Human foot morphology is an important subject for physical anatomical analysis in several biomedical disciplines, including orthopedics, orthotic design and sports sciences [1
]. Different environments and everyday habits (e.g., frequency of sport activity, shoe wearing habits), as well as personal characteristics such as sex, body mass index, and age, have been shown to have a significant influence on adult foot morphology [1
]. Human foot shape also differs among ethnic groups [2
] and changes in the course of postnatal development [10
]. As a result, footprint shape has been used in a variety of disciplines such as orthopedics [11
], and footwear research [13
A common approach to study foot morphology is to analyze the two-dimensional footprint, despite the potential loss of information along the vertical dimension [1
]. The reason for the ubiquitous use of footprints is that they can be relatively easily obtained, measured, and preserved by using wax, plaster, foam or dynamic pressure plates [17
]. To fill the missing 3D shape information along the vertical dimension, feet tend to be classified into discrete types, such as pes planus (flat foot) and pes cavus (high-arched foot), by visual inspection of footprint shape [10
]. A wide range of different quantitative measures and indices of footprint shape, mainly based on the geometry of the medial longitudinal arch, have also been proposed [14
]. Based on these parameters, various foot typologies have been defined [10
]. Most of these quantifications are based on a small number of footprint shape characteristics, such as the sizes of different footprint regions, the curvature of the medial longitudinal arch, or the orientation of the forefoot relative to the rearfoot [14
Nonetheless, these quantitative measures are insufficient to describe the entire 3D foot shape. The study of Luximon et al. [21
] showed that generating 3D foot shape from 2D information for custom footwear design introduces error in the 3D foot shape, revealing that there is additional information in 3D shape compared to 2D footprint. Overall, a 3D foot scanner is recommended for collecting foot anthropometric data because it has relatively high precision, accuracy and robustness [22
]. A promising technique to examine this full 3D shape information is statistical shape modelling. This technique is used in dysmorphology training [23
] and various product design applications [24
]. Statistical shape modelling has also been successfully employed in foot classification [25
] based on metatarsal bones geometry, but only a partial 3D foot shape is described (i.e. the position of the metatarsal bones).
To date, statistical modelling of the full 3D foot shape has yet to be achieved. Such a model could be beneficial in various applications. In clinical examinations, a statistical model of healthy 3D foot shape could be used as a baseline to which a patient’s 3D foot scan can be compared. In footwear design, a 3D foot shape model could help produce footwear with a better accommodation for foot girth.
In the present paper, we propose a methodology to quantify the 3D shape of whole feet based on geometric morphometrics, which is a standard technique used for the analysis of 3D shapes in biological datasets [25
]. We employ geometric morphometrics on anatomically matched 3D meshes of feet from a healthy population. The aligned meshes preserve foot topology, and therefore statistical results, such as group means or principal components, describe actual foot shapes and foot shape deformations. Using geometric morphometrics, we examine the healthy 3D foot shape, the bilateral asymmetry of foot shape, and the difference in shape between different foot loadings. The influence of personal characteristics (e.g. body mass index, sex, age, frequency of sport activity) on the foot shape are also investigated.
Discussion and conclusion
We applied geometric morphometric methods to study 3D variations in foot shape on a database of 3D foot scans collected from healthy adults. Geometric morphometricics was previously used to study the variation of foot shape based on footprints [1
]. We expanded on that research by capturing shape variation in the vertical dimension. We further investigated the influence of several factors on foot shape.
Our results showed similar foot shape phenomena as has been reported in previous studies of 2D footprints. These findings include a high BMI being associated with wide and flat feet [1
], shoe size having a significant influence on foot shape [1
], and significant differences being found between sex in arch height, Achilles tendon width, and hallux angle [8
]. Our reported variations in foot shape with age also match previous literature [9
], and our lack of significant relationships regarding foot asymmetry, and foot loading match what has been previously reported on 2D footprints [35
The performed analysis on 3D foot shape revealed the advantages in using 3D shape compared to 2D, showing the foot shape variation in three dimensions. For example, the first PC of 3D foot shape (representing the major axes of variation) captured low-arched versus high-arched feet, as well as showing significant variation in the mediolateral position of the foot arch (Fig. 3a
). High-arched feet tend to have the midfoot moved medially compared to low-arched feet. The heel and Achilles tendon become more noticeable for flat feet (Fig. 3a
). The distances between toes and the ball width change along PC2. PC2 showed that feet with spread out toes have a wider ball width, compared to the feet that have smaller distance between toes (Fig. 3b
). A notable difference in ankle and heel width between narrow and wide feet (Fig. 3c
), as well as the difference in ball/waist/instep girth size are revealed along PC3. The variation in orientation of the hallux bone (PC4) showed that the cuboid bone becomes more noticeable when the hallux bone is angled medially (hallux varus). These results could not have been found with previous 2D footprint analysis.
