approximate entropy
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There is evidence that rotors could be drivers that maintain atrial fibrillation. Complex fractionated atrial electrograms have been located in rotor tip areas. However, the concept of electrogram fractionation, defined using time intervals, is still controversial as a tool for locating target sites for ablation. We hypothesize that the fractionation phenomenon is better described using non-linear dynamic measures, such as approximate entropy, and that this tool could be used for locating the rotor tip. The aim of this work has been to determine the relationship between approximate entropy and fractionated electrograms, and to develop a new tool for rotor mapping based on fractionation levels. Two episodes of chronic atrial fibrillation were simulated in a 3D human atrial model, in which rotors were observed. Dynamic approximate entropy maps were calculated using unipolar electrogram signals generated over the whole surface of the 3D atrial model. In addition, we optimized the approximate entropy calculation using two real multi-center databases of fractionated electrogram signals, labeled in 4 levels of fractionation. We found that the values of approximate entropy and the levels of fractionation are positively correlated. This allows the dynamic approximate entropy maps to localize the tips from stable and meandering rotors. Furthermore, we assessed the optimized approximate entropy using bipolar electrograms generated over a vicinity enclosing a rotor, achieving rotor detection. Our results suggest that high approximate entropy values are able to detect a high level of fractionation and to locate rotor tips in simulated atrial fibrillation episodes. We suggest that dynamic approximate entropy maps could become a tool for atrial fibrillation rotor mapping.
Cílem práce bylo zkoumat vztah mezi zobecněnou entropií diskrétní náhodné veličiny (tzv. f-entropií, třídou funkcí, zahrnující řadu indexů používaných pří měření biodiverzity) a minimální Bayesovskou pravděpodobností chyby při odhadu hodnoty této náhodné veličiny. Zejména studovat těsnost jejich vztahu. Morales a Vajda [1] nedávno zavedli míru zvanou průměrná nepřesnost (average inaccuracy), která kvantifikuje těsnost vztahu mezi aposteriorní Bayesovskou pravděpodobností chyby a mocninnými entropiemi. Tato míra je definována jako normalizovaný průměrný rozdíl horní a dolní meze aposteriorní Bayesovské pravděpodobnosti chyby za dané entropie. Tuto míru je možno zobecnit na jakoukoli striktně konkávní f-entropii a použít ji k vyjádření těsnosti vztahu této f-entropie k aposteriorní Bayesovské pravděpodobnosti chyby. Získaný vztah je však většinou poměrně složitý a není možné snadno analyticky porovnat průměrné nepřesnosti různých f-entropií. Navrhujeme hladkou aproximaci dolní meze aposteriorní Bayesovské pravděpodobnosti chyby za dané f-entropie, jejíž použití zjednoduší formuli průměrné nepřesnosti. Ukázali jsme, že při použití této aproximace má kvadratická entropie nejtěsnější vztah k aposteriorní Bayesovské pravděpodobnosti chyby mezi f-entropiemi. Kvadratická entropie má těsnější vztah k Bayesovské pravděpodobnosti chyby (ve smyslu popsaném v článku) než Shannonova entropie a další funkce příslušící do třídy f-entropií, jako např. Emlenův index, Ferreriho index, Goodův index a další.
We deal with the relation between the generalized entropy (f-entropy, a family of functions that include several biodiversity measures) of a discrete random variable and the minimal probability of error (Bayes error) when the value of this random variable is estimated. Namely the tightness of their relation is studied. Morales and Vajda [1] recently introduced a measure called average inaccuracy that aims to quantify the tightness of the relation between the posterior Bayes error and the power entropies. It is defined as a standardized average difference between the upper and the lower bound for the posterior Bayes error under given entropy. Their concept can be generalized to any strictly concave f-entropy and used to evaluate its relation to the Bayes probability of error. However, due to a complex form of the formula of the average inaccuracy, it is difficult to compare the average inaccuracies of most f-entropies analytically. We propose a smooth approximation of the lower bound for the posterior Bayes error under given f-entropy that simplifies the formula of the average inaccuracy. We show that under this approximation, the quadratic entropy has the tightest relation to the posterior Bayes error among f-entropies. The quadratic entropy has the tightest relation to the posterior Bayes error (in the sense described in this paper) than the Shannon’s entropy and other functions that belong to the family of f-entropies, like Emlen’s index, Ferreri’s index and Good’s index.
