close

Вход

Забыли?

вход по аккаунту

?

Rates of Change in width and length-width ratios of the diaphyses of the hand.

код для вставкиСкачать
Rates of Change in Width and Length-Width
Ratios of the Diaphyses of the Hand
A. F. ROCHE AND R. F. H E R M A "
Fels Research Institute, Yellour Springs, Ohio 45387
ABSTRACT
The minimum width and the length of each diaphysis of the hand
were measured on serial radiographs of 20 boys and 20 girls. These radiographs
were taken close to each birthday at ages from 3 to 13 years inclusive. The corresponding length-width ratios were calculated from these parameters. The b values
(indicating rates of change) were calculated for width and length-width ratio in
each diaphysis in each child. Communality indices (mean T between b values) were
calculated for individual diaphyses. These communality indices reflect the associations between each diaphysis and all the other diaphyses of the hand in their
rates of change in width and length-width ratio. The sex differences were not statistically significant for mean b values but they were significant for the communality
indices for width (boys higher) and length-width ratio (girls higher). Statistically
sign5cant neighborhood effects were present in communality indices for widths
within rays for the girls and for ratios within rays for both sexes, There were
statistically significant marginal effects in communality indices for widths in the
girls within rows and for length-width ratios in the boys within rays.
It is well known that diaphyses increase sentative diaphyses could provide useful inin width and length at different sites. formation, with less labor than that reThese sites are unlike in their cellular quired to measure all diaphyses. The
mechanisms and their genetic and hormonal controls (Ham and Leeson, '65). In
some clincal conditions the length and
width of bones are affected differentially
(Rubin, '64); more frequent usage of measurements of hand radiographs might improve the diagnosis of such conditions.
Such usage is infrequent, partly because
suitable standards are lacking. The relevant standards are restricted to the width
of the second metacarpal and the sum of
the widths of the second, third and fourth
metacarpals (Smithgall et al., '66; Garn
and Rohmann, '66; Bonnard, '68). Lengthwidth ratios of diaphyses in children are
lacking. Standard values for length-width
ratios in adults have been published
(Parish, '60). Necessarily, these values
in adults have been based on total length,
not diaphyseal length.
The present aim was to determine the
rates of change in width and length-width
ratios of the diaphyses of the hand and the
extent to which these rates of change
are intercorrelated. These intercorrelations
could help to identify the diaphyses that
are most representative in their patterns
of change in the parameters considered.
Measurements restricted to the repreAM. J. PHYS. ANTHROP.,32: 89-96.
radiographs used in this study had been
employed previously to analyze the rates
of total, diaphyseal and epiphyseal elongation (Roche and Hermann, '69).
MATEFUAL AND METHODS
Measurements were made on serial nonscreened, dorso-palmar radiographs of the
left hands of Melbourne children of British
ancestry (20 boys, 20 girls). These radiographs were taken near each birthday,
from the third to the thirteenth inclusive,
with radiographic positioning in accordance with the instructions of Greulich
and Pyle ('59) and a tube-film distance of
91.4 cm. The length of each diaphysis
was measured in its long axis and the
minimum width was recorded at right angles to the long axis. A complete series of
radiographs was available for each child.
However, diaphyseal length was not measured for distal phalanges in the girls at
13 years because, in ten of the girls,
epiphyseo-diaphyseal fusion had occurred
in these bones. All measurements were
made using a transparent ruler graduated
to 0.5 mm; the differences between repeated measurements did not exceed 0.5
mm.
89
90
A. F. ROCHE AND R. F. HERMANN
A trend analysis, by the method of Ferguson ('66), showed that plottings of the
diaphyseal widths and length-width ratios
at successive ages in individuals were linear (table 1). The length-width ratios were
derived using lengths that had been recorded directly from the radiographs and
widths that were obtained from the regression lines. It has been shown that the age
changes in these lengths are linear (Roche
and Hermann, '69). Directly recorded
widths were not used because even slightly
irregular changes in them caused comparatively large fluctuations in the ratios.
