.16 epoch to analyze frequencies under 2 Hz. The device provides two entropy indices: state entropy (SE) and response entropy (RE). SE analyzes EEG in the frequency domain 0.8–32 Hz, while RE in the 0.8–47 Hz frequency domain. The difference between RE and SE is given by the EMG activity: it is assumed that an increase of entropy in the 32–47 Hz domain corresponds to an increase of frontal electromyographic activity, and this difference shows indirectly the quality of intraoperative analgesia). SE is between 0 and 91, and RE is between 0 and 100.

During anesthesia, the values displayed by the entropy monitor must be in the range of

The Aspect Medical company was the first to market a monitor for anesthesia depth, in 1994 [26]. It is based on the bispectral analysis of EEG signal [27]. The monitor analyzes the EEG recorded by prefrontal electrodes, based on an algorithm, undisclosed entirely up until today [28]. This algorithm calculates a score between 0 (isoelectric line) and 100 (patient awake). This algorithm was validated by correlating the clinical sedation score, lack of response to pain stimulation and EEG parameters for approximately 1500 patients (cumulating approximately 5000 hours of recordings). BIS monitoring evaluates well the degree of sedation/hypnosis of anesthesia, and not directly the anesthetic depth. It was validated for all volatile and intravenous anesthetic, except ketamine. As this generates thalamocortical dissociation, the EEG is similar to that of an awake patient. During sevoflurane anesthesia, ketamine may increase the BIS score, though anesthesia deepens [29]. In the case of propofol anesthesia, analgesic dose of ketamine does not influence the bispectral index [30–32]. Though xenon has a similar mechanism to ketamine and was not used in the validation process of the BIS monitor, it modifies the EEG similarly to propofol [33]. As for correlating the BIS score, older studies have stated that BIS under 50 does not ensure hypnosis [34]. A more recent study reveals that

log(*N*[*f*1, *<sup>f</sup>*2]) (2)

Important Issues in Coma and Neuromonitoring http://dx.doi.org/10.5772/intechopen.79448 87

*SN*[*f*1, *<sup>f</sup>*2] <sup>=</sup> *<sup>S</sup>*[ \_\_\_\_\_\_\_\_\_\_ *<sup>f</sup>*1, *<sup>f</sup>*2]

N[f1, f2] = number of frequencies between f1and f2.

*3.2.3. Bispectral index*

where S = entropy,

P = apparition probability,

log = binary logarithm.

As EEG is a signal composed of several types of waves, with a disorderly aspect, the more disorderly (more types of waves), the higher the entropy. An isoelectric EEG signal has a null entropy. This type of entropy, applied to EEG signals, was used to monitor anesthetic depth during desflurane anesthesia [22]. The Datex-Ohmeda company (now acquired by GE) developed a device that analyzes EEG signal entropy and displays it as a score.

**Figure 4.** EEG power spectrum density (PSD). In this figure, median frequency (MEF) and spectral edge frequency (SEF) are displayed on the PSD graph.

The EEG signal entropy calculation is based on the following algorithm:

$$\text{SN}\left[f1, f2\right] = \frac{\text{S}\left[\mathfrak{f}1, f2\right]}{\log(\text{N}\left[\mathfrak{f}1, f2\right])}\tag{2}$$

where [f1, f2] = frequencies between which the EEG signal is analyzed,

N[f1, f2] = number of frequencies between f1and f2.

The EEG signal is acquired at a frequency of 400 Hz, and to analyze it, several epochs (windows) are used, between 0.92 and 60.16 seconds, in order to cover all EEG signal frequencies. The shortest epoch is used to analyze frequencies between 32 and 47 Hz, and the 60.16 epoch to analyze frequencies under 2 Hz. The device provides two entropy indices: state entropy (SE) and response entropy (RE). SE analyzes EEG in the frequency domain 0.8–32 Hz, while RE in the 0.8–47 Hz frequency domain. The difference between RE and SE is given by the EMG activity: it is assumed that an increase of entropy in the 32–47 Hz domain corresponds to an increase of frontal electromyographic activity, and this difference shows indirectly the quality of intraoperative analgesia). SE is between 0 and 91, and RE is between 0 and 100.

