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Revista Brasileira de Anestesiologia

Print version ISSN 0034-7094On-line version ISSN 1806-907X

Rev. Bras. Anestesiol. vol.54 no.3 Campinas May/June 2004 



Entropy: a new method of measuring depth of anesthesia. Comparative study with bispectral index during clinical evaluation in tracheal intubation of patients anesthetized with sevoflurane*


Entropía: un nuevo método de mensuración de la profundidad de la anestesia. Estudio comparativo con el índice bispectral en la evaluación clínica de la entubación traqueal con sevoflurano



Rogean Rodrigues Nunes, TSA, M.D.

Diretor Clínico e Chefe do Serviço de Anestesiologia do Hospital São Lucas, de Cirurgia & Anestesia; Mestre em Cirurgia - Área de Concentração: Anestesiologia pela UFC; Membro da Sociedade Brasileira de Engenharia Biomédica; Graduando em Engenharia Eletrônica pela Universidade de Fortaleza





BACKGROUND AND OBJECTIVES: Spectral entropy, a new EEG analysis method based on the quantification of EEG chaos, was developed to monitor anesthetic depth. The spectral entropy involves two distinct types of analysis: state entropy (SE), which includes low frequency signals (< 32 Hz), and response entropy (RE), which includes signals up to 47 Hz. This study aimed at comparing entropy-derived values to BIS-derived values and sub-cortical (autonomic and somatic) responses recorded during tracheal intubation in patients submitted to general anesthesia with sevoflurane.
METHODS: Participated in this study 36 patients ASA I, aged 20 to 44 years, assigned to four groups (G1-G4) of nine patients submitted to tracheal intubation (TI). In all groups anesthesia was induced with sevoflurane, associated or not to fentanyl, according to the following regimens: G1 = sevoflurane plus 2.5 µ fentanyl; G2 = sevoflurane plus 5 µ fentanyl; G3 = sevoflurane plus 7.5 µ fentanyl; and G4 = sevoflurane plus saline solution. The following parameters were monitored: SBP, DBP, HR, BIS, SE, RE, sevoflurane expired concentration (EC) and motor response to TI at three moments: M1 = immediately before induction; M2 = immediately before tracheal intubation and M3 = one minute after tracheal intubation.
RESULTS: BIS and SE values have linearly varied in all groups, with significant differences between M2 and M3 for Groups 1 and 4. At M3, BIS and SE values in G4 were above those for the threshold between consciousness and unconsciousness. Hemodynamic changes were not clinically significant, with the exception of HR increase between M1 and M3 for G4 (p < 0.05%). In G1, 66% of patients have reacted to TI maneuvers as compared to 100% in G4.
CONCLUSIONS: Our findings suggest that sevoflurane alone or in association with 2.5 µ or 5 µ fentanyl does not effectively block CNS cortical and subcortical components responses during tracheal intubation, being sevoflurane plus 7.5 µ fentanyl the best association to control anesthetic components.

Key Words: ANALGESICS, Opioids: fentanyl; ANESTHETICS, Volatile: sevoflurane; MONITORING, bispectral index, state entropy, response entropy


JUSTIFICATIVA Y OBJETIVOS: Entropía espectral, un novo método de análisis del EEG, fundamentado en la cuantificación del caos del EEG, fue desarrollado para monitorización de la profundidad anestésica. Él separa la monitorización en dos tipos de análisis: entropía de estado (SE), que incluye señales de baja frecuencia (< 32 Hz) y entropía de respuesta (RE), que incluye señales con frecuencia hasta 47 Hz. El objetivo de este estudio fue comparar los valores de entropía con los del BIS y respuestas sub-corticales a entubación orotraqueal, en pacientes sometidas a la anestesia general con sevoflurano.
MÉTODO: Participaron del estudio 36 pacientes con edades entre 20 y 44 anos, ASA I, distribuidos en cuatro grupos de nueve, sometidos a la entubación orotraqueal (IOT). En todos los grupos, la anestesia fue inducida con sevoflurano, asociado o no al fentanil, de acuerdo con lo siguiente: (G1 = sevoflurano y 2,5 µ de fentanil; G2 = sevoflurano y 5 µ de fentanil; G3 = sevoflurano y 7,5 µ de fentanil y G4 = sevoflurano y solución fisiológica). Fueron evaluados los siguientes parámetros: PAS, PAD, FC, BIS, SE, RE, concentración expirada del sevoflurano (CE) y respuesta motora a la IOT en tres momentos: M1 = inmediatamente antes de la inducción; M2 = inmediatamente antes de la entubación traqueal y M3 = un minuto después a entubación traqueal.
RESULTADOS: Los valores de BIS y SE variaron de manera linear en todos los grupos, con diferencias significativas entre M2 y M3 en los grupos G1 y G4, teniendo ambos (BIS y SE) presentando valores arriba de los limítrofes entre consciencia e inconsciencia en el momento M3 del G4. En relación al RE, apenas el G3 no mostró variaciones estadísticamente significativas entre los momentos M2 y M3. Las variaciones hemodinámicas no ultrapasaron valores clínicamente significativos, excepto elevaciones de la FC en el G4 entre los momentos M1 y M3 (p < 0,05%). En el G1, 66% de los pacientes reaccionaron a las maniobras de IOT y 100% en el grupo G4.
CONCLUSIONES: Este estudio indica que el sevoflurano aisladamente, asociado a 2,5 µ o 5 µ de fentanil, no bloquea efectivamente las respuestas de los componentes cortical y sub-cortical del SNC, siendo la dosis de 7,5 µ la mejor asociación al sevoflurano para control de estos componentes anestésicos.




