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Object: Brain entropy is a potential index in the diagnosis of mental diseases, but there are some differences in different brain entropy calculation, which may bring confusion and difficulties to the application of brain entropy. Based on the resting-state function magnetic resonance imaging (fMRI) we analyzed the differences of the three main brain entropy in the statistical significance, including approximate entropy (ApEn), sample entropy (SampEn) and fuzzy entropy (FuzzyEn), and studied the physiological reasons behind the difference through comparing their performance on obsessive-compulsive disorder (OCD) and the healthy control (HC). Method: We set patients with OCD as the experimental group and healthy subjects as the control group. The brain entropy of the OCD group and the HC are calculated, respectively, by voxel and AAL region. And then we analyzed the statistical differences of the three brain entropies between the patients and the control group. To compare the sensitivity and robustness of these three kinds of entropy, we also studied their performance by using certain signal mixed with noise. Result: Compare with the control group, almost the whole brain's ApEn and FuzzyEn of OCD are larger significantly. Besides, there are more brain regions with obvious differences when using ApEn comparing to using FuzzyEn. There was no statistical difference between the SampEn of OCD and HC. Conclusion: Brain entropy is a numerical index related to brain function and can be used as a supplementary biological index to evaluate brain state, which may be used as a reference for the diagnosis of mental illness. According to an analysis of certain signal mixed with noise, we conclude that FuzzyEn is more accurate considering sensitivity, stability and robustness of entropy. [ABSTRACT FROM AUTHOR]

Object: Brain entropy is a potential index in the diagnosis of mental diseases, but there are some differences in different brain entropy calculation, which may bring confusion and difficulties to the application of brain entropy. Based on the resting-state function magnetic resonance imaging (fMRI) we analyzed the differences of the three main brain entropy in the statistical significance, including approximate entropy (ApEn), sample entropy (SampEn) and fuzzy entropy (FuzzyEn), and studied the physiological reasons behind the difference through comparing their performance on obsessive-compulsive disorder (OCD) and the healthy control (HC).Method: We set patients with OCD as the experimental group and healthy subjects as the control group. The brain entropy of the OCD group and the HC are calculated, respectively, by voxel and AAL region. And then we analyzed the statistical differences of the three brain entropies between the patients and the control group. To compare the sensitivity and robustness of these three kinds of entropy, we also studied their performance by using certain signal mixed with noise.Result: Compare with the control group, almost the whole brain's ApEn and FuzzyEn of OCD are larger significantly. Besides, there are more brain regions with obvious differences when using ApEn comparing to using FuzzyEn. There was no statistical difference between the SampEn of OCD and HC.Conclusion: Brain entropy is a numerical index related to brain function and can be used as a supplementary biological index to evaluate brain state, which may be used as a reference for the diagnosis of mental illness. According to an analysis of certain signal mixed with noise, we conclude that FuzzyEn is more accurate considering sensitivity, stability and robustness of entropy.

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Fuzzy entropy (FuzzyEn), which employs the fuzzy probability to characterize the similarity between vectors, is a robust nonlinear statistic to quantify the complexity or regularity of nonlinear time series. The aim of this study is to investigate the statistical properties of FuzzyEn and improve the subspace denoising technique using FuzzyEn. We first show the asymptotic normality of FuzzyEn and derive its variance for finite sample behavior. We then analyze the two pending and fundamental issues in subspace denoising, i.e., depending on the so-called “noise floor” and the unaltered noise existing in signal subspace, from the point of view of fuzzy logic. A FuzzyEn-assisted subspace iterative soft threshold (FESIST) denoising method, which can effectively overcome the deficiency in the existing subspace filtering (SSF) techniques, is presented. The effectiveness of the method is first demonstrated on two synthetic chaotic series and then tested on real biological signals. The results demonstrate the superiority of the proposed method over existing SSF techniques, as well as the empirical mode decomposition and wavelet decomposition approaches. [ABSTRACT FROM AUTHOR]

