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PubMed1999

Diabetic alteration of cardiac vago-sympathetic modulation assessed with tone-entropy analysis.

No clear evidence of diabetic alteration of cardiac sympatho-vagal balance has been reported to date. We assessed heart rate variability of diabetic patients with the tone-entropy analysis that has been published elsewhere (Oida et al. 1997). Tone reflects the cardiac vago-sympathetic balance and entropy the total autonomic efferent activity. Diabetic influence on tone and entropy was examined in two groups of patients (38-52 years and 60-69 year, total 106) stratified according to the occurrence of impaired glucose tolerance or diabetes mellitus. Ten healthy middle-aged volunteers were also examined as a reference. Electrocardiographic data were collected at rest for 10 min. Tone increased and entropy decreased significantly with severity of diabetic disorders. The alterations were depicted as a curvi-linear relation in tone-entropy space, which superimposed adequately on the standard tone-entropy values obtained in a pharmacological experiment. The results demonstrate that the vago-sympathetic balance is altered with diabetic disorders: vagal predominance is impaired significantly in proportion to a withdrawal of total autonomic efferent activity.

Adult↗

PubMed2005

An entropy-based statistic for genomewide association studies.

Efficient genotyping methods and the availability of a large collection of single-nucleotide polymorphisms provide valuable tools for genetic studies of human disease. The standard chi2 statistic for case-control studies, which uses a linear function of allele frequencies, has limited power when the number of marker loci is large. We introduce a novel test statistic for genetic association studies that uses Shannon entropy and a nonlinear function of allele frequencies to amplify the differences in allele and haplotype frequencies to maintain statistical power with large numbers of marker loci. We investigate the relationship between the entropy-based test statistic and the standard chi2 statistic and show that, in most cases, the power of the entropy-based statistic is greater than that of the standard chi2 statistic. The distribution of the entropy-based statistic and the type I error rates are validated using simulation studies. Finally, we apply the new entropy-based test statistic to two real data sets, one for the COMT gene and schizophrenia and one for the MMP-2 gene and esophageal carcinoma, to evaluate the performance of the new method for genetic association studies. The results show that the entropy-based statistic obtained smaller P values than did the standard chi2 statistic.

Entropy↗

PubMed2000

Electroencephalogram approximate entropy correctly classifies the occurrence of burst suppression pattern as increasing anesthetic drug effect.

BACKGROUND: Approximate entropy, a measure of signal complexity and regularity, quantifies electroencephalogram changes during anesthesia. With increasing doses of anesthetics, burst-suppression patterns occur. Because of the high-frequency bursts, spectrally based parameters such as median electroencephalogram frequency and spectral edge frequency 95 do not decrease, incorrectly suggesting lightening of anesthesia. The authors investigated whether the approximate entropy algorithm correctly classifies the occurrence of burst suppression as deepening of anesthesia. METHODS: Eleven female patients scheduled for elective major surgery were studied. After propofol induction, anesthesia was maintained with isoflurane only. Before surgery, the end-tidal isoflurane concentration was varied between 0.6 and 1.3 minimum alveolar concentration. The raw electroencephalogram was continuously recorded and sampled at 128 Hz. Approximate entropy, electroencephalogram median frequency, spectral edge frequency 95, burst-suppression ratio, and burst-compensated spectral edge frequency 95 were calculated offline from 8-s epochs. The relation between burst-suppression ratio and approximate entropy, electroencephalogram median frequency, spectral edge frequency 95, and burst-compensated spectral edge frequency 95 was analyzed using Pearson correlation coefficient. RESULTS: Higher isoflurane concentrations were associated with higher burst-suppression ratios. Electroencephalogram median frequency (r = 0.34) and spectral edge frequency 95 (r = 0.29) increased, approximate entropy (r = -0.94) and burst-compensated spectral edge frequency 95 (r = -0.88) decreased with increasing burst-suppression ratio. CONCLUSION: Electroencephalogram approximate entropy, but not electroencephalogram median frequency or spectral edge frequency 95 without burst compensation, correctly classifies the occurrence of burst-suppression pattern as increasing anesthetic drug effect.

