The relationship between gait mechanics and running ground reaction forces is widely regarded as complex. This viewpoint has evolved primarily via efforts to explain the rising edge of vertical forcetime waveforms observed during slow human running. Existing theoretical models do provide good rising-edge fits, but require more than a dozen input variables to sum the force contributions of four or more vague components of the body's total mass (m b ). Here, we hypothesized that the force contributions of two discrete body mass components are sufficient to account for vertical ground reaction forcetime waveform patterns in full (stance foot and shank, m 1 =0.08m b ; remaining mass, m 2 =0.92m b ). We tested this hypothesis directly by acquiring simultaneous limb motion and ground reaction force data across a broad range of running speeds (3.0-11.1 m s −1) from 42 subjects who differed in body mass (range: 43-105 kg) and foot-strike mechanics. Predicted waveforms were generated from our two-mass model using body mass and three stride-specific measures: contact time, aerial time and lower limb vertical acceleration during impact. Measured waveforms (N=500) differed in shape and varied by more than twofold in amplitude and duration. Nonetheless, the overall agreement between the 500 measured waveforms and those generated independently by the model approached unity (R 2 =0.95 ±0.04, mean±s.d.), with minimal variation across the slow, medium and fast running speeds tested (ΔR 2 ≤0.04), and between rear-foot (R 2 =0.94±0.04, N=177) versus fore-foot (R 2 =0.95±0.04, N=323) strike mechanics. We conclude that the motion of two anatomically discrete components of the body's mass is sufficient to explain the vertical ground reaction force-time waveform patterns observed during human running.
Running performance, energy requirements and musculoskeletal stresses are directly related to the action-reaction forces between the limb and the ground. For human runners, the force-time patterns from individual footfalls can vary considerably across speed, footstrike and footwear conditions. Here, we used four human footfalls with distinctly different vertical force-time waveform patterns to evaluate whether a basic mechanical model might explain all of them. Our model partitions the body's total mass (1.0M b ) into two invariant mass fractions (lower limb=0.08, remaining body mass=0.92) and allows the instantaneous collisional velocities of the former to vary. The best fits achieved (R 2 range=0.95-0.98, mean=0.97±0.01) indicate that the model is capable of accounting for nearly all of the variability observed in the four waveform types tested: barefoot jog, rear-foot strike run, fore-foot strike run and fore-foot strike sprint. We conclude that different running ground reaction force-time patterns may have the same mechanical basis.
Although running shoes alter foot-ground reaction forces, particularly during impact, how they do so is incompletely understood. Here, we hypothesized that footwear effects on running ground reaction force-time patterns can be accurately predicted from the motion of two components of the body’s mass (mb): the contacting lower-limb (m1 = 0.08mb) and the remainder (m2 = 0.92mb). Simultaneous motion and vertical ground reaction force-time data were acquired at 1,000 Hz from eight uninstructed subjects running on a force-instrumented treadmill at 4.0 and 7.0 m/s under four footwear conditions: barefoot, minimal sole, thin sole, and thick sole. Vertical ground reaction force-time patterns were generated from the two-mass model using body mass and footfall-specific measures of contact time, aerial time, and lower-limb impact deceleration. Model force-time patterns generated using the empirical inputs acquired for each footfall matched the measured patterns closely across the four footwear conditions at both protocol speeds ( r2 = 0.96 ± 0.004; root mean squared error = 0.17 ± 0.01 body-weight units; n = 275 total footfalls). Foot landing angles (θF) were inversely related to footwear thickness; more positive or plantar-flexed landing angles coincided with longer-impact durations and force-time patterns lacking distinct rising-edge force peaks. Our results support three conclusions: 1) running ground reaction force-time patterns across footwear conditions can be accurately predicted using our two-mass, two-impulse model, 2) impact forces, regardless of foot strike mechanics, can be accurately quantified from lower-limb motion and a fixed anatomical mass (0.08mb), and 3) runners maintain similar loading rates (ΔFvertical/Δtime) across footwear conditions by altering foot strike angle to regulate the duration of impact. NEW & NOTEWORTHY Here, we validate a two-mass, two-impulse model of running vertical ground reaction forces across four footwear thickness conditions (barefoot, minimal, thin, thick). Our model allows the impact portion of the impulse to be extracted from measured total ground reaction force-time patterns using motion data from the ankle. The gait adjustments observed across footwear conditions revealed that runners maintained similar loading rates across footwear conditions by altering foot strike angles to regulate the duration of impact.
Background Although postural control deficits are common following a concussion, the current clinical assessments for postural control tend to resolve within 3 to 10 days after injury. There is a lack of sensitive tools to examine subtle changes in postural control during the recovery phase following sports‐related concussion. Only a limited number of studies have examined nonlinear dynamics of postural control; no study has examined this metric longitudinally during the recovery phase following a sports‐related concussion. Objective To examine sway and complexity index of postural control in collegiate athletes during day 3, day 21, and day 90 following a concussion and compare them with noninjured controls. Design Prospective longitudinal case‐control study. Setting University cerebrovascular research laboratory. Participants Thirty‐one male and female collegiate athletes on day 3 following a concussion. Twenty‐eight athletes returned on day 21, and 21 completed assessments on day 90. Twenty‐nine sports‐matched noninjured controls. Methods Center of pressure (COP) measurements obtained during 60‐second quiet standing on a force plate system with either eyes opened or closed. Postural sway was estimated as range and variability of COP in the anteroposterior (AP) and mediolateral planes. Main Outcome Measurements Complexity index of AP COP utilizing multiscale entropy analysis. Results Postural sway measured as AP range (P = .03) and variability (P = .04) during quiet standing with eyes closed were higher on day 3 compared to the controls. Postural sway in the concussed group was comparable to the noninjured controls by day 21 postinjury. However, postural control dynamics utilizing complexity index was lower on day 3 (P < .001) and persisted on day 21 (P < .006) and day 90 (P < .02), despite resolution of abnormal postural sway 21 days postinjury. Conclusion Complexity index utilizing nonlinear dynamics might be a more sensitive objective biomarker for examining postural control following a concussion, with implications for return‐to‐play and interventions. Future studies with a larger sample size are needed to validate this finding. Clinical Trial Number NCT02754206. Level of Evidence III.
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