## 2 Methods
### Data Analysis  
The Nexus software (version 2.10.3, Vicon, Oxford, UK) was used to reconstruct the 3D coordinates of the skin markers during running. Markers' trajectories were filtered using a Woltring low-pass filter (cutoff frequency = 10 Hz), and processed in Visual3D (C-Motion, Germantown, MD, USA) for joint angles calculation using the joint coordinate system (15). Accordingly, the present convention for joint rotations was established: dorsi/plantarflexion was assumed to be the rotation about the \(Z\)-axis (medio-lateral) of the proximal segment, abduction/adduction the rotation about the \(Y\)-axis (vertical) of the distal segment, and everyon/inversion the rotation about the axis orthogonal to the previous two. Ground reaction forces were sampled at 1000 Hz and used to determine stance events and phases. All kinematic data were normalized to the running stance phase duration. The average of each variable across 10 consecutive trials was calculated and used for statistical analysis for each subject. All calculations were performed in Matlab R2015a (MathWorks, Natick, MA, USA). Rotations about the three axes of the joint coordinate system for the following pairs of segments were analyzed: shank and foot (Sha-Foo); shank and calcaneus (Sha-Cal); calcaneus and midfoot (Cal-Mid); midfoot and metatarsus (Mid-Met), and calcaneus and metatarasus (Cal-Met). Sagittal- and transversal-plane motion between hallux and metatarsus (Met-Hal) were also analyzed. Moreover, sagittal-plane inclination of the first (F2G) second (S2G) and fifth metatarsal bones (V2G) to the ground, and the transverse-plane divergence between first and second metatarsal bones (S2F) and between second and fifth metatarsal bones (S2V) were analyzed. The medial longitudinal arch angle (MLA) was defined as the 3D angle between two vectors, with apex at the marker on the talo-navicular joint and bounded by the markers on the calcaneus (projected on the ground) and on the head of the first metatarsal bone [16]. Figure 1: Diagram of the analyzed foot segments with relevant anatomical landmarks and coordinate reference frames (see [PERSON] et al., 2007). These were assumed to be rigid segments. CA: upper central ridge of the calcaneus posterior surface, ST: medial apex of the sustentaculum tali, PT: lateral apex of the peroneal tubercle, TN: medial apex of the tuberosity of the navicular, VMB: base of the fifth metatarsal, dorsolateral aspect of the fifth metatarso-cuboid joint, FMB: base of the first metatarsal, dorsomedial aspect of the first metatarso-cuneiform joint, VMH: Head of the fifth metatarsal, dorsolateral aspect of the fifth metatarsophalangeal joint, FHH: head of the first metatarsal, dorsolateral aspect of the first metatarsophalangeal joint, SMH: Head of the second metatarsal, dorsomedial aspect of the second metatarsophalangeal joint, SMB: second metatarsal base, assumed to coincide with the most distal and dorsal aspect of the middle cuneiform, PM: Most distal and dorsal point of the head of the proximal phalanx of the hallux, IC: midpoint of the straight line between PT and ST, ID: midpoint of the straight line between TN and VMB. Groups were compared using the t-test and Chi-squared test or Fisher's exact test for anthropometric, demographic, and training variables (age, Arch Index, and Foot Posture Index) using an alpha level of 0.05. Outcome variables were compared between groups using functional data analysis (FDA), which allow analysis of the full time series of each variable represented by mathematical functions, allowing the analysis of more than a few sets of points. In the functional analysis of variance (fdANOVA), the parameters of the dependent variable are functions, and the design matrix remains a general linear model [17]. This was performed by applying spline bases to the time series before performing fdANOVA using RStudio Software Version 1.2.1335 and the package fdANOVA [18]. For further analysis, we performed fdANOVA to gain a better understanding of the whole movement patterns.