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PubMed2003

Image stacking with entropy values in conventional angiography: initial experience.

The entropy method for stacking a series of angiographic images is presented and compared with the maximum opacity method, which is already established. The entropy method comprises calculation of the entropy of the time course for each image pixel. This accentuates image areas where a contrast agent bolus is passing. Quantitative analysis of the contrast-to-noise ratio and qualitative analysis of 11 cases were performed, the latter by eight independent viewers. Results indicate that the entropy images show more vascular detail in small peripheral vessels and increased contrast-to-noise ratio by up to a factor of 1.97 compared with maximum opacity images.

Adult↗

PubMed1998

Edema, oncotic pressure, and free entropy: novel considerations for the treatment of edema through attention to thermodynamics.

Over 170 years after Richard Bright and a century after Ernest H. Starling, the development, location, and severity of edema in patients with renal impairment continue to baffle the predictions of most nephrologists. While much of the phenomenon can be explained by levels of serum proteins, or hydrostatic pressures, there are stunning exceptions well known to any practicing nephrologist. Some of the derangement is undoubtedly due to unmeasured but well-known variables, such as membrane permeability; however, other factors such as free entropy of plasma are also clearly involved. The study of other polyelectrolyte colloids, similar to plasma proteins, for industrial purposes has led to the identification of various phenomena such as counterion condensation that can result in loss of entropy and consequently osmotic pressure. Variables known to result in a loss of free entropy, such as pH, oxidation products and ligand binding, are discussed. Older equations developed by van't Hoff and Donnan might require replacement by newer mathematical models such as the nonlinear Poisson-Boltzmann equation or the Monte Carlo simulator. Attempts to restore free entropy to plasma would be a more physiological treatment of edema than diuretic use. Implications are noted for future drug development to treat edema.

Blood Proteins↗

PubMed2004

Estimating the temporal interval entropy of neuronal discharge.

To better understand the role of timing in the function of the nervous system, we have developed a methodology that allows the entropy of neuronal discharge activity to be estimated from a spike train record when it may be assumed that successive interspike intervals are temporally uncorrelated. The so-called interval entropy obtained by this methodology is based on an implicit enumeration of all possible spike trains that are statistically indistinguishable from a given spike train. The interval entropy is calculated from an analytic distribution whose parameters are obtained by maximum likelihood estimation from the interval probability distribution associated with a given spike train. We show that this approach reveals features of neuronal discharge not seen with two alternative methods of entropy estimation. The methodology allows for validation of the obtained data models by calculation of confidence intervals for the parameters of the analytic distribution and the testing of the significance of the fit between the observed and analytic interval distributions by means of Kolmogorov-Smirnov and Anderson-Darling statistics. The method is demonstrated by analysis of two different data sets: simulated spike trains evoked by either Poissonian or near-synchronous pulsed activation of a model cerebellar Purkinje neuron and spike trains obtained by extracellular recording from spontaneously discharging cultured rat hippocampal neurons.

Action Potentials↗

PubMed2002

The role of approximate entropy in predicting ventricular defibrillation threshold.

BACKGROUND: The role of myocardial tissue mass on ventricular defibrillation threshold (DFT) is unclear. We hypothesized that changes in tissue mass modulate DFT by changing ventricular fibrillation (VF) wavefront regularity (entropy). METHODS AND RESULTS: The right ventricles (RV) of seven farm pigs were isolated, superfused and perfused through the right coronary artery with oxygenated Tyrode's solution at 37 degrees C. The epicardial surface was stained with the voltage sensitive dye, di-4-ANEPPS, and activation wavefront numbers (AWN) during VF were determined from the optical maps using a CCD camera (96 x 96 pixels over a 3.5 x 3.5 cm area). The RV mass was progressively reduced by sequential cutting of 1 to 2 g of tissue (approximately 12 cuts in total) distal to the perfusion site. After each cut, VF was reinduced, optical maps obtained, and the 50% probability of successful DFT(50) determined using an up-down algorithm. After each cut, the approximate entropy (ApEn) was also computed using 5 seconds of VF data obtained with a bipolar electrode and a pseudo-electrocardiogram. Tissue mass reduction of up to one third of the RV mass (ie, from 48.4 +/- 4.25 g to 34 +/- 4.7 g) caused little or no change in the DFT, ApEn or AWN. However, further progressive reduction of the RV mass near the critical mass of VF resulted in a significant (P < 0.05) progressive decrease in all three measured parameters. DFT energy was reduced by 27% (1.47 +/- 0.34 J vs. 1.02 +/- 0.14 J). There was a significant (P < 0.01) correlation between the DFT and ApEn, which significantly further increased (P < 0.001) near the critical mass. In a separate series of 6 isolated RVs, the ApEn correlated well with the Kolmogorov-Sinai (K-S) entropy, the standard method of calculating entropy. CONCLUSION: Tissue mass reduction significantly reduces DFT when the mass reduction increases VF wavefront regularity.

