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Articular and diaphyseal remodeling of the proximal femur with changes in body mass in adults.

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AMERICAN JOURNAL. OF PHYSICAL ANTHROPOLOGY 86:397413 (1991)
Articular and Diaphyseal Remodeling of the Proximal Femur With
Changes in Body Mass in Adults
CHRISTOPHER B. RUFF, WILLIAM W. SCOTT, ANI)
ALLIE Y.-C. LIU
Department of Cell Biology and Anatomy (C.B.R., A.Y.X.L.1 and
Department of Radiology (W. W.S.), The Johns Hopkins University School
of Medicine, Baltimore, Maryland 21205
KEY WORDS
Skeletal adaptation, Biomechanics, Allometry,
Weight prediction
ABSTRACT
Proximal femoral dimensions were measured from radiographs of 80 living subjects whose current body weight and body weight at
initial skeletal maturity (18 years) could be ascertained. Results generally
support the hypothesis that articular size does not change in response to
changes in mechanical loading (body weight) in adults, while diaphyseal
cross-sectional size does. This can be explained by considering the different
bone remodeling constraints characteristic of largely trabecular bone regions
(articulations) and largely compact cortical bone regions (diaphyses). The
femoral neck shows a pattern apparently intermediate between the two,
consistent with its structure. When the additional statistical “noise”created by
an essentially static femoral head size is accounted for, the present study
supports other studies that have demonstrated rather marked positive allometry in femoral articular and shaft cross-sectional dimensions to body mass
among adult humans. Body weight prediction equations developed from these
data give reasonable results for modern U.S. samples, with average percent
prediction errors of about 10%-16% for individual weights and about 2% for
sample mean weights using the shaft dimension equations. When predicting
body weight from femoral head size in earlier human samples, a downward
correction factor of about 10% is suggested to account for the increased
adiposity of very recent U S . adults.
In an earlier study.(Ruff, 1988), it was
hypothesized that diaphyses respond t o
changes in mechanical loadings mainly
through alterations in compact cortical bone
geometry, while articulations undergo normal nonpathological remodeling mainly
through changes in trabecular bone density
or architecture, but not external joint size or
shape.’ This hypothesis is tested further in
the present study by comparing femoral
head and diaphyseal size (as well as femoral
neck size) with current body weight and body
weight at 18years in a living human sample.
‘Throughout this study, the term remodeling is used to designate any alteration in adult skeletal morphology and as such
includes both “modeling”(uncoupled bone formation or resorption) and “remodeling” (coupled bone resorption followed by
formation) processes, as customarily defined and used in bone
histomorphometric studies (e.g.,see Martin and Burr, 1989:143144).
@ 1991 WILEY-LISS, INC
Since adults vary in body weight over their
lifetimes and a change in weight (mass) constitutes a direct change in mechanical loading of the lower limb, femoral diaphyseal
cross-sectional size in adults should be more
highly correlated with current body weight
than with weight at 18 years. Conversely, if
femoral head size is essentially fixed at 18
years and does not respond to subsequent
changes in mechanical loading, it should be
more highly correlated with weight at age 18
than current weight. Femoral neck size
might be expected to show an intermediate
pattern of correlation if this region combines
aspects of bone remodeling characteristic of
both diaphyses and articulations.
As secondary aims, the present study data
Received March 5,1990;accepted April 26,1991
398
C.B. RUFF ET AL
are also used to examine the general allometric scaling of proximal femoral dimensions
and to develop equations for the prediction of
body weight from these dimensions.
MATERIALS AND METHODS
Eighty individuals, all out-patients at
Johns Hopkins Hospital, make up the study
sample. The sample characteristics are
given in Table 1. The subjects range in age
from 24 to 81 years, with a mean of 52 years,
and are about equally divided between males
and females. Almost two-thirds are white
and slightly more than one-third are black.
They were all seen in either an orthopedic
clinic or emergency room at the hospital,
where they were given a standard anteroposterior bilateral hip radiograph to check for a
possible hip fracture following an accident or
for hip arthritis. None of the subjects in this
study had sustained a fracture. Those whose
films indicated severe arthritis in both hips
were not used; in those with arthritis in one
hip, only the normal hip was measured. Hips
were internally rotated to avoid distortion
caused by hip anteversion (this brings the
femoral head and proximal shaft into about
the same coronal plane, or distance above
the radiographic film).
It was not feasible to measure directly the
magnification factors for each individual hip
radiograph. However, knowing the tube-film
and table-film distances, and given an estimate of the hip-table distance, the appropriate magnification factor can be calculated.
Computed tomography scans of the pelvic
region in 10 other randomly selected patients also seen at the hospital, covering a
range of body sizes, were measured to determine the average magnitude and variability
of hip-table distance (measured from the
center of the femoral head) in a supine patient. Distances for 8 of 10 of these patients
fell in a narrow range between 9.5 and 10.0
cm; the other two fell between 11.0 and 12.0
cm. For the radiographic set-up in the
present study, this corresponds to a total
range in magnification factors of 18.5%21.5%, with the great majority between
18.5% and 19.0%. Thus differences in body
size should have relatively little effect on
magnification. Therefore a constant magnification factor of 19% was used to correct
radiographic measurements.
Proximal femoral dimensions measured in
the study are shown in Figure 1. They include superoinferior head and neck breadths
and mediolateral subperiosteal and cortical
breadths of the proximal diaphysis. Measurements of the head and neck were taken
perpendicular to the cervical axis, with the
neck breadth taken at the position of deepest
concavity of its superior surface, i.e., at minimum breadth. Because the radiographs included only the proximal femur, we could not
directly standardize the location of the diaphyseal section using a percentage of bone
length, as had been done in several previous
in vitro studies (e.g., Ruff and Hayes, 1983).
However, it was found, using radiographs of
a sample of excised femora sampled from a
similar population (Ruff and Hayes, 19881,
that a section 80% of bone length from the
distal end, included in previous studies (e.g.,
Ruff and Hayes, 1983, 1988), corresponded
closely to a distance of two-thirds of femoral
head diameter distal to the center of the
lesser trochanter, as illustrated in Figure 1.
It is possible that use of a femoral head
dimension to locate the diaphyseal section
could introduce a bias in the relative position
of the section and thus the measured diaphyseal dimensions. To test for this, the position
of the measured section relative to another
“size”measure not dependent on the femoral
head-the distance along the diaphyseal
axis from the lesser trochanter to the superior surface of the femoral neck (Fig. 1)-was
also determined in a subsample of the study
radiographs. The ratio of this distance to the
distance from the section to the superior
surface of the neck can be used as an index of
the relative position of the section on the
diaphysis. This index was found not to be
correlated with the size of the femoral head
(r = - .02); thus use of femoral head diameter does not appear to introduce any systematic bias in locating the position of the diaphyseal section.
