Verification of accuracy and repeatability of the registration of 3D model with 2D image in single plane perspective system
Using RSA technology and three-dimensional model and two-dimensional image single plane registration technology, the motion data difference of bone block and joint of the hindfoot is calculated (Table 1, 2). Among the four tarsal bones of talus, scaphoid, cuboid, and calcaneus, the cuboid has the largest translation error in the same plane of X-ray imaging, which can reach -1.57 ± 3.07 mm; The talus has the largest rotation error, which can reach -0.45 ± 0.7 °. In any other plane perpendicular to this plane, the scaphoid has the largest translation error, which can reach 3.07 ± 2.52 mm; The talus has the largest rotation error, which can reach -0.87 ± 0.32 °. In hindfoot, in the same plane of X-ray imaging, the maximum translation error from the talonavicular joint can reach -0.13 ± 0.4mm; The talus has the largest rotation error, which can reach -1.87 ± 1.05 °. In any other plane perpendicular to this plane, the subtalar joint has the largest translation and rotation errors, which can reach 2.05 ± 0.95 mm and -1.8 ± 2.33 ° respectively.
Table 1
Differences in hindfoot bone motion data measured by RSA technique and Fluo software single-plane registration technique
Bone | Translation(mm) | Rotation (°) |
∆x | P | ∆y | P | ∆z | P | ∆α | P | ∆β | P | ∆γ | P |
Talus | 3.00±2.21 | 0.23 | 0.57±1.73 | 0.29 | -0.21±0.38 | 0.47 | -0.45±0.7 | 0.65 | 0.48±2.92 | 0.27 | -0.87±2.32 | 0.44 |
Calcaneus | 1.5±0.51 | 0.55 | 0.22±0.4 | 0.67 | -0.16±0.41 | 0.91 | -0.20±0.23 | 0.34 | 0.86±1.82 | 0.75 | -0.27±1.12 | 0.57 |
Navicular | 3.07±2.52 | 0.79 | 0.38±1.12 | 0.46 | -0.87±0.90 | 0.48 | -0.25±1.25 | 0.37 | 0.90±2.30 | 0.72 | -0.70±1.94 | 0.95 |
Cuboid | 2.19±2.4 | 0.77 | 0.63±1.47 | 0.35 | -1.57±3.07 | 0.37 | 0.02±0.9 | 0.48 | 0.16±3.4 | 0.53 | -0.70±1.94 | 0.48 |
P < 0.05 indicated a statistical difference. |
Table 2
Differences of hindfoot motion data measured by RSA technique and Fluo software single plane registration technique
Joint | Translation(mm) | Rotation (°) |
∆x | P | ∆y | P | ∆z | P | ∆α | P | ∆β | P | ∆γ | P |
Subtalar joint | 2.05±0.95 | 0.51 | -0.28±0.19 | 0.42 | 0.19±0.51 | 0.23 | -1.87±1.05 | 0.63 | 0.76±2.24 | 0.19 | -1.8±2.33 | 0.61 |
Talonavicular joint | -1.01±0.2 | 0.59 | 0.33±0.4 | 0.67 | 0.27±0.78 | 0.48 | -0.24±2.03 | 0.46 | -1.0±3.26 | 043 | -0.17±2.17 | 0.75 |
Calcaneocuboid joint | 1.00±0.72 | 0.37 | -0.29±0.38 | 0.56 | -0.29±0.86 | 0.60 | 0.56±2.89 | 0.52 | -0.12±2.91 | 0.57 | 0.61±2.69 | 0.83 |
P < 0.05 indicated a statistical difference. |
Average Trend And Rom Of The Hindfoot
Fig. 6 shows the trend of seven consecutive steps of each joint touching the ground on the X, Y, and Z axes. After studying 14 normal feet, it is concluded that the average values of seven consecutive postures of subtalar joint rotating around the X-axis (plantar flexion and back extension) are -1.78 ± 1.49 °, -0.27 ± 1.71 °, 1.32 ± 2.12 °, 3.27 ± 1.98 °, 2.83 ± 2.62 °, -0.98 ± 1.63 °, -2.92 ± 1.23 ° respectively, and the average ROM of rotation is 6.93 ± 2.47 ° (Fig. 7A, B); The average value of rotation (varus valgus) of subtalar joint around Y-axis in seven consecutive steps is 2.90 ± 3.74 °, - 0.15 ± 3.09 °, - 1.89 ± 3.66 °, - 5.30 ± 5.54 °, - 5.80 ± 4.74 °, 0.65 ± 5.16 °, 6.55 ± 4.98 °, and the average ROM of rotation is 13.65 ± 3.64 ° (Fig. 7C, D); The average value of rotation (internal rotation and external rotation) of subtalar joint around Z-axis in seven consecutive steps were 4.27 ± 2.68 °, 2.06 ± 3.06 °, - 1.18 ± 2.69 °, - 3.33 ± 2.47 °, - 2.63 ± 4.47 °, 1.50 ± 3.05 ° and 6.32 ± 3.16 °, respectively. The average ROM of rotation was 10.74 ± 2.52 ° (Fig. 7E, F).