Spectral entropy, a new EEG analysis method based on the quantification of EEG chaos, was developed to monitor anesthetic depth 1,2. As with BIS, spectral entropy also uses a 0 to 100 scale. In addition, it involves two distinct types of analysis: state entropy, which includes low frequency signals up to 32 Hz (quantifies cortical cerebral activity - hypnosis), and response entropy, which includes signals up to 47 Hz (evaluates surface EMG activity - sub-cortical component).

This study aimed at comparing entropy-derived values (both state and response entropy) to BIS-derived values to evaluate cortical and sub-cortical (autonomic and somatic) responses during tracheal intubation (TI) in patients submitted to general anesthesia with sevoflurane associated or not to fentanyl.



After the Institution's Ethics Committee approval, participated in this randomized double-blind study 36 patients of both genders, aged 20 to 44 years, physical status ASA I, Mallampati class I, normal head extension and body mass index between 21 and 28. Exclusion criteria were patients under drugs knowingly affecting EEG and sevoflurane MAC, drug abusers, use of sedatives in the last 48 hours or neuromuscular diseases. Patients were induced with sevoflurane and distributed in four groups of nine patients (G1, G2, G3 and G4, according to opioid (fentanyl) dose. Anesthesia was induced with sevoflurane by tidal volume technique, with initial vaporizer percentage demand established in 5% of O2 flow equal to 4 L.min-1 until reaching bispectral index = 65 3 (threshold between consciousness and unconsciousness), moment in which fentanyl was injected in the following doses: G1 (2.5 µ, G2 (5 µ, G3 (7.5 µ and G4 (saline solution). Tracheal intubation was performed 5 minutes after by the same anesthesiologist and with just one type of blade (Macintosh) 4, with anesthetic (sevoflurane) expired concentration adjusted at this time to maintain BIS = 30 (stabilized in 5 minutes), with manual ventilation under mask.

Three successive moments were evaluated for each group (M1 = immediately before anesthetic induction; M2 = immediately before tracheal intubation; and M3 = one minute after tracheal intubation). The following parameters were evaluated: bispectral index (BIS), state entropy (SE), response entropy (RE), sevoflurane expired concentration (EC), systolic blood pressure (SBP), diastolic blood pressure (DBP) and heart rate (HR). Skeletal muscle motor response was also recorded as adequate anesthetic depth parameter 5 during tracheal intubation. Clinically accepted lowest hemodynamic parameters limits were: SBP: 75 mmHg and DBP: 55 mmHg. Upper limits were considered clinically significant when above 30% of M1 values. As to HR, values 30% above M1 were also considered clinically significant. As to entropy values, state entropy varies 0 to 91 (between 40 and 60 during adequate anesthesia) and response entropy varies 0 to 100 (with adequate values between 40 and 60), being its values equal to or higher than SE when there is EMG activation. This activation is seen as a gap between RE and SE 6 which should be maintained below 10. Electrodes (BIS and entropy) were placed on fronto-temporal regions so that BIS would evaluate left channel and entropy would evaluate right channel, being initial measurement recorded after asking patients to remain with eyes closed. No patient was premedicated.

Results were submitted to statistical analysis through Analysis of Variance. Tukey's test was applied among levels of involved factors, considering significant p < 0.05.



Demographics data are shown in table I.