All radiographic measurements were
taken with Helios dial calipers with needle
points to a precision of .1 mm. If both hips
could be measured (see above), the average
of the two sides was used in subsequent
analyses. In addition to head, neck, and
shaft subperiosteal breadths, the measured
shaft cortical breadths were used to calculate indices proportional to two cross-sectional geometric properties: cortical area
(CA) and the second moment of area in the
mediolateral plane (about the anteroposterior axis; IJ. As discussed elsewhere (e.g.,
Ruff and Hayes, 19831, CA is proportional to
axial rigidity or strength of a long bone,
52.3
(24-81)
50.6
54.1
54.3
48.9
15.7
17.2
15.3
18.1
16.5
76.7
17.7
(42-135)
15.6
80.8
18.9
72.4
16.5
75.4
19.6
79.0
Current BW
(kg)
Mean
SD
64.9
13.7
(34- 100)
71.6
10.4
57.9
13.5
63.2
12.2
67.9
15.9
BW at 18 Yr
(kg)
Mean
SD
31.0
3.0
(24.5-38.1)
32.1
2.9
29.7
2.5
30.9
3.0
31.0
2.9
Shaft Bd.
(mm)
Mean
SD
6.9
1.4
(4.2-12.3)
7.3
1.5
6.5
1.1
6.8
1.3
1.5
7.0
Med. cortex
(mm)
Mean
SD
‘BW, body weight; Bd., subperiosteal breadth; Med. and Lat. cortex, medial and lateral cortical breadths (see Fig. 1)
41
39
51
29
n
80
Grow
Total
(range)
Male
Female
White
Black
Current age
(wars)
Mean
SD
TABLE 1. SamDle characteristics’
6.0
1.1
(3.0-8.2)
1.1
6.3
1.0
5.8
1.1
5.9
1.0
6.3
Lat. cortex
(mm)
Mean
SD
47.0
4.0
(39.7-55.1)
49.5
2.8
44.3
3.2
47.1
4.0
46.8
3.9
Head Bd.
(mm)
Mean
SD
33.2
3.8
(26.2-44.0)
35.3
3.4
31.0
2.7
33.4
3.9
32.7
3.5
Neck Bd.
(mm)
Mean
SD
400
C.B. RUFF ET AL
not possible to determine directly the accuracy of the body weights given by the patients. However, the means of the given
weights match well with mean weights for
the U.S. population as a whole, a s determined by U.S. National Health Surveys, suggesting little systematic bias in patient recall. For adults aged 25-74 years, weighted
for race in the same proportions a s the
present study, mean body weights in the
1971-1974 HANES survey (Abraham et a].,
197913,Table 11)are 78.3 kg in men and 68.1
kg in women. These compare to 80.0 kg and
72.4 kg for mean current weights of males
and females in the present study (Table 11,
falling within the 65th and 68th percentiles,
respectively, of the HANES samples (Abraham et al., 1979b, Tables 9 and 10; combined
ages 25-74 years, weighted by race, our calculations). The 18-year-old recalled body
weights of 71.6 kg and 57.9 kg for males and
females of the present study sample (Table
1)are very close to mixed race national averages for this age group: 72.6 kg and 58.5 kg
for 18-24 year men and women, respectively,
measured in 1960-1962 (Stoudt e t al., 1965,
Table 11, or68.7kgand57.5 kgfor 18.0-18.5year-old men and women measured in 19661970 (Hamill et al., 1973). Given the longer
elapsed time period, it is very likely that the
Fig. 1. Line tracing of radiograph showing proximal
weights recalled for age 18 have more associfemoral breadths measured in the study: femoral head,
neck, and diaphyseal subperiosteal breadths, and medial
ated error than the current weights. Howand lateral diaphyseal cortical breadths (see text). Dotever, it appears from the above that this
ted lines represent cervical and diaphyseal axes.
greater error is probably random and not
directional. The probable effect of this factor
on the study results is discussed later.
The basic analysis was carried out by comwhile I, is proportional to bending strength paring correlations between femoral dimenin the mediolateral plane. Assuming (by ne- sions and current and 18-year-old body
cessity) a circular section, these properties weights in the sample.’ Eighteen years was
can be calculated from the radio aphic chosen a s the onset of “adulthood” because
! - d2); this is the approximate age when union of
breadths as follows: CA = pi/4 * (DF
I, = pi/64 * (D4 - d4); where D and d refer the femoral head epiphysis is completed
to the subperiosteal and medullary diameters of the section, respectively. I t should be
emphasized that because measurements
were available for only one plane and a sim‘It has been persuasively argued that the product-moment
ple symmetrical model of the cortex was correlation coefficient, r, is a n incomplete and sometimes misused, while the cortex of the proximal femur leading indicator of the strength of relationship between two
variables and that other indices such as standard errors of
is certainly not circular or symmetric (e.g., estimate
(SEE) or percent standard errors of estimate (OSEE)
Ruff and Hayes, 19831,these indices are only should also be examined (e.g., Smith, 1984). However, in the
present case, i.e., comparisons between correlations of a bone
proportional to true cross-sectional geomet- dimension
with current and previous body weight, the two
ric properties and are included here only for types of indices are equivalent. This is because the SEE of y
is
directly
related
to r when values for y (here the bone dimencomparative purposes.
remain the same, since SEE = SD d 1 r2, where SD is the
Current and past body weights of the sub- sion)
standard deviation of y (Zar, 1984271);.(Since the mean oi(y also
jects in the study were determined by patient remains the same, this is also true for the OSEE of y.) SEs and
%SEESfor the prediction of body mass from femoral dimensions
recall through questioning by the attending using different properties and sample groupings are given later
physician a t the time of examination. It was (Table 4).
~
401
FEMORAL REMODELING IN ADULTS
TABLE 2. Correlations of proximal femoral dimensions with current body weight and body weight
at 18 Years of ape1
Raw data
Group
Dimension2
Current
18 Years
Total
Shaft Bd
Shaft CA
Shaft I,
Head Bd
Neck Bd
,603
,575
,623
.486
,533
Male
Shaft Bd
Shaft CA
Shaft I,
Head Bd
Neck Bd
Shaft Bd
Shaft CA
Shaft I,,
Head Bd
Neck Bd
Shaft Bd
Shaft CA
Shaft I,
Head Bd
Neck Bd
Shaft BD
Shaft CA
Shaft I,
Head Bd
Neck Bd
,532
,409
,528
,497
,516
.487
.483
,521
,508
,480
,413
(286)
,419
.537
,492
Female
White
Black
~.
