Associations between the Rates of Maturation of the Bones of the Hand-wrist A. F. ROCHE The Fels Research Institute, Yellow Springs, Ohio 45387 ABSTRACT Skeletal maturation rates for the age interval 3 to 13 years were analyzed using bone-specific assessments (Greulich-Pyle ) of serial radiographs of 40 children. The mean rates of skeletal maturation resembled those of the population from which the atlas standards had been derived. There was a linear trend of skeletal age against chronological age for most bones in each sex. Regression lines were fitted to these data and the b values of the regression lines were calculated. Communality indices were calculated from an intercorrelation matrix of these b values. There was a statistically significant rank order correlation between the sexes in the communality indices. They tended to be higher in the girls than i n the boys and were relatively low f o r the radius, ulna and carpals. Communality indices within groups of bone.; were high in all rows, especially the metacarpals, but i n each sex they were comparatively low i n the first ray (metacarpal plus the phalanges of the corresponding digit) and i n the fifth ray of the boys. Neighborhood effects o n the levels of association of maturation rates were present, particularly i n the carpus, but marginal effects were not noted. Considering the widespread interest in skeletal maturation among clinicians and research workers, surprisingly little attention has been given to either the rates or levels of maturation of individual bones. In many children, there are variations between the levels of maturity of the handwrist bones (Pyle et al., '48; Acheson, '66). Consequently, a single area skeletal age for the hand-wrist must be obtained by combining bone skeletal ages either mathematically after bone-specific assessments or subjectively by overall appraisal of the maturity of the area. There is no agreement concerning the best basis for selection and weighting of bone skeletal ages to obtain a n area skeletal age. One relevant factor is the extent to which the individual bones are representative of the hand-wrist in their levels and rates of maturation. Variations between the handwrist bones in this respect could be anticipated because they vary in their intercorrelations of age at onset of ossification (Robinow, '42; Gasn and Rohmann, '59). Furthermore, the ages at onset of ossification and the ages at which these bones become mature are not related closely (Garn et al., '61; Stuart et al., '62). The present study sought to determine the correlations between each hand-wrist bone and all the other bones of the area in their rates of maturation. In addition, an analysis was made of the extent to AM. J. PHYS. ANTHROP.,33' 341-348. which these rates were correlated among carpal bones and among bones grouped in rows or rays. The bones of a ray are the phalanges of one digit plus the corresponding metacarpal. Possible neighborhood and marginal effects on the levels of association of skeletal maturation rates were investigated, within both rows and rays. MATERIAL AND METHODS Assessments were made of non-screened radiographs of the left hand-wrists of "normal" children of British ancestry living in Melbourne, Australia. Each radiograph was taken i n accordance with the instructions of Greulich and Pyle ( ' 5 9 ) , using a tube-film distance of 91.4 cm and directing the central ray towards the distal end of the third metacarpal. The present sample of 20 boys and 20 girls was selected randomly from those among 45 boys and 58 girls who had a complete series of radiographs taken near each birthday from the third to the thirteenth inclusive. Additionally, they were radiographed threemonthly from three to four years and sixmonthly from four to six years. The physical growth, dietary intakes, physical activity, illness experience and socio-economic status of these children have been reported (for references, see Roche, '67a). Skeletal maturity was assessed bone by bone using the atlas of Greulich and Pyle 341 342 A. F. ROCHE ('59). The skeletal ages assigned to the individual bones were interpolated between the atlas standards when this was considered appropriate. These interpolations were to monthly intervals up to and including the skeletal age of five years after which they were to three-monthly intervals. All the assessments were made by one observer whose intraobserver errors did not exceed those reported by other experienced workers (Hansman and Maresh, '61; Anderson et al., '65; Acheson et al., '66). A trend analysis was made of the equally-spaced, bone-specific assessments against chronological age (Ferguson, '66). Essentially this was an analysis of variance between ages with subsequent splitting off of one degree of freedom for linear regression from the between ages line. The F ratio was between the