A biomechanical study of load carriage by two paired subjects in response to increased load mass
Experimental protocol
Twenty healthy male adults participated in the study. To limit the effects of differences in the participants’ anthropometry, the volunteers were matched according to their height and weight.
The leg and hand dominances of each participant was noted before running the experiment. The subjects were placed at random on the left ((#1—right hand holding the load) or the right (#2—left hand holding the load) side of the carried object. It happened by chance that three lefthanders were affected to #2. The individuals had an average height of (mean ± SD) 1.77 ± 0.07 m (#1), and 1.77 ± 0.05 m (#2), and an average weight of 74.78 ± 9.00 kg (#1), and 74.54 ± 12.38 kg (#2). The load was symmetrical in shape, and its weight was evenly balanced between the participants who were positioned randomly with respect to the object transported to counteract the effect of a dominant side (Fig. 1A).
The study was carried out with healthy individuals who wrote their informed consent to participate in the experiment and to be filmed and photographed. The experiment was non-interventional, and the movements performed by the volunteers were no more risky than those they perform in daily activities. The study was approved by the Research Ethics Committee of the University of Toulouse, France (Number IRB00011835-2019-11-26-172, Université Fédérale de Toulouse IRB #1).
The instructions given to the volunteers were: “Move the load together from point A to point B” and “Any communication between you is forbidden during the experiment”. Point A and point B laid 20 m apart. No explicit instruction was given as to how fast the volunteers should perform the task. The volunteers were tested with three conditions called CT20, CT30, and CT40 corresponding to a load representing on average 20%, 30%, and 40% of the sum of their body masses respectively. The three conditions were tested in random order for each pair. To avoid adaptations due to familiarization or learning, only one trial per pairs and condition was recorded.
Kinematics and kinetics
Thirteen MX3, and TS40 Vicon cameras (Vicon©, Oxford) were used to capture the positions of ninety-one retro-reflective markers taped on the system formed by the paired individuals and the load they carry (hereafter called Poly-Articulated Collective System—PACS): 42 markers on each individual31,32, and seven on the load (Fig. 1A). The acquisition frequency was set to 200 Hz. In order to record the walking patterns of the individuals at a stable speed, and thus to exclude the acceleration and deceleration phases at the beginning and end of each trial, the calibrated volume (30m3) corresponded to the central part of the walkway. This covered about two steps. Concerning kinematic analysis, the PACS was reconstructed with the Vicon Nexus™ 1.8.5 software. Reconstruction was impossible for one pair of individuals who had lost one reflective marker. The two lateral handles on each side of the load were equipped with a 6-axis force sensor (Sensix®, France) (Fig. 1B), allowing to record the reaction forces and moments at a sampling frequency of 2000 Hz. The kinematic and kinetic measurement errors were 1 mm for 1 m for the positions (Vicon system) and ± 0.01 N for the forces (Sensix sensors), respectively. The sensors frames were located with the help of screwed reflective markers. The data were filtered with 4th order Butterworth filters with a cut-off frequency of 5 Hz for the kinematic data, and of 10 Hz for the kinetic data. To ensure at least one complete walking cycle for each subject of a pair, the gait cycle of the PACS was defined from the first heel strike of individual #1 to the third heel strike of individual #2.
COM determination and related parameters
The carried object, which constituted the 33th segment of the PACS, was built in aluminum and was therefore extremely rigid. It was completely symmetrical about its sagittal plane (Fig. 1B) and therefore its weight was evenly balanced between the participants. The object was equipped with a rod at its center where standard cast iron discs could be slid to increase its weight. The CoM of the object was determined at the intersection point of the vertical lines obtained by hanging the object without discs with a thread fixed at different positions. When the object was loaded, the position of its CoM was then adjusted by taking into account the added cast iron discs and by considering a homogeneous mass distribution inside the discs.
The De Leva Anthropometric table33 allowed us to estimate the mass mi as well as the CoM of each segment i (CoMi) of the PACS, and thus to compute its global CoM (CoMPACS) as follows:
$${varvec{G}}{text{PACS}} = frac{1}{{m_{PACS} }}mathop sum limits_{i = 1}^{n = 33} m_{i} {varvec{G}}_{i}$$
(1)
with GPACS corresponding to the 3D position of the CoMPACS in the frame R (the global coordinate system), mPACS to 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 corresponding to the 3D position of the CoMi in R.
