Downloaded By: [Texas Technology University] At: 22:54 16 September 2007 ERGONOMICS, 1995, VOL. 38, No.9, 1911-1920 Analysis of foot shape variation based on the medial axis of foot outline MAKIKO KOUCHI Human-Environment System Department, National Institute of Bioscience and Human-Technology, I-I Higahi, Tsukuba, Ibaraki 305, Japan Keywords: Foot; Pronation; Overhang of navicular bone; Foot outflare; Shoe. The variations in foot outline forms are analyzed by using flexion angles of the medial axis of foot outline. Foot outline and 12 conventional measurements taken on the right foot of 443 male and 297 female subjects with no visible pathological deformation of the foot were used for analyses. The results indicate that the foot is outflared in most of the subjects. Medial bulge and lateral concavity of foot outline are responsible for the foot outflare, and they are not correlated with each other. Medial bulge is due to the overhang of navicular bone that is caused by the pronation of the foot. Its intensity is negatively correlated with dorsal arch height. Lateral concavity is partly due to the abduction of talus and calcaneus relative to the tarsometatarsal bones anterior to them. These three-dimensional morphological characteristics of outflared feet intimately relate to the fit and comfort of the shoe. The flexion angles of medial axis of foot outline provide a useful tool in morphological analysis of the foot for the following reasons; (I) they carry the information on the three-dimensional foot shape that cannot be represented by conventional measurements; and (2) the data is easily obtained and calculations are easily made with minimum expense. 1. Introduction The variation of human foot shape plays an important role in the fitting between foot and shoe, for, even in the same shoe, feet of different shape receive localized pressure at different parts. A shoe last has been designed and modified manually to fit to a particular foot based on the experience of craftsmen. Systematic analysis of foot shape variation is necessary to identify the causes of misfit and to establish an objective method to modify a shoe last to fit to feet of different shapes. If the morphological characteristics of a human foot are important in shoe fitting and their range of variation are clarified, then engineering may be introduced into the shoe last design and modification. The lack of an appropriate method to extract the shape characteristics of a human foot has hindered this type of approach. The outline of a foot contour projected on the standing plane, which has been used by shoe manufacturers, contains information on the morphological characteristics of the foot that cannot be represented by conventional variables such as dimensions, angular measurements and proportions. Therefore, the analysis of foot outline forms may provide useful information to construct a morphology-based strategy for improving the fit between the foot and shoe. An outline form can be numerically expressed by using Fourier descriptors (Lestrel and Brown 1976) or by the vector angle method (Kouchi and Yamazaki 1990). In the 0014-0139195 $10·00 © 1995 Taylor & Francis Ltd. Downloaded By: [Texas Technology University] At: 22:54 16 September 2007 1912 M. Kouchi latter, an outline is approximated by a polygon with equidistant vertices, and a sequence of angles between the edges and the x-coordinate axis is used to represent the outline form. In both cases multivariate analysis methods can be applied for identifying the important morphological features and for type classification. This type of approach, however, does not provide more information than that carried by the variables used for the analysis. Medial axis, or skeleton, is useful for the analysis of irregular form on which anatomical landmarks are not determined (Bookstein 1991). Foot outline has an elongated irregular form, and the landmarks on it are defined as the maximum protrusion, and are difficult to define precisely. Also, the intuitive midline of a foot outline is not straight, and the results of previous studies suggest the importance of midline bends as a morphological feature of the foot (Freedman et al. 1946, Kouchi and Yamazaki 1990). The aims are: (I) to show the usefulness of medial axis of foot outline in extracting and summarizing the morphological features of the foot; and (2) to analyze the variation in foot shape by using the flexion angles of medial axis. Subjects and method 2. 