Rheoencephalography (REG) is a simple and inexpensive technique that intends to monitor cerebral blood flow (CBF), but its ability to reflect CBF changes has not been extensively proved. Based on the hypothesis that alterations in CBF during apnea should be reflected in REG signals under the form of increased complexity, several entropy metrics were assessed for REG analysis during apnea and resting periods in 16 healthy subjects: approximate entropy (ApEn), sample entropy (SampEn), fuzzy entropy (FuzzyEn), corrected conditional entropy (CCE) and Shannon entropy (SE). To compute these entropy metrics, a set of parameters must be defined a priori, such as, for example, the embedding dimension m, and the tolerance threshold r. A thorough analysis of the effects of parameter selection in the entropy metrics was performed, looking for the values optimizing differences between apnea and baseline signals. All entropy metrics, except SE, provided higher values for apnea periods (p-values < 0.025). FuzzyEn outperformed all other metrics, providing the lowest p-value (p = 0.0001), allowing to conclude that REG signals during apnea have higher complexity than in resting periods. Those findings suggest that REG signals reflect CBF changes provoked by apneas, even though further studies are needed to confirm this hypothesis.

Entropy measures have been extensively used to assess heart rate variability (HRV), a noninvasive marker of cardiovascular autonomic regulation. It is yet to be elucidated whether those entropy measures can sensitively respond to changes of autonomic balance and whether the responses, if there are any, are consistent across different entropy measures. Sixteen healthy subjects were enrolled in this study. Each subject undertook two 5-min ECG measurements, one in a resting seated position and another while walking on a treadmill at a regular speed of 5 km/h. For each subject, the two measurements were conducted in a randomized order and a 30-min rest was required between them. HRV time series were derived and were analyzed by eight entropy measures, i.e., approximate entropy (ApEn), corrected ApEn (cApEn), sample entropy (SampEn), fuzzy entropy without removing local trend (FuzzyEn-g), fuzzy entropy with local trend removal (FuzzyEn-l), permutation entropy (PermEn), conditional entropy (CE), and distribution entropy (DistEn). Compared to resting seated position, regular walking led to significantly reduced CE and DistEn (both p ≤ 0.006; Cohen's d = 0.9 for CE, d = 1.7 for DistEn), and increased PermEn (p < 0.0001; d = 1.9), while all these changes disappeared after performing a linear detrend or a wavelet detrend (<~0.03 Hz) on HRV. In addition, cApEn, SampEn, FuzzyEn-g, and FuzzyEn-l showed significant decreases during regular walking after linear detrending (all p < 0.006; 0.8 < d < 1), while a significantly increased ApEn (p < 0.0001; d = 1.9) and a significantly reduced cApEn (p = 0.0006; d = 0.8) were observed after wavelet detrending. To conclude, multiple entropy analyses should be performed to assess HRV in order for objective results and caution should be paid when drawing conclusions based on observations from a single measure. Besides, results from different studies will not be comparable unless it is clearly stated whether data have been detrended and the methods used for detrending have been specified. [ABSTRACT FROM AUTHOR]

Grip force control is a crucial function for human to guarantee the quality of life. To examine the effects of age on grip force control, 10 young adults and 11 late middle-aged adults participated in visually guided tracking tasks using different target force levels (25, 50, and 75% of the subject's maximal grip force). Multiple measures were used to evaluate the tracking performance during force rising phase and force maintenance phase. The measurements include the rise time, fuzzy entropy, mean force percentage, coefficient of variation, and target deviation ratio. The results show that the maximal grip force was significantly lower in the late middle-aged adults than in the young adults. The time of rising phase was systematically longer among late middle-aged adults. The fuzzy entropy is a useful indicator for quantitating the force variability of the grip force signal at higher force levels. These results suggest that the late middle-aged adults applied a compensatory strategy that allow allows for sufficient time to reach the required grip force and reduce the impact of the early and subtle degenerative changes in hand motor function. [ABSTRACT FROM AUTHOR]

