This study was designed to compare neuromuscular response between boys and men during sustained maximal voluntary contraction (MVC). Fifteen boys (YB, 10.5 +/- 0.9 yr) and 12 men (AM, 21.5 +/- 4.5 yr) participated in the experiment. Arm's cross sectional area (CSA) and maximal force (F(max)) of elbow flexor were measured before subjects performed a 30-s sustained MVC. Mean power frequency (MPF) and muscle fiber conduction velocity (MFCV) were calculated from myoelectric signals of the biceps brachii. F(max)/CSA, MPF, and MFCV changes were expressed by slopes of linear regressions. Maximal MPF (I-MPF) and MFCV (I-MFCV) were derived from the intercept of each regression. AM had significantly greater F(max)/CSA (P < 0.05), I-MPF (P < 0.05), and I-MFCV (P < 0.01) than YB. F(max)/CSA (P < 0.001), MPF (P < 0.001), and MFCV (P < 0.01) declined significantly more for AM than YB. MPF/MFCV ratio increased, i.e., MPF decreased more than MFCV, for both groups but this was significantly (P < 0.001) more pronounced for AM. Taken together, those results suggest that more fatigable Type II motor units are involved in men, resulting in greater lactic acid and ions accumulations during fatigue. This difference in muscle's metabolic and ionic state could be responsible for a greater reflex-induced decrease of motor units firing rates in men compared with boys. This firing rate decrease could be explained using the "muscular wisdom" hypothesis and would express a nervous command adaptation to sustain a maximal contraction.

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.

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.