First published online April 17, 2009
Journal of Experimental Biology 212, 1413-1420 (2009)
Published by The Company of Biologists 2009
doi: 10.1242/jeb.020636
The material properties of acellular bone in a teleost fish
Jaquan M. Horton* and
Adam P. Summers
Department of Ecology and Evolutionary Biology, University of California
Irvine, CA 92697, USA and Friday Harbor Laboratories, University of
Washington, Friday Harbor, WA 98250, USA
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Fig. 1. Dorsal radiograph image of an adult Myoxocephalus
polyacanthocephalus showing skeletal morphology and the relative position
of the dorsal ribs along the body. Note: the ribs project in a
posterior–lateral direction and provide no lateral protection of the
visceral cavity. Also there is a callus located on the midpoint of rib nine of
the left side of the fish. Scale bar, 4 cm.
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Fig. 2. Silhouette images from various individuals showing the morphological
variation in the cross-sectional area (CSA) of both bone material and the
hollow cylinder (shown in white) at one of three positions (25%, 50%, 75%)
along the length of the rib. Note: r1/25=rib 1, 25% position.
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Fig. 3. Geometric CSA of the first to twelfth ribs of M.
polyacanthocephalus. The CSA significantly decreased caudally for all
individuals (quadratic regression; R2=0.87;
F1,47=25.11; P<0.001). Individuals differed
significantly due to the size variability but the overall trends were the same
(P<0.001). A substantial difference was found in CSA between the
first and second ribs, which was roughly 40%, and a relatively minor CSA
difference between subsequent ribs of approximately 10%. The maximum CSA was
1.25 mm2 at the first rib and 0.21 mm2 at the twelfth
rib. Values adjacent to the rib number on the x-axis correspond to
the number of ribs tested. Numbers in parentheses above a data point indicate
the total number of ribs containing a callus ring at some point along its
structure. Arrows indicate relative position of the first and twelfth rib in
the fish body. All data were pooled. Black bars denote the mean, the box
represents the 95% confidence interval, and the whiskers are the maximum and
minimum values of a given data point. TL, total length.
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Fig. 4. The positional effect of the CSA along the length of a rib bone. (A)
Variation in CSA along the length of the ribs at three locales (25%, 50%,
75%). The mean CSA decreased significantly distally for all individuals
(R2=0.95; F2,10=25.11,
P<0.001). Note that the high maximum and minimum data values,
illustrated by the whiskers, correspond to individual differences; however,
trends were the same across individuals. (B) Relative CSA at the three
positions along the length of the rib referenced by the midpoint of the rib
(50%), indicated by the dashed line. Compared with the midpoint the proximal
position had a 21% greater area in contrast to a 7% reduction distally. All
data were pooled. Black bars denote the mean, the box represents the 95%
confidence interval, and the whiskers are the maximum and minimum values of a
given data point. Values adjacent to rib position on the x-axis
correspond to the total number of sections tested from a given locale. (C)
Silhouettes of the CSA at three points along the length of a rib: 25%, 50% and
75%, from left to right.
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Fig. 5. Mean second moment of area (INA) of the first to
twelfth ribs of M. polyacanthocephalus. INA was found to
decrease significantly caudally for all individuals (quadratic regression;
R2=0.71; F1,47=25.11;
P<0.001). Individuals differed significantly due to the size
variability but the overall trends were the same (P<0.001). A
sizeable difference was found in INA values between the
first and second ribs, which was approximately 48%, and a relatively minor
difference between subsequent ribs of roughly 10%. The maximum
INA was 0.12 mm4 at the first rib and 0.01
mm4 at the twelfth rib. Values adjacent to the rib number on the
x-axis correspond to the number of ribs tested. Arrows indicate the
relative position of the first and twelfth rib in the fish body. All data were
pooled. Black bars denote the mean, the box represents the 95% confidence
interval, and the whiskers are the maximum and minimum values of a given data
point.
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Fig. 6. Variation in INA along the length of the ribs at three
relative positions (25%, 50% and 75%). (A) The mean INA
significantly decreased distally for all individuals
(R2=0.87; F2,10=5.99,
P=0.02), and between positions. The maximum and minimum data values
indicated by the whiskers correspond to individual differences in
INA for a given rib, as no size effect was found
(P>0.05) and trends were the same across individuals. The maximum
INA was 0.252 mm4 found at the 25% position and
the minimum was 0.001 mm4 at the 75% position. (B) Relative
INA at three positions along the length of the rib
referenced to the midpoint (50%). The proximal position was found to be 56%
greater than the midpoint, compared with the 8% increase at the distal locale.
