AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 90:207-213 (1993) Radiographic Estimation of Long Bone Cross-Sectional Geometric Properties JACQUELINE A. RUNESTAD, CHRISTOPHER B. RUFF, JAMES C. NIEH, RICHARD W. THORINGTON, JR. AND MARK F. TEAFORD Department of Cell Biology and Anatomy, Johns Hopkins University School of Medicine, Baltimore, Maryland 21205 (JA.R., C.BJi., M.F.T.) and Division of Mammals, National Museum of Natural History, Smithsonian Institution, Washington, DC20560 (J.CM., R.W.T.) KEY WORDS Biomechanics, Small mammals, Diaphyses, Imag- ing techniques ABSTRACT Because of their biomechanical significance, cross-sectional geometric properties of long bone diaphyses (areas, second moments of area) have been increasingly used in a number of form/function studies, e.g., to reconstruct body mass or locomotor mode in fossil primates or to elucidate allometric scaling relationships among extant taxa. In the present study, we test whether these biomechanical section properties can be adequately esti- mated using biplanar radiographs, as compared to calculations of the same properties from computer digitization of cross-sectional images. We are par- ticularly interested in smaller animals, since the limb bone cortices of these animals may not be resolvable using other alternative noninvasive techniques (computed tomography). The test sample includes limb bones of small (25- 5,000 g) relatively generalized quadrupedal mammals?mice, six species of squirrels, and Macaca fascicularis. Results indicate that biplanar radio- graphs are reasonable substitutes for digitized cross-sectional images for deriving areas and second moments of area of midshaft femora and humeri of mammals in this size range. Potential application to a variety of questions relating to mechanical loading patterns in such animals is diverse. , C 1993 Wiley-Liss, Inc. Patterns of limb mechanical loading desirable to substitute radiographs for ac- should reflect positional behavior and body tual cross-sectional images because: (1) mass and, hence, have been the focus of there may be no convenient natural breaks many biomechanical studies. Since long and museum specimens may not be sec- bone diaphyses can be modelled as engineer- tioned, (2) CT may not be available and may ing beams (e.g., Huiskes, 1982), cross-sec- not produce sufficient resolution below a tional diaphyseal properties employed in certain size limit,1 and (3) X-ray machines beam analyses?areas and second moments are readily available at many institutions, of area?can be used to draw inferences re- including museums. Measurements of bone garding the mechanical loadings of limbs (Burr et al., 1981, 1982, 1989; Demes and Jungers, 1989; Lovejoy et al., 1976; Ruff, 1987; Ruff and Hayes, 1983a,b; Schaffler et Received D~??*" *? i?i; ??*#?! July ie. 1992. al., 1985) Ideally cross-sectional properties ^%TCZC a^uS'sZ 3 are Calculated through Computer dlgltiza- Medicine. 725 N. Wolfe St., Baltimore, MD 21205. tion of CrOSS-Sectional images from natural 'We have found that long bone cortices less than roughly 1 mm i_i .. ji i-ji thick are not well resolved by most CT scanners. The majority of breaks, sectioned bones, or computerized to- the specimens inc]uded in tnis studv (all of the mice and squir. mOgraphic (CT) images. However, it is Often rels. see below) had cortical thicknesses in this size range. ? 1993 WILEY-LISS, INC. 208 J.A. RUNESTAD ET AL. cortices from radiographs taken in mediolat- eral and anteroposterior orientations can be used to calculate section properties by using a simplified geometrical model?a circular or elliptical ring?and standard engineering formulae (e.g., Shigley, 1976). Such an ap- proach has been used in a variety of studies, including studies of living people and hu- man cadavers (Klenerman et al., 1967; Smith and Walker, 1964), human archeolog- ical and paleontological studies (Ben-Itzhak et al., 1988; Fresia et al., 1990), and studies of extant nonhuman primates (Demes and Jungers, 1989; Demes et al., 1991). Use