Description of the instrumented set-up
The apparatus used in this research consisted of a static dynamometer (Biodex Medical Systems, NewYork, USA) with an adjustable chair on which subjects sat leaning back with their foot attached to a force platform (AMTI model MC3–1000, Advanced Manufacturing Technology Inc., Massachusetts, USA) (Fig. 2). This experimental set-up allowed for the measurement of vertical and horizontal forces (Fy and Fz) and moments of force (Mx, My) exerted under the foot at the center of the force transducer. These kinetic values were digitized from the output of strain gauge amplifiers using an acquisition card and fed into a computer at a frequency of 100 Hz. A software (Labview; National Instruments, Texas, USA) was developed to calculate the joint moments at the hip, knee and ankle by inverse dynamics using the data collected from the AMTI force platform and the subjects’ anthropometric information.
The height and position of the chair were adjusted to ensure that the foot was positioned at 55 degrees (γ angle) from the horizontal plane, with 20 degrees of hip flexion (α angle) and 125 degrees of knee flexion (β angle) (Fig. 2). This position was chosen since it largely corresponds to the mean values of joint angle changes during walking [18], allowing for the exertion of positive and negative moments at each joint. All three angles were validated using a goniometer.
The angles (α, β and γ) were entered into the software as well as the values for the different lever arm distances (Lt, Ll, LRAj, HRAj) measured using a measuring tape. The distance (dz) between the center of the AMTI transducer and the plate was provided by the manufacturer.
Based on the measurements of the lever arms (Lt, Ll, HRAJ, LRAJ, dz) and angles (α, β,γ) illustrated in Fig. 2, it was possible to calculate the distance between the AMTI force transducer center of reference and the articular center of rotation of the hip (rhj), knee (rkj) and ankle joint (raj) in the y and z directions using eqs. 1–6, where β1 = γ - α and β2 = β − 90- γ + α.
$$ {raj}_y=\mathrm{LRAJ} $$
(1)
$$ {raj}_z=\mathrm{HRAJ}+{d}_z $$
(2)
$$ {rkj}_y=\mathrm{LRAJ}+\mathrm{Ll}\ast \sin \left(\upbeta 2\right) $$
(3)
$$ {rkj}_z=\mathrm{HRAJ}+{d}_z-\mathrm{Ll}\ast \cos \left(\upbeta 2\right) $$
(4)
$$ {rhj}_y=\mathrm{LRAJ}+\mathrm{Ll}\ast \sin \left(\upbeta 2\right)+ Lt\ast \cos \left(\upbeta 1\right) $$
(5)
$$ {rhj}_z=\mathrm{HRAJ}+{d}_z-\mathrm{Ll}\ast \cos \left(\upbeta 2\right)- Lt\ast \sin \left(\upbeta 1\right) $$
(6)
By measuring the location of the center of pressure exerted on the AMTI platform in relation to the y axis (COPy), by calculating the direction of the force vectors applied at AMTI force platform located at the end of the LL (Fy,Fz) and by using rhj, rkj, raj, it was possible to calculate the different joint moments exerted at the hip (Mh), knee (Mk) and ankle (Ma) (Eq. 7).
$$ \left[\begin{array}{c} Ma\\ {} Mk\\ {} Mh\end{array}\right]=\left[\begin{array}{l}{COP}_y-{raj}_{\mathrm{y}}-\left({raj}_z-{d}_z\right)\\ {}{COP}_y-{rkj}_y-\left({rkj}_z-{d}_z\right)\\ {}{COP}_y-{rhj}_y-\left({rhj}_z-{d}_z\right)\end{array}\right]\times \left[\begin{array}{c}{F}_z\\ {}{F}_y\end{array}\right] $$
(7)
Validation of the joint moments
To validate the joint moments measured using the apparatus and the experimental methodology, an instrumented leg with three joints corresponding to the hip, knee and ankle was mounted on the AMTI transducer (Fig. 3). A cable equipped with a turnbuckle and strain gauges was tethered at each joint to simulate a muscle group. The moment from the strain gauges was calculated by modifying the tension in the cable and measuring the perpendicular distance between the cable (d’) and the center of rotation of the joint. Validation of the inverse dynamics data at the instrumented leg was done by comparing the expected moments at the hip (Mh), knee (Mk) and ankle (Ma) joints calculated from the AMTI transducer to the moments calculated from calibrated strain gauges positioned at the hip (Mh’), knee (Mk’) and ankle (Ma’) for 11 trials during which the tension was progressively increased at each joint.
