## 1 Introduction  
Hallux valgus (HV) is defined as the progressive deviation of the big toe by abduction of the hallux and adduction of the first metatararsal [1]. The development of HV is influenced by extrinsic (e.g., wearing high heels and tight shoes) and intrinsic (e.g., genetics, elasticity of the ligaments, age, and flat feet) factors [2; 3; 4]. This deformity has many effects. It alters foot function, gait, and weight-bearing patterns, causes pain, increases the risk of falling, results in difficulties in shoe fitting, and interferes with the alignment of the lesser toes [5; 6], such as the dislocation of the second metatararsal [7].  
The human foot is like a tripod, consisting of three flexible arches: the medial longitudinal arch (MLA), the lateral longitudinal arch, and the transverse arch. These arches work together and respond to the weight put on the foot while walking by providing shock absorption [8]. This study focuses on the transverse arch, which is in the forefoot [9], and is formed by the five metatarsal heads (MTHs) (Figure 1).  
As HV deformity causes the medial shifting of the first MTH, and because the first MTH itself is a part of the transverse arch, we hypothesized that feet with HV deformity would have a different transverse arch structure compared to feet without HV deformity. Furthermore, during the terminal stance of gait, 90% to 110% of the body weight is unilaterally transferred and supported by the forefoot and hallux, altering the alignments of the small joints [10]. In HV deformity, the alignment of the hallux is already altered. Therefore, we believed that the structure of the transverse arch would also be affected by loading in feet with HV compared to feet without HV.  
Recently, ultrasound (US) usage has become more popular, as it provides high-resolution images at an affordable cost and enables easy manipulation [11], and it was previously used to assess forefoot structure [12, 13]. [PERSON] et al. [14] introduced an US machine, called the weight-bearing plantar ultrasound imaging device (WBPUID), which enables viewing of the transverse arch in weight-bearing conditions. In this study, we use the WBPUID to view the structure of the transverse arch in a simulated terminal stance, as there is a lack of devices that can measure the structure of the transverse arch in motion. To simulate the terminal stance, 90% of body weight was transferred on the tested foot, relying on the fact that 90% to 110% of body weight is being transferred on the foot in the terminal stance. We named this position as the 90% weight-shift (90% W.S.) position.  
Substantial evidence concerning the structure of the transverse arch in feet with HV deformity is lacking. Therefore, this study focuses on the differences in the structure of the transverse arch between feet with and without HV deformity. We specifically took measurements from elderly women because they are more predisposed to this deformity, as they are reported to have more elasticity and to wear tight and high-heeled shoes, which affect the alignment of the first ray [2, 3, 4], and aging being an important risk factor for HV [2, 15]. What's more, we use an affordable device and an easy method for a smoother analysis of the structure of the transverse arch in loading conditions. We hypothesized that with increasing loads, the transverse arch of feet with HV deformity would be wider in length and lower in height than feet without HV deformity. The loading positions were sitting, quiet standing, and 90% W.S. on the tested foot using a weight-bearing US as an assessment device. With this study, we aim to provide a perspective and an understanding of the differences in the transverse arch structure in feet with and without HV deformity, as well as of the effects of loading, along with the feasibility of our measurement methods.  
Figure 1: Representation of the three arches of the foot. The transverse arch is marked in red and it is contact with the ground during terminal stance.