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Associations between the rates of maturation of the bones of the hand-wrist.

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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.
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