Mean SBP, DBP and HR in the three studied moments are shown in table II and figure 1, figure 2 and figure 3. It is observed statistically significant decrease (p < 0.05) in moments M1 and M3 only, for G1, G2 and G3. There have been no statistically significant SBP changes in G4. In comparing M1 and M3, there has been statistically significant difference in DBP in G1 and G4 only (p < 0.05), which has not been observed for G2 and G3. In comparing M1 and M3, there have been statistically significant HR differences for all groups. Clinically, however, according to prefixed criteria, changes were not significant, except for HR increase in G4. There has been motor reaction to TI in 66% of G1 patients. In G4, all patients had motor reaction to intubation maneuvers.

Mean BIS, SE and RE values are shown in table III and figure 4, figure 5 and figure 6. It is observed that BIS has not shown statistically significant differences in G2 and G3 between moments M1 and M3, being observed statistically significant BIS increase between M2 and M3 for G1 and G4 (p < 0.05), reaching threshold values between consciousness and unconsciousness (above 68) (Figure 4).

SE has not shown statistically significant difference between M2 and M3 when G2 and G3 were compared, being observed statistically significant differences between M2 and M3 for G1 and G4 (changes parallel to BIS).

There have been, however, statistically significant RE increases between M1 and M3 for G1, G2 and G4. For G3, p value was > 0.05 and SE-RE gap was lower than 10 between M2 and M3.



It has been Claude Shannon 7 who, in the late 1940s, has developed the modern concept of "logic" or "information" entropy as part of information or uncertainty measurement. Information theory dealt with the newly born data communication science. Shannon's entropy (H) is given by the following equation (canonic entropy):

H=-Spk log pk, where pk are the probabilities of a discrete event k.

It is a data dispersion measurement. Data with wide and flat probability distribution will have a high entropy value. Data with narrow and peaked distribution will have a low entropy value. When applied to EEG, entropy is a statistical descriptor of EEG signal variability (comparable to other descriptors, such as spectral edge or low frequency passages during general anesthetic induction).

There are several concepts and analytical techniques aimed at quantifying stochastic signals irregularities, such as EEG. Entropy is one of those concepts. While physical concept, entropy is proportional to the logarithm of the number of available microstates to a thermodynamic system, thus being related to the amount of "disorder" existing in the system. However, the word "disorder" is difficult to define. Boltzman has shown that thermodynamic entropy could be accurately defined as the proportionality constant k (Blotzman's) multiplied by the logarithm of the number of independent microstates (w) available to the system (microcanonic entropy):

S = k log (w)

Boltzman was able to explain changes in observable macro-parameters (such as temperature) as from kinetic energy changes of a collection of individual molecules and has become the pioneer of statistical mechanics science. Thermodynamic entropy has a well-established physical basis. It is possible to derive Shannon's entropy (or "information" entropy) (H) from Boltzman's thermodynamic formula (S). But it must be clearly stated that the existence of a formal analogy between H and S does not imply the existence of material basis for an equation between H and S with regard to cortical function. There are, however, major neurophysiological clues that the usefulness of information entropy estimators as measure of cortical function is due to the fact that, as cortex goes from consciousness to unconsciousness, there is a true neuronal decrease in the logarithm of the number of accessible microstates (S) 8,9. So, the word "entropy" may represent more than a simple statistical measurement of EEG pattern; may be, in a way, it would truly reflect intra-cortical information flow.

Entropy is the logarithm of the number of modes in which microstates may rearrange and still produce the same macrostate. The difference between true thermodynamic entropy and other information entropies is that kinetic energy distribution of individual molecules is not necessarily involved with information entropy estimators. By abstracting the word "energy" for the concept of heat and thermodynamics, it could reflect any change in the activity of "particles" making up the observed system. "Energy", then, represents changes in cortical pyramidal membrane potential; these changes promote potential local cortex field fluctuations.

Shannon was the first to define entropy in the information theory, in 1948. Then, in 1984, Johnson and Shore 10 have applied it to the power spectrum of a signal. Within this context, entropy describes irregularity, complexity or level of uncertainty of a signal. Let's see a simple example: a signal in which sequential values are alternately of one certain fixed magnitude and then of other has zero entropy value, that is, signal is totally regular and predictable. A signal with sequential values generated by a random numbers generator has higher complexity and entropy levels. Better clinical understanding of surface electromyography, state entropy and response entropy is critical, that is: surface electromyography (EMGS) gives the algebraic sum of electric activity in a population of muscle fibers. There is a direct ratio between EMGS amplitude and muscle stress during isometric muscle contraction (without movement) 11. In conscious patients without anesthetics, high tone activity observed by electromyography is positively correlated to the level of stimulation, alertness or psychological stress. Increased EMGs phase activity is associated to periods of somatic stress, for example pain 12. For unconscious patients monitoring, EMGs should be measured on frontal muscles, which have a relatively fixed length, thus minimizing the potentially complicating influence of fiber length variations (isotonic contraction). These muscles are also preferred for being innervated by special visceral efferent fibers of the facial nerve. It is important to remind that these muscles are derived from branchial arches which are considered visceral formations.

