On the Effect of Vibrotactile Stimulation in Essential Tremor

(1) Background: Vibrotactile stimulation has been studied for tremor, but there is little evidence for Essential Tremor (ET). (2) Methods: This research employed a dataset from a previous study, with data collected from 18 individuals subjected to four vibratory stimuli. To characterise tremor changes before, during, and after stimuli, time and frequency domain features were estimated from the signals. Correlation and regression analyses verified the relationship between features and clinical tremor scores. (3) Results: Individuals responded differently to vibrotactile stimulation. The 250 Hz stimulus was the only one that reduced tremor amplitude after stimulation. Compared to the baseline, the 250 Hz and random frequency stimulation reduced tremor peak power. The clinical scores and amplitude-based features were highly correlated, yielding accurate regression models (mean squared error of 0.09). (4) Conclusions: The stimulation frequency of 250 Hz has the greatest potential to reduce tremors in ET. The accurate regression model and high correlation between estimated features and clinical scales suggest that prediction models can automatically evaluate and control stimulus-induced tremor. A limitation of this research is the relatively reduced sample size.

Exploring the Hidden Complexity: Entropy Analysis in Pulse Oximetry of Female Athletes

This study examines the relationship between physiological complexity, as measured by Approximate Entropy (ApEn) and Sample Entropy (SampEn), and fitness levels in female athletes. Our focus is on their association with maximal oxygen consumption (VO2,max). Our findings reveal a complex relationship between entropy metrics and fitness levels, indicating that higher fitness typically, though not invariably, correlates with greater entropy in physiological time series data; however, this is not consistent for all individuals. For Heart Rate (HR), entropy measures suggest stable patterns across fitness categories, while pulse oximetry (SpO2) data shows greater variability. For instance, the medium fitness group displayed an ApEn(HR) = 0.57±0.13 with a coefficient of variation (CV) of 22.17 and ApEn(SpO2) = 0.96±0.49 with a CV of 46.08%, compared to the excellent fitness group with ApEn(HR) = 0.60±0.09 with a CV of 15.19% and ApEn(SpO2) =0.85±0.42 with a CV of 49.46%, suggesting broader physiological responses among more fit individuals. The larger standard deviations and CVs for SpO2 entropy may indicate the body's proficient oxygen utilization at higher levels of physical demand. Our findings advocate for combining entropy metrics with wearable sensor technology for improved biomedical analysis and personalized healthcare.

Stability Analysis of Metal Active-Gas Welding Short-Circuiting Transfer Based on Input Pulsating Energy

In this study, a platform for a welding experiment, used to collect input and output electrical signals, was constructed, and the algorithm for the input pulsating energy interpolation line (IPEI) was given. Experiments with MAG surface straight line welding were conducted at various voltages. Analysis of the IPEI in relation to the welding current was performed while combining real-world welding occurrences with high-speed camera images of droplet transfer. It was established that the IPEI can be employed as a characteristic parameter to assess the stability of the short-circuiting transfer process in MAG welding. The three criteria for assessing the stability were the spectrum, approximation entropy, and coefficient of variation. A comparative analysis was conducted on each of these approaches. It was determined that the most effective technique is approximation entropy. The approximation entropy of the welding current and IPEI are also highly consistent, with a correlation coefficient as high as 0.9889.

Correlation dimension and entropy in the assessment of sex differences based on human gait data

Introduction

It is proved that there are differences between gait performed by females and males, which appear in movements of selected body parts. Despite numerous state-of-the-art studies related to the discriminative analysis of motion capture data, the question of whether measures of signal complexity and uncertainty can extract valuable features for the problem of sex distinction still remains open. It is the subject of the paper.

Methods

Correlation dimension, as well as approximate and sample entropies, are selected to describe motion data. In the numerical experiments, the collected dataset with 884 samples of 25 females and 30 males was used. The measurements took place in the Human Motion Laboratory (HML), equipped with a highly precise motion capture system. Two variants of data representation were investigated-time series that contain joint rotations of taken skeleton model as well as positions of the markers attached to the human body. Finally, a comparative analysis between the populations of females and males using descriptive statistics, non-parametric estimation, and statistical hypotheses verification was carried out.

Results

There are statistically significant sex differences extracted by the taken measures. In general, the movements of lower limbs result in greater values of correlation dimension and entropies for females, while selected upper body parts play a similar role for males. The dissimilarities are mainly observed in hip, ankle, shoulder, and head movements.

Discussion

Correlation dimension and entropy measures provide robust and explainable features of motion capture data with a valuable description of the human locomotion system. Thus, beyond the importance of discovered differences between females and males, their interpretation and understanding are also known.

Effect of Selected Music Soundtracks on Cardiac Vagal Control and Complexity Assessed by Heart Rate Variability

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.

Beta-blockers and mechanical dyssynchrony in heart failure assessed by radionuclide ventriculography

BACKGROUND

Radionuclide ventriculography (RNVG) can be used to quantify mechanical dyssynchrony and may be a valuable adjunct in the assessment of heart failure with reduced ejection fraction (HFrEF). The study aims to investigate the effect of beta-blockers on mechanical dyssynchrony using novel RNVG phase parameters.

METHODS

A retrospective study was carried out in a group of 98 patients with HFrEF. LVEF and dyssynchrony were assessed pre and post beta-blockade. Dyssynchrony was assessed using synchrony, entropy, phase standard deviation, approximate entropy, and sample entropy from planar RNVG phase images. Subgroups split by ischemic etiology were also investigated.

RESULTS

An improvement in dyssynchrony and LVEF was measured six months post beta-blockade for both ischemic and non-ischemic groups.

CONCLUSIONS

A significant improvement in dyssynchrony and LVEF was measured post beta-blockade using novel measures of dyssynchrony.

Can Respiration Complexity Help the Diagnosis of Disorders of Consciousness in Rehabilitation?

BACKGROUND

Autonomic Nervous System (ANS) activity, as cardiac, respiratory and electrodermal activity, has been shown to provide specific information on different consciousness states. Respiration rates (RRs) are considered indicators of ANS activity and breathing patterns are currently already included in the evaluation of patients in critical care.

OBJECTIVE

The aim of this work was to derive a proxy of autonomic functions via the RR variability and compare its diagnostic capability with known neurophysiological biomarkers of consciousness.

METHODS

In a cohort of sub-acute patients with brain injury during post-acute rehabilitation, polygraphy (ECG, EEG) recordings were collected. The EEG was labeled via descriptors based on American Clinical Neurophysiology Society terminology and the respiration variability was extracted by computing the Approximate Entropy (ApEN) of the ECG-derived respiration signal. Competing logistic regressions were applied to evaluate the improvement in model performances introduced by the RR ApEN.

RESULTS

Higher RR complexity was significantly associated with higher consciousness levels and improved diagnostic models' performances in contrast to the ones built with only electroencephalographic descriptors.

CONCLUSIONS

Adding a quantitative, instrumentally based complexity measure of RR variability to multimodal consciousness assessment protocols may improve diagnostic accuracy based only on electroencephalographic descriptors. Overall, this study promotes the integration of biomarkers derived from the central and the autonomous nervous system for the most comprehensive diagnosis of consciousness in a rehabilitation setting.