Complexity of heartbeat interval series is typically measured by entropy. Recent studies have found that sample entropy (SampEn) or fuzzy entropy (FuzzyEn) quantifies essentially the randomness, which may not be uniformly identical to complexity. Additionally, these entropy measures are heavily dependent on the predetermined parameters and confined to data length. Aiming at improving the robustness of complexity assessment for short-term RR interval series, this study developed a novel measure-distribution entropy (DistEn). The DistEn took full advantage of the inherent information underlying the vector-to-vector distances in the state space by probability density estimation. Performances of DistEn were examined by theoretical data and experimental short-term RR interval series. Results showed that DistEn correctly ranked the complexity of simulated chaotic series and Gaussian noise series. The DistEn had relatively lower sensitivity to the predetermined parameters and showed stability even for quantifying the complexity of extremely short series. Analysis further showed that the DistEn indicated the loss of complexity in both healthy aging and heart failure patients (both p < 0.01), whereas neither the SampEn nor the FuzzyEn achieved comparable results (all p ≥ 0.05). This study suggested that the DistEn would be a promising measure for prompt clinical examination of cardiovascular function. [ABSTRACT FROM AUTHOR]

This paper presents a new complexity metric to evaluate the unpredictability of a frequency-hopping/spread-spectrum (FH/SS) sequence based on fuzzy entropy (FuzzyEn). According to the property of the FS/SS sequence, the definition of a fuzzy membership function for a complexity metric is presented and a basic theorem for FuzzyEn complexity is proved. Simulation and analytical results show that the proposed FuzzyEn works and can effectively discern the changing complexities of the FH/SS sequences, which are compared with a complexity metric based on approximate entropy (ApEn). The FuzzyEn scheme has obvious advantages in robustness to resolution parameters and sensitivity to vector dimensions. [ABSTRACT FROM AUTHOR]

• A novel scheme was proposed for automated seizure detection using electroencephalography (EEG). • Subbands and cumulative sum of subbands were raised and their effect was investigated. • 12 cases were studied and accuracies of nearly 100% and 93.62% for the first 11 and 12th cases, respectively. We here proposed a novel fusion method of frequency slice wavelet transform (FSWT)-based fuzzy entropy (FuzzyEn) and Higuchi's fractal dimension (HFD), t-distributed stochastic neighbor embedding (t-SNE) and K-nearest neighbor (KNN) to achieve the goal of automated detection of epileptic electroencephalography (EEG). Fifteen EEG subbands were first separated from the original EEG via FSWT, then their cumulative sum of subbands (CSoS) including forward CSoS and backward CSoS were computed. FuzzyEn and HFD were then employed to quantify the nonlinear properties of these subbands and CSoS, and followed by mapping the high-dimensional features into the two-dimensional space using t-SNE. Finally, the two-dimensional features were fed into KNN for classification. Eight binary-class, three ternary-class and one quinary-class cases, in total twelve classification tasks of the Bonn EEG database were conducted. The proposed approach attained accuracies of approximately 100% and 93.62% in the first 11 and 12th cases, respectively. Experimental results not only manifest our proposal is superior to most of existing methods, but also demonstrate subbands and CSoS based nonlinear features enhance the performance of epileptic seizure detection. [ABSTRACT FROM AUTHOR]

Rheoencephalography (REG) is a simple and inexpensive technique that intends to monitor cerebral blood flow (CBF), but its ability to reflect CBF changes has not been extensively proved. Based on the hypothesis that alterations in CBF during apnea should be reflected in REG signals under the form of increased complexity, several entropy metrics were assessed for REG analysis during apnea and resting periods in 16 healthy subjects: approximate entropy (ApEn), sample entropy (SampEn), fuzzy entropy (FuzzyEn), corrected conditional entropy (CCE) and Shannon entropy (SE). To compute these entropy metrics, a set of parameters must be defined a priori, such as, for example, the embedding dimension m, and the tolerance threshold r. A thorough analysis of the effects of parameter selection in the entropy metrics was performed, looking for the values optimizing differences between apnea and baseline signals. All entropy metrics, except SE, provided higher values for apnea periods (p-values < 0.025). FuzzyEn outperformed all other metrics, providing the lowest p-value (p = 0.0001), allowing to conclude that REG signals during apnea have higher complexity than in resting periods. Those findings suggest that REG signals reflect CBF changes provoked by apneas, even though further studies are needed to confirm this hypothesis. [ABSTRACT FROM AUTHOR]