# Calculation of the Rearfoot Angle Representing Flatfoot from Comparison to the Cavanagh Arch Index
## 1 Introduction  
The human foot can be divided into three parts: rearfoot, arch of the foot, and forefoot [1]. When walking or running in the mid-stance phase, the body weight passes over the foot as the body comes forward. This aspect is where the foot supports the body weight, and the arch provides necessary shock absorption for the foot [2]. The pronator type of foot rolls far inward during the weight-bearing phase of the stride. This foot type is characterized by a very low or flat arch or commonly called flatfoot type [3]. The absorption of shock loads on this type of foot is low, so it easily tires during activities; however, in over-pronation conditions, most of the burden will be supported by the heel, which can cause heel pain [4] and/or plantar fascitis [5]. Flatfoot soles can be further divided into two types, namely fixed flatfoot and flexible flatfoot [6]. The difference between these two types can be detected when the subject is standing and lying on their back foot (no weight carried by the subject). On the flatfoot subject with the previously mentioned treatment, the flatfoot remains detected when it is not burdened. In contrast, on the flexible flatfoot subject with similar treatment, the condition is significantly reduced or even becomes normal. Patients with flexible flatfoot are mostly children who generally can become normal as they age. Adolescents can also become normal after wearing orthotic shoes with a certain curvature of the medial arch for a certain period [7]. Previous studies have quantified flatfoot type by 2D footprints based on suitability for static standing [6]. The foot is measured from the width of the instep at its widest part. If the measurement is less than 1 cm, the foot type is classified as a flatfoot. The type of foot isexpressed in terms of the Arch Index (AI) value, which is obtained by dividing the midfoot area by the total area of the foot, excluding the toes. The foot is categorized as flatfoot if AI \(\geq\) 0.26 [8]. The measurement of the Clarke angle (\(\alpha\)) is based on the tangent of the angle between the two lines, i.e., (1) the line connecting the most medial aspect of the heel to the most medial metatarsals and (2) the line connecting the most lateral point of the medial foot border to the most medial metatarsal. If the Clarke angle measurement \(\alpha\) < 42\({}^{\circ}\), it is categorized as a flatfoot [9]. In another method, flatfoot can be determined based on Plantar Arch Index (PAI). The PAI is a relationship between the central and posterior regions of the footprints. The PAI is calculated from the following steps: (1) a line is drawn tangentially to the medial forefoot edge and at the heel region; (2) the mean point of the line is calculated; (3) from this mean point, a perpendicular line is drawn crossing the footprint; (4) a similar procedure is repeated at the heel tangency; (5) measurements are obtained of the width of the central region of the footprint so-called A and of the heel region so-called B; (6) the PAI is then calculated from the ratio of A and B. If the PAI value is greater than 0.89, it is indicative of flatfoot [10]. Some authors recommend using the Chippaux-Smirak Index (CSI) as a screening instrument for flatfoot in preschool-aged children. The CSI is defined as the ratio of the maximum width at the middle arch of the footprint and the maximum width at the forefoot metatarsus region of the footprint. The criterion for determining the signs of flatfoot in preschool-aged children is CSI > 62 [11]. The pronation of the foot can also be seen from the rearfoot angle (RFA), which is the angle between the two lines that pass through the Achilles tendon and the posterior heel/calcaneus when a person stands upright [12]. The pronation is caused by the permanent angular movement of the ankle into the foot. It is clinically used to determine heel valgus and varus, i.e., the inclination of the heel bone. If the ankle leans inward, it is called flatfoot or valgus foot.