of radiographs to estimate digitized section properties involves some extrapola- tion and assumptions regarding bone cross- sectional shape; however, the validity of such assumptions has been tested only for samples of human humeri (Fresia et al., 1990; Klenerman et al., 1967) and carnivore mandibles (Biknevicius and Ruff, 1992). The purpose of the present study is to compare biomechanical cross-sectional properties calculated from biplanar radiographs to those calculated by computer digitization of cross-sectional images of femora and humeri in smaller mammalian species in order to assess the utility of X-ray data in interpret- ing loading patterns in the long bones of small mammals. In addition, we address the question of whether a model taking into ac- count differing cortical thicknesses in oppo- site walls of long bones is more accurate than the more commonly used symmetrical hollow beam model. Biknevicius and Ruff (1992) found that an asymmetrical model better represented carnivore mandibular cross sections. MATERIALS AND METHODS Radiographs of associated femora and hu- meri of four lab mice averaging 25 g (Mus musculusposchiavinus bred toM. m. domes- ticus) and of two individuals for each of six sciurid species {Eutamias minimus, Glauco- mys volans, Tamias striatus, Spermophilus lateralis, Sciurus carolinensis, and Spermo- philus beecheyi), ranging between 41 and 729 g, from the Smithsonian Institution col- lections, were X-rayed in standard anterio- posterior and mediolateral views (Table 1). (Note that the body mass of an individual TABLE 1. Specimens and body masses' Specimens N Body Mass fg> lab mice 4 25 Eutamias minimus 2 41 Glaucomys volans 2 77 Tamias striatus 2 107 Spermophilus lateralis 2 180 Sciurus carolinensis 2 550 Spermophilus beecheyi 2 729 Macaca fascicularis, females 5 3240 Macaca fascicularis, males 3 4967 1 Mouse and macaque body masses are averages of individual weights. Sciurid masses are respective subspecies means of USNM collection. squirrel can vary considerably due to sea- sonal changes in fat storage. Therefore, sub- speciesmeans rather than individually asso- ciated weights are listed in Table 1.) The dimensions measured in this study were thicknesses of medial, lateral, anterior, and posterior cortices, as well external diame- ters in both planes. These distances were measured from X-ray images to a nominal precision of 0.001 mm using a Reflex Micro- scope (Reflex Measurement, Ltd.). This mi- croscope records the position of a central la- ser point in a set of Cartesian coordinates coupled to the movement of the stage. The X-ray images were positioned on a light box on the stage so that the transverse section to be measured was parallel to the transverse axis of the microscope. As the section was moved under the microscope (via stage movement) along the transverse axis, coor- dinate positions of the laser point were re- corded at periostea! and endosteal bound- aries. In this manner, periosteal and endosteal diameters, as well as cortical thicknesses, were measured. To calibrate the microscope, measurements of a glass stage micrometer were repeated eight times, showing a coefficient of variation of only 4% for a breadth of 0.05 mm. To test the preci- sion of the measuring process itself, radio- graphs of two epoxy resin bone-simulating phantoms (see Ruff and Leo, 1986, fn 9, p. 190) constructed to be in the size range of bones of the larger squirrels (outer diame- ters 5.3 and 3.5 mm and inner diameters 2.9 and 2.4 mm, respectively), were measured six times. These yielded CVs of less than 1% for repeated measurements of outer and in- ner diameters of both cylinders. For the ac- tual bone radibgraphic images used in the X-RAY MEASUREMENT OF CROSS-SECTIONAL GEOMETRY 209 a. symmetrical b. asymmetrical Fig. 1. Diagrams of symmetrical and asymmetrical cross sections. analysis, the average CV for >200 individ- ual breadths measured three times each was 2.4%. The lab mice and squirrel femora and bu- rner! were sectioned at or near midshaft and camera