Effects of Motor Task Difficulty on Postural Control Complexity during Dual Tasks in Young Adults: A Nonlinear Approach

Few studies have evaluated the effect of a secondary motor task on the standing posture based on nonlinear analysis. However, it is helpful to extract information related to the complexity, stability, and adaptability to the environment of the human postural system. This study aimed to analyze the effect of two motor tasks with different difficulty levels in motor performance complexity on the static standing posture in healthy young adults. Thirty-five healthy participants (23.08 ± 3.92 years) performed a postural single task (ST: keep a quiet standing posture) and two motor dual tasks (DT). i.e., mot-DT(A)—perform the ST while performing simultaneously an easy motor task (taking a smartphone out of a bag, bringing it to the ear, and putting it back in the bag)—and mot-DT(T)—perform the ST while performing a concurrent difficult motor task (typing on the smartphone keyboard). The approximate entropy (ApEn), Lyapunov exponent (LyE), correlation dimension (CoDim), and fractal dimension (detrending fluctuation analysis, DFA) for the mediolateral (ML) and anterior-posterior (AP) center-of-pressure (CoP) displacement were measured with a force plate while performing the tasks. A significant difference was found between the two motor dual tasks in ApEn, DFA, and CoDim-AP (p < 0.05). For the ML CoP direction, all nonlinear variables in the study were significantly different (p < 0.05) between ST and mot-DT(T), showing impairment in postural control during mot-DT(T) compared to ST. Differences were found across ST and mot-DT(A) in ApEn-AP and DFA (p < 0.05). The mot-DT(T) was associated with less effectiveness in postural control, a lower number of degrees of freedom, less complexity and adaptability of the dynamic system than the postural single task and the mot-DT(A).

[Clinical application of acupuncture-moxibustion for the treatment of spirit based on approximate entropy of electrooculogram signal]

According to the theory of acupuncture-moxibustion for the treatment of spirit, starting from the relationship between eye movement and spirit, the application of electrooculogram (EOG) signal acquisition and analysis technology for the clinical treatment of spirit by acupuncture-moxibustion is discussed. Based on the nonlinear dynamic characteristics of EOG signals, it is proposed to apply the approximate entropy algorithm to extract the EOG signal characteristics in autism spectrum disorder children under different behavior states, which could realize the preliminary exploration of the correlation between EOG signals and cognitive activities. This could provide a possibility to objectively reflect the patient' s current mental state, and could be used as a potential method to grasp spirit in clinical acupuncture- moxibustion treatment. Furthermore, considering the characteristics of acupoint stimulation on the body surface, the EOG signal acquisition and analysis technology could further be combined with biofeedback technology, and a new idea for clinical acupuncture-moxibustion to treat spirit guided by biofeedback of EOG is proposed.

CEGH: A Hybrid Model Using CEEMD, Entropy, GRU, and History Attention for Intraday Stock Market Forecasting

Intraday stock time series are noisier and more complex than other financial time series with longer time horizons, which makes it challenging to predict. We propose a hybrid CEGH model for intraday stock market forecasting. The CEGH model contains four stages. First, we use complete ensemble empirical mode decomposition (CEEMD) to decompose the original intraday stock market data into different intrinsic mode functions (IMFs). Then, we calculate the approximate entropy (ApEn) values and sample entropy (SampEn) values of each IMF to eliminate noise. After that, we group the retained IMFs into four groups and predict the comprehensive signals of those groups using a feedforward neural network (FNN) or gate recurrent unit with history attention (GRU-HA). Finally, we obtain the final prediction results by integrating the prediction results of each group. The experiments were conducted on the U.S. and China stock markets to evaluate the proposed model. The results demonstrate that the CEGH model improved forecasting performance considerably. The creation of a collaboration between CEEMD, entropy-based denoising, and GRU-HA is our major contribution. This hybrid model could improve the signal-to-noise ratio of stock data and extract global dependence more comprehensively in intraday stock market forecasting.

Sensorimotor Cortical Activity during Respiratory Arousals in Obstructive Sleep Apnea

Intensity of respiratory cortical arousals (RCA) is a pathophysiologic trait in obstructive sleep apnea (OSA) patients. We investigated the brain oscillatory features related to respiratory arousals in moderate and severe OSA. Raw electroencephalography (EEG) data recorded during polysomnography (PSG) of 102 OSA patients (32 females, mean age 51.6 ± 12 years) were retrospectively analyzed. Among all patients, 47 had moderate (respiratory distress index, RDI = 15−30/h) and 55 had severe (RDI > 30/h) OSA. Twenty RCA per sleep stage in each patient were randomly selected and a total of 10131 RCAs were analyzed. EEG signals obtained during, five seconds before and after the occurrence of each arousal were analyzed. The entropy (approximate (ApEn) and spectral (SpEn)) during each sleep stage (N1, N2 and REM) and area under the curve (AUC) of the EEG signal during the RCA was computed. Severe OSA compared to moderate OSA patients showed a significant decrease (p < 0.0001) in the AUC of the EEG signal during the RCA. Similarly, a significant decrease in spectral entropy, both before and after the RCA was observed, was observed in severe OSA patients when compared to moderate OSA patients. Contrarily, the approximate entropy showed an inverse pattern. The highest increase in approximate entropy was found in sleep stage N1. In conclusion, the dynamic range of sensorimotor cortical activity during respiratory arousals is sleep-stage specific, dependent on the frequency of respiratory events and uncoupled from autonomic activation. These findings could be useful for differential diagnosis of severe OSA from moderate OSA.

Exploring the Potential of Machine Learning for the Diagnosis of Balance Disorders Based on Centre of Pressure Analyses

Balance disorders are caused by several factors related to functionality deficits in one or multiple sensory systems such as vision, vestibular, and somatosensory systems. Patients usually have difficulty explaining their dizziness, often using ambiguous words to describe their symptoms. A common practice by clinicians is to objectively evaluate the patient's dizziness by applying the Sensory Organization Test (SOT), which measures the contribution of each sensory system (vestibular, visual, somatosensory). The SOT protocol can record up to 2000 measurements in 20 s to generate the Equilibrium Score (EQS) with its five load sensors. EQS is an indicator that reflects how well a patient can maintain balance. However, its calculation only considers two instances from these 2000 measurements that reflect the maximum anterior and posterior sway angle during the test performance; therefore, there is an opportunity to perform further analysis. This article aims to use the Centre of Pressure (COP) time series generated by the SOT and describes a methodology to pre-process and reduce the dimensionality of this raw data and use it as an input for machine learning algorithms to diagnose patients with balance disorder impairments. After applying this methodology to data from 475 patients, the logistic regression model (LR) produced the highest f1-score with 76.47%, and the support vector machine (SVM) performed almost as well, with an f1-score of 76.19%.

Temporal complexity of EEG encodes human alertness

OBJECTIVE

Automatic human alertness monitoring has recently become an important research topic with important applications in many areas such as the detection of drivers' fatigue, monitoring of monotonous tasks that require a high level of alertness such as traffic control and nuclear power plant monitoring, and sleep staging. In this study, we propose that balanced dynamics of Electroencephalography (EEG) (so called EEG temporal complexity) is a potentially useful feature for identifying human alertness states. Recently, a new signal entropy measure, called Range Entropy (RangeEn), was proposed to overcome some limitations of two of the most widely used entropy measures, namely Approximate Entropy (ApEn) and Sample Entropy (SampEn), and showed its relevance for the study of time domain EEG complexity. In this paper, we investigated whether the RangeEn holds discriminating information associated with human alertness states, namely Awake, Drowsy, and Sleep and compare its performance against those of SampEn and ApEn.