2.1. Subjects and data Subjects are 443 males and 297 females without visible pathological deformations of the fool. Mean age, height and weight of the subjects are shown in table I. Foot outline Table 1. Age, height and weight of subjects. Male (n = 443) Female (n = 297) Item Mean SD Min Max Mean SD Min Max Age (years) Height (em) Weight (kg) 41·0 166·6 62·7 11·29 5·76 9·12 18·0 145·0 40·5 75·0 181·0 92·9 26·0 156·5 52·8 10·24 5·82 8·65 18·0 140·0 35·0 64·0 170·0 91·2 Figure I. Landmarks and measurements of the foot. D, dorsal arch point; MF, metatarsale fibulare; MT, metatarsale tibiale; P, ptemion; SF, sphyrion fibulare, A I, ball flex angle; A2, toe I angle; A3, toe Vangie; B I, foot breadth; B2, heel breadth; C I, foot circumference; C2, instep circumference; HI, dorsal arch height; H2, sphyrion fibulare height; Ll, foot length; L2, fibular instep length; and L3, instep length. Downloaded By: [Texas Technology University] At: 22:54 16 September 2007 1913 Medial axis offoot outline and 12 measurements of right foot were used for the analysis. All the data were taken with the subjects standing barefoot, with their weight distributed equally on both feet. All the data were taken in 1987 with a foot-measuring system developed in a project by The Japan Leather and Leather-Goods Industries Association. Data were obtained to update the Japanese Industrial Standard for shoes (Japan Leather and Leather-Goods Industries Association 1987, 1988). This system takes foot outline, foot print, lateral foot outline, foot cross-sections at instep and ball, and 24 measurements optically without touching the subject (Kouchi and Yamazaki 1990). The twelve measurements used are shown in figure J. Foot axis is the line connecting pternion (P) and the tip of the second toe. Length measurements are projected length on foot axis. Dorsal arch point is the highest point on the dorsum at 54% of the foot length from P. The following two indices are calculated: foot index = foot breadth X 100lfoot length; and foot axis index = MT-faX JOOIMF-fa, where MT-fa and MF-fa are distances from MT (metatarsale tibiale) or MF (metatarsale fibuJare) to the foot axis (figure I). 2.2. Medial axis (skeleton) Figure 2 shows an example of medial axis and its flexion angles. A foot outline is described by data points at intervals of about 2 mm. The coordinate system is defined as follows: the x-axis corresponds to the foot axis, and the y-axis is perpendicular to the x-axis crossing P, the origin. Indentations between the toes are enveloped before the calculation of medial axis. Medial axis corresponds to the intuitive midline of an outline form. To avoid confusion with bones, the term medial axis is used instead of skeleton. The medial axis is calculated according to the algorithm of subroutine DIST of SPIDER, a subroutine package for image processing (Electrotechnical Laboratory 1980). Using an image processing method, an internal shape of the outline is divided into pixels at intervals of I mm for each direction, x and y. Then a distance from the outline is calculated for each pixel based on four-neighbour distance. On the four-neighbour distance, the pixel adjoins only four directions, upper, lower, left, and right direction. The unit of the distance is defined as a distance between the adjoining pixels. The medial axis is obtained as the points that have local maximum of the distance. The medial axis of foot outline has two triple points, heel triple point (HTP) and toe triple point (TIP), and between them it curves like an'S' with two inflexion points in most of the cases. To represent the flexions of the medial axis between the two triple points, two angular measurements are calculated according to the following procedure. A regression line is calculated using data points of the medial axis whose x coordinate belong to each of the following three ranges (figure 2): (I) regression line I(RL I), from x Figure2. Flexionanglesof medialaxisof foot outline.A, one-thirdof foot lengthfrom P; AFA, anterior flexion angle; AFP, anterior flexion point; B, inflexion point determined by eye inspection; C, medial bulge; D, lateral concavity; HTP, heel triple point; PFA, posterior flexion angle; PFP, posterior flexion point; RLI - RL3, regression lines; and TIP, toe triple point. Downloaded By: [Texas Technology University] At: 22:54 16 September 2007 1914 M. Kouchi HTP to one-third of foot length from origin, P (figure 2, A); (2) regression line 2 (RL2). from one-third of foot length from origin to the anterior intlexion point (AlP) determined by eye inspection (figure 2. B); and (3) regression line 3 (RL3), from AlP to TIP. Acute angles made by RL I and RL2, and by RL2 and RL3 are named posterior tlexion angle (PFA) and anterior flexion angle (AFA) respectively and are used for further analysis. The intersection of RL I and RL2 and that of RL2 and RL3 are named posterior flexion point (PFP) and anterior tlexion point (AFP) respectively. One-third of foot length from P is used instead of the posterior intlexion point (PIP) because there are cases in which the posterior tlexion angle is too small to determine PIP by eye inspection. AlP is determined as the data point with the smallesty and whose x is largerthan one-third of foot length and smaller than two-thirds offoot length. When more than two data points satisfy this condition, the one whose x is close to the median of them is chosen. Interobserver error in determining AlP is very small. Mean absolute differences of PFA and AFA calculated for 40 randomly selected subjects by two different observers are 0·14 and 0·29° respectively. The maximum absolute differences of PFA and AFA are < 1°. There are two causes for the medial axis of foot outline to flex at PIP, which is located at about one-third of the foot length from P. One is medial bulge (figure 2. C) and the other is lateral concavity (figure 2. D) of foot outline. To determine which is responsible in an individual case. medial axis is calculated for the corrected foot outline with medial bulge removed when PFA is equal to or larger than 4°, and the corrected posterior tlexion angle (CPFA) is calculated as shown in figure 3. The difference between PFA and CPFA represents the intensity of medial bulge, and will be referred to as 1MB in the following text. CPFA is due to the lateral concavity of foot outline, or eversion of the heel (forefoot). 2.3. Statistics A r-test is used for testing the significance of sex difference. In order to clarify the relation between foot outline form and conventional variables. correlation coefficients between angular variables of medial axis and conventional variables are calculated. Also, small-PFA group and large-1MB group are compared by using a r-test. The former consists of foot outlines with minimal intlare or outtlare having PFA smaller than the 15th centi Ie. The latter consists of foot outlines showing conspicuous outtlare due to the medial bulge, whose 1MB are larger than the 85th centile. Figure 4 shows an example of a foot outline belonging to a small-PFA group (figure 4A) and examples belonging to a large-1MB group (figure 4B, C). In large-1MB group, foot outlines with large 1MB and small CPFA (figure 4B) and those with large 1MB and large CPFA (figure 4C) are included. 3. Results Figure 5. which shows the distribution of PFA, indicates that most of the feet are more or less outtlared. There is no significant sex difference in the position of PFP and AFP of the medial axis. The mean position ofPFP is 31·4% of foot length from P (calculated when PFA;;" 4°), and that of AFP is 57-4% of foot length from P. Table 2 presents the basic statistics of the angular measurements of medial axis. PFA and 1MB are significantly larger, and AFA is significantly smaller in females. No sex difference is observed in CPFA. PFA is highly correlated with CPFA and 1MB, but CPFA and 1MB are not correlated with each other. AFA is not correlated with other angular measurements of medial axis. Downloaded By: [Texas Technology University] At: 22:54 16 September 2007 Medial axis offoot outline 1915 Figure 3. Original (A) and corrected (B) foot outlines. a. Medial bulge: CPFA. corrected posterior flexion angle: and PFA. posterior flexion angle. c Figure4. Examples of medialaxis of foot outline. A, straightat the heel, both 1MB and CPFA are small; B, with large1MB and very small CPFA; and C, markedly outflared, both 1MB and CPFA are large. The angular measurements of medial axis have very low correlations with age, body size (height and weight), Rohrer index, or foot size (foot length, foot breadth and foot circumference) and most of the correlation coefficients are statistically insignificant. Table 3 presents the correlation coefficients between the angular measurements of medial axis and conventional foot variables with absolute value > 0·3. Most of the variables that show higher correlation with angular measurements of medial axis are not dimensions, but angles or indices. PFA is significantly correlated with foot axis index in both sexes. Correlation coefficient between PFA and fibular instep length observed in females becomes much smaller when foot length is partialled out. Abduction of heel (CPFA) is not correlated with foot measurements or indices. AFA is correlated with toe Vangie, foot axis index and foot index in both sexes. Negative correlation between 1MB and