Protocol
Figure 1 shows the study flowchart. First, we conducted an experiment to obtain normal sit-to-stand movement times in the study subjects. For the first and second computer simulations, we created a simulation model for sit-to-stand movement. The simulation model outputs the moment waveforms of the hip, knee, and ankle joints by using height, body mass, sit-to-stand movement time, and joint angles of sit-to-stand movement (Fig. 2). In the first computer simulation, we confirmed the similarity of the kinetics in the simulation model and the experiment. In the second computer simulation, we examined the hip moment impulse in the sagittal plane during various sit-to-stand movement times using the simulation model tested in the first computer simulation.
Experiment and analysis
Twenty healthy subjects were recruited for the present study (5 men and 15 women; mean age, 18.8 ± 0.8 years; mean height, 1.65 ± 0.09 m; mean body mass, 53.9 ± 7.2 kg). The inclusion criteria were as follows: (1) no self-reported body pain, (2) no orthopedic and neurological disease, and (3) no surgeries. Informed consent was obtained in writing from all subjects prior to the study, which was approved by the ethics committee of the Niigata University of Health and Welfare (No. 17797–170412).
The subjects were asked to stand up with both arms on their chest at a natural self-selected speed from a chair measuring 0.4 m in height [14]. Five trials were performed for each subject. A three-dimensional motion capture system (Vicon, Oxford, UK) with 13 cameras was used to capture the sit-to-stand movements of each subject. Twenty-one reflective markers were attached on the bilateral acromion processes, anterior superior iliac spines, greater trochanters, lateral and medial epicondyles of the femur, lateral and medial malleoli, first and fifth metatarsal heads, heels, and at the midpoint of the posterior superior iliac spine of each subject. The sampling rate of the motion capture system was 100 Hz. Three force plates (AMTI, Watertown, MA) were used. The sampling rate of the force plates was 1000 Hz. The marker trajectories and ground reaction forces (right foot and both buttocks) were low-pass filtered using a fourth-order Butterworth filter with a cut-off frequency of 6 Hz.
We analyzed the right leg for each experimental sit-to-stand movement trial. The hip joint center was set using Bell’s method [30]. The knee joint center was set as the midpoint of the lateral and medial epicondyles of the femur and the ankle joint center was set as the midpoint of the lateral and medial malleoli. Body parameters (position of the center of mass, segment mass, and radius of gyration) were set based on a previous study [31]. The start time was defined as the time when the vertical ground reaction force of the buttocks was zero. The finish time was defined as the time when the vertical velocity of the right acromion was slower than 0.05 m/s.
A link segment model having four segments (right foot, right shank, right thigh, and HAT [head, arms, and trunk]) was used to analyze all experimental sit-to-stand movement trials. The hip, knee, and ankle joint moments during an experimental sit-to-stand movement for each subject were calculated based on inverse dynamics from foot to HAT (iterative Newton–Euler method [32]) using actual marker trajectories and ground reaction forces.
To calculate hip moment impulse in the sagittal plane during experimental sit-to-stand movement, anterior–posterior and superior-inferior components of ground reaction forces (i.e., two-dimensional components) were used. The hip, knee, and ankle joint moment impulses were calculated by integration of their respective joint moments during sit-to-stand movement as follows:
$${\text{I}}_{\text{j}} = \int\limits_{\text{t}_{0}}^{\text{T}} {{\text{M}}_{\text{j}} {\text{(t)dt}}}$$
I: joint moment impulse in the sagittal plane; j: hip, knee, or ankle joint; t0: timing of seat-off; T: timing of completion of sit-to-stand movement; and M: joint moment in the sagittal plane.
Additionally, the hip, knee, and ankle joint angles (Fig. 2) during all sit-to-stand movements (100 trials = 20 subjects × 5 trials) were calculated for use in the computer simulations.
Computer simulation and analysis
We created the simulation model with a link segment model for the first and second computer simulations. Using the segment length ratios reported by Contini [33], we calculated the segment lengths of the link segment model using height. Further, using the ratios of the segment masses reported by de Leva [31], we calculated the segment masses of the link segment model using body mass. In the first and second computer simulations, the joint angles obtained from the experimental sit-to-stand movements were used to reproduce the same kinematics (Fig. 1).
In the first computer simulation, the movement times obtained from the experiment were used to calculate the joint moments and moment impulses in the sagittal plane of the hip, knee, and ankle joints during sit-to-stand movements (Fig. 1). Thus, 100 sit-to-stand movements (20 subjects × 5 trials) were analyzed in the first computer simulation. Similarities across the hip, knee, and ankle joint moment waveforms between the first computer simulation and the experiment were evaluated using Pearson’s correlation coefficients. Moreover, to confirm whether the joint moment waveforms of the first computer simulation were quantitatively reasonable compared to those of the experiment, we used “normalized integral error” [34]. In the second computer simulation, 15 patterns of sit-to-stand movement based on different times (0.5–4.0 s at intervals of 0.25 s) were entered for each sit-to-stand movement. Therefore, 1500 sit-to-stand movements (20 subjects × 5 trials × 15 sit-to-stand movement times) were analyzed in the second computer simulation.
To calculate the hip joint moment during a sit-to-stand movement in the second computer simulation, we first changed the sampling rate of joint angles obtained from the experiment trials from 100 to 1000 Hz. For example, when a sit-to-stand movement time in an experimental trial is 0.98 s, the number of frames of the joint angles during the sit-to-stand movement was changed from 98 frames (i.e., 100 Hz) to 980 frames (i.e., 1000 Hz) using a linear interpolation. After that, we changed the number of frames for a target sit-to-stand movement time (0.5–4.0 s at intervals of 0.25 s) using a linear interpolation for the second computer simulation. In the above example, to simulate a sit-to-stand movement of 0.75 s in the second computer simulation, the number of frames was changed from 980 to 750 frames. After this procedure, the inverse dynamics from HAT to foot were used (see [14] for detail procedure). Incidentally, velocities (or angular velocity) and accelerations (or angular acceleration) of center of masses were calculated using the central difference formula. Moreover, the hip moment impulse during the sit-to-stand movement was calculated by integrating the hip joint moment. All sit-to-stand movements in the two computer simulations were assumed to have bilateral symmetry.
We performed multiple comparisons to confirm whether the changes in sit-to-stand movement times affect hip moment impulses (or peak hip extension moments). Significance was assumed for p < 0.05, and all p values that were obtained using a paired t test or Wilcoxon signed-rank test were adjusted using Holm correction. All analyses of the sit-to-stand movements in the experiment and the two computer simulations were conducted using MATLAB (MathWorks, USA) and Scilab (Scilab Enterprises, France), and statistical analyses were conducted using R language (R Development Core Team).