lucida images drawn of the result- ant cross sections (magnification 10-25 times). Using a modified version of the com- puter program SLICE (Nagurka and Hayes, 1980), the images were manually digitized and the geometric properties of the sections calculated (see Ruff and Hayes, 1983a). The results were then compared to calculations based on radiographic measurements taken with the Reflex Microscope. Radiographic and CT images of femora for five Macaca fascicularis females (average weight 3,240 g) and three M. fascicularis males (4,967 g) were included from a previ- ous study (Ruff, 1987). Due to their larger size, radiographic images of these speci- mens were manually measured to 0.1 mm, using needle-nose calipers. Using a symmetrical hollow beam model, outer (periostea!) and inner (endosteal or medullary) diameters were entered into standard engineering formulae for cortical area and second moments of area (e.g., Shig- ley, 1976). This model assumes that opposite cortical walls are of equal thickness as shown diagrammatically in Figure la (e.g., anterior and posterior walls are the same). Cortical area, CA (a measure of bone axial strength), is calculated as: AP stands for anteroposterior and ML for mediolateral. The second moment of area about the coronal plane (Ix) and that about the sagit- tal plane (Iy) are calculated as: Ix = it x ((ML outer diameter x AP outer diameter3) - (ML inner diameter x AP inner diameter3))/64 Iy = IT x ((AP outer diameter x ML outer diameter3) - (AP inner diameter x ML inner diameter3))/64 The polar second moment of area (J) is sim- ply Ix plus Iy. The term Ix is a measure of bending rigidity in the sagittal plane about a frontal axis, Iy is a measure of bending rigid- ity in the frontal plane about a sagittal axis, and J corresponds to torsional rigidity (Ruff and Hayes, 1983a). We also entered the radiographic mea- surements into formulae for an asymmetri- cal model that does not assume that opposite cortices are of equal thickness (see Fig. lb). (These formulae require considerable expla- nation and are thoroughly discussed in Biknevicius and Ruff, 1992, and are not listed here.) In addition, dummy cortical thicknesses were entered into the formulae, creating one sample with opposite cortical walls of equal thickness and another sample with walls up to twice as thick as opposite walls, keeping inner and outer diameters (and thus cortical areas) the same. This was done to test how dissimilar opposite walls can be before use of the more involved asym- metrical model provides any advantage. To test the strength of the relationship between digitized and estimated properties, calculations from biplanar radiographs were compared to those from SLICE using the least-squares regression technique (SYS- TAT: Wilkinson, 1989).2 Symmetrical model results were compared to asymmetrical model results using this technique as well. Coefficients of determination (i^'s) and per- CA = w x ((ML outer diameter x AP outer diameter) - (ML inner diameter x AP inner diameter))/4 2Use of a statistical mode! accounting for error in both axes, such as Model IIIRMA), produces identical results due to very high correlations (see below). 210 J.A. RUNESTAD ET AL. Table 2. Regression statistics of radiograph data vs. digitized cross-sectional data (as derived from SLICE program)' * Intercept Slope Comparison r2 SEE (std. err.) (std. err.) 3 z Humerus without macaques (N = 16): CO J 0.995 16 -0.064 (0.037) 0.999(0.019) E DC 0.993 20 -0;015 (0.048) 0.995 (0.023) ?fc IY 0.994 17 -0.115(0.042) 1.002 (0.020) ? 