The average rotation (plantar flexion and back extension) of the talonavicular joint around the X-axis in seven consecutive postures were -1.16 ± 1.56 °, 1.14 ± 2.37 °, 2.29 ± 2.49 °, 4.81 ± 2.95 °, 5.35 ± 2.44 °, 1.27 ± 1.76 ° and - 3.43 ± 1.25 °, respectively. The average ROM of rotation was 9.19 ± 2.86 ° (Fig. 7G, H); The average rotation (varus and valgus) of the talonavicular joint around the Y-axis in seven consecutive steps were 6.39 ± 5.05 °, 1.67 ± 5.70 °, - 1.93 ± 5.80 °, - 9.06 ± 4.35 °, - 7.47 ± 6.05 °, - 1.01 ± 6.63 ° and 4.07 ± 2.82 °, respectively. The average ROM of rotation was 18.41 ± 3.80 ° (Fig. 7I, J); The average rotation (internal rotation and external rotation) of the talonavicular joint around the Z-axis in seven consecutive steps were 2.88 ± 3.07 °, - 0.53 ± 4.11 °, - 2.24 ± 3.74 °, - 6.87 ± 3.0 °, - 6.39 ± 4.63 °, 0.54 ± 5.98 ° and 7.08 ± 4.65 °, respectively. The average ROM of rotation was 16.11 ± 4.44 ° (Fig. 7K, L).
The average value of rotation (plantar flexion and back extension) of calcaneocuboid joint around the X-axis in seven consecutive postures were -0.89 ± 1.30 °, -0.26 ± 1.74 °, 1.04 ± 1.42 °, 1.89 ± 1.42 °, 3.04 ± 1.92 °, 0.32 ± 1.32 ° and -1.43 ± 1.87 °, respectively. The average ROM of rotation was 4.89 ± 1.44 ° (Fig. 7M, N); The average rotation (varus and valgus) of the heel cuboid joint around the Y-axis in seven consecutive postures were 0.52 ± 2.07 °, - 1.16 ± 2.63 °, - 2.69 ± 2.66 °, - 5.31 ± 2.85 °, - 5.94 ± 3.61 °, - 2.33 ± 3.78 ° and 1.01 ± 2.89 °, respectively. The average ROM of rotation was 8.22 ± 2.30 ° (Fig. 7O, P); The average rotation (internal rotation and external rotation) of the heel cuboid joint around the Z-axis in seven consecutive postures were 1.39 ± 2.94 °, 0.45 ± 2.87 °, - 1.84 ± 2.98 °, - 3.59 ± 2.51 °, - 3.76 ± 3.14 °, - 0.18 ± 3.49 ° and 3.98 ± 3.46 °, respectively. The average ROM of rotation was 9.11 ± 3.30 ° (Fig. 7Q, R).
After studying 10 stage Ⅱ flatfoot, it is concluded that the average values of seven consecutive postures of subtalar joint rotating around the X-axis (plantar flexion and back extension) are 1.22 ± 2.54 °, 3.57 ± 2.89 °, 5.75 ± 2.03 °, 6.25 ± 1.74 °, 8.43 ± 1.77 °, 5.83 ± 1.79 °, 1.60 ± 0.71 °, respectively. The average ROM of rotation was 8.11 ± 1.39 ° (Fig. 7A, B), which was statistically significant (P < 0.05, Table 3); The average value of rotation (varus valgus) of subtalar joint around Y-axis in seven consecutive walking postures was 3.58 ± 5.64 °, - 1.84 ± 6.83 °, - 7.82 ± 5.57 °, - 11.27 ± 8.51 °, - 14.24 ± 6.06 °, - 10.22 ± 7.69 °, - 6.15 ± 7.01 °, and the average ROM of rotation was 19.77 ± 5.08 ° (Fig. 7C, D), which was greater than that of normal feet and had statistical significance (P < 0.05, Table 3); The mean value of rotation (internal rotation and external rotation) of subtalar joint around Z-axis in seven consecutive walking postures were 3.21 ± 4.43 °, 1.06 ± 4.22 °, - 3.55 ± 2.81 °, - 5.94 ± 4.12 °, - 5.03 ± 2.48 °, 0.54 ± 3.82 ° and 1.41 ± 3.44 °, respectively. The mean ROM of rotation was 10.12 ± 2.99 ° (Fig. 7E, F). There was no significant difference between its ROM and normal foot (P > 0.05, Table 3).
