Changes in tissue morphology, bone shape, and posture of the foot influence the biomechanics of the lower extremity. For example, foot types (mainly, normal, planus, and cavus feet) (Buldt et al., 2015a), foot posture (mainly, normal, pronated, and supinated feet) (Hollander et al., 2019), toe morphology (Mei et al., 2015a), hallux valgus (Hannah et al., 2016), and manipulated forefoot shapes (abducted hallux versus adducted hallux) (Mei et al., 2016; Xiang et al., 2020a; Xiang et al., 2020b) have been previously reported in the literature. Pathological conditions, such as diabetic-related foot deformities (Guiotto et al., 2013; Lu et al., 2015) can also influence the biomechanics. Figure 1 outlines the most common popular shape metrics (Figure 1) and postures in the foot (Figure 1 and Figure 2) with highlighted regions of variations in pronation (blue) and supination (red) when compared to those of the neutral foot posture. The highlights in pronated and supinated foot postures are modes generated from the principal component analysis (PCA) in the statistical shape modeling (SSM) using an open-source Musculoskeletal Atlas Project (GIAS2 package) developed at the Auckland Bioengineering Institute (Zhang et al., 2014). The SSM typically refers to the techniques of describing the characteristics of deformable objects with different shape features, presenting mean shape (appearance) and key variations in these object groups (Sarkalkan et al., 2014; Mei et al., 2021a).

The current measurement of foot morphology, shape, and posture using 2D footprints, anthropometric measurements, anatomical palpation, 3D surface scanning, ultrasound imaging, computed tomography (CT), or magnetic resonance imaging (MRI) are mainly under static (non-weight or weight-bearing) conditions (Razeghi and Batt, 2002; Redmond et al., 2006; Crofts et al., 2014). However, the foot may present different postures, shapes, and morphologies during dynamic activities (short and long term). Prolonged repetitive impact on bones and soft tissue can alter the shape, biomechanical response, and adaptation (Garofolini and Taylor, 2019). In particular, increased muscle volume and cross-sectional area of foot muscles (abductor halluces, flexor digitorum brevis, and abductor digiti minimi) and bone density (calcaneus) were concluded in a recent review study (Garofolini and Taylor, 2019), which may rely on training volume and experience.

Long-distance running, or endurance running, is a key evolutionary skill presented by bipeds in addition to walking (Bramble and Lieberman, 2004). Long-distance running has gained global popularity with increased marathon participation, particularly in amateurs. However, the increased participation is associated with higher risks of running-related injury (Hulme et al., 2017).

The arch (either high arch or flat foot) in the midfoot region is commonly used to classify and categorize the foot posture in foot biomechanics. Specifically, it has been quantified using the 2D footprint artificial intelligence (AI) and classified as high arch (AI < 0.21), normal arch (0.21 < AI < 0.26), and low arch (AI > 0.26) (Cavanagh and Rodgers, 1987). This metric has been used during static and dynamic measurements (Scholz et al., 2017) and is sensitive to forefoot and midfoot plantar pressures during walking and running (Mei et al., 2020). The lower arch has been associated with increased hallux and medial mid-foot pressures and reduced medial forefoot pressures (Jonely et al., 2011). Increased reported ankle and knee pain have also been associated with lower foot arch (Riskowski et al., 2013), whereas the high arch is primarily associated with ankle pain only (Riskowski et al., 2013). Altered frontal and transverse rearfoot motion and reduced midfoot motion during initial contact are associated with high arch feet, while reduced midfoot motion during pre-swing is associated with low arch feet (Buldt et al., 2015a). While the foot arch is a useful measure in adults, there is a caveat that it might be a less useful measurement in developing and overweight individuals. For example, the dynamic artificial intelligence was not associated with any kinematics, kinetics, or spatiotemporal information in children except for a greater external foot rotation associated with a lower arch (Hollander et al., 2018b). The artificial intelligence is also influenced by training levels and running experience (Fascione et al., 2009) despite the biomechanical evaluation being not reported. Overweight adults (with high BMI) showed pronated and flatter feet with reduced ankle inversion–eversion motion and higher plantar loading underneath the foot (Butterworth et al., 2015), which led to uncertainty of either the change of foot structure or increased weight contributing to a greater plantar loading.

