Analysis of foot skeletal structure by 3D foot scanner on smartphone

Background: The inuence of foot skeletal structure on hallux valgus (HV) is poorly understood, so its detailed understanding at an early stage is required for prevention. In this study, a system using a 3D foot scanner on smartphone was developed for the purpose of clarifying relationships between skeletal features and the degree of HV risk. Methods: This system analyzes the foot skeletal structure by sending 2D video images recorded on smartphone to a computer or cloud server, where the 3D foot skeleton model is constructed by the 2D images. This system was developed to identify 10 skeletal features that are expected to be associated with hallux valgus. The participants comprised 419 individuals (40–89 years), and they maintained a standing pose with their toes 12 cm apart and heels 8 cm apart during the video recording. The height and weight were additionally measured to calculate BMI. Results: The study results showed that age-based variations in the foot skeletal features were observed slightly for men whereas distinctively for women. It was observed for women that the great toe-rst metatarsal head-heel (GFH) angle increases with age, so it suggests that the increase of the GFH angle characterizes the development of HV. The multiple regression analysis reveals that the features determining the GFH angle are the second toe-heel-navicular angle and the axis of the bone distance among the skeletal features related to the midfoot, and the transverse arch length and height among those related to the forefoot. Their adjusted coecients of determination were 0.52 and 0.48 for men and women, respectively. Conclusion: Using a 3D foot scanner on smartphone, we developed a simple method to access the skeletal structure of the foot related to HV risk.


Background
Hallux valgus (HV) is a common deformity characterized by abnormal angulation, rotation and lateral deviation of the great toe at the rst metatarsophalangeal joint, and it occurs widely across all age groups. The prevalence for HV is 23% in adults aged 18-65 years and 35.7% in elderly people older than 65 years [1], and it is also higher for women than for men (30% vs. 13%) [1].
It has been reported that assessing the skeletal features of the foot is effective for examining HV [2]. Several factors have been reported to be associated with HV, such as gender [1,3], age [1], BMI [2], rst metatarsal length [4,5], atfoot [6], osteoarthritis [7,8] and footwear [9]. However, the degree to which foot skeletal in uences HV is poorly understood [10]. As HV is highly prevalent, understanding the skeletal features of the foot at an early stage is required for prevention of HV. Quantitative analysis of foot shape is important for not only clinical assessment of foot deformities [11] but also a number of applications related to the ergonomic design of footwear, foot orthotics, insoles and so on.
There are mainly two methods for assessing the skeletal features of the foot region: laser 3D surface scanners and Xray. Laser 3D surface scanners are expensive but they are often used to create custom-made shoes that are perfectly matched to the shape of the foot [11,12]. They have been used to assess aspects of foot shape such as length and circumference, but no prior study has examined their use for analyzing the skeletal features of the foot. On the other hand, X-ray is invasive and can be used only in medical institutions. In principle, as it produces a 2D image, there is room for error in measurement because of the photography angle, and furthermore the assessment process is dependent on the doctor's subjectivity. Nix et al. noted that HV is not adequately de ned using X-ray, and there is no attempt to adjust for signi cant differences between groups [13].
Therefore, in this study, a simple 3D foot scanner system was implemented by a smart phone and a remote computer. The aim of this study was to clarifying the skeletal features of the foot measured for men and women in different age groups. We suggest that some of them can be preventive indexes for the risk of HV.