Frontal muscles EMGS provides a simple and noninvasive measurement of an autonomic tone aspect. Voluntary and involuntary frontal muscles contractions are responses represented by innervations through different pathways, since EMGS tone activity (baseline) and phase activity (abruptly increased) may be differently affected by abnormal alertness levels or by neuromuscular blockers 13-15.

Decreased alertness following general anesthetic induction is typically associated to dramatic frontal tone activity decrease. Several authors 14,16,17 have concluded that increased phase activity in the presence of drugs depressing EMGS amplitude is an indicator of inadequate anesthesia. In addition, these authors have also observed that EMGS-measured phase activity may be observed in the presence of neuromuscular blockers.

It has been shown that at least three fundamentally different types of stimulations - emotion, sounds and ischemia - may evoke surface EMG amplitude phase increase during stages of decreased alertness.

EMGS may be useful for opioids titration: facial muscles are not only voluntary, but also innervated by emotive centers located in brainstem (related to emotions/stress). Although intraoperative EMG activation by patients' movement is a quantal phenomenon, minor EMGS changes may reflect analgesic inadequacy (sub-cortical component with inadequate block). Mathews et al.18 have shown that postoperative opioids decrease EMGS. In addition, EMGS may act faster than BIS in emergence reactions. Kern et al. 19 have concluded that EMGs has correspondence in response to noxious stimulations applied to volunteers. Shander et al. 20 have also shown that EMGS may predict analgesic requirements, providing more effective intraoperative analgesic control (sub-cortical component). Lennon 21, in a study called Effect of partial neuromuscular blockade on intraoperative electromyography in patients undergoing resection of acoustic neuromas, has concluded that moderate neuromuscular block levels may be reached without impairing facial nerve EMG monitoring. Edmonds 15 has shown that EMGS in response to stress (pain) may measure brainstem function which is independent of consciousness level (cortex). Dutton 22 in a recent study called Craniofacial electromyogram activation response: another indicator of anesthetic depth, has concluded that EMG response may be used to estimate anesthetic depth.

A biopotential captured on patient's frontal region includes significant EMG component created by muscle activity. EMG signal has a wide spectrum similar to noise and, during anesthesia, it typically predominates in frequencies above 30 Hz. EEG signal component predominates in lower frequencies (up to approximately 30 Hz) contained in electrodes biopotentials. At higher frequencies, EEG power is exponentially decreased.

The sudden appearance of EEG signal data very often indicates that patient is responding to some external stimulation, such as painful stimulations, that is, it may be nociception as a consequence of a surgical event. These responses may be result of inadequate anesthetic level. If stimulation continues without the administration of additional analgesics, it is very possible that hypnosis will become more superficial. So, EMG signal may be an indication of emergence. Note that, due to higher EMG signal frequency, sampling time may be significantly shorter than for EEG signal data which are of lower frequency. With this, EMG data may be calculated with higher frequency so that the general diagnostic indicator may rapidly indicate changes in patient's status.

For better clarity, two entropy indicators should be considered, one on EEG-dominant frequency range and the other on complete frequencies range, including EEG and EMG components. "State" entropy (SE) is calculated on the frequency range 0.8 Hz to 32 Hz. It includes the EEG-dominant part of the spectrum and primarily reflects patients' cortical status. Time windows for SE are ideally chosen for each specific frequency component and vary 60 s to 15 s. "Response entropy" is calculated on frequency range 0.8 Hz to 47 Hz, including EEG-dominant and EMG-dominant part of the spectrum. Time windows for RE are ideally chosen for each frequency, being the longest = 15.36 s and the shortest (applied to frequencies between 32 Hz and 47 Hz) = 1.92 s.

