<oologkalJoumal ofthe Linnean Socieg (2000), 130: 499-510. With 3 figures
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doi: 10.1006/zjls.1999.0238, available online at http://www.idealibrary.com on
Incidence and mechanical significance of
pneumatization in the long bones of birds
J. CUB0 AND A. CASINOS FLS*
Department $Animal Biology (Vutebrates), Universip of Barcelona, 08028 Barcelona, Spain
Received August 1998; accepted&r publication October 1999
The incidence of pneumatization in avian long bones was studied, by direct observation, in
a large sample of species. Only proximal bones (humerus and femur) presented pneurnatization
in the sample studied. The incidence obtained was related to the variation of the maximum
cortical thickness and mechanical properties, such as bending strength and flexural Young’s
modulus. Cortical thickness, bending strength and flexural Young’s modulus were sigtllficantly
lower in pneumatized bones than in marrow-filled bones. Furthermore, some congruence
was found between pneumatization and systematic groups when compared. In this sense,
Charadriformes was the only order studied with total absence of long bone pneurnatization.
Results on cortical thickness appear to be in agreement with modelling predictions previously
made and with results obtained on other groups of flying vertebrates. The possible selective
advantage of reduction in cortical thickness in relation to flying is suggested.
0 2000 The Linnean Soriety of London
ADDITIONAL KEY WORDS:-ortical
- systematics.
thickness - strength - Young’s modulus - bending
CONTENTS
Introduction . . . .
Material and methods
Results . . . . .
Discussion . . . .
Acknowledgements .
References . . . .
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499
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503
506
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509
INTRODUCTION
It now seems clear that merely hollow bones (no tissue filling the marrow cavities;
see, for example, Kardong, 1998) are a generalized theropod condition (Fastovsky
& Weishampel, 1996). However, only modern birds possess bone pneumatization,
* Corresponding author E-mail: [email protected]
+
0024-4082/00/ 120499 12 $35.00/0
499
0 2000 The Linnean Society of London
500
J. CUB0 AND A. CASINOS
that is bones with pneumatic foramina: openings in the wall of the bone for the air
sacs to enter the internal bone cavities. No Mesozoic dinosaur nor any Cretaceous
bird has them (Fastovsky & Weishampel, 1996). At the same time, the traditional
generalized assumption that, due to penumatization, the avian skeleton is lighter
than the mammalian skeleton, is questionable (Prange et al., 1979). In fact some
skeletal structures-such as the humerus, ulna-radius, tibiotarsus and fibula-display
larger masses in birds than in mammals (Cubo & Casinos, 1994). Unfortunately,
data on the incidence of pneumatization in the avian skeleton are rather scarce and
always partial (Bellairs & Jenkin, 1960; Portmann, 1950; Winkler, 1985).Although
Portmann (1950)accepted that pneumatization may relate to the supposed lightness
of the avian skeleton, he showed there does not appear a strict relationship between
degree of pneumatization and flight ability. For example, he pointed out that both
gulls (flying birds) and kiwi (running bird) lack pneumatization, and if in Aepyornis
the femur is pneumatized, in Dinomis it is not, despite the fact that both are running
birds. According to the review carried out by Winkler (1985), the only general rule
seems to be that the postcranial skeletons of diving birds (e.g. Spheniscidae) appear
to be less pneumatized and, furthermore, within the same systematic group, skeletons
of large species appear to be more highly pneumatized than those of smaller species.
In addition, for a limited sample, Currey (1984) and Currey & Alexander (1985)
found that cortical thickness, measured as the ratio of the internal to the external
diameter in the sagittal direction, is lower in pneumatized bones than in marrowfilled bones. Finally, Alexander (1982), Currey (1984) and Currey & Alexander
(1985) modelled the optimal thickness of the walls of pneumatized and marrowfilled bones, with regards to their mechanical properties. However, as far as we
know, to date no empirical data on the mechanical significance of pneumatization
vs. marrow-filled bones have been published.
The aim of the present research was to study the incidence of pneumatization in
avian long bones and the mechanical consequences of the pneumatization process,
quantified by means of maximum cortical thickness, bending strength and flexural
Young’s modulus.