Development of a Foot Morphology 3D Scanner on Smartphone
In this study, a 3D scanner system that can analyze the skeletal features of an individual's own foot was developed.
The key characteristic of this system is that its main hardware is a smartphone. As smartphones are now widely used devices, many people will be able to use this system using the devices' built-in cameras.
This system analyzes the skeletal features of the foot by sending 2D video images recorded on the smartphone to a computer or cloud server. Thus, the system does not require particularly high speci cations. The video images can be recorded manually as long as the frame does not leave the foot during the recording. The spatial resolution of this system is 0.5 mm in an optimal environment, and the reproducibility is high [14].
The features of the foot region assessed in this study were the tip of the hallux, tip of the second toe, inside of the rst metatarsal head, navicular bone, protruding part of the calcaneus, outside of the fth metatarsal head, and talus head, all of which can be automatically detected by this system. To con rm that the system can correctly detect these skeletal features, they were also identi ed via palpation by a physical therapist who understands the skeletal construction of the foot. Good agreement was con rmed in both results, so it can be considered that the developed method properly grasps the skeletal features. distance between the sole and the talus head at the highest point of the instep; the navicular height (NH) is the distance between the sole and the navicular bone; and the instep (IS) angle is the angle formed among the tip of the hallux, the talus head and the heel (see Fig. 1 (a)). The second toe-heel-navicular (SHN) angle is the angle formed among the tip of the second toe, the navicular bone and the heel (see Fig. 1 (b)). The transverse arch length (TAL) is the distance between the inside of the rst metatarsal head and the outside of the fth metatarsal; the transverse arch height (TAH) is the maximal distance between the sole and the line touching the upper surface of the forefoot giving the TAL (see Fig. 1 (c)). The metatarsophalangeal heel (MPH) angle is the angle formed among the inside of the rst metatarsal head, the heel and the outside of the fth metatarsal head; the great toe-rst metatarsal head-heel (GFH) angle is the angle formed among the tip of the hallux, the inside of the rst metatarsal head and the heel; and the axis of the bone distance (ABD) is the distance from the center line between the heel and the tip of the second toe when the coordinate point of the talus head is projected to the oor (see Fig. 1 (d)). In addition to these, to determine the in uence of toe length, the great toe-second toe ratio (GSR) is measured, which is the ratio of the distance between the tip of the second toe and the heel to the one between the tip of the hallux and the heel. Consequently, the 10 aforementioned features are calculated by a 3D foot scanner, however, these distance-based features are in uenced by the foot length, in other words, the size of each parameter varies depending on the size of the foot. Therefore, they were standardized by dividing each by the distance between the heel and the hallux (the length of the foot) and multiplying by 100. In addition, to assess the in uence of personal physique, the height and weight for each individual participant were also measured to calculate BMI.
From the above de nitions of the foot skeletal features, it can be understood that the IH is an index measuring the transverse arch, the SHN angle is an indicator of pronated feet, TAL and TAH are indices of the lateral arch, the GFH angle is an indicator of HV, and the ABD indicates the point at which the skeleton is out of alignment. Note that the HV angle, which is de ned as the angle between the longitudinal axis of the rst metatarsal and that of the proximal phalanx [15], is clinically used to grade the severity of HV, such as Mild: 15-20°, Moderate: 21-39° and Severe: ≥ 40° [ 15]. In this study, much attention is paid to the GFH angle as a substitute for the HV angle that can be measured only by x-ray. Furthermore, if the skeletal features of the foot related to the GFH angle can be clari ed, a preventive method can be proposed. Finally, Table 1 summarizes the 10 skeletal features.

Measurement Methods
The measurements were taken using a commercially available smartphone (iPhone 6). The participants maintained a standing pose with their toes 12 cm apart and their heels 8 cm apart during the measurement. An individual measurer held the smartphone and recorded an approximately 12-sec video images panning each subject's feet. The features of the subject's feet identi ed by a physical therapist's palpation were noted by sticking on a 4-mm diameter marker. Note that as the measurements were similar between the left and right feet, the 3D foot skeletal model only on the right foot images were constructed. Data are presented as the mean ± SD Statistics Analysis SPSS version 24 was used for statistical analysis on the measured data. In the analysis, comparisons of the skeletal feature means were performed using Student's t-test for unpaired data; statistically signi cant differences between the feature means were assessed using one-way ANOVA with Tukey's post hoc test; relationships among the features were explored using Pearson's correlation coe cient; In the analysis, the GFH angle is considered as the approximate value of the hallux valgus angle. Therefore, multiple linear regression was used to nd features strongly associated with the GFH angle; and the p-value of 0.05 was considered statistically signi cant.

