Ruff et al - 1991 - AJPA

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 to 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 18 years in a living human sample.

‘Throughout this study, the term remodeling is used to desig- nate 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, 1989:143- 144).

Since adults vary in body weight over their lifetimes and a change in weight (mass) con- stitutes 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

@ 1991 WILEY-LISS, INC

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 anteropos- terior 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. Mea- surements 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 min- imum 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 anteroposte- rior axis; IJ. As discussed elsewhere (e.g., Ruff and Hayes, 19831, CA is proportional to axial rigidity or strength of a long bone,

TAB

LE 1

. Sa

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Cur

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age

C

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nt B

W

BW a

t 18

Yr

Shaf

t Bd.

M

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orte

x L

at. c

orte

x H

ead

Bd.

N

eck

Bd.

(w

ars)

(k

g)

(kg)

(m

m)

(mm

) (m

m)

(mm

) (m

m)

Gro

w

n M

ean

SD

Mea

n SD

M

ean

SD

Mea

n SD

M

ean

SD

Mea

n SD

M

ean

SD

Mea

n SD

Tot

al

80

52.3

16

.5

76.7

17

.7

64.9

13

.7

31.0

3.

0 6.

9 1.

4 6.

0 1.

1 47

.0

4.0

33.2

3.

8

Mal

e 41

50

.6

15.7

80

.8

15.6

71

.6

10.4

32

.1

2.9

7.3

1.5

6.3

1.1

49.5

2.

8 35

.3

3.4

Fem

ale

39

54.1

17

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72.4

18

.9

57.9

13

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29.7

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5 6.

5 1.

1 5.

8 1.

0 44

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75

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16.5

63

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12.2

30

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6.8

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47.1

4.

0 33

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3.9

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29

48.9

18

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79.0

19

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67.9

15

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31.0

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3 1.

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3.9

32.7

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(ran

ge)

(24-

81)

(42-

135)

(3

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(24.

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(4.2

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3)

(3.0

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400 C.B. RUFF ET AL

Fig. 1. Line tracing of radiograph showing proximal femoral breadths measured in the study: femoral head, neck, and diaphyseal subperiosteal breadths, and medial and lateral diaphyseal cortical breadths (see text). Dot- ted lines represent cervical and diaphyseal axes.

while I, is proportional to bending strength in the mediolateral plane. Assuming (by ne- cessity) a circular section, these properties can be calculated from the radio aphic breadths as follows: CA = pi/4 * (D - d2); I, = pi/64 * (D4 - d4); where D and d refer to the subperiosteal and medullary diame- ters of the section, respectively. I t should be emphasized that because measurements were available for only one plane and a simple symmetrical model of the cortex was used, while the cortex of the proximal femur is certainly not circular or symmetric (e.g., Ruff and Hayes, 19831, these indices are only proportional to true cross-sectional geometric properties and are included here only for comparative purposes.

Current and past body weights of the subjects in the study were determined by patient recall through questioning by the attending physician a t the time of examination. It was

!F

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, as 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 as 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 (Abra- ham 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 18.0-18.5- year-old men and women measured in 1966- 1970 (Hamill et al., 1973). Given the longer elapsed time period, it is very likely that the weights recalled for age 18 have more associated error than the current weights. How- ever, it appears from the above that this 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 comparing correlations between femoral dimensions and current and 18-year-old body weights in the sample.’ Eighteen years was chosen as the onset of “adulthood” because this is the approximate age when union of the femoral head epiphysis is completed

‘It has been persuasively argued that the product-moment correlation coefficient, r, is a n incomplete and sometimes mis- leading indicator of the strength of relationship between two variables and that other indices such as standard errors of estimate (SEE) or percent standard errors of estimate (OSEE) should also be examined (e.g., Smith, 1984). However, in the present case, i.e., comparisons between correlations of a bone dimension with current and previous body weight, the two types of indices are equivalent. This is because the SEE of y is directly related to r when values for y (here the bone dimension) remain the same, since SEE = SD d 1 ~ r2, where SD is the standard deviation of y (Zar, 1984271);. (Since the mean oi(y also remains the same, this is also true for the OSEE of y.) SEs and %SEES for the prediction of body mass from femoral dimensions using different properties and sample groupings are given later (Table 4).

