Spectral entropy: a new method for anesthetic adequacy

Abstracts

JUSTIFICATIVA E OBJETIVOS: O uso de sinais clínicos para avaliar a adequação da anestesia, embora empregado universalmente, não são confiáveis. Vários equipamentos surgiram objetivando o melhor manuseio intra-operatório das drogas anestésicas, alguns deles mensurando diretamente a atividade cortical cerebral (hipnose). Entretanto, nenhum deles apresenta características diretas de avaliação da atividade sub-cortical (resposta motora). CONTEÚDO: A entropia espectral mensura a irregularidade, complexidade ou a quantidade de desordem do eletroencefalograma e tem sido sugerida como um indicador do estado anestésico. O sinal é coletado na região fronto-temporal e tratado através da equação de Shannon (H = - Sp k log p k, onde p k são as probabilidades de um evento discreto k), resultando em dois tipos de análises: 1. Entropia de estado (SE), que consiste na avaliação da atividade elétrica cortical cerebral (0,8-32Hz) e 2. Entropia de resposta (RE), que analisa as freqüências de 0,8 - 47Hz (contêm componentes eletroencefalográficos-cortical e eletromiográficos-sub-cortical). CONCLUSÕES: A ativação da musculatura frontal pode indicar inadequação do componente sub-cortical (nocicepção). Esta ativação é observada como um "gap" entre SE e RE. Deste modo, é possível avaliar diretamente tanto o componente cortical (SE), como o sub-cortical (RE), possibilitando melhor adequação dos componentes anestésicos.

MONITORIZAÇÃO; MONITORIZAÇÃO; MONITORIZAÇÃO

MISCELLANEOUS

Spectral entropy: a new method for anesthetic adequacy^*

Entropia espectral: un nuevo método para adecuación anestésica

Rogean Rodrigues Nunes, TSA, M.D.^I; Murilo Pereira de Almeida, M.D.^II; James Wallace Sleigh, M.D.^III

^IDiretor 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

^IIProfessor Adjunto IV do departamento de Física da UFC; Ph.D. em Matemática Aplicada pela Brown University (Providence, RI, USA); M.Sc. em Engenharia Civil pela PUC/RJ; Engenheiro Civil pela UFC

^IIIProfessor of Anaesthesiology and Intensive Care, Waikato Clinical School, Medical and Health Sciences, University of Auckland, New Zealand; MBChB (Cape Town ) 1979, FFARCS (UK) 1985, FANZCA 1995

^{Correspondence}

SUMMARY

BACKGROUND AND OBJECTIVES: Though universally employed, clinical signs to evaluate anesthetic adequacy are not reliable. Over the past years several pieces of equipment have been devised to improve intraoperative handling of anesthetic drugs, some of them directly measuring cerebral cortical activity (hypnosis). None of them, however, has offered the possibility of directly evaluating sub-cortical activity (motor response).

CONTENTS: Spectral entropy measures irregularity, complexity or amount of EEG disorders and has been proposed as indicator of anesthetic depth. Signal is collected from the fronto-temporal region and processed according to Shannon's equation (H = - Sp_k log p_k, where p_k represents the probability of a discrete k event), resulting in two types of analyses: 1) state entropy (SE), which evaluates cerebral cortex electrical activity (0.8 - 32Hz) and 2) response entropy (RE), containing both subcortical electromyographic and cortical electroence- phalographic components and analyzes frequencies in the range 0.8 - 47Hz.

CONCLUSIONS: Frontal muscles activation may indicate inadequacy of the subcortical component (nociception). Such activation appears as a gap between SE and RE. This, it is possible to directly evaluate both cortical (SE) and subcortical (RE) components providing better anesthetic adequacy.

Key Words: MONITORING, bispectral index, state entropy, response entropy

RESUMEN

JUSTIFICATIVA Y OBJETIVOS: El uso de señales clínicos para evaluar la adecuación de la anestesia, aun cuando utilizada universalmente, no son confiables. Varios equipamientos surgieron objetivando el mejor manoseo intra-operatorio de las drogas anestésicas, algunos de ellos mensurando directamente la actividad cortical cerebral (hipnosis). Entretanto, ninguno de ellos presenta características directas de evaluación de la actividad sub-cortical (respuesta motora).

