The linear analysis for heart rate variability (HRV), including time domain method, frequency domain method and timefrequency analysis, has reached a lot of consensus. The nonlinear analysis has also been widely applied in biomedical and clinical researches. However, for nonlinear HRV analysis, especially for shortterm nonlinear HRV analysis, controversy still exists, and a unified standard and conclusion has not been formed. This paper reviews and discusses three shortterm nonlinear HRV analysis methods (fractal dimension, entropy and complexity) and their principles, progresses and problems in clinical application in detail, in order to provide a reference for accurate application in clinical medicine.
Wavelet entropy is a quantitative index to describe the complexity of signals. Continuous wavelet transform method was employed to analyze the spontaneous electroencephalogram (EEG) signals of mild, moderate and severe Alzheimer's disease (AD) patients and normal elderly control people in this study. Wavelet power spectrums of EEG signals were calculated based on wavelet coefficients. Wavelet entropies of mild, moderate and severe AD patients were compared with those of normal controls. The correlation analysis between wavelet entropy and MMSE score was carried out. There existed significant difference on wavelet entropy among mild, moderate, severe AD patients and normal controls (P<0.01). Group comparisons showed that wavelet entropy for mild, moderate, severe AD patients was significantly lower than that for normal controls, which was related to the narrow distribution of their wavelet power spectrums. The statistical difference was significant (P<0.05). Further studies showed that the wavelet entropy of EEG and the MMSE score were significantly correlated (r=0.601-0.799, P<0.01). Wavelet entropy is a quantitative indicator describing the complexity of EEG signals. Wavelet entropy is likely to be an electrophysiological index for AD diagnosis and severity assessment.
Heart sound signal is a kind of physiological signal with nonlinear and nonstationary features. In order to improve the accuracy and efficiency of the phonocardiogram (PCG) classification, a new method was proposed by means of support vector machine (SVM) in which the complete ensemble empirical modal decomposition with adaptive noise (CEEMDAN) permutation entropy was as the eigenvector of heart sound signal. Firstly, the PCG was decomposed by CEEMDAN into a number of intrinsic mode functions (IMFs) from high to low frequency. Secondly, the IMFs were sifted according to the correlation coefficient, energy factor and signal-to-noise ratio. Then the instantaneous frequency was extracted by Hilbert transform, and its permutation entropy was constituted into eigenvector. Finally, the accuracy of the method was verified by using a hundred PCG samples selected from the 2016 PhysioNet/CinC Challenge. The results showed that the accuracy rate of the proposed method could reach up to 87%. In comparison with the traditional EMD and EEMD permutation entropy methods, the accuracy rate was increased by 18%–24%, which demonstrates the efficiency of the proposed method.
Vigilance is defined as the ability to maintain attention for prolonged periods of time. In order to explore the variation of brain vigilance in work process, we designed addition and subtraction experiment with numbers of three digits to induce the vigilance to change, combined it with psychomotor vigilance task (PVT) to measure this process of electroencephalogram (EEG), extracted and analyzed permutation entropy (PE) of 11 cases of subjects' EEG and made a brief comparison with nonlinear parameter sample entropy (SE). The experimental results showed that:PE could well reflect the dynamic changes of EEG when vigilance decreases, and has advantages of fast arithmetic speed, high noise immunity, and low requirements for EEG length. This can be used as a measure of the brain vigilance indicators.
In recent years, exploring the physiological and pathological mechanisms of brain functional integration from the neural network level has become one of the focuses of neuroscience research. Due to the non-stationary and nonlinear characteristics of neural signals, its linear characteristics are not sufficient to fully explain the potential neurophysiological activity mechanism in the implementation of complex brain functions. In order to overcome the limitation that the linear algorithm cannot effectively analyze the nonlinear characteristics of signals, researchers proposed the transfer entropy (TE) algorithm. In recent years, with the introduction of the concept of brain functional network, TE has been continuously optimized as a powerful tool for nonlinear time series multivariate analysis. This paper first introduces the principle of TE algorithm and the research progress of related improved algorithms, discusses and compares their respective characteristics, and then summarizes the application of TE algorithm in the field of electrophysiological signal analysis. Finally, combined with the research progress in recent years, the existing problems of TE are discussed, and the future development direction is prospected.
The study on complexity of glucose fluctuation not only helps us understand the regulation of the glucose homeostasis system but also brings us a new insight of the research methodology on glucose regulation. In the experiments, we analyzed the complexity of the temporal structure of the 72 hours continuous glucose time series from a group of 93 subjects with type Ⅱ diabetes mellitus using the multi-scale entropy method. We adapted the most recently improved refined composite multi-scale entropy (RCMSE) algorithm which could overcome the shortcomings on the 72 hours short time series analysis. We then quantified and compared the complexity of continuous glucose time series between groups with type Ⅱ diabetes mellitus with different mean absolute glycemic excursion (MAGE) and glycated hemoglobin (HbA1c). The results implied that the complexity of glucose time series decreased on lower MAGE group compared to high MAGE group, and the entropy on scale 1 to 6 which corresponded to 5 to 30 min had significant differences between these two groups; the complexity of glucose time series decreased with the increasing HbA1c level but the entropy had no statistical difference among groups at different scales. Therefore, RCMSE provided us with a new prospect to analyze the glucose time series and it was proved that less complexity of glucose dynamics could indicate the impaired gluco-regulation function from the MAGE point of view or HbA1c for patients, and the glucose complexity had the potential to become a new biomarker to reflect the fluctuation of the glucose time series.