APPROACH

We used EEG data from 60 healthy subjects of both sexes and different ages acquired during whole night sleeps. Using a 30-second sliding window, we computed the three entropy measures of EEG and performed statistical analyses to evaluate the ability of these entropy measures to discriminate among the different human alertness states.

MAIN RESULTS

Although the three entropy measures contained useful information about human alertness, RangeEn showed a higher discriminative capability compared to ApEn and SampEn especially when using EEG within the Beta frequency band.

SIGNIFICANCE

Our findings highlight the EEG temporal complexity evolution through the human alertness states. This relationship can potentially be exploited for the development of automatic human alertness monitoring systems and diagnostic tools for different neurological and sleep disorders, including insomnia.

Standing Posture in Motor and Cognitive Dual-Tasks during Smartphone Use: Linear and Nonlinear Analysis of Postural Control

Analysis of the center of pressure (CoP) during cognitive or motor dual-tasking is widely used to characterize postural control. Most studies use traditional measures of CoP to quantify postural control, but given its complexity, nonlinear analysis of CoP is of growing interest in the area. This study aims to analyze CoP behavior in healthy young adults during standing posture performance while simultaneously performing motor or cognitive tasks on a smartphone, using linear and nonlinear analysis of CoP. Thirty-six healthy participants (23.08 ± 3.92 years) were found eligible for this study. They performed a single task (ST), cognitive dual-task (cog-DT), and motor dual-task (mot-DT). The total excursion of CoP, displacement of CoP in the anterior-posterior and medial-lateral directions, mean total velocity of CoP, and mean anterior-posterior and medial-lateral velocities of CoP were measured with a force plate. Approximate entropy (ApEn) of the anterior-posterior (ApEn-AP) and medial-lateral (ApEn-ML) displacement of CoP were also calculated. The results showed that dual-task costs for the total excursion, displacement in the anterior-posterior direction, mean total velocity, and mean anterior-posterior velocity of CoP were greater during the cog-DT than the mot-DT (p < 0.05). In the nonlinear analysis of the CoP, there was no difference (p > 0.05) between the cog-DT and mot-DT for ApEn values of the anterior-posterior and medial-lateral time series of the CoP. Both linear and nonlinear analyses showed differences between the cog-DT and ST (p < 0.05), revealing a decline in postural control during the cog-DT compared with the ST. In conclusion, performing a cog-DT causes sway impairments and lower postural control efficacy compared with motor single and dual-tasks. Furthermore, both linear and nonlinear analyses were able to distinguish between conditions.

Catching Wandering Minds with Tapping Fingers: Neural and Behavioral Insights into Task-unrelated Cognition

When the human mind wanders, it engages in episodes during which attention is focused on self-generated thoughts rather than on external task demands. Although the sustained attention to response task is commonly used to examine relationships between mind wandering and executive functions, limited executive resources are required for optimal task performance. In the current study, we aimed to investigate the relationship between mind wandering and executive functions more closely by employing a recently developed finger-tapping task to monitor fluctuations in attention and executive control through task performance and periodical experience sampling during concurrent functional magnetic resonance imaging (fMRI) and pupillometry. Our results show that mind wandering was preceded by increases in finger-tapping variability, which was correlated with activity in dorsal and ventral attention networks. The entropy of random finger-tapping sequences was related to activity in frontoparietal regions associated with executive control, demonstrating the suitability of this paradigm for studying executive functioning. The neural correlates of behavioral performance, pupillary dynamics, and self-reported attentional state diverged, thus indicating a dissociation between direct and indirect markers of mind wandering. Together, the investigation of these relationships at both the behavioral and neural level provided novel insights into the identification of underlying mechanisms of mind wandering.

Shoulder movement complexity in the aging shoulder: A cross-sectional analysis and reliability assessment

Healthy individuals perform a task such as hitting the head of a nail with an infinite coordination spectrum. This motor redundancy is healthy and allows for learning through exploration and uniform load distribution across muscles. Assessing movement complexity within repetitive movement trajectories may provide insight into the available motor redundancy during aging. We quantified complexity of repetitive arm elevation trajectories in the aging shoulder and assessed test-retest reliability of this quantification. In a cross-sectional study using 3D-electromagnetic tracking, 120 asymptomatic subjects, aged between 18 and 70 years performed repetitive abduction and forward/anteflexion movements. Movement complexity was calculated using the Approximate Entropy (ApEn-value): [0,2], where lower values indicate reduced complexity. Thirty-three participants performed the protocol twice, to determine reliability (intraclass correlation coefficient [ICC]). The association between age and ApEn was corrected for task characteristics (e.g., sample length) with multiple linear regression analysis. Reproducibility was determined using scatter plots and ICC's. Higher age was associated with lower ApEn-values during abduction (unstandardized estimate: -0.003/year; 95% confidence interval: [-0.005; -0.002]; p < .001). ICC's revealed poor to good reliability depending on differences in sample length between repeated measurements. The results may imply more stereotype movement during abduction in the ageing shoulder, making this movement prone to the development of shoulder complaints. Future studies may investigate the pathophysiology and clinical course of shoulder complaints by assessment of movement complexity. To this end, the ApEn-value calculated over repetitive movement trajectories may be used, although biasing factors such as sample length should be taken into account.

The Impact of the COVID-19 Pandemic on the Unpredictable Dynamics of the Cryptocurrency Market

The global economy is under great shock again in 2020 due to the COVID-19 pandemic; it has not been long since the global financial crisis in 2008. Therefore, we investigate the evolution of the complexity of the cryptocurrency market and analyze the characteristics from the past bull market in 2017 to the present the COVID-19 pandemic. To confirm the evolutionary complexity of the cryptocurrency market, three general complexity analyses based on nonlinear measures were used: approximate entropy (ApEn), sample entropy (SampEn), and Lempel-Ziv complexity (LZ). We analyzed the market complexity/unpredictability for 43 cryptocurrency prices that have been trading until recently. In addition, three non-parametric tests suitable for non-normal distribution comparison were used to cross-check quantitatively. Finally, using the sliding time window analysis, we observed the change in the complexity of the cryptocurrency market according to events such as the COVID-19 pandemic and vaccination. This study is the first to confirm the complexity/unpredictability of the cryptocurrency market from the bull market to the COVID-19 pandemic outbreak. We find that ApEn, SampEn, and LZ complexity metrics of all markets could not generalize the COVID-19 effect of the complexity due to different patterns. However, market unpredictability is increasing by the ongoing health crisis.