MATERIAL AND METHODS
The long bones (humerus, radius, ulna, femur, tibiotarsus and tarsometatarsus)
of 35 adult specimens, belonging to 24 species, were studied (Table 1).The systematic
scheme of Cracraft (1981) was followed. Bones were fresh material, obtained from
recently dead animals of known body mass and were kept wet during experiments.
Of methods suggested by Hogg (1980) to recognize pneumatized bones, direct
examination was considered the most useful, since broken bones, resulting from
mechanical tests (see below) were available. A microscope was used to make more
accurate direct observations. The criterion adopted to establish that a bone was
pneumatized was the total absence of marrow in the diaphyses; epiphyses were not
analysed. In the whole sample studied, diaphyses were marrow-filled or hollow: no
ambiguous state was found. At the same time, within a given bone of a particular
species, the hollow or marrow-filling condition was constant. After breaking, the
sections of the bones, at the only fracture point, were ground down until smooth
cross-sections were obtained.
PNEUMATIZATION IN AVIAN BONES
50 1
TABLE1 . List of the species studied. Numerals in parentheses following species names indicate the
number of individuals studied. Abbreviations: F =femur; H =humerus; R = radius; U =ulna; Ta =
tarsometarsus; Ti= tibiotarsus. 1 =bone with marrow; O=pneumatized bones; - presence or absence
of marrow was not checked. Body masses of the specimens studied are given between parentheses.
H
U
R
F
Ti
Order Galliforrnes
P h i a n u s colchicus (2) (1 023 g, 826 g)
0
I
1
0
I
Order Gruiforrnes
Otis ktrax(1) (271 g)
0
I
1
0
Ta
Order Falconiformes
Accipi& gentilis ( I ) (1 024 g)
Accipiler nisuc (2) ( I 6 1 g, I63 g)
Asia otus (2) (262 g, 203 g)
Buteo buko ( I ) (497 g)
Cirm cianeus ( I ) (295 g)
Falco columbarius ( I ) (10 I g)
Fako tinnunculus (3) ( 168 g, I35 g, 1 10 g)
Olus scops (3) (77 g, 63 g, 69 g)
7ylo alba (2) (233 g, 275 g)
Order Charadriiformes
Aka torda ( I ) (489 g)
Burhinus oedicnemus ( I ) (207 g)
Caldrk alpina ( I ) (49 g)
Celocheldon nilotica ( I ) ( 157 g)
Lam ndibunduc (2) (2I2 g, 159 g)
S h a alblfmns ( I ) (39g)
S h a h i m n d o ( 1 ) (1199)
Order Colurnbiformes
Columba palumbus ( I ) (401 g)
I
0
1
0
-
0
I
Order Piciformes
Picus &id& (3) ( I 30 g, 158 g, I58 g)
0
I
Order Coraciiformes
Memps apim& ( I ) (57 g)
0
I
Order Psittaciformes
&op~iti~amonachus (1 ) ( I 33 g)
Njmphicw hollandicw ( I ) (58 g)
Order Passeriforrnes
Oriolus ori0lus ( I ) (48 g)
I
1
1
I
1
1
1
1
I
1
0
1
Bending strength and flexural Young’s modulus (tangential modulus) were calculated by means of three-point bending tests carried out with an INSTRON 85 l l
machine (Fig. 1). Bones were loaded along the sagittal axis, at the mid-point of the
length, until breaking, with an actuator speed of 0.5 mm/min. A 10 kN load cell
was used. For each bone, stiffness (slope of force-extension curve), and maximum
load were obtained directly from the machine, by means of the specific software,
with appropriate assumptions and modifications. See, for example, Spatz et al. (1996)
for a similar methodology. Cross sections (see above) were analysed with a Hitachi
video camera, mounted on a microscope, to calculate internal and external diameters
and second moment of area of each bone. See Cub0 & Casinos (1998) for more
details on the method. For the second moment of area, the classical formula
502
J. CUB0 AND A. CASINOS
Figure 1. Schematic arrangement for the three-point bending tests used in the present research. See
text for more details.
