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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
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
* Author for correspondence (e-mail: jhorton{at}uci.edu)
Accepted 11 February 2009
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Summary |
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 TOP Summary INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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Key words: acellular bone, material properties, Young's modulus, stiffness, ribs
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INTRODUCTION |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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;
Moss, 1960), a distinction
based on whether osteocytes are embedded within the mineralized matrix
(Moss, 1960). The presence of
osteocytes creates a morphologically distinctive skeletal material with an
extensive interconnected network of microscopic canals (canaliculi) associated
with cell lacunae (Gray, 1941;
Moss, 1961;
Mjor, 1962;
Wassermann and Yaeger, 1965;
Cowin, 2007). Dendritic
processes radiate from the osteocytes and project into these canals allowing
for direct communication between the adjacent osteocytes and the external
environment via gap junctions
(Aarden et al., 1994;
Donahue, 2000;
Kusuzaki et al., 2000). Within
this network, osteocytes function as mechanoreceptors that facilitate
metabolic activities such as calcium hydrolysis, bone modeling and bone
remodeling (Lanyon, 1993;
Burger and Klein-Nulend, 1999;
Burr et al., 2002).
Osteocytes are a significant presence in cellular bone, as their numbers
range from 31,000 to 93,000 cells mm–3 for mammalian species
(Mullender et al., 1996).
Although acellular bone lacks osteocytes within the bone matrix, it is still
capable of recruiting periosteal osteocytes to regulate bone modeling and
remodeling (Takagi and Yamada,
1992; Kranenbarg et al.,
2005b), and to offset acalcemic conditions in both the environment
and diet (Takagi and Yamada,
1993). However, when a calcium deficiency exists in both water and
diet, callus formation during fracture repair in acellular bone is poor
compared with that in cellular bone (Moss,
1962). Nevertheless, acellular bone is able to adapt to changes in
loading regime by modeling and remodeling to decrease the strain resulting
from an applied load.
Acellular bone is a plesiomorphic character in vertebrates found in both
primitive craniates and vertebrate lineages
(Ørvig, 1965;
Ørvig, 1989). The
dermal bones of several extinct jawless craniates (notably the Heterostraci,
Anaspida and Thelodonti) were of aspidin, a type of acellular bone. However,
the exoskeletal head shields of the Osteostraci (jawless vertebrates) were
covered with cellular bone (Hanken and
Hall, 1993), as were components of the feeding apparatus of
Conodonts, the earliest known vertebrates
(Sansom et al., 1992), and
elasmoid fish scales (Meunier et al.,
2003; Meunier et al.,
2004). However, teleost fishes are the only vertebrates with a
skeleton composed solely of acellular bone
(Moss, 1961). Mapping
acellular bone on the teleost phylogeny suggests an increasing trend toward
acellularity, with the superorder Percomorpha containing a little more than
85% of known acellular bony fishes
(Kranenbarg et al., 2005a).
The multiple origins of acellularity within teleosts indicate a possible
selective advantage of this type of bone, yet there is no consensus for the
functional role of acellular bone, as the factors that have been investigated
such as environment, activity level and gross morphology do not predict the
presence of acellularity (Moss and
Freilich, 1963; Moss,
1965). Therefore, the adaptive significance or selective pressures
that lead to the repeated evolution of acellular bone in the teleosts remain
unclear.
A functionally important mechanical property of bones is stiffness, both in
the whole element sense and in the material sense. For example, the long bones
of vertebrates must be stiff enough to provide the necessary support to act as
efficient levers (Currey,
2002). Moreover, the mechanical properties of bones are influenced
by several hierarchical levels of organization, including composition and
microstructure (Fratzl and Weinkamer,
2007). One factor that affects stiffness is porosity at the
microscale (1–100 µm), as an increase in bone porosity will cause a
substantial reduction in stiffness. Schaffler and Burr
(Schaffler and Burr, 1988)
derived a formula from experimentation that suggests that bone with normal
mammalian cellularity will be about 73% as strong as bone without the cell
spaces. This raises the possibility that the adaptive significance and
selective pressures that lead to the repeated evolution of acellular skeletons
in teleost fishes is an increase in stiffness relative to cellular bone.