Empirical Mode Decomposition-Derived Entropy Features Are Beneficial to Distinguish Elderly People with a Falling History on a Force Plate Signal

Fall risk prediction is an important issue for the elderly. A center of pressure signal, derived from a force plate, is useful for the estimation of body calibration. However, it is still difficult to distinguish elderly people’s fall history by using a force plate signal. In this study, older adults with and without a history of falls were recruited to stand still for 60 s on a force plate. Forces in the x, y and z directions (Fx, Fy, and Fz) and center of pressure in the anteroposterior (COPx) and mediolateral directions (COPy) were derived. There were 49 subjects in the non-fall group, with an average age of 71.67 (standard derivation: 6.56). There were also 27 subjects in the fall group, with an average age of 70.66 (standard derivation: 6.38). Five signal series—forces in x, y, z (Fx, Fy, Fz), COPX, and COPy directions—were used. These five signals were further decomposed with empirical mode decomposition (EMD) with seven intrinsic mode functions. Time domain features (mean, standard derivation and coefficient of variations) and entropy features (approximate entropy and sample entropy) of the original signals and EMD-derived signals were extracted. Results showed that features extracted from the raw COP data did not differ significantly between the fall and non-fall groups. There were 10 features extracted using EMD, with significant differences observed among fall and non-fall groups. These included four features from COPx and two features from COPy, Fx and Fz.

Brain Entropy Study on Obsessive-Compulsive Disorder Using Resting-State fMRI

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.

Associations between Neurocardiovascular Signal Entropy and Physical Frailty

In this cross-sectional study, the relationship between noninvasively measured neurocardiovascular signal entropy and physical frailty was explored in a sample of community-dwelling older adults from The Irish Longitudinal Study on Ageing (TILDA). The hypothesis under investigation was that dysfunction in the neurovascular and cardiovascular systems, as quantified by short-length signal complexity during a lying-to-stand test (active stand), could provide a marker for frailty. Frailty status (i.e., "non-frail", "pre-frail", and "frail") was based on Fried's criteria (i.e., exhaustion, unexplained weight loss, weakness, slowness, and low physical activity). Approximate entropy (ApEn) and sample entropy (SampEn) were calculated during resting (lying down), active standing, and recovery phases. There was continuously measured blood pressure/heart rate data from 2645 individuals (53.0% female) and frontal lobe tissue oxygenation data from 2225 participants (52.3% female); both samples had a mean (SD) age of 64.3 (7.7) years. Results revealed statistically significant associations between neurocardiovascular signal entropy and frailty status. Entropy differences between non-frail and pre-frail/frail were greater during resting state compared with standing and recovery phases. Compared with ApEn, SampEn seemed to have better discriminating power between non-frail and pre-frail/frail individuals. The quantification of entropy in short length neurocardiovascular signals could provide a clinically useful marker of the multiple physiological dysregulations that underlie physical frailty.

The interplay between executive control, behavioural variability and mind wandering: Insights from a high-definition transcranial direct-current stimulation study

While the involvement of executive processes in mind wandering is largely undebated, their exact relationship is subject to an ongoing debate and rarely studied dynamically within-subject. Several brain-stimulation studies using transcranial direct current stimulation (tDCS) have attempted to modulate mind-wandering propensity by stimulating the left dorsolateral prefrontal cortex (DLPFC) which is an important hub in the prefrontal control network. In a series of three studies testing a total of N = 100 participants, we develop a novel task that allows to study the dynamic interplay of mind wandering, behavioural varibility and the flexible recruitment of executive resources as indexed by the randomness (entropy) of movement sequences generated by our participants. We consistently find that behavioural variability is increased and randomness is decreased during periods of mind wandering. Interestingly, we also find that behavioural variability interacts with the entropy-MW effect, opening up the possibility to detect distinct states of off-focus cognition. When applying a high-definition transcranial direct-current stimulation (HD-tDCS) montage to the left DLPFC, we find that propensity to mind wander is reduced relative to a group receiving sham stimulation.

The Changes of qEEG Approximate Entropy during Test of Variables of Attention as a Predictor of Major Depressive Disorder

Evaluating brain function through biosignals remains challenging. Quantitative electroencephalography (qEEG) outcomes have emerged as a potential intermediate biomarker for diagnostic clarification in psychological disorders. The Test of Variables of Attention (TOVA) was combined with qEEG to evaluate biomarkers such as absolute power, relative power, cordance, and approximate entropy from covariance matrix images to predict major depressive disorder (MDD). EEG data from 18 healthy control and 18 MDD patients were monitored during the resting state and TOVA. TOVA was found to provide aspects for the evaluation of MDD beyond resting electroencephalography. The results showed that the prefrontal qEEG theta cordance of the control and MDD groups were significantly different. For comparison, the changes in qEEG approximate entropy (ApEn) patterns observed during TOVA provided features to distinguish between participants with or without MDD. Moreover, ApEn scores during TOVA were a strong predictor of MDD, and the ApEn scores correlated with the Beck Depression Inventory (BDI) scores. Between-group differences in ApEn were more significant for the testing state than for the resting state. Our results provide further understanding for MDD treatment selection and response prediction during TOVA.

A Novel Hybrid Approach for Partial Discharge Signal Detection Based on Complete Ensemble Empirical Mode Decomposition with Adaptive Noise and Approximate Entropy

To eliminate the influence of white noise in partial discharge (PD) detection, we propose a novel method based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and approximate entropy (ApEn). By introducing adaptive noise into the decomposition process, CEEMDAN can effectively separate the original signal into different intrinsic mode functions (IMFs) with distinctive frequency scales. Afterward, the approximate entropy value of each IMF is calculated to eliminate noisy IMFs. Then, correlation coefficient analysis is employed to select useful IMFs that represent dominant PD features. Finally, real IMFs are extracted for PD signal reconstruction. On the basis of EEMD, CEEMDAN can further improve reconstruction accuracy and reduce iteration numbers to solve mode mixing problems. The results on both simulated and on-site PD signals show that the proposed method can be effectively employed for noise suppression and successfully extract PD pulses. The fusion algorithm combines the CEEMDAN algorithm and the ApEn algorithm with their respective advantages and has a better de-noising effect than EMD and EEMD.

Deciphering the Morphology of Motor Evoked Potentials

Motor Evoked Potentials (MEPs) are used to monitor disability progression in multiple sclerosis (MS). Their morphology plays an important role in this process. Currently, however, there is no clear definition of what constitutes a normal or abnormal morphology. To address this, five experts independently labeled the morphology (normal or abnormal) of the same set of 1,000 MEPs. The intra- and inter-rater agreement between the experts indicates they agree on the concept of morphology, but differ in their choice of threshold between normal and abnormal morphology. We subsequently performed an automated extraction of 5,943 time series features from the MEPs to identify a valid proxy for morphology, based on the provided labels. To do this, we compared the cross-validation performances of one-dimensional logistic regression models fitted to each of the features individually. We find that the approximate entropy (ApEn) feature can accurately reproduce the majority-vote labels. The performance of this feature is evaluated on an independent test set by comparing to the majority vote of the neurologists, obtaining an AUC score of 0.92. The model slightly outperforms the average neurologist at reproducing the neurologists consensus-vote labels. We can conclude that MEP morphology can be consistently defined by pooling the interpretations from multiple neurologists and that ApEn is a valid continuous score for this. Having an objective and reproducible MEP morphological abnormality score will allow researchers to include this feature in their models, without manual annotation becoming a bottleneck. This is crucial for large-scale, multi-center datasets. An exploratory analysis on a large single-center dataset shows that ApEn is potentially clinically useful. Introducing an automated, objective, and reproducible definition of morphology could help overcome some of the barriers that are currently obstructing broad adoption of evoked potentials in daily care and patient follow-up, such as standardization of measurements between different centers, and formulating guidelines for clinical use.

