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PubMed2006

Exploration of statistical dependence between illness parameters using the entropy correlation coefficient.

UNLABELLED: The entropy correlation coefficient (ECC) is a useful tool for measuring statistical dependence between variables. We employed this tool to search for pairs of variables that correlated in the chronic fatigue syndrome (CFS) Computational Challenge dataset. Highly related variables are candidates for data reduction, and novel relationships could lead to hypotheses regarding the pathogenesis of CFS. METHODS: Data for 130 female participants in the Wichita (KS, USA) clinical study [1] was coded into numerical values. Metric data was grouped using Gaussian mixture models; the number of groups was chosen using Bayesian information content. The pair-wise correlation between all variables was computed using the ECC. Significance was estimated from 1000 iterations of a permutation test and a threshold of 0.01 was used to identify significantly correlated variables. RESULTS: The five dimensions of multidimensional fatigue inventory (MFI) were all highly correlated with each other. Seven Short Form (SF)-36 measures, four CFS case-defining symptoms and the Zung self-rating depression scale all correlated with all MFI dimensions. No physiological variables correlate with more than one MFI dimension. MFI, SF-36, CDC symptom inventory, the Zung self-rating depression scale and three Cambridge Neuropsychological Test Automated Battery (CANTAB) measures are highly correlated with CFS disease status. DISCUSSION: Correlations between the five dimensions of MFI are expected since they are measured from the same instrument. The relationship between MFI and Zung depression index has been previously reported. MFI, SF-36, and Centers for Disease Control and Prevention (CDC) symptom inventory are used to classify CFS; it is not surprising that they are correlated with disease status. Only one of the three CANTAB measures that correlate with disease status has been previously found, indicating the ECC identifies relationships not found with other statistical tools. CONCLUSION: The ECC is a useful tool for measuring statistical dependence between variables in clinical and laboratory datasets. The ECC needs to be further studied to gain a better understanding of its meaning for clinical data.

Adult↗
PubMed2005

[Improvement in the performance of the adaptive neighborhood contrast enhancement technique based on entropy].

This paper presents an improved adaptive-neighborhood-contrast-enhancement (ANCE) method for the improvement of medical image quality. The ANCE method consists of computing the local contrast around each pixel using a variable neighborhood whose size depends on the statistical properties around the given pixel. The obtained contrast image is then transformed into a new contrast image using a contrast enhancement function. Finally, a contrast-enhanced image is obtained by applying inverse contrast transform to the previous step. This technique provides the advantages of enhancing or preserving image contrast while suppressing noise. However, it does have a drawback. The performance of the ANCE method largely depends on how to determine the parameters used in the processing steps. The present study proposes a novel method for optimal and automatic determination of several parameters using entropy. To quantitatively compare the performance of the proposed method with that of the ANCE method, computer-simulated images are generated. The output-to-input SNR level and the mean squared error are used as comparison criteria. Results demonstrated the superiority of the proposed method. Moreover, we have applied our new algorithm to echocardiograms and mammograms. Our results showed that the proposed method has the potential to become useful for improving the image quality of medical images.

Computer Simulation↗
PubMed1999

A data base of minimally frustrated alpha helical segments extracted from proteins according to an entropy criterion.

A data base of minimally frustrated alpha helical segments is defined by filtering a set comprising 822 non redundant proteins, which contain 4783 alpha helical structures. The data base definition is performed using a neural network-based alpha helix predictor, whose outputs are rated according to an entropy criterion. A comparison with the presently available experimental results indicates that a subset of the data base contains the initiation sites of protein folding experimentally detected and also protein fragments which fold into stable isolated alpha helices. This suggests the usage of the data base (and/or of the predictor) to highlight patterns which govern the stability of alpha helices in proteins and the helical behavior of isolated protein fragments.

Algorithms↗
PubMed1997

[Approximate entropy analysis of changes in heart rate dynamics associated with aerobic training].

To elucidate the effects of aerobic training on heart rate dynamics, heart rate variability (HRV) of eight students before and after a six-month aerobic training and HRV of six athletes, were analyzed with conventional time and frequency domain methods as well as with the approximate entropy(ApEn). The results showed that after a six-month aerobic training, heart rate ApEn significantly decreased (P < 0.01, P < 0.05) during both supine control and -6.67 kPa/30 min lower body negative pressure (LBNP). The heart rate ApEn of the athletes during supine control and early stage of LBNP testing was significantly lower (P < 0.01, P < 0.05) than that of the students before training. It was found that the values of ApEn were negatively correlated with the duration of LBNP in the student group (P < 0.01). However, both the time and frequency domain analyses were unable to detect the aforementioned changes. The results suggest that aerobic training can decrease the complexity of heart rate dynamics, and the synchronization in heart rate control during LBNP is probably a sustained process.

