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First published online March 14, 2008
Journal of Experimental Biology 211, 1148-1162 (2008)
Published by The Company of Biologists 2008
doi: 10.1242/jeb.012419
Variability in forelimb bone strains during non-steady locomotor activities in goats
1 Concord Field Station, Department of Organismic and Evolutionary Biology,
Harvard University, 100 Old Causeway Road, Bedford, MA 01730, USA
2 Sibley School of Mechanical and Aerospace Engineering, 222 Upson Hall, Cornell
University, Ithaca, NY 14853, USA
* Author for correspondence (e-mail: cmoreno{at}oeb.harvard.edu)
Accepted 4 February 2008
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Summary |
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 TOP Summary INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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Key words: bone strain, variability, curvature, non-steady locomotion, skeletal mechanics, goat
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INTRODUCTION |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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In contrast to non-steady locomotion, limb bone strains have been measured
in a variety of animals during steady, level locomotion across a range of
gaits and speeds (Lanyon,
1976
; Carter et al.,
1980; Biewener and Taylor,
1986; Blob and Biewener,
1999; Lieberman et al.,
2003). These studies show that strain magnitudes, measured at a
bone's midshaft, increase with speed, consistent with increased limb loading
(Biewener et al., 1983a;
Main and Biewener, 2004).
However, the pattern and distribution of strain, quantified in terms of the
orientation of principal strains and the distribution of axial, bending and/or
shear strain components measured at the time of peak strain, tend to remain
fairly uniform across different speeds and gaits
(Rubin and Lanyon, 1982;
Biewener and Taylor, 1986;
Main and Biewener, 2004). It
is important to note that cross-sectional strain patterns often change over
the course of a loading cycle, with substantial shifts in the location and
orientation of the neutral axis (Gross et
al., 1992; Biewener and Dial,
1995; Main and Biewener,
2004). Nevertheless, it is generally believed that bone shape and
mechanical function are most strongly influenced by the peak strains
experienced by a bone over some history of loading cycles
(Carter, 1987;
Mosley et al., 1997;
Robling et al., 2001;
Burr et al., 2002). Previous
work, therefore, has provided insight into the underlying structural design of
limb bones in relation to steady, forward locomotion but has largely ignored
the pattern of bone strains experienced during non-steady activity.
Animals must be capable of executing vigorous non-steady behaviors, such as
rapid turning and sudden accelerations, which are likely to be especially
critical during predator–prey interactions. Consequently, adequate
support of mechanical loads during these more variable, though perhaps less
frequent, activities is likely to be as important to skeletal design as
support of loads during steady locomotion. Indeed, peak stresses determined
from in vivo bone strains in the horse radius, metacarpus and tibia
(Biewener et al., 1983a;
Biewener et al., 1988) during
jumping were significantly greater, and the distribution of strains more
variable, than with steady-speed locomotion.
Variation in bone strain patterns reflects the predictability of limb and
bone loading regimes. Load predictability, in turn, is probably an important
determinant of a structure's safety factor, often defined as the ratio of the
structure's breaking or yield strength relative to the expected maximum load
during use. Other factors, such as the cost of building and maintaining the
structure, and the cost of failure are also important determinants of a
structure's safety factor (Alexander,
1981). With increased variation in loading (reduced
predictability) the safety factor of a structure, such as a limb bone, can be
expected to decrease. Consequently, evaluating peak bone strains and strain
distributions across a range of locomotor activities is important for
assessing skeletal safety factors.
Bone shape probably influences strain patterns by predisposing different
surfaces of the bone to certain types of strain. For example, many long bones
are curved along their length, and although this may increase the peak strains
developed within the bone due to increased bending loads, it may also improve
a bone's loading predictability (Lanyon,
1987; Bertram and Biewener,
1988; Bertram and Biewener,
1992) by limiting the principal direction of bending to a
particular plane. In a comparison of midshaft bone strains in the horse radius
(curved) and the metacarpus (straight), strain patterns during steady
locomotion and jumping were found to be more variable in the straighter
metacarpus (Biewener et al.,
1983a). In addition, the uniform anatomical arrangement of
muscles, tendons and ligaments, which transmit substantial forces to the
skeleton, might also be expected to limit the range of loads that a bone
experiences, favoring increased load predictability.
To assess how bone morphology might influence, and possibly constrain,
functional loading patterns, we compared in vivo bone strains acting
in the midshaft of the radius and metacarpus of juvenile goats performing a
variety of natural behaviors in an outdoor arena and compared them with
strains measured during steady treadmill locomotion. We hypothesized that
strains measured during outdoor non-steady behaviors would be more variable in
pattern and magnitude than those measured during treadmill locomotion. Similar
to horses and other ungulates (Bertram and
Biewener, 1992), goats have a curved, caudally concave radius and
a fairly straight metacarpus. Consequently, we also hypothesized that during
non-steady activities the curved radius would experience less variability in
strain pattern and higher peak strains than the straighter metacarpus.