The analysis that examines the influence of the factors on foot shape, revealed some information about the vertical variations visible only for 3D foot shape. Higher BMI results in a thicker forefoot along the dorsoplantar axis, a wider Achilles tendon, a wider heel, and a wider ankle which can be seen only in the 3D foot scan (Fig. 4
). In particular, the 3D foot shape revealed that older people tend to have a wider heel, a less noticeable Achilles tendon, but also the hallux valgus, and higher toes compared to younger people (Fig. 5
). The difference in ankle width, Achilles tendon width, and heel width between males and females is also distinct in the 3D foot shape (Figs. 6
). The influence of shoe size on foot shape showed that a bigger shoe size was associated with narrow Achilles tendon, hallux varus, a narrow heel, extended heel in posterior direction, and a lower arch. People that are more physically active tend to have a more narrow Achilles tendon, a more narrow midfoot, and higher toes (Fig. 8
). To the best of our knowledge, these results were not previously observed.
Despite the advantages of 3D methods over 2D, our approach has some limitations. Three-dimensional analysis of the foot shape, requires the input of 3D foot scans and hence, the availability of a 3D scanner. This is a notable disadvantage over 2D footprint analysis methods. Additionally, the findings presented herein were observed on a cohort of only 62 individuals. These individuals were also all adults and therefore did not cover the full range of mature foot shapes [37
]. Finally, it should be noted that ethnicity was not considered as part of this study. As a result of these constraints, it is possible that the shape variability described here is not a complete representation of the possible 3D foot shapes present in a healthy population. Despite this limitation, we do show that our 3D foot shape model captures morphological information not present in a 2D footprint model. Furthermore, the theoretical properties of geometric morphometrics have been well-studied and the results we have shown fall well within the range of what is reliable for this analysis technique [38
Our findings could prove valuable in various areas of application. For example, they could allow footwear manufacturers to adapt the 3D design of a shoe based on how a customer’s factors influence their 3D foot shape. Our results show that the current approach of creating the shoes based only on 2D footprints [10
] does not fully capture the wide variability in foot morphology. As a result, the quality of a shoe fit could be improved upon by using the comprehensive 3D foot shape in shoe design.
Our findings on 3D foot shape might also prove useful in routine clinical examinations. Our statistical analyses on healthy individuals could possibly aid in further standardizing and automating clinical evaluation. A recent study by Knapik on injury risk based on the plantar surface shape came to a similar conclusion [13
]. In the study of Knapik, there tended to be a bimodal relationship between BMI and injury risk among the men. Our findings showed that the 3D foot shape changes as BMI changes. Therefore, taking this relationship into consideration during future research could potentially result in decreasing the foot injury risk. Relatedly, the study of Billis et al. [12
] emphasizes the importance in everyday clinical practice to use more than one assessment technique of foot posture. Usage of the 3D foot shape during such a clinical examination might give more insight into the relationships between different foot parts, thereby improving diagnosis. These are just a few areas that could benefit from the reported findings.
In summary, healthy 3D foot shape, which we quantified using geometric morphometrics, gives more insight of the complex shape of the foot as compared to 2D footprint analysis. We found that the personal characteristics of sex, age, BMI, frequency of sport activity and shoe size, all significantly influence the 3D foot shape. This information about healthy 3D foot shape has the potential to be used for various purposes within several biomedical disciplines, including in the design of more accurate footwear and in the facilitation of more objective clinical diagnosis techniques. Our future work will be focused on extending our results from this study to these two areas of application.