Relationships of three arch height indices related to different foot lengths between sitting and standing postures

Arch height index (AHI) between sitting and standing is an important reference in assessing foot mobility and foot classification in podiatry clinic. The relationships of three types of AHIs related to different foot lengths in sitting and standing postures are desired to be investigated in clinical applications. The purpose of this study is to investigate the relationships of three arch height indices (AHIs) calculated from total foot length, medial ball length and lateral ball length between sitting and standing postures and to examine the performances of them. Three AHIs of right feet of 150 subjects, including 83 males and 67 females, were measured using 3D foot scanner with an accuracy level of 0.05 cm in sitting and standing postures in this study. The results showed that three AHIs were significantly different from each other, and had the same performances between sitting and standing postures. AHI values in the sitting posture were all larger than those in the standing posture, and AHI-MBL has a better explaining power on AHI-TFL than AHI-LBL on AHI-TFL in both postures. The time and priority of using these three AHIs in evaluating foot types with normality and deformity were suggested.


INTRODUCTION
Arch height index (AHI) between sitting and standing is an important reference in assessing foot mobility and foot classification in clinic of podiatry (Cowan et al., 1993;Yen et al., 1998;Kaufman et al., 1999;Williams et al., 2001;Lees et al., 2005;Franettovich et al., 2007;Xiong et al., 2010;Kramer and Lautzenheiser, 2022).AHI is usually defined as the dorsal arch height normalized to the total foot length (TFL), that is, the height of the medial longitudinal arch normalized by the total foot length (called AHI-TFL).This definition is appropriate for the normal foot, but not for the foot with deformity, such as hallux valgus, tailor's bunion or claw toe.In a deformed foot, the TFL of the foot is usually affected by the deformity, and the AHI value will then be different.To reduce the effect of the foot deformity on AHI, researchers used the truncated foot length instead of the TFL to calculate AHI (Williams andMcClay, 2000, McPoil et al., 2008b).The truncated foot length is measured as the length from the heel to the medial ball point, that is, the medial ball length (MBL).AHI calculated from MBL is also called AHI-MBL.It has been reported that AHI-MBL is more reliable than AHI-TFL in deformed foot (Williams and McClay, 2000).Another advantage of AHI-MBL instead of AHI-TFL is the easy identification of medial ball point of foot, which could reduce the error of measurement of AHI-MBL.However, the disadvantage lies on, in gait analysis, the biomechanical characteristics of medial ball point.The medial ball point is a key point for body weight transmission during exercise.During prolonged lower limb movement, the distance between medial ball point and the heel point could easily be changed, which consequently affects the value of AHI-MBL.Such a phenomenon can often be observed in the foot shape of athletes (Krauss et al., 2010;Arnold and Bishop, 2013).On the other hand, in gait analysis, it is the lateral ball point that is somewhat less likely to be affected by prolonged lower limb movement.Measurement related to the lateral ball point is lateral ball length (LBL), which is the distance between lateral ball point to the heel point.Considering the advantages of both less effect by prolonged lower limb movement and easy identification of foot shape correspondingly, another alternative index of AHI-TFL could be AHI calculated from lateral ball length, called AHI-LBL; however, this index is less studied and discussed.Therefore, there is a desire to investigate the relationships of these three kinds of AHI in sitting and standing postures in clinical applications.
Researchers had measured AHI using different methods, such as callipers method, photography, or radiography.The data from these methods usually had the issue of intra-and inter-rater reliabilities with different degree of rater intervention in process, and their strength was then limited.In addition, the time consumption of these methods or the invasiveness of measurement also limits their applications by clinicians in different clinical sites and the possibility of conducting measurement of large-scaled database.These issues should only be solved only if an AHI measurement system could be adopted, as McPoil et al. (2008a) had concluded: "Future research should focus on developing a method to obtain the arch height difference that can be done easily and quickly in the clinic".With the advent of 3D foot scanning technology, AHI could now be measured with least amount of rater intervention in the AHI measurement.It could measure the 3D foot form and extract the foot measurement easily and quickly, usually in a few seconds for one foot.With the cost available nowadays, usually in $1000 -$10000 USD, 3D foot scanners had recently been applied in establishing 3D foot database of large scale (Robinette et al., 1999;Houston et al., 2006;Luo et al., 2009;Yu and Tu, 2009;Telfer and Woodburn, 2010;Yu et al., 2010;Kimura et al., 2011;Tu, 2014;Tu et al., 2020).
Weight bearing (WB) conditions on the subject's foot in a sitting or standing posture were also usually concerned in AHI measurement.When the subject adopted a sitting posture during the measurement process, 10%WB and 0%WB conditions were usually used (Zifchock et al., 2006;Butler et al., 2008;McPoil et al., 2008a;McPoil et al., 2009;Pohl and Farr, 2010;Cornwal and McPoil, 2011;McPoil et al., 2013;Zifchock et al., 2017;Zifchock et al., 2019).In the sitting posture with 10%WB, the subject adopted a natural sitting posture with the measured foot resting on the measurement platform.This was a stable posture for the subject.In the sitting posture with 0%WB, the subject was asked to sit on a chair with their measured foot dangling in the air, and the rater had a platform to place under the foot and then measure it.This posture was relatively unstable compared to the posture with 10%WB.When the subject is in a standing posture, 50%WB and 90%WB on the measured foot have usually been asked to be adopted (Williams and McClay, 2000;Zifchock et al., 2006;Mall et al., 2007;McPoil et al., 2008a;Cobb et al., 2011).In the standing posture with 50%WB, the subject was asked to place their body weight equally on both feet, and in the standing posture with 90%WB, the subject was asked to place 90% of their body weight on the measured foot.For the subject, the standing posture with 50%WB was easier to be achieved and more stable for the AHI measurement.Taking sitting posture with 10% and standing posture with 50% in measurement would be easier for subjects to be achieved and stable in AHI measurement.
The purpose of this study is to investigate the relationships of three AHIs related to different foot lengths between sitting and standing postures.