,625
,718
,712
,411
,500
,636
,626
.658
.554
,631
,566
,495
,574
,403
,420
,320
,456
,405
(.087)
(.065)
,493
,470
,519
,539
.544
,504
,489
,532
,462
,462
Log-transformed
Current
18 Years
,623
,598
,639
,491
,533
,552
,421
.538
.499
.500
.621
,701
,670
.374
.464
,477
.458
,488
,501
,464
,387
(252)
,359
.547
,483
.665
.637
.687
.532
.595
,316
,404
,354
(.052)
(.032)
,496
,443
.499
.520
,499
.557
.526
.561
,441
.463
,472
,471
,482
,512
,472
'Coefficients in parentheses not significant; all other r's significant at at least P < .05.
lBd, subperiosteal breadth; CA, cortical area index; I,, second moment of area in M-L plane index (see Fig. 1 and text)
(Krogman, 1962). Because of the study design, it was not possible to apply standard
statistical tests (e.g., the Fisher Z transformation [Zar, 19841) to determine the significance of differences between these correlation coefficients. Such tests assume independence of samples, which is obviously
not the case here: not only is one of the
variables the same (i.e., the femoral dimension), but the two body weights are themselves intercorrelated (r = .68 between current and 18-year-oldbody weight in the total
sample). Therefore the results of the analysis were examined only for general patterns
of differences between coefficients and for
their consistency with respect to the study
hypothesis.
RESULTS
Correlation coefficients for the proximal
femoral dimensions with current body
weight and body weight at 18years are given
in Table 2. Results are presented for the total
combined sample as well as for four subgroups broken down by race or sex (as in
Table 1).Coefficients for both raw and logtransformed data are given. Correlation co-
efficients for the total sample raw data are
also plotted in Figure 2.
In every comparison, the shaft dimensions-subperiosteal breadth, CA and I, indices-are more highly correlated with current body weight than with body weight at 18
years of age. Correlations of shaft dimensions with current body weight range from
.41 to .72, while correlations with former
body weight range from .25 (nonsignificant)
to 5 3 .
In contrast, in general, femoral head
breadth is not more highly correlated with
current body weight than with body weight
at 18 years of age. In fact, in most (6 of 10)
comparisons, including those for the total
combined sample, head breadth is more
highly correlated with former body weight,
although the differences in magnitudes of
coefficients are generally much less than for
shaft dimensions. The white subgroup shows
slightly higher correlations of head breadth
with current than former body weight, but
the differences are very small. The only
marked deviation from the general pattern
occurs in the female subgroup, which shows
fairly low correlations of head breadth with
402
C.B. RUFF ET AL.
O”O
1
._
s
x
U
lil weight 18 yrs
060
m
c
z
c
._
-
050
9
0
0
0 40
SHAFT60
W C A
SHAFTIY
HEAOBO
NECK60
Property
Fig. 2. Correlations of proximal femoral dimensions
with current body weight and body weight at 18 years in
the total sample (raw data). BD, subperiosteal breadth;
CA, cortical area index; IY,second moment of area index
(see Fig. 1 and text).
current body weight (r = .37-.41) but even
lower correlations with former body weight
(r = .05-.09, nonsignificant).
Femoral neck breadth follows a pattern
intermediate between femoral head and
shaft dimensions: Correlations are somewhat higher with current body weight than
with body weight at 18 years (except among
blacks), but the differences between correlation coefficients are invariably smaller than
those for shaft breadths (Fig. 2).
To examine general scaling effects, i.e.,
change in femoral dimensions with change
in body size, the slopes of log-transformed
regressions of femoral dimensions on current body weight for the total sample were
calculated and are given in Table 3. (The
same analyses were also carried out for each
subgroup and for weight at 18 years; results
are generally similar to those for the total
combined sample.) Because correlation coefficients are always well below 1.0, different
methods of line fitting can give very different
results. Therefore regression coefficients using three methods-lease squares, major
axis, and reduced major axis-are shown
(Kuhry and Marcus, 1977). Standard errors
were calculated using equations given by
Hofman (1988).Values for theoretical isometry (geometrical similarity) for each property are also listed as a baseline for comparison.
As expected, the three techniques of line
fitting produce quite divergent results in
most cases. Least-squares regression coefficients are invariably the lowest (as
expected), always negatively allometric
although including theoretical isometry
within their 95% confidence intervals (approximately 2 2 SE here), except for femoral
head breadth. Reduced major axis coefficients are positively allometric for shaft dimensions, negatively allometric for head
breadth, and isometric for neck breadth. Major axis slopes are generally positively allometric, except for shaft breadth, although
isometry is within the 95% CI range of head
and neck breadth slopes. It will be argued
later that the reduced major axis slopes are
the most reliable here, indicating positive
allometry for shaft breadth, and that the
apparent isometry or negative allometry of
head and neck breadths is an artifact of
changes in body weight with age in this
sample.
DISCUSSION
Bone remodeling mechanisms
The results of this study are generally
consistent with the hypothesis that changes
in mechanical loading of long bones among
adults are more likely to produce changes in
cross-sectional diaphyseal geometry than
changes in articular size. In a sample of 80
individuals, measures of femoral diaphyseal
robusticity are consistently more highly correlated with current body weight than with
body weight at the onset of adulthood. Conversely, femoral head size shows no such
consistent pattern, and in fact in the majority of comparisons it is more highly correlated with body weight at age 18 years,
although the difference is not as strongly
marked.
There are at least two confounding factors
that must be considered in interpreting
these results, however. One is the problem of
using patient-recalled body weights, which
certainly introduces some error. As shown
earlier, comparison with appropriate U.S.
national standards indicates little systematic bias in either current or prior recalled
body weights in this study, but this possibility cannot definitely be ruled out. In any
case, it is quite likely that the recalled body
weights for age 18 were subject to more
random error than the recalled current body
weights. This artifact of the study design
may partially explain why the predicted pattern of higher correlations of femoral head
breadth with former body weight than with
current body weight were not well marked or
403
FEMORAL REMODELING IN ADULTS
TABLE 3. Regression coefficients (slopes) of proximal femoral dimensions on current body weight,
lag,,-transformed data, total sample, using three methods of line fitting
Dimension’
Shaft Bd
Shaft CA
Shaft I,
Head Bd
Neck Bd
Theoretical
isometrv2
-33.1
...
,667
1.333
,333
,333
Least
sauares
Reduced
major
axis
,278
.594
1.113
.1905
,273
.4385
.9945
2.2935
.21!i5
,332
SE3
Major
axis
SE4
.039
-308
...
.044
.089
,150
.9935
1.7425
,387
,512
.151
,237
,078
,092
,038
,041
‘See Table 2 for definitions of femoral dimensions.
‘Theoretical slopes (b)in the equation log(y) = log(a) b .log(x),equivalent to the power function y = axb,where y =femoral dimension and x
= body weight. Since body weight is in linear dimensions to the third power, theoretical isometry for breadths is 1/3, for CA (a linear
dimension squared) 2/3, and for I, (a linear dimensions to the fourth power) 4/3.
”Standard error of both least-squares and reduced major axis slopes (Hofman, 1988).With 78 degrees of freedom, the 95%confidence limits
are approximately i2 SE around the slope. Note, however,that the confidence limits about the reducedmajor axis slope are not symmetrical
(Hofman, 1988; Rayner, 1985).
4Standard error of major axis slope (Hofman, 1988).
5Theoretical isometry outside the 95%confidence limits of this slope.