The aim of this study was to measure flexural stiffness and second moment of area (I) in order to determine the modulus of elasticity (Young's modulus, E) in an exemplar acellular fish bone to: (1) test whether acellular bone is stiffer than literature values for cellular bone in other fish and terrestrial vertebrates; (2) determine the variation in stiffness across the rib series from the anterior to the posterior direction; (3) assess variation in the stiffness of ribs from proximal to distal; and (4) partition variation in the flexural stiffness of the ribs into a structural component (I) and a material component (E).
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MATERIALS AND METHODS |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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Rib dissection
Ribs were dissected from the left side of fresh frozen fish. Excess
connective tissue was removed under a dissection microscope with jeweler's
forceps. Ribs were measured, and marked with a permanent felt-tip marker at
three positions along their length (25%, 50% and 75% of total length) –
proximally to distally, and stored in teleost Ringer solution at 6°C for
no more than 48 h before tests were performed. The first 12 ribs of M.
polyacanthocephalus were used for this study; ribs 13 and 14 are reduced
and extremely fragile and were difficult to remove without fracturing.
Material testing and area analysis
We used a three-point bending test to measure flexural stiffness of fish
ribs. Tests were performed on a custom-made fixture mounted in a Synergie 100
test system (MTS, Eden Prairie, MN, USA) with either a 500N load cell or a 50N
load cell depending on rib size. Ribs were supported by two load points with a
1 cm span and centrally loaded with a minimal force (approximately 0.005N) to
secure the bone in place, and to ensure zero rotation along the long axis. The
slight natural curvature of the rib bones ensured that each specimen and
location were tested in the same anatomical orientation: the medial surface of
the rib was depressed by the indenter, and the two supports were in contact
with the lateral surface. We then loaded the rib four times at each location
(25%, 50% and 75%), in a random order, to a maximum deflection of 0.3 mm at a
test speed of 0.1 mm s–1; data were acquired at 120Hz. Bone
has a very small viscous component, so our choice of indenting speed (strain
rate) should not affect the measured flexural stiffness. The deflection
distance was chosen to minimize the possibility of micro-crack formation; and
analysis of the multiple tests at each location did not show any trend toward
decreasing stiffness. Some ribs had callused areas but these were well away
from the region we tested.
After testing a rib we manually sectioned the bone (0.5–1.0 mm thick)
from each of the tested positions using a microtome blade. We then took
digital images of the rib cross-section at the point of load contact using a
Zeiss dissecting scope (Stemi 2000-C, Jena, Germany) with a top-mounted Spot
Insight color camera (IN-320, Sterling Heights, MI, USA). Photographs were
transferred to a Macintosh computer using the Spot (v. 3.3.2) software program
in a jpeg format. Cross-sectional area (CSA) was measured from the ribs of
seven individuals, whereas six were used for material testing. Analysis of
photographs and raw output data from material testing was performed using a
customized MatLab (v. 7.0) script that calculated the second moment of area
with respect to a neutral axis through the center of area parallel to the
major axis of the ellipse that best fitted the outline of the cross-section.
The rib was tested with the medial surface up, so this neutral axis would be
perpendicular to both the long axis of the rib and the direction of
deflection. Cross-sectional images were scaled, and both first (geometric) and
second moments of area about the neutral axis (NA) were quantified. The script
then used the equation:
 | (1) |
Of substantial concern is the determination of E from a beam
equation with assumptions that we violated in some way. The most pressing of
these is the assumption that the deformations are caused solely by bending
rather than shear, which is certainly true for very long thin beams. The
literature for prismatic beams of bone indicates that if the ratio of
supported length to depth is less than 15:1 then shear plays a substantial
role and the modulus will potentially be substantially underestimated
(Spatz et al., 1996). Our
ratios ranged from 7.5 to 36, with many samples below the cutoff for solid
beams. Because there is not even an empirical formula for hollow cylindrical
structures we assessed the effect of aspect ratio on stiffness with a
regression. There was no relationship between the two variables, and a
breakpoint analysis did not show the expected decline in stiffness as the
ratio decreased. We attribute this to the hollow cross-section of the beam.