variance estimates of the deviations from linearity and those oE the interactions between subjects and ages. The F values for each bone in each sex indicated that there was no real tendency for the data to vary from linearity in most bones (table 1). The majority of the significant variations occurred in the metacarpals and proximal phalanges of the boys; these just reached the P < 0.05 level. There were fewer signjficant variations in the girls; most of these were in carpals and they reached higher levels of significance. Despite these few significant differences from linearity i t was considered reasonable to summarize the data by fitting regression lines and calculating b values that reflected the slopes of these lines. These b values were interpreted as indices of the rates of maturation of individual bones. A complete intercorrelation matrix (28 X 28) of b values was calculated in each sex. Copies of these matrices are available from The Librarian, Fels Research Institute, Yellow Springs, Ohio 45387. The values of the correlation coefficients ( T ) were used to obtain a mean T for each bone using z transforms (Fisher, '58). Each mean T was called a communality index and denoted the extent to which the rate of maturation of a particular bone, in these boys or girls, was correlated with the corresponding rates of all other bones of the hand-wrist combined. TABLE 1 F-ratios f o r deviations from linear regressions of skeletal age against chronological age (20 boys; 20 girls) Bone Radius Ulna Capitate Hamate Triquetr a1 Lunate Scaphoid Trapezium Trapezoid Metacarpal I Metacarpal I1 Metacarpal I11 Metacarpal IV Metacarpal V Proximal phalanx I Proximal phalanx I1 Proximal phalanx I11 Proximal phalanx IV Proximal phalanx V Middle phalanx I1 Middle phalanx I11 Middle phalanx IV Middle phalanx V Distal phalanx I Distal phalanx I1 Distal phalanx I11 Distal phalanx IV Distal phalanx V 1 P < 0.05: 2 P Boys Girls 0.97 1.34 0.87 1.01 0.93 0.70 1.28 1.39 1.11 0.90 1.87 2.07 2.25 2.11 1 1.83 2.17 * 2.24 2.12 1 2.13 1.29 1.18 1.19 2.07 1.81 0.67 0.77 0.80 0.79 0.65 2.69 2 0.97 1.24 1.01 3.21 1.30 2.49 3.39 e 0.93 0.69 0.61 0.54 0.52 0.83 1.25 1.23 1.29 1.04 1.58 1.75 1.56 1.16 0.69 0.79 0.87 0.84 0.78 < 0.01. deviation sum of squares (k-2) degrees of freedom ' and w - within-groups sum of squares (N-k) decrees of freedom ' k, number of chronol&al age groups; N, number of observations. - Sa2 S,Z ,'where ' d - ~. FINDINGS The means and standard deviations for the rates of maturation ( b values) of the individual bones, and the means for all bones combined, indicate that, between 3 and 13 years, the hand-wrist areas of the present children matured at approximately the same rates as those of the Cleveland children from whom the Greulich-Pyle atlas standards ('59) were derived (table 2). The mean rates for different bones ranged from 0.91 for the scaphoid to 1.14 for proximal phalanx I1 in the boys. The spread of mean rates was narrower in the girls. The mean rates for particular bones were slightly more variable in the girls than in the boys. The most variable bones in each sex were the ulna, lunate and trapezium; in the girls the scaphoid also was very variable. 343 HAND-WRIST MATURATION TABLE 2 Means and standard deviations of the b values for skeletal age against chronological age. These b values indicate rates of skeletal maturation Boys Radius Ulna Capitate Hamate Triquetral Lunate Scaphoid Trapezium Trapezoid Metacarpal I Metacarpal I1 Metacarpal I11 Metacarpal I V Metacarpal V Proximal phalanx I Proximal phalanx I1 Proximal phalanx I11 Proximal phalanx IV Proximal phalanx V Middle phalanx I1 Middle phalanx I11 Middle phalanx I V Middle phalanx V Distal phalanx I Distal phalanx I1 Distal phalanx I11 Distal phalanx IV Distal phalanx V Mean of all bones Girls Mean S.D. Mean S.D. 1.04 1.00 1.02 1.02 0.99 1.05 0.91 1.14 1.05 1.03 1.06 1.06 1.06 1.06 1.06 1.16 1.05 1.05 1.06 1.01 1.01 1.01 1.04 1.06 1.04 1.04 1.04 1.04 0.07 0.14 0.07 0.07 0.12 0.15 0.11 0.31 0.11 0.06 0.07 0.07 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.09 0.09 0.09 0.10 0.09 0.09 0.09 0.09 0.09 1.06 0.98 1.04 1.03 1.02 1.02 1.07 1.09 1.03 1.07 1.04 1.05 1.04 1.05 1.04 1.05 1.05 1.04 1.05 1.00 0.99 1.00 1.02 1.02 1.03 1.02 1.02 1.03 0.08 0.17 0.08 0.09 0.11 0.14 0.19 0.18 0.11 0.08 0.10 0.10 0.10 0.10 0.09 0.09 0.09 0.09 0.10 0.11 0.12 0.12 0.12 0.09 0.10 0.10 0.10 0.10 1.04 1.03 N = 20 except f o r Middle Phalanx V in girls where N = 19. This bone was deformed and could not be assessed in one girl. The b values were from linear regression equations Y=a+bX. The communality indices reflect the extent to which the rates of maturation of each bone were correlated with the rates of maturation of all other hand-wrist bones (table 3 ) . These indices varied between bones, although the rank order correlation between the sexes in the values