Participants
Twenty healthy male participants (height 171.8 ± 5.1 cm; body mass 65.2 ± 7.8 kg; age 21.5 ± 2.5 years), without pes planus or other pathologies volunteered to participate in this study. Forefoot abduction is associated with flattening of the medial longitudinal arch [20], and the pes planus presents as an abduction of the forefoot during standing. Thus, the foot posture was evaluated using the “too many toes” sign [21], and participants who had been observed with one or more toes along the lateral aspect from the back in the standing position (i.e. forefoot abduction) were excluded. Based on this evaluation, as we excluded participants with pes planus, the target participants had only normal foot posture. Participants were recruited from the student population of Niigata University of Health and Welfare. All participants provided informed consent prior to participation. The present study was reviewed and approved by the ethical committee (No. 17575-150,422) at our institution.
Experimental protocol
The reflective markers (9.5 mm in diameter) were fixed to the right shank and foot at the most anterior prominence of the tibial tuberosity, most proximal apex of the fibula head, distal apex of the medial malleolus, distal apex of the lateral malleolus, Achilles tendon attachment, most medial apex of the sustentaculum tali, lateral apex of the peroneal tubercle, most medial apex of the tuberosity of the navicular, most lateral apex of the tuberosity of cuboid, dorso-medial aspect of the first metatarso-cuneiform joint (first metatarsal base), dorso-medial aspect of the first metatarso-phalangeal joint (first metatarsal head), dorso-medial aspect of the second metatarso-cuneiform joint (second metatarsal base), dorso-medial aspect of the second metatarso-phalangeal joint (second metatarsal head), dorso-medial aspect of the fifth metatarso-phalangeal joint (fifth metatarsal head), and most distal and dorsal point of the head of the proximal phalanx head of the hallux (Fig. 1a, b). The marker attachment was based on the foot model by Leardini et al. [22]. The repeatability [23] of this model has been confirmed in previous studies. Prior to data acquisition, static standing in the anatomical position was measured in each participant to calculate offset values for all joint rotation, which were eventually subtracted from the corresponding values over the walking stance.
The participants walked barefoot on a treadmill (Auto Runner AR-100; Minato Medical Science, Osaka, Japan) set to walking speed of 1.3 m s−1 because the coupling angle is very sensitive to small angle changes [3] and the difference in walking speeds among participants may increase variability of the coupling angle among participants. Walking speed in this study was set in reference to the speed used in previous studies [5, 24, 25], and this speed was verbally confirmed to each participant that it is roughly the usual speed preliminarily. During the tasks, measurements were performed by using a three-dimensional motion analysis system (Vicon Motion Systems, Oxford, UK) that included 13 infrared cameras. Before data collection, the participants were allowed to accustom themselves to the speed of the treadmill for at least 1 min. The walking biomechanics were continuously measured at 10 strides on the treadmill for each participant.
Data analysis
Raw marker trajectory data were captured and filtered during walking, by using a second-order, zero-lag Butterworth, low-pass filter with a cutoff frequency of 6 Hz. The following four segments were defined in the kinematics model: (i) the shank comprising the tibia and fibula; (ii) the rearfoot (i.e., calcaneus); (iii) the midfoot comprising the navicular, cuneiform, and cuboid; and (iv) the forefoot comprising the first to fifth metatarsals. In this study, the three-dimensional joint angles were calculated at the distal segment, expressed relative to the adjacent proximal segment by using a right-handed orthogonal Cardan Xyz sequence of rotations (a sequence of plantarflexion/dorsiflexion, eversion/inversion, and abduction/adduction), which was selected to be equivalent to the joint coordinate system [24, 26, 27]. Hence, the joint angles were calculated as plantarflexion/dorsiflexion, eversion/inversion, and abduction/adduction of the rearfoot with respect to the shank, midfoot with respect to the rearfoot, and forefoot with respect to the midfoot.
