## 4 Discussion
### Adaptation of IdC Due to Hand Disability and Visual Impairment  
When using the IdS to analyze S10 and S12 para swimmers, we found that all participants displayed synchronized inter-limb coordination patterns. Meanwhile, [PERSON] et al. discovered that 65% of professional swimmers use synchronous limb movements, and 95% of amateur swimmers use asynchronous limb movements [3]. Similar to the study by [PERSON] [3], we discovered that the IdS effectively distinguishes the non-synchronized and synchronized movements between the upper- and lower-limb for para swimmers. However, when analyzing individuals with high swimming proficiency who can maintain good upper and lower limb synchrony despite differences in disability severity and affected body parts, the IdS alone fails to offer adequate information to elucidate how body disabilities affect the coordination of upper and lower limbs. Using the IdIC, the synchronized coordination pattern was further analyzed between different groups. The visualization of the IdIC (Figure 4) showed that limb disability (S10 para swimmers) had a more significant impact on the variation in the IdIC (gray curve under stroke phase A, B, C, and D in Figure 4) than visual impairment (S12 para swimmers, Figure 4c,d), particularly during stroke phases B and C on the affected side (S10 para swimmers, Figure 4a). In these phases, the diverged distribution of the kicking behavior showed no significant difference from the uniform random distribution in Table 3.  
Conversely, the IdIC tended to converge at a particular phase on the unaffected side of S10 para swimmers and on both sides of S12 para swimmers. For example, for S12 para swimmers, both sides at the start (phase B) and end (phase D, i.e., start of the recovery) of the propulsive phase tend to converge at in-phase kicking patterns (\(p<0.01\)). All swimmers adopted a pattern of one arm stroke corresponding to three leg kicks in cycles in Figure 4. However, the data revealed differences in the three continuous kicks in a pull cycle between S10 and S12 para swimmers. In our study, the kicking curve (green curve in Figure 4a) for the affected side of S10 para swimmers displayed significantly more variation at the beginning of the stroke phases compared to the kicking curve of expert swimmers with zero IdS, as previously examined by [PERSON] [3]. Similar to the study by [PERSON] [3], S12 para swimmers in this study showed the three repetitive kicking cycles within a stroke cycle, while the curve shape of the three kick cycles on the affected side of S10 para swimmers in a stroke cycle showed an adapted form (a new attractor) where the shorter duration was seen at the second upbeat phase cycle and longer consequent downbeat phase at the third cycle, as shown in in Figure 4a. These findings suggested that the adapted kicking curve within a pull cycle provided evidence that the S10 swimmers tried to coordinate their kicking to a particular relative phase corresponding to their stroke phases. However, they still displayed higher variation at stroke phases B, C, and D, and showed more random distribution in all four kicking phases. The hand disability in the S10 para swimmer group probably affected the symmetry (or balance) between the left and right sides. S10 para swimmers, on the affected side, showed a more random distribution of the kicking phases (between in- and out-phase) and directions (between up and downbeat) according to the result of the chi-square test in Table 3. However, the kicking curve in Figure 4a reveals that the shape between the three kicks within a stroke cycle is not perfectly paired compared to the unaffected side. The kicking curve for the affected side (Figure 4a) exhibited a higher rate of angle development in the second upbeat and a consecutive lower rate of angle development at the third downbeat. This shortened upbeat phase probably constructed the consecutive, more prolonged downbeat phase. The longer downbeat phase in Figure 4a may help compensate for the extended non-propulsive phase D on the affected side.