of these indices was highly significant statistically ( P < 0.01). The indices were relatively high for all metacarpals and phalanges in each sex except for some of these bones in the boys (metacarpals I and V, proximal phalanx I and the middle phalanges). The indices were low for the ulna and for most of the carpals in each sex, and for the radius in the boys. The indices were close to zero for the ulna and trapezium in the boys. All the correlation coefficients between the skeletal maturation rates of the ulna and other hand-wrist bones were close to zero in the boys. The coefficients were very low between the trapezium and other hand-wrist bones except the lunate and trapezoid in the boys. The mean of the communality indices for all bones was higher in the girls than in the boys, indicating that the rates of maturation of the individual bones were more highly correlated in the hand-wrist areas of the girls than of the boys. Communality indices were calculated within groups of hand-wrist bones (table 4). These indices were all positive but they were low for the radius and ulna, particularly in the boys, and for the carpals in each sex. Within the rows of metacarpals and phalanges, the indices were very high; each index for the girls was higher than the corresponding index for the boys. In each sex, the communality index for the metacarpals was less than those for the TABLE 3 Communality indices (mean r ) for rates of skeletal maturation of the bones of the hand-wrist Bone Radius Ulna Capitate Hamate Triquetral Lunate Scaphoid Trapezium Trapezoid Metacarpal I Metacarpal I1 Metacarpal I11 Metacarpal IV Metacarpal V Proximal phalanx I Proximal phalanx I1 Proximal phalanx I11 Proximal phalanx IV Proximal phalanx V Middle phalanx I1 Middle phalanx I11 Middle phalanx I V Middle phalanx V Distal phalanx I Distal phalanx I1 Distal phalanx 111 Distal phalanx I V Distal phalanx V Mean of all bones Boys Girls 0.441 - 0.020 0.557 0.611 0.369 0.342 0.468 0.026 0.201 0.719 0.812 0.812 0.804 0.769 0.771 0.831 0.831 0.828 0.810 0.769 0.776 0.775 0.710 0.701 0.807 0.814 0.812 0.811 0.788 0.419 0.759 0.819 0.512 0.659 0.386 0.477 0.374 0.868 0.909 0.914 0.907 0.899 0.889 0.919 0.918 0.918 0.916 0.909 0.921 0.919 0.906 0.851 0.899 0.920 0.711 0.800 0.921 0.917 Each mean r was derived from the mean of the z transforms of r. 344 A. F. ROCHE TABLE 4 Communality indices ( m e a n r ) f o r rates of maturation in groups of hand-wrist bones Groups of bones Boys Girls Radius and ulna Carpals Metacarpal row Proximal phalanx row Middle phalanx row Distal phalanx row 0.125 0.613 0.957 0.980 0.980 0.975 0.503 0.593 0.976 0.988 0.985 0.991 Ray I Ray I1 Ray 1111 Ray IV Ray V 0.835 0.872 0.870 0.862 0.835 0.931 0.935 0.949 0.949 0.941 Each mean r was obtained from the mean of the z transforms of r. separate rows of phalanges. The communality indices for corresponding rays were each higher in the girls than in the boys. In both the boys and the girls these indices were low in the first ray; in the boys they were low also in the fifth ray. Possible neighborhood effects on the levels of associations between bones in their maturation rates were analyzed by comparisons between the mean correlations of pairs of adjacent (e.g., metacarpals I11 and IV) and pairs of non-adjacent bones (e.g., metacarpals I1 and IV). All the bones included in the pairs were nonmarginal except in the carpus where each pairing included a marginal bone. The marginal short bones of the hand are those at the ends of rows (e.g., metacarpals I and V ) or rays (e.g., distal phalanx 11). It was considered that neighborhood effects would be demonstrated if the correlations between adjacent pairs were higher than those between non-adjacent pairs. The mean r was higher for adjacent than for non-adjacent bones in 5 of the 6 comparisons made (table 5). In the remaining comparison, the mean T was the same for the adjacent and non-adjacent bones. This tendency to a higher correlation between adjacent bones was statistically significant (x2 = 4.16; P < 0.05). The differences between adjacent and non-adjacent pairs of bones in the levels of correlation of skeletal maturation rates were comparatively large in the carpals, both in the boys and in the girls. Possible marginal effects were analyzed by calculating mean correlations between the skeletal maturation rates of pairs of bones, all of which were adjacent. In the “marginal” pairings, one bone was marginal and the other was non-marginal. In the “non-marginal” pairings both bones were non-marginal. The slight differences between corresponding mean correlation indices and the variable directions of these differences indicate that real marginal effects were not present. The correlations between rates of skeletal maturation were compared for pairs of bones selected because of their possible relevance to interpretation