Are uniform regional safety factors an objective of adaptive modeling/remodeling in cortical bone?
1 Utah Bone and Joint Center, Salt Lake City, UT 84115, USA
2 Bone and Joint Research Laboratories, Department of Veterans Affairs
Medical Center, Salt Lake City, UT 84148, USA
3 Orthopedic Bioengineering Research Laboratory, University of Utah, Salt
Lake City, UT 84112, USA
* Author for correspondence (e-mail: jskedros{at}utahboneandjoint.com)
Accepted 22 February 2003
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Summary |
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Key words: horse, safety factor, bone adaptation, cortical bone, equine third metacarpal, bone remodeling
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Introduction |
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Lanyon et al. (1979)
hypothesized that a possible objective for regional variations in material
organization between cortical locations of a limb bone diaphysis may be the
maintenance of uniform stresses throughout a bone's cross-section. Examining
mature ovine radii at mid-diaphysis, they found that the narrower caudal
`compression' cortex had a lower elastic modulus than the thicker, less-highly
strained cranial (dorsal) `tension' cortex. Riggs et al.
(1993
) reported similar
elastic modulus differences between the cranial `tension' and caudal
`compression' cortices of the equine radius at mid-diaphysis, even though
these regions have nearly equivalent cortical thickness. These elastic modulus
differences were attributed to significant regional variations between the
cranial and caudal cortices, including more oblique-to-transverse collagen
fiber orientation, lower mineral content, and increased remodeling with
secondary osteons in the caudal cortex. These authors suggested that since
cranial versus caudal stresses are significantly different in each
species, and the associated remodeling responses appeared to amplify this
difference, the non-uniform stress distribution represents a goal of
developmental adaptation. Because yield and ultimate stress of cortical bone
are lower in tension than in compression
(Reilly and Burstein, 1975
),
and the non-uniform stress distributions of ovine and equine radii resulted in
roughly equivalent safety factors between the cranial and caudal cortices, the
achievement of equivalent or uniform `regional' safety factors (e.g. cranial
cortex = caudal cortex) was offered as an explanation for a major goal of
adaptation in these bones (Lanyon et al.,
1979
; Riggs et al.,
1993
).
Safety factors, when considered in skeletal biomechanics, usually refer to
an entire bone (Rubin and Lanyon,
1982; Biewener,
1993
). In the present study we further examine the idea of
`regional' safety factors; for example, those from a distinct cortical
location within the same transverse cross-section
(Lanyon et al., 1979
;
Riggs et al., 1993
). In either
case, `safety factor' refers to the ratio of yield stress (or strain) to peak
physiological stress (or strain), and represents a means of quantifying how
strong the bone is in relation to how strong it needs to be to avoid fracture
(safety factor = yield or ultimate stress/peak physiological stress).
If adaptive remodeling/modeling sufficiently modifies material and/or
structural organization to ultimately produce uniform regional safety factors
in equine and ovine radii, then other appendicular long bones that experience
habitual bending should be similarly adapted. The present study tests this
hypothesis in the equine third metacarpal (MC3), which has had functionally
generated intracortical strains estimated by a sophisticated finite element
model (Gross et al., 1992)
(Fig. 1). The habitual strain
distribution of the equine MC3 is characterized by habitual bending; the
neutral axis passes through the cranio-lateral cortex, the position of which
produces a narrow band of tension in this region. The remainder of the
cortical cross-section experiences a wide range of compression magnitudes that
are maximal in the caudo-medial cortex. The present study followed the methods
of Riggs et al. (1993
), and
applied them to the MC3 as opposed to the radius. Compression and tension
testing was performed on machined specimens from cortical locations that
characteristically receive in vivo tension (cranio-lateral cortex),
as well as a range of compression magnitudes (higher in the caudo-medial
cortex; lower in the cranio-medial cortex). Analyzing these specimens in the
context of their habitual tension or compression strain mode is important for
an accurate assessment of their physiological mechanical properties. Regional
intracortical safety factors were calculated using the measured mechanical
parameters, including elastic modulus, yield and ultimate stress, yield and
ultimate strain, and in vivo strain data obtained from the finite
element model of Gross et al.
(1992
).
