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First published online September 14, 2007
Journal of Experimental Biology 210, 3319-3327 (2007)
Published by The Company of Biologists 2007
doi: 10.1242/jeb.006189
The contribution of mineral to the material properties of vertebral cartilage from the smooth-hound shark Mustelus californicus
1 Comparative and Evolutionary Physiology, Department of Ecology and
Evolutionary Biology, 321 Steinhaus Hall, University of California, Irvine, CA
92697-2525, USA
2 Department of Chemical Engineering, University of South Florida, Tampa, FL
33612, USA
* Author for correspondence (e-mail: porterm{at}uci.edu)
Accepted 17 July 2007
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Summary |
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Key words: elasmobranch cartilage, mineral content, stiffness, strength, viscoelastic, elastic
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Introduction |
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
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). For instance,
we can study mechanics of the crystal structure in apatite, individual
trabeculae in spongy bone, compact bone, or an entire long bone. At each of
these levels we can test the mechanical properties of tissue and determine how
these properties will influence the performance of the animal. This hierarchy
presents opportunities to understand biological materials themselves as well
as the arrangement of the materials within a structure.
The relationship between mineral content and properties of hard biological
materials, particularly mammalian bone, has been explored in depth
(Currey, 1999;
Currey, 2002). Small changes in
mineral content can have large effects on material properties in hard tissues,
and those with larger mineral fractions are stiffer and stronger than those
materials with less mineral. A biological example of this relationship is the
rostrum of the Blaineville's beaked whale Mesoplodon densirostris,
which is composed of 96% mineral, resulting in an incredibly stiff material
(46 GPa) (Rogers and Zioupos,
1999; Zioupos et al.,
1997). The fin whale Balaenoptera physalus tympanic bulla
has 14% less mineral and is 35% less stiff
(Currey, 1979). More dramatic
still is the red deer antler Cervus elaphus, with 40% less mineral
than M. densirostris and a 78% decrease in stiffness
(Currey, 2002). However, the
relationship between the amount of mineral and material properties is
confounded in the aforementioned examples by testing different bones from
different animals and thus different structures.
Structure (arrangement of mineral) is also a significant predictor of
material properties. Lordosis of vertebrae in sea bass Dicentrarchus
labrax L. resulted in structural changes in vertebral morphology; there
was an increase in both bone volume and second moment of area (mm4)
in the lordotic compared to non-lordotic vertebrae
(Kranenbarg et al., 2005a).
Although there is a great deal of literature dedicated to understanding the
influence of mineral amount and arrangement in bone, the nature of this
relationship is not well known in other mineralized materials.
Elasmobranch vertebral cartilage is `areolar'; it has a web-like
infiltration of mineral in a hyaline cartilage matrix that varies in
morphology by species (Moss,
1977; Ridewood,
1921). Portions of the mineral in elasmobranch vertebrae are
arranged in elaborate patterns that vary by species, and these interspecific
mineralization patterns are variable enough to be of systematic importance
(Fig. 1)
(Ridewood, 1921). For example,
the mineral in the vertebrae of the shortfin mako Isurus oxyrinchus
is arranged in plates around the centra, while vertebrae of the silky shark
Carcharhinus falciformis are covered with a thick crust of mineral
(Fig. 1)
(Porter et al., 2006).
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). In
elasmobranch cartilage, a 16% increase in mineral content resulted in an 81%
increase in ultimate strength and a 95% increase in stiffness. The seven
species examined had a diversity of vertebral mineral patterns, such that the
relationship between mineral structure and mineral amount was confounded.
Mineralized biological materials are described as anisotropic elastic
solids up to their yield points and do not display substantial time-dependent
behavior (Vogel, 1988;
Vogel, 2003;
Wainwright et al., 1976). This
has been verified in bone tested using biologically relevant loading regimes
(Currey, 1989). Cartilage, in
contrast, is a viscoelastic material having both fluid and solid
characteristics, and therefore displays strain-rate dependent mechanical and
material properties. Unmineralized cartilage, such as bovine articular
cartilage, becomes stiffer with increasing strain rate
(Li et al., 2003;
Park et al., 2004).
Cartilaginous vertebrae of elasmobranchs also have a large mineral component
and so may not exhibit the viscoelastic behavior seen in mammalian
cartilage.
