TECHNICAL NOTE Computed Tomography and Biomechanical Analysis of Fossil Long Bones WILLIAM L. JUNGERS ' AND R. J. MINNS ' Department of Anatomical Sciences, Health Sciences Center, State University of New York at Stony Brook, Stony Brook, New York 11 794 and Department of Engineering Science, University of Durham, Durham, DHI 3LE, England KEY WORDS Computed tomography Biomechanics - Fossil long bones . Cross-sectional geometry . ABSTRACT Computerized transverse axial scanning (computed tomography) is a relatively new radiographic technique designed to recover precise cross-sectional images (tomograms) of 3-dimensional objects. This highly sensitive process permits tissues of similar density to be separated and displayed unambiguously. These special features are, therefore, ideal for analyzing the cross-sectional geometry of intact fossil long bones, even when they are highly mineralized and their medullary cavities are occluded by matrix. In order to demonstrate the utility of this method in assessing the complex relationship between fossil structure and probable function, geometrical and biomechanical properties of midshaft tomograms of femora and tibiae have been analyzed for a comparative primate sample consisting of Megaladapis edwardsi (an extinct giant prosimian from Madagascar), Zndri indri (the largest extant prosimian), and Homo sapiens. The diaphyseal form of a given adult long bone results from a complex interaction between tissue deposition and resorption (Enlow, '63; Hoyte and Enlow, '66; Frost, '63, '73). Local mechanical stresses and strain in bone are believed to figure prominently in this remodelling process (Currey, '68; McElhaney, "70; Amtmann, '71; Liikova and Heit, '71; Lanyon and Baggot, '76). The general notion that bone tissue is deposited in proportion to mechanical loads and is resorbed in the absence of such stresses is known as Wolff's Law. A more precise statement of these relationships has recently been formulated by Lovejoy e t al. ('761, who suggest t h a t the final form of any long bone represents: an expression of remodelling to prevent strains in excess of the elastic limit under external loading figurations t o which it is accustomed. (p. 489) Analyses of cortical bone distribution in diaphyseal cross-sections tend to support this proposition, inasmuch as the amount and spatial orientation of cortical bone appear to enhance flexural and torsional strength in close correspondence to habitual loading patAM. J. PHYS. ANTHROP. (1979)50: 285-290 terns (Frankel and Burstein, '65; Pauwels, '68; Preuschoft, '71; Kummer, '72; Badoux, '73; Amtmann, '78). Lovejoy et al. ('76) have recently extended formal biomechanical analysis of tubular bones to archeological specimens of Amerind tibiae. Because the resilience of these specimens could not be tested dynamically, they were instead sectioned a t regular intervals, and the theoretical bone strength against bending and torsion was calculated for each section. Judicious application of such analytical techniques allows one to make "comparisons of different locomotor and stress patterns upon t h e same skeletal link" (Lovejoy et al., '76: p. 4891. Employment of this methodology in the mechanical assessment of fossil long bones has been limited to date to fortuitous breaks or fragmentary specimens (e.g., Preuschoft and Weinmann, '731, since postcranial remains of fossils are usually too rare to be sacrificed by sectioning. We offer here a new methodology for assessing the mechanical characteristics and crosssectional geometry of fossil long bones with- 285 286 WILLIAM L. JUNGERS AND R. J. MINNS out damaging intact specimens. Computerized transverse axial scanning (computed tomography) is a relatively new radiological tool that recovers “slices” of any given 3-dimensional subject. The object is scanned in successive layers from a multitude of angles by a narrow beam of X-rays; absorption values of the material across a particular layer are computed and used to construct a picture of the internal structure in cross-section (Ambrose, ’73; Hounsfield, ’73). The high sensitivity of tomography permits tissues of similar density to be separated and displayed unambiguously. This special feature is of considerable value when fossils are heavily mineralized and the medullary cavity is occluded by matrix. The system used in this study is t h e EM1 5005 Whole Body Scanner of t h e Radiology Department, Carle Clinic (Urbana, Illinois). Description of this equipment and additional details of the technique are described in a review article by New et al. (‘74). The fossil specimens used to demonstrate the utility of computed tomography are hindlimb elements of an extinct giant lemuroid of Madagascar, Megaladapis edwardsi. The fossil sample includes a femur and tibia from Lamboharana and a tibia from Ampoza; all three bones are intact and exhibit varying degrees of mineralization and medullary cavit y occlusion. The hindlimb morphology