Uncertainty analysis for stride-time-derived modelling of lower limb stiffness: applying Taylor series expansion for error propagation on Monte-Carlo simulated data

Knowledge of uncertainty is valuable mainly in correctly appraising measured effects. In lower limb stiffness, which affects injury risk and athletic performance, uncertainty is often related to vertical (Kvert) and leg (Kleg) stiffness. Imprecisions in measurements of body mass (M), leg length (L), contact (tc) and flight (tf) time propagate through the calculations, augment stiffness uncertainty and inflate relevant effects. This study estimated the limits of this uncertainty as probable (Eprob) and upper bound (Eupper) errors by applying Taylor series expansion on Monte-Carlo simulated data. Eprob and Eupper were 1285 ± 221 N/m (3.9 ± 0.2%) and 1441 ± 248 N/m (4.4 ± 0.3%) in Kvert, and 222 ± 61 N/m (2.1 ± 0.1%) and 375 ± 109 N/m (3.6 ± 0.3%) in Kleg, respectively. To avoid the complexities of full Taylor series expansion, Eprob was predicted (R2 ≈ 1) more simply as 0.89Eupper in Kvert and 11 + 0.56Eupper in Kleg. These uncertainties reflect mostly errors in tc and tf, and uncertainty in Fmax, at kinematic sampling of 300 Hz and running at 4-5 m/s. With slower sampling or faster running these uncertainties rise, and their impact on similar lower limb stiffness effects could be substantial. Applying Taylor series expansion for error propagation on Monte-Carlo simulated data is valid for uncertainty analysis in any multivariable functional relationship.

Hopping skill in individuals with Down syndrome: A qualitative and quantitative assessment

INTRODUCTION

Individuals with Down syndrome (DS) show a delayed acquisition of gross motor skills. Among gross motor skills, hopping is a particular form of jumping that can be performed using one leg. Despite its large use during play and physical activity, this skill in adults with DS has not received much attention so far. Here, we aim at investigating hopping skill in adults with DS both from a quantitative and qualitative point of view.

METHODS

Center of mass and dominant leg kinematics during hopping over distance were recorded from 24 adult individuals with DS and from 21 typically developed adults (TD) using two inertial measurement units positioned on the posterior aspect of the lower back and on the lateral malleolus of the hopping leg. From linear acceleration and angular velocity signals, hopping frequency (HF), cycle, stance and flight duration (CD, SD, FD), vertical stiffness (K_V) and peak to peak linear acceleration and angular velocities about the cranio-caudal, antero-posterior and medio-lateral axes were extracted. A qualitative process assessment of the hopping skill was carried out using the performance criteria of the test for gross motor development (TGMD-3). The extracted parameters were submitted to analysis of covariance, with stature as a covariate to rule-out possible confounding effects.

RESULTS

The qualitative assessment highlighted a poorer hopping performance in the DS group compared to the TD group. DS participants showed higher HF and K_V, shorter CD, SD, FD and lower angular velocity about the cranio-caudal axis compared to the TD group. Significant correlations between the temporal parameters of the quantitative assessment and the results of the qualitative assessment were observed.

DISCUSSION

The poorer motor competence in hopping in individuals with DS compared to TD peers may be related to the shorter flight time and higher vertical stiffness observed in TD peers. The adopted instrumental approach, overcoming the limitations of subjective evaluations, represents a promising opportunity to quantify motor competence in hopping.

The relationship between vertical stiffness during bilateral and unilateral hopping tests performed with different strategies and vertical jump performances

Vertical stiffness has been highlighted as a potential determinant of performance and may be estimated across a range of different performance tasks. The aim of the current study was to investigate the relationship between vertical stiffness determined during 9 different hopping tests and performance of vertical jumps. Twenty healthy, active males performed vertical hopping tests with three different strategies (self-selected, maximal, and controlled) and three different limb configurations (bilateral, unilateral preferred, and unilateral non-preferred), resulting in nine different variations, during which vertical stiffness was determined. In addition, participants performed squat jump (SQJ) and countermovement jump (CMJ) during which jump height, CMJ stiffness, and eccentric utilization ratio (EUR) were determined. Vertical stiffness in bilateral and unilateral preferred tasks performed with a self-selected and maximal, but not controlled, strategy was associated with stiffness in the CMJ (r = 0.61-0.64; p < 0.05). However, stiffness obtained during unilateral preferred and non-preferred hopping with self-selected strategy was negatively associated with performance in SQJ and CMJ tasks (r = -0.50 to -0.57; p < 0.05). These findings suggest that high levels of vertical stiffness may be disadvantageous to static vertical jumping performance. In addition, unilateral hopping with a self-selected strategy may be the most appropriate task variation if seeking to determine relationships with vertical jumping performance. HighlightsStiffness obtained during unilateral hopping with a preferred strategy was negatively associated with vertical jumping performancesStiffness obtained during hopping with preferred and maximal strategies was associated with stiffness obtained during a countermovement jumpIn this population, hopping stiffness may therefore be reflective of an individual's countermovement jump strategyHigh levels of stiffness may be disadvantageous to static-start vertical jumping.

