Accurate estimation of peak vertical ground reaction force using the duty factor in level treadmill running

Abstract

This study aimed to (1) construct a statistical model (SMM) based on the duty factor (DF) to estimate the peak vertical ground reaction force ( $F_{v,\max }$ ) and (2) to compare the estimated $F_{v,\max }$ to force plate gold standard (GSM). One hundred and fifteen runners ran at 9, 11, and 13 km/h. Force (1000 Hz) and kinematic (200 Hz) data were acquired with an instrumented treadmill and an optoelectronic system, respectively, to assess force-plate and kinematic based DFs. SMM linearly relates $F_{v,\max }$ to the inverse of DF because DF was analytically associated with the inverse of the average vertical force during ground contact time and the latter was very highly correlated to $F_{v,\max }$ . No systematic bias and a 4% root mean square error (RMSE) were reported between GSM and SMM using force-plate based DF values when considering all running speeds together. Using kinematic based DF values, SMM reported a systematic but small bias (0.05BW) and a 5% RMSE when considering all running speeds together. These findings support the use of SMM to estimate $F_{v,\max }$ during level treadmill runs at endurance speeds if underlying DF values are accurately measured.

Keywords: biomechanics; curve fitting; gait analysis; linear regression; statistical model.