CONTENIDO: La entropia espectral mensura la irregularidad, complejidad o la cantidad de desorden del electroencefalograma y ha sido sugerida como un indicador del estado anestésico. El señal es colectado en la región fronto-temporal y tratado a través de la ecuación de Shannon (H = - Sp_k log p_k, donde p_k son las probabilidades de un evento discreto k), resultando en dos tipos de análisis: 1. Entropia de estado (SE), que consiste en la evaluación de la actividad eléctrica cortical cerebral (0,8-32Hz) y 2. Entropia de respuesta (RE), que analiza las frecuencias de 0,8-47Hz (contiene componentes electroence- falográficos-cortical y electromiográficos-sub-cortical).

CONCLUSIONES: La activación de la musculatura frontal puede indicar inadecuación del componente sub-cortical (nocicepción). Esta activación es observada como un "gap" entre SE y RE. De este modo, es posible evaluar directamente tanto el componente cortical (SE), como el sub-cortical (RE), posibilitando mejor adecuación de los componentes anestésicos.

INTRODUCTION

EEG changes are correlated to anesthetic concentrations in the effector site, but predominantly describe the hypnotic effect of such agents. Several methods have been applied to raw EEG signal: 95% spectral edge frequency (derived from power spectrum), bispectral analysis (incorporates the degree of phase coupling among sinusoidal components) ¹, approximate entropy (quantifies data regularity in a temporal series) and spectral entropy (quantifies data regularity in the frequency domain) ^2,3. The differential of devices using spectral entropy analysis is that, in addition to processing EEG signal (cortical), they also analyze frontal electromyographic activity (sub-cortical) ⁴, which may provide important subsidies for better anesthetic components control.

The Concept of Entropy

It was Claude Shannon ⁵ who, in late 1940s, developed the modern concept of "logic" or "information" entropy as part of information or uncertainty measurement. Information theory was dealing with the newly born data communication science. Shannon's entropy (H) is given by the following equation:

H = - Sp_k log p_k, where p_k are the probabilities of a discrete k event.

It is a measure of data dispersion. Data with wide and flat probability distribution will present a high entropy level. 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 anesthesia).

There are several concepts and analytical techniques to quantify irregularities of stochastic signals, such as EEG. Entropy is one of them. As a physical concept, entropy is proportional to the logarithm of the number of microstates available to a thermodynamic system, thus being related to the magnitude of system disorder.

However, it is difficult to define "disorder". Boltzmann ⁶ (Figure 1) has shown that thermodynamic entropy could be accurately described as the proportionality constant k (Boltzmann's) multiplied by the logarithm of the number of independent microstates (w) available in the system:

Brazilian Journal of Anesthesiology, 2004; 54: 3: 404 - 422

Spectral entropy: a new method for anesthetic adequacy

Rogean Rodrigues Nunes; Murilo Pereira de Almeida; James Wallace Sleigh

S = k log (w)

Boltzmann was able to explain changes in macro-parameters (such as temperature) as from changes in kinetic energy of a collection of individual molecules and has become a pioneer in statistical mechanics science. Thermodynamic entropy has a well-established physics basis. It is possible to derive Shannon's entropy equation (or "information" entropy) (H) from Boltzmann's thermodynamic formula (S).

There are important neurophysiological signs that the usefulness of information entropy estimators as a measure of cortical function is due to the fact that, as cortex enters unconsciousness, there is a true neuronal decrease in the logarithm of the number of accessible microstates (S) ^7,8. So, "entropy" could mean more than a mere statistical measure of EEG pattern and, in a way, could truly reflect intracortical information flow.

Entropy is the logarithm of the number of modes in which a microstate 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. In a thermodynamic system, collision events spread kinetic energy through the substance. Entropy is a measure of such dispersion. In the cerebral cortex, synaptic events spread electric charges through the cortex. Assuming that cortical information processing is linked to electrical charges distribution and transfer, EEG entropy measures cortical pyramidal cells activity.

