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Curvature of the forelimb bones of anthropoid primates Overall allometric patterns and specializations in suspensory species.

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AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 83:477498 (1990)
Curvature of the Forelimb Bones of Anthropoid Primates: Overall
Allometric Patterns and Specializations in Suspensory Species
SHARON M.SWARTZ
Committee on Evolutionary Biology, The University of Chicago,
Chicago, Illinois 60637
KEY WORDS
Biomechanics, Bone curvature, Brachiation
ABSTRACT
It has prerio?xs!g been reported that brachiating primates,
particularly gibbons, are Characterizedby distinctively straight forelimb long
bones, yet no hypotheses have been proposed to explain why straight limb
bones may be adaptive to suspensory locomotion. This study explores quantitatively the curvature of the long bones in 13 species of anthropoid primates
and analyzes the functional consequences of curvature in biomechanical
terms. These analyses demonstrate that, whereas the humeri of gibbons and
spider monkeys are functionally less curved than those of other taxa, the ulnae
of brachiators are neither more nor less curved than those of other anthropoids, and the gibbon radius is far more curved than would be predicted from
body size alone. The humerus is likely significantly less curved in brachiators
because of its torsion-dominated loading regime and the greatly increased
stress magnitude developed in torsionally loaded curved beams. The large
curvature of the radius is localized in the region of attachment of the supinator
muscle. Analysis presented here of muscle mass allometry in catarrhines
demonstrates that gibbons are characterized by an extremely massive supinator, and the large radial curvature is therefore most likely due to forearm
muscle mechanics. This study also demonstrates that the overall pattern of
limb bone curvature for anthropoids is distinct from the pattern reported for
mammals as a whole. This distinctive scaling relationship may be related to
the increased length of the limb bones of primates in comparison to other
mammals.
The lon bones of mammals characteristically disp ay some longitudinal curvature,
and in some cases this curvature is striking.
The ma itude of this curvature varies
among ?i ifferent bones, among taxa, and
among animals of different body size. Recent
experimental work has shown that the ontogenetic development of normal bone curvature, like the size and position of bony crests
and processes, is dependent on the presence
of normally functioning musculature; when
owing bones are not mechanical1 stimuated by normal muscle activity an weight
bearing, the resulting adult bone form shows
a substantial reduction in longitudinal curvature compared to normal bones (Lanyon,
1980). Furthermore, skeletal mechanics
may influence and be influenced by variation in bone curvature, as exemplified in the
recent demonstration of the consequences of
f
P-
@ 1990 WILEY-LISS, INC.
B
curvature for bone stress in mammals of
size (Biewener, 1983).
bones of brachiating
of gibbons and spider
monkeys, are not only elon ated and slender
but have also been descri ed as exce tionally straight (Zapfe, 1961;Hill, 1962;&ussman, 1965, 1967; Kummer, 1970; Schultz,
1973; Andrews and Groves, 1976). Brachiators thus appear to combine a pattern of
distinctive bone curvature with a specialized
form of locomotion. Based on this correlation, straight bones have been interpreted as
a functional ada tation to brachiation
(Knussman, 1965; f;ummer, 1970; Simons,
%
Received July 28,1988; accepted May 14,1990.
Address reprint requests to Dr. S.M. Swartz, Program in Ecology and Evolutionary Biology, Division of Biology and Medicine,
Brown University, Providence, RI 02912.
478
S.M. SWARTZ
1972). However, bone curvature of brachiators has never been quantitatively compared
with that in other primates, nor has an
explanation been put forward to show why
straight bones might be advantageous to
a suspensory animal.
The suggestion that bone curvature is
modified in species with highly specialized
locomotor behavior calls attention to bone
curvature as a functionally relevant aspect
of interspecificvariation in long bone design.
While many studies of skeletal mechanics
haw not considered the role of curvature in
determining bone stress (e. , Alexander,
1974, 1981; Alexander and ternon, 1975;
Pauwels, 19801, curvature can significantly
alter stresses and should be included in the
analysis of the function of the limb skeleton
in s ecific mechanical circumstances. Biomec anical analysis may help explain the
significance of differences in curvature
among taxa that differ in locomotor behavior. Comparative analysis of bone curvature
K
with it represent a unique “natural experiment”that can contributeto our understanding of whether bone curvature can function
as a biomechanical adaptation to altered
skeletal loading.
This study quantitatively describes patterns of long bone curvature in suspensory
and nonsuspensory anthropoid rimates
and documentsvariation in longitu1pinal curvature among bones and among taxa. This
information is used to address three questions. 1)Has the unique mechanical environment imposed on the forelimb by brachiation, particularly the large tensile forces
exerted on the limb as a whole by weight and
centripetal force, resulted in the evolution of
a unique pattern of skeletal curvature in
gibbons and spider monkeys that is biomechanically related to locomotion? 2) Are the
broad patterns of scaling of curvature within
the monophyletic anthropoid primate lineage the same as those described for mammals as a group? 3) Can the analysis of bone
curvature in primates help evaluate competing hy otheses about the origin and fundamenta significance of curvature?
P
MECHANICAL CONSEQUENCES OF
BONECURVATURE
Curvature affects the distribution and
magnitude of stresses in long bones, most
im ortantly by producing bending stresses
in ones subjected to purely axial loading
and by augmentin bending stresses in eccentrically end-loa ed bones. The longitudinal curvature of a limb bone will act to
increase stress under axial loads by effectively providin a moment arm ihenceforth
desi ated as t e curvature moment arm, C)
fort e axial force vector (Fig. 1).The resulting bending stress in the bone’s outermost
cortex is given by
\
%
8“
a
Ub
=
zk
(FaC)X
,
I
where = bending stress; Fa = applied axial force, X = distance from the neutral
lane of bending to the bone’s surface, and
= moment of inertia of the bone’s crosssection (Beer and Johnston, 1981; WainFig. 1. Axial loading of a curved column depicting the wright et al., 1976). Bending stress under
effect of curvature on the magnitude of bending stress. axial load will be zero when bones are
The peak bending stress due to axial load, vbrwill be a straight (C = 0) and will increase in ro orfunction of the bending moment (Fa%);X, the max?mum tion to C. Curvature quantified by C?dif!ers
distance from the bone’s cortex to the neutral axis (assumed to lie midway between the two cortices);and I, the from the radius of curvature, the radius of
moment of inertia of the cross-section.
the circle whose perimeter corresponds with
f
479
ANTHROPOID BONE CURVATURE
the arc of interest (Fig. 2). The effect of
“curvature” on the magnitude of bending
stresses is determined b C , not the radius of
curvature, and hence is the biomechanicall relevant variable in this analysis.
Tie bending resulting from bone curvature can have a major effect on bone stress
distribution: In vivo bone strain analysis of
the horse radius shows that the bending
3
component of stress is three times greater
than the compressive com onent and that
greater than 70% of the ben ing stress is due
to curvature rather than to transverse a plied loads (Biewener, 1983;Biewener et af
1983).Bending stresses will also result whei
a bone is loaded eccentrically (off-axis),such
as when reaction forces or muscle pull are
not in-line with the bone’s long axis; curva-
x
(1) radius of curvature a = radius of curvature b
Ca > c b
a
(2) radius of curvature u
z
ca =
radius of curvature b
cb
b
radius of
curvature b
Fig. 2. Illustration of the distinction between curvature quantified as radius of curvature and as curvature
moment arm (GI. In 1,two curved columns, A and B, have identical radii of curvature, but column A has a greater C
than column B, and will therefore experience greater bending stresses under the same applied axial load. In 2,
columns A and B have identical Cs, but the radius of curvature of A is greater than the radius of curvature of column
B. Column B appears more curved than column A and, in keeping with this ap earance, is characterized by a smaller
radius of curvature. However, the augmentation of bending stress under axiafloading due to curvature will be equal
in A and B because of their identical Cs.
480
S.M. SWARTZ
ture can either counteract or augment these
extrinsic bending moments, depending on its
orientation.