New Fast ApEn and SampEn Entropy Algorithms Implementation and Their Application to Supercomputer Power Consumption

Approximate Entropy and especially Sample Entropy are recently frequently used algorithms for calculating the measure of complexity of a time series. A lesser known fact is that there are also accelerated modifications of these two algorithms, namely Fast Approximate Entropy and Fast Sample Entropy. All these algorithms are effectively implemented in the R software package TSEntropies. This paper contains not only an explanation of all these algorithms, but also the principle of their acceleration. Furthermore, the paper contains a description of the functions of this software package and their parameters, as well as simple examples of using this software package to calculate these measures of complexity of an artificial time series and the time series of a complex real-world system represented by the course of supercomputer infrastructure power consumption. These time series were also used to test the speed of this package and to compare its speed with another R package pracma. The results show that TSEntropies is up to 100 times faster than pracma and another important result is that the computational times of the new Fast Approximate Entropy and Fast Sample Entropy algorithms are up to 500 times lower than the computational times of their original versions. At the very end of this paper, the possible use of this software package TSEntropies is proposed.

Anterior-Posterior Balance Perturbation Protocol Using Lifelike Virtual Reality Environment

Virtual reality (VR) paradigms have proved to be a valid method to challenge and perturb balance. There is little consensus in the literature on the best protocol design to perturb balance and induce postural sway. Current VR interventions still lack a well-defined standardized metric to generate a virtual environment that can perturb balance in an efficacious, lifelike, and repeatable manner. The objective of this study was to investigate different configurations of amplitude and frequency in an anterior-posterior translation VR environment, that is, lifelike and scaled. Thirteen young adults with no conditions affecting balance were recruited. Balance was challenged by anterior-posterior sinusoidal movement of the lab image within the VR headset. Four different amplitudes of the sinusoidal movement were tested: 1, 5, 10, and 20 cm, with each amplitude being presented at 2 test frequencies : 0.5 and 0.25 Hz. Mean center of pressure velocity was significantly greater than baseline at 0.5 Hz and amplitudes of 10 and 20 cm. Mean center of pressure at approximate entropy was greater than baseline at 0.5 Hz and amplitude of 20 cm. The results suggest that sinusoidal movement of a realistic VR environment produces altered balance compared with baseline quiet standing, but only under specific movement parameters.

An Entropy-Based Approach for Anomaly Detection in Activities of Daily Living in the Presence of a Visitor

This paper presents anomaly detection in activities of daily living based on entropy measures. It is shown that the proposed approach will identify anomalies when there are visitors representing a multi-occupant environment. Residents often receive visits from family members or health care workers. Therefore, the residents’ activity is expected to be different when there is a visitor, which could be considered as an abnormal activity pattern. Identifying anomalies is essential for healthcare management, as this will enable action to avoid prospective problems early and to improve and support residents’ ability to live safely and independently in their own homes. Entropy measure analysis is an established method to detect disorder or irregularities in many applications: however, this has rarely been applied in the context of activities of daily living. An experimental evaluation is conducted to detect anomalies obtained from a real home environment. Experimental results are presented to demonstrate the effectiveness of the entropy measures employed in detecting anomalies in the resident’s activity and identifying visiting times in the same environment.

Epileptic seizure recognition using EEG wavelet decomposition based on nonlinear and statistical features with support vector machine classification

Epileptic seizure (ES) is a neurological brain dysfunction. ES can be detected using the electroencephalogram (EEG) signal. However, visual inspection of ES using long-time EEG recordings is a difficult, time-consuming and a costly procedure. Thus, automatic epilepsy recognition is of primary importance. In this paper, a new method is proposed for automatic ES recognition using short-time EEG recordings. The method is based on first decomposing the EEG signals on sub-signals using discrete wavelet transform. Then, from the obtained sub-signals, different non-linear parameters such as approximate entropy (ApEn), largest Lyapunov exponents (LLE) and statistical parameters are determined. These parameters along with phase entropies, calculated through higher order spectrum analysis, are used as an input vector of a multi-class support vector machine (MSVM) for ES recognition. The proposed method is evaluated using the standard EEG database developed by the Department of Epileptology, University of Bonn, Germany. The evaluation is carried out through a large number of classification experiments. Different statistical metrics namely Sensitivity (Se), Specificity (Sp) and classification accuracy (Ac) are calculated and compared to those obtained in the scientific research literature. The obtained results show that the proposed method achieves high accuracies, which are as good as the best existing state-of-the-art methods studied using the same EEG database.

Complexity Analysis of Surface Electromyography for Assessing the Myoelectric Manifestation of Muscle Fatigue: A Review

The surface electromyography (sEMG) records the electrical activity of muscle fibers during contraction: one of its uses is to assess changes taking place within muscles in the course of a fatiguing contraction to provide insights into our understanding of muscle fatigue in training protocols and rehabilitation medicine. Until recently, these myoelectric manifestations of muscle fatigue (MMF) have been assessed essentially by linear sEMG analyses. However, sEMG shows a complex behavior, due to many concurrent factors. Therefore, in the last years, complexity-based methods have been tentatively applied to the sEMG signal to better individuate the MMF onset during sustained contractions. In this review, after describing concisely the traditional linear methods employed to assess MMF we present the complexity methods used for sEMG analysis based on an extensive literature search. We show that some of these indices, like those derived from recurrence plots, from entropy or fractal analysis, can detect MMF efficiently. However, we also show that more work remains to be done to compare the complexity indices in terms of reliability and sensibility; to optimize the choice of embedding dimension, time delay and threshold distance in reconstructing the phase space; and to elucidate the relationship between complexity estimators and the physiologic phenomena underlying the onset of MMF in exercising muscles.

Fractional-Order Chaotic Memory with Wideband Constant Phase Elements

This paper provides readers with three partial results that are mutually connected. Firstly, the gallery of the so-called constant phase elements (CPE) dedicated for the wideband applications is presented. CPEs are calculated for 9° (decimal orders) and 10° phase steps including ¼, ½, and ¾ orders, which are the most used mathematical orders between zero and one in practice. For each phase shift, all necessary numerical values to design fully passive RC ladder two-terminal circuits are provided. Individual CPEs are easily distinguishable because of a very high accuracy; maximal phase error is less than 1.5° in wide frequency range beginning with 3 Hz and ending with 1 MHz. Secondly, dynamics of ternary memory composed by a series connection of two resonant tunneling diodes is investigated and, consequently, a robust chaotic behavior is discovered and reported. Finally, CPEs are directly used for realization of fractional-order (FO) ternary memory as lumped chaotic oscillator. Existence of structurally stable strange attractors for different orders is proved, both by numerical analyzed and experimental measurement.

Application of Time-Scale Decomposition of Entropy for Eye Movement Analysis

The methods for nonlinear time series analysis were used in the presented research to reveal eye movement signal characteristics. Three measures were used: approximate entropy, fuzzy entropy, and the Largest Lyapunov Exponent, for which the multilevel maps (MMs), being their time-scale decomposition, were defined. To check whether the estimated characteristics might be useful in eye movement events detection, these structures were applied in the classification process conducted with the usage of the kNN method. The elements of three MMs were used to define feature vectors for this process. They consisted of differently combined MM segments, belonging either to one or several selected levels, as well as included values either of one or all the analysed measures. Such a classification produced an improvement in the accuracy for saccadic latency and saccade, when compared with the previously conducted studies using eye movement dynamics.