Shannon was the first to define entropy in the information theory in 1948. Then, in 1984 ⁹, Johnson and Shore 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 look at a simple example: a signal where sequential values alternate between one fixed magnitude and other has zero entropy, that is, the signal is totally regular and predictable. A signal where sequential values are determined by randomized numbers generator has higher complexity levels and entropy.

The Concept of Uncertainty

Consider an experiment A, for example, throwing a coin in the air, with two possible results A₁ and A₂, with associated probabilities p₁ and p₂, being p₁ + p₂ = 1. This representation may be illustrated as follows:

In this case, probability in relation to results may be represented as follows:

Now, consider an experiment B associated to the following probability scheme:

It is reasonable to think that there are different uncertainty levels for experiments A and B, based on a psychological sense. This suggests, as a principle for the task of probabilities, that uncertainty resulting from the probability scheme of an experiment should be maximally subject to restrictions of any other available information related to the experiment. To create this quantitative concept, a mathematical expression for uncertainty and a probability scheme are necessary, that is, Shannon's Entropy:

, where:

p_i represents the probability related to the experiment and n the number of probabilities.

In applying this equation to the experiment above, we obtain:

For the scheme A, a value of E = 0.69 and for the scheme B, a value of E = 0.056, showing that the level of uncertainty for scheme B is much lower as compared to scheme A ¹⁰. This may also be applied to power distribution analysis of an EEG signal, determining the level of uncertainty, for example, of a patient being unconscious based on the power distribution analysis in the frequency domain.

Figure 2 shows power spectrum of an anesthetized patient without spectral entropy (Shannon's) analysis.

Brazilian Journal of Anesthesiology, 2004; 54: 3: 404 - 422

Spectral entropy: a new method for anesthetic adequacy

Rogean Rodrigues Nunes; Murilo Pereira de Almeida; James Wallace Sleigh

Entropy is an intuitive parameter in the sense that it is possible to visually distinguish a regular from an irregular signal. In addition, entropy is independent of absolute scales, such as signal amplitude or frequency: a simple sine wave is perfectly regular, regardless being fast or slow. For EEG applications, this is a significant property since, as we know, there are absolute individual frequencies variation on EEG rhythms.

There are many ways to calculate the entropy of a signal. In the time domain, one may consider, for example, approximate entropy (Pincus ¹¹, Bruhn ¹²) or Shannon's entropy (Shannon ⁵. Bruhn ¹³). In the frequency domain, one may calculate spectral entropy (Shannon ⁵, Johnson ⁹). To optimize the speed in which information is derived from the signal, one may combine time and frequency domains. Spectral entropy algorithm has the specific advantage of being able to explicitly separate contributions to entropy coming from any frequency range. For an optimal response time, one may develop calculations in a way that time window length for each frequency is individually selected. This leads to a concept that could be named "Spectral entropy with balanced time and frequency".

What Does This Mean to EEG?

Since EEG allows, to a certain extent, the visualization of cortical processes, changes in EEG entropy should measure changes within the cerebral cortex itself. Considering that the main conscious cortex function is information processing and generation, it would be fair to assume that some kind of "information measurement" would be very useful. The problem is that the word "information", similarly to "disorder"; has several meanings and connotations, and should be carefully and scientifically defined to be applied within this context. Perhaps the simplest and most practical description of EEG entropies would be: "measures of the extent to which limitations (in our case, general anesthesia) decrease the number of accessible status available to the cortex". It follows that, while one could expect that, a higher number of microstates would be associated to a more "complex" system, entropy per se does not necessarily provide a direct measure of the "complexity" of a system, which has other variability implications in response to inputs, etc.

If entropy can be defined as the logarithm of the number of more commonly accessible cortical microstates, the question raised is: What are cortical microstates? There are increasingly more neurophysiological evidences that cognitive activity involves the transient formation and dissolution of interconnecting neuronal cortical structures ("activation" and "acquiescence") (John et al., 1997 ¹⁴).