Besides altering bending stress magnitude in axial loading, bone curvature affects
the geometry of muscle packaging in the
limb (Lanyon, 1980). Because limb muscles
are often fusiform in shape, curvature may
represent a mechanism to provide space for
expanded muscle bellies of more massive
muscles.
CURVATURE AND SKELETAL BIOMECHANICS
lfii RR_4CHI_4TnF.
S ecialized locomotor behavior such as
fore imb suspension substantially alters
primitive patterns of skeletal loadinf and
curvature can thus have a different ef ect on
the mechanics of the limb in sus ensory
locomotion than on the limb of a wa king or
running quadruped. In particular, during
suspensory locomotion,the limb as a whole is
subjected to rimarily tensile rather than
com ressive oads because the limb suspenis the body from the hand rather than
serving as a compressive support column;
the external forces acting on the limb in
brachiation will subject it to tension, while
external forces in most other locomotor
modes will cause compression and bending.
Although body weight exerts tensile force on
the forelimb of a suspensory animal, the
loading of the bony skeleton is not dictated
exclusively by the extrinsic loading of the
limb. Soft tissues play a crucial role in mediating the stress distribution in the limb
bones, both bv the active alteration of the
forces exerted on the bones by muscular
contraction and by passive force transmission by ligaments and connective tissue
sheaths. Muscular activit in suspensory
support may reduce overal bone stress levels by exerting compressive forces to balance
extrinsic tensile loads, may produce bending
stresses, or may even produce compressive
bone stresses.
While curvature influences the overall
magnitude of bending stresses generated under axial loading and determines where in
the bone's shaft bending stresses will be
greatest, the magnitude of the bending moments produced is not affected by whether
those axial loads are tensile or compressive.
Since bendin stress due to curvature, (r ,is
equal to (Fa )(X)/I, a change in sign oPF,
(indicatin compression versus tension) will
change on y the sign and not the magnitude
of fTb. If the magnitude of bending stresses
P
P
P
P
f
t
induced by curvature is an important desi
constraint in long bones, we can expect t e
bones of suspensory animals to differ adaptively in curvature if the magnitude of regularly experienced stresses is altered in brachiation. Therefore, bones ex eriencing
reduced external loading might lisplay increased curvature without increasing bending stress ma itude to intolerable levels,
while bones t at experience an increased
magnitude of axial loading should show
adaptive decrease in limb bone curvature to
limit the magnitude of curvature-induced
oendin stresses.
- In
( a! dition to axial loadin , torsion may
figure importantly in the ske eta1 loading of
a brachiator, since during the sequential
suspension from alternating hands there is a
large amount of rotation of the body about
the long axis of the forelimb as well as rotation of the forelimb itself about its long axis
(Avis, 1962; Kummer, 1970; Fleagle, 1974;
Jenkins, 1981). The effects of curvature on
the stress distribution of a torsionally loaded
structure are complex, but, most critically,
shear stresses due to torsion will increase in
direct pro ortion to increasing orthogonal
distance rom the axis about which the
torque is applied (T = Tp/J, where T is torsional stress, T is applied torque, p is the
distance from the axis of the shaft, and J is
the polar moment of inertia) (Beer and
Johnston, 1981). Thus, the magnitude of
shear stresses developed in the surface of a
curved bone will be much greater in the
regions of greatest curvature than in portions of the bone shaft that are close to the
torsional axis (determined by the positior, s.i
the joints). This is particularly significant in
that the shear strength of bone IS far lower
than its tensile or compressive strength
(shear strength G 60 MPa; tensile strength
180 MPa; compressive strength Z250
MPa: Yamada, 1973; Currey, 1984). Shear
stresses in bones are usually small relative
to tensile or compressive stresses (e.g., 2540 times in the horse; Biewener et al., 1983),
so the shearing safety factor (ratio of failure
stress to stress of normal locomotion) of
bones is usual1 very large compared to the
safety factor or compression or tension.
However, when there is unusually great torsional loading, particularly of a curved bone,
this shearing safety factor could be greatly
reduced. Therefore, if forelimb bones of suspensory rimates are subjected to increased
torsiona loading relative to cursorial animals, it will be selectively advantageous to
8"
8"
18
P
P
P
481
ANTHROPOID BONE CURVATURE
reduce curvature in these bones to limit ing upward and supported with modelling
compound. Care was taken to ensure that
shear stresses.
each bone was ositioned in a standardized
MATERIALS AND METHODS
orientation wit respect to anatomical landThe sample used for this study consists of marks; the procedure was re eated for the
the lon bones (humerus, radius, ulna, fe- medial as ect of each bone. T e bones were
mur, ti ia, fibula) of 12 adult individuals photograp ed, and the negative images proeach (six males and six females)of 13 species jected onto a Houston Instruments digitizing
of anthro oid primates (total number of tablet (HIPAD DT-114) from which C was
individua s = 156).All individuals were col- measured. Curvature can be defined with
lected in the wild and were fully adult as respect to any orientation lane; however,
determined by com lete epiphyseal fusion of most bones appear to have t eir largest and
ail long bones. ~ l species
e
iri~iid*dhrr; thus mechaxicalfy most significant CUFX
listed in Table 1, along with mean re orted ture in either an anteroposterior or mediobody weights (from Jungers, 19857 and lateral orientation. Furthermore, bending
a generalized locomotor classification stresses are likely to be eatest for many
(adapted from Rose, 1974). The sample rep- bones in the AP lane ue to the largely
resents a wide ran e of bod sizes (1.9-170 dorsal and ventra positioning of the most
kg), phylogenetic a finity ( ew World mon- active muscle groups and the orientation of
keys, cercopithecine and colobine Old World ground reaction force within a parasa ‘ttal
assing throu h the point of fmb/
monkeys, and hominoids),and habitual locomotor mode (brachiation,terrestrial quadru- groun contact. The L plane ma also be
pedalism, climbing, etc., in various propor- im ortant for bending, particulary in the
ragus, where ML curvature in primates is
tions) within the anthropoid lineage.
C (curvature moment arm) was measured marked, and in the humerus and femur,
at the region of maximal curvature ( eatest where the medial displacement of the head
moment arm) in antero osterior an medio- relative to the shaft will increase ML bendlateral views (Fig. 3). ach bone was ori- ing. C was determined with respect to the
ented with its ventral (anterior) aspect fac- axial component of force acting on the bone
-R
K
K
E
P
R
f d
B
E
f.
P
Kir
P
B
TABLE 1. Mean sex-specific body mass and overall locomotor classification for the species sampled in this study
Species
Pan troglodytes
Gorilla goriEla
Pongo pygmaeus
Hylobates lar
Cebus apella
Allouatta palliata
Ateles geoffroyi
Papio anubis
Macaca fascicularis
Cercopithecus mitis
Colobus guereza
Presbytis rubicundus
Nasalis larvatus
Body mass (kg)
Male
60.0
Female
17.;
Male
169.5
Female
71.5
Male
81.7
Female
37.8
Monomorphic
5.7
Male
Female
Male
Female
Monomorphic
3.3
1.9
11.6
6.3
7.7
Male
Female
Male
Female
Male
Female
Male
Female
Male
Female
Male
Female
25.1
14.1
4.9
3.1
6.3
4.0
10.1
8.0
6.2
5.7
20.4
9.8
Adapted from Jungers (1985) with permission of the publisher.
Locomotor classification
Knuckle-walking, climbing,
same suspension
Knuckle-walking, some climbing
Quadrupedal walking, climbing,
suspension
Brachiation, climbing,
bipedalism
Quadrupedalism with some
limb an d tail suspension, climbing
Arboreal quadrupedalism, with some
limb an d tail suspension, climbing
Limb an d tail suspension, climbing,
an d arboreal quadrupedalism
Terrestrial quadrupedal walking and
running
Arboreal quadrupedalism, some
climbing
Arboreal quadrupedalism, some
climbing
Arboreal quadrupedalism, climbing,
leaping
Arboreal quadrupedalism, climbing
Arboreal quadrupedalism, climbing,
some suspension
482
S.M. SWART2
bone (Fig. 3). Measurements taken in anterior view depicted mediolateral (ML) curvature; anteroposterior (AP) curvature was
measured in medial view. This method of
uantifying curvature focuses specificallyon
&e displacement of the material of the bone
shaft from the force transmission from joint
to joint and therefore encompasses both the
curvature of the shaft per se and the position
of the shaft relative to the joints. Hence,
len h and angulation of the femoral neck
an anteversion of the femoral and humeral
head and ntizk will influenit: measurements
of C for these bones. These measures are not,
therefore, directly comparable to those of
other investigators assessed from the shaft
exclusively but are the most appropriate for
this biomechanical analysis.