The increased INA at the proximal position of the ribs is
generally associated with the prominent hole typically found at this location.
All data were pooled. Black bars denote the mean, the box represents the 95%
confidence interval, and the whiskers are the maximum and minimum values of a
given data point. Values adjacent to rib position on the x-axis
correspond to the total number of sections tested from a given locale. (C)
Silhouettes of the CSA at three points along the length of a rib: 25%, 50% and
75%, from left to right.
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Fig. 7. (A) Mean Young's modulus (E) of the first 12 ribs from the cranial
to caudal direction of M. polyacanthocephalus. The range fell between
3.67 and 8.40 GPa with a series mean ± s.e.m. of 6.48±0.31 GPa.
A quadratic effect of rib stiffness was found for all individuals
(R2=0.30; F1,47=9.28,
P<0.01; quadratic coefficient=–0.097). The material
stiffness increased to a peak value of 8.40 GPa at rib number 5 and then
gradually decreased caudally. Comparison of material stiffness values of
acellular bone in this study with those of cellular bone in other fishes are
denoted by the symbols on the y-axis: carp (Cyprinus carpio)
rib bone in a transverse plane (*) and longitudinal plane
( ) tested by nanoindentation
(Roy et al., 2000 ), and pelvic
metapterygia ( ) of Polypterus sp. tested by
three-point bending (Erickson et al.,
2002). (B) Positional differences in material stiffness along the
length of a rib; values are in sequential position order as indicated in the
key. The stiffness decreased significantly distally at each of the three
positions for all individuals (F2,144=4.16;
P=0.018); ribs number 11 and 12 exhibited non-significant trends. The
three data points in a given column bounded by dashed lines correspond to, and
are used to determine, mean elastic modulus of the same rib found above in A.
Values adjacent to the rib number on the x-axis correspond to the
number of ribs tested. Graphs contain pooled data; black bars are the mean,
box represents the 95% confidence interval, and whiskers are the maximum and
minimum values of the data.
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Fig. 8. Flexural stiffness (EI) of the first 12 ribs in the cranial to
caudal direction of M. polyacanthocephalus. Data followed the same
trend as first and second moments of area for ribs along the body. The mean
EI differed significantly between ribs (linear effect:
R2=0.79; F1,48=134.86;
P<0.001), and between position (linear effect:
F2,148=14.77; P<0.001). The maximum mean value
was 0.312, the minimum mean value was 0.031. Values adjacent to the rib number
on the x-axis correspond to the number of ribs tested. Graphs contain
pooled data; black bars are the mean, box represents the 95% confidence
interval, and whiskers are the maximum and minimum values of the data.
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Fig. 9. Moment ratio: empirical vs theoretical second moment of area
(It) for each rib. The contribution of the hollow cylinder
morphology to flexural stiffness was calculated from the ratio of the measured
INA of a rib to that of a solid cylinder with the same
first moment of area as the rib section:
 ; where
AR is the area of the rib cross-section. A value greater
than 1 indicates that the rib structure with a hollow cylinder better resists
bending, whereas a value less than 1 indicates that a solid cylinder better
resists bending. A value of 1 – illustrated by the dashed line –
indicates that the rib is just as good at resisting flexion as a solid
cylinder. Values adjacent to the rib number on the x-axis correspond
to the number of ribs analyzed. Graph contains pooled data; black bars are the
mean, box represents the 95% confidence interval, and whiskers are the maximum
and minimum values of the data.
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Fig. 10. Mean mineral content (% dry mass) of the first to twelfth ribs of M.
polyacanthocephalus. All ribs were found to contain the same percentage
mineral material, as no significant difference was found between ribs
(R2=0.457; P=0.484) or individuals
(F13,27=0.91; P=0.744). The mean percentage
mineral was 70.89% dry mass. Values adjacent to the rib number on the
x-axis correspond to the number of ribs analyzed at a give locale.
Arrows indicate the relative position of the first and twelfth rib in the fish
body. All data were pooled. Black bars denote the mean, the box represents the
95% confidence interval, and the whiskers are the maximum and minimum values
of a given data point.
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© The Company of Biologists Ltd 2009
