AMERICAN JOURNAL OF HUMAN BIOLOGY 14:74±80 (2002)

Prediction of Cross-Sectional Geometry From Metacarpal Radiogrammetry: A Validation Study RICHARD A. LAZENBY* Anthropology Program, University of Northern British Columbia, Prince George, British Columbia, Canada

ABSTRACT Regression models have been developed to adjust algebraic estimates of second metacarpal cortical bone geometry to actual values (as determined through invasive analysis). These models, derived from an archaeological sample of European origin, have high efficacy in predicting actual values but have not been validated on non-European samples. This paper reports a validation study for these models applied to a historic/proto-historic sample of Inuit from the central Canadian Arctic (n = 166; ages and sexes pooled as per the original study). In that the Inuit sample has been argued to exhibit distinct skeletal biology, this represents a robust test of the predictive models. The algebraic models again produced biased overestimates of actual values, whereas the predictive regression models were found to provide good estimates of actual values for measures of bone strength (Total Area, bending about the Ix and Iy axes), but not for estimates of mass (Cortical Area). This difference may exist in either functional or systemic differences in skeletal physiology and aging bone Ó 2002 Wiley-Liss, Inc. loss in the Inuit. Am. J. Hum. Biol. 14:74±80, 2002.

The second metacarpal remains a preferred site for evaluating bone mass and skeletal dynamics in both anthropological and clinical spheres (Livshits et al., 1998; Osei-Hyiaman et al., 1999; Mays, 2000). There is now a wealth of comparative data addressing questions of inter- and intrasexual cortical bone growth, aging, and senescence, asymmetry and functional laterality from populations with measurable biocultural and biogeographical diversity. Typically, however, second metacarpal studies have used uniplanar radiographic methods and estimate cortical bone parameters (strength and rigidity) using algebraic models that assumed a cylindrical diaphysis, and thus a circular cross-section in the tradition established by Barnett and Nordin (1961) and Garn (1970). Whereas newer technologies, such as peripheral quantitative computed tomography (pQCT) and dual-energy X-ray absorptiometry, can now provide detailed and accurate representations of skeletal mass and geometry in distal limb segments (Hasegawa et al., 2001), the relative ease, cost-effectiveness, and minimally invasive nature of hand-wrist radiography, as well as arguments for accuracy and precision (Meema and Meindok, 1992), are commonly cited reasons for replicating this approach, particularly in non-clinical fields of study (Mays, 2000). However, it has become apparent that uniplanar, circular algebraic

ã 2002 Wiley-Liss, Inc. DOI 10.1002/ajhb.10021

models provide significant overestimates of cortical bone size and mass (Lazenby, 1995, 1997a). Attempts to accommodate non-circular geometry using orthogonal biplanar radiography and extended geometric computation have been proposed (Biknevicius and Ruff, 1992; Ohman, 1993); however, such models can only be applied to skeletonized material as the requisite anteroposterior images of the metacarpal cortex cannot be obtained from living individuals. Recently, Lazenby (1998) provided a series of reduced major axis (RMA) regression equations that enable prediction of actual geometric properties from either uniplanar or biplanar radiographic data. These models were derived from a large (n = 356) EuroCanadian 19th century historic archaeological sample, and tests of the models on a hold-out sample from the same collection indicated a high degree of efficacy in prediction (mean difference (log values) = )0.001 to )0.012; all nonsignificant, (see Lazenby, 1998; Table 1)). However, as with all similar approaches to questions of

Contract grant sponsor: Natural Sciences and Engineering Research Council of Canada; Contract grant number: OPG 0183660. *Correspondence to: Anthropology Program, University of Northern British Columbia, 3333 University Way, Prince George, BC Canada V2N 4Z9. E-mail: [email protected] Received 26 April 2001; Revision received 30 July 2001; Accepted 24 August 2001

75

VALIDATION METACARPAL GEOMETRY ESTIMATES

TABLE 1. Descriptive statistics and results of a paired t-test for estimated and predicted values versus actual values determined by sectioning Section Total area Observed Circular algebraic elliptical algebraic Circular RMA Elliptical RMA Cortical area Observed Circular algebraic Elliptical algebraic Circular RMA Elliptical RMA Ix Observed Elliptical algebraic Elliptical RMA Iy Observed Circular algebraic Elliptical algebraic Circular RMA Elliptical RMA