Empirical body mass measurements
taken from the individuals com rising the
skeletal sample analyzed provi e the best
possible size estimate for biomechanical allometric analyses. However, skeletal collections for which accurate field body mass data
have been measured are rare, and extra olating published s ecies mean body weig ts
to a particular ske eta1 collection may introduce serious inaccuracies due both to geographic variation in body mass in many species and other differences in the composition
of the population from which skeletal measurements are made and the population
from which bod mass data were acquired.
Surro ates for ody mass, while imperfect
(e.g., mith, 19811, must be substituted in
these cases. For each individual, femoral
circumference just below the lesser trtrchanter was also measured to estimate bod
size. This variable is hi hly correlated wit
body mass in anthropoi s, and, althou h the
recise sample composition of this stu y difFig. 3. Tracing of a gibbon radius in anterior view Fers from that in other studies, regression
illustrating the method for measuring curvature mo- equations for the relationship of these variment arm, C, the moment arm of the axial force acting ables to body mass have been reported for
through the centers ofthe proximal and distal joints. C is
the orthogonal distance from 1 (the chordjoining the two anthropoids (Steudel, 1981, 1985). Using
joint centers) to the oint midway between the medial these re ession equations and the meaand lateral, or dorsafand ventral, cortex at the level of sured va ues for each variable, estimators
greatest curvature.
that are proportional to (isometric with)
body mass were constructed. In anthropoid
primates, femoral circumference is proportional to (body mass)' 36 (Steudel, 1985);
hence (femoral circumference)278 is proportional to (body mass)' O0. The validity of this
and was measured as the orthogonal dis- estimate is supported by the isometric relatance from a chord, 1(drawn from the proxi- tionship between the sex-specific means of
mal joint center to the distal 'oint center), to the femoral circumference estimating varia point midwa between t e medial and able and the literature body weight reported
lateral or dorsa and ventral cortices of the in Table 1 (r = 0.975; slope = 1.003, SE =
$-
(f
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P
8
8
%
Y
Y
il
r";
9i
483
~THROPOIDBONECURVATURE
0.047). Undoubtedly, other methods of assessing body size would produce somewhat
different results, but the general pattern of
relationships will be quite similar. It is possible, however, that such body size estimating variables are subtly biased by locomotor
mode and will therefore skew results accordingly. In particular, orangutans a pear to be
characterized by relatively smal er femoral
dimensions than other taxa, probably due to
forelimb dominated locomotor behavior
(Ruff, 1987). In this case, true body size of
orangutans ma!d be greater than indicated
b the estimate. It does not, however, appear
t at a slight underestimation of body size for
orangutans would alter the conclusions of
this analysis.
After accounting for missing values, total
sample sizes for each long bone ranged from
140 to 152. All re ession analyses were
based on sex-speci ic species means. The
functional relationships between curvature
and body size were then estimated using
reduced major axis (model II) regression
analyses on natural log-transformed data.
Reduced major axis rather than least
squares regression was used in all anal ses
because body weight-estimating varia les
(the “independent variables”) were not determined without measurement error and
because, as Kendall and Stuart (1979) have
shown, if the error variance is unknown, the
reduced major axis is the maximum likelihood or least biased estimator of the functional relationship.
To compare the degree of curvature among
Iocomotor groups directlv, it is necessary to
controi for size in some fashion. One way to
do so is to normalize curvature moment arm
to some independent measure of bone size,
particularly one that relates directly to the
relevant biomechanical consideration, resistance to bending stress. In anthropoid primates, relative long bone length varies with
locomotor mode and is therefore inappropriate as a size-normalizing variable. Long
bone diameters, however, show close to s o metric scaling in anthropoids (Aiello, 1981;
Steudel, 1985; Swartz, 1988), and gibbons
and spider monkeys do not deviate from the
eneral anthropoid pattern as they do for
Eone length. Moreover, a bone’sresistance to
bending stresses will be a function of its
cross-sectional area and the second moment
of area of the cross section; these, in turn, are
a function of bone diameter, but not of bone
length. While moment of inertia would be the
optimal choice for a normalizing variable,
P
i
F
%
cross-sectional geometry was not measured
directly in these skeletons. For an ellipse,
moment of inertia will be dictated strictly b
diameter and cortical thickness, so the midl
shaft diameter in the plane of bendin was
selected as the best available normafizing
variable to reflect bending resistance. These
normalized curvature values were then compared amon suspensory and nonsuspensory
species and etween the most highly suspensory species (Hylobates Zar) and the facultativel suspensory Atelesgeoffroyi. Because of
the arge number of comparisons, significance values of P < 0.0014 instead of
P < 0.05 (36 comparisons) were used to establish differences between group means.
To assess the potential si ificance of the
relationship between C and ifferential muscle mass development, sup
yses were carried out on
measurements collected
1972b).These data consist of the dry weights
of each muscle of the forearm, hand, shank,
and foot of 140 individuals of 15 species of
catarrhine primates (see Table 2 for list of
species and Sam le sizes). Subgroups of the
total samples o muscles were selected for
further analysis (i.e., forearm flexors, pronators, etc.); the muscles included and composition of each group are given in Table 3.
Because body weights were unavailable for
these specimens, the summed mass of all
muscles intluded in the analysis was used as
a substitute size variable to permit examination of scaling of different muscle-group
masses. The precise relationship of this variable to body weight is necessarily unknown,
but it can serve as a reasonable approxima-
fi
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TABLE 2. Sample composition for muscle weight
analysis (Tuttle, 1969b, 1970, 1972a, bi
Species
Pan troglodytes
Gorilla gorilla
Pongo pygmaeus
Hylobates lar
Symphalangus syndactylus
Cercopithecus aethiops
Cercopithecus nictitans
Macaca arctoides
Macaca fascicularis
Macaca mulatta
Macaca nemestrina
Erythrocebus patas
Papio cynocephalus
Theropithecus gelada
Colobus polykomos
Presbytis cristatus
Sample size
14
9
11
6
9
5
6
9
9
10
8
7
6
7
6
5
484
S.M. SWARTZ
TABLE 3. Muscles included in relative muscle weight analysis (data are from Tuttle, 1969b, 1970, 1972a, 6 )
FORELIMB MUSCLES:
1. hrachioradialis
2. flexor digitorum superficialis
3. flexor digitorum profundus
4. flexor pollicis longus
5. flexor carpi radialis
6. flexor carpi ulnaris
7. palmaris longus
8. extensor carpi radialis longus
9. extensor carpi radialis brevis
10. extensor carpi ulnaris
11. extensor digitorum
12. extensor digiti I1 (et 111)
13. extensor digiti IV (et V)
14. abductor poillc1s longus
15 extensor pollicis longus
16. extensor pollicis brevis
17. pronator teres
18. pronator quadratus
19. supinator
20. abductor pollicis brevis
21. flexor pollicis brevis
22. abductor pollicis brevis
23. opponens pollicis
24. adductor pollicis
25, dorsal interosseous I1
26 dorsal interosseous I11
27 dorsal interosseous IV
28 palmar interosseous I1 contrahens I1
29 ualmar interosseous I11 contrahens IV
30 ialmar interosseous IV contrahens V
31. lumbrical I1
32 . lumbrical I11
33. lumhrical IV
34. lumhrical V
35. abductor digiti minimi
36. flexor digiti minimi
37. opponens digiti minimi
HINDLIMB MUSCLES:
38. flexor digitorum tihialis
39. flexor digitorum fibularis
40. peroneus longus
41. peroneus hrevis
42. peroneus digiti V
43. popliteus
44. plantaris
45. gastrocnemius
46. soleus
47. extensor digitorum longus
48. extensor hallucis longus
49. tihialis anterior
50. abductor hallucis longus
ai. Libiaiis puster;u~
52. abductor hallucis hrevis
53. flexor hallucis brevis
54. opponens hallucis
55. adductor hallueis-oblique head
56. adductor hallucis-transverse head
57. dorsal interosseous I1
58. dorsal interosseous I11
59. dorsal interosseous IV
60. palmar interosseous I1 or I11
contrahens I1
61. palmar interosseous IV
contrahens IV
62. palmar interosseous V
contrahens V
63. lumhrical I1
64. lumbrical I11
65. lumhrical IV
66. lumbrical V
67. abductor digiti V
68. flexor digiti V
69. flexor accessorius
70. extensor hallucis hrevis
71. extensor digitorum brevis
I,
+
+
+
+
+
+
:
tion of size and permits anal sis of the rela- largely misleading. The elongated forelimb
the propnrtiiinal weights o different fore- bones of gibbons and spider monkeys h a w
large radii of curvature merely because of
arm muscle groups.
