BIS and Entropy in the elderly

The interaction of many poorly defined, physiological, pharmacological, and pathological factors make titration of general anaesthesia in the elderly difficult. There may be a potential clinical benefit using the processed electroencephalogram (EEG) to monitor hypnotic level in this population. We prospectively studied 16 patients aged over 65 years having hip fractures repaired under general anaesthesia by experienced anaesthetists blinded to Bispectral Index (BIS(XP)) and Entropy values. Pre-induction EEG indices did not correlate with age or mini-mental state examination (MMSE). During maintenance of anaesthesia, BIS(XP) and Response Entropy (RE) values were within the recommended range of 40-60, 45% and 32% of the total time, respectively. BIS(XP) and Response Entropy (RE) values were above 60 for 11% and 13% of the total time, respectively, and below 40 for 44% and 55% of the total time, respectively. BIS(XP) correlated well with RE in 12 patients, but in the other four patients there was a difference of more than 20 points between BIS(XP) and RE.     

Hypothermia and the Approximate Entropy of the Electroencephalogram

Background: The electroencephalogram is commonly used to monitor the brain during hypothermic cardiopulmonary bypass and circulatory arrest. No quantitative relationship between the electroencephalogram and temperature has been elucidated, even though the qualitative changes are well known. This study was undertaken to define a dose-response relationship for hypothermia and the approximate entropy of the electroencephalogram.

Methods: The electroencephalogram was recorded during cooling and rewarming in 14 patients undergoing hypothermic cardiopulmonary bypass and circulatory arrest. Data were digitized at 128 Hz, and approximate entropy was calculated from 8-s intervals. The dose-response relationship was derived using sigmoidal curve-fitting techniques, and statistical analysis was performed using analysis of variance techniques.

Results: The approximate entropy of the electroencephalogram changed in a sigmoidal fashion during cooling and rewarming. The midpoint of the curve averaged 24.7[degrees]C during cooling and 28[degrees]C (not significant) during rewarming. The temperature corresponding to 5% entropy (T0.05) was 18.7[degrees]C. The temperature corresponding to 95% entropy (T0.95) was 31.3[degrees]C during cooling and 38.2[degrees]C during rewarming (P < 0.02).     

Entropy and bispectral index during anaesthesia in children

Entropy is a new EEG based technology developed as a measure of depth of anaesthesia. The Entropy algorithm quantifies the degree of disorder in the EEG. During anaesthesia the disorder of the EEG, or entropy, falls. Entropy is independent of absolute frequency or amplitude of the EEG. This may make it suitable for paediatric anaesthesia. In this prospective observational blinded study we recorded the Entropy and Bispectral Index in 23 children undergoing general anaesthesia with isoflurane and nitrous oxide, supplemented with peripheral nerve blockade. We recorded Entropy at several times during anaesthesia, pre-awakening and 1-minute post-awakening. Entropy pre-awakening and 1 minute after awakening was compared to a value during anaesthesia in three age groups; less than one-year-old (infants), one to five years (toddlers) and five to twelve years (children). The correlation between BIS and Entropy was also calculated. Entropy post-awakening was higher than during anaesthesia for all age groups. Entropy pre-awakening was higher than during anaesthesia for the children and toddlers. This was not as apparent in infants. There was a strong correlation between BIS and Entropy for children and toddlers. The correlation was less for infants. This study demonstrates that, in children, Entropy is lower during anaesthesia when compared to awake values. Further evaluation in the paediatric population is worthwhile.     

Numerical Entropy and Adaptivity for Finite Volume Schemes

We propose an a-posteriori error/smoothness indicator for standard semi-discrete finite volume schemes for systems of conservation laws, based on the numerical production of entropy. This idea extends previous work by the first author limited to central finite volume schemes on staggered grids. We prove that the indicator converges to zero with the same rate of the error of the underlying numerical scheme on smooth flows under grid refinement. We construct and test an adaptive scheme for systems of equations in which the mesh is driven by the entropy indicator. The adaptive scheme uses a single nonuniform grid with a variable timestep. We show how to implement a second order scheme on such a space-time non uniform grid, preserving accuracy and conservation properties. We also give an example of a p-adaptive strategy.     

