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Results for “sample entropy”

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PubMed2006

Reflection of heart rate regulation on linear and nonlinear heart rate variability measures.

The aim of this study was to examine the dependence of heart rate variability (HRV) measures on RR interval length and to find out relationships between linear and nonlinear measures. The spectral powers in very low (VLF), low (LF) and high (HF) frequency regions, short-term scaling exponent alpha(1) and sample entropy (SampEn) were determined. All spectral powers increased with increasing RR interval length until they reached a plateau. Neighbouring spectral powers were strongly correlated. The largest fraction of the spectrum consisted of VLF (from about 40 to 95%) and the smallest of HF, although HF was most sensitive to changes in RR interval length. SampEn is also increased with increasing RR interval, reaching a plateau. The dependence of alpha(1) on RR showed a deflection point at 0.5 s. Nonlinear measures can be expressed by spectral powers: alpha(1) by a linear function of ln(LF/HF) and SampEn by a quadratic function of ln HF. We concluded that during the day an increase of HR up to 120 beats min(-1) was reflected in a reduction in HF and LF and to a smaller extent in VLF and by decreased complexity and increased correlation in RR interval series. In sleep, HRV measures are at a plateau. We suggest that below intrinsic value, HR is regulated mainly by changes of parasympathetic activity, reflected in linear and nonlinear HRV measures.

Adult↗

PubMed2006

Assessment of the autonomic control of heart rate variability in healthy and spinal-cord injured subjects: contribution of different complexity-based estimators.

We investigated how complexity-based estimators of heart rate variability can detect changes in cardiovascular autonomic drive with respect to traditional measures of variability. This was done by analyzing healthy subjects and paraplegic patients with different autonomic impairment due to low (vascular impairment only) or high (cardiac and vascular impairment) spinal cord injury, during progressive autonomic activations. While traditional techniques only quantified the effects of the autonomic activation, not distinguishing the effects of the lesion level, some recently proposed complexity estimators could also reveal the pathologic alterations in the autonomic control of heart rate. These estimators included the detrended fluctuation analysis coefficient (sensitive to both low and high autonomic lesions), sample entropy (sensitive to low-level lesions) and the largest Lyapunov exponent (sensitive to high-level lesions). Thus complexity-based methods provide information on the autonomic function from the heart rate dynamics that cannot be obtained by traditional techniques. This finding supports the combined use of both complexity-based and traditional methods to investigate the autonomic cardiovascular control from a more comprehensive perspective.

Adult↗

PubMed2006

Weaning from mechanical ventilation: a retrospective analysis leading to a multimodal perspective.

Practitioners' decision for mechanical aid discontinuation is a challenging task that involves a complete knowledge of a great number of clinical parameters, as well as its evolution in time. Recently, an increasing interest on respiratory pattern variability as an extubation readiness indicator has appeared. Reliable assessment of this variability involves a set of signal processing and pattern recognition techniques. This paper presents a suitability analysis of different methods used for breathing pattern complexity assessment. The contribution of this analysis is threefold: 1) to serve as a review of the state of the art on the so-called weaning problem from a signal processing point of view; 2) to provide insight into the applied processing techniques and how they fit into the problem; 3) to propose additional methods and further processing in order to improve breathing pattern regularity assessment and weaning readiness decision. Results on experimental data show that sample entropy outperforms other complexity assessment methods and that multidimensional classification does improve weaning prediction. However, the obtained performance may be objectionable for real clinical practice, a fact that paves the way for a multimodal signal processing framework, including additional high-quality signals and more reliable statistical methods.

Algorithms↗

PubMed2005

Heart rate variability in young patients with diabetes mellitus and healthy subjects explored by Poincaré and sequence plots.

Autonomic neuropathy is a common complication of the diabetes mellitus (DM). The significance of its early diagnosis is very high because the mortality of the patients with this complication is elevated. Considering the effort to apply new mathematical methods to cardiac dysregulation diagnosis, the major aim of the study was to ascertain which of the new heart rate variability (HRV) parameters are different in young patients with DM type 1 compared with control group. The next aim was to assess the HRV changes during prolonged (40 min) supine rest. The heart rate was continuously recorded during supine rest in 17 young patients with DM type 1 (10 women, 7 men) aged 22.4 +/- 1.0 years (mean +/- SEM). The control group consisted of 17 healthy matched probands. The HRV (time/frequency domains, Poincare and sequence plots, sample entropy) was analysed in two intervals - T1 starting at fifth minute and T2 starting at 30th minute of supine rest. The major results of our study are: the reduced Poincare plot pattern measures in the young DM group; the lower percentage of points in the third quadrant of sequence plot (this parameter was not correlated with the mean heart rate) and significant changes in HRV during supine rest in DM group (in contrast to control subjects). In conclusion, HRV parameters based on nonlinear dynamics were able to distinguish cardiac dysregulation in young patients with DM from the control group. The percentage of points in the third quadrant of sequence plot provides information that is not dependent on mean heart rate. Poincare and sequence plots, together with the rate of HRV changes during supine rest, can provide clinically relevant information usable in diagnosis of the cardiac dysregulation.