Animals↗

PubMed2006

Spectral entropy and bispectral index as measures of the electroencephalographic effects of propofol.

Recently, Datex-Ohmeda introduced the Entropy Moduletrade mark for measuring depth of anesthesia. Based on the Shannon entropy of the electroencephalogram, state entropy (SE) and response entropy (RE) are computed. We investigated the dose-response relationship of SE and RE during propofol anesthesia in comparison with the Bispectral Indextrade mark (BIS). Twenty patients were studied without surgical stimulus. Anesthesia was induced by a constant propofol infusion of 2000 mg/h (451 +/- 77 microg x min(-1) x kg(-1)) via a large forearm vein. Propofol was infused until substantial burst suppression occurred (more than 50%) or mean arterial blood pressure decreased to <60 mm Hg. Hereafter, infusions were stopped until recovery of BIS values up to 60 was reached. Subsequently, the constant propofol infusion of 2000 mg/h was restarted to increase depth of anesthesia and again decreased (infusion was stopped) within the BIS value range of 40-60. The coefficient of determination (R2) and the prediction probability (P(K)) were calculated to evaluate the performance of SE, RE, and BIS to predict changing propofol effect-site concentrations. R2 values for SE, RE, and BIS of 0.88 +/- 0.08, 0.89 +/- 0.07, and 0.92 +/- 0.06, respectively, were similar. The calculated P(K) values, however, revealed a significant difference between SE and RE compared with BIS, with P(K) = 0.77 +/- 0.09, 0.76 +/- 0.10, and 0.84 +/- 0.06, respectively. BIS seems to show slight advantages in predicting propofol effect-site concentrations compared with SE and RE, as measured by P(K) but not as measured by R2.

Adult↗

PubMed2006

Compression entropy contributes to risk stratification in patients with cardiomyopathy.

Sudden cardiac death (SCD) is a leading cause of mortality with an incidence of 3 million cases per year worldwide. Therapies for patients who have survived an SCD episode or have a high risk of developing lethal ventricular arrhythmia are well established and depend mainly on risk stratification. In this study we investigated the suitability of the non-linear measure compression entropy (Hc) for improved risk prediction in cardiac patients. We recorded 24-h Holter ECG for 300 patients with congestive heart failure (CHF). During a mean follow-up period of 12 months, 32 patients died due to a cardiac event. Hc depends on the compression parameters window length w and buffer length b, which were optimised by analysing a subgroup of patients. Compression entropies based on the beat-to-beat interval (BBI) were subsequently calculated and compared with standard heartrate variability parameters. Statistical analysis revealed significant differences between high- and low-risk CHF patients in standard HRV measures, as well as compression entropy based on the BBI (cardiac death, p = 0.005; SCD, p = 0.02). In conclusion, the implementation of non-linear compression entropy analysis in multivariate analysis seems to be useful for enhanced risk stratification of cardiac death, especially SCD, in ischaemic cardiomyopathy patients.

Aged↗

PubMed2002

[Indices based on entropy for measuring social inequalities in health].