Coordination dynamics of hopping on a mini-trampoline in adults and children

BACKGROUND

While mini-trampolines have been used among a variety of groups including children as an intervention tool, the motor behavior children adopt while hopping on this soft, elastic surface is unknown. Identifying coordinative structures and their stability for hopping on a mini-trampoline is imperative for recommending future interventions and determining appropriateness to populations with motor dysfunctions.

RESEARCH QUESTION

Do children demonstrate similar biomechanical and coordination patterns as adults while hopping on a mini-trampoline?

METHODS

Fifteen adults aged 18-35 years and 14 children aged 7-12 years completed bouts of continuous two-legged hopping in-place on a stiff surface for 10 s at a time and on a mini-trampoline for 30 s at a time. 3-D motion capture tracked whole-body movement. We evaluated whole-body vertical stiffness as a ratio of peak vertical force and peak vertical displacement, as well as spatiotemporal parameters of hopping. Coordinative structures were evaluated as continuous relative phase angles of the foot, shank, thigh, and pelvis segments.

RESULTS AND SIGNIFICANCE

Adults did not modify whole-body vertical stiffness on a mini-trampoline, while children increased whole-body vertical stiffness to compensate for the reduced surface stiffness. Both groups conserved the coordinative structure for hopping on a mini-trampoline by modulating hopping cycle timing. Moreover, children hopped with an adult-like coordinative structure, but required greater shank-thigh and thigh-pelvis out-of-phase motion. However, the consistency of their coordination was diminished compared to adults. Children aged 7-12 years old have formed a stable coordinative structure for spring-mass center-of-mass dynamics that is preserved on this soft, elastic surface. However, children might be developing control strategies for preferred whole-body vertical stiffness, particularly when required to dampen peak vertical forces. These results highlight the importance of evaluating the emerging motor behavior to manipulated environmental constraints, particularly when considering the utility and appropriateness of mini-trampoline interventions for children with motor dysfunctions.

Asymmetry between lower limbs during rested and fatigued state running gait in healthy individuals

Although normal gait is often considered symmetrical in healthy populations, differences between limbs during walking suggest that limbs may be used preferentially for braking or propulsion. The purpose of this study was to evaluate kinematic and kinetic variables, at both rested state and following a two-stage treadmill fatiguing run, for asymmetry between limbs. Kinematic (240Hz) and kinetic (960Hz) running data were collected bilaterally for 20 physically active individuals at both rested and fatigued states. Symmetry angles were calculated to quantify asymmetry magnitude at rested and fatigued states. Paired t-tests were used to evaluate differences between right and left limbs at rested and fatigued states, as well as rested and fatigued states symmetry angles. Variables that have been previously associated with the development of overuse injuries, such as knee internal rotation, knee stiffness, loading rate, and adduction free moment, were found to be significantly different between limbs at both rested and fatigued states. Significant differences in vertical stiffness were found, potentially indicating functional asymmetry during running. Symmetry angle was used to investigate changes in percentage of asymmetry at rested and fatigued states. Small (1-6%), but significant decreases in vertical stiffness, loading rate, and free moment symmetry angles indicate that these variables may become more symmetrical with fatigue. Knee internal rotation and knee stiffness became more asymmetrical with fatigue, increasing by 14% and 5.3%, respectively. The findings of the current study indicate that fatigue induced changes in gait may progress knee movement pattern asymmetry.

Validity and reliability of three methods of stiffness assessment

BACKGROUND

Stiffness is commonly assessed in relation to injury and athletic performance. The purpose of this research was to compare the validity and reliability of 3 in vivo methods of stiffness assessment using 1 cohort of participants.

METHODS

To determine inter-day reliability, 15 female netballers were assessed for stiffness twice within 1 week using unilateral hopping (vertical stiffness), free oscillations of the calf, and myometry of various muscles of the triceps surae. To establish convergent construct validity, stiffness was compared to static and dynamic strength measurements.

RESULTS

Test-retest stiffness results revealed that vertical stiffness produced moderate to high reliability results and myometry presented moderate to very high reliability. In contrast, the free oscillation technique displayed low to moderate reliability. Vertical stiffness demonstrated a significant correlation with rate of force development during a squat jump, whilst myometer stiffness measurements from 3 sites in the lower limb revealed significant correlations with isometric rate of force development. Further, significant negative correlations were evident between the eccentric utilisation ratio and various myometer stiffness results. No relationships were established between the free oscillation technique and any of the performance measurements.

CONCLUSION

These results suggest that vertical stiffness and myometry are valid and reliable methods for assessing stiffness.