dorsal arch height indicates a tendency that the stronger the medial bulge, the lower the dorsal arch height. The results of the comparison between a small-PFA group and a large-1MB group are presented in table 4. In males, foot size is not significantly different between the two groups, and the only dimension showing significant difference between the two groups is dorsal arch height. In females, the small-PFA group has a significantly larger foot, and thus several dimensions show significant differences between the two groups. Among these dimensions. dorsal arch height has highly significant differences between the two groups (p < 0·001). When the foot size difference between the two female Downloaded By: [Texas Technology University] At: 22:54 16 September 2007 M. Kouchi 1916 N 60 Male N=443 50 40 30 20 In- 10 o o -5 10 PFA ~ 15 20 25 (dogl N 40 Female N=297 30 20 10 0 n-5 -nf 0 Figure 5_ Table 2. 10 PFA 15 PFA AFA CPFA 1MB 25 (dogl Histogram of PFA. Flexion angles (0) of medial axis of foot outlilne. Male Item 20 Female n Mean SD Min Max n Mean SD Min Max Difference r-test 443 443 392 392 8·01 9·26 2·98 5.80 3·60 2·81 1-98 2·22 -1-4 0·5 -1·5 0·6 20·7 18·7 8·4 14·2 297 297 270 270 8·84 8-65 3·22 6-38 3·80 2·87 2·11 2-21 -4·8 1·4 -1·8 0-5 18·8 16·4 10·4 13-3 - 2-98t 2-82t - 1·44 ns - 3·43t tSignificant at the I % level. ns, Not significant. PFA, posterior flexion angle; AFA, anterior flexion angle; CPFA, corrected posterior flexion angle; and 1MB, intensity of medial bulge. Table 3. Correlation coefficients between angular measurements of medial axis offoot outline, foot measurements and indices. Coefficients with absolute values> 0·3 are shown. Male r(PFA, r(AFA, r(AFA, r(AFA, r(AFA, r(IMB, Female foot axis index) toe I angle) toe VangIe) foot axis index) foot index) dorsal arch h.) 0-37 -0·33 0·71 - 0·55 0·32 -0·38 r(PFA, fibular instep I.) r(PFA, ball flex angle) r(PFA, foot axis index) r(AFA, toe Vangie) r(AFA, foot axis index) r(AFA, foot index) r(lMB, dorsal arch h.) -0·36 - 0·36 0-33 0·60 -0·42 0-43 -0·37 PFA, posterior flexion angle; AFA, anterior flexion angle; and 1MB, intensity of medial bulge. Downloaded By: [Texas Technology University] At: 22:54 16 September 2007 Medial axis offoot outline Table 4. 1917 Variables with significant difference between the smaJl-PFA and large-1MB groups. Small-PFA Large-IMB Difference Item Mean SD Mean SD r-test Male (n = 66) Height (em) H I Dorsal arch height (mm) A I Ball flex angle (0) A2 Toe I angle A3 Toe Vangie Foot axis index PFA (0) 1MB 167·7 60·6 77·6 6·4 16·1 79·8 2·6 6·55 4·48 2·10 5·41 4·68 8-48 1·51 165·5 55·8 76·2 10·4 12·7 89·6 12·6 9·2 5·63 4·46 2·41 4·35 5·40 10·18 2·61 1·22 :j: :j: :j: :j: :j: :j: Female (n = 45) Height (em) Weight (kg) L1 Foot length (mm) L2 Fibular instep length L3 Instep length B2 Heel breadth C2 Instep circumference H I Dorsal arch height AI Ball flex angle (0) Foot axis index PFA (0) AFA 1MB 159·2 56·8 230·3 147·5 166·4 62·6 225·9 54·7 78·7 81·6 2·7 7·8 6·07 11·36 9·82 7·67 7·90 3·45 13-16 3·92 2·97 10·73 2·25 3·05 154·7 51·2 225·4 141·1 163·3 60·1 219·6 49·7 76·5 90·3 12·8 9·8 9·7 5·38 8·70 10·22 6·88 8·36 2·75 10·05 3·85 2·99 11·28 2·31 2·80 1·18 t :j: :j: t :j: t :j: t :j: :j: :j: :j: :j: Significant at the t 5% and :j: I % levels. PFA, posterior flexion angle; AFA, anterior flexion angle; and 1MB, intensity of medial bulge. groups is taken into consideration, it is suggested that the large-1MB group has lower plantar arch height and flatter cross-section shape at instep than the small-PFA group, since there is minimal difference in instep circumference in spite of significantly lower dorsal arch height in the large-1MB group. 4. Discussion 4.1. Foot outline form and skeletal structure of the foot The present findings agree with those by Freedman et al. (1946) in that the great majority of the subjects are characterized by a greater or lesser degree of foot outflare, and the degree of foot flare correlated poorly with foot length and breadth. This fact indicates the importance of the flexion of the medial axis of the foot outline as a morphological characteristic of the foot. For the angular measurements of medial axis of foot outline to be useful in summarizing morphological features of the foot, foot outline form must reflect the three-dimensional skeletal structure of the foot. The main cause of medial bulge of foot outline is the overhang of navicular bone as shown in figure 6. The overhang of navicular bone is one of the characteristics of a pronated foot (Kelly 1947), and it becomes more prominent when the foot is intentionally pronated. The negative correlation between Downloaded By: [Texas Technology University] At: 22:54 16 September 2007 1918 M. Kouchi Figure 6. Dorsoplantar roentgenogram of a foot with marked medial bulge. PFA = 9·3; CPFA = 2·2; and 1MB = 7·1. 