+
consistent across subsamples. Increased
random error in patient recall will increase
the variance of 18 year body weights while
not increasing the covariance with other
properties. Thus this will tend to spuriously
decrease correlations between any structural variable and 18 year body weight, relative to correlations with current body
weight. If this factor could be corrected, i.e.,
by slightly increasing all correlations with
18 year weight, this would have the effect of
increasing the difference in correlations with
current and previous body weight for femoral head size, as well as decreasing the difference for shaft measurements (Fig. 2). Thus,
in effect, the “true” difference in magnitude
between correlations with current and previous body weights may be similar but opposite
in direction for shaft and articular dimensions, more consistent with the hypothesis.
It is possible that the same artifact partly
explains the apparently aberrant results for
femoral head breadth among the female sub:
group. Correlations with 18 year body
weight are relatively low for all properties
among females, while correlations with current body weight are relatively high (Table
2). Although there is no way to test this with
the present study data, it is possible that
recall of 18 year body weight is subject to
more error among females than among
males, reducing correlations. Alternatively,
there may be other unknown variables that
contribute to the very low correlations of
femoral head (and neck) breadth with previous body weight among females.
The second potentially confounding factor
is the unknown effect of differences in other
mechanical loadings on the skeletons of
these individuals. Body weight is only one
component of the total mechanical load that
must be borne by the proximal femur. Variation in other factors such as activity level and
relative muscularity almost certainly reduced the correlations observed here. It is
uncertain to what degree this would have
differentially affected correlations with each
femoral dimension. There is, however, ample
evidence from both laboratory and “natural”
experiments that long bone diaphyseal
cross-sectional geometry is very sensitive to
such effects (e.g., see Jones et al., 1977;
Houston, 1978; Woo et al., 1981),while articular external dimensions may not be (e.g.,
see Poss, 1984). In fact, it is partly on this
basis that the present study’s hypothesis
was formed (Ruff, 1988). If this is true, then
this would have preferentially reduced correlations between femoral shaft dimensions
and body weight, especially current body
weight, while having less of an effect on
correlations between femoral head size and
body weight. More studies where both body
weight and activity patterns are known are
needed to address this question.
As discussed previously (Ruff) 1988),
changes in mechanical loading of articulations among adults can have marked affects
on trabecular and subchondral bone structure of the articulation (e.g., Pauwels, 1976;
Poss, 1984). We did not attempt to measure
parameters such as trabecular density in our
sample, but would predict that such parameters would show a higher correlation with
current body weight than with weight in
early adulthood.
The femoral neck appears to exhibit an
intermediate pattern between the femoral
404
C.B. RUFF ET AL
head and diaphysis, being slightly but not
markedly more correlated with current body
weight than with weight at 18 years. This is
consistent with the structure of the femoral
neck, which includes significant components
of both trabecular and compact cortical bone.
Thus a mode of bone remodeling intermediate between that of articulations and diaphyses, with some remodeling occurring
through trabecular structural changes and
some occurring through changes in compact
cortical bone geometry, seems reasonable.
Some authors have claimed that the femoral
neck region in adults does not include an
osteogenic periosteal layer, which could preclude changes in subperiosteal dimensions,
i.e., external neck breadth (see below). However, the studies that we are aware of have
either presented no supporting evidence for
this assertion (Phemister, 1934; Sherman
and Phemister, 1947)or have examined only
unusual samples of individuals, i.e., older
femoral neck fracture patients (who could
have impaired remodeling capabilities in
this region) (Banks, 1964). Other clinical
studies indicate that subperiosteal deposition of bone in the femoral neck is possible in
adults (Lloyd-Roberts, 1953; Martel and
Braustein, 1978). Also, studies of the crosssectional geometry of the femoral neck show
that this region can undergo an increase in
subperiosteal dimensions with aging (Ruff
and Hayes, 1988; Beck et al., in press).
Therefore, a combination of both cortical and
trabecular remodeling of the femoral neck
with age, consistent with our results, is plausible.
The present study does not address the
effects of variation in mechanical loading of
articulations and diaphyses during the preadult period of growth and development,
prior to epiphyseal union. Studies of immature animals-human and nonhuman-indicate that changes in mechanical loading of
diaphyses produce essentially the same general effect as in adults, i.e., changes in cortical geometry (Watson, 1974; Woo et al.,
1981). The extent to which variation in joint
loading during this period could also lead to
changes in joint size or trabecular architecture is unknown. Again, more studies comparing the effects of mechanical stimuli on
pre-adult long bone shafts and articulations
are needed to address this question.
Intraspecific scaling
As noted earlier, the choice of a line fitting
technique makes a large difference in calcu-
lated regression slopes when correlation coefficients are relatively low (i.e.,below .9).As
shown by many authors, this is virtually
always the case for intraspecific analyses
(e.g.,Smith, 1981; Steudel, 1982;Martin and
Harvey, 1985; Oleksiak, 1986; Ruff, 1987,
1988; McHenry, 19881, except in some species with extreme sexual dimorphism in size
(Steudel, 1982). As discussed by Rayner
(1985) as well as by others (e.g., Kuhry and
Marcus, 1977;Hofman, 19881,least-squares,
reduced major axis, and major axis methods
of line fitting are all special cases of a more
general structural model, with each making
a specific assumption about the ratio of error
variances of dependent (y) and independent
(x) variables. Least-squares analysis assumes that there is no error variance in x,
i.e., x is measured without error. (“Error”
here refers to both measurement error and
biological variation unrelated to the particular functional relation under investigation.)
This is clearly not the case with the present
data, either for the regression of femoral
dimensions on body mass or for body mass on
bone dimensions. Major axis analysis assumes that the x and y error variances are
equal. This is almost certainly also not true
for the present study; error variances in body
weight are almost bound to be much greater
than those for femoral dimensions (see Page1
and Harvey, 1989).Reduced major axis analysis (rma, also sometimes referred to as
“standard major axis”) assumes that the ratio of the two error variances are proportional to the ratio of the two total sample
variances for x and y. This assumption seems
clearly more reasonable in the present case.
When the error variances are not known, the
rma method has been advocated as giving
the maximum likelihood or least biased estimate of the underlying functional relationship (Kendall and Stuart, 1979), as well as
exhibiting other desirable characteristics
(Rayner, 1985). Consequently, it has come
into increasing favor for allometric scaling
analyses (e.g., Rayner, 1985; Hofman, 1988;
Swartz, 1989). The only serious drawback to
using rma arises when correlation coefficients are very low (Gould, 1975; Jolicoeur,
1975;Rayner, 19851,which is generally not a
problem in the present analysis (Table 2).
The rma slopes for femoral dimensions on
body weight (Table 3) are very positively
allometric for shaft cross-sectional measurements, negatively allometric for femoral
head dimensions, and close to isometric for
femoral neck breadth. Positive allometry of
FEMORAL REMODELING IN ADULTS
femoral shaft measurements on body weight
is also characteristic of other modern adult
human samples that have been studied. Reported data for Terry Collection Blacks by
Oleksiak (1986), Rightmire (1986), and
McHenry (1988) yield rma slopes ranging
between .41 and .52 for measures of proximal
femoral diaphyseal breadth on body weight
(our conversions);these compare well to our
value of .44, while isometry is .33. Similar
results are obtained using four sexlpopulation
means for average femoral midshaft breadth
(Ruff, 1987, and unpublished data), with an
rma slope of .51 for breadth on body weight
(r = .934).