Table 3
Comparison of range of motion of hindfoot between the normal foot and stage II flatfoot.
| ROM of subtalar joint (°) | ROM of talonavicular joint (°) | ROM of calcaneocuboid joint (°) |
X-axis | Y-axis | Z-axis | X-axis | Y-axis | Z-axis | X-axis | Y-axis | Z-axis |
Normal | 6.93±2.47 | 13.65±3.64 | 10.74±2.52 | 9.19±2.86 | 18.41±3.80 | 16.11±4.44 | 4.89±1.44 | 8.22±2.3 | 9.11±3.30 |
Flatfoot | 8.11±1.39 | 19.77±5.08 | 10.12±2.99 | 13.56±4.14 | 31.91±8.45 | 17.13±5.38 | 5.29±1.82 | 8.49±2.68 | 9.45±3.44 |
P | 0.023 | 0.001 | 0.21 | 0.001 | 0.001 | 0.16 | 0.45 | 0.33 | 0.76 |
ROM: Range of motion; P < 0.05 indicated a statistical difference. |
The average rotation (plantar flexion and back extension) of the talonavicular joint around the x-axis in seven consecutive postures were 0.40 ± 6.57 °, 2.62 ± 5.95 °, 7.67 ± 8.65 °, 8.02 ± 8.14 °, 11.51 ± 8.71 °, 2.95 ± 8.07 °, - 0.09 ± 7.19 °, respectively. The average ROM of the rotation was 13.56 ± 4.14 ° (Fig. 7G, H), which was greater than that of the normal foot and had statistical significance (P < 0.05, Table 3); The average rotation (varus valgus) of the talonavicular joint around the y-axis in seven consecutive walking postures were 2.04 ± 12.03 °, - 3.35 ± 12.74 °, - 12.11 ± 15.60 °, - 18.89 ± 9.23 °, - 27.66 ± 8.57 °, - 19.04 ± 8.18 °, - 15.02 ± 8.34 °, and the average ROM of rotation was 31.91 ± 8.45 ° (Fig. 7I, J), which was greater than that of the normal foot and had statistical significance (P < 0.05, Table 3); The average rotation (internal rotation and external rotation) of the talonavicular joint around the Z-axis in seven consecutive walking postures were 2.67 ± 4.89 °, - 1.34 ± 5.60 °, - 4.74 ± 3.52 °, - 8.54 ± 4.92 °, - 8.65 ± 3.78 °, - 2.45 ± 2.26 ° and 1.82 ± 3.98 °, respectively. The average ROM of rotation was 17.13 ± 5.38 ° (Fig. 7K, L). There was no significant difference between the ROM and the normal foot (P > 0.05, Table 3).
The average value of rotation (plantar flexion and back extension) of calcaneocuboid joint around the X-axis in seven consecutive postures were -0.29 ± 2.22 °, -0.75 ± 2.50 °, 1.69 ± 2.01 °, 1.77 ± 1.77 °, 3.21 ± 2.09 °, -0.52 ± 3.05 °, -0.65 ± 2.43 °, and the average ROM of rotation was 5.29 ± 1.82 ° (Fig. 7M, N). There was no significant difference between its ROM and that of normal feet (P > 0.05, Table 3); The average rotation (varus and valgus) of the calcaneocuboid joint around the Y-axis in seven consecutive postures were 0.04 ± 2.20 °, - 1.43 ± 2.82 °, - 3.15 ± 2.83 °, - 5.51 ± 3.24 °, - 6.45 ± 4.43 °, - 2.88 ± 4.51 ° and 0.65 ± 2.91 °, respectively. The average ROM of rotation was 8.49 ± 2.68 ° (Fig. 7O, P). There was no significant difference between the ROM and the normal foot (P > 0.05, Table 3); The average rotation (internal rotation and external rotation) of the heel cuboid joint around the Z-axis in seven consecutive postures were 1.45 ± 3.69 °, 0.64 ± 3.09 °, - 1.65 ± 3.00 °, - 3.25 ± 2.91 °, - 3.66 ± 2.86 °, 1.23 ± 3.27 ° and 4.46 ± 3.86 °, respectively. The average rotation ROM was 9.45 ± 3.44 ° (Fig. 7Q, L). There was no significant difference between its ROM and that of normal feet (P > 0.05, Table 3).
