AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 68: 225-232 (1985) Computed Tomography and Automated Image Analysis of Prehistoric Femora DALE R. SUMNER, BRENT MOCKBEE, KATHLEEN MORSE, THOMAS CRAM, AND MICHAEL PITT Department of Orthopedic Surgery, Rush Presbyterian St. Luke’s Medical Center (0.R.S.), Chicago, Illinois 60612, Department of Radiology (B.M., M.P.), University of Arizona, Tucson, Arizona 85724, and Interactive Graphics Engineering Laboratory (K.M., TC.), University ofArizona, Tucson, Arizona 85721 KEY WORDS Femur, Cross-sectional geometry, Biomechanics, Computed tomography, Morphology ABSTRACT Non-invasive characterization of limb bone cross-sectional geometry would be useful for biomechanical analyses of skeletal collections. Computed tomography (CT) is potentially the method of choice. Additionally, CT images are suitable for automated analysis. CT is here shown to be both accurate and precise in the analysis of cross-sectional geometry of prehistoric femora. Beam hardening artifacts can be reduced by using a water bath. As the availability of CT for research increases, both bone density and geometry could be determined simultaneously with this method. Biomechanical analysis of skeletal morphology is becoming more common in anthropology. Characterization of long bone crosssectional geometry is critical to this approach. Cross-sectional geometry has now been studied in humans (Ruffand Hayes, 1983a; 1983b; and references cited therein), non-human primates (Burr et al., 1981; 1982) and in other species (Rybicki et al., 1977; Piotrowski et al., 1983). Cross-sectional geometric properties of relevance to biomechanics include cortical area, area moments of inertia and the position of the principal axes (Fig. 1).The spatial distribution of bone tissue can also be quantified by constructing two ratios: IXAY and IMAW IMIN. The biomechanical significance of these properties has been discussed previously in the anthropology literature (see references cited above). Anthropologists are interested in variability and because of their access to large skeletal collections have the ability to assess the effects of factors such as age and sex on intrapopulational variability. This approach has been particularly useful in the analysis of changes in cross-sectional geometry associated with aging. For instance, Ruff and Hayes (1982) were able to corroborate the hypothesis of Smith and Walker (1964) that 0 1985 ALAN R. LISS, INC. subperiosteal expansion compensates for loss of bone mineral in aging in males and females. Studies of cross-sectional geometry are restricted by the limited number of skeletal samples which can be physically sectioned. Non-destructive methods of skeletal analysis include radiogrammetry, photon absorptiometry and computed tomography. Radiogrammetry has well-known limitations (Cohn, 1981). Photon absorptiometry has been adapted to calculating the cross-sectional moment of inertia about the anteroposterior and mediolateral axes (Martin and Burr, 1984). This technique is non-invasive and potentially accessible to many researchers. A disadvantage is that not all aspects of the bone’s cross-sectional geometry are available. Cortical area and medullary area can be determined, but the location of the principal axes and the magnitude of the moments of inertia about these axes remain unknown. Computed tomography (CT) appears to be the method of choice. Computed tomography is well-suited to quantitative morphology (Robb, 1982; Tate and Cann, 1982).The basic principle of CT is Received November 28, 1984; revised May 3, 1985; accepted May 22, 1985. 226 D.R. SUMNER ET AL. Ix = f y 2 d A A Iy = jx2dA Ixy = /xydA J = jr2dA IP B IA major axis IMAX = 7 7 lYtlX -k Ixy2t-!-(Iy- Ix) minor axis IP Fig. 1. Cross-sectional geometry. A) Second moments of area about the AP (IX) and ML (IY) axes, the cross product (IXY) and the polar moment of inertia (3.B) Location of the principal axes and formulae used to cal- culate the maximum (IMAX) and minimum (MMIN)principal second moments of area. Redrawn after Martin and Atkinson (1977) and Nagurka and Hayes (1980). that with multiple angular projections “the amount of attenuation of each square of tissue can be calculated knowing only the amount of attenuation of the beam as it passes completely through the body” (Winter and King, 1983:8). In most commercially available scanners a n