Adolescent↗

PubMed2006

Linear and non-linear heart rate variability measures in chronic and acute phase of anorexia nervosa.

Previous results on heart rate variability (HRV) analysis in anorexia nervosa (AN) include some apparently conflicting data. In order to find out the reason for different results and to improve understanding of autonomic control in AN we compare HRV in acute and chronic AN. Spectral powers, fractal scaling exponent and sample entropy were computed from 24 h RR series derived from Holter ECG recordings in 17 anorexic patients, nine chronic and eight healthy women. We found that all linear and non-linear HRV measures change in different direction in acute and chronic AN. Acute AN is characterized by decreased HR and increased HRV. In chronic AN, HR is increased, HRV reduced and the difference between awake and sleeping values is high. HRV measures are associated with body mass index only in chronic AN. As HRV measures are significantly different between acute and chronic AN, we propose that HRV analysis might provide additional data in clinical practice.

Acute Disease↗

PubMed2005

Correlation properties and regularity of heart period time series: influence of posture and heart disease.

Nonlinear measures of heart period variability (HPV) were determined in supine rest and standing posture in children and young adults with heart disease and compared to the control. The aim was to study influence of posture and heart disease on heart period dynamics. It was found that standing increases short-term scaling exponent in all subjects and decreases sample entropy in healthy and less severely ill patients. Severely ill patients compared to control have higher short-term scaling exponent in supine. Changes in nonlinear measures of HPV upon standing are more pronounced in healthy than diseased subjects due to different vagal activity.

Adolescent↗

PubMed2006

Spectral reconstruction methods in fast NMR: reduced dimensionality, random sampling and maximum entropy.

The need to reduce data acquisition times of multidimensional NMR experiments has fostered considerable interest in novel data acquisition schemes. A recurring theme is that of reduced dimensionality experiments, in which time evolutions in the indirect dimensions are incremented together, rather than independently. Spectral analysis of such data is carried out using methods such as filtered back-projection, GFT, or parametric signal modeling. By using Maximum Entropy reconstruction of reduced-dimensionality data, we show that the artifacts that arise in reduced dimensionality experiments are intrinsic to the data sampling, and are not, in general, the result of the methods used to compute spectra. Our results illustrate that reduced dimensionality is a special case of non-uniform sampling in the time domain. We show that MaxEnt reconstruction yields more accurate spectra for reduced dimensionality data than back-projection reconstruction and that randomly choosing time increments based on an exponentially weighted distribution is more efficient, with fewer artifacts, than the systematic coupling of time increments used in most reduced dimensionality approaches.

Artifacts↗

PubMed2005

Assessing phylogenetic relationships of Lycium samples using RAPD and entropy theory.

AIM: To evaluate the phylogenetic relationships among related species of Lycium samples. METHODS: Random amplified polymorphic DNA (RAPD) fingerprinting and lab-on-a-chip electrophoresis techniques were used to analyze the characteristics of Lycium species. Seven species and 3 varieties of Lycium were studied. Based on RAPD fingerprint data obtained from 11 primers, we proposed a new index, called dispersivity, using entropy theory and projection methods to depict the diversity of the DNA fingerprints. RESULTS: Using the proposed dispersivity, primers were sorted and the dendrograms of the 7 species and 3 varieties of Lycium were constructed synthetically by merging primer information. CONCLUSION: Phylogenetic relationships among Lycium samples were constructed synthetically based on RAPD fingerprint data generated from 11 primers.

DNA Fingerprinting↗

PubMed2005

Translational clinical trials: an entropy-based approach to sample size.

Translational clinical trials are small studies of therapies emerging from the laboratory. These trials are essential for generating early evidence regarding the effects of treatment on specific targets in the disease pathway and for guiding the next studies to be done. The statistical properties of such studies have been neglected, in part, because they do not fit the well-known clinical trials developmental paradigm. This paper discusses the translational trial setting, and presents an information (entropy) based approach to understanding the properties and use of these trials. The combination of biological knowledge with a designed experiment (albeit a small one) is a powerful device for resolving much of the considerable uncertainty surrounding an emerging therapeutic concept. An approach to motivating the sample size for translational trials is presented.

Animals↗

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↗

PubMed2026

Reducing state anxiety with alpha-frequency transcranial alternating current stimulation.