1MB and dorsal arch height also implies the relation between medial bulge of foot outlline and the pronation of the fool. Nishino (1959) divided the foot into four groups: normal, spread, excavated (high arched), and flat foot groups, based on 13 angular measurements and one index taken from dorsoplantar roentgenograms. The characteristic feature of his flat foot group is the medial shift of the head of talus, navicular bone and medial cuneiform in relation to the line connecting the central point of the first metatarsal head and the midpoint of the posterior margin of calcanean eminence. This situation causes the overhang of the navicular bone, and thus a medial bulge of the foot outline. Also, Nishino's flat foot group includes a much higher percentage of low-arch subjects judged from lateral roentgenograms than other groups. The relationship between overhang of navicular bone and low dorsal arch height observed by Nishino corresponds to the present finding. In a pronated foot, the whole foot tilts inward and dorsal arch height and plantar arch are low. These characteristics correspond with those of the large-1MB group. The lateral concavity of foot outline is due to the deformation of soft tissue by weight bearing as well as to the alignment of foot bones, and the latter has greater effects. In Nishino's classification, subgroup PI of the flat foot group is characterized by smaller fibular instep length and abduction of talus and calcaneus in relation to the tarsometatarsal part of the foot anterior to them. In this situation the foot looks flexed at Chopart's joint, and its outline form shows the lateral concavity. In other words, the foot is prominently outflared as the example shown in figure 4C. The foot outline form thus provides information regarding the three-dimensional foot structure such as pronation and the alignment of foot bones. Further study on the relation of medial axis of foot outline and three-dimensional foot shape is currently being conducted by the present author. 4.2. Importance of morphology in the fitting between the foot and shoe The present results suggest that there is great inter-individual variation in threedimensional skeletal structure, and that the foot is pronated and outflared in most of the present subjects. On the contrary, in all the shoe lasts so far measured, medial axis has no posterior flexion; a shoe last is shaped for foot with neither pronation nor outflare. Therefore, the inner border of the shoe's upper is pressed down by the low plantar arch of the pronated foot, which has large PFA and large 1MB. When outflare is conspicuous as the example shown in figure 4C, everted forefoot causes pressure against the outer forepart of the shoe, and the fifth toe in turn receives uncomfortable pressure. When both 1MB and CPFA are large, the medial bulge deforms the topline, and gaping around the top line of the shoe results owing to everted heel. The tarsal bones are rigidly articulated against each other and are far less movable than phalangeal bones, even when the tarsal part causes the morphological misfit, thus Downloaded By: [Texas Technology University] At: 22:54 16 September 2007 Mediai axis offoot outline 1919 phalangeal parts are under uncomfortable pressure. In other words, the undue pressure on toes cannot be relieved necessarily by changing the design of the forepart of the last. Since the majority of Japanese have pronated and outflared foot whose threedimensional shape is considerably different from that of the 'ideal' foot, development of a shoe last for such feet will improve the fit between feet and shoes in the general population. In addition classifying foot shape into a few types based on proper morphological characteristics, and developing shoe lasts for each type of foot may be a realistic solution to cope with the wide variation of the human foot shape. 