of Megaladapis departs dramatically from that of all closely related extant forms, and has been suggested to be adapted to resist substantial transverse bending moments (Jungers, ’77). For comparative purposes a femur and tibia of an Zndri indri, the largest living prosimian, and a femur and tibia of a female Homo sapiens were included in the analysis. All seven specimens were wrapped in cushions containing polyvinylchloride beads in order to eliminate potential computer artifact caused by the interposition of air between specimens and scanner. Each specimen was scanned a t midshaft with a scan time of 24 seconds and a computer reconstruction time of 80 seconds. Scaled tracings were then made of t h e tomograms, which were subsequently photographed (fig. 1; anatomical axes indicated by the X and Y arrows). The following geometrical and mechanical properties of each cross-section were calculated using a method of graphical integration by a GRAPHINT computer program (Minns et al., ‘75): a. Total area of cortical bone; b. The coordinates of the centroid of the section with respect to a fixed set of axes (the anatomical axes in this case, XX and YY); c. The second moments of area, Z (or area moments of inertia), around the anatomical axes and principal axes, X’X’and Y’Y’ (axes of minimum and maximum I depending on the shape of the given section); d. The product moment of inertia with respect to XX and YY axes (Ixy) ; e. The polar second moment of area, J (or polar moment of inertia), about the centroidal axis. The angle (0) between the anatomical and principal axes was computed from the relationship, tan 20 = 2 Ixy Ixx-Iyy ~ X 1 Y Fig. 1 Midshaft tomograms of fossil and extant primate long bones: A, human femur; B, human tibia; C, lndri indri femur; D,lndri indri tibia; E, Megaladapis edwardsi femur; F and G , Megaladapis edwardsi tibiae. Anatomical axes are indicated by X and Y arrows. Cortical bone is shown by parallel hatching. TOMOGRAPHY AND FOSSIL LONG BONES 287 TABLE 1 Geometrical properties of midshaft cross sections Section lcm') Area IYY (cm4) Ixx (cm') A B D 3.086 1.920 0.910 0.706 F G 3.206 2.860 1.420 0.463 0.106 0.048 3.238 1.560 1.398 1.408 1.245 0.120 0.124 1.296 0.969 0.705 C E I 4.311 0.078 -0.184 -0.009 0.018 0.073 0.318 0.283 J IY'Y' Icm') Ix'x' (cm'J (cm4) 0' (radians) 1.492 0.422 0.102 0.044 3.241 1.699 1.499 1.336 1.286 0.124 0.128 1.293 0.831 0.603 2.828 1.708 0.226 0.171 4.534 2.529 2.103 -0.733 -0.218 -0.436 0.222 -0.035 -0.408 -0.340 IXY (cm') Clockwise rotation is positive; counterclockwise rotation is negative Y , Y' 10mm 1 Fig. 2 Midshaft tomogram of female human tibia. The centroid of the section occurs at the intersection of the anatomical axes, XX and YY. The principal axes, X'X' and Y Y ' (axes with maximum and minimum area moments of inertia in this case), are shown in relation to the anatomical axes. @ is the angle between principal and anatomical axw. Summary data of these mechanical characteristics for each section is presented in table 1. Angle 0 and its spatial relationship t o the anatomical and principal axes are illustrated for the midshaft section of the human tibia (fig. 2). Detailed derivations of these geometrical properties can be found in standard textbooks on mechanics or strength of materials. Stresses developed in a given section below the elastic limit of bone are inversely proportional to the magnitude of the area moment of inertia about its principal axes (Wainwright et al., '76). As Lovejoy et al. ('76) point out, therefore, one indication of t h e bending strength of a given cross-section is its area moment of inertia. Axial stresses are more simply inversely proportional to total cortical area. If, however, one wishes t o consider the 288 WILLIAM L. JUNGERS AND R . J. MINNS bending moment each bone can tolerate up to the occurrence of plastic deformation as the primary index of strength, it is necessary to consider an additional variable, c, the perpendicular distance from a given principal axis to the most distant fiber from that axis. This is accomplished by calculating t h e section modulus, Ilc, about both principal axes (table 2). Finally, it is necessary to normalize the section modulus by some power of the bone's length if one is to compare relative strengths of tubular bones of different lengths. We have adopted the procedure of Lovejoy et al. ('76) for this normalization by dividing the section modulus by the bone's length squared (table 2). Relative to those of Megaladapis, the femora and tibiae of Homo sapiens and Indri indri are markedly weaker regardless of which principal axis is considered. This discrepancy is due in part to the considerable girth of the Megaladupis specimens coupled with pronounced reduction in their length (Jungers, '77). The more nearly circular crosssections of the human and Indri femora have comparable bending strengths about each of their principal axes, while the Megaladapis femur exhibits clearly