BACKGROUND: Anxiety reactivity to acute stress is a transdiagnostic vulnerability factor. We tested whether a single session of alpha-frequency transcranial alternating current stimulation (tACS) targeting the frontoparietal control network reduces stress-evoked state anxiety in healthy adults. METHODS: In a randomized, blinded, sham-controlled study, 42 participants (mean age 58.9 years) completed an acute stress task before and after stimulation. The task was an adapted moving-circles paradigm in which circle collisions triggered a brief aversive event (mild electric shock plus unpleasant noise and a white flash). Active stimulation consisted of 20 min of 10-Hz tACS (2.0 mA/channel; 30-s ramp up/down) delivered via electrodes at F3, P3, Cz, and T7 (0° phase at F3/P3; 180° at Cz/T7). Sham stimulation used the same montage and ramp periods but no sustained current. RESULTS: State anxiety showed a significant Time × Protocol interaction (F(1,35) = 4.22, p = .047): STAI-S decreased after active tACS (Δ = -3.16) but increased slightly after sham (Δ = +1.17). Perceived stress appraisal (SAAS) did not change. Resting-state alpha power at F3/P3 showed no reliable pre-post effects. During the task, left-frontal relative alpha differed by protocol and showed a trend toward larger increases following active tACS. Electrodermal and pupil indices changed across sessions in both groups, with no differential stimulation effects. CONCLUSIONS: A single alpha-tACS session produced a modest, selective reduction in stress-evoked state anxiety, supporting oscillatory neuromodulation as a scalable approach to dampen anxiety reactivity.

Humans↗

PubMed2005

First-order interface localization-delocalization transition in thin Ising films using Wang-Landau sampling.

Using extensive Monte Carlo simulations, we study the interface localization-delocalization transition of a thin Ising film with antisymmetric competing walls for a set of parameters where the transition is strongly first order. This is achieved by estimating the density of states (DOS) of the model by means of Wang-Landau sampling (WLS) in the space of energy, using both single-spin-flip as well as N-fold way updates. From the DOS we calculate canonical averages related to the configurational energy, like the internal energy and the specific heat, as well as the free energy and the entropy. By sampling micro-canonical averages during simulations we also compute thermodynamic quantities related to magnetization like the reduced fourth-order cumulant of the order parameter. We estimate the triple temperatures of infinitely large systems for three different film thicknesses via finite size scaling of the positions of the maxima of the specific heat, the minima of the cumulant, and the equal weight criterion for the energy probability distribution. The wetting temperature of the semi-infinite system is computed with help of the Young equation. In the limit of large film thicknesses the triple temperatures are seen to converge toward the wetting temperature of the corresponding semi-infinite Ising model in accordance with standard capillary wave theory. We discuss the slowing down of WLS in energy space as observed for the larger film thicknesses and lateral linear dimensions. In the case of WLS in the space of total magnetization we find evidence that the slowing down is reduced and can be attributed to persisting free energy barriers due to shape transitions.

Journal Article↗

PubMed2004

Entropy and information in neural spike trains: progress on the sampling problem.

The major problem in information theoretic analysis of neural responses and other biological data is the reliable estimation of entropy-like quantities from small samples. We apply a recently introduced Bayesian entropy estimator to synthetic data inspired by experiments, and to real experimental spike trains. The estimator performs admirably even very deep in the undersampled regime, where other techniques fail. This opens new possibilities for the information theoretic analysis of experiments, and may be of general interest as an example of learning from limited data.

Journal Article↗

PubMed1987

Efficiency of a model human image code.

Hypothetical schemes for neural representation of visual information can be expressed as explicit image codes. We may test whether a given code is sufficient, in the sense of retaining all the information that the human perceives, and necessary, in the sense of retaining only that information. The latter is a test of efficiency. Here, we explore a code modeled on the simple cells of the primate striate cortex. The Cortex transform maps a digital image into a set of subimages (layers) that are bandpass in spatial frequency and orientation. The layers are sampled so as to minimize the number of samples and still avoid aliasing. Samples are quantized in a manner that exploits the bandpass contrast-masking properties of human vision. The entropy of the samples is computed to provide a lower bound on the code size. Finally, the image is reconstructed from the code. We devise psychophysical methods for comparing the original and reconstructed images to evaluate the sufficiency of the code. When each resolution is coded at the threshold for detection artifacts, the image-code size is about 1 bit/pixel.

Humans↗

PubMed1995

Limitations of the maximum entropy principle in devising drug input rate.