Aerospace Medicine↗
PubMed1997

Change in heart rate dynamics after aerobic training detected by approximate entropy and its association with orthostasis.

Findings from the 1973 Skylab mission and early studies led to the conclusion that high level of aerobic capacity might be detrimental to the orthostatic tolerance of returning astronauts. Numerous studies have addressed the problem with conflicting results, further work is needed to establish the relationship between aerobic capacity and orthostasis. During the last two decades, the technique for heart rate variability (HRV) signal analysis developed and have provided a non-invasive probe to examine quantitatively changes in cardiac autonomic balance. In the past, spectral analysis has been used in these studies. During the early 90's, a new mathematical approach and formula termed approximate entropy(ApEn) has been introduced as quantification of regularity and complexity. More recently, ApEn has been used to quantitate the loss of normal nonlinear heart rate variability in a variety of pathological conditions, aging, as well as bed rest deconditioning. The present study was undertaken to assess the effect aerobic training on orthostatic tolerance and HRV analyzed by both conventional AR spectral and ApEn analysis.

Adult↗
PubMed2001

Does the Kolmogorov entropy give more information about the organization of the voluntary movement?

Nonlinear temporal and spatial dynamic changes of human EEG signals during voluntary finger movements were investigated with tracking Kolmogorov entropy (K2). Segments with higher values of K2 defined dynamic transients, distinguishing consecutive phases of the movement organization. The maximum of K2, determined immediately before the movement onset, was specific only for the contralateral sensorimotor area. This nonlinear characteristic, computed over time for EEG single records, indicates the local dynamic properties and detect those EEG patterns, where the underlying process changes the dynamics prior to the task performance. In addition to the present mechanisms, found by the linear methods, qualitatively new mechanisms of neuronal activity were discovered in brain functioning during the organization of voluntary movements.

Brain↗
PubMed1999

[The comparison between approximate entropy and complexity in the study of sleep EEG].

The Paper introduces two algorithms as a complexity measure. One is the algorithm defined by Kaspar and Schuster, the other is a recently developed statistic quantifying regularity and complexity--Approximate entropy (ApEn). They have been applied for the study of sleep EEG. According to the laboratory application and comparison, the result shows that ApEn is a valued complexity measure.

Algorithms↗
PubMed2001

[Maximal entropy principle wavelet denoising].

In the filed of wavelet denoising, an essential problem is how to determine the cutting threshold of wavelet coefficients that divides the coefficients corresponding to signal and noise respectively. The wavelet denoising method discussed here determines this threshold by using the maximal entropy principle (MEP) of information theory. From the basic principle of probability theory, it can be deduced that the detailed wavelet coefficients sequence of an arbitrary distributed random noise sequence satisfies a normal distribution. Based on this conclusion, an optimal threshold is determined using MEP. Such that the coefficients whose absolute values are less than the threshold satisfies a normal probabilistic distribution. This threshold is an optimal value that distinguishes the wavelet coefficients of signal and noise in view of statistics. The simulation analysis using spectral data and the comparison with other methods showed that this method provides a best improvement of signal-to-noise ratio, and its performance is least sensitive to the change of signal-to-noise ratio.

Algorithms↗
PubMed2004

Entropy calculator: getting the best from your multiple protein alignments.

Amino acid sequence alignment is an extremely useful tool in protein family analysis. Most family characteristics, such as the localization of functional residues, structural constraints and evolutionary relationships may be retrieved through the observation of the conservation pattern highlighted by the alignments. A quantitative score for the conservation in the alignment allows different stages of an alignment to be compared and consequently the alignment information to be efficiently exploited. Many scoring methods have been proposed during the last three decades. Claude Shannon's theory of communication (1948) paved the way for a consistent scoring of protein alignments by considering the residue (or symbol) frequency. A number of modifications have been proposed since that time, but the core statistical approach is still considered one of the best. By combining many database managing tools for treatment of protein sequences, a ClustalW software integration, a flexible symbols treatment and gap normalization functions, Entropy Calculator software has been developed. This new tool provides a global and optimal approach to multiple sequence alignment scoring by offering an easy graphic interface and a series of modification options that help in interpreting alignments and allow conservation pattern inferences to be performed.

Amino Acid Sequence↗
PubMed2005

[Analyzing sleep EEG using correlation dimension and approximate entropy].