The vertical amplitude (Az = Zmax − Zmin, in meters) of the CoMPACS trajectory along two consecutive steps, and the length of two consecutive steps by each individual were also computed.
Assessment of energetic exchanges
To assess energetic exchanges, forward kinetic work, vertical work, and external work of the forces applied to the CoMPACS were computed25.
Forward kinetic work (Wkf) was defined as the positive work needed to move the CoMPACS forward, and it was calculated as the sum of the increments of forward kinetic energy (Ekf) along the time curve:
$$E_{{{text{kf}}}} = { }frac{1}{2} m overrightarrow{V_{f}}left( {text{t}} right)^{{2}} _{/R}$$
(2)
with m being the mass of the individual, and (overrightarrow {{V_{f} }}) (t)/R the linear forward velocity of the CoMPACS in the frame R. The x-, y- and z-axis of the frame R, corresponding to the medio-lateral, antero-posterior, and vertical directions respectively, are illustrated in Fig. 1A.
Vertical work (Wv) was defined as the positive work needed to move the CoMPACS against gravity, and it was calculated as the sum of the increments of the vertical kinetic energy (Ekv) plus the potential energy (Epot) along the time curve with:
$$E_{{{text{kv}}}} = { }frac{1}{2} m overrightarrow{V_{v}}left( {text{t}} right)^{{2}} _{/R}$$
(3)
and
$$E_{{{text{pot}}}} = mgh_{{/{text{R}}}}$$
(4)
where (overrightarrow {{V_{v} }}) (t)/R is the linear vertical velocity of the CoMPACS in R, g = 9.81 m s−2 is the acceleration due to gravity, and h/R is the height of the CoMPACS in R.
The external work (Wext), corresponding to the positive external work needed to raise and accelerate the CoMPACS, was computed as the sum of the increments of the external mechanical energy (Eext) along the time curve with:
$$E_{{{text{ext}}}} = E_{{{text{pot}}}} + E_{{{text{kv}}}} + E_{{{text{kf}}}}$$
(5)
The energy recovered (called recovery rate (RR)10) by the CoMPACS in the sagittal plane was computed with the following formula17:
$$RR = { 1}00frac{{W{text{kf}} + W{text{v}} – W{text{ext}}}}{{W{text{kf}} + W{text{v}}}}$$
(6)
RR is the percentage of kinetic energy converted into potential energy7,24,25,34,35 and vice versa.
In the present study, internal work was also considered in order to encompass the coordination between all body segments. Based on the assumption of a conservative Poly-Articulated Model (PAM), internal work (Wint) was computed as the sum of the increments of the Eint,k along the time curve with:
$$E_{{{text{int}},{text{k}}}} = frac{1}{2}~mathop sum limits_{{i = 1}}^{{33}} (m_{i} overrightarrow {{V_{{~i}} }} left( {text{t}} right)^{{text{2}}} _{{/{text{R}}*}} + m_{{text{i}}} K_{{i^{2} }} {text{ }} times vec{omega }^{2} _{i} /_{{{text{R}}*}} )$$
(7)
where mi is the mass of the ith segment, (overrightarrow {{V_{i} }})(t)/R* the linear velocity of its CoM in the sagittal plane of the barycentric coordinate system (R*), Ki its radius of gyration around its CoM, and (vec{omega }_{i})2/R* its angular velocity in R* 36.
