Both a single sacral marker and the whole-body center of mass accurately estimate peak vertical ground reaction force in running.

While running, the human body absorbs repetitive shocks with every step. These shocks can be quantified by the peak vertical ground reaction force (F <sub>v,max</sub> ). To measure so, using a force plate is the gold standard method (GSM), but not always at hand. In this case, a motion capture system might be an alternative if it accurately estimates F <sub>v,max</sub> . The purpose of this study was to estimate F <sub>v,max</sub> based on motion capture data and validate the obtained estimates with force plate-based measures. One hundred and fifteen runners participated at this study and ran at 9, 11, and 13 km/h. Force data (1000 Hz) and whole-body kinematics (200 Hz) were acquired with an instrumented treadmill and an optoelectronic system, respectively. The vertical ground reaction force was reconstructed from either the whole-body center of mass (COM-M) or sacral marker (SACR-M) accelerations, calculated as the second derivative of their respective positions, and further low-pass filtered using several cutoff frequencies (2-20 Hz) and a fourth-order Butterworth filter. The most accurate estimations of F <sub>v,max</sub> were obtained using 5 and 4 Hz cutoff frequencies for the filtering of COM and sacral marker accelerations, respectively. GSM, COM-M, and SACR-M were not significantly different at 11 km/h but were at 9 and 13 km/h. The comparison between GSM and COM-M or SACR-M for each speed depicted root mean square error (RMSE) smaller or equal to 0.17BW (≤6.5 %) and no systematic bias at 11 km/h but small systematic biases at 9 and 13 km/h (≤0.09 BW). COM-M gave systematic biases three times smaller than SACR-M and two times smaller RMSE. The findings of this study support the use of either COM-M or SACR-M using data filtered at 5 and 4 Hz, respectively, to estimate F <sub>v,max</sub> during level treadmill runs at endurance speeds

Does Characterizing Global Running Pattern Help to Prescribe Individualized Strength Training in Recreational Runners?

This study aimed to determine if concurrent endurance and strength training that matches the global running pattern would be more effective in increasing running economy (RE) than non-matched training. The global running pattern of 37 recreational runners was determined using the Volodalen <sup>®</sup> method as being aerial (AER) or terrestrial (TER). Strength training consisted of endurance running training and either plyometric (PLY) or dynamic weight training (DWT). Runners were randomly assigned to a matched (n = 18; DWT for TER, PLY for AER) or non-matched (n = 19; DWT for AER, PLY for TER) 8 weeks concurrent training program. RE, maximal oxygen uptake V̇O <sub>2</sub> max) and peak treadmill speed at V̇O <sub>2</sub> max (PTS) were measured before and after the training intervention. None of the tested performance related variables depicted a significant group effect or interaction effect between training and grouping (p ≥ 0.436). However, a significant increase in RE, V̇O <sub>2</sub> max, and PTS (p ≤ 0.003) was found after the training intervention. No difference in number of responders between matched and non-matched groups was observed for any of the performance related variables (p ≥ 0.248). In recreational runners, prescribing PLT or DWT according to the global running pattern of individuals, in addition to endurance training, did not lead to greater improvements in RE

Critical speed estimated by statistically appropriate fitting procedures.

Intensity domains are recommended when prescribing exercise. The distinction between heavy and severe domains is made by the critical speed (CS), therefore requiring a mathematically accurate estimation of CS. The different model variants (distance versus time, running speed versus time, time versus running speed, and distance versus running speed) are mathematically equivalent. Nevertheless, error minimization along the correct axis is important to estimate CS and the distance that can be run above CS (d'). We hypothesized that comparing statistically appropriate fitting procedures, which minimize the error along the axis corresponding to the properly identified dependent variable, should provide similar estimations of CS and d' but that different estimations should be obtained when comparing statistically appropriate and inappropriate fitting procedure. Sixteen male runners performed a maximal incremental aerobic test and four exhaustive runs at 90, 100, 110, and 120% of their peak speed on a treadmill. Several fitting procedures (a combination of a two-parameter model variant and regression analysis: weighted least square) were used to estimate CS and d'. Systematic biases (P < 0.001) were observed between each pair of fitting procedures for CS and d', even when comparing two statistically appropriate fitting procedures, though negligible, thus corroborating the hypothesis. The differences suggest that a statistically appropriate fitting procedure should be chosen beforehand by the researcher. This is also important for coaches that need to prescribe training sessions to their athletes based on exercise intensity, and their choice should be maintained over the running seasons

A Single Sacral-Mounted Inertial Measurement Unit to Estimate Peak Vertical Ground Reaction Force, Contact Time, and Flight Time in Running.