As described in the scientific literature, indices used to measure social inequalities in health have positive features, but they also have shortcomings, depending on how they are applied. The objective of this article is to put forward and to demonstrate, in both theoretical and practical terms, the advantages of measurements of inequality based on the notion of entropy, which is well known in physics and in information theory. The article defines and presents the main properties of indices based on the notions of entropy and redundancy. The application of the indices is illustrated with two fictitious data sets and also with real data derived from basic health indicators for the Americas, from the Pan American Health Organization. Indices based on the notion of entropy have properties that include: a) not varying with scale changes, b) being symmetrical, c) incorporating a socioeconomic dimension, and d) being easy to interpret thanks to the condition of equivalence between entropy and a system with two categories.

Americas↗

PubMed2000

[Approximate entropy and its application in heart rate variability analysis].

Objective. To introduce approximate entropy in the analysis of heart rate variability, and to discuss the changes of the complexity of cardiovascular system during orthostatic standing posture. Method. ECG of 8 subjects were recorded during supine and orthostatic standing postures. Approximate entropy was used to analyze HRV. Result. Compared to supine before orthostatic standing posture, R-R intervals at 0-5 min, 5-10 min, 10-15 min and 15-20 min during orthostatic standing posture were decreased significantly, while approximate entropy at 0-5 min and 15-20 min decreased significantly. It showed that the complexity of cardiovascular system was decreased and the modulation of cardiovascular system changed. Conclusion. It is feasible that approximate entropy be used for heart rate variability analysis.

Adolescent↗

PubMed2002

Multiscale entropy to distinguish physiologic and synthetic RR time series.

We address the challenge of distinguishing physiologic interbeat interval time series from those generated by synthetic algorithms via a newly developed multiscale entropy method. Traditional measures of time series complexity only quantify the degree of regularity on a single time scale. However, many physiologic variables, such as heart rate, fluctuate in a very complex manner and present correlations over multiple time scales. We have proposed a new method to calculate multiscale entropy from complex signals. In order to distinguish between physiologic and synthetic time series, we first applied the method to a learning set of RR time series derived from healthy subjects. We empirically established selected criteria characterizing the entropy dependence on scale factor for these datasets. We then applied this algorithm to the CinC 2002 test datasets. Using only the multiscale entropy method, we correctly classified 48 of 50 (96%) time series. In combination with Fourier spectral analysis, we correctly classified all time series.

Adult↗

PubMed2005

Effects of nitrous oxide on spectral entropy of the EEG during surgery under balanced anaesthesia with sufentanil and sevoflurane.

BACKGROUND: Spectral entropy of the electroencephalogram (EEG) has been proposed to monitor anaesthetic depth. We investigated the effect of nitrous oxide on response (RE) and state entropy (SE) of the EEG during lumbar disc surgery under anaesthesia with sufentanil and sevoflurane. METHODS: In an open study, anaesthesia was induced with propofol and sufentanil, and maintained with 2% end-tidal sevoflurane concentration in air/oxygen (FiO2 = 0.4) in 25 patients. During surgery, nitrous oxide was randomly administered either at 0 or at 60% end-tidal concentration in 10 (control group) and 15 patients (nitrous oxide group), respectively. RE and SE were recorded at 2.5 min intervals for 10 min before randomization and for 25 min either continuously (control) or after achieving the target nitrous oxide concentration. RESULTS: Two patients who received nitrous oxide were excluded from statistical analysis because of protocol violation. Nitrous oxide provoked a significant decrease in RE and SE from 46.2 +/- 11.1 and 44.3 +/- 11.1 to a lowest value of 27.8 +/- 8.3 and 27.1 +/- 8.9, respectively. The decrease in entropy persisted during the 25 min recording period. CONCLUSIONS: Addition of nitrous oxide during balanced anaesthesia with sufentanil and sevoflurane provokes a decrease in response and state entropy of the EEG during lumbar disc surgery.

Adult↗

PubMed2002

A maximum entropy algorithm for rhythmic analysis of genome-wide expression patterns.