Adult↗

PubMed2003

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 (T 0.05 ) was 18.7 degrees C. The temperature corresponding to 95% entropy (T 0.95 ) was 31.3 degrees C during cooling and 38.2 degrees C during rewarming ( P < 0.02). CONCLUSIONS: Approximate entropy is a suitable analysis technique to quantify the electroencephalographic changes that occur with cooling and rewarming. It demonstrates a delay in recovery that is of the same magnitude as that seen with conventional interpretation of the analog electroencephalogram and extends these observations over a greater range of temperatures.

Adult↗

PubMed2006

The effects of ketamine and rocuronium on the A-Line auditory evoked potential index, Bispectral Index, and spectral entropy monitor during steady state propofol and remifentanil anesthesia.

BACKGROUND: The authors studied the effects of ketamine and rocuronium on the Bispectral Index, A-Line auditory evoked potential index, state entropy, and response entropy during a calculated steady state anesthesia with propofol and remifentanil. METHODS: After ethics committee approval, 42 patients were allocated to four groups. Baseline measurements were performed after implementing a calculated steady state anesthesia with propofol and remifentanil. The control group received no additional medication. The ketamine group received a bolus and continuous infusion of ketamine. The rocuronium group received a bolus of rocuronium. The rocuronium-ketamine group received both. All data were stored during 15 min after baseline. After inspection of the raw data, the authors conducted an explorative statistical analysis. RESULTS: No significant changes were found in the control group for any of the monitors. Mean values decreased in the rocuronium group for the A-Line auditory evoked potential index, Bispectral Index, and response entropy, but not for state entropy. In the ketamine group, the A-Line auditory evoked potential index and Bispectral Index did not change significantly, but state and response entropy increased. In the rocuronium-ketamine group, the A-Line auditory evoked potential index and Bispectral Index did not decrease as found in the rocuronium group. Response and state entropy increased significantly. CONCLUSIONS: The response of all monitors after ketamine administration is not affected by simultaneous administration of rocuronium. Interpretation of all studied indices must be done cautiously while taking into account the clinical setting during measurement.

Adolescent↗

PubMed2000

Kulback-Leibler and renormalized entropies: applications to electroencephalograms of epilepsy patients.

Recently, "renormalized entropy" was proposed as a novel measure of relative entropy [P. Saparin et al., Chaos, Solitons and Fractals 4, 1907 (1994)] and applied to several physiological time sequences, including electroencephalograms (EEGs) of patients with epilepsy. We show here that this measure is just a modified Kullback-Leibler (KL) relative entropy, and it gives similar numerical results to the standard KL entropy. The latter better distinguishes frequency contents of, e.g., seizure and background EEGs than renormalized entropy. We thus propose that renormalized entropy might not be as useful as claimed by its proponents. In passing, we also make some critical remarks about the implementation of these methods.

Biophysical Phenomena↗

PubMed2006

Comparison of entropy-based regularity estimators: application to the fetal heart rate signal for the identification of fetal distress.

This paper considers the multiscale entropy (MSE) approach for estimating the regularity of time series at different scales. Sample entropy (SampEn) and approximate entropy (ApEn) are evaluated in MSE analysis on simulated data to enhance the main features of both estimators. We applied the approximate entropy and the sample entropy estimators to fetal heart rate signals on both single and multiple scales for an early identification of fetal sufferance antepartum. Our results show that the ApEn index significantly distinguishes suffering from normal fetuses between the 30th and the 35th week of gestation. Furthermore, our data shows that the MSE entropy values are reliable indicators of the fetal distress associated with the presence of a pathological condition at birth.

Algorithms↗

PubMed2000

Optimal region of average side-chain entropy for fast protein folding.

Search and study the general principles that govern kinetics and thermodynamics of protein folding generates new insight into the factors that control this process. Here, we demonstrate based on the known experimental data and using theoretical modeling of protein folding that side-chain entropy is one of the general determinants of protein folding. We show for proteins belonging to the same structural family that there exists an optimal relationship between the average side-chain entropy and the average number of contacts per residue for fast folding kinetics. Analysis of side-chain entropy for proteins that fold without additional agents demonstrates that there exists an optimal region of average side-chain entropy for fast folding. Deviation of the average side-chain entropy from the optimal region results in an anomalous protein folding process (prions, alpha-lytic protease, subtilisin, some DNA-binding proteins). Proteins with high or low side-chain entropy would have extended unfolded regions and would require some additional agents for complete folding. Such proteins are common in nature, and their structure properties have biological importance.