(Means and standard deviations for width,
length and length-width ratios and their
annual increments for each diaphysis of
the hand are available from The Librarian,
Fels Research Institute, Yellow Springs,
Ohio 45387.) The b value for each regression line reflects the slope of the line and,
consequently, the rate of change in width
or length-width ratio. Communality indices were calculated from a complete intercorrelation matrix of the b values for
each sex (Garn and Rohmann, '59; Roche
and Hermann, '69). These indices (mean
r ) reflect the extent to which the rates of
change, from 3 to 13 years, in the width
TABLE 1
or the length-width ratio of a diaphysis
are correlated with corresponding changes
in the other diaphyses of the hand.
RESULTS
Widths
There were only slight sex differences in
mean b values for corresponding diaphyses, except in the distal phalanges (table
2); even for these diaphyses, considered
as a group, the difference was not statistically significant. The rank order correlation between the mean b values in the
boys and the girls was statistically significant ( r = 0.877; P. < 0.01).
The communality indices between the
rates of change in diaphyseal width were
higher in the boys than in the girls to a
statistically significant extent ( t = 2.895;
P. < 0.01). The rank order correlation between the sexes for these communality indices was not statistically significant, partly
because of large sex differences between
the values for some diaphyses, e.g., middle
phalanx 5 (table 3). Mean communality
indices were calculated for diaphyses
grouped in rows (e.g., metacarpals) or rays
(e.g., metacarpal 3 and the phalanges of
the third digit). In general, these mean
F-ratios for deviations f r o m linear regressions of
w i d t h and length-width ratios against age
(20 boys; 20 girls)
Diaphysis
M1
2
3
4
5
PP 1
2
3
4
5
MP2
3
4
5
DP1
2
3
4
5
Boys
TABLE 2
Mean b values (slopes) of regression lines for
diaphyseal length and length-width ratio
(20 boys; 20 girls)
Girls
~~
Width
Ratio
Width
Ratio
0.15
0.09
0.09
0.18
0.04
0.12
0.28
0.58
0.32
0.08
0.15
0.44
0.35
0.14
0.31
0.52
0.78
1.56
0.59
0.29
0.54
0.81
0.39
0.33
0.12
0.91
0.64
0.46
0.35
0.48
0.71
0.76
0.16
0.09
0.49
0.20
0.24
0.12
0.19
0.62
0.18
0.35
0.21
0.26
0.12
0.55
0.18
0.35
0.26
0.28
0.17
0.14
0.18
0.72
0.76
0.51
0.49
0.48
0.33
0.24
0.25
0.71
0.61
0.47
0.26
0.59
0.89
0.39
0.43
0.53
0.18
0.07
0.13
0.10
0.14
0.28
M metaca a19 PP proximal phalanx; MP, middle
phaianx, and%P: di&al phalanx.
None of these F-ratios are statistically significant;
therefore the patterns of change against age are linear.
Boys
Diaphysis
M1
2
3
4
5
PP 1
2
3
4
5
MP2
3
4
5
DP 1
2
3
4
5
Girls
Width
Ratio
Width
Ratio
0.245
0.275
0.236
0.177
0.198
0.204
0.229
0.225
0.212
0.186
0.174
0.177
0.178
0.160
0.167
0.200
0.200
0.178
0.155
0.520
0.574
0.658
0.608
0.514
0.214
0.224
0.212
0.166
0.207
0.249
0.243
0.223
0.233
0.367
0.270
0.237
0.215
0.245
0.265
0.243
0.158
0.176
0.215
0.222
0.204
0.188
0.182
0.171
0.177
0.160
0.139
0.154
0.167
0.158
0.143
0.130
0.427
0.498
0.590
0.510
0.445
0.216
0.201
0.213
0.180
0.208
0.224
0.227
0.212
0.232
0.307
0.245
0.220
0.206
0.246
0.234
M metac al; PI', proximal phalanx; MP. middle
phdanx, an%P, distal phalanx.
