## 4 Discussion
We think that the transverse arch of the With-HV group adopts a similar protective mechanism where muscular forces are acting on the transverse arch. HV feet have weaker intrinsic muscles than normal feet, and such individuals with HV feet are subjects for strengthening and rehabilitation exercises for HV prevention [28; 29], particularly in the abductor hallucis muscle [11; 27]. Intrinsic muscles of the foot are also regarded as accessory toe flexors that contribute to the stabilization of the foot when certain deformity occurs or excessive weight is being loaded by stiffening the arch and increasing its height [24; 30]. In addition, a previous study about HV mentioned that intrinsic muscles are likely to activate earlier and have a higher activation than other muscles during gait [5]. Therefore, we could hypothesize that these muscles are a part of an active contractile mechanism that contributes to the stiffness of the arch [24; 31; 32] by attempting to protect its height; however, they are not strong enough to adduct the metatarsals and protect further widening of TAL. Furthermore, HV deformity involves the pronation and adduction of the first metatarsal [19; 21]. This change also affects the sesamoid bones. The positioning of the sesamoids in relation to the first metatarsal also differs between weight-bearing and non-weight-bearing conditions [33]. The information regarding this positioning is still controversial in the literature. While [PERSON] et al. [34] mentioned that the first metatarsal, not the sesamoid, shifts laterally, others [21; 35] have mentioned the possibility of the pronation of the entire metatarso-sesamoid complex, depending on the degree of laxity of the ligaments. Considering the pronation of the entire metatarso-sesamoid complex in HV, we could explain the decrease in MS height and increase in LS height in the With-HV group compared with those in the Without-HV group; when the complex is pronated, the MS goes downward and its height is shortened, while the LS goes upward and its height is increased. Lastly, the decrease in TAH during loading can be explained by the flexibility and dropping of the arch [19] and its propulsion ability. Under loading conditions, the transverse arch can be classified into two types: the hyper-flexible type, where the arch flattens at weight-bearing, and the hypo-flexible type, where the arch does not flatten during weight-bearing [19; 36]. As TAH in the With-HV group decreased with increasing loads, we suggest that the transverse arch of the With-HV group is of the hyper-flexible type. This study has many limitations. First, we considered the feet, regardless of whether HV was a bilateral deformity or not, and we did not consider the sesamoid classification grades, and considered the first metatarsal and sesamoid bones as one complex that pronates. Second, we have not measured the strength of the muscles acting on the foot. Third, the measurement positions were static and a simulation of the terminal stance of gait; in actual gait, muscle forces and center of pressure might act differently on the structure of the transverse arch. However, our results on the effects of loading on the bony structure of the transverse arch in normal and HV feet suggest that in HV cases, passive elastic elements (such as the DTML) are hyper-mobile and act on the widening of the transverse arch, while active force-generating elements (such as the intrinsic muscles) act on the transverse to prevent its collapse and propel the necessary forces for gait. These findings can be used to improve and popularize muscular exercise regimens that are employed to prevent HV and allow better shoe fit for people with HV, such as the development of shoes allowing the widening of the transverse arch. For further research, it would be important to evaluate the transverse arch structure in parallel with muscle activity in order to validate this muscular-action theory and have a clearer idea about the muscles participating in the transverse arch function.