their great length and thus ap ear straight,
RESULTS
but the forearm bones do not ave reduced
Interspecific comparisons
Cs despite the visual impression of straightCorn arisons of mean normalized curva- ness on which previous investigators have
ture va ues among gibbons, spider monkeys, commented.
In the hindlimb skeleton, gibbons also
and nonsuspensory primates demonstrate
that in both gibbons and spider monkeys the show some significant deviatrons in bone
humeri are significantly straighter than curvature from the pattern observed in other
rimates. The AP and ML curvature o f the
ibulae and the ML curvature of the femora
of gibbons are substantially eater than
those of other primates. Spi er monkeys
share this pattern in that they have significantly more curved fibulae than do nonsusthose of nonsuspensory primates, gibbon ra- pensory primates.
dii are significant1 more curved mediolaterRegression analysis
ally than those o all other species. These
Body size and C are strongly positively
data show that the appearance o f straightness of the forelimb bones of brachiators is correlated in 11 of the 12 regression analy-
P
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485
ANTHROPOID BONE CURVATURE
TABLE 4 . Matrix of tests of mean differences of diameter normalized bone curvature among nonsuspensory
primates, Hylobates, and Ateles’
Humerus
AP
ML
Hylobates vs.
nonsusp.
Atetes vs.
nonsusp.
Hylobates
vs. Ateles
Radius
AP
ML
Diameter normalized curvature
Ulna
Femur
AP
ML
AP
ML
=
>
AP
-
<
<
=
>
<
<
=
-
-
-
-
-
-
-
>
--
-
-
-
-
-
-
Tibia
ML
-
Fibula
AP
ML
>
>
-
>
>
-
-
-
‘Differencesthat are not significant are indicated as =;< indicates that thebones of the first group in the comparison are significantly less
cnr-~ed:’indirat,Ps the bones ofthe first group are significantly more curved.
TABLE 5. Regression summary statistics: maximum bone curvature us. body size estimate
Humerus
Humerus
Radius
Radius
Ulna
Ulna
Femur
Femur
Tibia
Tibia
Fibula
Fibula
ML
AP
ML
AP
ML
AP
ML
AP
ML
AP
ML
AP
r
Slope (s.e.)
0.614
0.694
0.702
0.393 (0.060)
0.369 (0.054)
0.400 (0.036)
Not significant
0.927
0.857
0.969
0.849
0.828
0.629
0.620
0.602
0.594 (0.046)
0.516 (0.054)
0.359 (0.018)
0.410 (0.043)
0.426 (0.048)
0.270 (0.042)
0.353 (0.055)
0.472 (0.077)
ses, with the AP curvature of the radius as
the only exception (see Table 5 for regression
statistics and Figs. 4 and 5 for regression
plots). In this analysis, a scaling relationship
is taken to demonstrate positive allometry if
C scales to body size estimate at a slope of
eater than 0.33, the expected value fw any
$inear dimension under geometric similarity. The regression slopes range from 0.270
to 0.594. In eight of these 11analyses there
is significant positive allometry of 6 with
respect to body size estimate. This represents a clear trend toward disproportionate
increase in curvature with size in most
bones, although the absolute magnitude of
curvature, as indicated by intercept values,
differs greatly from bone to bone and, for
a sin le bone, in different planes (Figs. 4
and 57.
The relatively low C values of gibbon and
spider monkey humeri; the large Cs of gibbon radii; and the similarity of ulnar C
among gibbons, spider monkeys, and nonsuspensory rimates are clear in the regression plots ( igs. 4 and 5). However, the plot
for the AP curvature of the ulna (Fig. 4E)
P
Allometry
++
+
+
+
+
+
+
+
raises an additional issue. Visual inspection
sug ests that the nonsus ensory
! l es a species with mar edly re uced inulclu
nar curvature (olivebaboons, Papio anubis).
The lack of difference in normalized C between gibbons and nonsus ensory animals
may be due to the effect o the inclusion of
this outlying species in the nonsuspensory
sample. When AP ulnar C in bbons and
spider monkeys is compared wit that in the
nonsuspenso groups with baboons excluded from t e sam le, gibbon ulnae have
significantly reduces Cs compared with
those of the remainder of nonsuspensory
animals and those of spider monkeys; the
spider monkeys still show no significant difference from the nonsuspensory group. Baboon ulnae, however, ap roach those of gibbons in AP ulnar C rec fuction. Separating
baboons from the nonsuspensory group has
no effect on any other comparisons.
Analysis of relative muscle mass
Because bone curvature may arise as a
response to differential packing of muscle
mass on two opposite surfaces of a bone
YP
K
P
xr
f
486
S.M. SWARTZ
BONE CURVATURE MOMENT ARM versus BODS SIZE ESTIMATE:
FORELIMB
-
Humerus - Mediolateral
Humerus Anteroposterior
A 0
r = 0.613
slope = 0.393 (0.060)
slope = 0.369 (0.054)
,
.I
.1
I
1
-
Radius Anteroposterior
I
-
Radius Mediolateral
10
D.
C.
~
A.
.,:.o
,.,..,
.
*,.*.**I
r = 0.701slope = 0.100(0 036)
not significant
.I
.I
10
1
100
1
1
r = 0.857
slope = 0.516 (0.054)
I
10
I
1
10
I00
-
-
Ulna Mediolateral
Ulna Anteroposterior
4
I00
10
1
100
10
1
.I
I
I
100
r = 0.92:
slope = 0.593 <0.046)
.l
1
10
100
Fig. 4. Log-log regression plot of sex-specificspecies means of C for the humerus, radius, and ulna vs. body size
estimate (C in em on the abscissa of each plot and body size estimate in
on the ordinate). A Humerus
anteroposterior. B: Humerus mediolateral. C: Radius anteroposterior. D: Radius mediolateral. E: Ulna anteroposterior. F: Ulna mediolateral. In A-D and F, nonsuspensory species are represented by solid squares, Hylobates by open
triangles,Ateles by o en circles, andPongo by open squares. In the plot of ulna anteroposterior curvature (E),baboons
(Papio) are indieatelby closed circles.
487
ANTHROPOID BONE CURVATURE
BONE CURVATURE MOMENT ARM versus BODY SIZE ESTIMATE:
HINDLIMB
Femur - Anteroposterior
-
Femur Mediolateral
10
B.
r = 0.969
slope = 0.359 (0.018)
slope = 0.410 (0.043)
.1
I
1
1
10
.1
f
I
1
100
10
1
100
-
-
Tibia Mediolateral
Tibia Anteroposterior
c.
.
r = 0.629
slope = 0.270 (0.042)
I
,
1
100
10
-
10
r = 0.620
slope = 0.353 (0.055)
r = 0.602
slope = 0.472 (0.077)
f
I
100
Fibula - Mediolateral
Fibula Anteroposterior
.o1
r = 0.828
slope = 0.426 (0.0118)
I
-I
10
1W
.01
1
10
Fig. 5 . Log-log regression plot of C of the femur, tibia and fibula vs. body size estimate. A
Femur anteroposterior. B: Femur mediolateral. C: Tibia anterogosterior. D: Tibia mediolateral.