The beam equation also assumes a constant cross-section. Though there was a
distinct taper to the ribs we chose a very short span so as to minimize the
difference between cross-section at the two end supports and we measured first
and second moments of area at the indenter. The gross appearance of the ribs
is that of a monotonically tapering beam, so we would not expect more than a
10% difference in CSA from one end of the tested section to the other. The
very slight curvature of the rib amounted to a ratio of radius of curvature to
depth of more than 8, so we can ignore the curvature
(Young and Budynas, 2002).
We quantified the contribution of the hollow cylinder morphology to the
flexural stiffness of the rib by calculating 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 (It):
 | (2) |
Compositional analysis
After material testing, whole hydrated ribs (including segments used for
cross-sectional photos) were weighed, and lyophilized for 30 h. Dry mass
(organic plus mineral material) was recorded for the samples before ribs were
placed in a 500°C furnace for 24 h to remove the organic content from the
dry mass. The remaining ash content was weighed immediately upon removal from
the furnace, to avoid possible water gains from room humidity. Water content
was calculated by subtracting the dry mass from the original bone mass,
whereas the mineral content is expressed as mass of ash divided by the dry
mass.
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RESULTS |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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The geometric CSA of the ribs decreased significantly from the first to the twelfth rib for all individuals (quadratic regression; R2=0.87; P<0.001; Fig. 3). Both the linear term (F1,47=163.23; P<0.01) and the quadratic term (F1,47=25.11; P<0.001) were significant. The quadratic regression best fits the data due to the difference in mean CSA between the first and second rib, which was roughly 40%, and the relatively minor difference in mean CSA between subsequent ribs of approximately 10% (Fig. 3). The absolute maximum CSA was 1.25 mm2 at the first rib and 0.21 mm2 at the twelfth rib. Although individuals differed significantly (P<0.001), raw data from each individual exhibited the same trend shown in Fig. 3.
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A structure's resistance to bending is determined not only by its stiffness (E) but also by the second moment of area. The second moment of area (INA) was found to decrease caudally for all individuals (quadratic regression; R2=0.71; F1,47=25.11; P<0.001); and, while individuals differed, the trends were the same (Fig. 5). Results were similar to the geometric, or first moment of area, data (see Fig. 3), including the considerable difference between the mean INA values of the first and second rib, of 48%, and subsequent ribs that differed by no more than 10% (Fig. 5). The maximum average INA was 0.12 mm4 at the first rib and 0.01 mm4 at the twelfth rib. Although individuals differed significantly (P<0.001), raw data from individuals exhibited a similar INA trend as shown in Fig. 5.
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The mean INA was found to significantly decrease distally along the length of a rib for all individuals (R2=0.87; F2,10=5.99, P=0.016; Fig. 6A). 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, and trends were the same across individuals. Furthermore, the absolute maximum INA was 0.252 mm4 found at the 25% position and the absolute minimum was 0.001 mm4 at the 75% position (see Fig. 6A). To determine the relative difference between INA at each of the three positions we normalized the data by using the midpoint position (50%) as the reference. The proximal position was found to be 56% greater than the midpoint, compared with the relatively small 8% increase at the distal locale (Fig. 6B). The increased INA at the proximal position of the ribs is generally associated with the prominent hole typically found at this location.
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The mean Young's modulus, or stiffness (E), of the acellular ribs ranged from 3.67 to 8.40GPa with a mean ± s.e.m. of 6.48±0.31GPa (Fig. 7A). A quadratic effect was found for all individuals (R2=0.30; F1,47=9.28, P<0.01; quadratic coefficient=–0.097), as rib stiffness increased to a peak value of 8.40GPa at rib number 5 and then gradually decreased caudally. As expected, no significant linear effect was found (R2=0.20; F1,47=0.53; P=0.47); stiffness data did not exhibit the same trends as first and second moments of area (see Figs 3 and 5). No interaction was found between fish size and rib stiffness (P=0.22).
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The flexural stiffness (EI), the product of the two primary factors that ultimately contribute to bending resistance of a structure, showed similar trends to the first and second moments of area but not to material stiffness (Fig. 8). 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 geometric data permitted us to generate a moment ratio, which showed that the hollow cylinder increases the flexural stiffness by 12.0% on average over a solid cylinder of similar external dimensions (Fig. 9). A value greater than 1 indicates that the rib structure with a hollow cylinder better resists bending, whereas a value less than 1 means a higher bending resistance for the solid cylinder; if equal, an indistinguishable difference in efficiency between the two structures would result.
