Impact of PCA Pre-Normalization Methods on Ground Reaction Force Estimation Accuracy.

Ground reaction force (GRF) components can be estimated using insole pressure sensors. Principal component analysis in conjunction with machine learning (PCA-ML) methods are widely used for this task. PCA reduces dimensionality and requires pre-normalization. In this paper, we evaluated the impact of twelve pre-normalization methods using three PCA-ML methods on the accuracy of GRF component estimation. Accuracy was assessed using laboratory data from gold-standard force plate measurements. Data were collected from nine subjects during slow- and normal-speed walking activities. We tested the ANN (artificial neural network) and LS (least square) methods while also exploring support vector regression (SVR), a method not previously examined in the literature, to the best of our knowledge. In the context of our work, our results suggest that the same normalization method can produce the worst or the best accuracy results, depending on the ML method. For example, the body weight normalization method yields good results for PCA-ANN but the worst performance for PCA-SVR. For PCA-ANN and PCA-LS, the vector standardization normalization method is recommended. For PCA-SVR, the mean method is recommended. The final message is not to define a normalization method a priori independently of the ML method.

On the Genuine Relevance of the Data-Driven Signal Decomposition-Based Multiscale Permutation Entropy.

Ordinal pattern-based approaches have great potential to capture intrinsic structures of dynamical systems, and therefore, they continue to be developed in various research fields. Among these, the permutation entropy (PE), defined as the Shannon entropy of ordinal probabilities, is an attractive time series complexity measure. Several multiscale variants (MPE) have been proposed in order to bring out hidden structures at different time scales. Multiscaling is achieved by combining linear or nonlinear preprocessing with PE calculation. However, the impact of such a preprocessing on the PE values is not fully characterized. In a previous study, we have theoretically decoupled the contribution of specific signal models to the PE values from that induced by the inner correlations of linear preprocessing filters. A variety of linear filters such as the autoregressive moving average (ARMA), Butterworth, and Chebyshev were tested. The current work is an extension to nonlinear preprocessing and especially to data-driven signal decomposition-based MPE. The empirical mode decomposition, variational mode decomposition, singular spectrum analysis-based decomposition and empirical wavelet transform are considered. We identify possible pitfalls in the interpretation of PE values induced by these nonlinear preprocessing, and hence, we contribute to improving the PE interpretation. The simulated dataset of representative processes such as white Gaussian noise, fractional Gaussian processes, ARMA models and synthetic sEMG signals as well as real-life sEMG signals are tested.

The Refined Composite Downsampling Permutation Entropy Is a Relevant Tool in the Muscle Fatigue Study Using sEMG Signals.

Surface electromyography (sEMG) is a valuable technique that helps provide functional and structural information about the electric activity of muscles. As sEMG measures output of complex living systems characterized by multiscale and nonlinear behaviors, Multiscale Permutation Entropy (MPE) is a suitable tool for capturing useful information from the ordinal patterns of sEMG time series. In a previous work, a theoretical comparison in terms of bias and variance of two MPE variants-namely, the refined composite MPE (rcMPE) and the refined composite downsampling (rcDPE), was addressed. In the current paper, we assess the superiority of rcDPE over MPE and rcMPE, when applied to real sEMG signals. Moreover, we demonstrate the capacity of rcDPE in quantifying fatigue levels by using sEMG data recorded during a fatiguing exercise. The processing of four consecutive temporal segments, during biceps brachii exercise maintained at 70% of maximal voluntary contraction until exhaustion, shows that the 10th-scale of rcDPE was capable of better differentiation of the fatigue segments. This scale actually brings the raw sEMG data, initially sampled at 10 kHz, to the specific 0-500 Hz sEMG spectral band of interest, which finally reveals the inner complexity of the data. This study promotes good practices in the use of MPE complexity measures on real data.

The Impact of Linear Filter Preprocessing in the Interpretation of Permutation Entropy.

Permutation Entropy (PE) is a powerful tool for measuring the amount of information contained within a time series. However, this technique is rarely applied directly on raw signals. Instead, a preprocessing step, such as linear filtering, is applied in order to remove noise or to isolate specific frequency bands. In the current work, we aimed at outlining the effect of linear filter preprocessing in the final PE values. By means of the Wiener-Khinchin theorem, we theoretically characterize the linear filter's intrinsic PE and separated its contribution from the signal's ordinal information. We tested these results by means of simulated signals, subject to a variety of linear filters such as the moving average, Butterworth, and Chebyshev type I. The PE results from simulations closely resembled our predicted results for all tested filters, which validated our theoretical propositions. More importantly, when we applied linear filters to signals with inner correlations, we were able to theoretically decouple the signal-specific contribution from that induced by the linear filter. Therefore, by providing a proper framework of PE linear filter characterization, we improved the PE interpretation by identifying possible artifact information introduced by the preprocessing steps.

Improvement of Statistical Performance of Ordinal Multiscale Entropy Techniques Using Refined Composite Downsampling Permutation Entropy.