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Materials and methods |
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Mechanical testing
One randomly selected MC3 from each pair was sectioned transversely at 50%
of overall length. A 5 mm-thick transverse segment immediately proximal to the
mid-diaphyseal transection was used to obtain specimens for compression
testing. Using a diamond blade saw and continuous water irrigation, six 5
mmx5 mmx5 mm cubes were cut from each of the ten bones; cortical
locations were cranio-lateral (N=2; 20 total specimens), lateral
(N=1; 10 total specimens), caudo-medial (N=2; 20 total
specimens) and cranio-medial (N=1; 10 total specimens)
(Fig. 2A). These locations were
representative of bone from cortical areas that experience tensile strains, as
well as a range of compression magnitudes.
|
Mechanical testing was conducted on saline-moistened specimens that had
equilibrated at room temperature according to methods of Riggs et al.
(1993). Although they used 8
mmx8 mmx8 mm cubes in compression testing of equine radii, we used
5 mmx5 mmx5 mm cubes because of narrower cortices in some
locations.
From the contralateral bones, a 50 mm-thick segment of cortex was sectioned
transversely such that the midpoint was at 50% of bone length. Rectangular
slabs cut from this segment were milled to match the size and shape of the
dumb-bell shaped specimens used for tension testing by Riggs et al.
(1993) as described by Evans
et al. (1992
)
(Fig. 3). Two specimens from
the `tension' (cranio-lateral) cortex and two from the `compression'
(caudo-medial) cortex were milled from each bone
(Fig. 2B). Only three tension
specimens were milled from two bones with narrow cortices (38 total
specimens).
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During specimen machining, orientation of the long axes of tension and
compression specimens remained parallel to the original longitudinal
diaphyseal axis. To avoid untoward effects of freezing on mechanical behavior,
all specimens were allowed to equilibrate in a moist state at room temperature
for 24 h prior to testing (Evans et al.,
1992).
Using an Instron Model 4303 (Canton, MA, USA) with a 25 kN load cell, cubic specimens moistened with saline were compressed to failure along the longitudinal diaphyseal axis unrestrained between parallel platens at a strain-controlled rate of 0.001 s-1. Certified material standards were used to calibrate the load cell and validate the accuracy of the crosshead displacement. Strain measurements were obtained from the measured crosshead displacement, and were corrected for machine compliance (determined by loading the machine against itself).
Tensile tests were performed using an MTS 858 Bionix (Eden Prairie, MN,
USA) testing machine with a 20 kN load cell interfaced with a ±2 kN
load cartridge. Tensile specimens were held by identical grips that spanned
the transverse breadth of the specimen ends. This allowed elongation along the
anatomical longitudinal axis. Specimens, moistened with saline, were loaded to
failure at a strain-controlled rate of 0.01 s-1. (The use of
different strain rates in compression and tension is in accordance with
Riggs et al., 1993; C. M.
Riggs, personal communication.) Strain measurements were obtained using an MTS
632.13F-20 extensometer (Eden Prairie) attached to each specimen with rubber
O-ring fasteners.
Elastic modulus, yield stress and strain, and ultimate stress and strain were determined for each specimen in both tension and compression testing, with yield point defined at 0.2% strain offset. Although this strain-offset yield criterion is arbitrary, it is commonly used to define material yield (ASTM: Standard Test Method for Young's Modulus, Tangent Modulus, and Chord Modulus, Designation E111-82. In 1992 Annual Book of ASTM Standards, Edited, pp. 288-293; Philadelphia, ASTM).
Mechanical data from specimens were excluded if they: (1) failed catastrophically (i.e. at low stress) early in testing, or (2) fractured outside the location between the two extensometer clips.
Regional safety factors
Normal physiological strain values used in calculating regional safety
factors were obtained from the finite elemental mesh of Gross et al.
(1992)
(Fig. 1). The value used for
each location was the mean of values from three adjacent mesh cells that most
closely corresponded to the locations from which specimens used in mechanical
testing were obtained. In accordance with the stressstrain relation of
Hooke's Law (
=E
; Gere and
Timoshenko, 1984
), physiological stress (
) data were
calculated using the elastic modulus (E) in tension and compression
(experimentally determined in the present study) and the published strain
(
) values (Gross et al.,
1992
). Yield safety factors were calculated as the ratios of yield
stress to peak physiological stress, and ultimate safety factors as the ratio
of ultimate stress to peak physiological stress.
Strain values reported by Gross et al.
(1992) were obtained from the
MC3 of a 460 kg, 5-year-old Thoroughbred that had not been race training for
at least 1 year prior to experimentation. The strain distributions published
in their studies of Thoroughbreds at sub-maximal speeds are `virtually
identical' to those that have been measured using the same methods at the
mid-diaphyses of quarter horses during similar gaits (T. S. Gross and C. T.
Rubin, personal communication).