Figure 2. Scheme of the cross-section of a hypothetical bone. Shadow zone corresponds to cortical
internal
area. Abbreviations: B, breadth of the bone; & (thick bar), breadth of the thin layer;
radius; R, external radius; W, width of the bone; xx, neutral axis;y, distance from the thin layer to
the neutral axis; z, width of the thin layer. See text for details.
m,
was used, where .t-Sy is a thin layer of the cross-sectional surface area placed at a
distancey from the neutral axis (Alexander, 1983) (Fig. 2). Second moment of area
was calculated for the sagittal direction in which the bone was loaded.
Using these data, the bending strength and the flexural Young modulus were
calculated using the following formulae (Jackson, 1992):
PNEUMATIZATION IN AVIAN BONES
503
o=- 3 P,,*S
2*B*d
E=
(F/x)*S3
48*Z
(3)
where o is the bending strength, E the flexural Young's modulus, P,, the maximum
load, S the span used, B and D the breadth and the width of the specimen,
respectively, F/x the stiffness and I the second moment of area (Figs 1 and 2).
The K parameter, the ratio of the internal to the external diameter, measures
the thickness of the cortical bone normalized to diameter for comparison of bones
of different size (Currey & Alexander, 1985) (Fig. 2). The minimum K parameter
and its orientation were calculated on each bone by using the IMAT program
(Cubo & Casinos, 1998).The orientation of the minimum K was reported by means
of angles expressed in degrees, considering the antero-posterior a x i s as 0". This
orientation ranges from -90" to 90". Negative values were transformed into positive
values in order to determine deviations in the orientation of the minimum K from
the sagittal axis.
Variations of bending strength, flexural Young's modulus and minimum K
parameter were analysed separately on marrow-filled and pneumatized (gas-filled)
bones. Marrow-filled and pneumatized femora were also studied separately to test
for differences between pneumatized and non-pneumatized patterns in a given type
of bone. This protocol could not be followed with humeri because of the small size
of the sample. See Results where the special treatment given to femora and humeri
in relation to other long bones is described. Standard deviation, mean, and 95%
mean confidence interval were calculated. At the same time the variation of the
orientation of the minimum K was also analysed by means of circular descriptive
statistics (Zar, 1984).Mean angles, their 95Y
' o' confidence limits and circular standard
deviations were calculated for the total sample as well as for marrow-filled and
pneumatized bones.
Finally, assuming the allometric equation
y =a*?
(4)
bending strength and flexural Young's modulus were regressed to body mass,
separately for marrow-filled and pneumatized bones. Model I of regression was
used, in accordance with previous work (Biewener, 1982).
RESULTS
Table 1 shows the incidence of pneumatization in the sample studied. Globally,
distal long bones (ulna, radius, tibiotarsus and tarsometatarsus) did not show
pneumatization. Only humeri and femora were pneumatized, although with very
different percentages, since while 70% of the humeri studied were pneumatized,
only 39% of the femora studied had no marrow. In relation to a possible congruence
between the incidence of pneumatization and systematics, some patterns arose,
despite limited sample sizes. Charadriiformes (7 species and 8 specimens studied)
J. CUB0 AND A. CASINOS
504
TABLE
2. Variation in maximum cortical thickness, expressed by means of the K parameter, bending
strength (a)and flexural Young's modulus Q between marrow-filled and gas-filled bones studied. In
each case, the femur subsample studied is indicated. Size of the sample (n), standard deviation, mean,
and mean confidence interval, are shown. Other abbreviations: GPa =gigapascals; MPa = megapascals
K
n
SD
Mean
Mean
confidence
interval
Marrow-filled
Total
Femur
123
18
0.11
0.05
0.65
0.74
0.63, 0.67
0.72, 0.76
Gas-filled
Total
Femur
30
9
0.04
0.03
0.77
0.80
0.76, 0.79
0.78, 0.82
Total
Femur
I22
18
51.20
26.79
200.19
153.87
191.02, 209.36
140.54, 167.20
Total
Femur
30
9
36.92
23.93
139.03
124.88
125.25, 152.81
106.49, 143.27
Total
Femur
1 I5
18
7.65
5.35
14.73
11.09
13.32, 16.14
8.43, 13.75
Total
Femur
30
9
4.10
4.16
7.67
6.88
6.14, 9.20
3.68, 10.08
u (MPa)
Marrow-filled
Gas-filled
E (GPa)
Marrow-filled
Gas-filled
was the only order with complete absence of pneumatization in long bones, in
accordance with the previous observation of gulls by Portmann (1950) (see above).