Running biomechanics influences the foot structure. Following long-distance running, foot arch and dorsal height reduce over a week and may take more than a week to return to pre-run profiles and has been linked with increased plantar loadings in the medial foot (metatarsals and arch) (Fukano and Iso, 2016; Fukano et al., 2018; Mei et al., 2018). These changes could affect the perceived comfort of the running footwear and contribute to running-related injuries (Cowley and Marsden, 2013; Hollander et al., 2018a). Following a running-induced fatigue intervention, plantar pressure has been reported to redistribute in the lateral metatarsals of flat arch feet and the medial metatarsals of high arch feet (Anbarian and Esmaeili, 2016). Following long-distance running, a pronated foot posture, reduced arch height, and increase in medial plantar pressure have been reported (Nagel et al., 2008; Schlee et al., 2009; Cowley and Marsden, 2013). The FPI (Redmond et al., 2006) following long-distance running has been moderately correlated with knee and ankle joint loads using the musculoskeletal model (Mei et al., 2019). Furthermore, runners with asymptomatic overpronated feet have larger abductor hallucis and flexor digitorum brevis and longus but smaller abductor digiti minimi, and peak eversion in the rearfoot and peak supination in the forefoot (Zhang et al., 2017). While, symptomatic overpronated runners have shown a smaller cross-sectional area in the flexor digitorum longus and abductor hallucis and thinner peroneus and abductor hallucis than those asymptomatic pronated runners, implying the training of intrinsic foot muscle for the possible prevention of injuries (Zhang et al., 2019).

Foot types (mainly, normal, planus, and cavus feet) and postures (mainly, normal, pronated, and supinated feet) have been reported to be associated with running-related injuries (Pérez-Morcillo et al., 2019), particularly the tibia stress under extreme foot types (Barnes et al., 2008), medial tibia stress, and patellofemoral pain with foot pronation (Lun et al., 2004; Neal et al., 2014; Selfe et al., 2016). The hip joint loading was found to be increased, whereas only a moderate correlation with foot pronation and ankle and knee loadings was reported (Mei et al., 2019).

This subsection is focused on foot pronation and potential contribution to running-related injuries, taking distance running as a typical example. Overpronated feet have been implicated in developing overuse injuries, despite there being no scientific evidence that overpronated feet are associated with the diagnosis of injuries or diseases. This misconception exists possibly because altered foot postures have often been observed in people who have musculoskeletal injuries, dysfunctions of the lower limb, and lower back pain (Levinger et al., 2010; McWilliams et al., 2010; Sharma et al., 2010; Menz et al., 2013; Arnold et al., 2019).

Pronation/supination are important biomechanical functions in gait, and a certain extent of natural pronation/supinations is required as a shock absorber during the early stance phase and as a rigid lever to push forward during the terminal stance phase (Hetsroni et al., 2008). During repetitive movements such as long-distance running, however, the high volume of impact forces during the early stance phase may lead to overpronation (Mei et al., 2019) by flattening the foot with arch collapses and transferring the foot eversion into the internal rotation of the tibia. There has been a belief that this overpronation possibly leads to overuse injuries by disrupting the coupling mechanism of the lower limb alignment as the gait may be compromised and adding the additional strain of the foot/ankle complex (Subotnick, 1985). Pronation is also a passive force that occurs within the initial heel strike during walking and running. That is, there would be less muscular control when the foot is overpronated, resulting in a lack of normal distribution of excessive force and instability of the foot/ankle (Subotnick, 1985). This patho-mechanical alteration of foot posture, therefore, has been proposed to cause foot diseases such as plantar fasciitis (Golightly et al., 2014), osteoarthritis (Reilly et al., 2009; Lithgow et al., 2020), metatarsalgia (Eustace et al., 1993), and stress fractures of the lower limb (Lysholm and Wiklander, 1987).

Overpronated feet, specifically at the subtalar joint, have been proposed to develop deterioration of the lower limb joint by disrupting normal alignment with external rotation of the tibia and calcaneal inversion which are not in the normal direction (Tiberio, 1987; Hintermann and Nigg, 1998). A previous study also showed that people with medial compartment knee osteoarthritis revealed a more pronated foot than healthy controls, possibly due in part to genu varum malalignment of the knee, which causes compensatory overpronation of the pronated foot (Levinger et al., 2010). Pronation with adduction of the talus with calcaneus eversion results in a greater compressive force in the medial midfoot, and this idea has been supported by several studies, reporting that people who have been diagnosed with midfoot osteoarthritis have a more pronated foot posture (Menz et al., 2010; Arnold et al., 2019; Arnold et al., 2021; Lithgow et al., 2020). Older adults, who were diagnosed with radiographic osteoarthritis of the talonavicular joint and navicular–first cuneiform joint, presented flatter feet with greater loading of the midfoot during walking (Menz et al., 2010). This mechanism has also been supported by a cadaver study, reporting a greater compression force at the dorsal talonavicular joint simulating a flattening foot (Kitaoka et al., 1996).