Statistical analysis
A one-way analysis of variance (ANOVA) design with Fisher's PLSD test for
evaluating multiple-paired comparisons was used to assess regional variations
for each of the mechanical parameters.
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Results |
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In general, averaged elastic modulus values were on the order of 30% higher in tension testing of bone habitually loaded in tension (17.81 GPa) when compared to compression testing of bone habitually loaded in compression (13.64 GPa, mean of caudo-medial and cranio-medial) (P<0.01).
In tension tests, yield stress values were nearly equivalent (P>0.5). In compression tests, the cranio-medial location exhibited the highest yield stress values compared to the lateral and caudo-medial cortical locations, which exhibited the lowest (P<0.05). Tension tests of habitually tensed bone revealed lower yield stress (148.59 MPa) compared to compression tests of habitually compressed bone (171.70 MPa, mean of caudo-medial and cranio-medial) (P=0.30 for caudo-medial versus cranio-lateral; P<0.001 for cranio-medial versus cranio-lateral).
In tension tests, ultimate stress values were not significantly different (P>0.5). In compression tests, ultimate stress data showed moderate regional variations (P<0.03 for caudo-medial versus cranio-lateral; P<0.01 for caudo-medial versus cranio-medial).
During tensile testing, premature catastrophic failure (failure at low stress) and/or failure outside the region between the extensometer clips resulted in seven specimen exclusions from the cranio-lateral region, and two exclusions from the caudo-medial region. No failures occurred at the gripped ends. Three compression specimens from the lateral cortex were also excluded for premature catastrophic failure (failure at low stress).
Safety factors
Calculated yield and ultimate safety factors
(Table 2 and
Fig. 4) show large regional
variations in both tension and compression modes of loading. The
cranio-lateral `tension' cortex has a tension safety factor of 37.7 while the
caudo-medial `compression' cortex has a compression safety factor of 5.7
(P<0.0001) (Fig.
5).
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Discussion |
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Although the strain distribution obtained by Gross et al.
(1992) is highly consistent in
quarter horses and Thoroughbreds (T. S. Gross and C. T. Rubin, personal
communication), there are a number of limitations in using the strain values
obtained from this finite element model. For example, the strain data of Gross
et al. (1992
) were obtained
from one mature horse, and homogenous material properties were assumed. C. Les
(personal communication) suggested to us that the use of homogeneous
(versus heterogeneous) material properties in this model would
underestimate cranial and caudal stresses, and overestimate medial and lateral
stresses. Additionally, age-related splint-bone fusions may affect the strain
distribution of the MC3 (Les et al.,
1995
). For example, uniform splint bone fusion could shift the
habitual neutral axis toward the medullary canal. This would increase safety
factors in the caudo-medial cortex and decrease safety factors in the
cranio-lateral cortex. However, when considering the limitations of applying
the finite element model and the most exaggerated influences that these
additional variables might have on a habitual strain distribution, it is clear
that the nearly sixfold difference in safety factors on opposing sides of the
neutral axis would, at most, be reduced to a threefold difference. This
estimate was largely based on a shift in the neutral axis and the
recalculation of regional safety factors using the highest strains on the
cranio-lateral `tension' periosteal cortical surface, and the lower strains
near the endosteal surface of the caudo-medial `compression' region
(Fig. 1).
Our calculation of safety factors involves a number of assumptions, and may
be problematic since the only values that were considered were normal
stresses. Since the normal stresses, and therefore normal strains, fall to
effectively zero at the neutral axis, bone along this axis will have,
essentially, an infinite safety factor. The presence of other strain
characteristics and their distributions, such as shear and strain energy
density, were estimated by Gross et al.
(1992) but not considered in
our calculations. Such alternative strain and/or strain-related stimuli may
influence the local cellular environment and the modeling/remodeling processes
that mediate the attainment of regional or overall safety factors.
Furthermore, Biewener et al.
(1983a
,b
)
clearly showed that during acceleration, deceleration and jumping, the
distribution of strains and peak stresses change significantly in the equine
MC3. Although Gross et al.
(1992
) made measurements
across a range of gait speeds, averaging of cycles may underestimate peak MC3
stresses resulting from acceleration and deceleration. Nunamaker
(2001
) has also shown that
strain in the equine MC3 is significantly dependent upon gait speed, the
dorsal surface shifting from predominant tension to predominant compression at
higher speeds. This challenges our assumptions about a `habitual' loading
state in this bone, implying that our sole focus on the finite element data of
Gross et al. (1992
) greatly
oversimplifies the loading environment that may influence regional safety
factors and other possible adaptive changes.
