DOI: 10.5061/dryad.kprr4xh5n
title: Dataset of biomechanical effects of the addition of a precision constraint on a collective load carriage task

description: Team lifting is a complex and collective motor task that possesses both
 motor and cognitive components. We study the collective load carriage
 adaptation due to an additional accuracy constraint. Ten dyads performed a
 first condition in which they collectively transported a load (CC), and a
 second one in which they transported the same load while maintaining a
 ball in a target position on its top (PC). The recovery-rate, amplitude,
 and period of the center-of-mass of the whole system (dyad + table,
 CoMPACS) were computed. We analyzed the forces and moments exerted at each
 joint of the upper limbs of the subjects. We observed a decrease in the
 overall performance of the dyads when the Precision task was added, i.e.,
 i) the velocity and amplitude of CoMPACS decreased by 1,7% and 5,8%,
 respectively, ii) inter-subject variability of the Moment-Cost-Function
 decreased by 95% and recovery rate decreased by 19,2% during PC. A kinetic
 synergy analysis showed that the subjects reorganized their coordinations
 in the PC. Our results demonstrate that adding a precision task affects
 the economy of collective load carriage. Notwithstanding, the joint
 moments at the upper-limbs are better balanced and co-vary more across the
 paired subjects during the precision task.
description: We recorded two conditions the first one were the subjects walked
 side by side at spontaneous speed while carrying a box (CC: Control
 Condition) and a second one were the individuals were instructed to
 transport the box, while performing an accuracy task consisting in keeping
 a ball in the center (PC:Pecision Condition). Motion
 capture data were collected using thirteen infrareds (11 MX3 and 2 TS40)
 transmitter-receiver video cameras (Vicon©, Oxford metric’s, Oxford,
 United Kingdom) sampled at 200 Hz. Forty-two retro-reflective markers were
 placed on bony landmarks and on the navel of each subject ( according to
 Wu et al., 2002, 2005) R. Soc. open sci. and fourteen on the box. The ball
 used during the PC tests was reflective as well and was tracked by the
 Vicon© system. In order to record the gait pattern at constant speed (i.e.
 to exclude the acceleration and deceleration phases at the beginning and
 end of each trial) the volume calibrated by the Vicon© system (30 m3) was
 located in the middle of the 20m-long walkway crossed by the subjects. The
 reflective marks were tracked to define the kinematics of the
 Poly-Articulated Collective System (PACS) formed by the two individuals
 and the load they carry (22,23). The data were recorded on one gait cycle
 defined by the first heel strike of the first subject and the third heel
 strike of the second subject of the PACS to ensure a cycle of each
 subject. The 3D reconstruction was performed using Vicon Nexus 1.8.5©
 software. The two lateral handles used to transport the box were equipped
 with Sensix® force sensors sampled at 2000 Hz. A 4th order Butterworth
 filter and a 5 Hz and 10 Hz cut frequency have been applied to analyze the
 positions of the markers and the forces exerted on the box handles,
 respectively The De Leva Anthropometric tables (24) was
 used to estimate the mass mi and the CoM of each segment i (CoMi) of the
 PACS and to compute its global CoM (CoMPACS) as follow: ????? = 1
 ?<sub>????</sub> ∑ ???? ?=33 ?=1  with GPACS the 3D position
 of the CoMPACS in the frame R (the global coordinate system),
 m<sub>PACS</sub> the mass of the PACS, n the number of PACS
 segments (i.e. 16 segments per volunteer plus one segment for the box) and
 Gi the 3D position of the CoMi in the frame R. The CoM of the box was
 determined at the intersection point of the vertical lines obtained by
 hanging it with a thread fixed at different positions. The material used
 for the box construction, i.e. wood and aluminium, was considered as not
 deformable. According to Holt et al., (2003), the amplitude (A = Zmax –
 Zmin, with Z the height of the CoMPACS, in meters,) and the period (peak
 to peak, in percent of the gait cycle) of the CoMPACS were also assessed.
 The forward kinetic (Wkf), as well as the vertical (Wv) and external work
 (Wext) of the CoMPACS were computed according to the method of Bastien et
 al. (2016). Then based on the external work, the percentage of energy
 recovered of the CoMPACS in the sagittal plane was computed (called
 recovery rate RR in Fumery et al., 2018a, 2018b). This parameter assess
 the amount of energy transferred between the potential and the kinetic
 energy (Eqn 2). ?? = 100 ?kf+?v−?ext ?kf+?v (2) The closer the value of RR
 to 100%, the more consistent the locomotor pattern is with the inverted
 pendulum system (IPS) model of locomotion (26–28,13). In this study, the
 trajectory of CoMPACS and CoM of an inverted pendulum have been
 investigated. Sensix force sensors recorded the forces
 and moments applied by each individual on the two box handles. Before the
 computation, the data of the sensors located by specific markers were
 transfer to the Galilean frame of the laboratory using rotation matrix. A
 cross correlation method has been applied in order to analyze the
 coordination between the forces produced by both subjects. To investigate
 whether the movement of the box results from an action-reaction strategy,
 we computed the time lag required for the position of the left side and
 right side of the box to be the same on the medio-lateral,
 antero-posterior and vertical axis in CC and PC. The coordination was
 assessed through the forces exerted on three directions (medio-lateral,
 antero-posterior and vertical axis). This results will reflect the level
 of coordination of two subjects during a collective transport In order to
 quantify muscular constraints produced at the upper limb, the Inverse
 Dynamic Method was used to estimate forces and moments at each joint of
 the upper limb. The Moment Cost Function was then computed (kg.m2 .s-2 ,
 Costes et al., 2018) as follow : MCF = √??_?? 2 + √??_?? 2 + √??_?? 2 +
 √??_?? 2 + √??_?ℎ 2 + √??_?ℎ 2 + √????? 2 + √?????  Where ML_wt, MR_wt,