FEMORAL REMODELING IN ADULTS 401

TABLE 2. Correlations of proximal femoral dimensions with current body weight and body weight at 18 Years of ape1

Raw data Log-transformed Group Dimension2 Current 18 Years Current 18 Years

Total Shaft Bd ,603 .487 ,623 ,477 Shaft CA ,575 .483 ,598 .458 Shaft I, ,623 ,521 ,639 ,488 Head Bd .486 ,508 ,491 ,501 Neck Bd ,533 ,480 ,533 ,464

Male

Female

White

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 ,625 ,718 ,712 ,411 ,500

Shaft Bd ,636 Shaft CA ,626 Shaft I, .658 Head Bd .554 Neck Bd ,631

,413 (286) ,419 .537 ,492 ,320 ,456 ,405

(.087) (.065) ,493 ,470 ,519 ,539 .544

,552 ,421 .538 .499 .500

,387 (252) ,359 .547 ,483

.621 ,316 ,701 ,404 ,670 ,354 .374 (.052) .464 (.032) .665 .637 .687 .532 .595

,496 ,443 .499 .520 ,499

Black Shaft BD ,566 ,504 .557 ,472 ~.

Shaft CA ,495 ,489 .526 ,471 Shaft I, ,574 ,532 .561 ,482 Head Bd ,403 ,462 ,441 ,512 Neck Bd ,420 ,462 .463 ,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 transfor- mation [Zar, 19841) to determine the significance of differences between these correlation coefficients. Such tests assume in- dependence 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 them- selves intercorrelated (r = .68 between current and 18-year-old body 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 18 years 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 log- transformed 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 lil weight 18 yrs

._ s

z

x 060 U m c

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. Ma- jor 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. Con- versely, 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 possibil- ity 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


TABLE 3. Regression coefficients (slopes) of proximal femoral dimensions on current body weight, lag,,-transformed data, total sample, using three methods of line fitting

Theoretical Least major Major Reduced

Dimension’ isometrv2 sauares axis SE3 axis SE4

Shaft Bd Shaft CA Shaft I, Head Bd

...

,667 1.333 ,333

-33.1 ,278 .4385 .039 -308 .044 .594 .9945

1.113 2.2935

...

.089 .9935 .151 ,150 1.7425 ,237

.1905 .21!i5 ,038 ,387 ,078 Neck Bd ,333 ,273 ,332 ,041 ,512 ,092

‘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 reduced major 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. Varia- tion 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 pre- clude changes in subperiosteal dimensions, i.e., external neck breadth (see below). How- ever, 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 cross- sectional 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 pre- adult period of growth and development, prior to epiphyseal union. Studies of imma- ture 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 shaft measurements on body weight is also characteristic of other modern adult human samples that have been studied. Re- ported 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 at 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 re- solved by considering the composition of the different samples and the remodeling characteristics of articulations. The present study sample includes individuals from 24 to 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 US. 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 younger- 18 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

would be predicted that body weight would not increase as much from younger to 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 to 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 ob- scuring 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

Raw data Loglo-transformed data Group Dimension2 Slope Int. SEE3 %SEE4 Slope Int. SEE %SEE

Total

Male

Female

White

Black

White male

White female

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

2.160 3.594

2.741 2.845

2.426 4.680

2.270 3.441

2.015 3.879

3.383 3.105

,0808 .493

2.700

.0951

,0575

,1614

,0988

.0873

-24.8 15.6 20.3 1.269 ~ ~.~

-34.6 14.2 18.5 1.424 29.3 14.6 19.0 ,6027

-54.9 13.7 16.9 1.595 -10.6 13.3 16.5 1.098

50.0 14.4 17.8 .3533 -35.1 17.5 24.1 1.272 -66.8 15.0 20.7 1.750 -1.0 13.4 18.5 ,9058

-31.5 13.9 18.4 -31.1 12.9 17.1

26.9 13.0 17.2 -15.2 18.3 23.2 -41.3 16.5 20.9

34.3 17.4 22.1 -85.8 14.7 17.8 -17.3 15.2 18.3

39.4 15.4 18.6

,325 ,419 .6204 ,201 .423 ,5610 ,986 ,219 ,4750 .288 46.2 11.9 17.5

28.3 9.8 14.4 ,6059 -11.8 9.8 14.4 1.240

-.342 -.353

,163 -.922

.165 ,885

-.341 -261 p.691 -.447 -.351

,111

-.209 -.342

.287 -1.612 -.019

,546 1.331 p.090

,134

16.3 21.2 14.4 18.8 14.8 19.3 14.0 17.3 13.3 16.5 14.7 18.1 18.2 25.2 15.1 20.9 13.6 18.8 15.0 19.9 13.0 17.3 13.5 17.9 18.6 23.6 17.1 21.6 17.5 22.2 15.2 18.4 15.3 18.5 16.0 19.4 13.5 19.8 10.6 15.6 10.7 15.7 Shaft CA ,0895

lLeast-squares sIopes andintercepts forequationsof the form y = bx + a, whereyis body weight(orloglo[weight])n (and xisfemoral breadth (or log,, [breadth]). Breadth in mm, CA in mm, weight in kg. Note that CA is a cortical area index, not true (absolute) CA (see text). >See Table 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 obtain- ing sufficiently accurate body masses indi- vidually 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, inter- cepts, 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. Be- cause 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 subgroups- white 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 13 females-was considered too small to gen- erate 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 fluctu- ations 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-