During anesthesia, the values displayed by the entropy monitor must be in the range of 40–60 in order to prevent waking up during the intervention [23–25].

#### *3.2.3. Bispectral index*

Spectral edge frequency (SEF) is the value of frequency from which we can draw a perpendicular to Ox that leaves 90 or 95% of the spectral power function under graphic area to the

If the patient is anesthetized, the values of these parameters will decrease proportionally with the degree of sedation (they will shift to the left), because during sedation, the high-frequency fast waves EEG activity ceases [21]. Surgical anesthesia is performed at the moment the EEG

Entropy represents the degree of disorder in a system. Ludwig Boltzmann defines entropy as the logarithmic function of the number of microstates corresponding to a macrostate. In 1949,

As EEG is a signal composed of several types of waves, with a disorderly aspect, the more disorderly (more types of waves), the higher the entropy. An isoelectric EEG signal has a null entropy. This type of entropy, applied to EEG signals, was used to monitor anesthetic depth during desflurane anesthesia [22]. The Datex-Ohmeda company (now acquired by GE)

**Figure 4.** EEG power spectrum density (PSD). In this figure, median frequency (MEF) and spectral edge frequency (SEF)

developed a device that analyzes EEG signal entropy and displays it as a score.

P(x)logP(x) (1)

i=1 n

left [20] (**Figure 4**).

shows mostly theta waves.

86 Current Topics in Intensive Care Medicine

Claude Shanon defines information entropy as being:

S = ∑

*3.2.2. EEG signal entropy*

where S = entropy,

P = apparition probability,

log = binary logarithm.

are displayed on the PSD graph.

The Aspect Medical company was the first to market a monitor for anesthesia depth, in 1994 [26]. It is based on the bispectral analysis of EEG signal [27]. The monitor analyzes the EEG recorded by prefrontal electrodes, based on an algorithm, undisclosed entirely up until today [28]. This algorithm calculates a score between 0 (isoelectric line) and 100 (patient awake). This algorithm was validated by correlating the clinical sedation score, lack of response to pain stimulation and EEG parameters for approximately 1500 patients (cumulating approximately 5000 hours of recordings). BIS monitoring evaluates well the degree of sedation/hypnosis of anesthesia, and not directly the anesthetic depth. It was validated for all volatile and intravenous anesthetic, except ketamine. As this generates thalamocortical dissociation, the EEG is similar to that of an awake patient. During sevoflurane anesthesia, ketamine may increase the BIS score, though anesthesia deepens [29]. In the case of propofol anesthesia, analgesic dose of ketamine does not influence the bispectral index [30–32]. Though xenon has a similar mechanism to ketamine and was not used in the validation process of the BIS monitor, it modifies the EEG similarly to propofol [33]. As for correlating the BIS score, older studies have stated that BIS under 50 does not ensure hypnosis [34]. A more recent study reveals that xenon anesthesia depth clinical signs correlate well with BIS score values [35].

The algorithm used incorporates spectral analysis, bispectral analysis and burst-suppression activity analysis (BS). Spectral analysis, described above, decomposes the signal based on the amplitude of each frequency, analyzing data individually and ignoring the relationship with other constituents. In the human brain, there are several EEG signal generators. While the patient is awake, the EEG signal is produced by the independently emitted activity of several generators, only slightly synchronized. As the patient falls asleep or is anesthetized, the number of active generators decreases and they become more synchronized. Bispectral analysis quantifies the phase-phase coupling between these EEG signal generators.

BIS components are *beta ratio* and *SyncFastSlow*. Beta ratio is the logarithm of the ratio of two frequency components of the spectral power (30–47 Hz and 11–20 Hz), while *SyncFastSlow* is the logarithm of the bispectral ratio of 0.5–47 Hz and 40–47 Hz [36].

$$\text{BetaRatio} = \log\left(\frac{\text{P} \, 30 \, -47}{\text{P} \, 11 \, -20}\right) \tag{3}$$

*3.2.4. Narcotrend monitoring*

*3.2.5. Consciousness index*

a system state [52].