 ML_el, MR_el, ML_sh, MR_sh, Mback and Mneck are the mean values over a
 PACS gait cycle of the three-dimensional left and right wrist, left and
 right elbow, left and right shoulder, top of the back and neck moments,
 respectively. √M2 represents the Euclidian norm of M (i.e. √M2 = √∑ (??) 3
 2 ?=1 , with Mi the i-th component of the vector M). Then, the MCF values
 of each individual was summed to obtain the total moment cost function
 (Total MCF). This Total MCF allows to quantify the global effort produced
 at the upper-limbs of the PACS during one gait cycle. Finally, the MCF
 difference (∆ MCF) was computed as the difference between the two
 individuals to investigate whether the subjects produced the same effort
 in the upper limbs during the load transport. We
 extracted the synergies by using a principal component analysis (PCA)
 applied to the wrist, elbow, shoulder, back, and neck joint moment on the
 right and left sides of the body. The PCA was used to reduce data
 dimensionality. It consisted in the eigen-decomposition of the co-variance
 matrix of the joint moment data (Matlab eig function). The joint moments
 data from one trial per condition were arranged in time × joint moment
 matrices. In this analysis we only used the y-component which is very
 close to the norm of the 3D joint moments, except that the y-component
 (medio-lateral) could be positive and negative. The joint moments were
 normalized by their amplitude and centered (mean removed) before
 application of the PCA. We called the eigenvectors extracted from the PCA,
 dynamic synergy vectors. We computed the VAF (Variance Accounted For)
 which corresponded to the cumulative sum of the eigenvalues, ordered from
 the greatest to the lowest value, normalized by the total variance
 computed as the sum of all eigenvalues. The synergy vectors retained were
 then rotated using a Varimax rotation method to improve interpretability.
 We first extracted the synergy vectors for each experimental condition and
 each participant separately. In this analysis the initial data matrices
 were constituted of all available time frames in line, concatenated from
 one trial per condition, and of eight columns corresponding to each joint
 moment, namely the right wrist, left wrist, right elbow, left elbow, right
 shoulder, left shoulder, back, and neck. Based on a previous study we
 extracted 3 synergies in this analysis. We then performed a second
 analysis to identify possible co-variations between the joint moments of
 the two participants in each pair. The columns of the initial matrices
 were thus constituted of the joint moments of the two loaded arms, i.e.,
 the right wrist, elbow, and shoulder joint moments of participant #1, plus
 the left wrist, elbow and shoulder joint moments of participant #2. Based
 on a previous study we extracted 2 synergies in this analysis. We used
 Pearson’s r to order the different synergies similarly between the
 different subjects and conditions. A performance score
 (Scorep) was assigned to each image of the videos captured by the Vicon©
 system (200 images/s). The score depended on the location of the ball in
 the target: 1 when the ball was inside the small circle, 0.5 when it was
 in-between the small and large circle and 0 when it was outside the large
 circle. The accuracy over the whole gait cycle was measured by an overall
 score (Scoreaccuracy), expressed in percentage, and calculated as follows:
 ????????????? = ∑ ?????? ×??? ????? ????? where tgait cycle represents the
 number of Vicon© images recorded along one gait cycle.
 The head, shoulders and pelvis rotation angles were computed
 around the vertical axis of each individual in the two conditions. The
 angle was positive when the subjects turned towards the box they carried,
 otherwise it was negative. The distance between the forehead and the
 sternum (distance FOR-STE) was also computed in order to investigate the
 flexion of the cervical spine. The data were analyzed
 with Matlab R2016b© and StatView 5.0© software. A paired t-test was used
 to compare the RRs, the amplitudes, the periods, the velocities of the
 vertical displacement of the CoMPACS, the head, shoulders and pelvis
 rotation angle and the length FOR-STE between the CC and PC condition. The
 significance threshold was set to 0.05. We computed with a
 cross-correlation method the time lag required for the position of the
 left side and right side of the box to be the same on the medio-lateral,
 antero-posterior and vertical axis in CC and PC. We used the average
 subspace angles to compare the subspaces spanned by the synergy vectors
 (Knyazev and Argentati, 2002). In order to decide whether the subspaces
 were more similar than expected by chance, the confidence interval (CI) of
 random comparisons was computed. For this analysis, we generated pairs of
 random subspaces constituted each of either 3 unit vectors of dimension 8
 (individual PCA analysis) or 2 unit vectors of dimension 6 (conjoint PCA
 analysis) and computed the mean subspace angle between them. The unit
 vectors were built using normally distributed pseudo-random numbers
 (Matlab randn function). We performed 10000 simulations in order to
 determine the 95%-CI of the mean subspace angle between the pairs of
 random subspaces. The confidence interval was 39.5°–70.0° (55.0±7.6°) for
 the individual PCA analysis and 36.3°–79.1° (57.7±10.7°) for the conjoint
 analysis. We used Student tests for single mean to compare the subspaces
 angles to the lower bound CI with the assumption that similarity was
 higher than expected by chance when the angles were lower than the lower
 bound CI. VAFs were compared with an ANOVA with one repeated measure
 (control vs. precision conditions) and one factor (participant #1 vs.
 participant #2) when synergies were extracted separately for each subject.
 For the conjoint analysis, a paired Student t-test was used. Subspace
 angles were compared with t-tests for dependent samples (paired t-test)
 when comparing the control and precision conditions and t-test for
 independent samples when comparing the two participants. Adjustments for
 multiple comparisons were performed by Bonferroni’s method. Initial level
 of significance was set to p&lt;0.05.