E: Fibula anteroposterior. F:Fibula mediolateral. Symbols an units as in Figure 4
100
488
S.M. SWARTZ
(Lanyon, 1980; see also below) and relative cluded here, extensor mass is a relatively
muscle size may va adaptively with loco- constant proportion of flexor mass (47%).
motor r
p (e.g., yuttle, 1972a; Fleagle,
Comparison of bone Curvature scaling
1977; ebo, 19871, curvature differences
in anthropoid primates with that in
among taxa could be due in art to taxonomic
other mammals
differences in patterns o relative muscle
Long bone curvature shows positive allomof various
etry in much of this sample of anthropoid
rimates. This result is somewhat different
regression analysis.
the scaling of bone curvature in mamOverall, this Sam le displays a highly reg- mals as a group (Biewener, 1983). Biewener
ular scaling of musc e mass, with very strong examined scaling of curvature moment arm
correlation between the mass of each fore- (normalized to bone length) with respect to
limb muscle group and the estimated size body size in 32 species of mamil;a!a ranging
variable (all r values greater than 0.97; in size from 0.020 to 3500 kg and found a
Fig. 6). This regularity is particularly note- slight but significant negative allometry of C
worthy given the inclusion of both juveniles normalized to bone length in the humerus,
and adults and both males and females in radius, and tibia and no significant correlathe sample. One feature of gibbon forearm tion for the femur. This result appeared conmusculature, however, is quite distinctive; sistent with the need of large animals to
gibbon supinator muscles are extremely develop mechanisms to reduce bone stresses
massive com ared with those of all other because body mass (and thus forces exerted
catarrhines. ibbons do not, however, devi- on the skeleton) increases relatively more
ate significantly from the other species stud- rapidly with size than the cross-sectional
ied in the massiveness of the flexor, exten- area of bones (and the associated ability of
sor, or pronator muscle groups with respect the bone to resist stress). To facilitate comto overall size. There are few other devia- parison between the present and earlier
tions from these patterns, notwithstanding studies, Biewener’s C measures were rethe ex ectation that differences in locomotor gressed against body mass; the reanalysis
capabi ities might be reflected in muscle su gests isometry for C of the humerus and
proportions. Earlier studies of these data ra ius, positive allometr in the femur, and
revealed some significant adaptive differ- ne ative allometr only or the tibia.
&opes obtaine from this analysis indiences amon taxa (Tuttle, 1967, 1969a,b,
1970, 1972b7, but this allometric approach cate that in three of four comparisons the
suggests that the majority of those reflect slopes for anthropoid primates do not differ
differences in relative weight among individ- significantly from those for the wider sample
ual muscles within a single muscle group of mammals (Table 6). However, for those
rather than mnscle groups as a whole ii.e , regressions in which the doper do not differ
one muscle of the flexor group may be rela- significantly, the intercepts for primates are
tively more massive than another, while the shifted downward,indicating that, at a given
flexors as a group do not vary with locomotor body size, primates have less curved bones
mode). The present analysis suggests that than other mammals (Fig. 8). Examination
body size is a more important determinant of of the residuals of regression analyses of the
mass of muscle groups than is locomotor entire primate plus nonprimate mammal
adaptation and that some of the differences samples shows that, in all four comparisons,
re orted earlier may be body size related.
the mean of the primate residuals is signifibhese data also suggest that scaling of cantly less than zero (P < 0.001) and signifflexor and extensor muscle mass with re- icantly less than the residual mean for
spect to size may reflect a fundamental un- nonprimates (P < 0.001).
derlying regularity in distribution of foreDISCUSSION
arm muscle mass in anthropoids. The slopes
This study demonstrates that gibbon and
of flexor mass and extensor mass regressions do not differ significantly (Fig. 71, but spider monkey forelimb bones are not unithe interce ts of these two regressions are formly straighter than those of their nonsussignificant y different, as determined by pensory relatives when curvature moment
analysis of covariance. This pattern indi- arm, the biomechanically relevant measurecates that, over the range of body sizes in- ment of curvature, is the standard of assess-
P
!ram
P
e
7
9
f
B P
loo
I0
Pronators
100
loo00
7
loo0
l
1
o
10
10
o
LOO
7
Supinators
loo
1000
1000
ioooo
10 K,
7
Fig. 6. Lo -lo plots of total muscle group mass (grams) vs. the grand total muscle majs
(grams) for tfe forearm, hand, shank and foot (see Table 3 for details of muscle saniple
composition). Nonsuspensory catarrhines are re resented by closed squares, and Hylobates is
represented by open triangles. The only notable Ieviation from the re Iar attern of scaling of
muscle group mass 1s the large gibbon supinator muscle. Data are f%m d t t l e (1969b, 19TO;
1972a,b).
7
1
iooO
Extensors
490
S.M. SWARTZ
.1
1t
I
I
I
I
,
1
1
2
3
4
5
6
7
I
Fig. 7. Combined[lot of flexor and extensor muscle mass vs. total muscle mass (grams). The slopes of these two
re ressions do not di er significantly, although the two muscle groups differ in intercept. For the extensor data,
iniividuals of nonsusDensorv sDecies are rewesented bv closed circles and the gibbons bv oaen circles. For the flexor
data, individuals of n;nsusp&f;ory s ecies are represeiited by closed squares, &d the gibb6ns by open squares. Data
are from Tuttle (1969b, 1970,1972aX).
TABLE 6. Comparison of regression slopes for C us body size for mammals and anthropoid primates'
Slope for anthropoids
Slope for mammals
Humerus AP
0.146 (0.060) (r2 = 0.026)
0.421 (0.036) (rq = 0.670)
0.398 (0.053) (rL= 0.291)
0.286 (0.041) (r2= 0.230)
Radius ML
Femur AP
Tibia AP
<
0.369 10.054)
ii.400 (0.036)
0.410 jc.043:
0.270 (0.042)
-
'Standard errors for theslopes are given in parentheses, followed by squared correlation coefficients. Data for mammals are modified from
Biewener (1983);results for primates are as in Table 5.
ment. The humeri of gibbons and spide.
monkeys have relatively reduced Cs in comparison with those of other primates, the
radii of gibbons but not of spider monke s
have marked1 increased ML Cs, and the s
of the ulnae o suspensory primates are similar to those of other rimates. In functional
terms, then, the fore imb skeleton of brachiators is not less curved overall than that of
nonsuspensory anthropoids and straight
bones can not be considered an adaptation to
suspensory locomotion per se, contrary to the
conventional ideas about bone curvature in
e
P
r?
brachiators (Zapfe, 1961; Hill, 1962; Knussman, 1965, 1967; Kummer, 1970; Andrews
and Groves, 1976).
No single pattern of curvature characterizes the entire forelimb skeleton of brachiators; the normalized Cs of the humerus, radius, and ulna of gibbons differ from each
other as much as any one of the three forelimb bones varies among s ecies. Because
curvature magnifies skeleta stresses, it was
redicted above that curvature will differ
getween suspensory and nonsuspensory species if load magnitude or torsional loading
P
491
ANTHROPOID BONE CURVATURE
Radius
Humerus
I00
0
A.
0
...
........ ........, -.,
I
01
I
1
10
..., .
loo
1000
loo00
Tibia
Femur
100
'
~
I
0
m
10
.I .O1
100
1000
10000
Fig. 8. Lo log plots of C (centimeters) versus body mass (literature values, in kilograms)for a brond sampling of
mammals wit% primate data superimposed,adagted inJart from,Biewener(1983). Re ession slopes for this sample
of speciesofdiverse phylogenetic affinit and bo y size iffer significantlyfrom slopesf% anthropoid primates for the
humerus. The rimate data are clearly &placed in the direction of reduced bone curvature in comparison with other
mammals. In tRe residuals of combined regressions for primates plus nonprimates, primates differ significantly from
zero and from other mammals, with lower-than-expected curvature values in each case.
differ in these locomotor behaviors. The distinctiveness of the curvature of each bone
emphasizes that brachiation is a complex
phenomenon in which different skeletal elements serve different functions, and highlights the necessity of considering how brachiating behavior differentia11 affects the
loading of each functionally Jfferentiated
element of the limb skeleton. These curvature data suggest that the gibbon and spider
monkey humeri (low C) may experience either large applied forces or large torques,
that gibbon radii (high C) may experience
low magnitude forces and low torques, and
that loadin of the ulna (no unique differences in C does not differ significantly
within this sam le.