Spectral Entropy as a Measure of Hypnosis in Children

Background: The Datex-Ohmeda S/5 Entropy Module (Datex-Ohmeda Division, Instrumentarium Corp., Helsinki, Finland), using time-frequency balanced Spectral Entropy, is a novel tool for monitoring the hypnotic state during anesthesia. The Entropy Module produces two values, State Entropy (SE) and Response Entropy (RE), and in adults, it has been shown to measure reliably the hypnotic effects of various drugs. In children, Spectral Entropy has been only preliminary studied. The authors' aim was to study Spectral Entropy as a marker of hypnotic state during general anesthesia in infants and children.

Methods: Twenty infants (aged 1 month-1 yr) and 40 children (aged 1-15 yr) were anesthetized for surgery using standardized sevoflurane-nitrous oxide-based anesthesia. The relationships between SE, RE, or Bispectral Index (BIS) and (1) a modified Observer's Assessment of Alertness/Sedation Scale, (2) non-steady state end-tidal concentration of sevoflurane, (3) steady state end-tidal concentration of sevoflurane, and (4) hemodynamic values were calculated using prediction probability, nonlinear regression, and correlation coefficients, as appropriate. The performances of SE, RE, and BIS were compared.

Results: The prediction probability values (+/- SEM) of SE, RE, and BIS versus the modified Observer's Assessment of Alertness/Sedation Scale in the induction phase were 0.83 +/- 0.06, 0.88 +/- 0.06, and 0.87 +/- 0.08 for children and 0.76 +/- 0.08,0.79 +/- 0.08, and 0.73 +/- 0.10 for infants; values in the emergence phase were 0.68 +/- 0.05, 0.74 +/- 0.04, and 0.64 +/- 0.05 for children and 0.64 +/- 0.07, 0.69 +/- 0.06, and 0.72 +/- 0.06 for infants, respectively. SE, RE, and BIS values were inversely proportionally related to the end-tidal concentration of sevoflurane for children, but for infants, the correlation was much less clear. No significant correlations were found between SE, RE, or BIS values and the hemodynamic values.     

Response Entropy is not more sensitive than State Entropy in distinguishing the use of esmolol instead of remifentanil in patients undergoing gynaecological laparoscopy

BACKGROUND: Monitoring of analgesia remains a challenge during general anaesthesia. Activation of Response Entropy (RE) to painful stimuli has been suggested to be a sign of inadequate analgesia. We evaluated the ability of RE to be more sensitive than State Entropy (SE) in measuring nociception in patients undergoing gynaecological laparoscopy. Our hypothesis was that while keeping SE at a predetermined level, RE would be higher in patients receiving a beta-blocking agent (esmolol) instead of an opioid (remifentanil) during a propofol/nitrous oxide anaesthesia. METHODS: Fifty-one women aged between 22-53 years were randomly assigned to receive esmolol (n=25) or remifentanil (n=26). SE was kept at 50+/-5. RE and SE were recorded at an interval of 30 s to 2 min and the areas under the RE and SE value-time curves (AUCRE and AUCSE) were calculated during the time of intubation and start of surgery as well as during the entire anaesthesia. The difference between RE and SE recordings in both groups was determined by subtracting the AUCSE from the corresponding AUCRE. Movements of the patients were recorded. RESULTS: No significant differences were detected in any of the several AUC values between the groups. The difference between RE and SE recordings was similar in both groups. Every patient in the esmolol group moved some time during the procedure interfering with surgery while no one in the remifentanil group moved. CONCLUSION: In patients undergoing gynaecological laparoscopic day-case surgery, RE seems not to be more sensitive than SE in guiding the use of opioids during general anaesthesia.     

Entropy during propofol hypnosis, including an episode of wakefulness

Depth of anaesthesia has proved to be a complex process to quantify. Monitors based on bispectral analysis of the electroencephalogram and auditory evoked potential have been available, but only recently has a monitor based on entropy become available. This study determined state entropy and response entropy in nine healthy volunteers during propofol hypnosis with a brief intervening period of wakefulness. Both the calculated entropy indices decreased with increasing levels of sedation (r2 = 0.58 and 0.61, respectively) and they showed a high correlation with each other (r2 = 0.94). However, an overlap was observed in real time indices between different stages of the Observer's Assessment of Alertness/Sedation Scale. Only three of the nine volunteers had explicit memories from the episode of wakefulness. Electroencephalographic entropy monitors seem to have potential for staging clinical hypnotic effects.     