The total mechanical energy of the PACS (Etot) was computed as the sum of the internal kinetic energy (Eint,k) of each segment, plus the potential energy (Epot), and the forward (Ekf ) and vertical (Ekv ) kinetic energy of the CoMPACS in the sagittal plane21,25,37,38:
$$E_{{{text{tot}}}} = E_{{{text{int}},{text{k}}}} + E_{{{text{pot}}}} + E_{{{text{kf}}}} + E_{{{text{kv}}}}$$
(8)
Finally, the total mechanical power (PmecaTot) was used to assess the amount of energy spent or gained by the CoMPACS per unit of time (Δt):
$$P_{{{text{mecaTot}}}} = frac{{W{text{ext}}}}{Delta t} + frac{{{ }W{text{int}}}}{Delta t} = P_{{{text{ext}}}} + P_{{{text{int}}}}$$
(9)
Calculation of internal efforts
The resultant joint moments at the wrist, elbow, shoulder, neck, and back joints were calculated using a bottom-up Newton–Euler recursive algorithm39. Cardanic angles were used to represent the rotation of the segments coordinate system relative to the global coordinate system40. The segment masses, inertia tensors, and center of mass locations were estimated for each subject according to the scaling equations proposed in Dumas et al. (2007)41. In order to estimate the muscular torque produced at all the joints of the upper-limbs, shoulders, neck, and back, the Moment Cost Function (MCF in kg m2 s−2, 42) was computed as follows:
$${text{MCF}} = sqrt {M_{L_wt}^{2} } + sqrt {M_{R_wt}^{2} } + sqrt {M_{L_el}^{2} } + sqrt {M_{R_el}^{2} } + sqrt {M_{L_sh}^{2} } + sqrt {M_{R_sh}^{2} } + sqrt {M_{back}^{2} } + sqrt {M_{neck}^{2} }$$
(10)
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. (sqrt {{text{M}}^{2} }) represents the Euclidian norm of M, i.e. (sqrt {sumnolimits_{i = 1}^{3} {left( {M_{i} } right)^{2} } }), with Mi the i-th component of the vector M.
We summed the MCF values of the two individuals of each pair to obtain the total moment cost function (TotMCF). The TotMCF allows to quantify the global muscular effort developed at the upper-limbs of the PACS during one gait cycle of the carrying of the load. The MCF difference (∆MCF) between the two individuals was also computed to investigate whether the volunteers developed the same efforts while carrying the object.
Kinetic synergy analysis
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 dimensionality13,35,43. It consisted in the eigen-decomposition of the co-variance matrix of the joint moment data (Matlab eig function). The joint moments data were arranged in time × joint moment matrices. We called the eigenvectors extracted from the PCA synergy vectors13. The number of synergies was determined from the VAF (Variance Accounted For), which corresponds 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. We defined the number of synergies as the first number for which the VAF was greater than 0.9. The synergy vectors retained were then rotated using a Varimax rotation method to improve interpretability44.
We extracted the synergy vectors for each experimental condition separately. We first performed an analysis on each individual separately. In this analysis the initial data matrices were constituted of all available time frames in line, concatenated, 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. The values in the matrix corresponded to the norm of the joint moment vector at a given time frame. 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. The synergy vectors were compared across conditions by computing Pearson’s r correlations on their PCA weightings, after being matched together, also using Pearson’s r to identify the best matches.
Statistical analysis
We used generalized linear mixed models (GLMM)45 to compare the velocity and the vertical amplitude of the CoMPACS, the length and duration of the gait cycles, the recovery rate, the external, internal, and total mechanical power produced by the PACS, the TotMCF and ∆MCF, the number of synergies, as well as the Pearson’s r-values across conditions.
The experimental condition was entered as a fixed factor in the model, and individuals as a random variable. We used a Gaussian GLMM for all variables, except for the comparison of the number of synergies across conditions, for which a Poisson GLMM was used. For Gaussian GLMMs we systematically inspected the normality of the model residuals with Q-Q plots. We used the functions lmer() and glmer() of the R package lme4 46 to run the Gaussian and the Poisson mixed models, respectively. The effect of experimental conditions was tested by comparing the deviance of the model with and without the fixed factor with a χ2 test. Multiple comparisons across experimental conditions were performed with the function glht() of the multcomp R package47 using the default Tukey test as post-hoc test. Pearson’s r were Fisher Z-transformed before running the analyses. The significance threshold was set to 0.05. All data in the text are given as mean ± SD. Since our sample size was low, which could lead to inflate the Type II error (not rejecting H0 when H0 is false), we followed the recommendations of Nakagawa & Foster (2004)49 and provide in the Supplemental Table S1 the value of Cohen d standardized effect size50, along with its 95% confidence interval51, for each studied parameter and each paired comparison between conditions. A confidence interval that largely extends on both sides of zero indicates an absence of effect that would probably not change with increasing the sample size.
Ethics statement
All methods used in this study were carried out in accordance with relevant guidelines and regulations. More