Mean

SD

r

Mean diff

T

P

49.12 49.42 54.39 48.32 49.76

8.74 10.53 9.78 9.31 8.97

0.75 0.89 0.75 0.89

)0.30 )5.27 0.80 )0.64

)0.543 )15.125 1.612 )1.966

NS 0.000 NS NS

32.03 29.14 33.96 27.48 29.74

5.65 6.32 6.48 5.79 5.87

0.71 0.83 0.71 0.83

2.89 )1.93 4.54 2.28

8.107 )6.915 13.462 8.826

0.000 0.000 0.000 0.000

195.66 230.11 196.29

69.93 82.80 72.19

0.87 0.87

)34.46 )0.64

)10.809 )0.225

0.000 NS

158.57 171.61 187.79 152.44 155.17

57.74 73.57 70.91 59.51 58.05

0.84 0.88 0.84 0.88

)13.04 )29.21 6.12 3.39

)4.178 )11.22 2.372 1.566

0.000 0.000 0.019 NS

``rÕÕ values report correlation of invasive (observed) with algebraic and predicted estimates. ``Mean diffÕÕ is the mean of the estimated or RMA value minus the observed value.

human population biology with both theoretically justifiable and demonstrated intraand intergroup variability, the issue of cross-population validity requires assessment. This paper reports a validation study of the aforementioned regression equations to predicting measures of cross-sectional size and strength from radiometric data for an archaeological sample of Inuit second metacarpals. MATERIALS AND METHODS Comparative data for the second metacarpal were obtained from n = 166 Inuit second metacarpals recovered from several archaeological sites in the central Canadian Arctic. The majority are ethnically Sadlermiut from Southampton Island, situated north of Hudson's Bay in the Northwest Territories, just below the Arctic Circle. The last representatives of the Sadlermiut disappeared between 1902±1903, succumbing to introduced disease (Hawkey and Merbs, 1995; Merbs, 1996). The Inuit sample is culturally, genetically, and ecogeographically distinct from the sample of EuroCanadian settlers used to develop the predictive models. Recent genetic analyses (Hayes, 2001) have reinvigorated the debate as to the cultural origins of the Sadlermiut, specifically that Southampton Island was a

refuge for a ``relicÕÕ Dorset population. Pending consensus on this issue, which has no specific bearing on the objectives of the present study, the term Inuit will continue to be used. Both physiological (cold adaptation) and cultural (dietary) arguments have been made for unique patterns of aging bone loss in Arctic groups (Lazenby, 1997b; Lazenby, 2001); thus, this constitutes a robust test of the validity ±± or shortcomings ±± of the models. Predictions from both uniplanar and biplanar radiography are compared with invasively and directly observed (actual) values. Of the sample of 166 bones, 126 were obtained as paired elements from 63 individuals (24 women, 39 men); an additional 40 individuals (18 women, 22 men) contributed either left (20) or right (20) bones. However, in keeping with the original study sexes and sides were pooled, as the intent was to examine the general relationship of radiographic cortical estimates to actual bone geometry. Imaging protocols (exposure settings, tube-to-film distance, positioning) and data collection methods were matched to those of the original study. Data for total and medullary cavity widths were collected from orthogonal anteroposterior (AP) and mediolateral (ML) radiographs, and estimates for Total Area (TA, mm2), Cortical Area (CA, mm2), and bending rigidity about the

76

R.A. LAZENBY

Fig. 1. Total Area. Plots of Circular (A) and Elliptical (B) Algebraic and RMA predicted values versus Observed (SLCOMM) values. Line indicates unity. R2 (circular) = 0.561; R2 (elliptical) = 0.506.

ML (Ix, mm4) and AP axis (Iy, mm4) were derived using the uniplanar circular or biplanar elliptical model as appropriate. (The elliptical model uses data from both projections. Although it can accommodate either an eccentric or concentric placement of the medullary cavity (Ohman, 1993), the concentric formulation was used in these studies as no significant differences have been found for position of the medullary cavity in the second metacarpal (Lazenby,

1998).) These estimates in turn were used to predict actual values using the RMA regression models reported in the original study. Both the estimated and predicted values were compared with data determined directly from invasive sectioning and SLCOMM digitization (Eschman, 1990). Results were compared using a paired t-test of SLCOMM versus estimated and predicted values, using Statistica 5.1 (Statsoft, 1997).

VALIDATION METACARPAL GEOMETRY ESTIMATES

77

Fig. 2. Cortical Area. Plots of Circular (A) and Elliptical (B) Algebraic and RMA predicted values versus Observed (SLCOMM) values. Line indicates unity. R2 (circular) = 0.505; R2 (elliptical) = 0.694.