Entropy Stable Scheme on Two-Dimensional Unstructured Grids for Euler Equations

We propose an entropy stable high-resolution finite volume scheme to approximate systems of two-dimensional symmetrizable conservation laws on unstructured grids. In particular we consider Euler equations governing compressible flows. The scheme is constructed using a combination of entropy conservative fluxes and entropy-stable numerical dissipation operators. High resolution is achieved based on a linear reconstruction procedure satisfying a suitable sign property that helps to maintain entropy stability. The proposed scheme is demonstrated to robustly approximate complex flow features by a series of benchmark numerical experiments.     

On the Five-Moment Maximum Entropy System of One-Dimensional Boltzmann Equation

The maximum entropy moment system extends the Euler equation to nonequilibrium gas flows by considering higher order moments such as the heat flux. This paper presents a systematic study of the maximum entropy moment system of Boltzmann equation. We consider a hypothetical one-dimensional gas and study a five-moment model. A numerical algorithm for solving the optimization problem is developed to produce the maximum entropy distribution function from known moments, and the asymptotic behaviour of the system around the singular region known as the Junk’s line, as well as that near the boundary of the realizability domain is analyzed. Furthermore, we study the properties of the system numerically, including the behaviour of the system around the Maxwellian and within the interior of the realizability domain, and properties of its characteristic fields. Our studies show the higher order entropy-based moment models to differ significantly from the Euler equations. Much of this difference comes from the singularity near the Junk’s line, which would be removed if a truncation of the velocity domain is employed.     

Electroencephalographic Approximate Entropy Changes in Healthy Volunteers during Remifentanil Infusion

Background: The aim of this study was to investigate the independent effect of remifentanil on the approximate entropy (ApEn) in frontoparietal montages. The authors investigated which montages were relevant to assess the remifentanil effect on the electroencephalogram. Spectral edge frequency and the canonical univariate parameter were used as comparators.

Methods: Twenty-eight healthy volunteers were enrolled. With recording of the electroencephalogram at the F3, F4, Cz, P3, and P4 montages, remifentanil was infused at the rate of 1-8 [mu]g [middle dot] kg-1 [middle dot] min-1 for 15-20 min. The relation between remifentanil concentration and the electroencephalographic parameters were tested by Spearman correlation. Signal-to-noise ratio, artifact robustness, coefficient of variation of the median baseline and maximal electroencephalographic effects, and ratio of average maximal electroencephalographic effect to interindividual baseline variability were measured. The performance of ApEn as an index of remifentanil effect site concentrations was tested by prediction probability.

Results: Approximate entropy showed significant correlation (R = -0.6465, P < 0.0001) with remifentanil concentration. It provided comparable signal-to-noise ratio, artifact robustness, and ratio of average maximal electroencephalographic effect to interindividual baseline variability to 95% spectral edge frequency. The coefficients of variation of the median baseline and maximal electroencephalo graphic effects were smallest in ApEn. Parietal montages showed higher ratios of average maximal electroencephalographic effect to interindividual baseline variability for all electroencephalographic parameters and lower coefficients of variation of the baseline values for ApEn and 95% spectral edge frequency than frontal montages. The prediction probability of ApEn was 0.7730.     

A One-Dimensional Second-Order Cell-Centered Lagrangian Scheme Satisfying the Entropy Condition

The numerical solutions of gas dynamics equations have to be consistentwith the second law of thermodynamics, which is termed entropy condition. However, most cell-centered Lagrangian (CL) schemes do not satisfy the entropy condition.Until 2020, for one-dimensional gas dynamics equations, the first-order CL schemewith the hybridized flux developed by combining the acoustic approximate (AA) fluxand the entropy conservative (EC) flux developed by Maire et al. was used. This hybridized CL scheme satisfies the entropy condition; however, it is under-entropic inthe part zones of rarefaction waves. Moreover, the EC flux may result in nonphysicalnumerical oscillations in simulating strong rarefaction waves. Another disadvantageof this scheme is that it is of only first-order accuracy. In this paper, we firstly constructa modified entropy conservative (MEC) flux which can damp effectively numerical oscillations in simulating strong rarefaction waves. Then we design a new hybridizedCL scheme satisfying the entropy condition for one-dimensional complex flows. Thisnew hybridized CL scheme is a combination of the AA flux and the MEC flux.In order to prevent the specific entropy of the hybridized CL scheme from beingunder-entropic, we propose using the third-order TVD-type Runge-Kutta time discretization method. Based on the new hybridized flux, we develop the second-orderCL scheme that satisfies the entropy condition.Finally, the characteristics of our new CL scheme using the improved hybridizedflux are demonstrated through several numerical examples.     