The model of Gross et al.
(1992), however, provides a
reasonable estimation of peak strains encountered during common, unremarkable
ambulation as this model represented a medium-speed trot, which the animal
tended toward in pasture. The hypothesis that uniform regional safety factors
represent a major goal of a bone's morphological adaptation reflects the
often-suggested idea that peak stresses or strains produced during vigorous
activities strongly influence bone adaptation
(Currey, 1984
;
Martin and Burr, 1989
;
Biewener, 1993
;
Nunamaker, 2001
). Recent
literature suggests that adaptive modeling may be sensitive to relatively few
highly intensive loading events (Biewener
and Bertram, 1994
; Skerry and
Lanyon, 1995
). Alternatively, there are experimental data
suggesting that a bone modeling-mediated organization is governed by aspects
of the strain environment that may not be linked to the relatively high
strains associated with peak and/or yield stresses
(Rubin et al., 1990
;
Rubin and McLeod, 1996
;
Fritton et al., 2000
). These
views, although disparate, both suggest that bone modeling is stimulated
preferentially by a small subset of its total strain experience. It is also
unclear if a relationship exists between the strains that influence bone
modeling/remodeling objectives and the strains that are potentially associated
with structural failure. These issues clearly pose a significant problem when
judging localized regional safety factors or their adaptive relevance from a
single load/strain distribution as was done in the present study.
Adaptive morphological variations may be more strongly influenced by
strains produced by habitual physiological bending, rather than less-frequent
peak or yield strains as suggested by the uniform-safety-factor hypothesis.
Experimental studies have demonstrated that limb bone diaphyses of terrestrial
animals typically receive spatially and temporally consistent strain
distributions during controlled, gait-related activities
(Lanyon et al., 1979;
Biewener et al., 1986
;
Biewener, 1993
;
Fritton and Rubin, 2001
). In
nearly all limb bone diaphyses that have been studied, the percentage of total
normal strain due to bending (hence tension and compression strains) exceeds
70% of the longitudinal strains experienced by a diaphyseal region
(Rubin, 1984
;
Fritton and Rubin, 2001
).
Additionally, peak in vivo tensile strains on limb bone diaphyses are
typically 7085% as large as peak compressive strains
(Biewener and Taylor, 1986
;
Biewener, 1993
). The regional
predominance of differing strain modes (e.g. tension versus
compression) and the corresponding disparity in strain magnitude (greater in
the compressed cortex) may evoke regional strain-related adaptive responses.
For example, compressed regions tend to have greater osteon population density
and/or more oblique-to-transverse collagen fiber orientation than opposing
tension cortices (Marotti,
1963
; Lanyon and Bourn,
1979
; Bouvier and Hylander,
1981
; Portigliatti Barbos et
al., 1984
; Martin and Burr,
1989
; Mason et al.,
1995
; Skedros et al.,
1994
,
1996
,
1997
,
2001b
;
Takano et al., 1999
;
Kalmey and Lovejoy, 2002
).
Prevalent bending of long bones may convey functional advantages. Frost
(1983) and Lanyon
(1980
) have suggested the
existence of a minimum strain threshold below which bone tissue homeostasis is
disrupted, and increased absorption leads to a negative bone balance. Bone
curvature may be a means of ensuring that strains safely exceed this
threshold. Lanyon (1980
)
postulated that improved attenuation and absorption of forces are structural
advantages of bending. He also considered the dangers of aberrant loads on a
bone designed only to withstand axial loading, and suggested that curvature
may be a way in which customary strain values might be brought within a
particular range.
An explanation more tenable than the achievement of uniform regional safety
factors is that structural/geometric variations in the equine MC3, such as
cortical thickness differences and cross-sectional shape asymmetry, are
naturally selected for enhancing `loading predictability' during typical use
(Bertram and Biewener, 1988).
The existence of a predictable loading regime and its coexisting predictable
strain distribution probably convey fundamentally important signals for limb
bone tissue/organ growth and maintenance
(Bertram and Biewener, 1988
;
Skedros et al., 1996
). If
maintaining a predictable strain environment is a goal of a bone's
hierarchical morphological organization, then which characteristics are most
likely to have been modified to achieve this loading predictability? Bertram
and Biewener (1988
) have argued
that this can be readily achieved by modeling processes, which affect
structural characteristics such as bone curvature, cross-sectional shape and
cortical thickness. These characteristics primarily affect stiffness and
strength of a whole bone. Since the equine MC3 lacks longitudinal curvature,
loading predictability in this bone is probably achieved by the asymmetry in
cortical thickness, which enhances whole-bone flexure in the cranio-lateral to
caudo-medial direction (Les,
1995
; C. Les, personal communication). Therefore, material
adaptations achieved via osteonal remodeling would neither be
required nor expected for achieving regional or whole-bone stiffness/strength
requirements in the vast majority of cases
(Woo et al., 1981
;
Rubin and Lanyon, 1982
;
Alexander, 1998
; A. A.