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 18 years, height, and the percent deviation of current weight for height from U.S. national averages, by sex and age group (Abraham et al., 1979a). Us- ing this last relative weight index, the subjects in Table 5 have been arranged in as- cending 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

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

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TABLE 6. Estimation of mean body weights of two human population samples using femoral head prediction equations

Predicted body weight’ General Sex Sexlrace

Sam& Sex w t 2 Pred WPE Pred %PE Pred %PE

US white autopsy Male 80 80.4 0 78.6 2 79.0 2 Female 67 67.7 -1 68.7 -2 67.3 0

Pecos Pueblo Male 59 68.8 -14 63.8 -8 Female 54 58.6 -8 58.5 -8

‘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 samples from mean femoral head diameter (comparable shaft dimensions were not available) and compared these to earlier independent estimates of mean body weight based on other methods. The samples included a recent U.S. white autopsy sample and an Amerindian archeological sample from Pecos Pueblo (Ruff, 1988:698). Mean body weights of males and females in these samples had been estimated from reconstructed stature and weight for height tables (U.S. white) or multiple regressions of weight on reconstructed stature and relative sitting height (Pecos) using appropriate reference samples (Ruff, 1987). These earlier estimates were compared with estimates based on femoral head size (Table 4) for the total combined sample, sex-specific, and for the U.S. white sample, sedrace-specific equations. Results are shown in Table 6.

Mean body weight predicted from femoral head breadth is remarkably close to that predicted previously for the U.S. white autopsy sample-within 1.5 kg for all predictions. General, sex-specific, and sedrace- specific formulae produced equally close predictions in this sample. The excellent cor- respondence of results is perhaps not unex- pected, given that this sample was drawn from the same general (i.e., US. ) population as that used in the present study (the individuals in the previous sample ranged from 21 to 59 years of age and had died about 1980). However, the results are still encour- aging, first, because they further support the validity of the present prediction equations when compared with estimates based on a totally different technique and, second, because they suggest that the present study sample, despite being drawn from hospital

clinics, is still broadly representative of the U.S. population. This also increases the confidence that these prediction equations can be applied to modern U.S. forensic cases in general.

In contrast, the body weight estimates for the Pecos Pueblo sample using the femoral head equations are consistently above those based on estimated stature and weight for height. Use of the sex-specific equation rather than the general formula produces a closer estimate for males, but not for females. Percent prediction error is about 8% for both sexes using the sex-specific equations, or about a 4-5 kg overestimate of body weight.

While one could argue that the weights estimated previously for Pecos are in error, there is a plausible explanation for why the femoral head equations would produce systematic overestimates of body weight in this sample. Various lines of evidence indicate that recent U.S. adult populations are both heavier for their height and gain relatively more weight during adult life than earlier U.S. populations and probably preindustrial populations in general. In national surveys, an average gain in weight for height among U.S. citizens was observed in even the short period from 1960-62 to 1971-74, a gain that was attributed to an increase in “excess ca- loric intake and sedentary habits” (Abraham et al., 1979a:12). This trend continues back at least as far as the early twentieth century, as illustrated in Figure 3. Furthermore, the increase in weight for height during adulthood is probably greater among the recent U.S. population than in other relatively contemporary but less mechanized and sedentary populations. Figure 4 compares the average adult gain with age in a weight for

410

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C.B. RUFF ET AL.

-

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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 US. 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 unse- lected, but it is possible that some very heavy (as well as very light) individuals were excluded. Weight for height in 1918 is 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 Na- vaho 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, premecha- nized populations than those in the 1971- 1974 U.S. national survey (as do the earlier twentieth century samples in Fig. 3). The recent U.S. sample clearly gains more in

US F

US M

Navaho M

Navaho F

I . I . 3 . I . I . - . I . I

10 20 3 0 4 0 50 60 70 8 0

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 co- workers (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 continuing increase 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 US. 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.


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 US. 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 gravita- tional 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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Ruff et al - 1991 - AJPA