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Compositional analysis
There was no significant difference in the mineral content (% dry mass)
between ribs (R2=0.457; P=0.484). In addition,
percentage mineral content did not differ between individuals
(F13,27=0.91; P=0.744;
Fig. 10). Therefore,
regardless of size or location, each rib contained the same amount of mineral
– 71% of dry mass.
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DISCUSSION |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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). However, the
mean stiffness (6.48 GPa) is lower than that reported for two species of fish
with cellular bone: the ribs of Cyprinus carpio [8.1 GPa; using
nano-indentation (Roy et al.,
2000)] and the pelvic metapterygia of Polypterus sp.
[17.6 GPa; using three-point bending
(Erickson et al., 2002)]. This
is contrary to our expectation that acellular bone would be stiffer because
the solid material should be stiffer than material permeated with holes and
channels. The flexural stiffness of a structure, which is the product of E and I, is the measure of an object's ability to resist bending. Variation in the ability of sculpin ribs to resist bending is primarily due to the geometric arrangement (INA) rather than stiffness (E) of the bone, as the flexural stiffness of the ribs along the body correlates with both first and second moments of area (Fig. 8) but not with material stiffness or mineral content (Figs 7 and 10). Our data show a range difference of almost 3 times for the elastic modulus, and approximately 13 times in second moment of area (Figs 5 and 6). It can therefore be concluded that the structural arrangement of the material (including mineral distribution) accounts for either the decrease or increase in stiffness, as seen across the rib series and along a rib. We conclude that structure dominates, assuming uniform mineral distribution, and is the primary determinant of variation in flexural stiffness.
The ribs of the great sculpin are hollow cylinders of bone
(Fig. 2), though neither of the
usual explanations for this morphology are likely causal factors in this fish.
In tetrapods, but not teleost fishes, the hollow bone marrow cavity contains
hematopoietic and mesenchymal stem cells
(Liem et al., 2000). A second
function of hollow bones is mechanical: hollow cylinders have an increased
second moment of area (I) relative to solid cylinders of the same
mass. Both flexural stiffness (EI) and Euler buckling
[F=(K
2EI)/l2]
are dependent on I, so a stiffer and less failure-prone bone can be
constructed of less material if it is hollow. One structure that takes
advantage of the added strength is the hollow tubes in the jaws of the
durophagous horn shark, Heterodontus francisci, which are 60 times
stiffer due to their shape (Summers et
al., 2004), allowing the organism to resist jaw deformation while
crushing hard prey. Our results have shown that while there is a small
increase in flexural stiffness due to the hollow cavity in ribs
(Fig. 9) the advantage is not
nearly as great as that seen in mammals and birds
(Biewener, 1982), or
cartilaginous fishes (Summers et al.,
2004). We suppose that the ribs of teleost fishes are hollow for
other reasons. The hollow core may increase the surface area for bone
resorption as it has been suggested that acellular bone is mobilized for
calcium homeostasis during calcium deficiency
(Takagi and Yamada, 1992).
Also, tubular structures are most efficient in dealing with multidirectional
loading or torsional stress (Currey, 2003), which are the likely loading
conditions of the ribs given their anatomical position; therefore the ribs may
be hollow to resist structural failure when they are subjected to multiple
loading regimes.
Although bone stiffness does not appear to explain the adaptive significance of acellular bone, their acellularity may have a beneficial effect on other material properties. Low stiffness values are normally correlated with decreased mineral levels. However, a decrease in mineral content may lead to a more compliant material better equipped to resist fatigue damage, whereas porous materials are typically better at limiting crack propagation. Future work on strength, toughness and fatigue resistance may reveal possible selective pressures that explain the multiple evolutions and recent prevalence of acellularity in teleost fishes.
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Footnotes |
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References |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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) tested by nanoindentation
(Roy et al., 2000
) of Polypterus sp. tested by
three-point bending (Erickson et al.,
2002
; 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.