Multiscale Transfer Spectral Entropy for Quantifying Corticomuscular Interaction

Corticomuscular coupling reflects nonlinear interactions and multi-layer neural information transmission between the motor cortex and effector muscle in the sensorimotor system. Transfer spectral entropy (TSE) method has been used to describe corticomuscular coupling within single scale. As an extension of TSE, multiscale transfer spectral entropy (MSTSE) is proposed in this paper to depict multi-layer of neural information transfer between two coupling signals. The reliability and effectiveness of MSTSE were verified on data generated by nonlinear numerical models and those of a force tracking task. Compared with TSE, MSTSE is more robust to the embedding dimension and performs optimally in the detection of the coupling properties. Further analysis of the physiological signals showed that the MSTSE provided more detailed band characteristics than the single scale TSE measurement. MSTSE indicates significant coupling scattered in alpha, beta and low gamma bands during the force tracking task. Besides, the coupling strength in the descending direction of the beta band was significantly higher than that in the ascending direction. This study constructs multi-scale coupling information to provide a new perspective for exploring corticomuscular interaction.

Exploring the relationship between the speed-resolved perfusion of blood flux and HRV following different thermal stimulations using MSE and MFE analyses

Our previous study employed the classic laser Doppler flux (LDF) to explore the complexity of local blood flow signals and their relationship with heart rate variability (HRV). However, microcirculation blood flow is composed of different velocity components. To investigate the complexity of local speed-resolved perfusion and HRV following stimulation with different temperatures in healthy subjects, multiscale entropy (MSE) and multiscale fuzzy entropy (MFE) were used to measure the complexity of local speed-resolved perfusion signals. MSE was also used to evaluate the complexity of HRV. The results indicated that thermal stimulation increased all components of local speed-resolved perfusion and that stimulation with different temperatures resulted in different changes in the complexity area index. However, the same stimulation had no effect on the MSE of HRV. Further research showed that 44°C thermal stimulation resulted in a weak correlation between the composite speed-resolved perfusion and the HRV complexity. The current study provides a new approach for studying the relationship between speed-resolved perfusion signals and cardiac function.

Bi-dimensional multiscale entropy: Relation with discrete Fourier transform and biomedical application

The multiscale entropy (MSE_1D) measure is now widely used to quantify the complexity of time series. The development of complexity measures for images is also a long-standing goal. Recently, the bi-dimensional version of MSE_1D has been proposed (MSE_2D) to analyze images. The interpretation of MSE_2D curves and the applications to real data are still emergent. Because the coarse-graining step in the MSE_2D computation changes the frequency content of the image, we hypothesized a possible dependence between MSE_2D and the discrete Fourier transform (DFT). To analyze this dependence, synthetic as well as biomedical images are analyzed. Our results reveal that i) the profile of MSE_2D is sensitive to both the amplitude and phase of the DFT; ii) MSE_2D could find applications in the biomedical field. This work brings valuable information for MSE_2D interpretation and opens possibilities to study images from an entropy point of view through spatial scales.

Exploring the Relationship between Blood Flux Signals and HRV following Different Thermal Stimulations using Complexity Analysis

To investigate the relationship between local blood flux and heart rate variability following different thermal stimulations, healthy subjects were recruited and subject to different thermal stimulations on the right forearm. Multiscale entropy and multiscale fuzzy entropy were used to measure the complexity of the local blood flux, and the approximate entropy was calculated to evaluate the HRV complexity. The results indicated that thermal stimulation significantly increased local blood flux and that different temperature stimulations resulted in different complexities in local blood flux. A 42 °C or 44 °C thermal stimulation, other than stimulations below 42 °C, resulted in a moderate correlation between local blood flux and heart rate variability complexity. The results provide a new perspective in terms of complexity to explore the relationship between skin blood flux signals and cardiac function.

Aging effect on microcirculation: A multiscale entropy approach on laser speckle contrast images

PURPOSE

It has long been known that age plays a crucial role in the deterioration of microvessels. The assessment of such deteriorations can be achieved by monitoring microvascular blood flow. Laser speckle contrast imaging (LSCI) is a powerful optical imaging tool that provides two-dimensional information on microvascular blood flow. The technique has recently been commercialized, and hence, few works discuss the postacquisition processing of laser speckle contrast images recorded in vivo. By applying entropy-based complexity measures to LSCI time series, we present herein the first attempt to study the effect of aging on microcirculation by measuring the complexity of microvascular signals over multiple time scales.

METHODS

Forearm skin microvascular blood flow was studied with LSCI in 18 healthy subjects. The subjects were subdivided into two age groups: younger (20-30 years old, n = 9) and older (50-68 years old, n = 9). To estimate age-dependent changes in microvascular blood flow, we applied three entropy-based complexity algorithms to LSCI time series.

RESULTS

The application of entropy-based complexity algorithms to LSCI time series can differentiate younger from older groups: the data fluctuations in the younger group have a significantly higher complexity than those obtained from the older group.

CONCLUSIONS

The effect of aging on microcirculation can be estimated by using entropy-based complexity algorithms to LSCI time series.