RESULTS AND DISCUSSION In the Inuit sample, the algebraic estimates based on circular or elliptical models tend to significantly over-estimate actual values determined by sectioning and digitization, as seen in the negative mean difference values in Table 1 and plots above the line of unity in Figures 1 to 4. The correlation of invasively-determined actual

values with either algebraically determined (circular or elliptical, as appropriate) or predicted estimates are moderately high (approximately 0.7±0.9; Table 1). Coefficients are higher for elliptical versus circular values, and all are significant at P < 0.05. This pattern of over-estimation and correlation mimics that seen in the original study of historic EuroCanadians. With the general exception of Cortical Area (CA), the

78

R.A. LAZENBY

Fig. 3. Ix. Plots of Elliptical Algebraic and RMA predicted values versus Observed (SLCOMM) values. Note that the circular model cannot provide an estimate for Ix, as the requisite data for the medial and lateral cortices is lacking in an AP radiograph. Line indicates unity. R2 (elliptical) = 0.755.

RMA prediction of actual values from the biased algebraic estimates provides a close approximation to actual values. This departs from the original study, in which the RMA transformation for CA resulted in a non-significant difference from actual values. Whereas the RMA adjustment of Circular Iy estimates was significantly different from actual values (Table 1), the plot of values (Fig. 4A) indicates a much better approximation than the simple algebraic estimate. The failure of the RMA models to provide good approximations to actual values for CA suggests that Inuit metacarpals differ in terms of the pattern of cortical thickness values around the circumference of the bone relative to that of the EuroCanadian settlers from whom the models were derived. In a Caucasian sample of men and women from the Baltimore Longitudinal Study on Aging, Fox et al. (1995) showed that the ``radialÕÕ and ``ulnarÕÕ (lateral and medial, as used here) cortices of the second metacarpal do not lose bone equally with age with the ulnar cortex losing bone more rapidly. In a study also using BLSA data, Roy et al. (1994) observed that a limitation of handwrist radiographs is the absence of data for the dorsal and palmar cortices, as these are likely under greater functional strain in

finger flexion and should be expected to show different patterns of age-related change than the medial and lateral cortices. Although both the Inuit and the European Settler samples originate from populations reasonably characterized as having a robust lifestyle (although the Inuit perhaps more consistently so (Lazenby, 2001)), the kinds of activities engaged in would perhaps have been sufficiently different to promote distinctive patterns of cortical bone accretion and thinning. There are also plausible differences in systemic bone metabolism related to diet (Mazess and Jones, 1972) and cold adaptation (Lazenby, 1997b), which may impinge on cortical bone geometric morphology. Thus, the inability of the RMA equations to predict CA may reflect different patterns for aging bone loss among Inuit. The differences observed for CA may also reflect a shape, rather than mass, difference for the metacarpal midshaft, as differently shaped metacarpals would mimic crosssections with different rates of bone loss around the circumference. One indicator of a shape difference would be the relative degree of circularity in the two samples, as measured by the ratio of orthogonal bending moments in which a value of 1.0 denotes a circular section. For the Inuit sample (pooled for sides and sex), the Ix/Iy ratio

VALIDATION METACARPAL GEOMETRY ESTIMATES

79

Fig. 4. Iy. Plots of Circular (A) and Elliptical (B) Algebraic and RMA predicted values versus Observed (SLCOMM) values. Line indicates unity. R2 (circular) = 0.704; R2 (elliptical) = 0.781.

mean was 1.26, range 0.76±2.02. The ratio for the original European Settler sample is 1.19, range 0.64±2.4. Whereas the Settler sample is somewhat less circular, the overlapping ranges do not support this explanation. The fact that the RMA formulae provide good predictions of actual values for TA, Ix and Iy reflects the fact that these latter measures are determined in the main by Total, rather than Medullary Width, and thus are somewhat inured to the vagaries of

population-specific differentials in cortical thinning. The results of this study indicate that 1) if one's interest is in estimating structural strength properties (TA, Ix, Iy) in the human second metacarpal, the RMA formulae provided in Lazenby (1998) can be considered valid across populations; 2) however, if one's interest is in estimating variation in bone mass (CA and its derivatives, e.g., Percent Cortical Area) the RMA equations