Results
Measurements of Features Table 3 shows the measurements obtained using the 3D foot scanner by gender. For men, no variation among age groups was observed for any features excluding GSR. For women, on the other hand, variations among age groups were observed for the NH, IS angle, MPH angle, TAL, TAH and GFH angle.  Correlations among Features Table 4 shows the correlation coe cients among the foot skeletal features measured by the 3D foot scanner. The GFH angle was correlated with the SHN angle, ABD, IS angle, MPH angle, TAL, TAH, and NH, respectively, for both men and women, and additionally with the IH for men. For both men and women, on the other hand, the ABD was correlated with the SHN angle, IH, and NH, respectively, the NH was correlated with the TAH and IS angle, respectively, the IS angle was correlated with the TAH, the MPH angle was correlated with TAL and TAH, respectively, and the TAL was correlated with the TAH. For both men and women, furthermore, the BMI was correlated with the TAH.
Multiple Regression Analysis for the GFH Angle Table 5 shows ve independent skeletal features related to the GFH angle for men and women, respectively. Four of them, which are common for men and women, comprise the SHN angle, TAL, TAH and ABD, and the remaining one is the BMI for men whereas the GSR for women. Concerning the strength of relationship, the regulated r2 was 0.52 for men whereas 0.51 for women. For both men and women, it was implicated that the skeletal features related to the forefoot and skeletal misalignment of the midfoot characterize the GFH angle.

Measurements of Features
In the measurement results, age-based variations in the foot features were observed slightly for men whereas distinctively for women. Particularly, it is surmised for women that the lower NH and increasing atness of the foot were related to aging. However, aging did not have a great impact on the SHN angle and ABD. The longitudinal arch of the foot is likely to be connected with the tibialis posterior muscle, the muscle strength in the sole and the transformations in the skeletal structure [16,17]. For these reasons, it is surmised that the lowering of the longitudinal arch is caused by severe declines in muscle function such as impairment of the tibialis posterior muscle [18], protrusion of the calcaneus [19] and pronation of the navicular bone [20] as well as the aging process. It is also surmised that the IS angle increases as the thickness of foot skeletal structure decreases with ages.

Correlations among Foot Features
The correlation coe cient between the MPH angle and the TAL is greater than 0.94 in Table 4 for both men and women, indicating a strong correlation, on the other hand, the TAL increases whereas the TAH decreases with age for women in Table 3. Taking into consideration that the MPH angle and TAL are skeletal features related to the width of the forefoot and the TAH is a skeletal feature related to the height of the forefoot, it is surmised that attening of the forefoot is associated with a broad foot. Particularly, it is surmised for women that the GFH angle increases with age, which indicates the development of HV.
Paying attention to the GFH angle, the skeletal features identi ed as being correlated with it include the SHN angle and ABD, which are those related to the midfoot. As the SHN angle increases, which means that the navicular bone sticks out more, the ABD also increases with the inside of the midfoot deviating more inward. Therefore, this suggests that foot pronation is associated with the increase of the GFH angle thus HV. This suggestion is supported by the result of a prior study [21] that the risk of HV is signi cantly increased in persons with pronated foot function.
In addition, it was found that the ABD is correlated with the SNH angle (r2 > 0.40), IH (which denotes the health of the foot's skeletal structure) (r2 > 0.33) and NH (which denotes the height of the longitudinal arch) (r2 > 0.34) in Table 4.
This suggests that misalignment of the skeletal structure of the midfoot is related to the health of feet, particularly, the formation of navicular and cuneiform bones. This misalignment is considered to be in uenced by both early childhood development and aging process [22].
Furthermore, correlation between the IH and the TAH was observed for both men (r2 = 0.52) and women (r2 = 0.38) in Table 4. The reason why the correlation is lower for women could be that the transverse arch re ected by the TAH is more strongly in uenced by footwear for women.
Finally, as for atfeet which means the fall of the longitudinal arch, many discussions have utilized footprints [23,24]. From the viewpoint of biomechanics, the main cause of atfeet may be the in uence of the tibialis posterior muscle or the muscles in the sole [25]. Considering pronation, the navicular bone moves directly below these muscles while causing 3D changes in various directions, such as supination of the subtalar joint, pronation of the navicular bone and supination of the forefoot. Therefore, assessing the 3D skeletal structure of the foot is effective for pronation, which is the very bene t of the proposed system.