On the other hand, in Falconiformes (9 species and 16 specimens studied) all humeri
were pneumatized, whereas the femora differed in two families: in Accipitridae
marrow was absent from all the femora; in Strigidae marrow was always present.
The limited sample size of the other orders studied made similar separate analyses
inadequate.
Table 2 shows results on the minimum K parameter, which means maximum
cortical thickness. The statistical analysis carried out for the whole sample showed
that confidence intervals of the means do not overlap at all: pneumatized bones
were significantly thinner than marrow-filled bones. These results are graphically
shown in Figure 3. A parallel result was obtained when sub-samples corresponding
to femora were compared. However, the confidence intervals of the means corresponding to both pneumatized and marrow-filled humeri overlapped, possibly
because of the reduced sizes of the respective sub-samples.
No difference was found in the orientation of the maximum cortical thickness
(minimum K) (Table 3). In both cases, the circular mean confidence intervals for
the whole sample included 45", which means an orientation equidistant from both
sagittal and transverse diameters.
Table 2 also shows the results obtained from mechanical parameters tested,
namely bending strength and flexural Young's modulus. Considering the whole
sample, the confidence intervals of the means show that marrow-filled bones are
stronger and stiffer than pneumatized bones, i.e. bending strength and Young's
modulus are significantly lower when marrow is absent. However, when the subsample of femora is analysed, confidence intervals of the means overlap.
PNEUMATIZATION IN AVIAN BONES
"0
505
0.2
0.4
0.6
0.8
1
0.2
0.4
0.6
0.8
1
4
2
0
;
0
K parameter
Figure 3. Graphic representation of the distribution of the K parameter in the marrow-filled (A) and
pneumatized bones (B). Number of species and K parameter are indicated in y-axis and x-axis,
respectively.
TABLE
3. Variation in the orientation of minimum K (Kq. See text for details. Abbreviations as in
Table 2
Ke
Total
Marrow-filled
Gas-filled
n
Circular
SD
circular
mean
circular
mean
confidence
interval
I54
I23
30
24.9
27.7
24.9
45.3
43. I
48.7
42.3, 48.3
39.6, 46.6
39.7, 57.7
In can be assumed that mechanical properties like strength and stiffness are
specific to the materials and independent of body mass (Currey, 1984). Previous
results on long bone strength (Biewener, 1982) seem to confirm this assumption.
Nevertheless, the statistical analysis of the mechanical results obtained with our
sample, showed that bending strength is correlated with body mass in the case of
J. CUB0 AND A. CASINOS
506
TABLE
4. Results of the correlations of bending streqgth (a) and flexural Young's modulus (4to body
mass for marrow-filled and gas-filled bones studied. Equations and confidence intervals for a
(y-interception) and b (slope) are indicated. Correlation coefficients are indicated by r. For other
abbreviations, see previous tables
Model I
Mechanical
n
properties (Pa) to
Body mass (9)
equation
cr (MPa) Marrow-filled
Gas-filled
122
30
0.081
0.556
y=220.680* x A -0.026
y=334.492* X " -0.170
E (GPa) Marrow-filled
115
30
0.224
0.175
y=29.218* x " -0.161
y=13.060* x " -0.137
Gas-filled
'
r
a confidence
interval
b confidence
interval
164.247, 296.503 -0.083, 0.032
195.287, 572.925 -0.269, -0.072
14.773, 57.789
2.560, 66.640
-0.292, -0.030
-0.436, 0.162
pneumatized bones (r=0.556, for 28 degrees of freedom, for R0.05) (Table 4).
The same result was found for the flexural Young's modulus of the marrow-filled
bones. In both cases slopes were negative, different from 0, since this value is
excluded by the slope confidence interval, which means that both parameters
decrease with body mass.