Using Permutation Entropy to Measure the Electroencephalographic Effects of Sevoflurane

Background: Approximate entropy (AE) has been proposed as a measure of anesthetic drug effect in electroencephalographic data. Recently, a new method called permutation entropy (PE) based on symbolic dynamics was also proposed to measure the complexity in an electroencephalographic series. In this study, the AE and PE were applied to electroencephalographic recordings for revealing the effect of sevoflurane on brain activity. The dose-response relation of PE during sevoflurane anesthesia was compared with that of AE.

Methods: Nineteen patients' electroencephalographic data were collected during the induction of general anesthesia with sevoflurane. PE and AE were applied to the electroencephalographic recordings, and the performance of both measures was assessed by pharmacokinetic-pharmacodynamic modeling and prediction probability. To ensure an accurate complexity measure of electroencephalographic recordings, a wavelet-based preprocessor was built in advance.

Results: Both PE and AE could distinguish between the awake and anesthetized states and were highly correlated to each other (r = 0.8, P = 0.004). The pharmacokinetic-pharmacodynamic model adequately described the dose-response relation between PE and AE and sevoflurane effect site concentration. The coefficient R2 between PE and effect site concentration was 0.89 +/- 0.07 for all patients, compared with 0.60 +/- 0.14 for AE. Prediction probabilities of 0.86 +/- 0.04 and 0.79 +/- 0.09 for PE and AE showed that PE has a stronger ability to differentiate between the awake and anesthetic states.     

Entropy and cortical activity: information theory and PET findings.

Functional segregation requires convergence and divergence of neuroanatomical connections. Furthermore, the nature of functional segregation suggests that (1) signals in convergent afferents are correlated and (2) signals in divergent efferents are uncorrelated. The aim of this article is to show that this arrangement can be predicted mathematically, using information theory and an idealized model of cortical processing. In theory, the existence of bifurcating axons limits the number of independent output channels from any small cortical region, relative to the number of inputs. An information theoretic analysis of this special (high input:output ratio) constraint indicates that the maximal transfer of information between inputs, to a cortical region, and its outputs will occur when (1) extrinsic connectivity to the area is organized such that the entropy of neural activity in afferents is optimally low and (2) connectivity intrinsic to the region is arranged to maximize the entropy measured at the initial segments of projection neurons. Under the constraints of the model, a low entropy is synonymous with high correlations between axonal firing rates (and vice versa). Consequently this antisymmetric arrangement of functional activity in convergent and divergent connections underlying functional segregation is exactly that predicted by the principle of maximum preservation of information, considered in the context of axonal bifurcation. The hypothesis that firing in convergent afferents is correlated (has low entropy) and spatially coherent was tested using positron emission tomographic measurements of cortical synaptic function in man. This hypothesis was confirmed.     

Bispectral Index, Entropy, and Quantitative Electroencephalogram during Single-agent Xenon Anesthesia

Background: The aim was to evaluate the performance of anesthesia depth monitors, Bispectral Index (BIS) and Entropy, during single-agent xenon anesthesia in 17 healthy subjects.

Methods: After mask induction with xenon and intubation, anesthesia was continued with xenon only. BIS, State Entropy and Response Entropy, and electroencephalogram were monitored throughout induction, steady-state anesthesia, and emergence. The performance of BIS, State Entropy, and Response Entropy were evaluated with prediction probability, sensitivity, and specificity analyses. The power spectrum of the raw electroencephalogram signal was calculated.

Results: The mean (SD) xenon concentration during anesthesia was 66.4% (2.4%). BIS, State Entropy, and Response Entropy demonstrated low prediction probability values at loss of response (0.455, 0.656, and 0.619) but 1 min after that the values were high (0.804, 0.941, and 0.929). Thereafter, equally good performance was demonstrated for all indices. At emergence, the prediction probability values to distinguish between steady-state anesthesia and return of response for BIS, State Entropy, and Response Entropy were 0.988, 0.892, and 0.992. No statistical differences between the performances of the monitors were observed. Quantitative electroencephalogram analyses showed generalized increase in total power (P < 0.001), delta (P < 0.001) and theta activity (P < 0.001), and increased alpha activity (P = 0.003) in the frontal brain regions.