Correct sleep scoring is the base of sleep studying; nonlinear features of EEG can represent different sleep stages. In this paper, correlation dimension (D2) and approximate entropy (ApEn) of sleep EEG have been calculated. The statistical results reveal that: D2 does not come to be saturated when the embedding dimension increases, but the relative value of D2 can effectively distinguish different sleep stages. ApEn has the advantage of calculating simply, steady result and representing preferably different sleep stages. ApEn and the relative value of D2 reveal, from different point of view, the same rule about EEG (brain) complexity changing, that is, both complexity and its fluctuation are maximal in the subject's awake hour, are decreasing with the deepening of sleep, but the complexity in REM is about the level between S1 and S2.

Electroencephalography↗
PubMed2006

Sample entropy of ECG time series of fearful flyers: preliminary results.

Research within the framework of the nonlinear dynamical systems (NDS) in the field of anxiety disorders has shown that greater irregularity/complexity appears in the output from healthy systems. In this study we measured the Heart rate variability (HRV) and the sample sntropy (SampEn) of the ECG mV time series of fearful flyers (N = 15) and a matched control group (N = 15) when confronted with three combinations of feared stimuli (pictures, sounds, and pictures with sounds) as well as relaxing stimuli (pictures and sounds). Fearful flyers had lower SampEn than controls in all conditions, including baseline. Non-phobics showed significant entropy decreases from baseline in two out of three exposure conditions. No differences on HRV were found between groups, and HRV was not sensitive to condition changes. The main finding of the study is that the SampEn calculated on very short ECG mV recordings (10 to 60 seconds, easy to obtain in clinical settings) may be a useful diagnostic measure since it can distinguish fearful from non-fearful flyers.

Adult↗
PubMed2006

Biophysics and clinical practice for regenerative processes in cirrhosis of the liver/of liver cirrhosis assisted by Delta-S Entropy Variation Systems.

AIM: The therapy in question uses an innovative bioengineering device denoted as ''Delta-S DVD Entropy Variation System''. Previous research indicated regression of cirrhosis as evaluated in its morphofunctional and symptomatological aspects. The aim of the study is to confirm and extend previous experimental observations by enhancing hemodynamic evaluation techniques. In order to clarify scar regression, it was decided to include in the endpoints a quantitative evaluation of portal hypertension called HVPG, which is sensitive to the breakdown of hepatic architecture and the influence of regeneration nodules and therefore the advance of cirrhosis. METHODS: The experimental design consists of a self-controlled study carried out on Child A-B cirrhosis patients with portal hypertension (hepatic venous pressure gradient, HVPG > or = 10 mmHg). Five patients were enrolled, 4 HCV positive, one with autoimmune cirrhosis, all showing extensive symptoms. RESULTS: At the end of the treatment all patients showed a reduction in portal hypertension (mean reduction HVPG = 40.2%, P<0.011), together with an improved ultrasound flowmeter pattern and a sharp decrease or disappearance of the symptoms. No adverse effects were reported. Efficacy on autoimmune cirrhosis was unaffected. CONCLUSIONS: By means of a quantitative analysis of portal hypertension and of functional aspects, this study confirms that the Delta-S DVD system can lead to the regression of the scar component of cirrhosis, promote the regeneration of functioning liver tissue with positive effects on hepatic functionality and prevent symptoms and the risk of varicose vein rupture.

Aged↗
PubMed1996

Joint entropy loci of M and P cells: a hypothesis for parallel processing in the primate visual system.

The M and P neurons connect the retinal inner plexiform layer to the magnicellular and parvicellular layers of the lateral geniculate nucleus and to layer 4 of the primary visual cortex. The M and P pathways transmit visual signals with different six-dimensional joint entropy for space, spatial frequency, time and temporal frequency. Beyond V1 layer 4, M and P influences mix in information processing streams which connect different visual cortical areas. Some visual cortical cells perform better than it is possible for linear filters, regarding to simultaneous spatial and spatial frequency localization of their response. This can be explained by nonlinear combination of M and P input on such cells.

Animals↗
PubMed1998

Coarse-grained entropy rates quantify fast Ca2+ dynamics modulated by pharmacological stimulation.

Calcium (Ca2+) is an ubiquitous intracellular messenger which regulates cellular processes, such as secretion, contraction, and cell proliferation. A variety of cell types respond to hormonal stimuli with periodic oscillations of the intracellular free Ca2+ concentration ([Ca2+]i) which can be modulated in their frequency in a dose-dependent manner. The period of these well-studied oscillations varies normally between 30 sec and a couple of minutes. Here we study [Ca2+]i oscillations in clonal beta cells (hamster insulin secreting cells, HIT) under pharmacological stimulation. Besides the well-known high-amplitude low frequency oscillations we try to analyze for the first time low-amplitude high frequency oscillations of [Ca2+]i under pharmacological stimulation which have not been explored in experimental approaches to date. Using coarse-grained entropy rates computed from information-theoretic functionals we demonstrate differences in temporal complexity of the fast low-amplitude [Ca2+]i dynamics corresponding to different phases of pharmacological stimulation which are additional to the well-known dose-dependent pattern of low-frequency high amplitude [Ca2+]i dynamics.