DISCUSSION
Long bones are tubular structures, which means they have values of K greater
than 0. It is interesting to consider the saving in mass produced by having tubular
bones. Pauwels (1980) and Currey & Alexander (1985) estimated values of 8% and
13% respectively for the maximum saving in mass by having tubular bones. Since
limb bones must be accelerated and decelerated during locomotion and lightness
favours flying ability, this saving in mass is thought to be important and positively
selected. At the same time bones must resist stresses acting on them. Therefore; it
can be assumed that an optimal cortical thickness, or optimal K, exists. Alexander
(1982), Currey (1984) and Currey & Alexander (1985) made predictions for this
optimal K. They found different values regarding Merent mechanical requirements,
depending on whether bones were pneumatized or marrow-fled.
The following considerations should be borne in mind when comparing the mean
minimum K values obtained in this study with the predictions of Currey & Alexander
(1985):
(1) Marrow-fdled bones studied have a mean minimum K value of 0.65. These
results are very similar to the optimum value of K predicted by Alexander (1982)
(0.6) and Currey & Alexander (1985)(0.67), assuming marrow density is 930 kg*mP3
and bone density is 2 100 kg*m-3. According to the predictions of their model, bones
with this K would be selected for minimum mass and be strong enough not to yield
or fail to fatigue. At the same t i e , Currey & Alexander (1985) modelled an optimum
K of 0.75 for a stiff enough bone in bending. This value is very close to that obtained
in the present study with the partial sample of marrow-fled femora (0.74). Currey
& Alexander's mean calculated for sagittal K in birds was about 0.7, which is
intermediate between the optima for strength and stiffness.
(2) Mean minimum K values obtained for pneumatized bones and for the
pneumatized femora subsample were 0.77 and 0.85 respectively. Low values of
PNEUMATIZATION IN AVIAN BONES
507
cortical thickness are thought to be a compromise between yield strength requirements
vs. local buckling prevention. Our present results are also similar to those obtained
by Currey & Alexander (1985; sagittal K range 0.69-0.86) and lower than the
optima K predicted by Alexander (1982) and Currey & Alexander (1985) (K =0.93).
Indeed, Currey and Alexander (1985) suggested that it is almost impossible for a
bird bone to have a K value higher than those observed for pneumatized bones.
Otherwise, it would be impossible to withstand traumas in this area.
(3) Currey & Alexander (1985) suggested that perhaps distal limb bones may tend
to have lower values of K either in terrestrial mammals or flying birds. This
assumption seems correct for flying birds, according to our results: the only proximal
bone studied, the femur, always has K values higher than the total sample.
(4) Currey & Alexander (1985) anticipated that in both terrestrial mammals and
flying birds larger animals would show a tendency to have lower values of K (higher
values of cortical thickness) than related smaller animals. This expectation seems to
be in agreement with a previous result of Cubo & Casinos (1998), showing that
cortical area scales with positive allometry in the avian hind limb bones. However,
when minimum K from either hind limb bones or the total sample of birds of the
present study were regressed against body mass, results showed that K was independent of body mass, since the correlation coefficients were 0.088 and 0.068,
respectively.
We have shown that the mean minimum K is significantly lower in marrow-filled
than pneumatized bones and that mean minimum K is also significantly lower in
the marrow-filled than in the pneumatized femora subsample (Table 2). Does this
morphological difference have some mechanical significance?Mean bending strength
and mean flexural Young’s modulus are significantly higher for marrow-filed bones
than for pneumatized bones. Sub-samples corresponding to femora follow the same
pattern, but differences are not significant (Table 2). We wonder whether with a
greater number of femora results might be different, taking into account the results
obtained on cortical thickness reported above. Therefore, our findings indicate that
cortical thickness may be relevant for bone strength and stfiess. The question is
whether the presence of marrow, with a density approximately half that of the bone
(Alexander, 1982),is also relevant to the mechanical behaviour of the bone. In their
model Currey & Alexander (1985) assumed that marrow merely contributed to the
mass of the bone, but other authors (see, for example, Kafka, 1983) claim marrow
may be important to increase bone strength. In this situation, we wonder whether
the variation found in mechanical parameters is a direct effect of the presence or
absence of marrow or independent of it. As far as we know, no study is available
on the variation of strength and/or stiffness in avian bone. However, Bou et al.