Analysis of Streamflow Complexity Based on Entropies in the Weihe River Basin, China

The study on the complexity of streamflow has guiding significance for hydrologic simulation, hydrologic prediction, water resources planning and management. Utilizing monthly streamflow data from four hydrologic control stations in the mainstream of the Weihe River in China, the methods of approximate entropy, sample entropy, two-dimensional entropy and fuzzy entropy are introduced into hydrology research to investigate the spatial distribution and dynamic change in streamflow complexity. The results indicate that the complexity of the streamflow has spatial differences in the Weihe River watershed, exhibiting an increasing tendency along the Weihe mainstream, except at the Linjiacun station, which may be attributed to the elevated anthropogenic influence. Employing sliding entropies, the variation points of the streamflow time series at the Weijiabu station were identified in 1968, 1993 and 2003, and those at the Linjiacun station, Xianyang station and Huaxian station occurred in 1971, 1993 and 2003. In the verification of the above points, the minimum value of t-test is 3.7514, and that of Brown-Forsythe is 7.0307, far exceeding the significance level of 95%. Also, the cumulative anomaly can detect two variation points. The t-test, Brown-Forsythe test and cumulative anomaly test strengthen the conclusion regarding the availability of entropies for identifying the streamflow variability. The results lead us to conclude that four entropies have good application effects in the complexity analysis of the streamflow time series. Moreover, two-dimensional entropy and fuzzy entropy, which have been rarely used in hydrology research before, demonstrate better continuity and relative consistency, are more suitable for short and noisy hydrologic time series and more effectively identify the streamflow complexity. The results could be very useful in identifying variation points in the streamflow time series.

EEG Signals Feature Extraction Based on DWT and EMD Combined with Approximate Entropy

The classification recognition rate of motor imagery is a key factor to improve the performance of brain-computer interface (BCI). Thus, we propose a feature extraction method based on discrete wavelet transform (DWT), empirical mode decomposition (EMD), and approximate entropy. Firstly, the electroencephalogram (EEG) signal is decomposed into a series of narrow band signals with DWT, then the sub-band signal is decomposed with EMD to get a set of stationary time series, which are called intrinsic mode functions (IMFs). Secondly, the appropriate IMFs for signal reconstruction are selected. Thus, the approximate entropy of the reconstructed signal can be obtained as the corresponding feature vector. Finally, support vector machine (SVM) is used to perform the classification. The proposed method solves the problem of wide frequency band coverage during EMD and further improves the classification accuracy of EEG signal motion imaging.

A Rail Fault Diagnosis Method Based on Quartic C2 Hermite Improved Empirical Mode Decomposition Algorithm

For compound fault detection of high-speed rail vibration signals, which presents a difficult problem, an early fault diagnosis method of an improved empirical mode decomposition (EMD) algorithm based on quartic C² Hermite interpolation is presented. First, the quartic C² Hermite interpolation improved EMD algorithm is used to decompose the original signal, and the intrinsic mode function (IMF) components are obtained. Second, singular value decomposition for the IMF components is performed to determine the principal components of the signal. Then, the signal is reconstructed and the kurtosis and approximate entropy values are calculated as the eigenvalues of fault diagnosis. Finally, fault diagnosis is executed based on the support vector machine (SVM). This method is applied for the fault diagnosis of high-speed rails, and experimental results show that the method presented in this paper is superior to the traditional EMD algorithm and greatly improves the accuracy of fault diagnosis.

A Class of Quadratic Polynomial Chaotic Maps and Their Fixed Points Analysis

When chaotic systems are used in different practical applications, such as chaotic secure communication and chaotic pseudorandom sequence generators, a large number of chaotic systems are strongly required. However, for a lack of a systematic construction theory, the construction of chaotic systems mainly depends on the exhaustive search of systematic parameters or initial values, especially for a class of dynamical systems with hidden chaotic attractors. In this paper, a class of quadratic polynomial chaotic maps is studied, and a general method for constructing quadratic polynomial chaotic maps is proposed. The proposed polynomial chaotic maps satisfy the Li–Yorke definition of chaos. This method can accurately control the amplitude of chaotic time series. Through the existence and stability analysis of fixed points, we proved that such class quadratic polynomial maps cannot have hidden chaotic attractors.

Implementation of Bagged SVM Ensemble Model for Classification of Epileptic States Using EEG

BACKGROUND

To decipher EEG (Electroencephalography), intending to locate inter-ictal and ictal discharges for supporting the diagnoses of epilepsy and locating the seizure focus, is a critical task. The aim of this work was to find how the ensemble model distinguishes between two different sets of problems which are group 1: inter-ictal and ictal, group 2: controlled and inter-ictal using approximate entropy as a parameter.

METHODS

This work addresses the classification problem for two groups; Group 1: "inter-ictal vs. ictal" for which case 1(C-E), and case 2(D-E) are included and Group 2; "activity from controlled vs. inter-ictal activity" considering four cases which are case 3 (A-C), case 4(B-C), case 5 (A-D) and case 6(B-D) respectively. To divide the EEG into sub-bands, DWT (Discrete Wavelet Transform) was used and approximate Entropy was extracted out of all the five sub-bands of EEG for each case. Bagged SVM was used to classify the different groups considered.

RESULTS

The highest accuracy for Group 1 using Bagged SVM Ensemble model for case 1 was observed to be 96.83% with testing data; which was similar to 97% achieved by using training data. For case 2 (D-E) 93.92% accuracy with training and 84.83% with testing data were obtained. For Group 2, there was a large disparity between SVM and Bagged Ensemble model, where 76%, 81.66%, 72.835% and 71.16% for case 3, case 4, case 5 and case 6 were obtained. While for training data set, 92.87%, 91.74%, 92% and 92.64% accuracy was attained, respectively. The results obtained by SVM for Group 2 showed a huge difference from the highest accuracy achieved by bagged SVM for both the training and the test data.

CONCLUSION

Bagged Ensemble model outperformed SVM model for every case with a huge difference with both training as well as test dataset for Group 2 and marginally better for Group 1.

Comparison of complexity and spectral indices of skin-surface laser-doppler signals in patients with breast cancer receiving chemotherapy and Kuan-Sin-Yin

This study tested the hypothesis that measuring and analyzing skin-surface blood flow dynamics can be used to noninvasively discriminate the different microcirculatory and physiological function states of breast-cancer patients with chemotherapy between receiving and not receiving Kuan-Sin-Yin (KSY) treatment. The 17 included patients were assigned randomly to 2 comparison groups: Group K (n = 10) received KSY treatment, while Group NK (n = 7) did not receive KSY treatment. Beat-to-beat, spectral, and approximate-entropy (ApEn) analyses were applied to the 20-minute laser-Doppler sequences. The self-reported quality of life and cancer-related symptoms of patients were also investigated. In posttests, Group NK had a significantly larger ApEn ratio than that in Group K, significantly smaller values of laser-Doppler-flowmetry variability indices, and a slightly higher relative energy contribution of the neural-related frequency band compared to those in the pretests. Almost all cancer-related symptoms showed improvements in Group K compared to in Group NK. The present findings indicated that the present analysis can be used to detect the significantly different responses in the laser-Doppler indices between taking and not taking KSY. The KSY effect was also noted to be accompanied with improvement of EORTC QLQ-C30 scores. These could lead to a rapid, inexpensive, and objective technique for enhancing clinical applications in quality-of-life monitoring of breast cancer therapy.