We introduce a maximum entropy-based analysis technique for extracting and characterizing rhythmic expression profiles from DNA microarray hybridization data. These patterns are clues to discovering genes implicated in cell-cycle, circadian, and other periodic biological processes. The algorithm, implemented in a program called ENRAGE (Entropy-based Rhythmic Analysis of Gene Expression), treats the task of estimating an expression profile's periodicity and phase as a simultaneous bicriterion optimization problem. Specifically, a frequency domain spectrum is reconstructed from a time-series of gene expression data, subject to two constraints: (a) the likelihood of the spectrum and (b) the Shannon entropy of the reconstructed spectrum. Unlike Fourier-based spectral analysis, maximum entropy spectral reconstruction is well suited to signals of the type generated in DNA microarray experiments. Our algorithm is optimal, running in linear time in the number of expression profiles. Moreover, an implementation of our algorithm runs an order of magnitude faster than previous methods. Finally, we demonstrate that ENRAGE is superior to other methods at identifying and characterizing periodic expression profiles on both synthetic and actual DNA microarray hybridization data.

Algorithms↗

PubMed2005

Lethality and entropy of protein interaction networks.

We characterize protein interaction networks in terms of network entropy. This approach suggests a ranking principle, which strongly correlates with elements of functional importance, such as lethal proteins. Our combined analysis of protein interaction networks and functional profiles in single cellular yeast and multi-cellular worm shows that proteins with large contribution to network entropy are preferentially lethal. While entropy is inherently a dynamical concept, the present analysis incorporates only structural information. Our result therefore highlights the importance of topological features, which appear as correlates of an underlying dynamical property, and which in turn determine functional traits. We argue that network entropy is a natural extension of previously studied observables, such as pathway multiplicity and centrality. It is also applicable to networks in which the processes can be quantified and therefore serves as a link to study questions of structural and dynamical robustness in a unified way.

Animals↗

PubMed2006

Metal ion-mediated reduction in surface entropy improves diffraction quality of crystals of the IRAK-4 death domain.

Interleukin-1 receptor-associated kinase-4 (IRAK-4) is an essential component of innate immunity in mice and humans. IRAK-4 is a bipartite protein composed of a death domain (DD) that mediates molecular recognition, and a catalytic kinase domain. Structure determination of the proteolytically stable, soluble IRAK-4 DD was hampered by poor diffraction quality. Addition of manganese (II) chloride to the crystallization solution produced significant improvements in diffraction, and the structure has been determined to 1.7-Angstrom resolution. Examination of the IRAK-4 DD crystal structure reveals a single manganese ion coordinated to surface residues lysine-21 and aspartate-24. Coordination of the manganese ion resulted in a reduction in the surface entropy at this region of the molecule, by generating a contact-forming and conformationally homogenous surface patch. Prior studies have shown that surface entropy reduction by mutation of surface residues with large flexible side chains (i.e., Lys and Glu) to smaller side chains results in the production of diffraction-quality crystals. The intrinsic high surface entropy of Lys residues can also be decreased by reductive methylation. Our results suggest that screening of manganese ions as a crystallization additive may also facilitate ordered crystallization by reduction of surface entropy. Given the quick and inexpensive nature of screening, this technique is likely to be amenable to high-throughput methods such as those employed by Protein Structure Initiatives.

Animals↗

PubMedDate not supplied

[Optimal relationship between average conformational entropy and average energy of interactions between residues for fast protein folding].

Based on the known experimental data and using the theoretical modeling of protein folding, we demonstrate that there exists an optimal relationship between the average conformational entropy and the average energy of contacts per residue, that is an entropy capacity, for fast protein folding. Statistical analysis of conformational entropy and the number of contacts per residue for 5829 protein structures from four general structural classes (all-alpha, all-beta, +/-/beta, alpha+beta) demonstrates that each class of proteins has its own class-specific average number of contacts and average conformational entropy per residue. These class-specific features determine the folding rates: a proteins are the fastest folding proteins, then follow beta and alpha+beta proteins, and finally alpha/beta proteins are the slowest ones.

Databases, Protein↗

PubMed2006

[Evaluation of the sedation level with propofol with electroencephalographic Entropy in comparison with bispectral index monitor].