(1991) carried out extensive research on bending moments at breaking in avian long
bones. Within the sample used (about 100 specimens for bending) variation of
maximum and minimum values of moments for animals with the same body mass
was twice as high or more, independent of whether bones were pneumatized or
not. Therefore, the null hypothesis to be tested is whether the differences in strength
found in the present research can induce variations in bending moments at breaking
within the range found by Bou et al. (1991).
According to Alexander (1983)
508
J. CUB0 AND A. CASINOS
where o is bone strength (as calculated in the present research), M, is the breaking
moment in bending, ys the maximum perpendicular distance from the neutral axis
to the outline, as in (l), and I, the second moment of area, with all the parameters
being considered relative to the sagittal axis. Therefore, assuming either marrowfilled or pneumatized bones to have elliptical cross sections:
o=
M.*yI
(l-Kq*Tn* r;"*rl
Given a mean value of strength in marrow-filled bones of 200 MPa and a K
value of 0.65 (Table 2),
Similarly, for the pneumatized bones (means,
Table 2, again).
CT=
139 MPa and K=0.77; see
In principle, we can assume that for the same body mass there is no geometric
difference between marrow-filled bones and pneumatized bones, with the only
exception of K. Therefore, calling C the quotient between the geometric parameters
4
we arrive at the following expressions:
@rMs O M ,
139=------1-0.773- 0.54
Therefore,
M, =
200*0.73-- 14.6/c
C
M, =
139*0.54
=7 5 / c
C
This means that, for the same body mass, the breaking moment in bending for
marrow-filled bones should be almost double that of pneumatized bones, a range
PNEUMATIZATION IN AVIAN BONES
509
of variation very similar to that found by Bou et al. (1991). According to this, it
seems there is no necessity to invoke a hydraulic strengthening effect (Kafka, 1983):
differences in cortical thickness alone could be sufficient to explain the higher
strength of marrow-filled bones. When results for Young’s modulus are considered,
conclusions are not very different: bending breaking moments of marrow-filled bones
ought to be 2.5 times higher than those of pneumatized bones, which, given the
results of Bou et al. (1991), is to be expected.
Swartz et al. (1992) showed that cortical thickness of forelimb bones of bats falls
within the range of previous values of K calculated for birds and pterosaurs by
Currey & Alexander (1 985). Therefore, the reduction of cortical thickness would be
a convergence of the three large groups of flying vertebrates (pterosaurs, birds and
bats). If according to the present analysis, hollow bones are less resistant in bending
and less stiff than marrow-filled bones, a question arises: what could be the selective
advantage of hollow bones? Swartz et al. (1992) argue that resistance to torsional
stresses, originated by downstroke movements in wings, can be important for flying
animals. Torsional stress is a direct function of the polar moment (J(Young, 1989)
and according to Swartz et al. (1992) this parameter would be maximized by circular
cross-sectional geometry of maximum outer diameter. So, hollow bone design would
involve a sacrifice of bending strength in order to obtain high values of torsional
strength, taking also into account that, as indicated above and previously (Cubo &
Casinos, 1994), the reduction of skeletal mass does not seem very important. Indeed,
the torsional effect in flying has been also advocated recently (Cubo & Casinos,
1998) to explain the disagreement between the directions of maximum bending
loads and maximum second moment of area in the avian humerus.
ACKNOWLEDGEMENTS
The Servei de Proteccio i Gestib de la Fauna (Generalitat de Catalunya) generously
provided the specimens used in this study. Alejandro de Giorgio (Serveis CientificoTkcnics, Universitat de Barcelona) prepared the IMAT program, following the
specifications of the authors. P. Zioupos (University of York) commented on the
paper; Robin Rycroft (Servei d’Assessorament LinGistic, Universitat de Barcelona)
corrected it for language. The editorial efforts of Marvalee H. Wake are much
appreciated. Thanks are also due to two anonymous referees. The project was
funded by DGICYT, grant no. PB 914282.
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