The distance between each joint’s center of rotation was used to estimate the length of the thigh (Lt) and leg (Ll) of the instrumented leg by taking a static picture of the experimental set-up, processing the image data with Matlab, and extrapolating the distance between specific points using a ruler as a reference. The distance between the ankle joint articular center and the center of the sensor axial force parallel to the platform (LRAJ) and the height of the ankle joint center relative to the AMTI force platform (HRAJ) were also measured by the image-extrapolation method.
Joint moments and muscular activity characterization
Participants
Five healthy subjects (1 man; 4 women) between the ages of 21 and 26 (22.8 ± 2.5 years of age), with no reported neurological conditions or musculoskeletal impairments limiting their mobility, took part in this study. The study was conducted at the Pathokinesiology Laboratory of the Centre for Interdisciplinary Rehabilitation Research of Greater Montreal (CRIR). Ethical approval was obtained from the Research Ethics Committees of the CRIR (1220–0317). The subjects received detailed information about the study prior to their participation and provided written consent.
Surface EMG recordings
Surface electromyography (EMG) of tibialis anterior (TA), soleus (SO), medial gastrocnemius (MG), vastus medialis (VM), rectus femoris (RF), biceps femoris (BF), semitendinosus (ST) and gluteus medius (GM) were recorded on the left (non-dominant) lower extremity using a portable telemetric system (NORAXON USA Inc., Scottsdale, Arizona; Telemyo 900) at a frequency of 1200 Hz (Hz). Self-adhesive surface electrodes (Ag/AgCl; Ambu BlueSensor M) were placed in accordance with SENIAM recommendations [19] on each muscle in a bipolar configuration with a 1 cm inter-electrode distance over the muscle belly, perpendicular to muscle fiber orientation, after each skin site was shaved and cleaned with alcohol [20]. EMG signals were visually inspected during static voluntary contractions performed against gravity and manual resistance according to a standardized protocol [21].
Assessment of dynamometry efforts
Subjects were seated in a semi-reclined position on the static dynamometer with the non-dominant foot secured on the force platform using large Velcro straps. A force feedback cursor was displayed on a screen placed beside the subject’s side for viewing. The cursor moved horizontally or vertically in relation to the Fz and Fy force exerted at the COP of the foot. Subjects were asked to gradually move the cursor within a corridor in a specific direction for approximately two seconds at 50% of their maximal effort. The level of 50% was chosen based on preliminary tests to optimize EMG signals without excessive muscle co-contractions. Once seated and positioned on the apparatus, subjects were given two minutes to familiarize themselves with the force feedback. Subjects were then asked to exert a progressive effort ten consecutive time in eight directions, covering 360 degrees in the transverse plane of the lower extremity (Fig. 4). A one-minute break was allowed between each direction to limit muscle fatigue. The joint moments at the hip, knee and ankle were calculated but not displayed. Subjects were asked to control only the direction and magnitude of the force vector they produced.
Data processing
The EMG recordings were filtered using a fourth-order Butterworth zero-lag bandpass filter with cut-off frequencies set at 10 and 400 Hz. The EMG values were subsequently root mean squared (RMS) with a centered 250 msec moving window to finally generate linear envelopes [22].
Kinetic and EMG data were collected for 10 dynamometry cycles (push to end of push) and an average of 5 consecutive cycles according to the minimal EMG RMS variation coefficient was retained for analysis. RMS values were amplitude normalized from their peak values and expressed between 0 to 1 to reduce inter- and intra-subject variability [23].
Joint moments at the ankle, knee and hip, and EMG envelopes were time normalized (0 to 100% in 1% increments) relative to each push cycle and averaged together. An average of the 90–100% cycle phase (end of push) was calculated for the joint moments and EMG normalized RMS for each subject.
Statistics
The mean and standard deviation (SD) moments for each joint measured by the strain gauges and the moments estimated by the AMTI force platform during validation were calculated across all trials. To assess concurrent validity between the expected moments estimated by the AMTI transducer and those calculated by the calibrated strain gauges across each joint, root mean square error (RMSE), Pearson correlation (r) and determination coefficients (R2) were used. Bland and Altman plots and limits of agreement with confidence intervals (CI) were calculated for each of the three joints to determine the level of agreement between the moments calculated by our apparatus and by the strain gauges [24, 25]. The mean and SD of each joint’s moment and EMG values during the end of the dynamometry cycle were calculated across all subjects for all eight directions.
To assess and quantify the similarity between the normalized values of the eight muscle groups measured across the directions on the static dynamometer and the weight value of the muscular synergies previously measured during gait in a group of healthy individuals [12], cosine similarity was used and the highest value was selected for each synergy [26]. Muscle weightings were categorized as similar when the cosine similarities were over 0.71 (p < 0.01). All statistical analyses were performed using SPSS v.24 (SPSS Inc., Chicago, IL, USA). The p-values were set at 0.05.