Exploring total cardiac variability in healthy and pathophysiological subjects using improved refined multiscale entropy

Multiscale entropy (MSE) and refined multiscale entropy (RMSE) techniques are being widely used to evaluate the complexity of a time series across multiple time scales 't'. Both these techniques, at certain time scales (sometimes for the entire time scales, in the case of RMSE), assign higher entropy to the HRV time series of certain pathologies than that of healthy subjects, and to their corresponding randomized surrogate time series. This incorrect assessment of signal complexity may be due to the fact that these techniques suffer from the following limitations: (1) threshold value 'r' is updated as a function of long-term standard deviation and hence unable to explore the short-term variability as well as substantial variability inherited in beat-to-beat fluctuations of long-term HRV time series. (2) In RMSE, entropy values assigned to different filtered scaled time series are the result of changes in variance, but do not completely reflect the real structural organization inherited in original time series. In the present work, we propose an improved RMSE (I-RMSE) technique by introducing a new procedure to set the threshold value by taking into account the period-to-period variability inherited in a signal and evaluated it on simulated and real HRV database. The proposed I-RMSE assigns higher entropy to the age-matched healthy subjects than that of patients suffering from atrial fibrillation, congestive heart failure, sudden cardiac death and diabetes mellitus, for the entire time scales. The results strongly support the reduction in complexity of HRV time series in female group, old-aged, patients suffering from severe cardiovascular and non-cardiovascular diseases, and in their corresponding surrogate time series.

Optimal Selection of Threshold Value 'r' for Refined Multiscale Entropy

Refined multiscale entropy (RMSE) technique was introduced to evaluate complexity of a time series over multiple scale factors 't'. Here threshold value 'r' is updated as 0.15 times SD of filtered scaled time series. The use of fixed threshold value 'r' in RMSE sometimes assigns very close resembling entropy values to certain time series at certain temporal scale factors and is unable to distinguish different time series optimally. The present study aims to evaluate RMSE technique by varying threshold value 'r' from 0.05 to 0.25 times SD of filtered scaled time series and finding optimal 'r' values for each scale factor at which different time series can be distinguished more effectively. The proposed RMSE was used to evaluate over HRV time series of normal sinus rhythm subjects, patients suffering from sudden cardiac death, congestive heart failure, healthy adult male, healthy adult female and mid-aged female groups as well as over synthetic simulated database for different datalengths 'N' of 3000, 3500 and 4000. The proposed RMSE results in improved discrimination among different time series. To enhance the computational capability, empirical mathematical equations have been formulated for optimal selection of threshold values 'r' as a function of SD of filtered scaled time series and datalength 'N' for each scale factor 't'.

Multiscale entropy analysis of different spontaneous motor unit discharge patterns

This study explores a novel application of multiscale entropy (MSE) analysis for characterizing different patterns of spontaneous electromyogram (EMG) signals including sporadic, tonic and repetitive spontaneous motor unit discharges, and normal surface EMG baseline. Two algorithms for MSE analysis, namely, the standard MSE and the intrinsic mode entropy (IMEn) (based on the recently developed multivariate empirical mode decomposition method), were applied to different patterns of spontaneous EMG. Significant differences were observed in multiple scales of the standard MSE and IMEn analyses (<;i>p<;/i> <; 0.001) for any two of the spontaneous EMG patterns, while such significance may not be observed from the single-scale entropy analysis. Compared to the standard MSE, the IMEn analysis facilitates usage of a relatively low scale number to discern entropy difference among various patterns of spontaneous EMG signals. The findings from this study contribute to our understanding of the nonlinear dynamic properties of different spontaneous EMG patterns, which may be related to spinal motoneuron or motor unit health.

Analysis of surface EMG baseline for detection of hidden muscle activity

OBJECTIVE

This study explored the feasibility of detecting hidden muscle activity in surface electromyogram (EMG) baseline.

APPROACH

Power spectral density (PSD) analysis and multi-scale entropy (MSE) analysis were used. Both analyses were applied to computer simulations of surface EMG baseline with the presence (representing activity data) or absence (representing reference data) of hidden muscle activity, as well as surface electrode array EMG baseline recordings of healthy control and amyotrophic lateral sclerosis (ALS) subjects.

MAIN RESULTS

Although the simulated reference data and the activity data yielded no distinguishable difference in the time domain, they demonstrated a significant difference in the frequency and signal complexity domains with the PSD and MSE analyses. For a comparison using pooled data, such a difference was also observed when the PSD and MSE analyses were applied to surface electrode array EMG baseline recordings of healthy control and ALS subjects, which demonstrated no distinguishable difference in the time domain. Compared with the PSD analysis, the MSE analysis appeared to be more sensitive for detecting the difference in surface EMG baselines between the two groups.

SIGNIFICANCE

The findings implied the presence of a hidden muscle activity in surface EMG baseline recordings from the ALS subjects. To promote the presented analysis as a useful diagnostic or investigatory tool, future studies are necessary to assess the pathophysiological nature or origins of the hidden muscle activity, as well as the baseline difference at the individual subject level.