The apparent negative scaling of femoral
head breadth in our sample a t first sight
seems at variance with both the results for
the shaft and some other intraspecific studies of adult humans that have indicated
positive allometry for this dimension.
Oleksiaks sample (1986) produces an rma
slope of .45 for femoral head breadth, and
Ruff (1988) also noted extreme positive allometry for femoral head dimensions among
humans (four sedpopulation-specific means
€or femoral head breadth yield an rma of .56).
McHenry (1991)has reported similar results
for a different sample of modern humans.
Rightmire’s data (1986)indicate a somewhat
lower but still positively allometric rma
slope of .36 for femoral head breadth.
These apparent contradictions can be resolved by considering the composition of the
different samples and the remodeling characteristics of articulations. The present
study sample includes individuals from 24 t o
81 years of age, with a majority over 50
years. Depending on the particular subgroup
examined, body weight in our sample
reaches its maximum in the sixth or seventh
decades. Increasing body weight into middle
age is typical of recent U S . populations
(Stoudt et al., 1965; Abraham et al., 197913;
also see below). Thus, if, as we propose,
articular size does not respond to changes in
adult body weight, the heavier older adults
in our sample will be associated with smaller
femoral heads relative to their current
weights and thus will pull down the regression slope for femoral head breadth (but not
shaft breadth). In contrast, the samples used
by Oleksiak (19861, Rightmire (19861, and
Ruff (1988) were predominantly younger18 to 65 years, 22 to 55 years, and 20 to
approximately 60 years, respectively. In addition, at least one of these samples-Pecos
Pueblo-was from a population in which it
405
would be predicted that body weight would
not increase as much from younger t o middle-aged adults (see below). Therefore the
slopes for femoral head breadth on body
weight would not be as much reduced in
these other samples. This probably also explains why body weight was nearly as highly
correlated (Oleksiak, 1986) or even more
highly correlated (Rightmire, 1986) with
femoral head breadth as with shaft breadth
in these other, younger samples. In fact, if
only adults under 60 years are considered in
the present study sample, correlations with
current weight are only slightly higher for
femoral shaft breadth than femoral head
breadth, and slopes are actually somewhat
higher for head breadth. Again, as with correlations, the intermediate rma slope for
femoral neck breadth (Table 3) is probably a
result of its combined articular-diaphyseal
remodeling mechanism.
Smith (1981) observed that even when the
confounding effect of differences in range of
values is removed, intraspecific allometric
correlations are still generally lower than
interspecific correlations. One interpretation of this phenomenon is that intraspecies
variability is subject to more “noise,” i.e.,
variation not related to true functional relationships (e.g.,see Gould, 1975:257;Steudel,
1982; Fleagle, 1985). The scaling of femoral
head size on body weight in our sample
appears t o be a good example of this type of
effect. A simple mechanical functional
model, in which levels ofjoint stress are kept
approximately constant, would predict that
femoral head size would change in parallel
with body mass throughout life.3 However,
constraints on articular remodeling in
adults apparently largely prohibit or limit
this potential response. Thus an intrinsic
biological limitation may contribute to intraspecific “noise,”reducing the correlation
between joint size and body weight and obscuring the underlying mechanical functional relationship, particularly in older
adults. Such a factor does not exist or is less
important for shafts, and thus these correlations are higher and the functional relationship clearer. This consideration would be of
less importance within species that probably
do not vary greatly in body mass through
adulthood (e.g., see Swartz, 1989). Other
factors, such as size-related differences in
3This is not meant to imply that other factors, such as joint
configuration, do not also affect articular loadings.
406
C.B. RUFF ET AL.
TABLE 4. Least-squares regression equations for predicting (current) body weight from proximal
femoral dimensions
Group
Dimension2
Slope
Total
Head Bd
Shaft Bd
Shaft CA
Head Bd
Shaft Bd
Shaft CA
Head Bd
Shaft Bd
Shaft CA
Head Bd
Shaft Bd
Shaft CA
Head Bd
Shaft Bd
Shaft CA
Head Bd
Shaft Bd
Shaft CA
Head Bd
Shaft Bd
Shaft CA
2.160
3.594
.0951
Male
Female
White
Black
White
male
White
female
2.741
2.845
,0575
2.426
4.680
,1614
2.270
3.441
,0988
2.015
3.879
.0873
3.383
3.105
,0808
.493
2.700
,0895
Raw data
Int.
SEE3
-24.8
-34.6
29.3
-54.9
-10.6
50.0
-35.1
-66.8
-1.0
-31.5
-31.1
26.9
15.6
14.2
14.6
13.7
13.3
14.4
17.5
15.0
13.4
13.9
12.9
13.0
-15.2
-41.3
34.3
-85.8
-17.3
39.4
46.2
-11.8
28.3
%SEE4
Slope
Loglo-transformed data
Int.
SEE
%SEE
20.3
18.5
19.0
1.269
~.~
1.424
,6027
16.9
16.5
17.8
1.595
1.098
.3533
-.342
-.353
,163
-.922
.165
,885
16.3
14.4
14.8
14.0
13.3
14.7
21.2
18.8
19.3
17.3
16.5
18.1
24.1
20.7
18.5
18.4
17.1
17.2
1.272
1.750
,9058
-.341
-261
p.691
18.2
15.1
13.6
,325
,419
.6204
-.447
-.351
,111
15.0
13.0
13.5
18.3
16.5
17.4
23.2
20.9
22.1
,201
.423
,5610
-.209
-.342
.287
18.6
17.1
17.5
14.7
15.2
15.4
17.8
18.3
18.6
,986
,219
,4750
-1.612
-.019
,546
15.2
15.3
16.0
25.2
20.9
18.8
19.9
17.3
17.9
23.6
21.6
22.2
18.4
18.5
19.4
11.9
9.8
9.8
17.5
14.4
14.4
.288
1.240
,6059
1.331
p.090
,134
13.5
10.6
10.7
19.8
15.6
15.7
~
lLeast-squaressIopes andintercepts forequationsof the form y = bx + a, whereyis body weight(orloglo[weight])n
(and xisfemoral breadth
(or log,, [breadth]). Breadth in m m ,CA in mm, weight in kg. Note that CA is a cortical area index, not true (absolute) CA (see text).
>SeeTable 2 and Figure 1 for definitions of femoral dimensions.
jStandard error of estimate of body weight (kg).
‘Percent standard error of estimate of body weight (SEE standardized by magnitude of body weight).
behavior, may also affect predicted intraspecific scaling patterns (e.g., Ruff, 1987).