0 CA 0.991 10 -0.025 (0.027) 0.998 (0.025) 5 Femur with macaques W- 24): I J 0.998 16 -0.083(0.040) 1.030(0.011) i DC 0.994 28 -0.081 (0.058) 1.029 (0.017) o IY 0.998 15 -0.051 (0.034) 1.029 (0.010) 3 -z CA 0.995 12 -0.069 (0.034)* 1.043(0.015) Femur without macaques (N = 16): J 0.992 18 -0.085 (0.043) 1.032 (0.025) DC 0.975 33 -0.100(0.072) 1.005 (0.043) IY 0.994 16 -0.045 (0.037) 1.043 (0.022) ~* CA 0.985 12 -0.065 (0.035) 1.029 (0.034) 1J = polar second moment of area; DC = second moment of area about coronal axis; IY = second moment of area about sagittal axis; CA = cortical area. cent standard errors of estimate (%SEE's)3 were used to evaluate the accuracy with which radiographic estimates predicted dig- itized values. In addition, regression slopes close to one and intercepts close to zero were taken to indicate random rather than direc- tional (e.g., size-related) errors in estima- tion. Data were log-transformed because of the large size range involved (two orders of magnitude), i.e., to more equally weight smaller and larger specimens in the compar- isons. Femoral regressions were run with and without the macaques due to the differ- ent techniques employed in obtaining digi- tized cross-sectional data (rodent data came from camera lucida drawings, macaque data from CT images). RESULTS Regression statistics of radiographic data versus corresponding SLICE data (logged) are shown in Table 2. The i^'s are almost all 0.99 or better, with intercepts close to zero and slopes close to one. The %SEE's range ^Standard error of the estimate shows the overall accuracy with which a regression-derived formula predicts the value of Y from the value of X (Zar, 19841. The standard error is propor- tional to the magnitude of Y, the dependent variable. Division by the mean value of Y yields a unitless value, which multiplied by 100 gives 3 SEE. For logged data, as in most of this analysis, the log SEE is converted to a 9SEE following a procedure described by Smith (1984). 0.06 + 0.999x, r*2 . 0.995 ? 2 0 2 4 Log Humeral J from Radiograph Fig. 2. Humeral midshaft polar second moment of area (J) from radiograph vs. from SLICE in lab mice and squirrels. between 10% and 20%, except for Ix of the femur (28% with macaques, 33% without macaques). Judging from both the slope and intercept data, the errors in estimation of digitized (SLICE) properties are random rather than directional. Figure 2 illustrates the regression of humeral J values calcu- lated from radiographs on corresponding values from SLICE digitization. As shown in Table 2, none of the regression slopes for the humerus significantly differs from one, and only one of the intercepts for the humerus significantly differs from zero (by analysis of covariance; Zar, 1984). Figure 3 illustrates regression of femoral J values calculated from radiographs on corresponding values from SLICE digitization. Several of the re- gression slopes and intercepts of the femur shown in Table 2 depart significantly from one or zero, respectively, but all slopes are within 0.05 of one, and all intercepts are within 0.1 of zero. JVonlogged radiographic data were also considered and yielded results similar to the log-log analyses with i^'s of 0.99 or better, and %SEE's between 10% and 17% for corti- cal area and polar second moment of area. We consider the log-log results more rele- vant, however, because the nonlogged anal- X-RAY MEASUREMENT OF CROSS-SECTIONAL GEOMETRY 211 LU O E s ? 0.08 * 1.03X. r?2 - 0.S ? 2 0 2 4 6 8 Log Femoral J from Radiograph Fig. 3. Femoral midshaft polar second moment of area (J) from radiograph vs. from SLICE in lab mice, squir- rels, and macaques. TABLE 3. Symmetrical hollow beam model us. asymmetrical hollow beam model statistics' % Intercept Slope Comparison r2 SEE (std. err.) (std. err.) Humerus (N = 16): J 1.000 0.005 -0.004(0.0011 1.000(0.001) IX 1.000 0.012 -0.008 (0.003) 0.998(0.001) IY 1.000 0.005 -0.003(0.001) 1.001(0.001) Femur IN = 24): J 1.000 0.004 -0.004(0.001) 1.000 (0.000) K 1.000 0.005 -0.006(0.001) 1.000(0.000) IY 1.000 0.007 -0.002 (0.002) 0.999 (0.001) For abbreviations see Table 2: femoral data include macaques. yses tended to be driven by the data scatter of only the larger species. Results of the symmetrical/asymmetrical hollow beam model comparisons are shown in Table 3 (logged data). All r^'s are one, and none of the slopes are significantly different from one. Statistically, most of the inter- cepts (-0.008?0.002) are different from zero, but the standard errors are so