Participants
A public dataset for the overground walking data of 300 participants, which was reported in a previous study [11], was used. To determine the sample size required to attain a reasonable power for the correlation analysis, an a priori power analysis was conducted using R Studio (power = 0.8, significance level = .05, effect size = 0.3 [medium] [12]). The results indicated that the appropriate number of participants was 84. Furthermore, according to a previous study [13], the mean age of patients suffering from hip osteoarthritis is more than 40 y. Therefore, the overground walking data of 84 adults aged between 40 and 69 y were selected randomly and used in the analyses. Table 1 lists the characteristics of all the participants. The study protocol was approved by the ethics committee of the National Institute of Advanced Industrial Science and Technology [11].
Table 1
Participant characteristics (n = 84).
|
Mean
|
SD
|
Minimum
|
Maximum
|
Age, years
|
55.5
|
8.7
|
40
|
68
|
Sex
|
42 males and 42 females
|
ー
|
ー
|
ー
|
Height, m
|
1.63
|
0.09
|
1.38
|
1.81
|
Body mass, kg
|
61.0
|
10.3
|
34
|
89
|
Body mass index
|
22.8
|
2.9
|
17.3
|
31.5
|
Experimental protocol and data acquisition
The details of the experimental protocol and data acquisition can be found in the existing report [11]. Briefly, data acquisition was performed in a room with a straight 10 m path for the participants to walk on [11]. Three-dimensional position data of 55 to 59 reflective markers attached to the participants’ body landmarks and the ground reaction forces were obtained using a 3D motion-capture-system (VICON MX, UK) with a sampling frequency of 200 Hz and force plates (AMTI, USA) sampled at 1000 Hz [11]. The participants were asked to walk barefoot at a comfortable, self-selected speed [11]. Prior to the experiment, the participants were allowed to perform sufficient practice walks to ensure the maintenance of the natural gait [11]. After the practice, the data for 10 gait cycles (five from the right leg and five from the left leg), as determined by the force plates, were recorded [11].
Data processing
For each participant, three trials for the left lower limb were selected randomly and analyzed. We analyzed the stance phase of the left limb (i.e., from the left heel contact to the left toe-off) for each participant, according to a previous study [10]. Furthermore, the three-dimensional marker trajectories, ground reaction forces, center of pressure, and moments of the force plates were filtered using a fourth-order Butterworth low-pass filter at a cut-off frequency of 6 Hz, as described in a previous study [14].
The external hip adduction moment during the stance phase of the left limb for each participant was calculated considering the inverse dynamics (Newton–Euler method). Subsequently, the hip adduction moment impulse was calculated by the integration of the hip adduction moment. The hip adduction moment impulse (Nms) was normalized using the body mass (Nms/kg), as described in an existing report [15]. The first and second peak hip adduction moments (Nm) were calculated at the first (0–50%) and second halves (50–100%) of the stance phase, respectively, and normalized using the body mass (Nm/kg).
The masses, mass positions, and inertia parameters of the segments, as reported in previous studies [16,17], were employed. The hip joint center was determined according to the method proposed by Hara et al. [18]. In particular, the knee joint center was defined as the midpoint of the medial and lateral epicondyles of the femur. The ankle joint center was defined as the midpoint of the medial and lateral malleoli. All the gait analyses were conducted using Scilab.
Musculoskeletal model
A musculoskeletal model was established, according to the findings of a previous study [19]. The number of degrees of freedom (DoF) of the musculoskeletal model was 11 (the pelvis [6 DoF], hip [3 DoF], knee [1 DoF], and ankle [1 DoF]), and the number of muscles was 55 [19]. The muscles were represented using the Hill model and consisted of a contractile, passive, and series element for each muscle [20]. The force-length and force-velocity relationships for the contractile elements were established [21]. In general, the passive elements for each muscle generate a passive force when the muscle is lengthened [21]. However, according to a previous study [22], the passive hip joint moment is small when the range of hip joint is from approximately extension 10° to flexion 30°, such as in the case of walking (i.e., the stance phase [23]). Therefore, the passive force for each muscle was neglected. The musculoskeletal model was scaled for each participant considering the leg lengths of each participant and a cadaver [19].
Muscle force and hip joint contact force
To estimate the muscle forces during the stance phase, static optimization (to minimize the square of the muscle activation [24,25]) was performed. Furthermore, the hip joint contact force during the stance phase was calculated based on a previous study [25]. The hip joint contact force impulse was calculated by integrating the hip joint contact force during the stance phase. The hip joint contact force (N) was normalized using the body mass (Ns/kg). The first and second peak hip joint contact forces (N) were calculated at the first (0–50%) and second halves (50–100%) of the stance phase, respectively, and normalized using the body mass (N/kg).
Statistics
The Shapiro–Wilk test was conducted to determine whether the variables (hip adduction moment impulse, first and second hip adduction moments, hip joint contact force impulse, and first and second peak hip joint contact forces) followed a normal distribution. Based on the results of the normality, Pearson's correlation or Spearman's correlation was used. The significance level was set as <0.05. As described in a previous study [12], the effect size (Large: 0.5<, Medium: 0.3–0.5, Small: 0.1–0.3, and Negligible: <0.1) was determined for each correlation.