Multiple Regression Analysis for the GFH Angle
It was revealed from Table 5 that dominant skeletal features determining the GFH angle are the SHN angle and the ABD among those related to the midfoot whereas the TAL and the TAH among those related to the forefoot for both men and women. In addition to these features, it was revealed that one of the dominant features is the BMI for men whereas GSR for women. Regarding the multiple regression analysis, the adjusted coe cient of determination was 0.52 for men versus 0.48 for women, multicollinearity was con rmed in relation to none of the independent features, and β was large for both men and women in the SHN angle and the TAL.
As for other features associated with HV, prior studies pointed out lower BMI and high heel use for women aged 20-64 whereas higher BMI and at feet for men [2,13]. Our results suggest that the etiologic mechanisms of HV may differ between men and women. Namely, although this study included neither extremely overweight nor underweight participants, it found an association of BMI with HV for men, which was not strong as compared to that in the prior study [2].

Overall Results
A prior study showed that the protrusion of the rst metatarsal and the lengths of the rst metatarsal and the proximal phalanx of the hallux were increased in both men and women with HV as compared to those in the control group [4], in other words, the rst toe is a key part related to HV. On the other hand, this study showed that a longer second toe was associated with a larger GFH angle, in other words, the second toe was a key part related to HV. The reason of this difference may be that the length of the rst metatarsal was compared with that of the second metatarsal in the prior study whereas the distance between the tip of the rst toe and the heel was compared with that between the tip of the second toe and the heel in this study. The proximal phalanx of the hallux deviates laterally towards the second toe as HV develops, so the distance between the tip of the hallux and the heel gets shortened, naturally resulting in the appearance of longer second toe.
In this study, it has been highlighted that the GFH angle as an index of HV is in uenced by the atness of the forefoot and misalignment of the skeletal structure of the midfoot. In a prior study, the NH was used as an index of atfeet, which was considered to in uence HV [26]. In this study, on the other hand, the independent variable derived from the multiple regression analysis was not the NH but the SHN angle. As the SHN angle and NH were inversely correlated (-0.3--0.2), it is quite natural that both height and position of the navicular bone can be key features for HV. The SHN angle is not on a horizontal plane, so simple 2D measurement systems cannot calculate it. On the other hand, the developed 3D scanner system can easily calculate the NH as well as the SHN angle, using an automatically constructed 3D foot skeleton model.
By using a 3D foot scanner on smartphone, we have been able to implement a simple quantitative method for assessing the skeletal structure of the foot. This will allow us to clarify the risk of HV.

LIMITATION
This study has several limitations. The measurement is performed from the outside of the foot, so there may be some errors between the GFH angle and the HV angle measured by x-ray. In addition, the measurement is performed manually, so handshake may introduce some errors in the measurement data. Furthermore, the 3D foot skeleton model is constructed by 2D images, so some errors may occur in the construction process.

Conclusions
In this study, a 3D foot scanning method using a smartphone was developed, and the skeletal structure of the foot was analyzed. One of the main results is that dominant skeletal features for determining the HV-related GFH angle are the SHN angle and ABD among those related to the midfoot whereas the TAH and TAL among those related to the forefoot. Another is that age-based variations in the foot skeletal features were observed slightly for men whereas distinctively for women.
Using a smartphone, it is possible to conduct a simple non-invasive assessment of the skeletal structure of the foot at any location. This will facilitate clari cation of the factors of skeletal structure contributing to HV, and it is expected to improve efforts to prevent HV.

Declarations
Ethics approval and consent to participate: the study design was approved by the ethical review board at the ryotokuji university (authorization number: 1909). Participants were provided oral and written explanations of the study and publication. All participants signed a consent form prior to the study.

Consent for publication: not applicable
Availability of data and materials: not applicable.
Competing interests: the authors declare that they have no competing interests.
Funding: this work was supported by jsps kakenhi, grant number 18h03559, 18k12161. The funding sources had no involvement in study design; in the collection, analysis and interpretation of data; in the writing of the report; and in the decision to submit the article for publication.
Authors' contributions: ty and ky planned the study, analyzed the data, and drafted the manuscript. Ty, ky, and ms performed all measurements and contributed to the data acquisition. Ty, ky, ms, tr, mk and sh analyzed all statistical data and contributed to drafting of the manuscript. Tr, yt and sh planned the study, including the instrumentation and contributed to the revision of the manuscript.

Figure 1
The Foot Skeletal Features