Evaluation of physiologic complexity in time series using generalized sample entropy and surrogate data analysis

Complexity in time series is an intriguing feature of living dynamical systems, with potential use for identification of system state. Although various methods have been proposed for measuring physiologic complexity, uncorrelated time series are often assigned high values of complexity, errouneously classifying them as a complex physiological signals. Here, we propose and discuss a method for complex system analysis based on generalized statistical formalism and surrogate time series. Sample entropy (SampEn) was rewritten inspired in Tsallis generalized entropy, as function of q parameter (qSampEn). qSDiff curves were calculated, which consist of differences between original and surrogate series qSampEn. We evaluated qSDiff for 125 real heart rate variability (HRV) dynamics, divided into groups of 70 healthy, 44 congestive heart failure (CHF), and 11 atrial fibrillation (AF) subjects, and for simulated series of stochastic and chaotic process. The evaluations showed that, for nonperiodic signals, qSDiff curves have a maximum point (qSDiff(max)) for q not equal 1. Values of q where the maximum point occurs and where qSDiff is zero were also evaluated. Only qSDiff(max) values were capable of distinguish HRV groups (p-values 5.10 x 10(-3); 1.11 x 10(-7), and 5.50 x 10(-7) for healthy vs. CHF, healthy vs. AF, and CHF vs. AF, respectively), consistently with the concept of physiologic complexity, and suggests a potential use for chaotic system analysis. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4758815]

Linear and nonlinear measures of fetal heart rate patterns evaluated on very short fetal magnetocardiograms

We analyzed the effectiveness of linear short- and long-term variability time domain parameters, an index of sympatho-vagal balance (SDNN/RMSSD) and entropy in differentiating fetal heart rate patterns (fHRPs) on the fetal heart rate (fHR) series of 5, 3 and 2 min duration reconstructed from 46 fetal magnetocardiograms. Gestational age (GA) varied from 21 to 38 weeks. FHRPs were classified based on the fHR standard deviation. In sleep states, we observed that vagal influence increased with GA, and entropy significantly increased (decreased) with GA (SDNN/RMSSD), demonstrating that a prevalence of vagal activity with autonomous nervous system maturation may be associated with increased sleep state complexity. In active wakefulness, we observed a significant negative (positive) correlation of short-term (long-term) variability parameters with SDNN/RMSSD. ANOVA statistics demonstrated that long-term irregularity and standard deviation of normal-to-normal beat intervals (SDNN) best differentiated among fHRPs. Our results confirm that short-and long-term variability parameters are useful to differentiate between quiet and active states, and that entropy improves the characterization of sleep states. All measures differentiated fHRPs more effectively on very short HR series, as a result of the fMCG high temporal resolution and of the intrinsic timescales of the events that originate the different fHRPs.

Sensitivity, specificity and predictive values of linear and nonlinear indices of heart rate variability in stable angina patients

Abstract Background Decreased heart rate variability (HRV) is related to higher morbidity and mortality. In this study we evaluated the linear and nonlinear indices of the HRV in stable angina patients submitted to coronary angiography. Methods We studied 77 unselected patients for elective coronary angiography, which were divided into two groups: coronary artery disease (CAD) and non-CAD groups. For analysis of HRV indices, HRV was recorded beat by beat with the volunteers in the supine position for 40 minutes. We analyzed the linear indices in the time (SDNN [standard deviation of normal to normal], NN50 [total number of adjacent RR intervals with a difference of duration greater than 50ms] and RMSSD [root-mean square of differences]) and frequency domains ultra-low frequency (ULF) ≤ 0,003 Hz, very low frequency (VLF) 0,003 – 0,04 Hz, low frequency (LF) (0.04–0.15 Hz), and high frequency (HF) (0.15–0.40 Hz) as well as the ratio between LF and HF components (LF/HF). In relation to the nonlinear indices we evaluated SD1, SD2, SD1/SD2, approximate entropy (−ApEn), α1, α2, Lyapunov Exponent, Hurst Exponent, autocorrelation and dimension correlation. The definition of the cutoff point of the variables for predictive tests was obtained by the Receiver Operating Characteristic curve (ROC). The area under the ROC curve was calculated by the extended trapezoidal rule, assuming as relevant areas under the curve ≥ 0.650. Results Coronary arterial disease patients presented reduced values of SDNN, RMSSD, NN50, HF, SD1, SD2 and -ApEn. HF ≤ 66 ms2, RMSSD ≤ 23.9 ms, ApEn ≤−0.296 and NN50 ≤ 16 presented the best discriminatory power for the presence of significant coronary obstruction. Conclusion We suggest the use of Heart Rate Variability Analysis in linear and nonlinear domains, for prognostic purposes in patients with stable angina pectoris, in view of their overall impairment.