X-ray tube is rotated around the body, numerous projections are obtained and mathematical techniques are used to reconstruct a cross-sectional image (Robb, 1982). The image is called a slice, but actually represents the distribution of X-ray attenuation in a series of volume elements (voxels). The computer stores a “CT number” for each voxel. These numbers are assigned values on a grey scale and the image can, therefore, be displayed on a monitor. CT images of dense objects may be distorted due to beam hardening. Beam hardening refers to preferential absorption of the lower energy X-rays of the polyenergetic beam (Robb, 1982). The beam, therefore, becomes more penetrating as it passes through a n object. Beam hardening is linear for soft tissues, but is nonlinear for dense objects such as bone. Reconstruction software can correct for some of the beam hardening distortion. The purpose of the present paper is to describe our application of CT to the study of cross-sectional geometry in prehistoric femora. In particular, use of a water bath to reduce beam hardening artifacts and the advantage of automated image analysis for enhancing precision are documented. MATERIALS AND METHODS The approach reported here couples automated image analysis with CT (Fig. 2). Three phases of data collection and reduction are recognized. Digital images are obtained with CT. These images are then processed and the data are reduced to a series of x,y coordinates which describe the subperiosteal and endosteal perimeters. Each image could be characterized in a number of ways. Here, the emphasis is on the cross-sectional properties described in the Introduction. Two experiments were done. First, the effect of beam hardening on accuracy was determined. Second, the precision of a n automated image analysis protocol was assessed. CT AND CROSS-SECTIONAL GEOMETRY Digital image Processing Computed Tomography 227 Image Characterization MFlNlTlON IMAGES COORDINATES CROSS-SECTIONAL GEOMETRY Fig. 2. Scheme of the analysis system. Scan technique A General Electric CTPT 8800 whole body scanner was used. The bones were scanned using 320 mPA, a tube potential of 120 kVp, 576 views per slice and a slice thickness of 1.5 mm. The images were reconstructed with the “bone” algorithm and, when analyzed on the CT monitor, a window level of 100 and a window width of 1,000 were used. Archaeologically derived whole femora and diaphyseal segments were placed in a plexiglass box filled with water (except a s noted below). Each intact femur was set in a standard position and sampled at 20%) 35%)50%) 65%, and 80% of its diaphyseal length. The diaphyseal segments were oriented in a n analogous fashion and one image was obtained from each segment. All slices were obtained perpendicular to the long axis of the diaphysis. Digital image processing We developed a n outlining routine for automated tracing of the subperiosteal and endosteal borders (following Keller et al., 1981). Although the outlining algorithm itself is strictly deterministic, neither Keller et al.’s method for generating the seed pixel nor ours is deterministic. Our method uses a root mean square calculation of a region known to be in the water bath to find the threshold CT value required by the outlining algorithm. Localization in the transverse plane and scaling were achieved by interactively locating the inside corners of the water box with the cursor on the monitor. The location of the slice in the longitudinal sense was known from the CT position indicator. Image characterization Cross-sectional image analyses were done on the CT monitor or with a Vicom digital im- age processor. The CT monitor was used to measure subperiosteal and endosteal diameters. The image processor was used for measuring the geometric properties described above, using the automatic outlining algorithm to define the bone’s edges. The x,y coordinates of the subperiosteal and endosteal boundaries were supplied to the “SLICE” computer program (Nagurka and Hayes, 1980) which calculated the cross-sectional geometric properties shown in Figure 1. Accuracy (beam hardening experiment) An experiment was performed to determine if a water bath were necessary to improve accuracy (i.e., reduce beam hardening artifacts) and, if so, to assess the effects of differential filling of the medullary cavity with water. Six diaphyseal segments from skeletally mature