Despite the act that bone is weaker in
torsion than in other modes of loading, the
humerus of suspensory primates may indeed
5
P
experience a significanttorsionai component
in its loading regime. Telemetered in vivo
bone strain measurements from brachiatin
gibbons indicate that the orientation of pea
principal strains at the humeral midshaft is
a proximately 45"to 60" to the long axis of
t e bone on both the dorsal and ventral
surfaces,a pattern characteristic of torsional
loading, while the shear strains indicative of
torsional loadin are not observed in the
radius or ulna ( wartz, 1988; Swartz et al.,
1989). Loading of the humerus of spider
monkeys has never been studied, but it is
plausible to expect a similar pattern of bone
strain based on kinematics. Because shear
stresses in curved beams are disproportionately large when loaded in torsion, the extreme straightness of the humerus of susensory animals may play an important
Functional role by reducing surface shear
a
R
8
492
S.M. SWAUTZ
stresses due to torsional loading of the upper brachiation, and active, powerful supination
may help to propel the gibbon's body though
arm in brachiation.
The kinematics of limbibody movements the second half of su port phase, although
during brachiation also sug ests that torsion this has yet to be verieed electromyographiof the supporting limb is ikely. Although cally. In keeping with the otential im orsuspensory locomotion has often been mod- tance of supination in propu sion, the gib on
elled as pendulum-like, the movements of a supinator muscle is extremely massive in
brachiating animal are far more complex comparison with su inator musculature in
than those of a simple ideal pendulum. One other catarrhines. arge radial curvature
important deviation of suspensory locomo- in gibbons may arise from 1)the necessity to
tion from pure pendular motion is that the provide adequate space for positioning the
body of the animal rotates about the axis of massive supinator or 2) the response of the
the sup ortin limb during the course of the radial shaft to pressure exerted on it during
swing. s the ody undergoes this large rota- frequent supinator activity andior 31 ehe IWtion with res ect to the stationary handhold, cessity to provide an increased moment arm
the limb wil be twisted along its long axis. for the su inator muscle about the axis of
Morphological and experimental evidence rotation o the radius, thereby augmenting
indicates that this twisting will be expressed the muscle's mechanical effectivenessfor exdifferently in the bcnes of the u per arm and erting forceful rotation.
Because a large C increases stress magnithe forearm. Cineradiograp ic analysis
demonstrates that little or no bone rotation tude in axial loading, on purely mechanical
ounds one might expect to find that reoccurs at the stabilized glenohumeral joint
in brachiatin spider monkeys (Jenkins %xed magnitude of extrinsic loading would
et al., 1978). owever, gibbons and spider be associated with the evolution of lar e
monkeys are capable of substantial rotation curvatures; when extrinsic loads are sma 1,
at the humeroradial joint, and forearm supi- stress augmentation due to curvature can be
nation at this joint during brachiation has tolerated without risk of failure. Alternabeen documented (approximately20" in spi- tively, within an individual's lifetime, reducder monkeys) (Jenkins et al., 1978; Jenkins, tion of bone loadin below the "normal"
1981). Gibbons and spider monkeys also stresses of a particu ar species appears to
share a highly specialized car a1 morphol- lead to significantly reduced bone curvature
ogy, which permits rotation etween the as a henotypically plastic res onse (Lanyon,
socket formed b the radius plus the roxi- 19807. In vivo bone strain ana ysis indicates
ma1 row of carpa s, and the distal carpa row, that the magnitude of strain in the highly
in which the capitate and hamate together curved radius of brachiating gibbons is comform a ball joint (Jenkins, 1981).Almost 90" parable to that observed durin walking in
of rotation can occur at this joint. and this other mammals (Swartz, 1988: wartz et al.,
midcarpa't mobility contributes ~ m p o r t a n t ~19891
~ ~ In fact, contrar to expectations for a
to the total supination of the forearm in limb loaded in overal tension, the radius
brachiation, providing about 70" of rotation experiences a combination of bendin and
(Jenkins, 1981). This enhanced capacity for compressive loading. These data in icate
free longitudinal rotation at the carpus and that extrinsic forces a plied to the gibbon
proximal radius minimizes the torsion of the radius may be reduceif in magnitude comulna distally and the radius both proximally pared with those of other mammals, since
and distally. Forearm supination combined even the stress-magnifyingeffect of extreme
with forward rotation of the body when the curvature does not produce unusually high
shoulder 'oint is stabilized against humeral stresses.
The curvature of the ulna of suspensory
rotation, owever, may result in the application of opposing rotatory moments at oppo- animals is no less than that in nonsuspensite ends of the humerus and thus substan- sor anthropoid primates as a whole, but
tially greater torsion than in the forearm.
gib on ulnae show reduced AP curvature
The radius of gibbons is distinct from that when baboons, which also possess very
of other anthropoid primates in its strikingly straight ulnae, are excluded from the nonlar e curvature moment arm that is greatest suspensory sample. Bone strain analysis inin t e proximal interosseous region, close to dicates that the magnitude of strain in the
the attachment site of the supinator muscle. gibbon ulna is similar to peak strain magniSu ination is a critical component of the tudes in other mammals. The predominant
lim movements during the support phase of loading mode, however, is axial tension
'i
P
i
E
A g
P
P
R
a
Y
Y
t:
'i
P
P
8
9
f
h
B
a
%
493
ANTHROPOID BONE CURVATURE
rather than the compression or compression
plus bending seen in other mammals
(Swartz, 1988; Swartz et al., 1989). If decreased curvature is an adaptation to compensate for increased bending stresses, we
would expect C to decrease in such a way as
to bring peak strain values to approximately
the same magnitude as in other mammals.
The observed low C of the ulna, in combination with recorded strain magnitudes that
are comparable to those of other mammals,
is consistent with this hypothesis.
Although this study focuses on the role of
bending stresses arising from axial loading
of curved bones, bending stresses are also
produced by loads that are not purely axial,
such as those exerted b eccentric muscle
pull or by reaction forces t at are not entirely
in line with the bone. The magnitude of these
bending forces is greatly influenced by bone
length, increasing in proportion to the distance from the point of application of the
force to the point at which stress magnitude
is assessed. Such bendin stresses due to
off-axis loads will be hspro ortionately
large in long-limbed s ecies i their elonated limb bones are su jected to transverse
forces of the same magnitude as bones of
shorter-limbed animals. This would suggest
that, all else being equal, reduced C may
provide an important advantage to an animal with extremely elongated limb bones;
the reduction of AP C in gibbon humeri and
ulnae may serve to limit bending stresses
arising from off-axis reaction forces.
The muscle mass analysis presented here
shows that the total flexor muscle mass is
si ificantly and uniformly greater than tcta extensor mass in the forearm in anthropoid primates. If relative muscle mass development were a major determinant of curvature, a constant ratio of muscle masses on
two o posite surfaces of a bone over a range
Iy sizes would be associated with a
of bo!
constant magnitude of curvature in the same
size range. Constant proportionality of
flexor to extensor muscle mass would then
be correlated with a constant magnitude of
AP curvature of the radius and ulna, re ardless of body size. AP radial curvature s ows
no significant correlation with body size and,
in fact, remains relatively constant over the
range of body sizes included in this sample.
The ulna, however, is substantially more
curved at larger body sizes (second steepest
ositive allometry of this sample). Moreover,
$ifferences in curvature between brachiators and nonsuspensory primates cannot be
L
E
tp
Y
a
explained by relative muscle mass development, with the exception of radial ML curvature. These results suggest that neither the
allometry of curvature nor significant differences in curvature amon taxa can be explained primarily as an ef ect of differential
muscle mass development.