This paper explores a methodology used to discriminate the electroencephalograph (EEG) signals of patients with vegetative state (VS) and those with minimally conscious state (MCS). The model was derived from the EEG data of 33 patients in a calling name stimulation paradigm. The preprocessing algorithm was applied to remove the noises in the EEG data. Two types of features including sample entropy and multiscale entropy were chosen. Multiple kernel support vector machine was investigated to perform the training and classification. The experimental results showed that the alpha rhythm features of EEG signals in severe disorders of consciousness were significant. We achieved the average classification accuracy of 88.24%. It was concluded that the proposed method for the EEG signal classification for VS and MCS patients was effective. The approach in this study may eventually lead to a reliable tool for identifying severe disorder states of consciousness quantitatively. It would also provide the auxiliary basis of clinical assessment for the consciousness disorder degree.
To explore the relationship between the drug-seeking behavior, motivation of conditioned place preference (CPP) rats and the frontal association cortex (FrA) electroencephalogram (EEG) sample entropy, we in this paper present our studies on the FrA EEG sample entropy of control group rats and CPP group rats, respectively. We invested different behavior in four situations of the rat activities, i.e. rats were staying in black chamber of videoed boxes, those staying in white chamber of videoed boxes, those shuttling between black-white chambers and those shuttling between white-black chambers. The experimental results showed that, compared with the control group rats, the FrA EEG sample entropy of CPP rats staying in black chamber of video box and shuttling between white-black chambers had no significant difference. However, sample entropy is significantly smaller (P < 0.01) when heroin-induced group rats stayed in white chamber of video box and shuttled between black-white chambers. Consequently, the drug-seeking behavior and motivation of CPP rats correlated closely with the EEG sample entropy changes.
The analysis parameters for the characterization of heart rate variability (HRV) within a very short time (＜1 min) usually exhibit complicate variation patterns over time, which may easily interfere the judgment to the status of the cardiovascular system. In this study, long-term HRV sequence of 41 cases of healthy people (control group) and 25 cases of congestive heart failure (CHF) patients (experimental group) was divided into multiple segments of very short time series. The variation coefficient of the same HRV parameter under multiple segments of very short time series and the testing proportion with statistically significant differences under multiple interclass t-test were calculated. On this account, part of HRV analysis parameters under very short time were discussed to reveal the stability of difference of the cardiovascular system function under different status. Furthermore, with analyzing the receiver operating characteristic (ROC) curve and modeling the artificial neural network (ANN), the classification effects of these parameters between the control group and the experimental group were assessed. The results demonstrated that ① the indices of entropy of degree distribution based on the complex network analysis had a lowest variation coefficient and was sensitive to the pathological status (in 79.75% cases, there has statistically significant differences between the control group and experimental group), which can be served as an auxiliary index for clinical doctor to diagnose for CHF patient; ② after conducting ellipse fitting to Poincare plot, in 98.5% cases, there had statistically significant differences for the ratio of ellipse short-long axis (SDratio) between the control group and the experimental group; when modeling the ANN and solely adopting SDratio, the classification accuracy to the control group and experimental group was 71.87%, which demonstrated that SDratio might be acted as the intelligent diagnosis index for CHF patients; ③ however, more sensitive and robust indices were still needed to find out for the very-short HRV analysis and for the diagnosis of CHF patients as well.
The result of the emotional state induced by music may provide theoretical support and help for assisted music therapy. The key to assessing the state of emotion is feature extraction of the emotional electroencephalogram (EEG). In this paper, we study the performance optimization of the feature extraction algorithm. A public multimodal database for emotion analysis using physiological signals (DEAP) proposed by Koelstra et al. was applied. Eight kinds of positive and negative emotions were extracted from the dataset, representing the data of fourteen channels from the different regions of brain. Based on wavelet transform, δ, θ, α and β rhythms were extracted. This paper analyzed and compared the performances of three kinds of EEG features for emotion classification, namely wavelet features (wavelet coefficients energy and wavelet entropy), approximate entropy and Hurst exponent. On this basis, an EEG feature fusion algorithm based on principal component analysis (PCA) was proposed. The principal component with a cumulative contribution rate more than 85% was retained, and the parameters which greatly varied in characteristic root were selected. The support vector machine was used to assess the state of emotion. The results showed that the average accuracy rates of emotional classification with wavelet features, approximate entropy and Hurst exponent were respectively 73.15%, 50.00% and 45.54%. By combining these three methods, the features fused with PCA possessed an accuracy of about 85%. The obtained classification accuracy by using the proposed fusion algorithm based on PCA was improved at least 12% than that by using single feature, providing assistance for emotional EEG feature extraction and music therapy.