Multiscale Permutation Entropy (MPE) analysis is a powerful ordinal tool in the measurement of information content of time series. MPE refinements, such as Composite MPE (cMPE) and Refined Composite MPE (rcMPE), greatly increase the precision of the entropy estimation by modifying the original method. Nonetheless, these techniques have only been proposed as algorithms, and are yet to be described from the theoretical perspective. Therefore, the purpose of this article is two-fold. First, we develop the statistical theory behind cMPE and rcMPE. Second, we propose an alternative method, Refined Composite Downsampling Permutation Entropy (rcDPE) to further increase the entropy estimation's precision. Although cMPE and rcMPE outperform MPE when applied on uncorrelated noise, the results are higher than our predictions due to inherent redundancies found in the composite algorithms. The rcDPE method, on the other hand, not only conforms to our theoretical predictions, but also greatly improves over the other methods, showing the smallest bias and variance. By using MPE, rcMPE and rcDPE to classify faults in bearing vibration signals, rcDPE outperforms the multiscaling methods, enhancing the difference between faulty and non-faulty signals, provided we apply a proper anti-aliasing low-pass filter at each time scale.

On the Statistical Properties of Multiscale Permutation Entropy: Characterization of the Estimator's Variance.

Permutation Entropy (PE) and Multiscale Permutation Entropy (MPE) have been extensively used in the analysis of time series searching for regularities. Although PE has been explored and characterized, there is still a lack of theoretical background regarding MPE. Therefore, we expand the available MPE theory by developing an explicit expression for the estimator's variance as a function of time scale and ordinal pattern distribution. We derived the MPE Cramér-Rao Lower Bound (CRLB) to test the efficiency of our theoretical result. We also tested our formulation against MPE variance measurements from simulated surrogate signals. We found the MPE variance symmetric around the point of equally probable patterns, showing clear maxima and minima. This implies that the MPE variance is directly linked to the MPE measurement itself, and there is a region where the variance is maximum. This effect arises directly from the pattern distribution, and it is unrelated to the time scale or the signal length. The MPE variance also increases linearly with time scale, except when the MPE measurement is close to its maximum, where the variance presents quadratic growth. The expression approaches the CRLB asymptotically, with fast convergence. The theoretical variance is close to the results from simulations, and appears consistently below the actual measurements. By knowing the MPE variance, it is possible to have a clear precision criterion for statistical comparison in real-life applications.

Flexible ECG signal modeling and compression using alpha stable functions.

In this paper, we propose a flexible modeling technique for the ECG signals. Modeling is achieved by considering the weighted summation of elementary functions representing the waveforms that describe each component of the cardiac cycle. We thus evaluate the benefit brought by α-stable functions with respect to Gaussian functions in terms of modeling precision. Seven records from the MIT-BIH arrhythmia database have been used to assess the performances of the proposed modeling method, including Normal beat, Premature Ventricular Contraction beat, Right Bundle Block Branch beat and Paced beat. When applied on the chosen records, it turns out that α-stable modeling always outperforms Gaussian modeling. Since each waveform is related to a particular physiological event in the ECG cardiac cycle, we also exploit flexibility of choosing α-stable modeling instead of Gaussian one for some event of medical interest in order to solve compression purpose efficiency-quality compromise. The comparison of the α-stable model applied in compression with other techniques proves the efficiency of the proposed method, mainly in term of quality score.

Redefining performance evaluation tools for real-time QRS complex classification systems.

In a heartbeat classification procedure, the detection of QRS complex waveforms is necessary. In many studies, this heartbeat extraction function is not considered: the inputs of the classifier are assumed to be correctly identified. This communication aims to redefine classical performance evaluation tools in entire QRS complex classification systems and to evaluate the effects induced by QRS detection errors on the performance of heartbeat classification processing (normal versus abnormal). Performance statistics are given and discussed considering the MIT/BIH database records that are replayed on a real-time classification system composed of the classical detector proposed by Hamilton and Tompkins, followed by a neural-network classifier. This study shows that a classification accuracy of 96.72% falls to 94.90% when a drop of 1.78% error rate is introduced in the detector quality. This corresponds to an increase of about 50% bad classifications.

Decomposition of Multi-Channel Intramuscular EMG Signals by Cyclostationary-Based Blind Source Separation.

We propose a novel decomposition method for electromyographic signals based on blind source separation. Using the cyclostationary properties of motor unit action potential trains (MUAPt), it is shown that the MUAPt can be decomposed by joint diagonalization of the cyclic spatial correlation matrix of the observations. After modeling the source signals, we provide the proof of orthogonality of the sources and of their delayed versions in a cyclostationary context. We tested the proposed method on simulated signals and showed that it can decompose up to six sources with a probability of correct detection and classification >95%, using only eight recording sites. Moreover, we tested the method on experimental multi-channel signals recorded with thin-film intramuscular electrodes, with a total of 32 recording sites. The rate of agreement of the decomposed MUAPt with those obtained by an expert using a validated tool for decomposition was >93%.

Assessment of the non-Gaussianity and non-linearity levels of simulated sEMG signals on stationary segments.