of the differences in segmentation between the first and second digits. In both the boys and the girls, metacarpal I was associated more closely in its rate of maturation with metacarpal I1 than with proximal phalanx I1 (table 6). Similarly, proximal phalanx I and distal phalanx I were associated more closely in this regard with the correspondingly named bones of the second ray than with middle phalanx 11. However, comparisons between correspondingly named bones of the first, third and fifth rays in their correlations of skeletal maturation rates showed that, for the metacarpals and proximal and distal phalanges, the bones of the third ray were correlated more highly with those of the fifth ray than with the correspondingly named bones of the first ray. TABLE 5 Correlations between hand-wrist bones in rates of maturation relevant to possible neighborhood and marginal e f f e c t s Groups of bones Carpals Adjacent Non-adjacent Metacarpals and phalanges Rows Adjacent Non-adjacent Rays Adjacent Non-adj acent Rows Marginal Non-marginal Rays Marginal Non-marginal Boys Girls 0.661 0.565 0.668 0.494 0.994 0.983 0.998 0.993 0.864 0.773 0.947 0.947 0.972 0.994 0.987 0.998 0.897 0.864 0.941 0.947 345 HAND-WRIST MATURATION TABLE 6 Correlations between rates of skeletal maturation relevant t o homologies in t h e first and second rays Correlations Metacarpal I v. Metacarpal I1 Metacarpal I v. Proximal Phalanx I1 Proximal Phalanx I v. Proximal Phalanx I1 Proximal Phalanx I v. Middle Phalanx I1 Distal Phalanx I v. Distal Phalanx I1 Distal Phalanx I v. Middle Phalanx I1 Metacarpal 111v. Metacarpal I Metacarpal 111v. Metacarpal V Proximal Phalanx I11 v. Proximal Phalanx I Proximal Phalanx I11 v. Proximal Phalanx V Distal Phalanx I11 v. Distal Phalanx I Distal Phalanx 111v. Distal Phalanx V DISCUSSION The present communality indices for skeletal maturation rates have highly significant rank order correlations (P < 0.01) with communality indices for age at onset of ossifxation (Carn and Rohmann, '59) both in the boys and the girls. This might have been unexpected because age a t onset of ossification and the interval from then to the completion of maturation are negatively correlated (Stuart et al., '62). Consequently, the assessment of hand-wrist skeletal maturity could be based on bones that are representative, for age at onset of ossification, as suggested by Garn e t al. ('64), and for skeletal maturation rates. This might exclude valuable information. A more appropriate use of communality indices is to identify highly correlated groups of bones; a weighted assessment of one member can provide a measure of maturity for the whole group. Some handwrist bones were almost identical i n their means and standard deviations for b values and i n their communality indices for rates of skeletal maturation in the children studied. Consequently, they provide redundant information. The possibility of omitting the assessment of all short bones except those of the third ray, i.e., metacarpal I11 and its corresponding phalanges, should be considered. On a similar basis, Tanner et al. ('62) omitted the bones of the third and fifth rays; this is justified on analysis of the scores they assigned to the maturity stages of each bone. These weighted scores minimized the variances between bones. Boys Girls 0.873 0.867 0.950 0.820 0.931 0.867 0.880 0.968 0.941 0.974 0.936 0.980 0.953 0.922 0.954 0.925 0.934 0.879 0.951 0.975 0.950 0.989 0.940 0.997 Very high correlations have been reported between bone skeletal ages and the mean hand-wrist skeletal age (Clarke and Hayman, '62); these may be misleading because of the long age range for which they were calculated. Clarke and Hayman selected five bones ( triquetral, metacarpal IV, proximal phalanx I, middle phalanx I1 and distal phalanx I ) that, when appropriately weighted, could provide a hand-wrist skeletal age. In the present boys, the triquetral and distal phalanx I were not highly representative in their skeletal maturation rates. If bones with low communality indices are weighted heavily (as in Acheson, '54), this would tend to maximize the variance of recorded skeletal age, in chronological age groups, and thereby maximize the discriminant ability of the measure. However, it is probably unwise to load bones that are unrepresentative for the area and probably unrepresentative of general skeletal maturity. The comparatively high variability of skeletal maturation rates in carpals, other than the capitate and hamate, is in agreement with findings relating to age at onset of ossification (Greulich and Pyle, '59; Hansman, '62; Stuart et al., '62) and skeletal maturity level (Wallis, '31; Hansman and Maresh, '61; Roche, '62). However; the carpals did not differ significantly in skeletal maturity from the other handwrist bones in a group of West African children (Mass6 and