The motion of hindfoot from the first step to the third step (initial touchdown)
The mean values of rotation of the subtalar joint of the normal foot around the X (metatarsal flexion and extension), Y (varus valgus), and Z (internal rotation and external rotation) axes from the first to the third step were 3.09 ± 1.72 °, − 4.80 ± 2.28 °, and − 5.45 ± 2.13 °, respectively, that is, the amplitude of external rotation of the calcaneal phase about the X, Y, and Z axes was 3.09 ± 1.72 °, 4.80 ± 2.28 °, and 5.45 ± 2.13 °, respectively; while the mean values of rotation of the subtalar joint of the flatfoot around the X, Y, and Z axes at this stage were 3.33 ± 2.78 °, − 11.40 ± 5.11 °, and − 6.76 ± 2.82 °, respectively, that is, the amplitude of external rotation of the calcaneal phase about the distance extension and valgus was 3.33 ± 2.78 °, 11.40 ± 5.11 °, and 6.76 ± 2.82 °, respectively, and the degree of external rotation of the calcaneal phase about the distance was greater than that of the normal foot, and the differences were statistically significant (P < 0.05, Fig. 8A, Table 4).
Table 4
Motion of the hindfoot from the first step to the third step, from the third step to the fifth step, and from the fifth step to the seventh step.
| ROM of subtalar joint (°) | ROM of talonavicular joint (°) | ROM of calcaneocuboid joint (°) |
Normal | Flatfoot | P | Normal | Flatfoot | P | Normal | Flatfoot | P |
Motion31(X) | 3.09 ±1.72 | 3.33 ±2.78 | 0.031 | 3.45±1.93 | 7.27±3.78 | 0.001 | 1.93±1.49 | 1.98±1.77 | 0.57 |
Motion31(Y) | -4.80±2.28 | -11.4±5.11 | 0.001 | -8.32±3.30 | -14.15±8.20 | 0.001 | -3.22±2.18 | -3.20±2.17 | 0.65 |
Motion31(Z) | -5.45±2.13 | -6.76±2.82 | 0.021 | -5.12±2.86 | -7.40±4.36 | 0.002 | -3.24±1.95 | -3.10±2.21 | 0.24 |
Motion53(X) | 1.51±1.91 | 2.69±1.49 | 0.013 | 3.06±1.52 | 3.84±5.34 | 0.034 | 2.00±1.75 | 2.15 ±1.44 | 0.32 |
Motion53(Y) | -3.90±3.04 | -6.42±2.95 | 0.020 | -5.55±5.90 | -15.56±15.48 | 0.0001 | -3.25±3.31 | -3.29±3.70 | 0.34 |
Motion53(Z) | -1.45±2.52 | -1.49±0.80 | 0.45 | -4.15±5.56 | -5.31±5.54 | 0.01 | -1.91±3.54 | -2.00±3.90 | 0.57 |
Motion75(X) | -5.75±2.99 | -6.83±1.50 | 0.03 | -8.79±2.95 | -11.60±5.18 | 0.001 | -4.47±1.58 | -3.87±1.59 | 0.11 |
Motion75(Y) | 12.36±3.19 | 8.09±7.67 | 0.001 | 11.55±5.33 | 7.34±8.31 | 0.002 | 6.95±2.79 | 7.10±3.10 | 0.33 |
Motion75(Z) | 8.96±3.08 | 6.45±1.94 | 0.01 | 13.48±5.49 | 10.47±5.50 | 0.008 | 7.75±2.85 | 8.12±2.87 | 0.56 |
Motion31 (X), motion31 (Y) and motion31 (Z) respectively represent the motion changes of each joint on the X, Y and Z axes from the first step to the third step; Motion53 (X), motion53 (Y) and motion53 (Z) respectively represent the motion changes of each joint on the X, Y and Z axes from the third step to the fifth step; Motion75 (X), motion75 (Y) and motion75 (X) represent the motion changes of each joint on the X, Y and Z axes from the fifth step to the seventh step. P < 0.05 showed statistical difference. |
The mean rotation of the talonavicular joint around the X (metatarsal flexion and extension), Y (varus valgus), and Z (internal rotation and external rotation) axes from the first to the third step in the normal foot was 3.45 ± 1.93 °, − 8.32 ± 3.30 °, and − 5.12 ± 2.86 °, respectively, that is, the amplitude of external rotation of the scaphoid relative to the extension and valgus of the distance was 3.45 ± 1.93 °, 8.32 ± 3.30 °, and 5.12 ± 2.86 °, respectively; while the mean rotation of the talonavicular joint of the flatfoot around the X, Y, and Z axes at this stage was 7.27 ± 3.78 °, − 14.15 ± 8.20 °, and − 7.40 ± 4.36 °, respectively, that is, the amplitude of external rotation of the scaphoid relative to the extension and valgus of the distance was 7.27 ± 3.78 °, 14.15 ± 8.20 °, and 7.40 ± 4.36 °, respectively, and the degree of external rotation of extension and valgus was greater than that of the normal foot and the difference was statistically significant (P < 0.05, Fig. 8B, Table 4).