Entropy↗

PubMed2005

Correlation of EEG spectral entropy with regional cerebral blood flow during sevoflurane and propofol anaesthesia.

ENTROPY index monitoring, based on spectral entropy of the electroencephalogram, is a promising new method to measure the depth of anaesthesia. We examined the association between spectral entropy and regional cerebral blood flow in healthy subjects anaesthetised with 2%, 3% and 4% end-expiratory concentrations of sevoflurane and 7.6, 12.5 and 19.0 microg.ml(-1) plasma drug concentrations of propofol. Spectral entropy from the frequency band 0.8-32 Hz was calculated and cerebral blood flow assessed using positron emission tomography and [(15)O]-labelled water at baseline and at each anaesthesia level. Both drugs induced significant reductions in spectral entropy and cortical and global cerebral blood flow. Midfrontal-central spectral entropy was associated with individual frontal and whole brain blood flow values across all conditions, suggesting that this novel measure of anaesthetic depth can depict global changes in neuronal activity induced by the drugs. The cortical areas of the most significant associations were remarkably similar for both drugs.

Adult↗

PubMed2006

Assessing the depth of dexmedetomidine-induced sedation with electroencephalogram (EEG)-based spectral entropy.

BACKGROUND: Adequate sedation of critically ill patients improves the outcome of intensive care. Maintaining an optimal level of sedation in the intensive care unit (ICU) is difficult because of a lack of appropriate monitoring methods to guide drug dosing. Dexmedetomidine, a selective alpha(2)-adrenoceptor agonist, has recently been introduced for the sedation of ICU patients. This study investigated the utility of electroencephalogram (EEG)-based spectral entropy monitoring (with M-ENTROPY, GE Healthcare, Helsinki, Finland) for the assessment of dexmedetomidine-induced sedation. METHODS: Eleven healthy, non-smoking men, aged 23.9 +/- 2.5 years (mean +/- standard deviation), were recruited. Spectral entropy was recorded before and during low (0.5 ng/ml) and high (5 ng/ml) plasma concentrations of dexmedetomidine. At the end of the infusion, subjects were awakened by verbal command and light shaking. RESULTS: Spectral entropy decreased from 84 +/- 5 to 66 +/- 16 (P= 0.029) during low dexmedetomidine levels and from 84 +/- 5 to 20 +/- 12 (P < 0.001) during high dexmedetomidine levels. Transitions during loss and regaining of consciousness were analysed separately. Entropy decreased from 76 +/- 8 before to 43 +/- 10 (P < 0.001) after loss of consciousness, and increased from 14 +/- 4 to 63 +/- 13 (P < 0.001) on regaining of consciousness. These changes were consistent across all subjects. Prediction probability and sensitivity values indicated a high predictive performance of the method. CONCLUSION: The depth of dexmedetomidine-induced sedation can be monitored with EEG-based spectral entropy. These results should be confirmed in a clinical setting.

Adult↗

PubMed2006

Does monitoring bispectral index or spectral entropy reduce sevoflurane use?

A decrease in volatile anesthetic consumption has been demonstrated using bispectral index (BIS), whereas data concerning spectral entropy are lacking. One hundred and forty adult patients scheduled for surgical procedures lasting more than 1 h were prospectively randomized to receive an anesthetic controlled either by BIS or by spectral entropy or solely by clinical variables. Anesthesia was induced with propofol and sufentanil. Sufentanil was infused continuously thereafter. Sevoflurane was administered in 1 L/min O2/N2O. The sevoflurane concentration was adjusted according to conventional clinical variables in the standard practice group, whereas the 40-60 interval was applied for the BIS and spectral entropy-guided groups. The sevoflurane vaporizer was weighed before and after anesthesia, and consumption was calculated. Groups were comparable for demographic data except for weight (heavier in the spectral entropy-guided group, P < 0.05). Compared with standard practice, patients with BIS or spectral entropy monitoring required 29% less sevoflurane (normalized sevoflurane consumption to the weights of the patients and to the durations of anesthesia; both P < 0.03) and a similar sufentanil dose. An unintended improvement in the standard practice group (positive bias) was observed. In conclusion, BIS and spectral entropy monitoring have the same sparing effect of sevoflurane.

Adolescent↗

PubMed2006

Low HRV entropy is strongly associated with myocardial infarction.