Primates and nonprimate mammals
Primates a pear to be distinctive among
elrelative strai htness of the
mammals in t?
long bones of the limbs (Fig. 8). his phenomenon may be related to the increased length
G f the long bones in primates in comparison
to other mammals. Indeed, for any gwen
body size, the long bones of primates are
4040% longer than those of typical mammals (Alexander, 1985). Because of this increased length, the transverse forces exerted
during normal locomotion of a primate will
roduce larger bending stresses than would
ge engendered in the bones of typical mammal encountering the same applied force. If
the bones of rimates were as curved as
other mamma s, the net bending stresses
developed in terrestrial locomotion would be
substantially greater than those in other
mammals. Decreased curvature in primates
may represent one mechanism through
which primates limit the total magnitude of
bending stresses while maximizing long
bone length.
Testing of alternative models of the
significance of bone curvature
different hypotheses have been
attempts to delineate the gensignificance of bone curvature. These four h potheses are li hone
curvature serves to ofyfset externally applied
bending moments, thereby reducing the
magnitude of bone stress and limiting tensile strains in the bone’s surface (Frost, 1964,
1973; Pauwels, 1980); 2) bone curvature
functions to accommodate adjacent musculature and to optimally position muscles and
their tendons with respect to joints (Lanyon,
1980); 3) bone curvature serves to optimize
functional strains (Lan on, 1980); and 4)
bone curvature is a mec anism for improving the predictability of direction of bone
loading (Bertram and Biewener, 1988).
These explanations are not mutually exclusive, although it is unlikely that they are all
equally important. To determine whether
this study can help evaluate these hy otheses, it is necessary to examine brief y the
proposed alternative explanations of bone
f
Br
P
K
P
494
S.M. SWARTZ
curvature, to determine how they differ in
their predictions about mechanical design of
the limb skeleton in anthropoid rimates.
Stress reduction. Although t e moment
arm that curvature provides for axial forces
will increase bendin stresses, Frost (1964)
and Pauwels (1980) ave proposed that the
bending forces due to curvature and the
bending stress produced externally by offaxis loading tend to be equal in magnitude
and opposite in orientation. Hence, bone curvature could function to counteract externally applied bendin moments and, as a
result, produce overal net stress of low magnitude (Pauwels, 1980). Similarly, it has
been suggested that curvature serves to
modulate externally applied loads in order to
avoid tensile stresses and kee the bone's
cortex in overall compression ( rost, 1964).
Pauwels has used theoretical analyses of the
human femur to demonstrate this counterbalancin effect; however, these models use
estimate muscle force values selected from
a wide range of possible forces. Other combinations of plausible muscle force magnitudes
and directions produce different results in
which bendin is not reduced. Verification of
the theoretica models of the stress reduction
hypothesis would require detailed information concernin the magnitude and orientation of muscle orces, the effects of ligaments
on skeletal stresses, and the effects of body
weight on bone loading. Until such information is available, theoretical models of this
kind cannot adequatelytest the stress reduction hypothesis.
Experimental evidence strongly suggests
that cawature rareiy reduces bending
stresses. Data from a variety of mammals
(Alexander, 1974; Alexander and Vernon,
1975;Biewener, 1983;Biewener et al., 1983;
Biewener and Taylor, 1986; Lanyon and
Ba got, 1976; Lanyon and Bourne, 1979;
Ru in and Lanyon, 1982) demonstrate that
the predominant source of strain in long
bones of walking and running animals is
bending. For example, in the horse radius
85%of recorded strain is due to bending, and
the orientation of these bending strains is
such that the curvature augments rather
than reduces the bending loads; i.e., curved
bones experience eater strain than if they
were not curved. n all, the stress reduction
hypothesis ap ears incorrect and is unlikely
to account or differences in curvature
among taxa.
Mu&e packin and differential developrnent. The secon hypothesis for bone curva-
R
a
P
P
8
7
f
Q
P
F
fi
ture focuses on the role of the musculature
that lies ad'acent to the bones. The gross
geometry of imb muscles is often characterized by relative1 expanded muscle bellies
between relative y narrow tendons or aponeuroses. Hence, curvature in long bone
shafts may function to allow for ositioning
of slender attachment tendons c ose to the
joints while still roviding ade uate space
for the muscle be1 ies in the mids aft region
(Lanyon, 1980). Moreover, soft tissues can
cause bone resorption when they exert pressure on the periosteum; blood vessels, tendons, tumors, etc., can cause Zone erosion
that roduces excavations in the bone surface PLanyon, 1980). Lanyon has proposed
that bone curvature may, therefore, reflect
the influence of those adjacent muscles that
exert the greatest pressure on the periosteum. This hy othesis is consistent with the
observation t at the radius and tibia of
many mammals are both concave with respect to the flexor musculature, allowing
space for a greater volume of chronically
active antigravity support muscles (Lanyon,
1980).
There are really two parts to this hy othesis. First, bones may be curved in orEper to
osition large muscles with respect to joints;
Rence the mere presence of relatively larger
muscle mass on one aspect of the limb should
lead to curvature, regardless of differences
in intensity and duration of activity in the
different muscle groups. Second, bones may
be curved due to relatively greater periosteal
ressure from muscles on one as ect of the
Emb; resumably, curvature wou d then reflect ifferential magnitude, frequency, and
duration of muscle activity on either side oi
the bone in addition to (or instead of) differential mass per se.
Strain generation. Because curvature results in the augmentation of com ressive
stresses with bending stresses un er axial
loading, curvature may increase, rather
than reduce, externally applied bending moments and ultimately function to increase
bone strain levels. Deformation of the bone
can facilitiate movement of fluid through
bone tissue (Piekarski, 1981)and ap ears to
be necessary for the maintenance o a minimum amount of bone mass as well; bone
mass is reduced in denervated limbs or limbs
in which muscles atrophy pathologically
(Lanyon, 1980).Therefore, it may be advantageous for bones to experience strains of
some intermediate magnitude that are great
enough
" to Drovide .phvsiolo&al benefit but
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~THROPOIDBONECURVATU~
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not so reat as to subject the bone to substantial ris of failure. If the combination of bone
loading and bone eometry produces strains
below the physio ogically optimum magnitude, strain levels could be increased in either of two ways: 1)increase in the magnitude of bone curvature in the appropriate
direction or 2) reduction in bone cross-sectional area and/or second moment of area
(Lanyon, 1980). Empirical results that indicate that curvature increases rather than
decreases bone stresses (Biewener, 1983;
199% are consistent with
Biewener et d.,
this hypothesis.
Predictability. It has been proposed that
the fundamental si ificance of bone curvature is that it resu ts in improved predictability in the pattern of bending stresses
developed in a bone (Bertram and Biewener,
1988). These workers argue that bending
stands in contrast to the unstable nature of
axial compressive loading, where eccentricity of load can result in a sudden and potentially catastrophic shift from purely compressive stresses to a pattern of bending
stresses. Moreover, intrinsic curvature of a
bone will tend to bias or constrain the orientation of bending developed within it. When
a straight column is subjected to a randomly
oriented bending load, it will be equally
likely to exhibit bending in any direction, but
a strongly curved bone will tend to bend in
the direction of its longitudinal curvature
regardless of the orientation of the applied
bending moment. For an extremely curved
column, the redictabilit of bending direction approac es unity. &creasing predictability in bioiogical systems oftez? entails R
cost, however. For example, Alexander
(1981, 1984) has demonstrated that there
a pears to be a trade-offbetween the predicta ility of loading and the safety factor of a
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a greater “margin
for error,” even if such a structure would
then be heavier and more costly metabolically to maintain and transport. As curvature and predictability increase, load-carrying capacity decreases, and, in fact,
strength declines steeply with even relatively small curvatures (Bertram and Biewener, 1988). The final design of a bone will
reflect the competing demands of load-carrying capacity and predictability, with the
optimum compromise for a particular bone
determined by the relative importance of
these factors in the normal use of an animal’s
limb.