Algorithms↗
PubMed2000

Entropy-driven hydrogen bonding: stereodynamics of a protonated, N,N-chiral "proton sponge".

The C2-symmetric ("[DL]") and achiral ("[meso]") diastereoisomers of the hydrogen iodide salt of 1,8-bis-(N-benzyl-N-methylamino)naphthalene ([2H]-[I] ) interconvert in solution. Direct interconversion of the diastereoisomers of [2H]+ must involve hydrogen bond fission (to give "[nonHB-2H+]") and rotation-inversion of the non-protonated nitrogen centre. The global activation parameters (deltaH++ and deltaS++) for diastereoisomer interconversion in [D7]DMF have been determined from rate data obtained by temperature-drop and magnetisation-transfer 13C NMR spectroscopy over a temperature range of 170 degrees C. The process is found to have a high entropy of activation in both directions (deltaS++=163(+/-4) and 169(+/-4) JK(-1)mol(-1)) and this is suggested to arise through hydrogen bonding of the ammonium centre in [nonHB-2H+] with the solvent ([D7]DMF). Comparison of the enthalpy of activation (deltaH++) with that earlier found for diastereoisomer interconversion of the free-base form 2 suggests that the intramolecular hydrogen bond in [2H]+ is roughly equal in enthalpic strength (deltaH) with that made with the solvent ([D7]DMF) in the non-hydrogen-bonded intermediate [nonHB-2H+]. As such, the hydrogen bonding in [2H]+ may be considered as predominantly an entropically driven process, without any unusual enthalpic strength.

Journal Article↗
PubMed1989

Vibrational free energy, entropy, and temperature factors of DNA calculated by a helix lattice approach.

The vibrational contribution to the free energy, entropy, and the temperature factors of the different atoms in the unit cell are calculated using the method of helix lattice dynamics for the DNA homopolymer poly(dG.poly(dC) in the B conformation. These results are compared to other theoretical calculations and the temperature (B) factors are compared to experiment as well. The problems encountered in using small molecule approximations to describe B factors in DNA like long chain molecules are discussed and a corrected estimate of the temperature factors are presented. Significant differences are found between the different theoretical approaches as reflected in the results of temperature factor calculations.

Amino Acid Sequence↗
PubMed2004

Interstitial Zn atoms do the trick in thermoelectric zinc antimonide, Zn4Sb3: a combined maximum entropy method X-ray electron density and ab initio electronic structure study.

The experimental electron density of the high-performance thermoelectric material Zn4Sb3 has been determined by maximum entropy (MEM) analysis of short-wavelength synchrotron powder diffraction data. These data are found to be more accurate than conventional single-crystal data due to the reduction of common systematic errors, such as absorption, extinction and anomalous scattering. Analysis of the MEM electron density directly reveals interstitial Zn atoms and a partially occupied main Zn site. Two types of Sb atoms are observed: a free spherical ion (Sb3-) and Sb2(4-) dimers. Analysis of the MEM electron density also reveals possible Sb disorder along the c axis. The disorder, defects and vacancies are all features that contribute to the drastic reduction of the thermal conductivity of the material. Topological analysis of the thermally smeared MEM density has been carried out. Starting with the X-ray structure ab initio computational methods have been used to deconvolute structural information from the space-time data averaging inherent to the XRD experiment. The analysis reveals how interstitial Zn atoms and vacancies affect the electronic structure and transport properties of beta-Zn4Sb3. The structure consists of an ideal A12Sb10 framework in which point defects are distributed. We propose that the material is a 0.184:0.420:0.396 mixture of A12Sb10, A11BCSb10 and A10BCDSb10 cells, in which A, B, C and D are the four Zn sites in the X-ray structure. Given the similar density of states (DOS) of the A12Sb10, A11BCSb10 and A10BCDSb10 cells, one may electronically model the defective stoichiometry of the real system either by n-doping the 12-Zn atom cell or by p-doping the two 13-Zn atom cells. This leads to similar calculated Seebeck coefficients for the A12Sb10, A11BCSb10 and A10BCDSb10 cells (115.0, 123.0 and 110.3 microV K(-1) at T=670 K). The model system is therefore a p-doped semiconductor as found experimentally. The effect is dramatic if these cells are doped differently with respect to the experimental electron count. Thus, 0.33 extra electrons supplied to either kind of cell would increase the Seebeck coefficient to about 260 microV K(-1). Additional electrons would also lower sigma, so the resulting effect on the thermoelectric figure of merit of Zn4Sb3 challenges further experimental work.

Journal Article↗