91
DIAPHYSES OF THE HAND
TABLE 3
Communality indices (mean r ) for rate of change
in width and length-width ratio
(20 boys; 20 girls)
Diaphysis
Boys
Girls
Width
Ratio
Width
Ratio
0.509
0.464
0.515
0.479
0.523
0.531
0.507
0.360
0.444
0.453
0.466
0.481
0.557
0.469
0.256
0.445
0.273
0.218
0.225
0.430
0.224
0.371
0.343
0.428
0.447
0.380
0.409
0.305
0.447
0.388
0.369
0.433
0.501
0.419
0.097
0.184
0.099
0.107
0.065
0.317
0.368
0.298
0.305
0.344
0.336
0.268
0.424
0.430
0.438
0.369
0.433
0.383
0.429
0.092
0.106
0.357
0.278
0.334
0.334
0.333
0.331
0.161
0.397
0.630
0.531
0.319
0.518
0.601
0.597
0.458
0.467
0.483
0.542
0.258
0.181
0.456
0.54 1
0.520
0.483
0.446
M1
2
3
4
5
PP 1
2
3
4
5
MP2
3
4
5
DP 1
2
3
4
5
Mean:
all bones
M, metacarpal; PP, proximal phalanx; MP, middle
phalanx, and DP, distal phalanx.
indices for diaphyses within rows or rays
were higher than those for the communalities between each diaphysis and all the
other diaphyses of the hand. These indices
tended to be higher for rows than for
rays. However, the mean communality indices were low for the distal phalanges in
the boys and the middle phalanges in the
girls (table 4). The mean communality
indices within rows or rays tended to be
higher in the boys than the girls except
for the distal phalanges and the fourth
ray. The middle phalanges had the highest
index of all rows in the boys but the lowest
in the girls. In the boys, the indices were
high for the first ray and low for the third;
in the girls, they were high for the fourth
ray and very low for the fifth. There were
statistically significant sex differences in
the rank order of communality indices
within both rows and rays.
The hypothesis that the rates of change
in width might be more highly correlated
between adjacent than non-adjacent diapyses was examined. Almost all comparisons between the correlations of adjacent
and non-adjacent pairs of diaphyses
showed that the adjacent pairs were more
highly correlated (table 5), thus supporting the hypothesis.
The hypothesis that correlations between
diaphyses of a row or ray in their rates of
change in width might be lower for diaphyses on the margin of a row or ray, e.g.,
metacarpal 5, distal phalanx 2, than for
non-marginal diaphyses in the same row
or ray was tested (table 6). For both the
boys and the girls, the observed tendencies
in rows and in rays supported this hypothesis but to an extent that was not statistically significant, except for rows of diaphyses in the girls (t = 2.315; P. < 0.05).
Length-width ratios
The mean b values were similar for both
the boys and the girls (table 2 ) and the
rank order correlation between the sexes
was statistically significant ( r = 0.935;
P. < 0.01). In the boys, the groups of middle and distal phalanges had higher mean
b values than in the girls, but to an extent
that was not statistically significant.
TABLE 4
Communality indices (mean r ) for rate of change in width and in length-width ratio
within groups of diaphyses of the hand
Girls
Boys
Rows and rays
Width
Ratio
Width
Ratio
Metacarpal row
Proximal phalanx row
Middle phalanx row
Distal phalanx row
0.619
0.521
0.678
0.314
0.562
0.581
0.555
0.459
0.475
0.507
0.375
0.361
0.461
0.625
0.444
0.566
Ray I
Ray I1
Ray 111
0.608
0.475
0.376
0.440
0.495
0.346
0.280
0.203
0.405
0.351
0.358
0.421
0.320
0.518
0.130
0.353
0.327
0.569
0.746
0.373
Ray IV
Ray V
92
A. F. ROCHE AND R. F. HERMANN
TABLE 5
Mean correlations between the rates o f change in width and in length-width ratio
relevant to possible neighborhood effects
Groups of diaphyses
Girls
Boys
Width
Ratio
Width
Ratio
Within rows Adjacent
Non-adjacent
0.570
0.420
0.696
0.583
0.614
0.482
0.593
0.549
Within rays Adjacent
Non-adjacent
0.582
0.409
0.548
0.030
0.430
0.127
0.522
0.300
TABLE 6
Mean correlations between the rates of change i n width and in length-width ratio
relevant to possible marginal effects
Girls
Boys
Groups of diaphyses
Width
Ratio
Width
Ratio
Within rows Marginal
Non-marginal
0.555
0.611
0.492
0.696
0.371
0.620
0.456
0.676
Within rays Marginal
Non-marginal
0.343
0.574
0.219
0.488
0.387
0.545
0.557
0.599
The communality indices for the rate
of change in length-width ratio for each
diaphysis (table 3) were higher in the
girls than in the boys to a statistically significant extent (t = 2.861; P. < 0.01). This
sex difference was particularly marked in
the metacarpals. When the indices for
these diaphyses were omitted, the sex difference between the mean indices for the
remaining diaphyses of the hand was not
statistically significant. The rank order
correlation of the communality indices between the two sexes was not statistically
significant.