prehistoric femora of unknown provenience were scanned under three conditions: 1)in air, 2) in a water bath, but with no water in the medullary cavity, and 3) in a water bath with water in the medullary cavity. The segments were not repositioned between scans. Modelling clay caps were used to obstruct the medullary cavity during the first two scans. These caps were carefully removed before the third scan. Subperiosteal and endosteal anteroposterior (AP) and mediolateral (ML) diameters were measured interactively on the CT monitor using software for measuring distances within images and on the actual specimens with a Helios dial caliper. In addition, the crosssectional geometric properties described in Figure 1 were calculated and compared for the latter two scan conditions. Precision experiments Two precision experiments were performed. First, for each of 28 individuals used in a growth and aging study (Sumner, 1984), 228 A B Figure 3. 229 CT AND CROSS-SECTIONAL GEOMETRY C Fig. 3. An AP diameter measured on the CT monitor. The same section is shown A) scanned in air, B) scanned in water, but with no water in the medullary cavity, and C) scanned fully immersed. The magnitude of the AP diameter is indicated in the lower right corner of each image. one of the five scan locations was outlined twice to assess the precision error of the outlining routine. Second, three pairs of femora were CT scanned on two separate occasions to assess the overall precision error of the combined CT-Vicom system. The femora were from one subadult between five and six years old, one 25 to 29 year old male and one 45 to 49 year old female. Each scan site was treated as a separate case to increase the sample size. Two images could not be analyzed, resulting in a sample of 28 images. and sign tests were used to assess the statistical significance and directionality of the error. RESULTS Accuracy The subperiosteal diameters were easily defined, but comparability of the endosteal diameters as measured on the CT monitor and the actual sections with the dial caliper was problematic because the endosteal border was difficult to define. The magnitude of the error was small for all three techniques Statistical evaluation for subperiosteal diameters (Table 1). The Accuracy and precision were calculated magnitude of the errors reported in Table 1 with the following formula: represents about .5 mm, which approaches the resolution of CT. The important finding lmeasurement 1 - measurement 21 100 was that the use of a water bath eliminated (measurement 1 + measurement 2Y2 directionality in the error for subperiosteal diameters. When the water bath was not Thus, accuracy and precision were calculated used, the subperiosteal diameters were conas the absolute magnitude of the difference sistently underestimated. This phenomenon between paired measurements. Paired t tests is illustrated in Figure 3. The medullary 230 D.R. SUMNER ET AL. TABLE I . Accuracy of computed tomography' Scan method' Subperiosteal diameters %Error3 Ties 1.9* 1.7 1.0 1 2 3 11 4 5 + Endosteal diameters % Error3 Ties 5.1* 5.1* 4.6* 1 8 7 0 0 0 1 2 2 0 1 1 + 11 9 9 'Mean percent errors for AP and ML subperiosteal and endosteal diameters are presented (n = 6 sections, with 1 AP and 1 ML subperiosteal diameter and 1 AP and ML endosteal diameter per section). The "-"sign indicates that the CT measurement was smaller than the caliper measurement. '1) Scanned in air; 2) scanned in water, but with no water in medullary cavity; 3) scanned in water, with water in the medullary cavity. 3Paired t test. * P < .05. TABLE 3. Precision error for the digital image Drocessine svstem' TABLE 2. Effect of water in medullary cavity on calculated cross-sectional geometric variables' Variable AREA IX IY IXnY IMAX IMIN IMAXnMIN THETA J % Error2 - Ties + Variable % Error2 10.2 12.6 9.1 4.0 9.1 13.0 4.0 13.4 10.8 3 1 4 0 0 0 0 0 0 0 1 1 AREA IX IY IXAY IMAX IMIN IXAY THETA 0.8 1.4 1.7 0.6 1.4 1.6 0.6 0.3 3 3 3 4 1 0 4 0 2 2 2 1 4 5 1 'Mean percent errors are presented for sections scanned 1) in a water bath with no water in the medullary cavity and 2) in a water bath with water in the medullary cavity (n = 5).The " - " sign indicates that the condition 1 measurement was less than the condition 2 measurements. 'Paired t tests: no significant differences. 'Mean percent errors are presented (n = 28). 