The goals of the present study were: (1) to determine the intraspecific variation in mineral content of vertebral cartilage in a single species; (2) to isolate the effect of mineral on the response to load of vertebral cartilage by serially removing mineral from vertebrae of the same morphology and comparing this to the effect of interspecific variation in mineral; (3) to compare the influence of mineral content on material properties in Mustelus to other elasmobranchs; and (4) to assess the viscoelastic behavior in elasmobranch cartilage by testing the strain rate dependence of vertebrae with and without mineral.
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Materials and methods |
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). We used five
adult animals (four males and one female who was not gravid) ranging from
76–81 cm in total length, caught off the coast of Southern California
during the spring and summer of 2005 (Table
1).
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Material properties
We removed at least 40 individual vertebrae from freshly frozen vertebral
columns. We chose vertebrae from the region directly under the first dorsal
fin to standardize for morphology and potential differences in material
properties that may occur from the anterior to posterior end of the column
(Fig. 1). We excised neural and
hemal arches from the centra leaving an unadorned disk of mineralized
cartilage. Vertebra mass, length (distance in mm from anterior surface to the
posterior surface), and diameter of the anterior surface were measured.
A total of 204 vertebrae were separated into three groups; time zero (four
vertebrae from each animal), control (16 vertebrae from each animal), and
demineralized (at least 16 vertebrae from each animal). Time zero vertebrae
were maintained in elasmobranch Ringers
(Forster et al., 1972) at room
temperature for no more than 2 h before being subjected to a uniaxial,
unconfined compressive test to failure between two nonporous platens. Control
centra were maintained in elasmobranch Ringers solution at 4°C with
continual gentle stirring while suspended in tissue cassettes. These centra
were treated similarly to the time zero centra, but control centra were tested
during the time course of the experiment (at the same times as the
demineralized treatments). Concurrently, we demineralized the remaining
vertebral centra from the five vertebral columns with a chelating agent,
ethylenediaminetetraacetic acid (EDTA). Centra were immersed in 4 l
elasmobranch Ringers with 83 mmol l–1 EDTA, minimum ratio of
one vertebra to 100 ml of EDTA. Vertebrae in solution were incubated in a cold
room at 4°C under the same conditions described above for the control
vertebrae.
Demineralized samples were x-rayed daily to qualitatively determine mineral loss. We determined mineral loss by comparing the radio-opaque, highly mineralized portions, of the vertebrae to x-ray films from previous days. We subjected a subset of four demineralized vertebrae and four control vertebrae from each animal to materials testing at intervals of 39, 87, 135 and 279 h. The diameter and length of each vertebra were measured with a dial caliper to the nearest 0.01 mm. Control and demineralized vertebrae pairs were randomly assigned to a strain rate group (1, 5, 10 or 20% of their length s–1) and were tested in a compressive test to failure using a MTS Mini Bionix 858 (Eden Prairie, MN, USA) with a 5 kg load cell.
Using published values for tail beat frequencies and silhouettes of fast
starts in sharks to determine curvature
(Domenici et al., 2004;
Graham et al., 1990), and
assuming the vertebral column acts as a uniform beam, we calculated the strain
rate that we expected vertebrae to experience. This upper bound on strain rate
is approximately 7% s–1, so we chose experimental strain
rates above and below this value. The strain rate we calculated is in
agreement with literature values for human spinal column connective tissue
(Stokes, 1987).
Compression testing resulted in load–displacement (N, mm) curves,
which were analyzed using a custom script written in Matlab version 7.0 R.12
(The Mathworks Inc., Natick, MA, USA). We generated stress–strain curves
and measured stiffness, ultimate strength, yield strength and yield strain for
each vertebra. The above variables provide information regarding the response
of mineralized cartilage to compressive loads. Stress was calculated using the
cross-sectional area of the anterior surface of the vertebrae. Stiffness is
the material's ability to resist compression and was measured as the linear
region of the stress–strain curve before the material yielded. Ultimate
strength is the maximum stress that can be applied to the material before it
fails or breaks (Currey, 2002;
Vogel, 2003;
Wainwright et al., 1976).
Yield strength and strain are measured at the clear inflection point seen in
stress–strain curves of mineralized tissues, where the material
transitions from elastic to plastic behavior and begins to permanently deform.