The mean communality indices for diaphyses grouped in rows tended to be
higher than those for each diaphysis with
all the other diaphyses of the hand; there
was no corresponding difference for the
indices between diaphyses grouped in rays
(table 4). The mean indices were high for
the proximal phalanges in each sex. The
row of distal phalanges did not differ
markedly from other rows in mean communality index, although each distal
phalanx had a low communality index with
all the other diaphyses of the hand. The
sex differences between the indices for
diaphyses grouped in rows or rays were
not statistically significant. The corn.
munality indices for rows of diaphyses
were larger than those for rays with the
exception of Rays I11 and IV in the girls.
In both the boys and the girls, the communality index for the fourth ray was high
and that for the second ray was low. The
rank order correlations between the boys
and the girls in the communality indices
for diaphyses grouped in rows or in rays
were not statistically significant.
There was a neighborhood effect in most
comparisons between adjacent and nonadjacent diaphyses within the rows and the
rays of the hand (table 5). The mean diferences beween the communality indices
of adjacent and non-adjacent diaphyses
were statistically significant for the rays
in the boys (t = 5.483; P. < 0.01) but not
for the girls. They were not significant in
either sex for the rows.
The non-marginal diaphyses of the rows
were more highly correlated than the corresponding marginal ones to an extent that
was statistically significant in the boys
( t = 2.121; P. < 0.05) but not in the girls
(table 6). A similar tendency occurred
DIAPHYSES OF THE HAND
93
The rates of change in diaphyseal length
and width are disassociated in many clinical conditions (Rubin, '64; Caffey, '67).
DISCUSSION
To assist in the diagnosis of these condiThe rates of diaphyseal elongation in tions, it is desirable to measure only highly
the hands of the same children were previ- representative diaphyses. Figure 1 inously analyzed (Roche and Hermann, '69). dicates the five diaphyses in each sex with
The communality indices for these rates the highest communality indices with the
of diaphyseal elongation, for the hand as other diaphyses of the hand for rate of
a whole, were significantly higher in the change in length, width and length-width
girls than in the boys (P. < 0.01). The com- ratio. Middle phalanx 4 in each sex and
munality indices for rate of change in proximal phalanx 3 in the girls are highly
representative. The means and standard
width tended to be higher in the boys than deviations for length, width and lengththe girls and the indices for rate of change width ratios in these diaphyses are given
in length-width ratio tended to be higher in table 7. It should be noted that the presin the girls; both these tendencies were ent data were derived from the left hands
statistically significant (P. < 0.01).
of children. In adults, the bones of the
With the exception of diaphyseal length right hand exceed those of the left in
within rays, the sex differences between width and length-width ratios (Parish,
the mean communality indices for rate '60).
of change in diaphyseal length, width or
Smithgall et al. ('66) and Garn and
length-width ratio were not statistically Rohmann ('66) have published standards
significant, when the diaphyses were for the width of the second metacarpal.
grouped in rows or rays. The TOWS with The present findings would not support
relatively high or low mean communality the choice of this bone as representative
indices varied between the sexes and be- of the bones of the hand in width. The
tween length, width and length-width ratio. communality indices for rate of change in
The mean indices tended to be high for width between this diaphysis and the
the fourth ray in the boys and for the other diaphyses of the hand ranked fifthird ray in the girls and to be low for the teenth in order of size in the boys and
first and fifth rays in each sex.
cleventh in order of size in the girls.
within rays, but it was not statistically significant in either the boys or the girls.