Approximate Entropy and Sample Entropy: A Comprehensive Tutorial

Approximate Entropy and Sample Entropy are two algorithms for determining the regularity of series of data based on the existence of patterns. Despite their similarities, the theoretical ideas behind those techniques are different but usually ignored. This paper aims to be a complete guideline of the theory and application of the algorithms, intended to explain their characteristics in detail to researchers from different fields. While initially developed for physiological applications, both algorithms have been used in other fields such as medicine, telecommunications, economics or Earth sciences. In this paper, we explain the theoretical aspects involving Information Theory and Chaos Theory, provide simple source codes for their computation, and illustrate the techniques with a step by step example of how to use the algorithms properly. This paper is not intended to be an exhaustive review of all previous applications of the algorithms but rather a comprehensive tutorial where no previous knowledge is required to understand the methodology.

Exploring Entropy Measurements to Identify Multi-Occupancy in Activities of Daily Living

Human Activity Recognition (HAR) is the process of automatically detecting human actions from the data collected from different types of sensors. Research related to HAR has devoted particular attention to monitoring and recognizing the human activities of a single occupant in a home environment, in which it is assumed that only one person is present at any given time. Recognition of the activities is then used to identify any abnormalities within the routine activities of daily living. Despite the assumption in the published literature, living environments are commonly occupied by more than one person and/or accompanied by pet animals. In this paper, a novel method based on different entropy measures, including Approximate Entropy (ApEn), Sample Entropy (SampEn), and Fuzzy Entropy (FuzzyEn), is explored to detect and identify a visitor in a home environment. The research has mainly focused on when another individual visits the main occupier, and it is, therefore, not possible to distinguish between their movement activities. The goal of this research is to assess whether entropy measures can be used to detect and identify the visitor in a home environment. Once the presence of the main occupier is distinguished from others, the existing activity recognition and abnormality detection processes could be applied for the main occupier. The proposed method is tested and validated using two different datasets. The results obtained from the experiments show that the proposed method could be used to detect and identify a visitor in a home environment with a high degree of accuracy based on the data collected from the occupancy sensors.

Chaotic Map with No Fixed Points: Entropy, Implementation and Control

A map without equilibrium has been proposed and studied in this paper. The proposed map has no fixed point and exhibits chaos. We have investigated its dynamics and shown its chaotic behavior using tools such as return map, bifurcation diagram and Lyapunov exponents’ diagram. Entropy of this new map has been calculated. Using an open micro-controller platform, the map is implemented, and experimental observation is presented. In addition, two control schemes have been proposed to stabilize and synchronize the chaotic map.

Entropy Mapping Approach for Functional Reentry Detection in Atrial Fibrillation: An In-Silico Study

Catheter ablation of critical electrical propagation sites is a promising tool for reducing the recurrence of atrial fibrillation (AF). The spatial identification of the arrhythmogenic mechanisms sustaining AF requires the evaluation of electrograms (EGMs) recorded over the atrial surface. This work aims to characterize functional reentries using measures of entropy to track and detect a reentry core. To this end, different AF episodes are simulated using a 2D model of atrial tissue. Modified Courtemanche human action potential and Fenton–Karma models are implemented. Action potential propagation is modeled by a fractional diffusion equation, and virtual unipolar EGM are calculated. Episodes with stable and meandering rotors, figure-of-eight reentry, and disorganized propagation with multiple reentries are generated. Shannon entropy (ShEn), approximate entropy (ApEn), and sample entropy (SampEn) are computed from the virtual EGM, and entropy maps are built. Phase singularity maps are implemented as references. The results show that ApEn and SampEn maps are able to detect and track the reentry core of rotors and figure-of-eight reentry, while the ShEn results are not satisfactory. Moreover, ApEn and SampEn consistently highlight a reentry core by high entropy values for all of the studied cases, while the ability of ShEn to characterize the reentry core depends on the propagation dynamics. Such features make the ApEn and SampEn maps attractive tools for the study of AF reentries that persist for a period of time that is similar to the length of the observation window, and reentries could be interpreted as AF-sustaining mechanisms. Further research is needed to determine and fully understand the relation of these entropy measures with fibrillation mechanisms other than reentries.

An Analysis of Entropy-Based Eye Movement Events Detection

Analysis of eye movement has attracted a lot of attention recently in terms of exploring areas of people’s interest, cognitive ability, and skills. The basis for eye movement usage in these applications is the detection of its main components—namely, fixations and saccades, which facilitate understanding of the spatiotemporal processing of a visual scene. In the presented research, a novel approach for the detection of eye movement events is proposed, based on the concept of approximate entropy. By using the multiresolution time-domain scheme, a structure entitled the Multilevel Entropy Map was developed for this purpose. The dataset was collected during an experiment utilizing the “jumping point” paradigm. Eye positions were registered with a 1000 Hz sampling rate. For event detection, the knn classifier was applied. The best classification efficiency in recognizing the saccadic period ranged from 83% to 94%, depending on the sample size used. These promising outcomes suggest that the proposed solution may be used as a potential method for describing eye movement dynamics.

Quaternion Entropy for Analysis of Gait Data

Nonlinear dynamical analysis is a powerful approach to understanding biological systems. One of the most used metrics of system complexities is the Kolmogorov entropy. Long input signals without noise are required for the calculation, which are very hard to obtain in real situations. Techniques allowing the estimation of entropy directly from time signals are statistics like approximate and sample entropy. Based on that, the new measurement for quaternion signal is introduced. This work presents an example of application of a nonlinear time series analysis by using the new quaternion, approximate entropy to analyse human gait kinematic data. The quaternion entropy was applied to analyse the quaternion signal which represents the segments orientations in time during the human gait. The research was aimed at the assessment of the influence of both walking speed and ground slope on the gait control during treadmill walking. Gait data was obtained by the optical motion capture system.

Range Entropy: A Bridge between Signal Complexity and Self-Similarity

Approximate entropy (ApEn) and sample entropy (SampEn) are widely used for temporal complexity analysis of real-world phenomena. However, their relationship with the Hurst exponent as a measure of self-similarity is not widely studied. Additionally, ApEn and SampEn are susceptible to signal amplitude changes. A common practice for addressing this issue is to correct their input signal amplitude by its standard deviation. In this study, we first show, using simulations, that ApEn and SampEn are related to the Hurst exponent in their tolerance r and embedding dimension m parameters. We then propose a modification to ApEn and SampEn called range entropy or RangeEn. We show that RangeEn is more robust to nonstationary signal changes, and it has a more linear relationship with the Hurst exponent, compared to ApEn and SampEn. RangeEn is bounded in the tolerance r-plane between 0 (maximum entropy) and 1 (minimum entropy) and it has no need for signal amplitude correction. Finally, we demonstrate the clinical usefulness of signal entropy measures for characterisation of epileptic EEG data as a real-world example.