However, while numerous studies have observed pronation/supination of the foot in people who have lower limb diseases, there is no scientific evidence supporting the causal relationship between the alteration of foot posture and diagnosis of injuries or diseases. A recent study on knee osteoarthritis with foot posture also put forward the question of foot postural changes leading to injuries or injuries resulting in posture changes (Al-Bayati et al., 2018). A comprehensive cohort study of running-related injuries in a large population of 1,680 runners reported that there was no significant association between anthropometric outcomes (e.g., high/low arch and rearfoot valgus) and risk factors of running-related injuries (Water et al., 1960). Similarly, a 1-year epidemiological prospective cohort study of 927 novice runners reported that foot pronation is not associated with an increased risk of running-related injuries (Nielsen et al., 2014). A systematic review study revealed a small effect between foot pronation and the risk of medial tibial stress syndrome, suggesting that foot pronation may not be directly associated with the foot injury (Neal et al., 2014). Furthermore, a more recent radiologic study reported that significant ankle kinematic changes associated with supination of the foot were not related to the diagnosis of diseases (Kim et al., 2019a; Kim et al., 2021). This study interestingly observed that novice runners, who did not show ankle kinematic changes after mid-distance barefoot running, revealed early indications of cartilage degeneration or deteriorating effects by increasing the T2 relaxation time in MRI-derived T2 maps. However, runners who showed a supinated foot type after mid-distance running did not change their T2 value on MRI. This study, therefore, suggests that supinated feet or significant ankle kinematic changes are less likely to develop foot/ankle injuries.

The idea of our understanding of the association between pronation/supination and running-related injuries is still not clear and no consensus has been reached on the foot posture with injuries (Nigg et al., 2019). Thus, to draw a conclusive result, we may require additional information such as the integrated longitudinal arch angle and Achilles tendon angle proposed for the determination of foot postures and biomechanics during walking and running (Limeres et al., 2019; Behling and Nigg, 2020). Due to multifactorial parameters being included for analysis, multivariate statistical models, such as principal component analysis (Limeres et al., 2019; Behling and Nigg, 2020), partial least square regression (Mei et al., 2020), and other nonlinear statistical models, are recommended to investigate the potential correlation.

Numerous foot imaging modalities have been adopted to capture the foot posture via shape which include the 3D plantar surface (Kimura et al., 2008; Thabet et al., 2014), dorsal surface (Blenkinsopp et al., 2012), and whole foot (Boppana and Anderson, 2019). Techniques of tracking in vivo foot motion have been previously developed and validated using makers in a biplane fluoroscopy system (Iaquinto et al., 2014), and midfoot postures have been analyzed to evaluate the longitudinal arch angle under conditions of barefoot (∼127.5°), footwear (∼130°), and orthoses (∼131°) (Mannen et al., 2018). However, challenges of multiaxial motion in the ankle complexity of tibiotalar and subtalar joints were found (Canton et al., 2020). The development of in vivo bone shapes in the foot has laid the foundation of classifying foot types from 3D perspectives (Ledoux et al., 2006). Recent attempts have been made to associate static foot bone images from 3D CT with 2D biplanar video-radiography images in vivo (Maharaj et al., 2020) and the development of the multi-segmental foot musculoskeletal model (Malaquias et al., 2017; Maharaj et al., 2021), but the cost of obtaining subject-specific bone geometry makes this method less translatable for practical use. Population-based modeling using ‘big data’ may provide an alternative for rapidly creating foot geometries from limited data [such as the popularly employed statistical shape modeling of functional foot bones (Grant et al., 2020)] and establishing relationships between form and function at the population level.

Statistical shape modeling (SSM) is a reduction technique that can be used to identify independent (orthogonal) geometrical features of a set of similar shapes and rank them (Cootes et al., 1995). The principal component analysis (PCA) is the most popular method to reduce dimensionality and computes the mean shape and orthogonal shape variations (modes) (King and Eckersley, 2019). This technique has been used widely in the biomechanics and anatomy space (Ambellan et al., 2019; Audenaert et al., 2019; Fernandez et al., 2019; Vallabh et al., 2019; Wang and Fernandez, 2020; Yeung et al., 2020). Applications include clinical medical image analysis (Heimann and Meinzer, 2009) and surgery and design of orthopedic implants (Sarkalkan et al., 2014).

To introduce one of the SSM technique, we took musculoskeletal modeling software GIAS2 (Zhang et al., 2014) (https://pypi.org/project/gias2/) being developed at the Auckland Bioengineering Institute as an example. Figure 2 demonstrates the workflow in the SSM of the foot surface shape (right side) and bone shape (left side) being employed from our research group. The steps include shape mesh segmentation (bone shape) or surface scan (surface shape), mesh fitting and alignment, and the principal component analysis (PCA) to compute the mean shape and key modes of variation.