Stress–strain curves from each vertebra were analyzed three times using
the Matlab script to ensure accurate estimation of the above properties.
We determined mineral content after material testing by ashing vertebrae at 400°C for at least 8 h to obtain the mineral mass. Preliminary experiments established that 8 h was sufficient time to completely ash the vertebral sample from this species of shark. We calculated percent mineral content by dividing the mineral mass by the dry mass of each vertebra.
Statistical analyses
Stiffness and strength were analyzed using a two-way ANOVA in JMPIN (SAS
Institute, Cary, NC, USA) with mineral content and strain rate as effects
(Zar, 1999). We examined the
overall effect of mineral content on stiffness and strength using linear
regression models. We examined the viscoelastic properties by binning our data
in two groups; vertebrae with greater than 45% mineral content (the vertebral
mineral content (%) found in M. californicus) and vertebrae with less
than 15% mineral. We are testing the unmineralized cartilaginous component of
the tissue when examining vertebrae with less than 15% mineral content. We
compared strain rate dependence in fully mineralized and demineralized
vertebrae with an analysis of variance (ANOVA).
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Results |
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
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Material properties
Strength increased significantly with mineral content in vertebrae that had
never been treated with EDTA, whether compared across several species
(R2=0.58; P<0.001) or looking exclusively at
M. californicus (R2=0.112; P<0.001)
(Fig. 4A). Stiffness increased
significantly with mineral content only across species where both mineral and
morphology were varying (R2=0.604; P<0.001)
(Fig. 4B)
(Porter et al., 2006).
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Strength and stiffness increase significantly as mineral content in the vertebral cartilage increases (R2=0.64; P<0.001 and R2=0.36; P<0.001, respectively) (Fig. 5A,B). At biologically relevant mineral contents (approximately 50% mineral), stiffness values vary greatly.
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Stiffness is a strain rate dependent material property in demineralized cartilage but not in mineralized cartilage (Table 2). Fully mineralized vertebrae are also significantly stiffer than demineralized vertebrae (Fig. 8). Increasing strain rate during compressive testing did not influence stiffness of mineralized Mustelus vertebrae (P=0.818). Stiffness in vertebrae with less than 15% mineral increased as the strain rate increased (F3,30=10.693; P<0.001).
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; Currey,
2002). Material properties of vertebrae from the gray smooth-hound
M. californicus are strongly influenced by the mineral content. We
can now compare the effect of mineral content to that of structure and
determine how it influences material properties. We tested the viscoelastic
response of mineralized elasmobranch cartilage and found that material
properties were not influenced by the biologically relevant strain rates
tested in this study. Our results suggest that, at these strain rates,
elasmobranch vertebral cartilage is acting as an elastic solid, validating
interpretations from quasistatic testing.
Mineral variation
The amount of mineralization in elasmobranch vertebral cartilage shows
variation at three levels of organization: within individual, intraspecific
and interspecific (Fig. 2;
Table 1). At the low end,
within individual variation is just 5% (Individual 2, 50–45%), while at
the high end, the 20 vertebrae from individual 5 varied over 32%
(64–32%), nearly the entire range for the species (35%)
(Fig. 2). The gray smooth-hound
is exceptionally variable in its mineralization; not only did the range of
mineralization exceed that of the other seven elasmobranch species previously
studied, but it also exceeded the range of all seven combined (24%)
(Porter et al., 2006). This is
in contrast to the pattern in mammals where variation is nearly exclusively at
the interspecific level (Currey,
2002). For example, mean mineral content from 25 bovine femurs was
66.7% and the standard error was only 0.17
(Currey, 1979). Interspecific
variation in mineral content is similar in mammals (37%) and elasmobranch
vertebrae (35%). An exemplar low mineral content value from mammalian tissues
is that of reindeer antler (59%), and bone can be as mineralized as
Blaineville's beaked whale rostrum (96%)
(Currey, 1979;
Rogers and Zioupos, 1999).
The high intraspecific variation we see in Mustelus may be caused
by one or more than one characteristic of elasmobranch vertebral cartilage.