Subjects
A total of 150 subjects, including 83 males and 67 females, were recruited to scan their right feet.They were recruited from the college or graduate students and aged in 18 to 24 years old.All subjects had no reported history of foot surgery or trauma.Subjects were included after the informed consent form was obtained.The heights and weights of the male, the female and the total (male and female combined) were listed in Table 1.

Apparatus
A 3D foot scanner developed by Industrial Technology Research Institute (ITRI) in Taiwan was used in this study.It was equipped with four measuring heads and a reinforced optical glass with a size of 450 × 280 × 5 mm, on which the foot stood and was measured.It took about 6 s to complete a scan.A control and analysis software, Anthro3D, was used to control the 3D foot scanner and to analyse the scan data.Its accuracy level had been reported as measurement errors below 0.05 cm in 1D measurements (Yu and Tu, 2009), which is much smaller than 0.2 cm, which in ISO 20685 was considered standard when measuring foot measurements, and were highly acceptable.

Procedures
The right feet of all subjects were scanned in sitting and standing postures.In sitting posture, the subject was asked to sit on a hydraulically adjustable chair.The height of the chair was adjusted such that his/her knee and ankle joint were at 90 degrees as shown in Fig. 1, and his/her right foot was puts on the optical glass and scanned.It is assumed to have 10%WB on the right foot in the sitting posture (Dempster and Gaughran, 1967;Zifchock et al., 2006).In standing posture, the subject was asked to assume a standing posture with equally weight bearing (50%WB) on both feet as shown in Fig. 2. The subject's right foot was on the optical glass to be scanned, and the left foot on the platform aside the 3D foot scanner, whose height is the same as the one of the optical glass.

Foot Measurement Items
Four measurements in sitting and standing postures were extracted from the foot scan by the Anthro3D software automatically, including TFL, MBL, LBL, and dorsal arch height.Seven foot landmarks were identified before extracting these four measurements, including 1 st toe tip (P1), 2 nd toe tip (P2), 3 rd toe tip (P3), medial ball point (P4), lateral ball point (P5), the heel point (P6), and dorsal arch height point (P7), as illustrated in Fig. 3.The line passing through the heel point and the tip of 2 nd toe was called foot axis (FA), which was the basic reference for lengths on foot.The TFL was the distance between the heel point and the tip of the longest toe (as 1 st toe tip in Fig. 3 (a)) and parallel to FA.The MBL was the distance between heel point and medial ball point and parallel to FA, and the LBL was the distance between heel point and lateral ball point and parallel to FA. Arch height was the vertical distance between dorsal arch height point and the plane on which the foot stands was dorsal arch height, as shown in Fig. 3

Data Analysis
Four measurements between sitting and standing were tabulated in total, male and female populations, and analyzed by Student T-test on gender.From these measurements, three AHIs in sitting and standing postures were calculated, including AHI calculated with total foot length (AHI-TFL), AHI calculated with medial ball length (AHI-MBL) and AHI calculated with lateral ball length (AHI-LBL).At first, each of three AHIs in sitting and standing postures were analyzed by Student T-tests on genders to know if there were differences or not for each AHI between genders.If there were significant differences of each AHI between genders, the further analyses should be gender-specific; if not, the male population and the female population could be taken as a whole population in each AHI, and the further analyses could be focused on this whole population.Each of three AHIs in sitting and standing postures were then analyzed by paired Student Ttest on postures to see if there were differences or not between postures.If postures affected AHI significantly, the differences of each AHI would then be shown.After analysis with respect to sitting and standing postures, three AHIs were also analyzed by paired Student T-test on each other to see if there were differences or not among three AHIs.Finally, AHI-MBL and AHI-LBL would be regressed on AHI-TFL respectively to see their relationships.