Biewener, personal communication). In contrast, Riggs et al.
(1993
) cite regional
variations in collagen fiber orientation and the corresponding regional
variations in elastic moduli as being important in influencing how the whole
mid-diaphyseal equine radius strains under functional loads. This disparity in
elastic modulus led Riggs et al.
(1993
) to support the
uniform-safety-factor hypothesis that was tested in this study.
If modeling processes are responsible for increased structural strength and
are more effective in controlling strains via directional bending,
then what purpose do the regional material variations such as osteon
population density and collagen fiber orientation produced by remodeling
serve? In recent studies examining regional material variations in equine
MC3s, regression analyses of histocompositional variations and mechanical
properties show strong correlations between regional collagen fiber
orientation and energy absorption in `strain-mode-specific' testing (e.g.
compression testing of bone from regions habitually loaded in compression
in vivo; Skedros et al.,
2000,
2001a
). While the magnitudes
of these variations may not be sufficient to affect how a bone's entire
cross-section strains under load (Gross et
al., 1992
), they might enhance other important mechanical
properties including local energy absorption, toughness and fatigue resistance
(Skedros et al., 2000
,
2001a
,
2003a
,b
).
Although the ultimate effects of bone remodeling may produce `enhanced' regional material properties, the causal mechanisms that mediate these regional variations are not clear. It is plausible that the varied manifestations of bone remodeling (e.g. differences in collagen fiber orientation, and secondary osteon orientation, population density, cross-sectional area and central canal porosity) may reflect responses to microdamage or strain transduction associated with strain distributions developed by a bone's particular shape. The shape may be advantageous and the remodeling the secondary consequence. Thus the regional variations in material properties may not be primary `objectives' in a context of biomechanical adaptation. In turn, since safety factors are likely to be only one of several considerations of bone modeling/remodeling, the achievement of adequate safety factors could be a consequence, rather than an objective, of bone modeling/remodeling. Clearly, the causal mechanisms that mediate the modeling/remodeling processes that produce and maintain an `adapted' bone diaphysis, and the ultimate goals of this adaptation, are not well understood.
It is important to note that in some cases apparently high regional
cortical safety factors may not be sufficient to avoid failure. For example,
the cranio-lateral cortex has a tension safety factor of 37.7, compared to a
compression safety factor of 5.7 in the caudo-medial cortex
(Table 2, Fig. 5). However, the majority
of stress fractures in the equine MC3 occur in the cranio-lateral cortex
(Nunamaker, 2001). Such
fractures are more common in Thoroughbreds, which probably reflects their
relatively fast racing speeds and lower cross-sectional moments of area.
However, in all racing breeds it is not entirely clear why microcracks tend to
form more frequently in the cranio-lateral cortex. Nunamaker
(2001
) has suggested that
prevalent tensile strains produced in this region during race training enhance
specific adaptations for tension. At higher racing speeds, however, this
tension-adapted region receives more prevalent, high magnitude compression
strains, which promote microcrack formation. Reilly and Currey
(2000
) showed that damage
formed in compression is highly detrimental to tensile mechanical properties.
Microdamage can also occur with different frequency and can exhibit different
characteristics (e.g. length and shape) in compression versus tension
cortices (Reilly et al., 1997
;
Boyce et al., 1998
;
Reilly and Currey, 1999
;
Muir et al., 1999
). Also, the
prevalence of shear strains, which can be more deleterious than tensile
strains, probably increases in the cranio-lateral cortex during racing, since
the neutral axis (where longitudinally oriented shear strains are maximal)
traverses this region at higher gait speeds
(Gross et al., 1992
). These
possibilities and the mechanical test results reported in recent studies
(Skedros et al., 2000
,
2001a
,
2003a
), suggest the importance
of other `types' of safety factors that are strongly dependent on
accommodating and/or resisting microcrack formation including fatigue
resistance, toughness and/or energy absorption.