small (0.001-0.003) that these differences are taken to be biologically insignificant. The tests with dummy cortical thick- nesses indicated that even asymmetry as great as two to one in thickness of opposite walls (greater than any asymmetry actually present in our bone specimens) had little ef- fect on calculation of second moments of area - r^'s were extremely close to one, slopes were within 0.1 of one, and intercepts were within 0.1 of zero. DISCUSSION Our results show that biplanar radio- graphs are reasonable substitutes for actual cross-sectional images in calculating the section properties (areas and second mo- ments of area) of long bone midshafts in small to medium-size mammals. This is con- sistent with the high correlations seen in the other two studies which have compared ra- diographically derived properties to those from digitized cross sections. For example, Fresia et al. (1990) found an r2 of 0.94 be- tween digitized and estimated polar second moments of area of human humeri (mid-dis- tal location), and Biknevicius and Ruff (1992) found mean percentage deviations of less than 10% for digitized and estimated second moments of area in mandibular sec- tions (asymmetric model). Results also indicate that the distribution of cortical bone, within single planes, is suf- ficiently symmetrical in the midregion of humeral and femoral diaphyses to warrant use of the simple hollow beam symmetrical formulae for calculation of cross-sectional geometric properties. This is perhaps not surprising as the regions of the bones sam- pled were, in fact, chosen because they are relatively regular, i.e., round or oval-shape. However, this is not necessarily true for other regions of the same bones (e.g., the proximal humerus) or other bones (e.g., the tibia), which are less symmetrical and/or regular in contour (Ruff, unpublished data). Biknevicius and Ruff (1992) found that the asymmetrical model better suited mandibu- lar cross sections in carnivores that are strongly asymmetrical in cortical bone dis- tribution. It also may not be valid to general- ize our results to other species with very prominent muscle crests, which would cause midshaft cross sections to depart notably from symmetrical elliptical shapes. An ex- ample of this would be the highly modified humeri of Oligocene palaeanodonts (proba- bly fossorial), which bear exaggerated mus- cle crests extending throughout the diaphy- ses (Rose and Emry, 1983). It is also important to note that maximum and mini- 212 J.A. RUNESTAD ET AL. mum second moments of area and their ori- entation can only be calculated from actual cross sections. However, for many applica- tions areas and second moments of area about anterior-posterior and medial-lateral axes are sufficient. In addition, as J equals the sum of Ix and Iy, torsional rigidity can be calculated from biplanar images. Other than basic measurement error and that inherent from relying on biplanar ra- diographs for calculation of cross-sectional properties, potential error sources here in- cluded the control (digitized) estimates themselves. The camera lucida images were made from cut surfaces, some of which were slightly crushed. The process of drawing the images is a less than perfect means of repro- ducing sections. Digitization of the images is also subject to error. In addition, CT scan resolution decreases with bones as small as macaque femora. Given these other error sources, the data scatter between digitized and estimated properties is remarkably small (Figs. 2, 3). As radiography is nondestructive and generally accessible, the use of biplanar ra- diographs to estimate biomechanical cross- sectional properties in long bone diaphyses has considerable potential for diverse appli- cations. The technique is applicable to both extant and fossil specimens, and is limited to neither larger specimens nor those with natural breaks. ACKNOWLEDGMENTS The authors thank Linda Coley of the Smithsonian Institution for technical assis- tance, Dr. Hannah Grausz of Johns Hopkins University for