Heart rate variability (HRV) is a marker of autonomous activity in the heart. An important application of HRV measures is the stratification of mortality risk after myocardial infarction. Our hypothesis is that the information entropy of HRV, a non-linear approach, is a suitable measure for this assessment. As a first step, to evaluate the effect of myocardial infarction on the entropy, we compared the entropy to standard HRV parameters. The entropy was estimated by compressing the tachogram with Bzip2. For univariate comparison, statistical tests were used. Multivariate analysis was carried out using automatically generated decision trees. The classification rate and the simplicity of the decision trees were the two evaluation criteria. The findings support our hypothesis. The meanNN-normalized entropy is reduced in patients with myocardial infarction with very high significance. One entropy parameter alone exceeds the discrimination strength of multivariate standards-based trees.

Algorithms↗

PubMed2006

Information entropy and the variability of space-time movement error.

The authors investigated the effects of movement time and movement distance on the information entropy and variability of spatial and temporal error in a discrete aiming movement. In Experiment 1, the authors held movement distance (100 mm) constant and manipulated 11 movement times (300-800 ms) of 8 participants. In Experiment 2, the authors tested 6 movement distances at 2 given movement times (15-60 mm at 300 ms; 40-240 mm at 800 ms) in 8 participants. The variability and entropy for spatial error increased with average movement velocity, whereas the variability and entropy for temporal error decreased as a function of average movement velocity. The common variance between variable error and entropy averaged about 84% and 72% for spatial and temporal errors, respectively, suggesting that the probabilistic approach of entropy reveals features that are not present in the standard deviation index of variability. The findings provide further evidence that information entropy may be a useful single-index representation of variability in the movement speed-accuracy relation.

Adult↗

PubMed2001

Entropy generation method to quantify thermal comfort.

The present paper presents a thermodynamic approach to assess the quality of human-thermal environment interaction and quantify thermal comfort. The approach involves development of entropy generation term by applying second law of thermodynamics to the combined human-environment system. The entropy generation term combines both human thermal physiological responses and thermal environmental variables to provide an objective measure of thermal comfort. The original concepts and definitions form the basis for establishing the mathematical relationship between thermal comfort and entropy generation term. As a result of logic and deterministic approach, an Objective Thermal Comfort Index (OTCI) is defined and established as a function of entropy generation. In order to verify the entropy-based thermal comfort model, human thermal physiological responses due to changes in ambient conditions are simulated using a well established and validated human thermal model developed at the Institute of Environmental Research of Kansas State University (KSU). The finite element based KSU human thermal computer model is being utilized as a "Computational Environmental Chamber" to conduct series of simulations to examine the human thermal responses to different environmental conditions. The output from the simulation, which include human thermal responses and input data consisting of environmental conditions are fed into the thermal comfort model. Continuous monitoring of thermal comfort in comfortable and extreme environmental conditions is demonstrated. The Objective Thermal Comfort values obtained from the entropy-based model are validated against regression based Predicted Mean Vote (PMV) values. Using the corresponding air temperatures and vapor pressures that were used in the computer simulation in the regression equation generates the PMV values. The preliminary results indicate that the OTCI and PMV values correlate well under ideal conditions. However, an experimental study is needed in the future to fully establish the validity of the OTCI formula and the model. One of the practical applications of this index is that could it be integrated in thermal control systems to develop human-centered environmental control systems for potential use in aircraft, mass transit vehicles, intelligent building systems, and space vehicles.

Algorithms↗

PubMed2006

[Study on the maximum entropy principle and population genetic equilibrium].

A general mathematic model of population genetic equilibrium about one locus was constructed based on the maximum entropy principle by WANG Xiao-Long et al. They proved that the maximum solve of the model was just the frequency distribution that a population reached Hardy-Weinberg genetic equilibrium. It can suggest that a population reached Hardy-Weinberg genetic equilibrium when the genotype entropy of the population reached the maximal possible value, and that the frequency distribution of the maximum entropy was equivalent to the distribution of Hardy-Weinberg equilibrium law about one locus. They further assumed that the frequency distribution of the maximum entropy was equivalent to all genetic equilibrium distributions. This is incorrect, however. The frequency distribution of the maximum entropy was only equivalent to the distribution of Hardy-Weinberg equilibrium with respect to one locus or several limited loci. The case with regard to limited loci was proved in this paper. Finally we also discussed an example where the maximum entropy principle was not the equivalent of other genetic equilibria.