Vagus nerve stimulation (VNS) is a therapeutic option in drug-resistant epilepsy. VNS leads to ≥ 50% seizure reduction in 50 to 60% of patients, termed "responders". The remaining 40 to 50% of patients, "non-responders", exhibit seizure reduction < 50%. Our work aims to differentiate between these two patient groups in preimplantation EEG analysis by employing several Entropy methods. We identified 59 drug-resistant epilepsy patients treated with VNS. We established their response to VNS in terms of responders and non-responders. A preimplantation EEG with eyes open/closed, photic stimulation, and hyperventilation was found for each patient. The EEG was segmented into eight time intervals within four standard frequency bands. In all, 32 EEG segments were obtained. Seven Entropy methods were calculated for all segments. Subsequently, VNS responders and non-responders were compared using individual Entropy methods. VNS responders and non-responders differed significantly in all Entropy methods except Approximate Entropy. Spectral Entropy revealed the highest number of EEG segments differentiating between responders and non-responders. The most useful frequency band distinguishing responders and non-responders was the alpha frequency, and the most helpful time interval was hyperventilation and rest 4 (the end of EEG recording).
Measures from the theory of nonlinear dynamics were applied on complex fractionated atrial electrograms (CFAEs) in order to characterize their physiological dynamic behavior. The results were obtained considering 113 short term atrial electrograms (A-EGMs) which were annotated by three experts into four classes of fractionation according to A-EGMs signal regularity. The following measures were applied on A-EGM signals: General Correlation Dimension, Approximate Entropy, Detrended Fluctuation Analysis, Lempel-Ziv Complexity, and Katz-Sevcik, Variance and Box Counting Fractal Dimension. Assessment of disorganization was evaluated by a Kruskal Wallis statistical test. Except Detrended Fluctuation Analysis and Variance Fractal Dimension, the CFAE disorganization was found statistically significant even for low significant level alpha = 0.001. Moreover, the increasing complexity of A-EGM signals was reflected by higher values of General Correlation Dimension of order 1 and Approximate Entropy.
Reconstructing the structural connectivity between interacting units from observed activity is a challenge across many different disciplines. The fundamental first step is to establish whether or to what extent the interactions between the units can be considered pairwise and, thus, can be modeled as an interaction network with simple links corresponding to pairwise interactions. In principle, this can be determined by comparing the maximum entropy given the bivariate probability distributions to the true joint entropy. In many practical cases, this is not an option since the bivariate distributions needed may not be reliably estimated or the optimization is too computationally expensive. Here we present an approach that allows one to use mutual informations as a proxy for the bivariate probability distributions. This has the advantage of being less computationally expensive and easier to estimate. We achieve this by introducing a novel entropy maximization scheme that is based on conditioning on entropies and mutual informations. This renders our approach typically superior to other methods based on linear approximations. The advantages of the proposed method are documented using oscillator networks and a resting-state human brain network as generic relevant examples.
- MeSH
- entropie MeSH
- informační systémy * MeSH
- korelace dat MeSH
- neuronové sítě MeSH
- teoretické modely MeSH
- Publikační typ
- práce podpořená grantem MeSH
The aim of our study was to evaluate rapid insulin pulses and insulin secretion regularity in fasting state in lean women with polycystic ovary syndrome (PCOS) in comparison to lean healthy women. PCOS (n=8) and controls (n=7) underwent every minute blood sampling for 60 min. Insulin pulsatility was assessed by deconvolution and insulin secretion regularity by approximate entropy methodology. PCOS had higher testosterone (p<0.02), prolactin (p<0.05) and lower sex hormone binding globulin (SHBG) (p<0.0006) levels than controls. Approximate entropy, insulin pulse frequency, mass, amplitude and interpulse interval did not differ between PCOS and controls. PCOS had broader insulin peaks determined by a common half-duration (p<0.07). Burst mass correlated positively with testosterone (p<0.05) and negatively with SHBG (p 0.0004) and common half-duration correlated positively with prolactin (p<0.008) and cortisol levels (p<0.03). Approximate entropy positively correlated with BMI (p<0.04) and prolactin (p<0.03). Lean PCOS patients tended to have broader insulin peaks in comparison to healthy controls. Prolactin, androgens and cortisol might participate in alteration of insulin secretion in PCOS-affected women. Body weight and prolactin levels could influence insulin secretion regularity.