BOYS
GIRLS
Fig. 1 Diagrams of the hand indicating for each sex the five diaphyses with the highest
communality indices, A, length; B, width, and C , length-width ratio.
94
A. F. ROCHE AND R.
F. K E R M A "
TABLE 7
Means and standard deviations f m the most representative diaphyses
Age
Diaphysis
years
3.0
MP4
4.0
MP4
5.0
MP4
6.0
MP4
7.0
MP 4
8.0
MP4
9.0
MP 4
10.0
MP4
11.0
MP4
12.0
MP4
13.0
MP 4
3.0
PP 3
4.0
PP 3
5.0
PP 3
6.0
PP 3
7.0
PP 3
8.0
PP 3
9.0
PP 3
10.0
PP 3
11.0
PP 3
12.0
PP 3
13.0
PP 3
Girls
Boys
Length
Width
mm
mm
Ratio
Length
Width
mm
mm
Ratio
13.6
5.4
2.5
13.2
5.3
2.5
( 0.79)
( 0.44)
( 0.16)
( 0.92)
( 0.30)
( 0.26)
14.5
5.5
( 0.97)
( 0.45)
2.6
( 0.17)
2.6
( 0.17)
2.7
( 0.18)
2.7
( 0.18)
2.7
( 0.22)
2.8
( 0.18)
2.8
( 0.20)
2.8
( 0.19)
2.9
I 0.19)
2.9
( 0.17)
15.3
5.9
( 0.92)
( 0.44)
16.1
( 1.10)
6.0
( 0.45)
16.8
6.2
( 1.07)
( 0.45)
17.4
6.4
( 0.45)
6.5
( 0.46)
6.8
( 0.44)
6.9
( 0.44)
7.0
( 0.41)
7.3
( 0.57)
( 1.21)
18.2
( 1.14)
18.7
( 1.22)
19.3
( 1.18)
20.2
( 1.28)
21.1
( 1.21)
14.2
5.5
2.6
( 1.01)
( 0.41)
( 0.15)
14.9
5.7
2.6
( 1.06)
( 0.35)
( 0.16)
15.5
( 1.13)
2.7
( 0.17)
16.4
5.9
2.8
( 1.10)
( 0.46)
( 0.16)
17.3
6.1
2.8
( 1.23)
( 0.47)
( 0.18)
17.8
6.3
2.8
( 1.29)
( 0.53)
( 0.22)
18.5
6.4
2.9
( 1.56)
( 0.52)
( 0.24)
19.4
6.6
2.9
( 1.82)
( 0.44)
( 0.26)
20.3
( 1.73)
20.9
( 1.38)
22.2
( 1.52)
23.5
( 1.59)
25.0
( 1.72)
26.3
( 1.76)
PP 3
Not representative in the boys
5.8
( 0.40)
6.8
3.0
( 0.47)
( 0.22)
6.9
( 0.44)
( 0.24)
3.1
6.2
3.5
( 0.50)
( 0.25)
6.6
3.6
( 0.51)
( 0.29)
6.9
3.7
( 0.57)
( 0.31)
7.0
3.8
( 0.55)
( 0.31)
27.7
7.3
3.9
( 1.71)
( 0.60)
( 0.30)
7.5
3.9
( 1.89)
29.1
( 0.53)
( 0.30)
30.3
7.6
( 0.56)
7.9
( 0.57)
8.0
( 0.53)
8.2
( 0.47)
8.4
( 0.49)
( 1.92)
31.9
( 2.05)
33.5
( 2.45)
35.4
( 2.36)
36.9
( 2.10)
4.0
( 0.32)
4.1
( 0.30)
4.2
( 0.35)
4.3
( 0.36)
4.4
( 0.39)
M P , middle phalanx. PP proximal phalanx.