Body weight prediction
Development of body mass prediction
equations from skeletal dimensions has
proved to be particularly difficult for humans, largely because of problems in obtaining sufficiently accurate body masses individually associated with skeletal remains in
a large, random, and representative sample
(e.g., Eriksen, 1982). To derive body weight
prediction equations in our sample, current
body weight was regressed on femoral dimensions, with results listed in Table 4 for
head breadth, shaft breadth, and shaft CA
index. Because the aim here is to minimize
error in estimation of the dependent variable
(weight), least-squares (model I) regression
is appropriate. Least-squares slopes, intercepts, and absolute and percent standard
errors of estimate (SEE, %SEE)are given for
both raw and log-transformed data for the
total sample and several subgroupings. Because these equations could be applied in
specific forensic situations, in addition to the
four sex- or race-specific subgroups (Tables
1,2),results for two additional subgroupswhite males (n - 25) and white females
(n = 2 6 t a r e also included in Table 4.(The
number of available blacks-16 males and
13females-was considered too small to generate reliable prediction equations for these
sedrace subgroups.)
Percent standard errors of estimate of
body weight range from about 14% to 25%,
corresponding to absolute errors of 2 10-19
kg, depending on the property and subgroup.
Errors are slightly smaller, i.e., body weight
prediction is slightly better, using raw
rather than log-transformed data. As expected given the previous results, prediction
of current weight is best using femoral shaft
breadth or CA index and worst using femoral
head breadth (except among white males).
Errors are higher for blacks than for whites,
possibly reflecting the smaller sample size of
blacks. They are also higher for females than
for males, possibly reflecting greater fluctuations in body weight among adult women
(Abraham et al., 1979a:11, b:9), or more
racial heterogeneity in scaling among
women than among men (white females
have the smallest errors in weight estimation).
A more rigorous test of the accuracy of
these prediction equations is to apply them
to a different, independent sample of individ-
FEMORAL REMODELING IN ADULTS
uals of known body weight. Therefore we
obtained data for eight randomly selected
subjects seen at the same clinics but not
included in the base sample. Actual body
weights were compared with weights predicted using equations based on the total
sample and specific to sex and sedrace (for
blacks, race). Since the raw data equations
produced smaller SEES than the log-transformed equations (Table 4), only raw data
equations were used. Following Smith
(1984),percent prediction errors (%PE)ofbody
weight were calculated as [(observed predicted)/predicted] x 100. (Note that positive %PEs indicate an underestimate of actual weight, and vice versa.) Both directional
and absolute mean %PEs were calculated for
the sample as a whole. Results are presented
in Table 5 . In addition to current weight, also
listed are weight at 18years, height, and the
percent deviation of current weight for
height from U.S. national averages, by sex
and age group (Abraham et al., 1979a). Using this last relative weight index, the subjects in Table 5 have been arranged in ascending order from most underweight to
most overweight for their statures.
On average, weight prediction errors
among these individuals are highest using
femoral head breadth, lower using femoral
shaft breadth, and lowest using femoral CA.
Use of sex- or sedrace-specific equations
generally slightly improves prediction of
body weight, particularly using the femoral
head. There is a tendency to underestimate
body weight by about 8%-10% from the femoral head and 4%-7% from the shaft breadth
equations. However, these directional errors
are greatly influenced by one extremely
overweight individual, subject 8. If this individual is eliminated, mean directional error
falls to 5% or less for femoral head breadth
and 3%or less for shaft breadth. Mean absolute %PEs are 1 7 7 ~ 1 9 %
for head breadth
(declining to 12%-13% without subject 81,
16%for shaft breadth (declining to 11%without subject 8),and 10%-13% for femoral CA.
Examination of the individual subject
data also reveals some interesting results.
Particularly illuminating are the findings
for the very obese current weight for height
outlier,. subject 8, a 59-year-old woman.
While the femoral head and shaft breadth
equations consistently underestimate her
weight by about 50%or more, the femoral CA
equations give estimates remarkably close to
her actual current weight-within 12%,and
for the best, sex-specific equation, within a
407
1% error. This individual had more than
doubled her weight since age 18 years. Our
results indicate that femoral head breadth
and proximal shaft subperiosteal breadth
did not increase in response to this increase
in weight, while shaft cortical thickness (and
thus CA) did. Despite being well above the
mean (current) female body weight of the
base sample, her femoral head and shaft
breadths are below the female means. In
contrast, her medial and lateral cortical
breadths are more than 1.5 SD above the
female means, consistent with her current
body weight. While it cannot be proven without true longitudinal data, these findings
strongly suggest that this subject’s femoral
shaft adapted to the increased mechanical
load of body weight during life primarily
through endosteal deposition of bone and
narrowing of the medullary cavity (it seems
unlikely that her current very thick cortices
could be due simply to a retention from early
adulthood, since these would have been
greatly “mismatched” with her former body
weight). If true, this pattern of bone remodeling would represent a reversal of the normal increase with aging in medullary cavity
diameter resulting from endosteal resorption (e.g., Garn, 1970;Ruff and Hayes, 1988).
Variation among the other individuals
listed in Table 5 also indicates that diaphyseal cortices respond more to changes in body
weight during adulthood than do articular
external dimensions. The errors in prediction of body weight from femoral head
breadth strongly parallel variation in the
relative weight index among the eight subjects (r = .929,P <.001, sedrace-specific formulae). In other words, relatively heavy individuals generally have femoral heads too
small for their weights, and relatively light
individuals generally have femoral heads too
large. In contrast, %PEs of body weight from
shaft cortical area are not significantly correlated with variation in relative weight
(r = .511, P > .lo). This indicates that cortical area “tracks” body weight more closely:
relatively heavy or light subjects do have
relatively thicker or thinner cortices, respectively. Interestingly, shaft subperiosteal
breadth shows a pattern more like that of
head breadth than shaft CA (r = 397,
P >.01, %PE and relative weight index),
again suggesting a large role of the endosteal
surface in responding to changes in body
weight.