Smooth-hounds are relatively short lived sharks (
10 years) compared to
the other species we have studied (20–60 years)
(Compagno, 1984). As sharks
age, their mineral content may asymptotically increase towards a maximum
dictated by the biochemistry of the cartilaginous matrix
(Dingerkus et al., 1991). As
an intriguing aside, the single female we tested had stiffer vertebrae than
the male sharks, even though all five animals were approximately the same size
(Table 1). This could be
related to hormonal changes that may be contributing to sexual dimorphisms
noted in elasmobranchs, or physiological differences associated with
reproductive cycle (Kajiura et al.,
2005). Furthermore, M. californicus is a rapidly growing
shark; females have been found to reach maturity after 2–3 years while
males are mature after 1–2 years. Rapid and differential growth rates
between sexes may potentially influence mineral content in the cartilaginous
axial skeleton (Yudin and Cailliet,
1990).
The physiological and mechanical factors mediating mineralization in
elasmobranch cartilages are largely unexplored, though we do know that it is a
`deposition only' system (Dean and
Summers, 2006). Hypermineralization in the form of trabeculae does
not appear to develop as a direct response to stresses imposed on the
skeleton, though trabeculae appear in regions where they will experience high
stresses (Summers, 2000).
Within a species the mineralization patterns are incredibly conserved, but
they do vary ontogenetically (Ridewood,
1921). We controlled for this uncertainty by testing mature
animals of similar total lengths (Table
1).
Structure, the microscopically visualized mineral distribution in a
cartilaginous matrix within shark vertebrae is consistent within a species, so
the variation we found in the material properties of the fully mineralized
smooth-hound vertebrae is largely due to the amount of material
(Fig. 2)
(Ridewood, 1921). In previous
work on seven shark species, vertebrae varied in both qualities –
structure and amount of material. By integrating these data sets we could
begin to tease apart the effect of shape independently of the effect of
material amount. We compared the effect of natural mineral content variation
in a single species to the confounded influence of mineral arrangement and
amount across the seven species tested earlier
(Porter et al., 2006) in
addition to M. californicus tested here. For example, in M.
californicus, varying mineral content by 10% does not increase the
stiffness as we might predict based on bone models
(Currey, 2002). However, when
we tested multiple structures from eight species, increasing mineral content
by 10% increased stiffness by 110 MPa (Fig.
4) (Porter et al.,
2006). Likewise, increasing mineral content by 10%, also increases
strength by 44% when varying structure and mineral content (multiple species)
but only 32% for just mineral content (within smooth-hound). Mineral
arrangement has a greater ability to influence material properties than the
amount. Our interpretation, that structure matters more than mineral content,
is consistent with the data from mammalian bone, where a 7.4% difference in
mineral content between antler and bovine femur (small change of mineral
amount for wildly different mineral arrangement) yields a 27% increase in
bending strength and a 45% increase in stiffness
(Currey, 1979). In other words,
structure (arrangement of mineral) trumps material (amount of mineral) in
determining response to load.
This is a caveat to the interpretation of the EDTA results. As
EDTA chelates the mineral there is the possibility that differences in
diffusion distance will lead to changes in the hard tissue morphology. Though
our radiographs do not appear to show substantial changes in mineral
arrangement until the content drops below 20%, even small changes could have
an effect on properties. This is made clear in observations of changes in
material properties with mineralization pattern in bony fish vertebrae
(Kranenbarg et al., 2005a;
Kranenbarg et al., 2005b). An
effective way to rule out this possible confounding effect would be to make
micro computed toniography (micro-CT) scans of each vertebra before testing to
memorialize the exact hard tissue arrangement
(Kranenbarg et al., 2005b;
Summers et al., 2004). We
remain confident of the EDTA results in light of the similar relationship
between material properties and mineral content seen when fully mineralized
vertebrae of M. californicus are compared with each other.
The relationships we propose here are in accordance with expectations from
other mineralized hard tissues (Currey,
1999). Stiffness and strength increase with mineral content and
they will show a nearly linear relationship to each other. There are of course
exceptions, suggesting that there may be a premium mineral content for some
skeletal tissues. High stiffness does not always mean high strength,
especially in tissues with extremely high mineral contents, because they
become brittle. A fin whale tympanic bulla with 86% mineral has an extremely
high stiffness (31.3 GPa) and low strength (33 MPa) compared to a bovine femur
having 67% mineral with lower stiffness (13.5 GPa) but higher strength (247
MPa) (Currey, 1999).