The mean rotation of the calcaneocuboid joint of the normal foot around the X (metatarsal flexion and extension), Y (varus valgus), and Z (internal rotation and external rotation) axes from the first to the third step was 1.93 ± 1.49 °, − 3.22 ± 2.18 °, and − 3.24 ± 1.95 °, respectively, that is, the amplitude of external rotation of the cuboid phase for calcaneal extension and valgus was 1.93 ± 1.49 °, 3.22 ± 2.18 °, and 3.24 ± 1.95 °, respectively; while the mean rotation of the calcaneocuboid joint of the flatfoot around the X, Y, and Z axes at this stage was 1.98 ± 1.77 °, − 3.20 ± 2.17 °, and − 3.10 ± 2.21 °, respectively, that is, the amplitude of external rotation of the cuboid phase for calcaneal extension and valgus was 1.98 ± 1.77 °, 3.20 ± 2.17 °, and 3.10 ± 2.21 °, respectively, and the degree of external rotation of extension and valgus was not significantly different from that of the normal foot (P > 0.05, Fig. 8C, Table 4).
The motion of hindfoot from the third step to the fifth step (mid stance phase)
The mean values of rotation of the subtalar joint of the normal foot around the X (metatarsal flexion and extension), Y (varus valgus), and Z (internal rotation and external rotation) axes from the third to the fifth step were 1.51 ± 1.91 °, − 3.90 ± 3.04 °, and − 1.45 ± 2.52 °, respectively, that is, the amplitude of external rotation of the calcaneal phase about the X, Y, and Z axes was 1.51 ± 1.91 °, 3.90 ± 3.04 °, and 1.45 ± 2.52 °, respectively; while the mean values of rotation of the subtalar joint of the flat foot around the X, Y, and Z axes at this stage were 2.69 ± 1.49 °, − 6.42 ± 2.95 °, and − 1.49 ± 0.80 °, respectively, that is, the amplitude of external rotation of the calcaneal phase about the extension and valgus was 2.69 ± 1.49 °, 6.42 ± 2.95 °, and 1.49 ± 0.80 °, respectively, and the degree of extension and external rotation was greater than that of the normal foot, and the difference was statistically significant (p < 0.05), but there was no significant difference in external rotation (P > 0.05, Fig. 8A, Table 4).
The mean rotation of the talonavicular joint from the third to the fifth stance around the X (metatarsal flexion and extension), Y (varus valgus), and Z (internal rotation and external rotation) axes of the normal foot was 3.06 ± 1.52 °, − 5.55 ± 5.90 °, and − 4.15 ± 5.56 °, respectively, that is, the amplitude of external rotation of the scaphoid relative to the dorsal extension and valgus axis of the distance was 3.06 ± 1.52 °, 5.55 ± 5.90 °, and 4.15 ± 5.56 °, respectively; while the mean rotation of the talonavicular joint around the X, Y, and Z axes at this stage was 3.84 ± 5.34 °, − 15.56 ± 15.48 °, and − 5.31 ± 5.54 °, respectively, that is, the amplitude of external rotation of the scaphoid relative to the dorsal extension and valgus was 3.84 ± 5.34 °, 15.56 ± 15.48 °, and 5.31 ± 5.54 °, respectively, and the degree of external rotation of the extension and valgus was greater than that of the normal foot and the difference was statistically significant (P < 0.05, Fig. 8B, Table 4).