2Paired t tests: no significant differences. TABLE 4. Precision error for the entire cross-sectional geometric protocol' Variable canal diameters were consistently overestimated, and this error was not corrected by using a water bath. Table 2 shows the results for comparison of the calculated geometric properties scanned in a water bath but without filling of the medullary cavity and with the sections totally immersed. The sample size is five rather than six because one of the cross-sectionswas not analyzable (due to a faulty hard disk area). These results show that differential filling of the medullary cavity caused an error of 4 to 13.4 percent. The area-dependent variables (AREA, IX,IY, IMAX, IMIN,J) tended to be underestimated when water did not fill the medullary cavity. AREA IX IY IXnY IMAX IMIN IMAX/IMIN THETA J % Error2 2.6 3.3 4.3 3.6 3.5 3.3 1.9 29.3 3.3 'Mean percent errors are presented (n = 28). 2Paired t tests: no significant differences. indicated that Scan location had no effect on this error. Precision error inherent in the entire protocol was evaluated by rescanning three individuals. The results are shown in Table 4. Precision The precision error was low for all variables Precision error inherent in the Vicom sys except THETA, the angle between the ML tem is summarized in Table 3. The source of axis and the principal major axis. Slight rethis error was differential positioning of the positioning errors affect THETA of cylindricursor in either corner of the water bath. The cal sections because the location of the error was remarkably small and statistically principal axes is somewhat arbitrary in these insignificant. One-way analysis of variance sections. CT AND CROSS-SECTIONALGEOMETRY DISCUSSION The accuracy of this system, as assessed by comparison of CT monitor measurements and dial caliper measurements on the actual specimens, is adequate for morphological research. Although the water bath reduced the error for subperiosteal diameters by less than one percent, it randomized the error with respect to direction. Error at this surface is particularly important because of the manner in which area moments of inertia are calculated (see Fig. 1).Therefore, use of a water bath or some other soft tissue equivalent is recommended when accuracy of measurement is the goal. A disadvantage of the water bath is that it introduces another source of error, differential filling of the medullary cavity. We did not test the accuracy of the system with the complete battery of variables used in the precision tests. Such verification procedures would require digitization of photographs or contact radiographs of the cut crosssections and comparison of the calculated geometric properties with those obtained by CT and automated outlining. Additionally, the effect of bone size on accuracy was not considered. The reproducibility of the measurement technique was very high and was only slightly reduced by repositioning. Precision of CT for bone geometry was also considered by Isherwood et al. (1976) in a n in vivo study. As might be expected, these authors had precision errors larger than those reported in the present (in vitro) study. Automated analysis of the digital images avoids other problems with CT, such a s defining the proper window level and width settings and hard copy distortion (Ruff and Leo, 1985), in addition to enhancing precision. Computed tomography can also be used to measure bone mineral content and density (Revak, 1980; Genant et al., 1981). Bone density is related to the strength and stiffness of the tissue (Carter and Hayes, 1976; 1977). Therefore, computed tomography has the potential to determine bone geometry and infer material properties. This is significant because the biomechanical behavior of a bone depends upon geometric and material properties (Carter and Spengler, 1978) and this behavior can be modeled from a n engineering perspective if loading conditions are assumed (Rybicki, 1980). The ability to perform engineering analyses of bones based on data obtained with computed tomography is important. Anthropologists could use this technique to under- 231 stand variation in mineral distribution and geometry within and between species. Experimentally and clinically, the causes and consequences of bone remodeling due to altered mechanical environments could be explored in longitudinal research designs. CONCLUSIONS Computed tomography is