Peak vertical ground reaction force (Fz,max), contact time (tc), and flight time (tf) are key variables of running biomechanics. The gold standard method (GSM) to measure these variables is a force plate. However, a force plate is not always at hand and not very portable overground. In such situation, the vertical acceleration signal recorded by an inertial measurement unit (IMU) might be used to estimate Fz,max, tc, and tf. Hence, the first purpose of this study was to propose a method that used data recorded by a single sacral-mounted IMU (IMU method: IMUM) to estimate Fz,max. The second aim of this study was to estimate tc and tf using the same IMU data. The vertical acceleration threshold of an already existing IMUM was modified to detect foot-strike and toe-off events instead of effective foot-strike and toe-off events. Thus, tc and tf estimations were obtained instead of effective contact and flight time estimations. One hundred runners ran at 9, 11, and 13 km/h. IMU data (208 Hz) and force data (200 Hz) were acquired by a sacral-mounted IMU and an instrumented treadmill, respectively. The errors obtained when comparing Fz,max, tc, and tf estimated using the IMUM to Fz,max, tc, and tf measured using the GSM were comparable to the errors obtained using previously published methods. In fact, a root mean square error (RMSE) of 0.15 BW (6%) was obtained for Fz,max while a RMSE of 20 ms was reported for both tc and tf (8% and 18%, respectively). Moreover, even though small systematic biases of 0.07 BW for Fz,max and 13 ms for tc and tf were reported, the RMSEs were smaller than the smallest real differences [Fz,max: 0.28 BW (11%), tc: 32.0 ms (13%), and tf: 32.0 ms (30%)], indicating no clinically important difference between the GSM and IMUM. Therefore, these results support the use of the IMUM to estimate Fz,max, tc, and tf for level treadmill runs at low running speeds, especially because an IMU has the advantage to be low-cost and portable and therefore seems very practical for coaches and healthcare professionals

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

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 <sub>v,max</sub> ) and 2) to compare the estimated F <sub>v,max</sub> to force plate gold standard (GSM). One hundred and fifteen runners ran at 9, 11, and 13km/h. Force (1000Hz) and kinematic (200Hz) data were acquired with an instrumented treadmill and an optoelectronic system, respectively, to assess force-plate and kinematic based DFs. SMM linearly relates F <sub>v,max</sub> to the inverse of DF because DF was analytically associated to the inverse of the average vertical force during ground contact time and the latter was very highly correlated to F <sub>v,max</sub> . 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 <sub>v,max</sub> during level treadmill runs at endurance speeds if underlying DF values are accurately measured

A Multivariate Polynomial Regression to Reconstruct Ground Contact and Flight Times Based on a Sine Wave Model for Vertical Ground Reaction Force and Measured Effective Timings.

Effective contact ( ) and flight ( ) times, instead of ground contact ( ) and flight ( ) times, are usually collected outside the laboratory using inertial sensors. Unfortunately, and cannot be related to and because the exact shape of vertical ground reaction force is unknown. However, using a sine wave approximation for vertical force, and as well as and could be related. Indeed, under this approximation, a transcendental equation was obtained and solved numerically over a grid. Then, a multivariate polynomial regression was applied to the numerical outcome. In order to reach a root-mean-square error of 0.5 ms, the final model was given by an eighth-order polynomial. As a direct application, this model was applied to experimentally measured values. Then, reconstructed (using the model) was compared to corresponding experimental ground truth. A systematic bias of 35 ms was depicted, demonstrating that ground truth values were larger than reconstructed ones. Nonetheless, error in the reconstruction of from was coming from the sine wave approximation, while the polynomial regression did not introduce further error. The presented model could be added to algorithms within sports watches to provide robust estimations of and in real time, which would allow coaches and practitioners to better evaluate running performance and to prevent running-related injuries

Estimating effective contact and flight times using a sacral-mounted inertial measurement unit.

Effective ground contact (t <sub>ce</sub> ) and flight (t <sub>fe</sub> ) times were proven to be more appropriate to decipher the landing-take-off asymmetry of running than usual ground contact (t <sub>c</sub> ) and flight (t <sub>f</sub> ) times. To measure these effective timings, force plate is the gold standard method (GSM), though not very portable overground. In such situation, alternatives could be to use portable tools such as inertial measurement unit (IMU). Therefore, the purpose of this study was to propose a method that uses the vertical acceleration recorded using a sacral-mounted IMU to estimate t <sub>ce</sub> and t <sub>fe</sub> and to compare these estimations to those from GSM. Besides, t <sub>ce</sub> and t <sub>fe</sub> were used to evaluate the landing-take-off asymmetry, which was further compared to GSM. One hundred runners ran at 9, 11, and 13 km/h. Force data (200 Hz) and IMU data (208 Hz) were acquired by an instrumented treadmill and a sacral-mounted IMU, respectively. The comparison between GSM and IMU method depicted root mean square error ≤22 ms (≤14%) for t <sub>ce</sub> and t <sub>fe</sub> along with small systematic biases (≤20 ms) for each tested speed. These errors are similar to previously published methods that estimated usual t <sub>c</sub> and t <sub>f</sub> . The systematic biases on t <sub>ce</sub> and t <sub>fe</sub> were subtracted before calculating the landing-take-off asymmetry, which permitted to correctly evaluate it at a group level. Therefore, the findings of this study support the use of this method based on vertical acceleration recorded using a sacral-mounted IMU to estimate t <sub>ce</sub> and t <sub>fe</sub> for level treadmill runs and to evaluate the landing-take-off asymmetry but only after subtraction of systematic biases and at a group level