It would be fair to assume that such coherent structures are effectively functional cortical microstates. EEG perceives the activity on the scalp as a broader range white noise spectrum (Stam et al., 1993 ¹⁵, Thomeer et al., 1994 ¹⁶).

If (1) the awaken state requires efficient generation of several cortical microstates, and (2) EEG signal microstates reflect, in a way, cortical microstates, then decreased EEG entropy (as seen in general anesthesia) indicates a decreased number of available cortical microstates (Weiss, 1992 ¹⁷).

The cortex-consciousness paradox, if we define entropy as "disorder", is that higher EEG entropy levels of the awaken cortex imply that cortex is more disorganized awaken as compared to unconsciousness. The paradox draws attention to problems inherent to equations involving entropy and disorder. We still have no means to identify high dimension signals generated by the conscious cortex during cognition and, for such, to call them "noise"! This is why we prefer to define entropy in terms of available microstates and not of "order". It might be more illustrative to describe entropy as "freedom of choice". Conscious cortex is free to move among a huge number of available microstates.

Spectral Entropy

There are several ways to estimate changes in the amplitude of EEG power spectrum. These methods use the amplitude component of the power spectrum as "probabilities" in entropy calculation. With the use of space-frequency, we are defining microstates in terms of change indices. A wide range of accessed frequencies (that is, a flat spectrum) implies several added change indices of pyramidal cell membrane potentials.

The prototype of this group is Spectral Entropy (S) (Inoye et al., 1991 ¹⁸, Fell et al., 1996 ¹⁹). S corresponds to Shannon's formula duly normalized and applied to power spectrum density of EEG signal. So:

S = Sp_k log p_k/log(N), where:

p_k are spectral amplitudes of k frequencies region.

Sp_k = 1, and N = number of frequencies.

So, the starting point for calculations is signal spectrum. Several spectral transformations are needed to obtain the spectrum. Here, however, we will hold to Fourier's transformed discontinuing ²⁰, which allows for the transformation of a set of signal values x(t_i) sampled during moment t_i within a signal's sample into a set of complex numbers X(f_i), of frequencies f_i.

where:

being: F_n(t_i) the n^th component of a total of N components, and a_n the coefficient associated to the n^th component.

Spectral components X(f_i) may be evaluated by an effective calculation technique called "Fourier's fast transformed" (FFT). Spectral entropy concept comes from an information measurement called "Shannon's entropy". When applied to signal power spectrum, spectral entropy is obtained ⁹. The following steps are necessary to calculate spectral entropy for a certain signal interval (epoch) within a given frequency range [f₁, f₂].

From Fourier's transformed X(f_i) of signal x(t_i), power spectrum P(f_i) is calculated by multiplying by themselves Fourier's transformed amplitudes of each element X(f_i):

(1)

where X^(f_i) is Fourier's complex conjugated X(f_i) and the star (*) indicates multiplication.

Power spectrum is then normalized. Normalized power spectrum P_n(f_i) is calculated by the establishment of a normalization constant C_n, so that the sum of normalized power spectrum on the selected frequency region [f₁, f₂] equals to 1:

(2)

This now represents a probabilities diagram.

During the sum stage, spectral entropy corresponding to the frequency range [f₁, f₂] is calculated as a sum:

(3)

Then, entropy value is normalized to vary between 1 (maximum irregularity) and 0 (total regularity). Value is divided by factor log (N[f₁, f₂]), where N[f₁, f₂] equals the total number of frequency components in the range [f₁, f₂]:

(4)

Figures 3 to 5 show these stages. Figures 3(a), 4(a) and 5(a) show three signal sections corresponding to different entropy values. In this simple example, we have considered signal sections with 8 spectral components, from which 0 frequency component (or the one assumed to be zero) was omitted, so that N = 7 frequency components are analyzed. Figure 3(a) shows a perfect sinusoidal wave. Figure 4(a) shows a sinusoidal wave with superimposed with white noise, while figure 5(a) illustrates a perfectly randomized white noise signal. Fourier's discontinuous spectra of such signals, normalized according to equation (2), were plotted in figures 3(b), 4(b) and 5(b), respectively. Then, normalized spectral components P_n(f_i) were plotted in figures 3(c), 4(c) and 5(c) using Shannon's function to obtain contributions:

Brazilian Journal of Anesthesiology, 2004; 54: 3: 404 - 422

Spectral entropy: a new method for anesthetic adequacy

Rogean Rodrigues Nunes; Murilo Pereira de Almeida; James Wallace Sleigh

Since: log(x)=n(x)/n(10), then we may replace the expression above:

Spectral Entropy with Balanced Time and Frequency

In real time signal analysis, signal values x(t_i) are sampled within a finite time window (epoch) with a selected length and a given sampling frequency. This time window moves step by step to provide updated spectrum estimates. Window length choice (epoch) is related to the choice of the frequency range under consideration, since time window has to be long enough to estimate slower signal variations (lower frequencies).

An EEG signal comprises a wide selection of frequencies, from slow delta frequencies (as from 0.5 Hz) to 50 Hz. A 0.5 Hz frequency would need up to 30 s time window to obtain 15 complete 0.5 Hz variation cycles. A 50 Hz frequency would need just 0.3 s of data to obtain the same number of complete cycles.

Clearly, a single time window with fixed length is not the best choice to get the information in the fastest and most reliable way. To find the optimal point between time and frequency resolution, the already mentioned algorithm uses a set of window lengths selected so that each frequency component is obtained from the most adequate window for that specific frequency. This way, information is extracted from the signal in the fastest possible way. The approach is closely related to the idea of the transformation of small waves, which being packets of finite variable range waves with a more or less constant number of variations, provide a break-even point between time and frequency resolution. The selected technique combines the advantage of small waves analysis with fast Fourier's analysis, as well as the possibility of explicitly considering the contribution of any given frequency range and the effective implementation in software. The basic idea is shown in figure 6.

Brazilian Journal of Anesthesiology, 2004; 54: 3: 404 - 422

Spectral entropy: a new method for anesthetic adequacy

Rogean Rodrigues Nunes; Murilo Pereira de Almeida; James Wallace Sleigh

Surface Electromyography, State Entropy and Response Entropy

Surface electromyography (EMGs) is the algebraic sum of the electric activity of a population of muscle fibers. There is a direct relationship between EMGs amplitude and muscle tension during isometric contraction ²¹. In conscious patients under no anesthetic effect, high tonic activity observed in electromyography is positively correlated to the level of stimulation, vigilance or psychological stress. Increased EMGs phase activity is associated to somatic stress periods, such as pain ²². For unconscious patients monitoring, EMGs should be performed on frontal muscles, which have a relatively fixed length, thus decreasing the potentially complicating influence of fiber length variation (isotonic contraction). These muscles are also preferred because they are innervated by special visceral efferent fibers of the facial nerve. It is important to remember that these muscles are derived from branchial archs which are considered visceral formations. Frontal muscles EMGs provides a simple and noninvasive measure of an autonomic tone aspect. Voluntary and involuntary frontal muscles contractions are responses brought by different pathways innervation, as well as tonic activity (basal) and phase activity (abruptly increased) may be differently affected by abnormal levels of vigilance or neuromuscular blockers ^23-25.

Decreased vigilance following general anesthesia is typically associated to dramatic decrease in tonic frontal activity. Some authors ^24,26,27 have concluded that increased phase activity in the presence of EMGs amplitude depressing drugs is an indication of inadequate anesthesia. In addition, these investigators have observed that phase activity measured by EMGs may be seen in the presence of neuromuscular blockers.

It has been shown that at least three different types of stimulations - emotion, sounds and ischemia - may evoke surface EMGs amplitude phase increase during low vigilance states.