4.3. Advantage of medial axis The variation of foot morphology has been investigated by using dimensions, angular measurements, and indices taken on living subjects (Baba 1975, Kouchi 1989, Okada et ai. 1990), or on roentgenograms (Yokokura 1928, 1929, Nishino 1959, Steel et ai. 1980, Takai 1984). These methods have the shortcomings of being unable to fully utilize the shape information and/or difficulties in obtaining data. One of the advantages of medial axis of foot outline is in its simplicity. Foot outline is taken by a foot measurement system in the present study, but almost the same data can be obtained by digitizing a foot outline taken with a scriber (Kouchi et al. 1992). Medial axis can be calculated by a general image processing software. Another advantage is that it carries information on the three-dimensional skeletal structure of the foot, such as pronation, which is almost independent of foot size and has been ignored. For these advantages, the flexion characteristics of the medial axis of foot outlline will provide a useful tool in morphological studies of the foot. 5. Conclusions In the study of the fit between the foot and shoe, morphological variations in the human foot have not been taken into consideration. Medial axis of foot outline provides a useful and powerful method to study the variations in human foot shape. Through the analyses of the flexion angles of medial axis calculated for the right foot outline of 443 male and 297 female subjects, the following conclusions are obtained: (I) the variability of human foot shape caused by the differences in the skeletal structure is not negligible; and (2) the most important factors in determining foot shape are pronation of the foot and abduction of talus and calcaneus in relation to the tarsometatarsal part of the foot. Since these characteristics intimately relate to the fit and comfort of the shoe, by focusing attention on these characteristics, it may be easier to evaluate the fit between the foot and shoe, and to determine the strategy to improve the shoe last. Acknowledgement The author expresses her gratitude to Keio University Tsukigase Rehabilitation Center for the roentgenogram. References BABA, K. 1975, Foot measurement for shoe construction with reference to the relationship betweenfoot length,foot breadth,and ball girth, Journal ofHuman Ergology, 3, 149-156. BOOKSTEIN, F. R. 1991, Morphometric Tools for Landmark Data (Cambridge University Press, Cambridge). ELECTROTECHNICAL LABORATORY 1980, SPIDER user's manual [in Japanese]. Downloaded By: [Texas Technology University] At: 22:54 16 September 2007 1920 Medial axis offoot outline FREEDMAN, A .. HUNTINGTON, E. c., DAVIS, G. c., MAGEE, R. B., MILSTEAD, V. M. and KIRKPATRICK, C. M. 1946, Foot dimensions of soldiers, Project No. T-13, Armoured Medical Research Laboratory, Fort Knox, Kentucky. JAPAN LEATHER AND LEATHER-GOODS INDUSTRIES ASSOCIATION 1987, Reports on the project of foot study (1986) [in Japanese]. JAPAN LEATHER AND LEATHER-GOODS INDUSTRIES ASSOCIATION 1988, Reports on the project of foot study (1987) [in Japanese]. KELLY, E. D. 1947, A comparative study of structure and function of normal, pronated, and painful feet among children, Research Quarterly, 4, 291-312. KOUCHI, M. 1989, An analysis of variations in Japanese foot shapes, Journal of the Anthropological Society of Nippon, 97, 373-388 [in Japanese with English summary]. KOUCHI, M. and YAMAZAKI, N. 1990, Analysis of variations in foot contours based on direction angles. Journal of the Anthropological Society of Nippon, 98,91-105 [in Japanese with English summary]. KOUCHI, M., YOKOI, T., ATSUMI, H., YAMASHITA, J., YOKOYAMA, K., YOSHIOKA, M., OGI, H., HOTTA, A., TANII, K., KISHI, Y. and IIDA, T. 1992, Reference Manual of Anthropometry in Ergonomic Designing. Technical Report, Industrial Products Research Institute [in Japanese]. LESTREL, P. E. and BROWN, H. D. 1976, Fourier analysis of adolescent growth of the cranial vault: a longitudinal study, Human Biology, 48, 517-528. NISHINO, H. 1959, Structural studies of the foot bones by dorsoplantar roentgenograms and frontal tomography. Journal of the Japanese Orthop. Surgical Society, 32, I I 17-1 135. OKADA, M., KOKUBO, H., SHINDO, M. and MORIMOTO, M. 1990, Multi-item anthropometry of the foot in Japanese aged 7 to 15, Journal ofthe Anthropological Society ofNippon, 98, 75-90 [in Japanese with English summary]. STEEL, M. W., JOHNSON, K. A., DEWITS, M. A. and ILSTRUP, D. M. 1980, Radiographic measurements of the normal adult foot, Foot and Ankle, 1, 151-158. TAKAI, S. 1984, Structural components of the arch of the foot analysed by radiogrammetric and multivariate statistical methods, Acta Anatomica, 119, 161-164. YOKOKURA, S. 1928, Standard of the lateral and medial longitudinal arches of Japanese foot and their classifications, Journal of the Japanese Orthopaedic Association, 3, 332-360. [in Japanese]. YOKOKURA, S. 1929, Standard of the lateral and medial longitudinal arches of Japanese foot and their classifications, II, Journal of the Japanese Orthopaedic Association, 4, 161-183. Manuscript received 20 November 1993 Manuscript accepted 5 July 1994