Model Selection for Body Temperature Signal Classification Using Both Amplitude and Ordinality-Based Entropy Measures

Many entropy-related methods for signal classification have been proposed and exploited successfully in the last several decades. However, it is sometimes difficult to find the optimal measure and the optimal parameter configuration for a specific purpose or context. Suboptimal settings may therefore produce subpar results and not even reach the desired level of significance. In order to increase the signal classification accuracy in these suboptimal situations, this paper proposes statistical models created with uncorrelated measures that exploit the possible synergies between them. The methods employed are permutation entropy (PE), approximate entropy (ApEn), and sample entropy (SampEn). Since PE is based on subpattern ordinal differences, whereas ApEn and SampEn are based on subpattern amplitude differences, we hypothesized that a combination of PE with another method would enhance the individual performance of any of them. The dataset was composed of body temperature records, for which we did not obtain a classification accuracy above 80% with a single measure, in this study or even in previous studies. The results confirmed that the classification accuracy rose up to 90% when combining PE and ApEn with a logistic model.

Breathing Irregularity Is Independently Associated With the Severity of Obstructive Sleep Apnea in Patients With Multiple System Atrophy

STUDY OBJECTIVES

Multiple system atrophy (MSA) is a neurodegenerative disease characterized by the combination of cerebellar ataxia, parkinsonism, and autonomic disturbance. Patients with MSA frequently have sleep-disordered breathing. In some patients with MSA, central sleep apnea manifests during the disease's natural course or as a treatment effect. Breathing instability may be involved in the development of obstructive sleep apnea (OSA); therefore, we investigated whether breathing instability affects the severity of OSA in patients with MSA.

METHODS

Patients with MSA and a control group of individuals who were matched for age, body mass index (BMI), and supine apnea-hypopnea index (AHI) were recruited. Breathing instability was evaluated by using polysomnography to determine the irregular pattern with approximate entropy (ApEn) of chest respiratory movements during wakefulness before sleep onset. The ApEn values were compared between the groups. The severity of OSA was evaluated with background parameters and ApEn values by regression analysis.

RESULTS

Twenty patients with MSA (9 men; mean age, 61 years; BMI, 24.1 kg/m²; supine AHI, 37.9 events/h) were compared to the control group. The ApEn values were higher in the patients with MSA than those in the control group (1.28 versus 1.11; P < .05). Multiple regression analysis showed that supine AHI was associated with ApEn values but not with BMI in patients with MSA and associated with BMI but not with ApEn values in the individuals in the control group.

CONCLUSIONS

Patients with MSA had more breathing irregularity. In patients with MSA, breathing instability may be a more influential factor for OSA than BMI.

COMMENTARY

A commentary on this article appears in this issue on page 1641.

Fractional Form of a Chaotic Map without Fixed Points: Chaos, Entropy and Control

In this paper, we investigate the dynamics of a fractional order chaotic map corresponding to a recently developed standard map that exhibits a chaotic behavior with no fixed point. This is the first study to explore a fractional chaotic map without a fixed point. In our investigation, we use phase plots and bifurcation diagrams to examine the dynamics of the fractional map and assess the effect of varying the fractional order. We also use the approximate entropy measure to quantify the level of chaos in the fractional map. In addition, we propose a one-dimensional stabilization controller and establish its asymptotic convergence by means of the linearization method.

Functional brain dynamic analysis of ADHD and control children using nonlinear dynamical features of EEG signals

Attention deficit hyperactivity disorder is a neurodevelopmental condition associated with varying levels of hyperactivity, inattention, and impulsivity. This study investigates brain function in children with attention deficit hyperactivity disorder using measures of nonlinear dynamics in EEG signals during rest. During eyes-closed resting, 19 channel EEG signals were recorded from 12 ADHD and 12 normal age-matched children. We used the multifractal singularity spectrum, the largest Lyapunov exponent, and approximate entropy to quantify the chaotic nonlinear dynamics of these EEG signals. As confirmed by Wilcoxon rank sum test, largest Lyapunov exponent over left frontal-central cortex exhibited a significant difference between ADHD and the age-matched control groups. Further, mean approximate entropy was significantly lower in ADHD subjects in prefrontal cortex. The singularity spectrum was also considerably altered in ADHD compared to control children. Evaluation of these features was performed by two classifiers: a Support Vector Machine and a Radial Basis Function Neural Network. For better comparison, subject classification based on frequency band power was assessed using the same types of classifiers. Nonlinear features provided better discrimination between ADHD and control than band power features. Under four-fold cross validation testing, support vector machine gave 83.33% accurate classification results.

Estimation of Complexity of Sampled Biomedical Continuous Time Signals Using Approximate Entropy

Non-linear analysis found many applications in biomedicine. Approximate entropy (ApEn) is a popular index of complexity often applied to biomedical data, as it provides quite stable indications when processing short and noisy epochs. However, ApEn strongly depends on parameters, which were chosen in the literature in wide ranges. This paper points out that ApEn depends on sampling rate of continuous time signals, embedding dimension, tolerance (under which a match is identified), epoch duration and low frequency trends. Moreover, contradicting results can be obtained changing parameters. This was found both in simulations and in experimental EEG. These limitations of ApEn suggest the introduction of an alternative index, here called modified ApEn, which is based on the following principles: oversampling is compensated, self-recurrences are ignored, a fixed percentage of recurrences is selected and low frequency trends are removed. The modified index allows to get more stable measurements of the complexity of the tested simulated data and EEG. The final conclusions are that, in order to get a reliable estimation of complexity using ApEn, parameters should be chosen within specific ranges, data must be sampled close to the Nyquist limit and low frequency trends should be removed. Following these indications, different studies could be more easily compared, interpreted and replicated. Moreover, the modified ApEn can be an interesting alternative, which extends the range of parameters for which stable indications can be achieved.

Verification of a Method for Measuring Parkinson's Disease Related Temporal Irregularity in Spiral Drawings

Parkinson’s disease (PD) is a progressive movement disorder caused by the death of dopamine-producing cells in the midbrain. There is a need for frequent symptom assessment, since the treatment needs to be individualized as the disease progresses. The aim of this paper was to verify and further investigate the clinimetric properties of an entropy-based method for measuring PD-related upper limb temporal irregularities during spiral drawing tasks. More specifically, properties of a temporal irregularity score (TIS) for patients at different stages of PD, and medication time points were investigated. Nineteen PD patients and 22 healthy controls performed repeated spiral drawing tasks on a smartphone. Patients performed the tests before a single levodopa dose and at specific time intervals after the dose was given. Three movement disorder specialists rated videos of the patients based on the unified PD rating scale (UPDRS) and the Dyskinesia scale. Differences in mean TIS between the groups of patients and healthy subjects were assessed. Test-retest reliability of the TIS was measured. The ability of TIS to detect changes from baseline (before medication) to later time points was investigated. Correlations between TIS and clinical rating scores were assessed. The mean TIS was significantly different between healthy subjects and patients in advanced groups (p-value = 0.02). Test-retest reliability of TIS was good with Intra-class Correlation Coefficient of 0.81. When assessing changes in relation to treatment, TIS contained some information to capture changes from Off to On and wearing off effects. However, the correlations between TIS and clinical scores (UPDRS and Dyskinesia) were weak. TIS was able to differentiate spiral drawings drawn by patients in an advanced stage from those drawn by healthy subjects, and TIS had good test-retest reliability. TIS was somewhat responsive to single-dose levodopa treatment. Since TIS is an upper limb high-frequency-based measure, it cannot be detected during clinical assessment.