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Computed tomography and biomechanical analysis of fossil long bones.

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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. This research
was supported in part by the generosity of the
Department of Anthropology, University of
Illinois a t Urbana-Champaign and by NSF
Grant BNS 7683114.
LITERATURE CITED
Ambrose, J. 1973 Computerized transverse axial scanning (tomography): Part 2. Clinical application. Br. J.
Radiology, 46: 1023-1047.
Amtmann, E. 1971 Mechanical stress, functional adaptation and the variation structure of the human femur
diaphysis. Ergeb. Anat. EntwickL-Gesch., 44: 1-89.
1978 Biomechanical interpretation of form and
structure of bone and bones. Roles of genetics and function in growth and remodelling. Burg Wartenstein Symposium No. 71. Relationships between anatomy and behavior in fossil and contemporary primates. Gustav
Fischer, New York.
290
WILLIAM L. JUNGERS AND R. J. MINNS
Badoux, D. M. 1973 Biomechanics of t h e third metatarsal hone in the horse. Proc. Kon. Ned. Akad. Wetersch.,
C76: 257-269.
Currey, J. D. 1968 Adaptations of bone to stress. J. Theoret. Biol., 20: 91-106.
Enlow, D. H. 1963 Principles of Bone Remodelling.
Charles C Thomas, Springfield, Illinois.
Frankel, V. H., and A. H. Burstein 1965 Load capacity
of tubular bone. I n : Biomechanics and Related Bioengineering Topics. R. M. Kenedi, ed. Pergamon Press,
Oxford, pp. 381-396.
Frost, H. M. 1963 Bone Remodelling Dynamics. Charles
C Thomas, Springfield, Illinois.
1973 Orthopaedic Biomechanics. Charles C
Thomas, Springfield, Illinois.
Hounsfield, G. N. 1973 computerized transverse axial
scanning (tomography): Part I. Description of system. Br.
J. Radiology, 46: 1016-1022.
Hoyte, D. A. N., and D. H. Enlow 1966 Wolffs law and t h e
problem of muscle attachment on resorptive surfaces of
hone. Am. J. Phys. Anthrop., 24: 205-214.
Jungers, W. L. 1977 Hindlimh and pelvic adaptations to
vertical climbing and clinging in Megaladupis, a giant
subfossil prosimian from Madagascar. Yrbk. Phys. Anthrop. 1976,20: 508-524.
Kimura, T. 1974 Mechanical characteristics of human
lower leg bones. J. Fac. Sci. (Univ. of Tokyo) Anthrop., 4:
319-393.
Kummer, B. K. F. 1972 Biomechanics of bone: rnechanical properties, functional structure, functional adaptation. In: Biomechanics: I t s Foundations and Objectives.
Y. C. Fung, N. Perrone, and M. Anliker, eds. PrenticeHall, Englewood Cliffs, New Jersey, pp. 237-271.
Lanyon, L. E., and D. G. Baggot 1976 Mechanical function
as an influence on the structure and form of hone. J. Bone
Joint Surg., 58-B:436-443.
Liikova, M., and J. Heft 1971 Reaction ofbone tomechanical stimuli. Part 2. Periosteal and endosteal reaction of
tibia1 diaphyses in rabbit to intermittent loading. Folia
morph., 19: 301-317.
Lovejoy, C. 0. 1978 Some comments on contemporary
methodological approaches to individual primate fossil
analysis. Burg Wartenstein Symposium No. 71. Relationships between anatomy and behavior in fossil and contemporary primates. Gustav Fischer, New York.
Lovejoy, C. O., A. H. Burstein and K. G. Heiple 1976 The
hiomechanical analysis of bone strength: a method and
its application to platycnemia. Am. J. Phys. Anthrop..44:
489-506.
McElhaney, J. H. 1970 Bone, the influence of function
on form. Physiological Systems Analysis for Engineers,
1970: 1-23.
Minns, R. J., G. R. Bremble and J. Campbell 1975 The
geometrical properties of t h e human tibia. J. Biomechanics, 8: 253-255.
New, P. F., W. R. Scott, J. A. Schnur, K. R. Davis and J. M.
Taveras 1974 Computerized axial tomography with the
EM1 scanner. Radiology, 110: 109-123.
Pauwels, F. 1968 Beitrag zur Funktionellen Anpassung
der Corticalis der Rohrenknochen. Untersuchungen an
drei rachitisch deformierten Femora. Z. Anat. Entwickl:
Gesch., 127: 121-137.
Piziali, R. L., T. K. Hight and D. A. Nagel 1976 An extended
structural analysis of long bones - application t o the
human tibia. J. Biomechanics, 9: 695-701.
Preuschoft, H. 1971 Mode of locomotion in subfossil
giant Iemurojds from Madagascar. Proc. 3rd. Int. Congr.
Primat., Zurich, 1970, 1: 79-90.
Preuschoft, H., and W. Weinmann 1973 Biomechanical investigations of Lirnnopithecus with special reference to
the influence exerted by body weight on hone thickness.
Am. J. Phys. Anthrop., 38: 241-250.
Vallois, H. V. 1912 Considerations sur la forme de l a section transversale du tibia chez les Lemuriens, les Singes
e t 1'Homme. Bull. et. Mem. SOC.
Anthrop. Paris, Series 6,
3: 97-108.
Wainwright, S . A,, W. D. Biggs, J. D. Currey and J. M.
Gosline 1976 Mechanical Design in Organisms. Halsted
Press, New York.
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