1 Numbers in parenthesis are the standard deviations of the mean.
The communality indices were not particularly low for the metacarpal, proximal
phalanx and distal phalanx of the first
ray, although this might have been expected because the positioning of this ray
is difficult to standardize. In each sex, the
lowest indices occurred in middle phalanx
5 and distal phalanx 5 (width) and the
fourth proximal phalanx (length-width
ratio).
Neighborhood and marginal effects were
present in the communality indices for
length, width and length-width ratio, but
the majority were not statistically significant (Roche and Hermann, '69 and present). Significant neighborhood effects were
limited to diaphyseal length within rows,
diaphyseal width within rays in the girls,
and length-width ratios within rays in each
sex. Significant marginal effects occurred
DIAPHYSES OF THE HAND
95
the age of three months to eleven years. Helv.
only for width within rows in the girls and
Paediat. Acta, 23: 445-483.
for length-width ratios within rays in the Caffey,
J. 1967 Pediatric X-ray Diagnosis. 5th
boys. Possibly, both neighborhood and
ed. Yearbook Medical Publishers, Inc., Chicago.
marginal effects are similar in nature and Ferguson, G. A. 1966 Trend analysis. In: Staare due to the presence of nearby diaphtistical Analysis in Psychology and Education.
McGraw-Hill Book Co., New York. Chapter 21
yses. The higher communality indices be(pp. 341-353).
tween neighboring diaphyses may reflect
S. M.,and C. G. Rohmann 1959 Comthe presence of a full complement of Garn,
munalities of the ossification centers of the
nearby diaphyses; the lower comrnunality
hand and wrist. Am. J. Phys. Anthrop., 17: 319indices of marginal diaphyses may be due
323.
to an incomplete complement of nearby
1966 The gain and loss of cortical bone
in Ohio Whites. Changes in total periosteal
diaphyses. There is some supporting eviwidth, medullary cavity width and cortical
dence for the view that the presence of
thickness in the second metacarpal in 1483
nearby bones is a factor in regulating the
male and 1515 female subjects 1.0 through
size of a bone (Roche, '67). The com80.0 years. Progress report to Nutrition Secmunality indices of diaphyses that are both
tion, Office of International Research, National
Institutes of Health. Privately published, The
marginal and non-adjacent were compared
Pels Research Institute, Yellow Springs, Ohio.
with those of diaphyses that are non- Greulich,
W. W., and S. I. Pyle 1959 Radio.
marginal and adjacent. The directions of
graphic Atlas of Skeletal Development of the
Hand and Wrist. 2nd ed. Stanford University
the differences indicated that these effects
Press, Stanford, Calif.
(neighborhood plus marginal) were presA. W., and T. S. Leeson 1965 Histology.
ent in each sex for length, width and for Ham,
5th ed. J. B. Lippincott Co., Philadelphia.
length-width ratio, but to an extent that Parish, J. G. 1960 Skeletal syndromes associ.
was statistically significant only for width
ated with arachnodactyly. Proc. Roy. SOC.Med.,
53: 515-518.
in the girls ( t = 3.098, JP. < 0.05).
ACKNOWLEDGMENT
The present study was supported in part
by grants FR-05537 and FR-00222 from
the National Institutes of Health, Bethesda,
Maryland.
LITERATURE CITED
Bonnard, G. D. 1968 Cortical thickness and diaphysial diameter of the metacarpal bones from
Roche, A. F. 1967 Absence of the lunate. Am.
J. Roentgen., ZOO: 523-525.
Roche, A. F., and R. F. Hermann 1969 The
rates of elongation of the short bones of the
hand. Am. J. Phys. Anthrop., i n press.
Rubin, P. 1964 Dynamic Classification of Bone
Dysplasias. Yearbook Medical Publishers Inc.,
Chicago.
Smithgall, E. B., F. E. Johnston, R. M. Malina
and M. A. Galbraith 1966 Developmental
changes in compact bone relationships in the
second metacarpal. Human Biol., 38: 141-151.
Документ
Категория
Без категории
Просмотров
6
Размер файла
526 Кб
Теги
length, change, hands, width, rate, ratio, diaphyseal
1/--страниц
Пожаловаться на содержимое документа