The shank coordinate system was defined as described by Cappozzo et al. [28]. Briefly, the origin is located at the midpoint of the medial and lateral malleolus. The vertical axis (z) was defined as the projection of the line joining the origin and the tibial tuberosity on the frontal plane passing through the origin and the lateral malleolus and fibular head. The transverse axis (x) was orthogonal to the z-axis and lies in this frontal plane. The y-axis is orthogonal to the x and z planes.
The analysis interval in this study was only during the stance phase, same as the previous study [13]. Following calculation of the joint angles during the task, the data were time normalized to the stance phase (100 data points) at each stride.
Calculation of the coupling angle
Intersegmental coordination was inferred from a coupling angle (γ) (Fig. 2). The coupling angle was calculated by using the modified vector coding technique in this study [13] [Eq. (1)].
$$ {\gamma}_{j{,}_i}={\mathrm{tan}}^{-1}\;\left(\frac{y_{j,i+1}-{y}_{j,i}}{x_{j,i+1}-{x}_{j,i}}\right) $$
(1)
where 0° ≤ γ ≤ 360°, x
i
, and y
i
represent the proximal and distal joint angles, respectively. In addition, i represents the percent stance of the j th stride. To determine the coupling angle within a participant (i.e., ten strides) and among the participants, the mean coupling angle (\( \overline{\gamma_i} \)) was calculated from the mean x
i
(\( \overline{x_i} \)) and the mean y
i
(\( \overline{y_i} \)) at each percentage of stance [Eqs. (2), (3), (4), (5)]. The calculations were performed using the circular statistics [13].
$$ \overline{x_i}=\frac{1}{n}\;\sum_{j=1}^n\left(\cos\;{\gamma}_{j,i}\right) $$
(2)
$$ \overline{y_i}=\frac{1}{n}\;\sum_{j=1}^n\left(\sin\;{\gamma}_{j,i}\right) $$
(3)
$$ \overline{\gamma_i}={\mathrm{tan}}^{-1}\left(\overline{y_i}/\overline{x_i}\right)\kern0.5em \overline{x_i}>0 $$
(4)
$$ \overline{\gamma_i}=180+{\mathrm{tan}}^{-1}\left(\overline{y_i}/\overline{x_i}\right)\kern0.5em \overline{x_i}<0 $$
(5)
The length of the coupling angle (\( \overline{R_i} \)) was calculated according to Eq. (6). Finally, coupling angle variability (CAV
i
) was calculated among the participants using Eq. (7) [29].
$$ {\overline{R}}_i=\sqrt{{\overline{x_i}}^2+{\overline{y_i}}^2} $$
(6)
$$ {CAV}_i=\sqrt{2\cdot \left(1-\overline{R_i}\right)}\cdot \frac{180}{\pi } $$
(7)
Categorization of coordination patterns
Intersegmental coordination was assessed as follows: between the rearfoot and midfoot plantarflexion/dorsiflexion, between the rearfoot and midfoot eversion/inversion, between the rearfoot and midfoot abduction/adduction, between the midfoot and forefoot plantarflexion/dorsiflexion, between the midfoot and forefoot eversion/inversion, and between the midfoot and forefoot abduction/adduction. The coupling angle represents an instantaneous spatial relationship from which four unique coordination patterns can be identified: (i) in-phase with proximal dominancy (the same direction and greater angular amplitude of proximal segment), (ii) in-phase with distal dominancy (the same direction and greater angular amplitude of distal segment), (iii) anti-phase with proximal dominancy (the opposite direction and greater angular amplitude of proximal segment), and (iv) anti-phase with distal dominancy (the opposite direction and greater angular amplitude of distal segment) [18]. For example, the in-phase with proximal dominancy in the rearfoot and midfoot coordination is adjoining segments that rotate in the same direction and greater angular amplitude of the rearfoot compared to midfoot motion. In the present study, the positive direction (+) of segmental rotation was defined as dorsiflexion, inversion, and adduction.
The stance phase was divided into the early stance (1%–33%), midstance (34%–66%), and late stance (67%–99%) based on a previous study [13]. These phases represent the loading response, midstance, and propulsion, respectively. Finally, the mean coupling angles were categorized into one of the four coordination patterns at each phase (Fig. 3; the unit circle was divided into 45° bins).