EMGs may be useful for opioids titration: facial muscles are not only voluntary, but also innervated by brainstem centers related to emotions/stress. Although the intraoperative electromyographic evaluation with patient's movement is a quantal phenomenon, minor EMGs changes may reflect inadequate analgesia (sob-cortical component with inadequate blockade). Mathews et al. ²⁸ have shown that postoperative opioids decrease EMGs. In addition, EMGs may respond faster than BIS in emergence reactions. Kem et al. ²⁹ have concluded that EMGs shows good correlation with responses to noxious stimulations applied to volunteers. Shander et al. ³⁰ have also shown that EMGs may predict analgesic requirements, allowing for a more effective intraoperative control of analgesia (sub-cortical element). Lennon ³¹ has concluded that moderate neuromuscular block levels may be achieved without impairing electromyographic monitoring of the facial nerve. Edmonds ²⁵ has shown that EMGs in response to stress (pain) may assess brainstem function, which is independent of consciousness level (cortex). Dutton ³² in a recent study has concluded that electromyographic response may be used to estimate anesthetic depth.

A biopotential captured in the frontal region includes a significant electromyographic component created by muscle activity. The electromyographic signal has a wide spectrum similar to noise and, during anesthesia, it typically predominates in the frequencies above 30 Hz. Electroencephalographic signal component predominates in lower frequencies (up to approximately 30 Hz) contained in biopotentials existing in the electrodes. At higher frequencies, electroence- phalographic power decreases exponentially (Figure 7).

Brazilian Journal of Anesthesiology, 2004; 54: 3: 404 - 422

Spectral entropy: a new method for anesthetic adequacy

Rogean Rodrigues Nunes; Murilo Pereira de Almeida; James Wallace Sleigh

Electroencephalographic signals of sudden appearance often indicates that patient is responding to some external stimulations, such as nociception as a consequence of some surgical event. These responses may be result of inadequate anesthesia. If stimulation continues and no additional analgesic is given, it is possible that the hypnotic level may get more superficial. So, electromyographic signal may indicate emergence imminence. Note that, due to the higher electromyographic signal frequency, sampling time might be significantly shorter than for lower frequency electroence- phalographic signals. This way, electromyographic data may be refreshed more frequently so that the method may rapidly indicate changes in patient's state.

For better clarity, one should consider two entropy indicators, one solely on the dominating EEG frequency range, and the other on the complete frequency range, including electroencephalographic and electromyographic components. "State entropy" (SE) is calculated on the frequency range 0.8 Hz to 32 Hz. It includes the electroence-phalographic-dominating part of the spectrum and, as a consequence, primarily reflects patient's cortical state. SE time windows are optimally chosen for each specific frequency component, varying 60 s to 15 s as previously explained. "Response entropy" (RE) is calculated on the frequency range 0.8 Hz to 47 Hz. It includes the electroencephalo- graphic-dominating part and the electromyographic-dominating part of the spectrum. RE time windows are optimally chosen for each frequency, being the longest equal to 15.36 s and the shortest equal to 1.92 s (applied to frequencies 32 Hz to 47 Hz).

The two entropy parameters should be normalized so that RE equals SE whenever electromyographic power (the sum of spectral power between 32 Hz and 47 Hz) equals zero. This way the difference between RE and SE will be an indicator of electromyographic activity. At this point, frequency range between 0.8 Hz and 32 Hz will be called 'R_low', and frequency range from 32 Hz to 47 Hz will be called 'R_high'. The combined 0.8 Hz to 47 Hz frequency range will be called 'R_low+high'. It follows from equations 1 to 4, that when spectral components within R_high equal zero, non-normalized entropy values S[R_low] and S[R_low+R_high] will coincide, while for normalized entropies there is SN[R_low] > SN[R_low+R_high] inequality. The normalization stage (4) is then redefined for SE as follows:

(5)

For RE, normalized entropy value is calculated according to equation (4):

(6)

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

With these definitions in mind, SE and RE have different information purposes for the anesthesiologist. State entropy is a sufficiently stable quantity to allow the anesthesiologist to have an idea of the cortical state of the patient at any time by checking a single number. SE time windows are selected so that transient fluctuations are removed from data. Response entropy, on the other hand, rapidly reacts to changes. The different roles of these parameters are typically shown during emergence, when RE is first increased together with muscle activation, being followed few seconds later by SE.