The second and fourth metacarpal `splint' bones (MC2 and MC4) may also have
important load sharing functionssupplementing the lower safety factors
of the caudal cortexsince they extend to approximately mid-diaphysis.
Piotrowski et al. (1983) have
shown that splint bones have important influences on inertial properties such
as the second moment of area (and hence bending rigidity) in the proximal
one-third diaphysis. Near mid-diaphysis, however, splint bones of younger
horses (<2 years old) typically are not fused to the MC3
(Les et al., 1995
), and
therefore have minimal influence on bending rigidity
(Piotrowski et al., 1983
).
Splint-bone fusion, which is more common in animals >2 years
(Les et al., 1995
), may
enhance local loading-carrying capacity (e.g. on the order of 1015%
increased bending rigidity in the cranio-caudal axis)
(Piotrowski et al., 1983
;
Nunamaker, 2001
). These facts
demonstrate that cortical thickness, which can be enhanced in the caudal
cortices by splint-bone fusion, may help resist deleterious loading
conditions. This is an important issue since the finite element mesh of Gross
et al. (1992
) was based on an
animal with unfused splint bones near mid-diaphysis. This justified the
exclusion of any load-carrying function of the splint bones in their finite
element mesh. In all animals used in the present study, the splint bones were
also not fused near mid-diaphysis.
In summary, results of the present study challenge the idea that the
achievement of uniform regional safety factors is a goal of adaptive
modeling/remodeling. Since this study only examined normal strain data, it is
plausible that safety factors based on other criteria may yield different
conclusions. Characterizing `habitual strains' can be quite difficult, and it
is clear that the distribution of strain in the equine MC3 varies considerably
with gait speed, acceleration, deceleration and jumping. The myriad of
plausible interpretations and caveats that readily emerge when considering the
`objectives' of bone modeling/remodeling processes, and the current lack of
consensus on the role of strain in mediating these processes, emphasize the
need for additional studies. In this context, and based on our calculations
showing non-uniform, normal-strain-based safety factors, we speculate that
regional safety factors will not show uniformity, regardless of how they are
defined or calculated. As suggested above and supported by mechanical testing
data in recent studies (Skedros et al.,
2000,
2001a
,
2003a
,b
),
it is likely that the non-uniform strain distribution strongly influences the
secondary development of the regional material heterogeneity in order to
enhance bone toughness, energy absorption and/or fatigue resistance. Such
strain-related heterogeneities might represent the ultimate goal of regional
adaptation in the equine MC3 and other long bones that are subject to habitual
bending.
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Acknowledgments |
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References |
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Alexander, R. McN. (1998). Symmorphosis and safety factors. In Principles of Animal Design: The Optimization and Symmorphosis Debate (ed. E. R. Weibel, C. R. Taylor and L. Bolis), pp. 28-35. Cambridge: Cambridge University Press.
Bertram, J. E. A. and Biewener, A. A. (1988). Bone curvature: Sacrificing strength for load predictability? J. Theor. Biol. 131,75 -92.[Medline]
Biewener, A. A. (1993). Safety factors in bone strength. Calcif. Tissue Int. 53,S68 -S74.[Medline]
Biewener, A. A. and Bertram, J. E. A. (1994).
Structural response of growing bone to exercise and disuse. J.
Appl. Physiol. 76,946
-955.
Biewener, A. A., Swartz, S. M. and Bertram, J. E. A. (1986). Bone modeling during growth: Dynamic strain equilibrium in the chick tibiotarsus. Calcif. Tissue Int. 39,390 -395.[Medline]
Biewener, A. A. and Taylor, C. R. (1986). Bone strain: A determinant of gait and speed? J. Exp. Biol. 123,383 -400.[Abstract]
Biewener, A. A., Thomason, J., Goodship, A. and Lanyon, L. E. (1983b). Bone stress in the horse forelimb during locomotion at different gaits: A comparison of two experimental methods. J. Biomech. 16,565 -576.[Medline]
Biewener, A. A., Thomason, J. and Lanyon, L. E. (1983a). Mechanics of locomotion and jumping in the forelimb of the horse (Equus): In vivo stress developed in the radius and metacarpus. J. Zool., Lond. 201, 67-82.
Bouvier, M. and Hylander, W. L. (1981). Effect of bone strain on cortical bone structure in macaques (Macaca mulatta). J. Morphol. 167, 1-12.[Medline]
Boyce, T. M., Fyhrie, D. P., Glotkowski, M. C., Radin, E. L. and Schaffler, M. B. (1998). Microdamage type and strain mode associations in human compact bone bending fatigue. J. Orthop. Res. 16,322 -329.[Medline]
Currey, J. D. (1984). The Mechanical Adaptations of Bones. Princeton: Princeton University Press.