BACKGROUND: Entropy, a newly available electroencephalographic monitor, demonstrates two parameters, response entropy (RE) and state entropy (SE). The aim of this study is to compare RE and SE with bispectral index (BIS) during anesthetic induction with propofol. METHODS: Fifteen patients received target controlled infusion of propofol starting at 3 microg x ml(-1). We measured RE, SE and BIS and recorded effect-site concentrations of propofol at three sedation levels: VR1; conscious state before infusion of propofol, VR2; no response to verbal command, and VR3; no response to verbal command and shaking. Spearman rank correlations and prediction probability for sedation level were analyzed. RESULTS: Effect-site concentrations of propofol at VR1, VR2, and VR3 were 0, 1.8 +/- 0.7, and 2.4 +/- 0.7, respectively. All three parameters showed significant correlations with sedation levels. Prediction probability values of SE, RE, and BIS were 0.905, 0.894, and 0.890, respectively. CONCLUSIONS: Response entropy and SE can provide similar information as BIS about the sedation level with propofol.

Adult↗

PubMed1991

Thermodynamics of drug-DNA interactions: entropy-driven intercalation and enthalpy-driven outside binding in the ellipticine series.

Viscosimetric and kinetic results allow one to characterize three modes of DNA binding in the ellipticine series: (1) Ellipticine and its 9 methoxy derivative, which present maximal DNA lengthening properties and bind DNA through a single step mechanism, can be considered as pure intercalators. (2) Ellipticinium derivatives and short-chain substituted oxazolopyridocarbazoles, which present intermediate DNA lengthening properties, bind DNA through a two-step mechanism, one being intercalation. (3) Long-chain substituted oxazolopyridocarbazole derivatives, which display the smallest DNA lengthening properties, bind DNA through a single-step mechanism, probably resulting from an outside binding mode. The viscosimetric and kinetic results are compared with the thermodynamic results obtained from the temperature dependence of the binding constants. It appears that drugs binding on the outside of the DNA double helix tend to have large enthalpy and small entropy contributions, whereas pure intercalating drugs have contributions from both enthalpy and entropy, with entropy dominating by about 2:1. Drugs showing two binding modes exhibit a continuum between the aforementioned extremes, with no breaks in behavior. From this comparison, a correlation between thermodynamic data and DNA binding modes is proposed. Possible molecular implications of both enthalpy and entropy to DNA binding free energy are discussed.

Buffers↗

PubMed2003

A box-counting-based algorithm for computing Shannon entropy in molecular dynamics simulations.

A box-counting-based algorithm (SEBC) has been developed for the numerical computation of the Shannon entropy from samples of continuous functions. Its performance was tested by applying it to several samples of known continuous distribution functions. The results obtained with SEBC reproduced those obtained by analytical or numerical integration. SEBC was also employed for computing the Shannon entropies of the steric energy, Sh(E(S)), of several amino acids from their in vacuo NVE molecular dynamics simulations using the AMBER-4 force field. The results obtained correlate linearly with the experimental standard thermodynamic entropies of these compounds. This work points to the possibility of introducing straightforward and reliable calculations of thermodynamic entropies from empirical linear relationships with Sh(E(S)) obtained from MD simulations.

Journal Article↗

PubMed2005

Estimation of the absolute internal-rotation entropy of molecules with two torsional degrees of freedom from stochastic simulations.

A method of statistical estimation is applied to the problem of evaluating the absolute entropy of internal rotation in a molecule with two torsional degrees of freedom. The configurational part of the entropy is obtained as that of the joint probability density of an arbitrary form represented by a two-dimensional Fourier series, the coefficients of which are statistically estimated using a sample of the torsional angles of the molecule obtained by a stochastic simulation. The internal rotors in the molecule are assumed to be attached to a common frame, and their reduced moments of inertia are initially calculated as functions of the two torsional angles, but averaged over all the remaining internal degrees of freedom using the stochastic-simulation sample of the atomic configurations of the molecule. The torsional-angle dependence of the reduced moments of inertia can be also averaged out, and the absolute internal-rotation entropy of the molecule is obtained in a good approximation as the sum of the configurational entropy and a kinetic contribution fully determined by the averaged reduced moments of inertia. The method is illustrated using Monte Carlo simulations of isomers of stilbene and halogenated derivatives of propane. The two torsional angles in cis-stilbene are found to be much more strongly correlated than those in trans-stilbene, while the degree of the angular correlation in propane increases strongly on substitution of hydrogen atoms with chlorine.

Journal Article↗