It is desirable to normalize both entropy parameters so that RE equals SE whenever EMG power (sum of spectral power between 32 Hz and 47 Hz) equals zero, because this way, the difference between RE and SE will be an indicator of EMG activity. Here, frequency range 0.8 Hz to 32 Hz will be called Rlow and frequency range 32 Hz to 47 Hz will be called Rhigh. Combined frequency range 0.8 Hz to 47 Hz will be called Rlow+high/. So, when spectral components within Rhigh equal zero, non-normalized entropy values S[Rlow] and SN[Rlow+Rhigh] will coincide, while for normalized entropies there is the inequality SN[Rlow] > SN[Rlow+Rhigh]. Normalization stage, then, is redefined for SE as follows:

For RE, normalized entropy value is calculated according to equation:

As a consequence, RE varies 0 to 1, while SE varies 0 to log(N[Rlow])/log(N[Rlow+high]) < 1. Both entropy values coincide when P(fi) = 0 for all fi of the [Rhigh] range. When there is EMG activity, spectral components in the range [Rhigh] are significantly different from zero and RE is higher than SE.

With these definitions, SE and RE have different information purposes for anesthesiologists. State entropy is a sufficiently stable quantity for the anesthesiologist, in rapidly checking a single number, to have an idea of patient's cortical status in any given moment. Time windows for SE are selected so that transient fluctuations are removed from data. Response entropy, on the other hand, rapidly reacts to changes. Different roles of such parameters are typically shown during emergence when first there is RE increase together with muscle activation, to be followed - some seconds after - by SE increase.

Tracheal intubation is a moment of major stress for patients, translated by hemodynamic, endocrine-metabolic 23 (sub-cortical) and cortical (central nervous system) changes. Randel et al. 24 have reported that patients ventilated with isoflurane in nitrous oxide and oxygen have presented sympathetic activation represented by heart rate increase without changes in pressure response to intubation, and premedication with opioids may prevent plasma epinephrine, but not norepinephrine, concentration increase after laryngoscopy and intubation. Other authors have evaluated the influence of intravenous 2 µ fentanyl associated to propofol in attenuating hemodynamic and cortical responses (through BIS) to intubation and have concluded that this technique has been effective in blocking hemodynamic responses without attenuating brain cortical activity response 25. Billar et al. 26 have shown that 2 µ fentanyl associated to propofol have decreased blood pressure and heart rate in response to intubation. In our study, we have compared the influence of sevoflurane alone (G4) and of sevoflurane associated to fentanyl (G1, G2 and G3), evaluating brain cortical (BIS and SE) and sub-cortical (RE), and hemodynamic (SBP, DBP and HR) responses, as well as motor response to intubation (clinical). As to brain cortical activity, there have been major BIS variations between moments M2 and M3 in G1 and G4, with values reaching thresholds between consciousness and unconsciousness only in G4, and being able to produce the so-called post-trauma stress, being this complication most likely when emergence is followed by pain 27. SE values were similar to BIS in monitoring brain cortical activity. All G4 patients and 66% of G1 patients had motor response to TI, which is not in line with Vernon et al. 28 who have evidenced that with BIS values below 40, the likelihood of movement is virtually zero, in anesthetic techniques both with propofol/alfentanil and with isoflurane/alfentanil. It is worth stressing, however, that movement is sub-cortical and BIS directly reflects the cortical component and only indirectly the sub-cortical component 29-31. Our results suggest dissociation between the levels of hypnosis and analgesia in G1, G2 and G4 since there has been movement at intubation in G1 and G4 and a gap above 10 in G2 (which has also represented p < 0.05 between moments M2 and M3 for RE values). Only G3 has not shown significant RE differences between M2 and M3, which could have reflected better anesthetic control. In G1, G2 and G3 patients, SBP, DPB and HR have significantly decreased from M1 to M3, and M3 has always shown the lowest scores. Clinically, however, these variations were not relevant. There have been no major changes in G4 in hemodynamic parameters (SBP and DBP) between M1 and M3 (p > 0.05), except for HR (p < 0.05) with highest values recorded in M3. There were no motor responses to tracheal intubation maneuvers in G2 and G3, which could suggest that 5 µ would be the optimal TI dose. Response entropy, however, has shown that G3 had the most efficient sub-cortical activity block. So, this study has shown that sevoflurane alone, or associated to 2.5 µ or 5 µ fentanyl has not effectively blocked CNS cortical and sub-cortical components response, as opposed to 7.5 µ which has promoted better control of such anesthetic components.



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Correspondence to
Dr. Rogean Rodrigues Nunes
Rua Gothardo Moraes, 155/1201 Bloco Dunas Papicu
60190-801 Fortaleza, CE

Submitted for publication June 30, 2003
Accepted for publication October 7, 2003



* Received from Serviço de Anestesiologia do Hospital São Lucas de Cirurgia & Anestesia, Fortaleza, CE; Trabalho vencedor do Prêmio Carlos Parsloe de 2003 em Anestesia Inalatória

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