admirably suited to quantitative morphology for four reasons. First, it is non-destructive to the sample of interest. Second, it is accurate and precise. Third, it is easily adapted to automated image analysis. Finally, computed tomography could provide the necessary' geometric and material property data needed for engineering analyses. ACKNOWLEDGMENTS This work was done at the University of Arizona with the aid of a Comins Grant from the Department of Anthropology to D.R.S. Medinet, Inc. graciously donated software and machine time on the Vicom system. This paper was written with the support of NIH Grant AM07375. LITERATURE CITED Burr, DB, Piotrowski, G , Martin, RB, and Cook, PN (1982) Femoral mechanics in the lesser bushbaby (Galago senegalensis): structural adaptations to leaping in primates. Anat. Rec. 202~419-429. Burr, DB, Piotrowski, G, and Miller, GJ (1981) Structural strength of the macaque femur. Am. J. Phys. Anthrop. 54~305-319. Carter, DR, and Hayes, WC (1976) Bone compressive strength: the influence of density and strain rate. Science 194~1174-1176. Carter, DR, and Hayes, WC (1977) The compressive behavior of bone as a two-phase porous structure. J. Bone Joint Surg. 59-A:954-962. Carter, DR, and Spengler, DM (1978) Mechanical properties and composition of cortical bone. Clin. Orthop. 135:192-2 17. Cohn, SH (ed.) (1981) Non-invasive Measurements of Bone Mass and their Clinical Application. Boca Raton, Florida: CRC Press. Genant, H, Boyd, D, Rosenfeld, D, Abols, Y, and Cann, CE (1981) Computed tomography. In SH Cohn (ed): Non-Invasive Measurements of Bone Mass and their Clinical Application. Boca Raton, Florida: CRC Press, pp. 122-149. Isherwood, I, Rutherford, RA, Pullan, BR, and Adams, PH (1976) Bone-mineral estimation by computer-assisted transverse axial tomography. Lancet 2~712-715. Keller, JM, Edwards, FM, and Rundle, R (1981) Automatic outlining of regions of CT scans. J. Comp. Asst. Tomog. 5~240-245. Martin, RB, and Atkinson, PJ (1977) Age and sex-related changes in the structure and strength of the human femoral shaft. J. Biomech. 10:223-231. Martin, RB, and Burr, DB (1984)Non-invasive measurements of long bone cross-sectional moment of inertia by photon absorptiometry. J. Biomech. 17~195-201. Nagurka, ML, and Hayes, WC (1980) An interactive 232 D.R. SUMNER ET AL. graphics package for calculating cross-sectional properties of complex shapes. J. Biomech. 23t59-64. Piotrowski, G, Sullivan, M, and Colahan, PT (1983)Geometric properties of equine metacarpi. J. Biomech. 26t129-139. Revak, CS (1980) Mineral content of cortical bone measured by computed tomography. J. Comp. Asst. Tomog. 4:342-350. Robb, RA (1982) X-ray computed tomography: an engineering synthesis of multiscientific principles. CRC Critical Reviews in Biomedial Engineering 7t265-333. Ruff, CB, and Hayes, WC (1982)Subperiosteal expansion and cortical remodeling of the human femur and tibia with age. Science 217t945-948. Ruff, CB, and Hayes, WC (1983a) Cross-sectional geometry of Pecos Pueblo femora and tibiae-a biomechanical investigation: I. Method and general patterns of variation. Am. J, Phys. Anthrop. 6Ot359-381. Ruff, CB, and Hayes, WC (198313)Cross-sectional geometry of Pecos Pueblo femora and tibiae-a biomechanical investigation: 11. Sex, age, and side differences. Am. J. Phys. Anthrop. 60:383-400. Ruff, CB, and Leo, FP (1985) Use of CT scanning in skeletal structural analysis. Am. J. Phys. Anthrop. 66:223 (abstract). Rybicki, EF (1980) The role of finite element models in orthopedics. In BR Simon (ed): International Conference on Finite Elements in Biomechanics. Vol. 1. Tucson: pp. 21-25. Rybicki, EF, Mills, EJ, and Turner, AS (1977)In uivo and analytical studies of forces and moments in equine long bones. J. Biomech. IOt701-705. Smith, RW, and Walker, RR (1964) Femoral expansion in aging women: implications for osteoporosis and fractures. Science 145156-157. Sumner, DR, (1984) Size, shape and bone mineral content of the human femur in growth and aging. Ph.D. thesis, University of Arizona. Tate, JR,and Cann, CE (1982)High-resolution computed tomography for the comparative study of fossil and extant bone. Am. J. Phys. Anthrop. 58:67-73. Winter, J, and King, W (1983) Basic principles of computed tomography. In M Greenberg, BM Greenberg, and IM Greenberg (eds): Essentials of body computed tomography. Philadelphia: W.B. Saunders Company, pp. 1-23.