The mean rotation of the calcaneocuboid joint of the normal foot around the X (metatarsal flexion and extension), Y (varus valgus), and Z (internal rotation and external rotation) axes from the third to the fifth step was 2.00 ± 1.75 °, − 3.25 ± 3.31 °, and − 1.91 ± 3.54 °, respectively, that is, the amplitude of valgus external rotation of the cuboid phase for calcaneal extension was 2.00 ± 1.75 °, 3.25 ± 3.31 °, and 1.91 ± 3.54 °, respectively; while the mean rotation of the calcaneocuboid joint around the X, Y, and Z axes at this stage was 2.15 ± 1.44 °, − 3.29 ± 3.70 °, and − 2.00 ± 3.90 °, respectively, that is, the amplitude of valgus external rotation of the cuboid phase for calcaneal extension was 2.15 ± 1.44 °, 3.29 ± 3.70 °, and 2.00 ± 3.90 °, respectively, and the degree of valgus external rotation of extension was not significantly different from that of the normal foot (P > 0.05, Fig. 8C, Table 4).
The motion of hindfoot from the fifth step to the seventh step (late stance phase)
The mean values of rotation of the subtalar joint of the normal foot around the X (metatarsal flexion and extension), Y (varus valgus), and Z (internal rotation and external rotation) axes from the fifth to the seventh step were − 5.75 ± 2.99 °, 12.36 ± 3.19 °, and 8.96 ± 3.08 °, respectively, that is, the amplitude of internal rotation of the calcaneal phase from the plantar flexion was 5.75 ± 2.99 °, 12.36 ± 3.19 °, and 8.96 ± 3.08 °, respectively; while the mean values of rotation of the subtalar joint of the flat foot around the X, Y, and Z axes at this stage were − 6.83 ± 1.50 °, 8.09 ± 7.67 °, and 6.45 ± 1.94 °, respectively, that is, the amplitude of internal rotation of the calcaneal phase from the plantar flexion was 6.83 ± 1.50 °, 8.09 ± 7.67 °, and 6.45 ± 1.94 °, respectively, and the degree of internal rotation was less than that of the normal foot and the difference was statistically significant (P < 0.05), but the degree of metatarsal flexion was greater than that of the normal foot (Fig. 8A, Table 4).
The mean rotation of the talonavicular joint around the X (metatarsal flexion and extension), Y (varus valgus), and Z (internal rotation and external rotation) axes from the fifth to the seventh step in the normal foot was − 8.79 ± 2.95 °, 11.55 ± 5.33 °, and 13.48 ± 5.49 °, respectively, that is, the amplitude of internal rotation of the scaphoid relative to the talometatarsal flexion and internal rotation was 8.79 ± 2.95 °, 11.55 ± 5.33 °, and 13.48 ± 5.49 °, respectively, while the mean rotation of the talonavicular joint around the X, Y, and Z axes at this stage in the flat foot was − 11.60 ± 5.18 °, 7.34 ± 8.31 °, and 10.47 ± 5.50 °, respectively, that is, the amplitude of internal rotation of the scaphoid relative to the talar flexion and internal rotation was 11.60 ± 5.18 °, 7.34 ± 8.31 °, and 10.47 ± 5.50 °, respectively, and the degree of internal rotation was less than that in the normal foot and the difference was statistically significant (P < 0.05), but the degree of metatarsal flexion was greater than that in the normal foot (Fig. 8B, Table 4).
The mean values of rotation of the calcaneocuboid joint of the normal foot around the X (metatarsal flexion and extension), Y (varus valgus), and Z (internal rotation and external rotation) axes from the fifth to the seventh step were − 4.47 ± 1.58 °, 6.95 ± 2.79 °, and 7.75 ± 2.85 °, respectively, that is, the amplitude of internal rotation of the cuboid phase about the X, Y, and Z axes of the calcaneus was 4.47 ± 1.58 °, 6.95 ± 2.79 °, and 7.75 ± 2.85 °, respectively; while the mean values of rotation of the calcaneocuboid joint of the flat foot around the X, Y, and Z axes at this stage were − 3.87 ± 1.59 °, 7.10 ± 3.10 °, and 8.12 ± 2.87 °, respectively, that is, the amplitude of internal rotation of the cuboid phase about the calcaneal flexion and internal rotation was 3.87 ± 1.59 °, 7.10 ± 3.10 °, and 8.12 ± 2.87 °, respectively, and the degree of internal rotation of the metatarsal flexion and internal rotation was not significantly different from that of the normal foot (P > 0.05, Fig. 8C, Table 4).