80

R.A. LAZENBY

may not provide valid results. In that the validation sample for this study arguably possesses a distinct skeletal physiology, further validation on samples bearing a closer ``affinityÕÕ to the original European Settler sample should be carried out to possibly extend the use of the RMA equations into the realm of bone mass, an important criterion of skeletal aging in past and present populations. The significant correlation of observed and estimated or predicted values indicates that the latter will characterize actual patterning in bone geometry. This being the case, comparative studies using the same class of data (e.g., all radiogrammetric) will provide valid observations of (relative, but not absolute) differences among groups. Thus, whereas use of the RMA regressions tested here is required of researchers wishing to contrast algebraic with invasively-determined data, or who wish to describe absolute differences between groups, it is not necessary to transform algebraically-determined estimates across different studies for comparative purposes. ACKNOWLEDGMENTS The author thanks Inuit Heritage Trust, Canadian Museum of Civilization, and Natural Sciences and Engineering Research Council of Canada. LITERATURE CITED Barnett E, Nordin BEC. 1961. Radiological assessment of bone density: I. The clinical and radiological problem of thin bones. Br J Radiol 34:683±692. Biknevicius AR, Ruff CB. 1992. Use of biplanar radiographs for estimating cross-sectional geometric properties of mandibles. Anat Rec 232:157±163. Eschman P. 1990. SLCOMM: A user-supported realtime digitizing package. Alberquerque, NM: Eschman Archaeological Services. Fox KM, Kimura S, Powell-Threets K, Plato CC. 1995. Radial and ulnar cortical thickness of the second metacarpal. J Bone Miner Res 10:1930±1934. Garn SM. 1970. The earlier gain and later loss of cortical bone. Springfield: CC Thomas.

Hasegawa Y, Schneider P, Reiners C. 2001. Age, sex, and grip strength determine architecural bone parameters assessed by peripheral quantititive computed tomography (PQCT) at the human radius. J Biomech 34:497±503. Hawkey DE, Merbs CF. 1995. Activity-induced musculoskeletal stress markers (MSM) and subsistence changes among ancient Hudson Bay Eskimos. Int J Osteoarch 5:324±338. Hayes MG. 2001. Ancestor-descendant relationships in North American Arctic prehistory: Ancient DNA evidence from the Aleutian Islands and the Eastern Canadian Arctic (abstract). Am J Phys Anthropol Suppl 32:787. Lazenby R. 1995. Non-circular geometry and radiogrammetry of the second metacarpal. Am J Phys Anthropol 97:323±327. Lazenby R. 1997a. Bias and agreement for radiogrammetric estimates of cortical bone geometry. Invest Radiol 32:12±18. Lazenby R. 1997b. Inuit bone loss, diet, and cold adaptation. Am J Hum Biol 9:329±341. Lazenby R. 1998. Second metacarpal cross-sectional geometry: rehabilitating a circular argument. Am J Hum Biol 10:747±756. Lazenby R. 2001. Sex dimorphism and bilateral asymmetry: modeling developmental stability and functional adaptation (abstract). Am J Phys Anthropol Suppl 32:96. Livshits G, Yakovenko K, Kletselman L, Karasik D, Kobyliansky E. 1998. Fluctuating asymmetry and morphometric variation in hand bones. Am J Phys Anthropol 107:125±136. Mays S. 2000. Age-dependent cortical bone loss in women from 18th and early 19th century London. Am J Phys Anthropol 112:349±361. Mazess RB, Jones R. 1972. Weight and density of Sadlermiut Eskimo long bones. Hum Biol 44:537±548. Meema HE, Meindok H. 1992. Advantages of peripheral radiogrammetry over dual-photon absorptiometry of the spine in the assessment of prevalence of osteoporotic vertebral fractures in women. J Bone Miner Res 7:897±903. Merbs CF. 1996. Spondylolysis of the sacrum in Alaskan and Canadian Inuit skeletons. Am J Phys Anthropol 101:357±367. Ohman JC. 1993. Computer software for estimating cross-sectional geometric properties of long bones with concentric and eccentric elliptical models. J Hum Evol 25:217±227. Osei-Hyiaman D, Ueji M, Toyokawa S, Takahashi H, Kano K. 1999. Influence of grip strength on metacarpal bone mineral density in postmenopausal Japanese women: a cross-sectional study. Calcif Tissue Int 64:263±266. Roy TA, Ruff CB, Plato CC. 1994. Hand dominance and bilateral asymmetry in the structure of the second metacarpal. Am J Phys Anthropol 94:203±211. Statsoft. 1997. Statistica. Tulsa: Statsoft.