The hypotheses compared
Can comparative bone curvature data
from anthropoid primates shed some light on
the relative validity of the four major roposed explanations of bone curvature? his
study, in combination with in vivo bone
strain analysis of brachiating gibbons
(Swartz, 1988; Swartz et al., 1989), confirms
that in suspenso primates bone curvature
does not serve eit er to reduce substantially
the magnitude of bone strain or to protect
bones from having one cortex loaded in tension by producing net compressive strains
throughout the cortex. The analysis of muscle mass data presented here, although preliminary, suggests that differential muscle
development er se does not account for the
majority of o served bone curvatures. Although the large gibbon su inator muscle is
associated with large radia curvature, other
C values in suspensory primates show no
relationship to the pattern of relative muscle
development, and this radial curvature in
brachiators may be more an adaptive response to the need for increased mechanical
advanta e for powerful supination and pronation t an a response to the resence of
more massive supinator muscu ature. The
observed constant proportionality of forearm
flexor and extensor muscle mass may be
related to the constancy of AP radial C, and
this relationship is consistent with the hypothesis that relative muscle development
determines curvature. However, overall,
data available to date are inconclusive with
regard to the influence of muscle size or, the
scaling of limb bone curvature. Before this
issue can be fully evaluated, it may be necessary to assess differential activity of muscle
masses in postural control in addition to
simple muscle mass. The hypothesis that
bone curvature can be explained as a mechanism for generation of sufficiently hi h levels of bone strain to produce physio ogical
benefit is consistent with the data presented
here; this mechanism may indeed prove
an important component of normal bone bi-
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“ E n the pattern of limb bone curvature in
brachiating primates be related to loading
predictability? Bertram and Biewener
(1988) argue that increased curvature increases the redictability of stress distribution in limb ones. As the variability of exter-
B
496
S.M. SWARTZ
nal loading increases, curvature should
increase in a compensatory fashion. From
this point of view, the reduced curvature of
the humerus would imply that the humeral
loading is si ificantly more predictable in
sus ensory t an in nonsuspensory anthropoi(P primates. Evaluating this possibilit
requires a comparison of loading predictabi.ity in suspensory and nonsuspensor animals. However, it is difficult to quantix load
predictabilit , and attempts to assess loading redicta ility in sus ensory locomotion
proc uce
f
ambiguous resu ts. It is plausible to
argue that lim%movements, limb bone orientation with respect to direction of progression, and overall limb loadin are uite
stereot ped in terrestrial qua rupeda ism
while rachiation involves moving in a
high1 variable way in a three-dimensionally
eomp ex fashion.Accordingly, suspensory locomotion may entail less predictable, more
variable loadin than other forms of locomotion. On the ot er hand, the pendulum-like
nature of brachiation and suspension of body
weight by the limb could result in more
regular, predictablelimb loadingthan would
be expenenced in quadrupedal locomotion.
Similar1 ,it is difficult to assess the redictability o limb loading in primates re ative to
that in other mammals. Although the hypothesis that bone curvature is due to a
trade-off between bone strength and loading
redictability provides a potentially powerful explanation of this phenomenon,before it
can be applied to the specific case of skeletal
design and suspensory locomotion, it is necessary to develop a way in which the conce t
of predictability c2n be made more expltclt p
operational.
In addition to loading magnitude, predictability is influenced by loading mode because compressive and tensile loading differ
fundamedally with regard to stabill’iy considerations. Compressive loading of a curved
beam represents a metastable or unstable
loading situation: The curvature augments
the bendin stress in the column, and each
incrementa increase in load will increase
curvature and the bone will tend toward
bucklin failure in bending. In contrast, tensile loa ing is far more stable. Although
curvature still augments bending stresses in
a bone loaded in tension, each increment of
increased load will tend to “straighten” the
bone and thus lower bending stresses.
Because tensional loading does not involve
the inherent instability associated with
compressive loading of curved beams, pre-
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dictability considerations ma differ substantiall for tensionally loaC fed and compressive y loaded columns. If this is so,
structures loaded predominant1 in tension
may have different patterns o curvature.
The data presented here, however, show no
significant differences between the curvature of ‘bbon ulnae and those of other anthropoi s in which axial tension is not likely
to be the dominant loading regime.
Curvature and skeletal adaptation
The phenomenon of bone curvature also
raises irie ibsilea offmdiona! role and adaptation in morphological design. If bone curvature is selectively advantageous,what is it
an adaptation to! Providing a thorough explanation of bone curvature as an adaptation
would require as prerequisites understanding of both the range of functional consequences of curvature and the history of the
origination of curvature in res onse to some
selection pressure (Gould an Vrba, 1982).
Demonstrating that curvature can have the
effect of functionally increasing the predictability of limb bone stress distributions does
not establish that it originated as a feature of
limb skeletons for this role (i.e., that it is an
adaptation) or even that it is maintained as a
feature of skeletons because of this function
(that it is an exa tation). Bone curvature
will have the efpfect of increasing bone
stresses under axial loading even if muscle
activity or packing are major determinants
of curvature, but may confer selective advantage not from causing this increase in stress
but rather from allowing a more effective
muscle attachment geometry. Understanbin the adaptive significance of differences
in one curvature among different taxa will
require as a first step clearly establishing
the multiple functional consequences of curvature in a realistic way. After the range of
effects of curvature on bone function are
established, it will be possible to examine
evolutionary changes in this design feature
and to evaluate bone curvature as an adaptation.
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CONCLUSIONS
The anthropoid primate lineage offers an
opportunity to examine patterns of long bone
curvature in a monophyletic group of great
locomotor and body size diversity. Among
anthropoids,curvature moment arm, the biomechanically relevant measure of bone
curvature, scales with significant positive
allometry in eight of 11 analyses, indicat-
ANTHROPOID BONE CURVATURE
ing disproportionately increasin bending
stresses in larger anthropoids. Tphese allometric slopes for curvature differ little from
those found among a broader group of mammals, but, at any given size, primate bones
are straighter than bones of nonprimates. In
addition to the analysis of curvature scaling
in anthropoids or mammals as a whole, curvature can be considered as a skeletal design
feature associated with functional specialization. By focusing on brachiating primates,
a “natural experiment” within mammalian
evoliutinn in which the pattern of limb loading is uniquely modified, this stuuy has
shown that curvature can vary amon taxa
in a manner consistent with the ef ect of
curvature on bending stresses in axially
loaded columns. In particular, the straightness of the gibbon humerus a pears a likely
modification for limiting s ear stresses
when a torsional loading is imposed on bone,
a material that is relatively weak in torsion.
The large ML curvature in the radius is
related to the increase in size and functional
importance of the su inator musculature,
but differential musc e mass development
does not appear to be the major determinant
of limb bone curvature. These results demonstrate quantitatively that the pattern of
curvature of the forelimb bones of gibbons
differs from that of their nonsuspensory relatives and that these differences appear to
be related to both the distinctive muscle
morphology in gibbons and the uni ue mechanical environment imposed on t e forelimb by brachiation.
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ACKYOJ~~LEU~EY~~
Museum specimens were enerously made
available for study by Dr. ruce Patterson,
Department of Mammals, Field Museum of
Natural History; Dr. Richard Thorington,
Department of Mammals, United States
Natural History Museum; Ms. Maria Rutzmoser, Department of Mammals, Museum of
Comparative Zoology-Harvard; and Dr.
Bruce Latimer, Department of Phyiscal Anthropolo , Cleveland Museum of Natural
History. %ussell Tuttle generously provided
access to his original muscle weight measurements. I thank Drs. A. Biewener, M.
LaBarbera, R. Tuttle, E. Lombard, J . Bertram, C. Jaslow, Mr. L. Frolich and three
anonymous reviewers for providing comments on earlier versions of the manuscri t.
Ie
Funds for this research were rovided by t!
Hinds Fund, University of dicago; the Eli
A. Nierman Foundation; the Louis B. Leakey
8
497
Foundation; and the Searle Graduate Fellowship Program.
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