- MeSH
- diabetes mellitus 2. typu metabolismus MeSH
- dospělí MeSH
- globulin vázající pohlavní hormony metabolismus MeSH
- hydrokortison krev MeSH
- inzulin krev sekrece MeSH
- inzulinová rezistence fyziologie MeSH
- lidé MeSH
- omezení příjmu potravy MeSH
- prolaktin krev MeSH
- pulzatilní průtok MeSH
- syndrom polycystických ovarií metabolismus MeSH
- tělesná hmotnost fyziologie MeSH
- testosteron krev MeSH
- Check Tag
- dospělí MeSH
- lidé MeSH
- ženské pohlaví MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
UNLABELLED: Listening to music is experimentally associated with positive stress reduction effect on human organisms. However, the opinions of therapists about this complementary non-invasive therapy are still different. PURPOSE: The aim of our study was to investigate the effect of selected passive music therapy frequencies without vocals on selected cardio-vagal and complexity indices of short-term heart rate variability (HRV) in healthy youth, in terms of calming the human. MAIN METHODS: 30 probands (15 male, averaged age: 19.7+/-1.4 years, BMI: 23.3+/-3.8 kg/m2) were examined during protocol (Silence baseline, Music 1 (20-1000 Hz), Silence 1, Music 2 (250-2000 Hz), Silence 2, Music 3 (1000-16000 Hz), and Silence 3). Evaluated HRV parameters in time, spectral, and geometrical domains represent indices of cardio-vagal and emotional regulation. Additionally, HRV complexity was calculated by approximate entropy and sample entropy (SampEn) and subjective characteristics of each phase by Likert scale. RESULTS: the distance between subsequent R-waves in the electrocardiogram (RR intervals [ms]) and SampEn were significantly higher during Music 3 compared to Silence 3 (p=0.015, p=0.021, respectively). Geometrical cardio-vagal index was significantly higher during Music 2 than during Silence 2 (p=0.006). In the subjective perception of the healthy youths evaluated statistically through a Likert scale, the phases of music were perceived significantly more pleasant than the silent phases (p<0.001, p=0.008, p=0.003, respectively). CONCLUSIONS: Our findings revealed a rise of cardio-vagal modulation and higher complexity assessed by short-term HRV indices suggesting positive relaxing effect music especially of higher frequency on human organism.
- MeSH
- dospělí MeSH
- elektrokardiografie MeSH
- hudba * psychologie MeSH
- lidé MeSH
- mladiství MeSH
- mladý dospělý MeSH
- nervus vagus MeSH
- srdce MeSH
- srdeční frekvence fyziologie MeSH
- Check Tag
- dospělí MeSH
- lidé MeSH
- mladiství MeSH
- mladý dospělý MeSH
- mužské pohlaví MeSH
- Publikační typ
- časopisecké články MeSH
Combined effects of temperature and mobile phase on the reversed phase chromatographic behavior of alkylbenzenes and simple substituted benzenes were investigated on a Blaze C8 polydentate silica-based column, showing improved resistance against hydrolytic breakdown at temperatures higher than 60 degrees C, in comparison to silica-based stationary phases with single attachment sites. For better insight into the retention mechanism on polydentate columns, we determined the enthalpy and entropy of the transfer of the test compounds from the mobile to the stationary phase. The enthalpic contribution dominated the retention at 80% or lower concentrations of methanol in the mobile phase. Entropic effects are more significant in 90% methanol and in acetonitrile-water mobile phases. Anomalies in the effects of mobile phase on the enthalpy of retention of benzene, methylbenzene and polar benzene derivatives were observed, in comparison to regular change in enthalpy and entropy of adsorption with changing concentration of organic solvent and the alkyl length for higher alkylbenzenes. The temperature and the mobile phase effects on the retention are practically independent of each other and--to first approximation--can be described by a simple model equation, which can be used for optimization of separation conditions.
- MeSH
- acetonitrily chemie MeSH
- benzenové deriváty chemie MeSH
- chemické modely MeSH
- hydrofobní a hydrofilní interakce MeSH
- lineární modely MeSH
- methanol chemie MeSH
- reprodukovatelnost výsledků MeSH
- teplota MeSH
- termodynamika MeSH
- vysokoúčinná kapalinová chromatografie metody MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
