Abstract

Abstract

Abstract

Abstract
This study presents and applies fractal Brownian motion assessment of the center of pressure (COP) excursion during feet ground contact on standard vertical jump impulse phase with long and short countermovement (CM) in relation with lower limb muscle stretch-shortening cycle (SSC) comparing it with no CM and SSC. Fifty-four tests were performed by a group of six healthy male students of sports and physical education degree without previous injury, specific training, or fitness ability. Three repetitions were performed by each subject of a squat jump (SJ) without CM and SSC, countermovement jump (CMJ) with long CM and SSC, as well as drop jump (DJ) with short CM and SSC after depth jump from a 40 cm step. During trial tests ground reaction force and force moments were acquired with force platform and impulse phases were segmented for COP coordinates computation. Fractal Brownian motion analysis of COP excursion during impulse phases conduced to detection of differences between critical time and displacement as well as short and long-term diffusion coefficient (Ds, Dl) and Hurst index scale exponent (Hs, Hl), with Ds, Dl presenting statistical significative correlations -0.491, -0.559 and Hs, Hl non statistical significative correlations 0.266 and -0.424 with MVJ height (ht) at 5% significance for explaining underlying mechanisms on CM and SSC at MVJ. Clinical Relevance- This work contributes with new method for the study expansion of the center of pressure excursion and stability during feet ground contact from orthostatic standing position to the impulse phase during standard maximum vertical jump as the most adequate method for assessment of lower limb muscle stretch-shortening cycle.

Abstract
This study presents principal component analysis (PCA) intra-subject variability of lower limb surface electromyography (sEMG) at different muscle stretch-shortening cycle (SSC). Several key steps are presented on the research of muscle force production for human in-vivo and noninvasive studies as well as on SSC contribution at gait, run, and jump with the need for separation of muscle and tendon behavior. Complexity and unpredicted multiple muscle actuation are highlighted with the need for extraction of PCA components from muscle stretch-shortening cycle sEMG, namely on lower limb stereotyped muscle patterns assessed on standard maximum vertical jump (MVJ). The purpose of this study is to apply PCA to sEMG linear envelopes of lower limb selected muscles at different MVJ, to detect lower number of components explaining maximum sEMG variability, representative of low dimensional signal control on muscles synergies. Different MVJ were assessed with subject specific PCA of lower limb sEMG during Counter Movement Jump (CMJ), Drop Jump (DJ), and Squat Jump (SJ). Intra-subject variability of sEMG PCA allowed the detection of two components explaining maximum variability with different profiles and muscle grouping at CMJ, DJ, and SJ. First component (PC1), representing larger signal variability, presented higher value at SJ and DJ than CMJ, with the need for a higher number of PC's to explain the same cumulative percentual variance at CMJ than DJ and SJ. Comparison with intra-subject linear (r) and cross-correlation (CCr) presented higher r and CCr at SJ and DJ than CMJ, with higher paired correlations at the muscles grouped on the same component. Comparison of intra-subject analysis with previous study on same subject single trial allowed subject-specific generalization of the preceding results.

Abstract
This study presents and applies in vivo lower limb frequency response analysis during standard maximum vertical jump (MVJ) with long and short counter movement (CM) and corresponding muscle stretch shortening cycle (SSC) for comparison without CM and SSC condition. The study makes use of algebraic relation at the frequency domain to obtain the response function from the input and output signals. Single-input/single-output (SI/SO) constant parameter linear system (CPLS) was applied with vertical ground reaction force (GRFz) input and center of gravity (CG) vertical displacement (Delta z) output, obtaining lower limb frequency response function during MVJ impulse phase. Piecewise linearity and limited input-output range of experimentally acquired GRFz and CG Delta z during MVJ impulse phase were assessed to confirm assumptions for CPLS application. Piecewise stationarity of the input and output signal was ensured by acquiring those signals on each MVJ type at similar conditions, guaranteeing experimental repetitions under statistical similar conditions on each CM. Different CM condition on each MVJ type were compared as regards to maximum vertical height, time period of the impulse phase, fundamental harmonic frequencies, convergence of the GRFz input and CG Delta z output Fourier series, their autospectral and cross-spectral density, as well as its input-output coherence, cross-spectrum gain factor, and phase of the frequency response function. Several differences were detected among CM condition, potentially contributing to explain differences on achieved performances at each CM and SSC.