The purpose of this paper was to evaluate the effects of the longitudinal single differential (LSD), the longitudinal double differential (LDD) and the normal double differential (NDD) spatial filters, the electrode shape, the inter-electrode distance (IED) on non-Gaussianity and non-linearity levels of simulated surface EMG (sEMG) signals when the maximum voluntary contraction (MVC) varied from 10% to 100% by a step of 10%. The effects of recruitment range thresholds (RR), the firing rate (FR) strategy and the peak firing rate (PFR) of motor units were also considered. A cylindrical multilayer model of the volume conductor and a model of motor unit (MU) recruitment and firing rate were used to simulate sEMG signals in a pool of 120 MUs for 5s. Firstly, the stationarity of sEMG signals was tested by the runs, the reverse arrangements (RA) and the modified reverse arrangements (MRA) tests. Then the non-Gaussianity was characterised with bicoherence and kurtosis, and non-linearity levels was evaluated with linearity test. The kurtosis analysis showed that the sEMG signals detected by the LSD filter were the most Gaussian and those detected by the NDD filter were the least Gaussian. In addition, the sEMG signals detected by the LSD filter were the most linear. For a given filter, the sEMG signals detected by using rectangular electrodes were more Gaussian and more linear than that detected with circular electrodes. Moreover, the sEMG signals are less non-Gaussian and more linear with reverse onion-skin firing rate strategy than those with onion-skin strategy. The levels of sEMG signal Gaussianity and linearity increased with the increase of the IED, RR and PFR.

Experimental muscle pain changes the spatial distribution of upper trapezius muscle activity during sustained contraction.

OBJECTIVE: To investigate the effect of local excitation of nociceptive muscle afferents on the spatial distribution of muscle activity. METHODS: Surface electromyographic (EMG) signals were recorded from the upper trapezius muscle of 10 healthy volunteers with a 5 x 13 electrode grid during 90-s isometric contractions before, during, 15 and 30 min after intramuscular injection of hypertonic (painful) or isotonic (non-painful) saline. From the multi-channel EMG recordings, two-dimensional maps of root mean square and mean power frequency were obtained. The centre of gravity of the root mean square map was used to quantify global changes in the spatial distribution of muscle activity. RESULTS: During sustained contractions, average root mean square increased, average mean frequency decreased and the centre of gravity moved cranially. During experimental muscle pain, compared to before injection, the average root mean square decreased and there was a caudal shift of the centre of gravity. Fifteen minutes after the painful injection the centre of gravity returned to its original position. CONCLUSIONS: Short-term dynamic reorganization of the spatial distribution of muscle activity occurred in response to nociceptive afferent input. SIGNIFICANCE: The study furnishes an extension of the pain adaptation model indicating heterogeneous inhibition of muscle activity.

An EMG fractal indicator having different sensitivities to changes in force and muscle fatigue during voluntary static muscle contractions.

During a sustained contraction, electromyographic signals (EMGs) undergo a spectral compression. This fatigue behaviour induces a shift of the mean and the median frequencies to lower frequencies. On the other hand, several studies conclude that the mean/median frequency can increase, decrease or remain constant with an increasing force level. Such inconsistency is embarrassing since the fatigue state may be influenced by the force level. In this paper, we propose a frequency indicator which is sensitive to the force level independently of the fatigue state evaluated at 70% of the maximal voluntary contraction. Ten healthy volunteers participated in the study and both surface EMGs (from the short head of the biceps brachii) and force signals were measured. This study compared force and fatigue effects on the EMGs during short (3-s) isometric contractions at different strength intensities and during a sustained isometric contraction until exhaustion. The EMGs partly show 1/falpha spectral behaviours since their power spectral densities may experimentally fit with two linear segments in a log-log representation. The measured "right" slope produces variations of force as 20 times the variations of fatigue. 1/falpha Behaviour may be related to stochastic fractals. This fractal indicator is a new frequency indicator that is thus complementary to other known classical frequency indicators when studying force during unknown fatigue states.

The vastus lateralis neuromuscular activity during all-out cycling exercise.

OBJECTIVE: The objective of this work was to study modifications in motor control through surface electromyographic (sEMG) activity during a very short all-out cycling exercise. METHODS: Twelve male cyclists (age 23+/-4 years) participated in this study. After a warm-up period, each subject performed three all-out cycling exercises of 6s separated by 2 min of complete rest. This protocol was repeated three times with a minimum of 2 days between each session. The braking torque imposed on cycling motion was 19 Nm. The sEMG of the vastus lateralis was recorded during the first seven contractions of the sprint. Time-frequency analysis of sEMG was performed using continuous wavelet transform. The mean power frequency (MPF, qualitative modifications in the recruitment of motor units) and signal energy (a quantitative indicator of modifications in the motor units recruitment) were computed for the frequency range 10-500 Hz. RESULTS: sEMG energy increased (P0.05) between contraction number 1 and 2, decreased (P < or =0.05) between contraction number 2 and 3 then stabilized between contraction number 3 and 7 during the all-out test. MPF increased (P < or =0.05) during the all-out test. This increase was more marked during the first two contractions. CONCLUSIONS: The decrease in energy and the increase in the sEMG MPF suggest a large spatial recruitment of motor units (MUs) at the beginning of the sprint followed by a preferential recruitment of faster MUs at the end of the sprint, respectively.