Does providing real-time augmented feedback affect the performance of repeated lower limb loading to exhaustion?

INTRODUCTION

This study aimed to determine whether real-time augmented feedback influenced performance of single-leg hopping to volitional exhaustion.

METHODS

Twenty-seven healthy, male participants performed single-leg hopping (2.2 Hz) with (visual and tactile feedback for a target hop height) or without feedback on a force plate. Repeated measures ANOVA were used to determine differences in vertical stiffness (k), duration of flight (tf) and loading (tl) and vertical height displacement during flight (zf) and loading (zl). A Friedman 2-way ANOVA was performed to compare the percentage of trials between conditions that were maintained at 2.2 Hz ± 5%. Correlations were performed to determine if the effects were similar when providing tactile or visual feedback synchronously with the audible cue.

RESULTS

Augmented feedback resulted in maintenance of the tf, zf and zl between the start and end of the trials compared to hopping with no feedback (p<0.01). With or without feedback there was no change in tl and k from start to end. Without feedback, 21 of 27 participants maintained >70% of total hops at 2.2 ± 5% Hz and this was significantly lower (p=0.01) with tactile (13/27) and visual (15/27) feedback. There was a strong correlation between tactile and visual feedback for duration of hopping cycle (Spearman's r=0.74, p ≤ 0.01).

CONCLUSION

Feedback was detrimental to being able to maintain hopping cadence in some participants while other participants were able to achieve the cadence and target hop height. This indicates variability in the ability to use real-time augmented feedback effectively.

The effect of leg compression garments on the mechanical characteristics and performance of single-leg hopping in healthy male volunteers

Background

Compression garments (CG) are commonly used by athletes to improve motor performance and recovery during or following exercise. Numerous studies have investigated the effect of CG on physiological and physical parameters with variable results as to their efficacy. A possible effect of commercially available CG may be to induce a change in leg mechanical characteristics during repetitive tasks to fatigue. This investigation determined the effect of CG on performance and vertical stiffness during single-leg-hopping to exhaustion.

Methods

Thirty-eight healthy, male participants, mean (SD) 22.1 (2.8) years of age performed single-leg hopping at 2.2 Hz to volitional exhaustion with a CG, without CG and with a sham. Differences in total duration of hopping (1-way repeated ANOVA) and dependant variables for the start and end periods (2-way repeated ANOVA) including duration of flight (t_f), loading (t_l) and contact (t_c) phases, vertical height displacement during flight (z_f) and loading (z_l) phases, normalised peak vertical ground reaction force (F_zN) and normalised vertical stiffness (k_N), were determined. Bonferroni correction was performed to reduce the risk of type 1 error.

Results

There was no significant difference (p = 0.73) in the total duration of hopping between conditions (CG (mean (SD)) 89.6 (36.3) s; without CG 88.5 (27.5) s; sham 91.3 (27.7) s). There were no significant differences between conditions for spatiotemporal or kinetic characteristics (p > 0.05). From the start to the end periods there was no significant difference in t_l (p = 0.15), significant decrease in t_f (p < 0.001), z_f and z_l (p < 0.001) and increase in t_c (p < 0.001). There was also a significant increase in k_N from start to end periods (p < 0.01) ranging from 9.6 to 14.2%.

Conclusions

This study demonstrates that commercially available CG did not induce a change in spatiotemporal or vertical stiffness during a fatiguing task. The finding that vertical stiffness increased towards the end of the task, while hopping frequency and duration of loading were maintained, may indicate that there was an alteration to the motor control strategy as fatigue approached.

Trial registration

Current Controlled Trials ACTRN12615000240549. Registered 17 March 2015.

Leg stiffness: comparison between unilateral and bilateral hopping tasks

Leg stiffness is a predictor of athletic performance and injury and typically evaluated during bilateral hopping. The contribution of each limb to bilateral leg stiffness, however, is not well understood. This study investigated leg stiffness during unilateral and bilateral hopping to address the following research questions: (1) does the magnitude and variability of leg stiffness differ between dominant and non-dominant legs? (2) Does unilateral leg stiffness differ from bilateral leg stiffness? and (3) Is bilateral leg stiffness determined by unilateral leg stiffness? Thirty-two physically active males performed repeated hopping tests on a force platform for each of the three conditions: bilateral hopping, unilateral hopping on the dominant leg, and unilateral hopping on the non-dominant leg. Leg stiffness was estimated as the ratio of the peak vertical force and the maximum displacement using a simple 1-D mass-spring model. Neither the magnitude nor variability of leg stiffness differed between dominant and non-dominant limbs. Unilateral leg stiffness was 24% lower than bilateral stiffness and showed less variability between consecutive hops and subjects. Unilateral leg stiffness explained 76% of the variance in bilateral leg stiffness. We conclude that leg stiffness estimates during unilateral hopping are preferable for intervention studies because of their low variability.