A computer program applying the principle of maximum entropy to the analysis of drug absorption rate has been developed. Plasma concentrations of amoxicillin obtained after oral and intravenous dosing have been analysed, together with simulated data corresponding to a complex input. Amoxicillin absorption rates devised by the program were similar to those obtained by a standard deconvolution method, although they were displayed as an almost continuous profile. However, improbable fluctuations were obtained with some data sets and the fraction absorbed was underestimated by 13%. With the simulated data, the maximum entropy program did not provide a better solution than the standard deconvolution procedure, and it was sensitive to the addition of random error and to the number of samples. The maximum entropy principle, as implemented in our computer program, may not have a better performance than standard deconvolution procedures, especially in human experiments where the number of blood samples is usually limited.

Administration, Oral↗

PubMed2001

Entropy fluctuations for directed polymers in 2+1 dimensions.

We find numerically that the sample to sample fluctuation of the entropy DeltaS is a more sensitive tool in distinguishing low from high temperature behaviors than the common corresponding fluctuation in the free energy. In 1+1 dimensions we find a single phase for all temperatures, since (DeltaS)(2) is always extensive. In 2+1 dimensions we find a behavior that at first sight might appear to be a transition from a low temperature phase where (DeltaS)(2) is extensive to a high temperature phase where it is subextensive. This is observed in spite of the relatively large system we use. The observed behavior is explained not as a phase transition but as a strong crossover behavior. We use an analytical argument to obtain (DeltaS)(2) for high temperature, and find that while it is always extensive it is also extremely small, and that the leading extensive part decays very quickly to zero as the temperature is increased.

Journal Article↗

PubMed2006

A supervised hidden markov model framework for efficiently segmenting tiling array data in transcriptional and chIP-chip experiments: systematically incorporating validated biological knowledge.

MOTIVATION: Large-scale tiling array experiments are becoming increasingly common in genomics. In particular, the ENCODE project requires the consistent segmentation of many different tiling array datasets into 'active regions' (e.g. finding transfrags from transcriptional data and putative binding sites from ChIP-chip experiments). Previously, such segmentation was done in an unsupervised fashion mainly based on characteristics of the signal distribution in the tiling array data itself. Here we propose a supervised framework for doing this. It has the advantage of explicitly incorporating validated biological knowledge into the model and allowing for formal training and testing. METHODOLOGY: In particular, we use a hidden Markov model (HMM) framework, which is capable of explicitly modeling the dependency between neighboring probes and whose extended version (the generalized HMM) also allows explicit description of state duration density. We introduce a formal definition of the tiling-array analysis problem, and explain how we can use this to describe sampling small genomic regions for experimental validation to build up a gold-standard set for training and testing. We then describe various ideal and practical sampling strategies (e.g. maximizing signal entropy within a selected region versus using gene annotation or known promoters as positives for transcription or ChIP-chip data, respectively). RESULTS: For the practical sampling and training strategies, we show how the size and noise in the validated training data affects the performance of an HMM applied to the ENCODE transcriptional and ChIP-chip experiments. In particular, we show that the HMM framework is able to efficiently process tiling array data as well as or better than previous approaches. For the idealized sampling strategies, we show how we can assess their performance in a simulation framework and how a maximum entropy approach, which samples sub-regions with very different signal intensities, gives the maximally performing gold-standard. This latter result has strong implications for the optimum way medium-scale validation experiments should be carried out to verify the results of the genome-scale tiling array experiments.

Artificial Intelligence↗

PubMed1996

On the origin of the cooperativity of protein folding: implications from model simulations.

There is considerable experimental evidence that the cooperativity of protein folding resides in the transition from the molten globule to the native state. The objective of this study is to examine whether simplified models can reproduce this cooperativity and if so, to identify its origin. In particular, the thermodynamics of the conformational transition of a previously designed sequence (A. Kolinski, W. Galazka, and J. Skolnick, J. Chem. Phys. 103: 10286-10297, 1995), which adopts a very stable Greek-key beta-barrel fold has been investigated using the entropy Monte Carlo sampling (ESMC) technique of Hao and Scheraga (M.-H. Hao and H.A. Scheraga, J. Phys. Chem. 98: 9882-9883, 1994). Here, in addition to the original potential, which includes one body and pair interactions between side chains, the force field has been supplemented by two types of multi-body potentials describing side chain interactions. These potentials facilitate the protein-like pattern of side chain packing and consequently increase the cooperativity of the folding process. Those models that include an explicit cooperative side chain packing term exhibit a well-defined all-or-none transition from a denatured, random coil state to a high-density, well-defined, nativelike low-energy state. By contrast, models lacking such a term exhibit a conformational transition that is essentially continuous. Finally, an examination of the conformations at the free-energy barrier between the native and denatured states reveals that they contain a substantial amount of native-state secondary structure, about 50% of the native contacts, and have an average root mean square radius of gyration that is about 15% larger than native.

Amino Acids↗