RESULTS
The result of four measurements between sitting and standing was tabulated in total, male and female population, as shown in  3.All p values were less than 0.001 with α = 0.05.There were significant differences of these four measurements between genders.
The results of each AHIs in sitting and standing postures analyzed with respect to gender by Student T-test were shown in Table 4.All p values were larger than 0.05 with α = 0.05.The result showed that there were no significant differences of each AHI between genders, and the male population and the female population could be taken as a whole population in each AHI in further analyses.
The results of each AHIs analyzed with respect to postures by paired Student T-test were shown in Table 5.All p values were less than 0.001 with α = 0.05.The results showed that there were significant difference of each AHI between sitting and standing postures, and AHI values in sitting posture were larger than ones in standing posture.The differences of AHIs between sitting and standing postures were 0.024 as mean and 0.008 as S.D. in AHI-TFL, 0.033 as mean and 0.012 as S.D. in AHI-MBL, and 0.034 as mean and 0.012 as S.D. in AHI-LBL.
The results of three AHIs analyzed by paired Student Ttest on each other were shown in Table 6.All p values were less than 0.001 with α = 0.05 in both sitting and standing postures.The results showed that there are significant differences among these three AHIs on each other.
The regression models of AHI-MBL on AHI-TFL and of AHI-LBL on AHI-TFL in sitting and standing postures were shown in Table 7.In sitting posture, the model of AHI-MBL on AHI-TFL has R 2 = 0.952, and the model of AHI-LBL on AHI-TFL has R 2 = 0.841.In standing posture, the model of AHI-MBL on AHI-TFL has R 2 = 0.936, and the model of AHI-LBL on AHI-TFL has R 2 = 0.850.The results showed that both AHI-MBL and AHI-LBL had good explaining power on the variance of AHI-TFL in both sitting and standing postures, and the AHI-MBL has better power on AHI-TFL than that of AHI-LBL on AHI-TFL.

DISCUSSION
3D foot scanner with Anthro3D software used in this study is easier and quicker to be used in measuring AHI between sitting and standing postures with accuracy.It is easier than the previous methods for no need of rater's intervention in measurement.There would be no the issue of intra-and inter-rater reliabilities.Without rater's intervention, the beforehand requisitions of rater's training to palpate or identify the foot landmarks could be reduced.Consequently, it reduces the measuring time.The measuring time consists of manipulation of rater's intervention and the measuring time of device.The 3D foot scanner could measure and identify one foot in less than 6 s with 0.05 cm as accuracy level.These advantages make the 3D foot scanner a good alternative system to measure AHI and to establish a large-scaled AHI database.Each of three AHIs (AHI-TFL, AHI-MBL, AHI-LBL) had significant difference between sitting and standing postures, but no significant difference between genders.

Fig. 1 .Fig. 2 .
Fig. 1.The subject's right foot scanned when his/her knee and ankle joint were at 90 degrees (b).Three AHIs in this study would be defined as arch height divided by TFL, arch height divided by MBL, and arch height divided by LBL respectively.Foot measurements and landmarks in this study: four measurements are TFL, MBL, LBL, and arch height; Seven landmarks include 1 st toe tip (P1), 2 nd toe tip (P2), 3 rd toe tip (P3), medial ball point (P4), lateral ball point (P5), the heel point (P6), and dorsal arch height point (P7)

Table 1 .
Heights and weights of the subjects

Table 2 .
In sitting posture of total population, foot length had a mean of 243.66 mm with a standard deviation (S.D.) of 17.07 mm, ranging in 202.29 to 277.31 mm.MBL had a mean of 178.39 mm with a S.D. of 13.19 mm, ranging in 146.10 to 206.17 mm.Lateral ball length had a mean of 156.89 mm with a S.D. of 11.72 mm, ranging in 128.19 to 179.95 mm.Dorsal arch height had a mean of 67.64 mm with a S.D. of 5.68 mm, ranging in 52.71 to 81.37 mm.In standing posture of total population, foot length had a mean of 247.38 mm with a S.D. of 16.95 mm, ranging in 205.95 to 278.87 mm.MBL had a mean of 181.15 mm with a S.D. of 13.11 mm, ranging in 147.15 to 207.13 mm.Lateral ball length had a mean of 157.82 mm with a S.D. of 11.78 mm, ranging in 130.16 to 180.12 mm.Dorsal arch height had a mean of 62.74 mm with a S.D. of 5.54 mm, ranging in 46.61 to 75.34 mm.The results of these four measurements analyzed by Student T-test with respect to male and female were shown in Table

Table 2 .
Four measurements in sitting and standing postures in total, male and female populations (Units: mm)

Table 3 .
Four measurements in sitting and standing postures analyzed by student t-test on genders (Unit: mm)

Table 4 .
AHIs in sitting and standing postures analyzed with respect to gender by student t-test

Table 5 .
AHIs analyzed with respect to postures by paired student t-test

Table 6 .
Three AHIs analyzed with respect to each other by paired student t-test

Table 7 .
Regression models of AHI-MBL and AHI-LBL on