superior strength in the transverse plane. The human and indriid tibiae are relatively stronger in their anteroposterior planes, while the tibiae of Megaladupis are similar to its femur in being much more resilient in the mediolateral plane. These results support the suggestion (Jungers, '77) that given the unusual inversion of the tibia on the femur at the knee of MegaZadapis, these hindlimb elements are especially well-adapted to resist transverse bending moments. It is also suggested here that the superior anteroposterior strength of the Indri TABLE 2 Section moduli and relatiue bendingstrengths Section modulus Section A B C D E F G Relative strength Ix'x' ly'y' 106 Ix'x' lob - C C c L' c L' 1.194 0.509 0.162 0.095 1.927 1.174 1.040 1.059 0.882 0.175 0.168 1.249 0.829 0.703 I~,,,, - - 8.628 4.062 2.517 1.749 39.029 36.074 43.344 7.653 7.038 2.719 3.095 25.297 25.473 29.299 c, perpendicular distance from a given axis t o most distant point from that axis. L, maximum length of a given element. tibia (compared to that in the mediolateral plane) is an adaptation to resist leaping-related stresses induced by muscular and substrate loading during takeoff and landing, and is not due solely t o the hypertrophy of the tibialis anterior muscle (Vallois, '12). The functional significance of diaphyseal form in human femora and tibiae has been considered in detail elsewhere (Amtmann, '71; Kimura, '74; Lovejoy et al., '76; Piziali et al., '76). Computed tomography extends the methodological scope of analysis of fossil primate remains which Lovejoy ('78) has classified as type 111: "the mechanical assessment and comparison of the specimen with analogous structures of extant animals." We submit that there is frequently a close relationship between this type of analysis and Lovejoy's category 11: "morphological comparisons including simple metric studies." As a case in point, we compared midshaft indices of anteroposterior diameterimediolateral diameter for our series of long bones to the ratios of Ix 'x '/Iy'y'. The second ratio indicates in which plane a given tubular bone is r e l a t i d y more resistant to bending moments. A bivariate plot of these indices is presented in figure 3. The correlation between the two is highly significant at r = 0.993 (p<O.OOl). A relatively high midshaft index reflects mediolateral compression of the shaft, and seems to also indicate a tubular structure which is relatively more resistant to bending stresses in the anteroposterior plane Le., a high ratio of Ix'x'/Iy'y'). Conversely, a low midshaft index indicates that the transverse diameter exceeds that of the anteroposterior, and that t h e bone has relatively superior bending strengths in the mediolateral plane (low Ix 'x '/ Iy'y'l. The midshaft index partially describes external diaphyseal shape, but also appears to contain information about structural adaptations closely related t o habitual loading patterns. For interspecific comparisons of extant and fossil long bone morphology in which computed tomography is impractical or impossible, one may a t least offer plausible hypotheses about the mechanical design of these elements on the basis of classical anthropometric techniques . However, in order to critically evaluate mechanical hypotheses about long bone function and adaptation in fossil and extant specimens, computed tomography may prove to be an indispensible tool. Conclusions reached from mechanical analysis of tubular cross-sections may in fact run counter to conventional 289 TOMOGRAPHY AND FOSSIL LONG BONES 4.0 3.0 Ix'x. 'YY' 2.0 0 1.0 2.0 3.0 A-P Diameter / M-L Diameter Fig. 3 Bivariate plot of t h e midshaft index (anteroposterior diameter divided by mediolateral diameter) versus t h e ratio of h'x'to Iy'y'. Letter designations refer to the same cross-sections illustrated in figure 1. The high correlation between these two indices suggests t h a t classical anthropometric ratios may also contain information about diaphyseal adaptation t o habitual loading patterns. wisdom about t h e shape and function of long bones. For example, Preuschoft and Weinmann ('73) demonstrated that resistance to bending increases with the third power of bone diameter a t a rate faster than that of body weight to bone diameter. Given analogous loading configurations, heavier animals may actually possess relatively more slender limb bones than their smaller counterparts. Computed tomography, in conjunction with careful interpretation of mechanical characteristics of long bones, offers a nondestructive method for adding to our knowledge and improving our empirical assessments of fossil structure and function. ACKNOWLEDGMENTS Special thanks go to Doctor John Conroy, Department of Radiology (Carle Clinic; Ur- bana, Illinois) for his cooperation and assistance with the EM1 5005 Whole Body Scanner, and to R. L. Orme and P. Brown for their help in analyzing the cross-sections. 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