Interaction between bradykinin potentiating nonapeptide (BPP9a) and beta-cyclodextrin: A structural and thermodynamic study

Herein, we demonstrate the physical and chemical characterizations of the supramolecular complex formed between beta-cyclodextrin (beta CD) and bradykinin potentiating nonapeptide (BPP9a), an endogenous toxin found in Bothrops jararaca. Circular dichroism results indicate a conformational change in the BPP9a secondary structure upon its complexation with beta CD. Nuclear magnetic resonance results, mainly from NOESY experiments, and theoretical calculations showed a favorable interaction between the tryptophan residue of BPP9a and the beta CD cavity. Thermodynamic inclusion parameters were investigated by isothermal titration calorimetry, demonstrating that beta CD/BPP9a complex formation is an exothermic process that results in a reduction in entropy. Additionally, in vitro degradation study of BPP9a against trypsin (37 degrees C, pH 7.2) showed higher stability of peptide in presence of beta CD. This beta CD/BPP9a complex, which presents new chemical properties arising from the peptide inclusion process, may be useful as an antihypertensive drug in oral pharmaceutical formulations. (C) 2011 Elsevier B.V. All rights reserved.

Entropy Production in Nonequilibrium Systems at Stationary States

We present a stochastic approach to nonequilibrium thermodynamics based on the expression of the entropy production rate advanced by Schnakenberg for systems described by a master equation. From the microscopic Schnakenberg expression we get the macroscopic bilinear form for the entropy production rate in terms of fluxes and forces. This is performed by placing the system in contact with two reservoirs with distinct sets of thermodynamic fields and by assuming an appropriate form for the transition rate. The approach is applied to an interacting lattice gas model in contact with two heat and particle reservoirs. On a square lattice, a continuous symmetry breaking phase transition takes place such that at the nonequilibrium ordered phase a heat flow sets in even when the temperatures of the reservoirs are the same. The entropy production rate is found to have a singularity at the critical point of the linear-logarithm type.

Finite-size corrections of the entanglement entropy of critical quantum chains

Using the density matrix renormalization group, we calculated the finite-size corrections of the entanglement alpha-Renyi entropy of a single interval for several critical quantum chains. We considered models with U(1) symmetry such as the spin-1/2 XXZ and spin-1 Fateev-Zamolodchikov models, as well as models with discrete symmetries such as the Ising, the Blume-Capel, and the three-state Potts models. These corrections contain physically relevant information. Their amplitudes, which depend on the value of a, are related to the dimensions of operators in the conformal field theory governing the long-distance correlations of the critical quantum chains. The obtained results together with earlier exact and numerical ones allow us to formulate some general conjectures about the operator responsible for the leading finite-size correction of the alpha-Renyi entropies. We conjecture that the exponent of the leading finite-size correction of the alpha-Renyi entropies is p(alpha) = 2X(epsilon)/alpha for alpha > 1 and p(1) = nu, where X-epsilon denotes the dimensions of the energy operator of the model and nu = 2 for all the models.

Irreversible spherical model and its stationary entropy production rate

The nonequilibrium stationary state of an irreversible spherical model is investigated on hypercubic lattices. The model is defined by Langevin equations similar to the reversible case, but with asymmetric transition rates. In spite of being irreversible, we have succeeded in finding an explicit form for the stationary probability distribution, which turns out to be of the Boltzmann-Gibbs type. This enables one to evaluate the exact form of the entropy production rate at the stationary state, which is non-zero if the dynamical rules of the transition rates are asymmetric.

Aging reduces complexity of heart rate variability assessed by conditional entropy and symbolic analysis

Increasing age is associated with a reduction in overall heart rate variability as well as changes in complexity of physiologic dynamics. The aim of this study was to verify if the alterations in autonomic modulation of heart rate caused by the aging process could be detected by Shannon entropy (SE), conditional entropy (CE) and symbolic analysis (SA). Complexity analysis was carried out in 44 healthy subjects divided into two groups: old (n = 23, 63 +/- A 3 years) and young group (n = 21, 23 +/- A 2). It was analyzed SE, CE [complexity index (CI) and normalized CI (NCI)] and SA (0V, 1V, 2LV and 2ULV patterns) during short heart period series (200 cardiac beats) derived from ECG recordings during 15 min of rest in a supine position. The sequences characterized by three heart periods with no significant variations (0V), and that with two significant unlike variations (2ULV) reflect changes in sympathetic and vagal modulation, respectively. The unpaired t test (or Mann-Whitney rank sum test when appropriate) was used in the statistical analysis. In the aging process, the distributions of patterns (SE) remain similar to young subjects. However, the regularity is significantly different; the patterns are more repetitive in the old group (a decrease of CI and NCI). The amounts of pattern types are different: 0V is increased and 2LV and 2ULV are reduced in the old group. These differences indicate marked change of autonomic regulation. The CE and SA are feasible techniques to detect alteration in autonomic control of heart rate in the old group.