Entropy during Burst Suppression

When burst suppression is started, RE and SE values are calculated as they would be during more superficial hypnosis levels. The part of the signal with suppressed EEG is treated as a perfectly regular signal with zero entropy, while burst-associated entropy is calculated as already described.

Usually, burst suppression is quantified by the representation of the relative suppression amount, called "burst suppression ratio" (BSR), within one minute to obtain a sufficiently stable estimate. The one-minute window has a sufficiently large sample of bursts and suppression to provide a stable indication of the relative amount of suppressed EEG; in fact, much shorter windows would result in highly fluctuating BSR values. For the same reason, a one-minute window - and not a varied set of time windows - is applied to all frequency components of SE and RE values whenever some suppressed interval (epoch) is detected during the previous minute of data.

Burst suppression is detected by the technique described by Särkelä et al. ³³. To eliminate baseline fluctuations, a local mean of each signal sample is subtracted. Then, the signal is divided in two frequency ranges by elliptic filters. Threshold frequencies of low and high filters are 20 Hz and 75 Hz, respectively. Low frequency range is used to detect burst suppression pattern, while high frequency range is used for detecting artifacts. An energy operator is used to estimate both signal power ranges of each 0.05 s interval (epoch). Suppression is detected when estimated signal power is below a prefixed threshold during at least 0.5 s without artifacts. BSR is the percentage of 0.05 s intervals (epochs) which may be considered as suppressed during the previous 60 s (Figure 8).

Brazilian Journal of Anesthesiology, 2004; 54: 3: 404 - 422

Spectral entropy: a new method for anesthetic adequacy

Rogean Rodrigues Nunes; Murilo Pereira de Almeida; James Wallace Sleigh

Optimizing the Use of Entropies

RE and SE parameters were designed to be read together with many other important information on the screen of a single monitor. To present more effectively entropy data, some changes have been made on the way these parameters are displayed thus optimizing their applicability. A 2-digit integer number (for example, 39) is easier to be read on a screen than a decimal value (0.39) or a 3-digit value (539). For this reason, original entropy values, which continuously vary 0 to 1, were converted into an integer scale 0 to 100.

A relatively high portion of the original mathematical scale of entropy values occupies a range where the level of hypnosis may be considered too deep. On the other hand, the most adequate hypnosis and emergence range remains between 0.5 and 1. So, a mere division of the original scale in equidistant integers from 0 to 100 would result in a somewhat poor resolution, of the frequency of interest and in an unnecessarily high resolution at deeper levels. So, the changing of the original continuous entropy scale [0 1] into an integer scale [1 100] was obtained through a non-linear transformation. This transformation is defined by a monotonous "spline" function F(S) able to plot scale [0 1] on the scale [1 100].

"Spline" functions are continuous, as continuous are their derivatives of any order. Hence, a transformation operation defined by monotonous "spline" function is perfectly smoothed, with no discontinuities or fluctuations. The F(S) function used for transformation is shown in figure 9, where its illustrated that the slope reaches its maximum in the range of anesthesia and clinical emergencies, allowing optimal resolution in this range. RE varies 0 to 100 and SE 0 to 91 (Figure 9).

Brazilian Journal of Anesthesiology, 2004; 54: 3: 404 - 422

Spectral entropy: a new method for anesthetic adequacy

Rogean Rodrigues Nunes; Murilo Pereira de Almeida; James Wallace Sleigh

If low frequency components amplitudes are especially high - like during very deep anesthesia - the difference between response and situation entropy, as they are originally obtained by equations (5) and (6), may remain below the integer number resolution displayed on the monitor's screen. To provide a detectable indication of electromyographic activity, the treatment of frequency components in the range [R_high] = [32 Hz , 47 Hz] is modified. Instead of applying the normalization constant C_n to all frequency components according to equation (2), in this situation a different normalization constant C_n^high for the range [R_high] is used. While C_n is below a threshold data C_n^limit, it is assumed that C_n^high will equal C_n, but if it goes beyond C_n^limit, C_n is considered equal to C_n^limit. This modification assures that electromyographic activity is detectable on screen in any situation.