Evans, G. P., Behiri, J. C., Vaughan, L. C. and Bonfield, W. (1992). The response of equine cortical bone to loading at strain rates experienced in vivo by the galloping horse. Equine Vet. J. 24,125 -128.[Medline]
Fritton, S. P., McLeod, K. J. and Rubin, C. T. (2000). Quantifying the strain history of bone: Spatial uniformity and self-similarity of low-magnitude strains. J. Biomech. 33,317 -325.[CrossRef][Medline]
Fritton, S. P. and Rubin, C. T. (2001). In vivo measurement of bone deformations using strain gauges. In Bone Mechanics Handbook, 2nd edition (ed. S. C. Cowin), pp. 8-1 to 8-41. Boca Raton: CRC Press.
Frost, H. M. (1983). The minimum effective strain: A determinant of bone architecture. Clin. Orthop. 175,286 -292.[Medline]
Gere, J. M. and Timoshenko, S. P. (1984). Mechanics of Materials, 2nd edition, pp.19 -20. Boston: PWS-Kent Publishing Company.
Gross, T. S., McLeod, K. J. and Rubin, C. T. (1992). Characterizing bone strain distributions in vivo using three triple rosette strain gauges. J. Biomech. 25,1081 -1087.[Medline]
Kalmey, J. K. and Lovejoy, C. O. (2002). Collagen fiber orientation in the femoral necks of apes and humans: Do their histological structures reflect differences in locomotor loading? Bone 31,327 -332.[CrossRef][Medline]
Lanyon, L. E. (1980). The influence of function on development of bone curvature. An experimental study on the rat tibia. J. Zool. (Lond.) 192,457 -466.
Lanyon, L. E. and Bourn, S. (1979). The influence of mechanical function on the development and remodeling of the tibia: An experimental study in sheep. J. Bone Joint Surg. Am. 61A,263 -273.[Medline]
Lanyon, L. E., Magee, P. T. and Baggott, D. G. (1979). The relationship of functional stress and strain to the processes of bone remodeling: An experimental study on the sheep radius. J. Biomech. 12,593 -600.[Medline]
Les, C. M. (1995). Material heterogeneity in the equine metacarpus: Documentation and biomechanical consequences.PhD thesis , University of California, Davis. p.244
Les, C. M., Stover, S. M. and Willits, N. H. (1995). Necropsy survey of metacarpal fusion in the horse. Am. J. Vet. Res. 56,1421 -1432.[Medline]
Marotti, G. (1963). Quantitative studies on bone reconstruction. 1. The reconstruction in homotypic shaft bones. Acta Anatomica. 52,291 -333.[Medline]
Martin, R. B. and Burr, D. B. (1989). Structure, Function and Adaptation of Compact Bone. New York: Raven Press.
Mason, M. W., Skedros, J. G. and Bloebaum, R. D. (1995). Evidence of strain-mode-related cortical adaptation in the diaphysis of the horse radius. Bone 17,229 -237.[CrossRef][Medline]
Muir, P., Johnson, K. A. and Ruaux-Mason, C. P. (1999). In vivo matrix microdamage in a naturally occurring canine fatigue fracture. Bone 25,571 -576.[CrossRef][Medline]
Nunamaker, D. (2001). Bucked shins in horses. In Musculoskeletal Fatigue and Stress Fractures (ed. D. B. Burr and C. Milgrom), pp. 203-219. Boca Raton: CRC Press.
Piotrowski, G., Sullivan, M. and Colahan, P. T. (1983). Geometric properties of equine metacarpi. J. Biomech. 16,129 -139.[Medline]
Portigliatti Barbos, M., Bianco, P., Ascenzi, A. and Boyde, A. (1984). Collagen orientation in compact bone: II. Distribution of lamellae in the whole of the human femoral shaft with reference to its mechanical properties. Metab. Bone Dis. Rel. Res. 5,309 -315.
Reilly, D. T. and Burstein, A. H. (1975). The elastic and ultimate properties of compact bone tissue. J. Biomech. 8,393 -405.[Medline]
Reilly, G. C. and Currey, J. D. (1999). The
development of microcracking and failure in bone depends on the loading mode
to which it is adapted. J. Exp. Biol.
202,543
-552.