Population-based approaches for understanding the foot have been reported in osteoarthritis populations (Trivedi et al., 2010), for the footwear type and foot discomfort in females (Dufour et al., 2009), flat arch with ankle pain and high arch with knee pain (Riskowski et al., 2013), and hallux valgus with foot pain (Dufour et al., 2014). Recent advances in foot imaging technology have enabled easy access and increased availability of 3D foot scanning systems (Telfer and Woodburn, 2010), providing increased foot morphology data for the study of shape variations, especially in populations of different ethnicities (Mei et al., 2021b; Mei et al., 2021a). A recent study highlighted published 1.2 million foot shape data on the features of populations from North America, Europe, and Asia and reported the distribution of geometrical metrics (such as length, width, and height) between males and females (Jurca et al., 2019). Apart from the measurements from 3D scanning technologies, the PCA on the 3D shape is one common and useful approach to extract meaningful information from these data (Mei et al., 2021a).

The SSM of the calcaneus and talus bones in the rearfoot revealed a smaller size in females but less asymmetry in both genders (Audenaert et al., 2019), specifically in the length and height of calcaneus and talus articular surface (Tümer et al., 2019a). In contrast to the normal foot, the calcaneus shape presents decreased height and increased length in high arch feet and increased posterior mass in the talus of flat arch feet (Moore et al., 2019). A statistical shape model of the foot surface reported variations in arch height, ball (metatarsophalangeal joint) width, toe distance, hallux orientation (valgus–varus), and toe length (Stanković et al., 2018). A higher BMI has been related to greater ankle width, Achilles tendon size, and width. Age was associated with heel width, Achilles tendon size, and hallux orientation. Gender was linked to ankle width, Achilles tendon size, and heel width. Classifying problematic feet using surface morphology has been reported which included hallux valgus, pes planus, and pes cavus profiles (Stanković et al., 2020).

A flat talar contact surface has been associated with chronic ankle instability (Tümer et al., 2019b). This flat talar surface may be associated with adaptation to constraining footwear on the basis of comparisons with the talus shape from archaeological records (Sorrentino et al., 2020). High arch feet have a more posteriorly positioned navicular tuberosity than normal arch feet (Moore et al., 2019). In the forefoot, metatarsal shapes are associated with foot types (high arch, normal, and flat arch) and bones vary in size (Telfer et al., 2017). Specifically, the flat arch foot has a reduced cross-sectional metatarsal area, and the first and fourth metatarsal sizes are linked to gender, with females presenting smaller sizes. Furthermore, the first metatarsal could be accurately reconstructed from sparse landmarks based on the SSM (Grant et al., 2020), which has the potential for rapid development of the musculoskeletal foot models (Grant et al., 2020).

One of the challenges with the SSM is creating a population of topologically consistent geometries for the principal component analysis. This problem has been addressed by using the ‘free-form’ deformation technique (Fernandez et al., 2004), where a generic geometry is morphed to different data (‘host mesh’). This has been demonstrated for the diabetic foot (Fernandez et al., 2012) and gout foot (Dalbeth et al., 2015) and, recently, for investigating ankle pressure in barefoot runners (Kim et al., 2019b). This technique has been used to check the similarity of foot shapes (Mochimaru et al., 2000), which are combined with plantar pressures for the application of footwear design (Kim et al., 2007). Another consideration which should be noted is that the prediction of four-dimensional (3D shapes varying over time) foot shapes become plausible from integrating multidisciplinary advanced statistics, artificial intelligence (AI), depth camera, and object detection techniques (Boppana and Anderson, 2019; Boppana and Anderson, 2021). The development of this technology may become a great improvement in shape changes in real time and provide an option of considering footwear and orthotics fit from a dynamic and functional perspective.

Recently, multivariate machine learning (partial least squares) regression models were first developed to correlate key shape metrics (artificial intelligence and hallux–toe distance) with walking (R-square values of 0.763 and 0.788) and running (R-square values of 0.786 and 0.789) plantar pressures using habitually barefoot and shod populations (Mei et al., 2020), showing a prediction accuracy of around 80%. Further sensitivity analysis reported that the forefoot shape metric (hallux–toe distance) was associated with medial forefoot pressures, especially during walking in habitually barefoot populations. Also, the midfoot shape metric (artificial intelligence) was associated with lateral forefoot pressures during walking in both habitually barefoot and shod populations. An improved predictive statistical model (support vector machine) also showed an increased prediction accuracy on the basis of the same data set (Xiang et al., 2022a). Rapid prediction of foot function from easily measured foot shape metrics may become the norm and extend into clinical diagnosis of foot pathologies and customized footwear development.