TREATMENT OF RAW SIGNAL FOR ARTIFACTS DETECTION AND REMOVAL

To analyze artifacts, electromyographic signal is divided in 0.64 s intervals (epochs), including 256 signal values. These intervals (epochs) are inspected to detect and remove the following artifacts:

Electrocauterization artifacts

The device is highly tolerable to electrocauterization, so very seldom data have to be rejected during electrocauterization. To detect these situations, power in 200 Hz to 1000 Hz frequency range is continuously measured. If power goes beyond a pre-established threshold, electromyographic data collected in 66 Hz to 86 Hz frequency range are inspected to check whether electrocauterization has affected the signal. If so, the interval (epoch) will be excluded from next analyses.

ECG and Pacemaker Artifacts

The high sampling frequency of 400 Hz makes it easy to distinguish between acute peaks associated to ECG and Pacemaker and the underlying electroencephalographic signal. These artifacts are then removed, subtracting distortion from the underlying signal, which is useful for entropy calculation.

EMG

As previously discussed, EMG is treated as a component-signal and not as an artifact.

Eye Movements and Blinking, Movement Artifacts

The 0.64 s interval (epoch) is too short for the reliable detection of all intervals (epochs) containing such artifacts. So, they are considered in two stages:

Stage 1. A stationary analysis is made for the signal within a time window of 24 * 0.64 = 15.36 s (including 6,144 signal values). Signal is classified as stationary or non-stationary according to statistical distribution of signal values throughout and within the 24 intervals (epochs).

Stage 2. For each interval (epoch), 5 signal characteristics in time and frequency domains are calculated. These characteristics are simultaneously considered in the corresponding five-dimension parametric space divided in "normal signal" and "artifact-contaminated signal" regions. Intervals (epochs) are accepted or rejected, depending on the parametric space they belong to. There are two sets of rejection rules: one set of stricter rules used when signal section is analyzed in Stage 1 and classified as non-stationary, and a set of less strict rules for when analyzed signal section is considered stationary.

Clinical Application

State entropy reading is related to the level of unconsciousness uncertainty (cortical activity), that is, the lower the state entropy the lower the level of unconsciousness uncertainty. Similarly, the lower the level of sub-cortical activity control uncertainty (electromyographic activity), the lower the response entropy value (Table I).

Brazilian Journal of Anesthesiology, 2004; 54: 3: 404 - 422

Spectral entropy: a new method for anesthetic adequacy

Rogean Rodrigues Nunes; Murilo Pereira de Almeida; James Wallace Sleigh

Electrodes Positioning and Usage Directions

1. Clean the skin with alcohol and let it dry;

2. Position circle #1 in the center of the frontal region, approximately 4 cm above the nose, and circle #3 on the anterior temporal region, between internal palpebral angle and the pileous line (Figure 10);

3. Press sensor borders to assure adhesion;

4. Firmly press circles 1, 2 and 3 for 5 seconds to assure adequate contact.

Brazilian Journal of Anesthesiology, 2004; 54: 3: 404 - 422

Spectral entropy: a new method for anesthetic adequacy

Rogean Rodrigues Nunes; Murilo Pereira de Almeida; James Wallace Sleigh

CONCLUSION

Frontal muscles activation may indicate inadequate sub-cortical component. This activation may be observed as a gap between state and response entropy. So, there is the possibility of directly evaluating both cortical (SE) and sub-cortical (RE) components, aiming at better anesthetic components adequacy.

REFERENCES

Submitted for publication June 12, 2003

Accepted for publication October 7, 2003

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*

Received from Serviço de Anestesiologia do Hospital São Lucas de Cirurgia & Anestesia, Fortaleza, CE

Publication Dates

• Publication in this collection
  02 July 2004
• Date of issue
  June 2004

History

• Accepted
  07 Oct 2003
• Received
  12 June 2003