*3.2.6. Approximate entropy*

This monitor was marketed in 2000 by the Monitor Technik company. The EEG signal is picked up by three electrodes in the frontal area. It is then filtered and noise is removed. EEG is analyzed in the 0.5–47 Hz frequency domain. The algorithm includes the relative power of alpha, beta, theta and delta frequencies, median frequency, spectral edge frequency and spectral entropy. This monitor displays values between 0 and 100. The depth of anesthesia is divided into five stages [49]. The values provided by this monitor are well correlated with the ones provided by BIS monitoring [50]. The Narcotrend monitor has been proven useful in the postoperative care of the patients who underwent propofol sedation during cardiac surgery [51].

Important Issues in Coma and Neuromonitoring http://dx.doi.org/10.5772/intechopen.79448 89

The monitor for the consciousness index is a wireless, portable monitor as well, with a 10-meters range. It is produced by Morpheus Medical. It provides a score with values between 0 and 100, and, similar to the BIS monitoring during anesthesia, the value of the consciousness index must be maintained between 40 and 60 to prevent waking up during anesthesia. This monitor analyzes EEG, using symbolic dynamic analysis. As EEG is a variation of potential through time, it can be seen as a dynamic system, in which every moment has a state that can be defined through a real number. The dynamic symbol method analyzes a dynamic system as being composed of a discrete sequence of abstract symbols that each correspond to

This monitor was compared with BIS monitoring and similar results were found [53].

dant information there is, the less complex the signal and deep the anesthesia is [54].

constant the distance between two vectors in a series is [55].

Entropy is the degree of disorder in a system, thus an extensive measurement of chaos. At the beginning of the twentieth century, the mathematicians Andrey Kolmogorov and Henri Poincare further developed the mathematical analysis of chaos. In 1991, Steven Pincus introduced the notion of approximate entropy. Approximate entropy measures the complexity of a system. As it is little influenced by noise, it has an advantage in the analysis of systems exposed to a strong source of noise. Mathematically, approximate entropy quantifies how

There is one other consciousness index that uses Lempel-Ziv complexity analysis. This method was established in 2013 by a team of researchers led by Adenauer Casali and Olivia Gosseries. This index was studied during midazolam sedation and propofol-xenon anesthesia, on a limited number of subjects. It is based on evaluating cortical reactivity and intercortical connectivity, using high-density EEG and transcranial magnetic stimulation on several cortical areas: superior occipital gyrus, superior medial frontal gyrus, superior parietal gyrus and premotor rostral cortex. EEG signals were analyzed using the Lempel-Ziv complexity algorithm, which approximates the amount of nonredundant information in a binary system, thus estimating the minimal amount of patterns required to describe a signal. The less EEG signal nonredun-

$$SyncFastFlow = \log\left(\frac{\text{B}}{\text{B}}\frac{0.5-47}{40-47}\right) \tag{4}$$

BIS monitors display several parameters, such as the BIS score value (between 0 and 100), which should be maintained during anesthesia between 40 and 60 to prevent waking up, signal quality index, suppression ratio for a 60 seconds epoch (SR), the minute burst count (BC), frontal electromyographic activity (EMG)—which results from analyzing the EEG signal in the 70–110 Hz frequency interval (assumed to be produced by spontaneous frontal muscles activity) and is between 30 and 55 dB [37].

BIS monitoring can be used in the intensive care wards as well, to monitor patient sedation [38]: in traumatic brain injury, a value under 60 correlates with a negative prognosis [39]. BIS monitoring may also be used to detect cerebral vasospasm in critical patients [40]; it has been proven that it correlates well with the consciousness level of the ICU patients, it aids in adjusting sedative dosage, it has a prognostic value and it is useful in monitoring induced coma for a status epilepticus [41–44].

EMG activity is not greatly influenced by the degree of curare neuromotor block, but the pain stimulus EMG variation during anesthesia depends on the degree of neuromuscular block [45].