Hunt, '63). This marked variability of carpal skeletal maturation is not directly relevant to the replicability of assessments. There are conflicting reports as to whether the replic- 346 A. F. ROCHE ability of assessments is lower for carpal bones than for other hand-wrist bones (Acheson et al., '64; Tanner and Whitehouse, '64; Roche et al.,'70). Neighborhood effects were demonstrated in the present data when correlations between the maturation rates of adjacent and non-adjacent bones were compared. The mechanism responsible for the similarity between the rates of maturation of neighboring bones is not clear but these effects were most marked in the carpus. The destruction of the cartilaginous model of a carpal bone with subsequent absence of the mechanical influences that this bone would have exerted on its neighbors, is associated with accelerated growth and maturation of adjacent carpals (Roche, '67b). Nevertheless, changes in maturity level apparently due to the development of articular surfaces for adjacent carpals may occur before these carpal bones ossify. For example, the dorsal margin of the radial epiphysis may be separated to lunate and scaphoid areas before the latter bones have ossified (fig. 1 ) . The present findings may be related to previous use of the same radiographs to analyze associations between the rates of diaphyseal and epiphyseal elongation and rates of change in diaphyseal width (Roche and Hermann, '70a,b). The mean communality indices for the rates of diaphyseal and epiphyseal elongation and Fig 1 Part of the left carpal area in a boy aged 3.5 years. Parts of the radius, ulna and metacarpal V are visible in addition to the capitate, hamate and triquetral. Note the division of the dorsal surface of the radial epiphysis into lunate and scaphoid areas, although the lunate and scaphoid have not yet ossified. In this boy, the lunate ossified between 4.0 and 4.5 years and the scaphoid between 4.5 and 5.0 years. HAND-WRIST MATURATION skeletal maturation were higher i n the girls than the boys; there was a n opposite difference for the diaphyseal width indices. Neighborhood effects were present for all four characteristics in both rows and rays of bones except for the correlations between epiphyseal elongation rates of bones grouped in rays. The present analysis indicates that the bones of the first ray are named correctly and is in agreement with findings based on elongation rates (Roche and Hermann, '70a). The trend of skeletal age against chronological age was not linear in some of the hand-wrist bones (table 1). Despite this, rectilinear regression lines were fitted to the data for each bone and the subsequent analyses were based on the slopes of these lines. The findings should be interpreted as indicating general patterns. Probably the same patterns would be found if the study were replicated on another sample or if different statistical techniques were employed to analyze the present data. The observed correlations may have been influenced by observer errors with systematic tendencies, varying between bones, for the errors to differ in direction at particular ages. This is unlikely because the interbone differences in mean rates of maturation were small and varied between the sexes although the radiographs were assessed in a random order. Possibly, the order in which the bones were assessed within each radiograph might have affected the correlation coefficients. There might have been a tendency to assign similar ages to bones in the same row, e.g. metacarpals, because they were assessed in series. However, the communality indices between the rates of growth of the short bones of the hand-wrist are higher for rows than for rays (Roche and Hermann, '70a,b) and the order in which these bones were measured would not have influenced the data recorded. These considerations support a conclusion that the higher correlations within rows than within rays of hand-wrist bones in their rates of growth and maturation are real. ACKNOWLEDGMENT This work was supported by grants FR00222, FR-05537, HD-04629 and HD-04660 347 from the National Institutes of Health, Bethesda, Maryland. LITERATURE CITED Acheson, R. M. 1954 A method of assessing skeletal maturity from radiographs; A report from the Oxford Child Health Survey. J. Anat. (Lond.), 88: 498-508. 1966 Maturation of the skeleton. In: Human Development. F. Falkner, ed. W. B. Saunders, Philadelphia, pp. 465-502. Acheson, R. M., J. H. Vicinus and G. B. Fowler 1964 Studies in the reliability of assessing skeletal maturity from x-rays. Part IT. The bone-specific approach. Hum. Biol., 36: 211228. 1966 Studies i n the reliability of assessing skeletal maturity from x-rays. Part 111. Greulich-Pyle atlas and Tanner-Whitehouse method contrasted. Hum. Biol., 38: 204-218. Anderson, M., S.-C. 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