Entropy↗

PubMed1995

Side-chain conformational entropy in protein folding.

An important, but often neglected, contribution to the thermodynamics of protein folding is the loss of entropy that results from restricting the number of accessible side-chain conformers in the native structure. Conformational entropy changes can be found by comparing the number of accessible rotamers in the unfolded and folded states, or by estimating fusion entropies. Comparison of several sets of results using different techniques shows that the mean conformational free energy change (T delta S) is 1 kcal.mol-1 per side chain or 0.5 kcal.mol-1 per bond. Changes in vibrational entropy appear to be negligible compared to the entropy change resulting from the loss of accessible rotamers. Side-chain entropies can help rationalize alpha-helix propensities, predict protein/inhibitor complex structures, and account for the distribution of side chains on the protein surface or interior.

Peptide Fragments↗

PubMed1994

Estimation of changes in side chain configurational entropy in binding and folding: general methods and application to helix formation.

Theoretical estimations of changes in side chain configurational entropy are essential for understanding the different contributions to the overall thermodynamic behavior of important biological processes like folding and binding. The configurational entropy of any given side chain in any particular protein can be evaluated from the complete energy profile of the side chain. Calculations of the energy profiles can be performed using the side chain single bond dihedrals as the only independent variables as long as the structures at each value of the dihedrals are allowed to relax through small changes in the valence bond angles. The probabilities of different side chain conformers obtained from these energy profiles are very similar to the conformer populations obtained by analysis of side chain preferences in the proteins of the Protein Data Bank. Also, side chain conformational entropies obtained from the energy profiles agree extremely well with those obtained from the Protein Data Bank conformer populations. Changes in side chain configurational entropy in binding and folding can be computed as differences in conformational entropy because, in most cases, the frequency of the rotational oscillation around the energy minimum of any given conformer does not appear to change significantly in the reactions. Changes of side chain conformational entropy calculated in this way were compared with experimental values. The only available experimental data--the effect of side chain substitution on the stability of alpha-helices--were used for this comparison. The experimental values were corrected to subtract the solvent contributions. This comparison yields an excellent agreement between calculated and experimental values, validating not only the theoretical estimates but also the separability of the entropic contributions into configurational terms and solvation related terms.

Amino Acids↗

PubMed2006

The effect of addition of nitrous oxide to a sevoflurane anesthetic on BIS, PSI, and entropy.

OBJECTIVE: N(2)O is a commonly used anesthetic that has amnestic and analgesic properties. Recently, devices that estimate depth of consciousness have been introduced in an attempt to better titrate anesthesia, however the effect of N(2)O on these monitors is unclear. METHODS: General anesthesia was induced and titrated to maintain normal blood pressure and pulse in healthy adults. Data were collected in three 10 minute intervals (Sevo, Sevo + N(2)O, Sevo). In Phase A, sevoflurane concentration was held constant during the N(2)O trial in 60 subjects monitored with either BIS, PSI, or Entropy. In Phase B, sevoflurane concentration was reduced as N(2)O was added, maintaining a constant overall "MAC" in 20 subjects monitored concurrently with BIS and Entropy. Sample size for both phases was designed to detect a 10 unit change in measure of processed EEG with alpha = .05 and statistical power = .80. RESULTS: In Phase A, supplementing sevoflurane with > 65% N(2)O increased MAC from 1.3 +/- 0.05 to 2.2 +/- 0.10, but did not significantly alter BIS nor PSI (p-value for differential MAC is < 0.05). Entropy, however, dropped significantly, with a change in state entropy (SE) from 31.1 +/- 7.3 to 18.9 +/- 3.7 and a corresponding rise when N(2)O was discontinued. In Phase B, supplementing sevoflurane with > 65% N(2)O with a concomitant reduction in sevoflurane resulted in an increase in both BIS (from 34 +/- 5 to 53.9 +/- 11.5) and SE (from 32 +/- 8.2 to 55.4 +/- 21.3). CONCLUSION: Supplementing sevoflurane with > 65% N(2)O did not result in a significant change in either BIS or PSI when sevoflurane concentration was kept constant. Entropy, however, significantly decreased as anesthetic depth increased. When sevoflurane concentration was reduced during N(2)O administration, both BIS and Entropy rose despite maintenance of anesthetic depth, indicating a variable concentration effect between volatiles and N(2)O.

Adult↗