## 1 Introduction  
Running, as a common form of exercise, is gaining increasing popularity among individuals. However, with the surge in running trends, running-related injuries also demonstrate an increase that cannot be ignored, contradicting the theoretical health benefits of active exercise [1]. Over millions of years, humans have evolved features related to energy efficiency, strength, stability, and temperature regulation, enabling exceptional performance in long-distance running [2]. However, reports indicate that the injury rates for long-distance runners range from 30% to 80% annually, with foot and ankle injuries constituting approximately one-fourth of these injuries [3]. Various factors, including lower limb joint characteristics [4], foot morphology [5], footwear features [6], and training parameters [7], contribute to the occurrence of running injuries [8; 9; 10]. Running is a complex movement involving multiple joints and muscles, with the hip, knee, and ankle working in concert to form a kinetic chain. The foot, a core component of the musculoskeletal system, plays a crucial role in running. Many running injuries have been associated with abnormal frontal plane motions of the foot [11]. Previous studies have highlighted the potential significance of height differences between the medial and lateral aspects of the foot in influencing abnormal frontal plane motion. There is evidence indicating a strong correlation between foot height asymmetry and running injuries, which is particularly notable among avid runners [12]. Furthermore, research has found that an increased height difference between the medial and lateral aspects of the foot leads to an asymmetric distribution of forces during foot strikes in runners, thereby increasing the load on lower limb joints and subsequently elevating the risk of injury [13]. Differences in foot morphology and the angle of the foot landing during running may impact the ankle, contributing to ankle injuries. Non-contact ankle sprains are reported to be common, and improper foot positioning during walking or running may lead to ankle injuries, representing a potential injury mechanism [14; 15]. During running, abnormal frontal plane motion of the foot can lead to aberrant loading and stress distribution on the knee and hip joints, consequently increasing the risk of injury. Research indicates that frontal plane abnormalities alter the trajectory of lower limb movement, resulting in additional stress on the knee joint during motion, thereby heightening the probability of soft tissue injury in the knee joint [16]. Regarding the knee, excessive dynamic knee valgus has been linked to anterior cruciate ligament tears and patellofemoral pain syndrome, and dynamic knee valgus can be altered by ankle range of motion and hip strength [17]. The hip joint, the proximal link in the lower extremity kinetic chain, shared with the knee joint, is essential, and hip joint dysfunction may serve as the foundation for injuries such as anterior cruciate ligament tears, liliotibial band syndrome, and patellofemoral joint pain [18]. There are numerous methods to prevent running injuries resulting from variations in frontal plane motion of the foot, with the use of footwear featuring height discrepancies between the medial and lateral sides gradually gaining popularity for this purpose [19; 20]. Although regular footwear offers protection and support for the feet, they may excessively cushion and restrict foot movement, potentially impacting lower limb muscle function, leading to decreased muscle functionality and increased risk of musculoskeletal injuries [21; 22]. Therefore, understanding individual foot morphology and selecting appropriate footwear is crucial. Research indicates that the transverse arch, through the action of the tarsal bones, contributes to over 40% of longitudinal foot stiffness. The robust structure of the human foot effectively supports walking or running, representing a key evolutionary adaptation among bipedal animals [23].