providing lab mice, Dr. Ken Rose of Johns Hopkins University for loan of micrometer and dissecting microscope, the Smithsonian Institution Department of Mammals for access to collections, the Smithsonian Institution Department of Ich- thyology for radiographic facilities, the Scholarly Studies Program of the Smithso- nian Institution, the Summer Intern Pro- gram of the Smithsonian Institution, and the Johns Hopkins University Department of Cell Biology and Anatomy for funds made available to J.A.R. for supplies and travel related to the project. LITERATURE CITED Ben-ltthak S, Smith P, and Bloom RA 0988) Radio- graphic study of the humerus in Neandertals and Homo sapiens sapiens. Am. J. Phys. Anthropol. 77:231-242. Biknevicius AR, and Ruff CB (1992) Use of biplanar radiographs for estimating cross-sectional geometric properties of the mandible. Anat. Rec. 232.157-163. Burr DB, Piotrowski G, and Miller GJ 0981) Structural strength of the macaque femur. Am. J. Phys. Anthro- pol. 54:305-319. Burr DB, Ruff CB, and Johnson C (1989) Structural adaptations of the femur and humerus to arboreal and terrestrial environments in three species of macaques. Am. J. Phys. Anthropol. 79:357-367. Burr DB, Piotrowski G, Martin RB, and Cook PN (19821 Femoral mechanics in the lesser bushbaby (Galago senegalensis): Structural adaptations to leaping in primates. Anat. Rec. 202:419-429. Demes B, and Jungers WL (1989) Functional differenti- ation of long bones in lorises. Folia Primatol. 52:58- 69. Demes B, Jungers WL, and Selpien K (1991) Body size, locomotion and long bone cross-sectional geometry in indriid primates. Am. J. Phys. Anthropol. 56:537-547. Fresia AE, Ruff CB, and Larsen CS (1990) Temporal decline in bilateral asymmetry of the upper limb on the Georgia Coast. In CS Larson led.): The Archaeol- ogy of Mission Santa Catalina de Guale: 2. BioeulturaJ Interpretations of a Population in Transition: Anthro- pological Papers of the American Museum of Natural History, pp. 121-150. Huiskes R (1982) On the modelling of long bones in structural analyses. J. Biomech. 75:65-69. Klenerman L, Swanson SAV, and Freeman MAR (1967) A method for the clinical estimation of the strength of a bone. Proc. R. Soc. Med. 67:850-854. Lovejoy CO, Burstein AH, and Heiple KG (1976) The biomechanical analysis of bone strength: A method and its application to platycnemia. Am. J. Phys. An- thropol. 44:489-506. Nagurka ML, and Hayes WC (1980) An interactive graphics package for calculating cross-sectional prop- erties of complex shapes. J. Biomech. 73:59-64. Rose KD, and Emry RJ (1983) Extraordinary fossorial adaptations in the Oligocene palaeanodonts Epoico- therium and Xenocranium (mammalia). J. Morph. 775:33-56. Ruff CB (1987) Structural allometry of the femur and tibia in hominoidea and Macaco.. Folia Primatol., 46:9-49. Ruff CB, and Hayes WC (1983a) Cross-sectional geome- try of Pecos Pueblo femora and tibiae?a biomechani- cal investigation: I. Method and general patterns of variation. Am. J. Phys. Anthropol. 60:359-381. Ruff CB, and Hayes WC (1983b) Cross-sectional geome- try of Pecos Pueblo femora and tibiae?a biomechani- cal investigation: II. Sex, age, and side differences. Am. J. Phys. Anthropol. 60:383-400. Ruff CB, and Leo FP (1986) Use of computed tomogra- phy in skeletal structure research. Amer. J. Phys. An- thropol. 29:181-196. X-RAY MEASUREMENT OF CROSS-SECTIONAL GEOMETRY 213 Schaffler MB, Burr DB, Jungers WL. and Ruff CB Smith RW, and Walker RR (1964) Femoral expansion in (1985) Structural and mechanical indicators of limb aging women: implications for osteoporosis and frac- specialization in primates. Folia Primatol. 45:61-75. tures. Science 145:156-157. Shiglev JE (1976) Applied Mechanics of Materials. New Wilkinson L (19891 SYSTAT: The System for Statistics. York: McGraw-Hill. Evanston, IL.: SYSTAT. Smith RJ(1984 lAllometric scaling in comparative biol- Zar JH (1984) Biostatistical Analysis, 2nd Ed. Engle- ogy: Problems of concept and method. Am. J. Physio). wood Cliffs, NJ.: Prentice-Hall. 256.152-160.