To investigate further the applicability of
the present weight prediction equations, we
Ht
Wt18
Wt
+17%
+49%
+6%
+I%
+2%
0%
-25%
-10%
%AUS
Wt/Ht
~
+5
18
13
69.5 -22
57.0 -5
79.0 -3
78.4 21
60.1 8
87.4 1
78.1 28
63.6 57
+11
70.8 -23
56.7 -4
76.8 0
76.0 25
60.2 8
87.4 1
75.6 32
64.1 56
+12
+6
19
13
70.8 -23
61.1 -11
76.7
0
81.0 18
64.0
1
89.8 -2
75.3 32
67.2 48
+8
+2
17
12
68.4 -20
58.6 -7
83.9 -9
80.5 18
73.3 -11
83.9 5
91.6 9
65.7 52
+5
-2
16
11
67.4 -19
54.5 0
83.2 -8
80.5 18
73.6 -12
83.2 5
89.3 12
63.8 56
i7
0
16
11
65.5 -17
59.2 -8
85.1 -10
82.9 15
75.1 -14
85.1 4
91.8 9
66.9 49
+4
-3
16
11
-
-
13
63.8 -15
62.6 -13
82.0 -6
77.7 22
85.4 -24
83.7 6
94.9 5
88.9 12
-2
10
-
57.6 -5
55.5 -2
81.7 -6
79.1 20
94.2 -31
82.7 7
89.5 12
100.2 0
-1
-
-
12
60.8 -10
64.9 -16
84.3 -9
78.7 21
85.8 -24
85.7 3
95.2 5
89.0 12
-2
Predicted body weight2
Femoral head BD equations
Femoral shaft BD equations
Femoral shaft CA equations
General
Sex
Sex/race
General
Sex
Sexhace
General
Sex
Sex/race
~
~
_
_
_
_
~
~
_
_
_
_
Pred %PE Pred %PE Pred %PE Pred %PE Pred %PE Pred %PE Pred %PI Pred%PE Pred%PE
'Y,years; W,white;B,black;M,male;F,female;Ht,height(cm);Wt18, bodyweightat 18years(kg);Wt,currentbodyweight(kg);Wt/HtOinAUS,weightforheight,percentaboveorbelow
U.S.
HANES national averages for sex/age group (combined race) (Abraham et al., 1979a).
'Body weight (kg) predicted from raw data equationsin Table 4: general (total sample),sex specific, and sexlrace specific (for blacks, race-specific equations used in lieu of sex/race equations).
%PE, percent prediction error, calculated as [(observed - predicted)/predicted] X 100.
1. 46y WF
170 45.4
54.4
2. 47y BF
147 44.9
54.4
76.7
3. 56y WM 171 68.0
4. 39y BM
184 88.4
95.2
64.9
5. 50y BF
156 49.9
6. 37y WM 180 77.1 88.4
7. 44y WM 180 79.4
99.8
99.8
8. 59y BF
155 47.6
Average %PE:
average %PEw/o subject 8:
Average (%PE(:
average I%PEI w/o subject 8:
Subject
Subject characteristics1
TABLE 5. Actual and predicted body weight in eight subjects
_
_
409
FEMORAL REMODELING IN ADULTS
TABLE 6. Estimation of mean body weights of two human population samples using femoral head
prediction equations
Sam&
US white autopsy
Pecos Pueblo
Sex
wt 2
General
Pred
WPE
Male
Female
Male
Female
80
67
59
54
80.4
67.7
68.8
58.6
0
-1
-14
-8
Predicted body weight’
Sex
Pred
%PE
78.6
68.7
63.8
58.5
2
-2
-8
-8
Sexlrace
Pred
%PE
79.0
67.3
-
2
0
-
‘Mean body weight (kg) predicted from mean femoral head breadth using equations in Table 4. See Table 5 for definition of %PE.
“Mean body weight previously estimated using other techniques (see text and Ruff, 1987), rounded to nearest kg. Figures for US.white
autopsy slightly different than reported for the sample used for cross-sectional diaphyseal analysis (Ruff, 1987, Table 1) because not all
individuals in that study were available for measurement of the femoral head (also see Ruff, 1988698). Also note a misprint in Ruff(1988,
Table 1): body weight for Pecos females should have been 53.8 kg, not 58.3 kg.
estimated average body weights in two other clinics, is still broadly representative of the
samples from mean femoral head diameter U.S. population. This also increases the con(comparable shaft dimensions were not fidence that these prediction equations can
available) and compared these to earlier in- be applied to modern U.S. forensic cases in
dependent estimates of mean body weight general.
based on other methods. The samples inIn contrast, the body weight estimates for
cluded a recent U.S. white autopsy sample the Pecos Pueblo sample using the femoral
and an Amerindian archeological sample head equations are consistently above those
from Pecos Pueblo (Ruff, 1988:698). Mean based on estimated stature and weight for
body weights of males and females in these height. Use of the sex-specific equation
samples had been estimated from recon- rather than the general formula produces a
structed stature and weight for height tables closer estimate for males, but not for fe(U.S. white) or multiple regressions of males. Percent prediction error is about 8%
weight on reconstructed stature and relative for both sexes using the sex-specific equasitting height (Pecos) using appropriate ref- tions, or about a 4-5 kg overestimate of body
erence samples (Ruff, 1987). These earlier weight.
estimates were compared with estimates
While one could argue that the weights
based on femoral head size (Table 4) for the estimated previously for Pecos are in error,
total combined sample, sex-specific, and for there is a plausible explanation for why the
the U.S. white sample, sedrace-specific femoral head equations would produce sysequations. Results are shown in Table 6.
tematic overestimates of body weight in this
Mean body weight predicted from femoral sample. Various lines of evidence indicate
head breadth is remarkably close to that that recent U.S. adult populations are both
predicted previously for the U.S. white au- heavier for their height and gain relatively
topsy sample-within 1.5 kg for all predic- more weight during adult life than earlier
tions. General, sex-specific, and sedrace- U.S. populations and probably preindustrial
specific formulae produced equally close populations in general. In national surveys,
predictions in this sample. The excellent cor- an average gain in weight for height among
respondence of results is perhaps not unex- U.S. citizens was observed in even the short
pected, given that this sample was drawn period from 1960-62 to 1971-74, a gain that
from the same general (i.e., U S . ) population was attributed to an increase in “excess caas that used in the present study (the indi- loric intake and sedentary habits” (Abraham
viduals in the previous sample ranged from et al., 1979a:12). This trend continues back
21 to 59 years of age and had died about a t least as far as the early twentieth century,
1980). However, the results are still encour- as illustrated in Figure 3. Furthermore, the
aging, first, because they further support the increase in weight for height during adultvalidity of the present prediction equations hood is probably greater among the recent
when compared with estimates based on a U.S. population than in other relatively contotally different technique and, second, be- temporary but less mechanized and sedencause they suggest that the present study tary populations. Figure 4 compares the avsample, despite being drawn from hospital erage adult gain with age in a weight for
410
C.B. RUFF ET AL.
74 r
130
US F
70
t
In
0
/
7
-
120
US M
X
I
c)
E
._
,”
Navaho M
-
110
I
2
Navaho F
m
._
:
-
100
1910
1920
1930
1940
1950
1960
1970
1980
Date (yrs)
Fig. 3. Increase in mean body weight from 1918 to
1972 of young U.S. men of the same height: 170 cm (67
in). Data for 1918 are the mean height and weight of 229
U S . army inductees, of which all but two were between
20 and 33 years (Gray and Mayall, 1920, Table 3). (Mean
body weight for this sample is identical if only men
exactly 67 in [n = 281 are included.) Weight for 194344
is the mean for registrants for military service, aged
20-34 years, of 67 in, reported as estimates from regressions of weight on height in 464,666 men (Karpinos,
1958, Table 416). Weight for 1960-62 is the mean from
the U S . Health Examination Survey (HES) for men of
18-34 years and 67 in (Roberts, 1966, Table 1). Weight
for 197G74 is the mean from the U.S. Health and
Nutrition Examination Survey (HANES) for men of
18-34 years and 67 in (Abraham et al., 1979a, Table 1).