Reilly, G. C. and Currey, J. D. (2000). The effects of damage and microcracking on the impact strength of bone. J. Biomech. 33,337 -343.[CrossRef][Medline]
Reilly, G. C., Currey, J. D. and Goodship, A. E. (1997). Exercise of young thoroughbred horses increases impact strength of the third metacarpal bone. J. Orthop. Res. 15,862 -868.[Medline]
Riggs, C. M., Vaughan, L. C., Evans, G. P., Lanyon, L. E. and Boyde, A. (1993). Mechanical implications of collagen fibre orientation in cortical bone of the equine radius. Anat. Embryol. 187,239 -248.[Medline]
Rubin, C. T. (1984). Skeletal strain and the functional significance of bone architecture. Calcif. Tissue Int. 36,11 -18.
Rubin, C. T. and Lanyon, L. E. (1982). Limb mechanics as a function of speed and gait: A study of functional strains in the radius and tibia of horse and dog. J. Exp. Biol. 101,187 -211.[Abstract]
Rubin, C. T. and McLeod, K. J. (1996). Inhibition of osteopenia by biophysical intervention. In Osteoporosis (ed. R. Marcus, D. Feldman and J. Kelsey), pp. 351-371. New York: Academic Press.
Rubin, C. T., McLeod, K. J. and Bain, S. D. (1990). Functional strains and cortical bone adaptation: Epigenetic assurance of skeletal integrity. J. Biomech. 23,43 -54.[Medline]
Skedros, J. G., Dayton, M. R. and Bachus, K. N. (2000). Relative effects of collagen fiber orientation, mineralization, porosity, and percent and population density of osteonal bone on equine cortical bone mechanical properties in mode-specific loading. Conference Proceedings of the 24th Annual Meeting of the American Society of Biomechanics, pp.173 -174. Chicago, IL: American Society of Biomechanics.
Skedros, J. G., Dayton, M. R. and Bachus, K. N. (2001a). Strain-mode-specific loading of cortical bone reveals an important role for collagen fiber orientation in energy absorption. Trans. Orthop. Res. Soc. 26, 519.
Skedros, J. G., Mason, M. W. and Bloebaum, R. D. (1994). Differences in osteonal micromorphologies between tensile and compressive cortices of a bending skeletal system: Indications of potential strain-specific differences in bone microstructure. Anat. Rec. 239,405 -413.[Medline]
Skedros, J. G., Mason, M. W. and Bloebaum, R. D. (2001b). Modeling and remodeling in a developing artiodactyl calcaneus: A model for evaluating Frost's mechanostat hypothesis and its corollaries. Anat. Rec. 263,167 -185.[CrossRef][Medline]
Skedros, J. G., Mason, M. W., Nelson, M. C. and Bloebaum, R. D. (1996). Evidence of structural and material adaptation to specific strain features in cortical bone. Anat. Rec. 246, 47-63.[CrossRef][Medline]
Skedros, J. G., Su, S. C. and Bloebaum, R. D. (1997). Biomechanical implications of mineral content and microstructural variations in cortical bone of horse, elk and sheep calcanei. Anat. Rec. 249,297 -316.[CrossRef][Medline]
Skedros, J. G., Sybrowsky, C. L., Dayton, M. R., Bloebaum, R. D. and Bachus, K. N. (2003a). The role of osteocyte lacuna population density on the mechanical properties of cortical bone. Trans. Orthop. Res. Soc. 28, 414.
Skedros, J. G., Hunt, K. J., Dayton, M. R., Bloebaum, R. D. and Bachus, K. N. (2003b). The influence of collagen fiber orientation on mechanical properties of cortical bone of an artiodactyl calcaneus: Implications for broad applications in bone adaptation. Trans. Orthop. Res. Soc. 28, 411.
Skerry, T. M. and Lanyon, L. E. (1995). Interruption of disuse by short duration walking exercise does not prevent bone loss in the sheep calcaneus. Bone 16,269 -274.[CrossRef][Medline]
Takano, Y., Turner, C. H., Owan, I., Martin, R. B., Lau, S. T., Forwood, M. R. and Burr, D. B. (1999). Elastic anisotropy and collagen orientation of osteonal bone are dependent upon the mechanical strain distribution. J. Orthop. Res. 17, 59-66.[Medline]
Woo, S. L.-Y., Keui, S. C., Amiel, D., Gomez, M. A., Hayes, W. C., White, F. C. and Akeson, W. H. (1981). The effect of prolonged physical training on the properties of long bone: A study of Wolff's law. J. Bone Joint Surg. Am. 63A,780 -787.[Abstract]