Entropy, complexity and disequilibrium in compact stars

We used the statistical measurements of information entropy, disequilibrium and complexity to infer a hierarchy of equations of state for two types of compact stars from the broad class of neutron stars, namely, with hadronic composition and with strange quark composition. Our results show that, since order costs energy. Nature would favor the exotic strange stars even though the question of how to form the strange stars cannot be answered within this approach. (C) 2012 Elsevier B.V. All rights reserved.

Hadron mass spectrum and the shear viscosity to entropy density ratio of hot hadronic matter

Lattice calculations of the QCD trace anomaly at temperatures T < 160 MeV have been shown to match hadron resonance gas model calculations, which include an exponentially rising hadron mass spectrum. In this paper we perform a more detailed comparison of the model calculations to lattice data that confirms the need for an exponentially increasing density of hadronic states. Also, we find that the lattice data is compatible with a hadron density of states that goes as rho(m) similar to m(-a) exp(m/T-H) at large m with a > 5/2 (where T-H similar to 167 MeV). With this specific subleading contribution to the density of states, heavy resonances are most likely to undergo two-body decay (instead of multiparticle decay), which facilitates their inclusion into hadron transport codes. Moreover, estimates for the shear viscosity and the shear relaxation time coefficient of the hadron resonance model computed within the excluded volume approximation suggest that these transport coefficients are sensitive to the parameters that define the hadron mass spectrum.

Entanglement entropy in long-range harmonic oscillators

We study the Von Neumann and Renyi entanglement entropy of long-range harmonic oscillators (LRHO) by both theoretical and numerical means. We show that the entanglement entropy in massless harmonic oscillators increases logarithmically with the sub-system size as S - c(eff)/3 log l. Although the entanglement entropy of LRHO's shares some similarities with the entanglement entropy at conformal critical points we show that the Renyi entanglement entropy presents some deviations from the expected conformal behaviour. In the massive case we demonstrate that the behaviour of the entanglement entropy with respect to the correlation length is also logarithmic as the short-range case. Copyright (c) EPLA, 2012

Quantification of fractal dimension and Shannon’s entropy in histological diagnosis of prostate cancer

Background: Prostate cancer is a serious public health problem that affects quality of life and has a significant mortality rate. The aim of the present study was to quantify the fractal dimension and Shannon’s entropy in the histological diagnosis of prostate cancer. Methods: Thirty-four patients with prostate cancer aged 50 to 75 years having been submitted to radical prostatectomy participated in the study. Histological slides of normal (N), hyperplastic (H) and tumor (T) areas of the prostate were digitally photographed with three different magnifications (40x, 100x and 400x) and analyzed. The fractal dimension (FD), Shannon’s entropy (SE) and number of cell nuclei (NCN) in these areas were compared. Results: FD analysis demonstrated the following significant differences between groups: T vs. N and H vs. N groups (p < 0.05) at a magnification of 40x; T vs. N (p < 0.01) at 100x and H vs. N (p < 0.01) at 400x. SE analysis revealed the following significant differences groups: T vs. H and T vs. N (p < 0.05) at 100x; and T vs. H and T vs. N (p < 0.001) at 400x. NCN analysis demonstrated the following significant differences between groups: T vs. H and T vs. N (p < 0.05) at 40x; T vs. H and T vs. N (p < 0.0001) at 100x; and T vs. H and T vs. N (p < 0.01) at 400x. Conclusions: The quantification of the FD and SE, together with the number of cell nuclei, has potential clinical applications in the histological diagnosis of prostate cancer.

Irreversibility by competition on a Glauber-Ising model by means of the entropy production.

An out of equilibrium Ising model subjected to an irreversible dynamics is analyzed by means of a stochastic dynamics, on a effort that aims to understand the observed critical behavior as consequence of the intrinsic microscopic characteristics. The study focus on the kinetic phase transitions that take place by assuming a lattice model with inversion symmetry and under the influence of two competing Glauber dynamics, intended to describe the stationary states using the entropy production, which characterize the system behavior and clarifies its reversibility conditions. Thus, it is considered a square lattice formed by two sublattices interconnected, each one of which is in contact with a heat bath at different temperature from the other. Analytical and numerical treatments are faced, using mean-field approximations and Monte Carlo simulations. For the one dimensional model exact results for the entropy production were obtained, though in this case the phase transition that takes place in the two dimensional counterpart is not observed, fact which is in accordance with the behavior shared by lattice models presenting inversion symmetry. Results found for the stationary state show a critical behavior of the same class as the equilibrium Ising model with a phase transition of the second order, which is evidenced by a divergence with an exponent µ ¼ 0:003 of the entropy production derivative.