Note that inclusion of some 18-19 year men in the two
most recent samples would only tend to decrease mean
body weight for these samples relative to the two earlier
samples (e.g., see Fig. 4), thus dampening the trend. The
two earlier samples were claimed to be relatively unselected, but it is possible that some very heavy (as well as
very light) individuals were excluded. Weight for height
in 1918is 13%less than in 1972. The mean weight ofthe
1918 sample 1 year after induction had increased to 68
kg. If the average of weight at induction and that of a
year later is used for this sample, the difference between
1972 and 1918 is about 10%.
height (ponderal) index (Wtn-It3) in a Navaho sample measured in 1955 (Sandstead
et al., 1956) and the most recent U.S. national survey (Abraham et al., 197913) (our
calculations from reported mean weight and
height data). The Navaho sample was from
two nonurban reservation populations, one
relatively remotely located. While these populations were not “preindustrial,”they probably represent environmental conditions
more similar to preindustrial, premechanized populations than those in the 19711974 U.S. national survey (as do the earlier
twentieth century samples in Fig. 3). The
recent U.S. sample clearly gains more in
I
10
.
I
20
.
3
30
.
I
.
40
I
.
50
-
.
60
I
.
70
I
80
Age (yrs)
Fig. 4. Change with age in a ponderal (weight for
height) index in two adult human samples, expressed as
a percentage of ponderal index a t age 18 years (weight in
kg, height in cm). Mean U.S. data from the HANES
national survey of 1970-1974, calculated from reported
mean heights and weights of 18-year-old youths and
adult men and women of each age group (Hamill et al.,
1973, Tables 5 and 12; Abraham et al., 1979b, Tables 4
and 11).Navaho data calculated from reported mean
heights and weights at each age collected on two Arizona
reservations in 1955 (Sandstead et al., 1956, Table 17).
The 18 year figure for the Navaho sample derived by
weighting the 1%19 year and 16-17 year figures reported (see also text, footnote 4).
weight relative to height through adulthood
than the Navaho sample, particularly
among females and particularly after the
fourth d e ~ a d e In
. ~ fact, Sandstead and coworkers (1956:43) specifically note that an
increasing percentage of Navaho individuals
in middle and old age would be characterized
as under “standard weight” when compared
with a relatively contemporary U.S. white
sample. Other nonindustrial populations,
such as Australian Aborigines (Abbie, 1967)
and East African Turkana (Little et al.,
1983) also show no gain in weight or weight
for height after the third or fourth decades.
4More frequent osteoporotic vertebral crush fractures with
subsequent loss in height may explain why U.S. females show
such a large continuingincrease in weight for height in the eighth
and ninth decades relative to other groups. However, this would
not be a significant factor in the 40 and 50 year age groups (Riggs
and Melton, 19861, where both U S . males and females have
already clearly separated in weight for height from the Navaho
samples. A ponderal index was chosen for this illustration rather
than absolute weight because of problems arising from secular
trends in general body size (stature and weight) among U S .
populations over the past century (e.g., Stoudt et al., 1965;
Abraham et al., 197913) that may or may not apply to Navahos in
particular.
411
FEMORAL REMODELING IN ADULTS
Thus it seems very likely that the present
femoral head equations, based on a reference
sample that is both relatively heavy and also
increases more in weight throughout adulthood, will systematically overestimate adult
body weight in most preindustrial (or even
earlier industrial) populations. Although it
is impossible to calculate precisely what this
systematic error will be, the results shown in
Table 6 and Figures 3 and 4 are all consistent
with an error on the order of about 10%.
Therefore, in using the present femoral head
equations to calculate body mass in earlier
human samples, it is recommended that
about 10% be subtracted from the estimate
to account for the increased adiposity of very
recent U S . adult populations.
The femoral shaft equations, particularly
if cortical thickness is included, clearly provide superior estimates of body weight compared with the femoral head equations in the
modern U.S. test sample (Table 5).However,
it is not clear that the same equations will
also provide better body weight estimates for
earlier human populations. As discussed
above, there is evidence that diaphyseal
cross-sectional geometry is very sensitive to
alterations in all mechanical loads, including muscular loadings as well as the gravitational loading produced by body weight per
se. It is virtually certain that the modern
U.S. reference sample used here to develop
prediction equations is not only systematically heavier for their stature or skeletal
size, but also systematically more sedentary
than earlier or preindustrial populations; in
fact, as noted above, the two factors are very
likely directly related. Thus earlier human
populations, with their probable higher activity levels, would be predicted to have relatively more robust diaphyses for their body
weights. This would again lead to a systematic overestimate of body weight in these
samples if the present shaft equations were
used, i.e., in a direction similar to the femoral
head equations but for a different reason.
The approximate magnitude of this error is
more difficult to estimate than that for the
femoral head, however, since, unlike body
weight, differences in activity level, muscular strength, and so forth, between human
populations are very difficult to determine
with any precision. Thus, paradoxically, precisely because of their greater sensitivity to
mechanical factors other than body weight,
diaphyseal dimensions may be more problematic for use in weight estimation when
applied across population samples who probably differ systematically, but to an unknown degree, in these other respects.
Again, more controlled studies of other population samples who vary in activity level
are needed to help resolve this issue.
CONCLUSIONS
1.) Proximal femoral diaphyseal size is
more highly correlated with current body
weight than with weight at the onset of
adulthood in a sample of 80 living individuals measured readiographically. Femoral
head size does not show such a consistent
pattern, with generally lower correlations
with current body weight. The results are
consistent with differences in hypothesized
remodeling mechanisms throughout adulthood, in which diaphyses respond to changes
in mechanical loading primarily through
changes in cortical geometry, while articulations respond primarily through changes in
subchondral trabecular architecture but not
external joint size. The femoral neck appears
to combine the remodeling mechanisms of
both articulations and diaphyses.
2.) Proximal femoral dimensions among
adult humans scale positively allometrically
with body mass, when appropriate statistical techniques are used and the additional
“noise”created by remodeling constraints on
articular size is factored out.
3.) Body weight of recent US. adults can
be predicted reasonably accurately on an
individual basis from proximal femoral shaft
dimensions, with average percent prediction
errors of 10%-16% in a test sample of eight
individuals. Application to earlier human
samples is more problematic, because of
probable systematic differences in relative
body weight and change in body weight
throughout life, and other factors such as
activity level. A downward adjustment of
about 10% in body weight is recommended
when using the femoral head equations on
earlier samples, to account for increased adiposity in the reference sample. More precise
estimates of the effects of activity level differences on diaphyseal remodeling are
needed before the shaft prediction equations
can be used with confidence on earlier human populations.
ACKNOWLEDGMENTS
We thank the physicians at Johns Hopkins
Hospital who helped collect the data upon
which this study was based and Dr. Erik
412
C.B. RUFF ET AL
Trinkaus for his comments on an earlier
version of this manuscript.
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