Viscoelastic response
Determining the response of viscoelastic materials to load is complicated
because they show a time dependent response absent in elastic materials. When
a quasistatic test, appropriate for elastic materials, is performed on a
viscoelastic material it reveals information valid only for the selected
strain rate. This is a drawback, but there is a real advantage to quasistatic
testing: the results are easily interpreted and the testing equipment and
analysis are relatively simple. Though virtually every biological material is
viscoelastic to some extent, many of them, including bone, function as nearly
purely elastic materials at biologically relevant strain rates. Typically,
unmineralized mammalian cartilage does not act as an elastic solid and there
is an extensive literature on dynamic testing of cartilage. However, we did
not find substantial strain rate dependency in the material properties of
mineralized shark vertebral cartilage at biologically relevant strain rates,
validating the interpretations from quasistatic testing for this material.
Yield strain, which is strain rate dependent in bone (human and bovine
models), is not strain rate dependent in fully mineralized vertebrae
(Fig. 6A)
(Carter and Caler, 1985;
Currey, 1988). Increased
mineral adds complexity to the mineralized structure in vertebrae; the
presence and subsequent failure of a mineralized structure within a
cartilaginous matrix could account for the presence of a yield point, and also
why ultimate strength is not strain rate dependent in the absence of
mineral.
The relatively small strain rate dependence of ultimate strength agrees
with findings in human and bovine bone
(Fig. 7;
Table 2)
(Carter and Caler, 1985;
Carter and Hayes, 1976). We can
best describe this using the `Cumulative Damage' model, which describes the
time dependent characteristics of human bone
(Carter and Caler, 1985). This
model suggests that when bone is loaded to a stress that might not normally
break it, and is then held at this stress, damage is accumulated in the form
of cracks and will eventually fracture the bone. When vertebrae are tested at
a low strain rate the mineral has time to accumulate damage, explaining the
strength differences we see between faster and slower strain rates. We point
out that ultimate strength differences in mineralized vertebrae are likely not
biologically relevant in light of the extensive overlap of values obtained at
each strain rate.
The stiffness of mineralized and demineralized vertebrae have strain rate
dependencies that are similar to bone and cartilage, respectively
(Fig. 8;
Table 2). Stiffness in
demineralized vertebrae was rate dependent but did not vary in mineralized
vertebrae (Fig. 8). Stiffness
in reindeer antler and bovine bone is also not strain rate dependent
(Currey, 1988;
Currey, 1989), but mammalian
cartilage, empirically and theoretically is highly strain rate dependent
(Li et al., 2003;
Li and Herzog, 2004).
Understanding vertebral response to load is important for understanding
vertebral column function and the effect of structure on swimming mechanics.
As a shark undulates through the water, one side of the vertebral column will
be loaded in compression and the other will be loaded in tension. Cyclical
loading occurs during swimming and will vary between animals employing
different swimming styles. Vertebral column loading in anguilliform swimmers
will be very different than in thunniform swimmers, suggesting that swimming
speed can also influence vertebral column loading. Additionally, thunniform
swimming sharks have musculotendinous systems that transmit forces farther
along the body, placing the vertebral column in compression, while in slower
swimming sharks the vertebral column will be loaded in tension and compression
on opposite sides of the animal simultaneously
(Donely et al., 2004;
Gemballa et al., 2006;
Shadwick and Gemballa, 2006).
As in bone, we have shown the mineral found in shark vertebral cartilage is an
important predictor of material properties (Figs
7 and
8)
(Currey, 2002).
Conclusions
We examined mineral variation, the effect of mineral content on material
properties, and viscoelastic responses of cartilaginous vertebrae from one
shark species, M. californicus. We found mineralization varies within
individuals, within this species and among species. The amount of mineral has
large effects on the material properties, but this effect is overshadowed by
the even larger influence of structure, or organization of the mineral, on the
material properties of elasmobranch vertebrae. Many of the material properties
examined here were not strain rate dependent at biologically relevant strain
rates; validating the interpretations from quasistatic tests on this tissue.
The importance of mineral in bony skeletons has long been discussed in the
literature and the effects of varying mineral on material properties are well
known, especially in mammalian skeletons. Only recently have we begun to
understand the mechanics of cartilaginous skeletons, presenting many
opportunities to examine the effects of sex, age, structure and ecological
niche.
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Acknowledgments |
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