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MATERIALS AND METHODS |
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Recording of ground reaction forces
Pre-operative ground reaction forces (GRFs) were collected while the
animals walked, trotted and galloped steadily across a level runway with two
embedded force platforms (0.4 mx0.6 m; model 9286A; Kistler, Amherst,
NY, USA) set flush with the runway's surface. The next day, surgery was
performed to attach the strain gauges. The following day, after collecting
strain data from both outdoor and treadmill trials, post-operative ground
reaction forces were recorded using the same runway. The pre-operative and
post-operative GRFs were zeroed and filtered and the mean peak vertical GRF
was found for each of the three gaits, using a custom MATLAB program (The
Mathworks, Inc., Natick, MA, USA). The ratio of pre-operative to
post-operative peak GRF was used as a correction factor by which the measured
strains were multiplied to account for lameness due to surgery.
Surgery
Each goat was surgically instrumented with strain gauges on either the
radius, metacarpus, or in the case of two animals, the left radius and the
right metacarpus. The animals were sedated with a mixture of ketamine (4 mg
kg–1) and xylazine (1 mg kg–1) administered
intravenously (jugular), then intubated and maintained under general
anesthesia at 0.5–2.0% isoflurane. For the implantation of strain gauges
on the radius, a 4–5 cm incision was made over the medial aspect of the
forearm. The lead wires from the gauges were then fed subcutaneously from an
opening near the shoulder to the medial opening on the limb. Skin and
underlying fascia were retracted to expose the bone's midshaft. The periosteum
at the midshaft was removed using a scalpel and a periosteal elevator and the
bone surface lightly scraped, cleaned and dried using methyl-ethyl-ketone.
Rosette strain gauges (FRA-1-11; Tokyo Sokki Kenkyujo Co., Ltd, Tokyo, Japan)
were attached to the cranial and caudal midshaft surfaces and a single-element
gauge (FLA-1-11) to the medial surface of the bone using self-catalyzing
cyanoacrylate adhesive. Strain gauge preparation was similar to previous
studies (Lanyon, 1976;
Biewener, 1992). A similar
approach and procedure were used to attach rosette strain gauges to the
cranial and caudal surfaces and a single-element gauge to the medial surface
of the metacarpus. In this case, gauge wires were fed subcutaneously from an
opening near the shoulder to a lateral opening on the limb, passing outside
the skin over the wrist to a medial incision over the metacarpus. Gauges were
bonded to the midshaft of each bone because this is the location at which the
greatest strains occur in long bones subjected to significant bending
(Biewener and Taylor, 1986).
Following gauge attachment, the skin openings were sutured with 3-0 vicryl and
the connector secured to the skin overlying the withers with 2-0 vicryl
suture. The animals were allowed to recover overnight before experimental
recordings were made, and flunixin (1 mg kg–1) was
administered (intramuscular) every 12 h following surgery to reduce pain.
Outdoor experiment
The outdoor arena consisted of a semi-rectangular area (
20
m2) enclosed by twisted wire fencing, approximately 1.5 m in
height, located beside an observation room where the cameras and equipment
were located (Fig. 1). A clear
plastic barrier was used to prevent the goats from entering the observation
area. A wooden ramp 0.78 mx1.25 m (widthxlength) with a 21°
angle to the ground was placed next to a 0.47 mx0.41 mx0.78 m
wooden box such that the goats could run up the ramp and jump off the box, or
jump onto the box and run down the ramp. Each trial lasted approximately 30 s
and consisted of the experimenter energetically chasing the animal around the
outdoor arena with the goal of evoking as wide a range of natural behaviors as
possible. The behaviors included straight runs across the arena, turns and
dodges, jumps and runs up and down the ramp, as well as braking and
accelerating. The goats were at ease running up and down the ramp, and had no
difficulty jumping onto and off the platform, with minimal signs of limping
due to surgery.
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Signals from the strain gauges were transmitted via lightweight
shielded cable (60 g m–1) to a bridge amplifier (Vishay 2120;
Micromeasurements, Raleigh, NC, USA). Voltage outputs from the bridge
amplifiers were recorded to a computer using a 12-bit A/D converter and
Axoscope software (version 8.0; Axon Instruments, Inc., Union City, CA, USA).
Prior to experimental recordings, each channel of the bridge amplifier was
balanced and calibrated (1000 µ
shunt calibration) while the animal
was held suspended in the air with no weight on its limbs. The overall
locomotor behaviors of each goat were filmed from the observation room using a
high speed digital video camera (Redlake Motionscope PCI; San Diego, CA USA)
at 60 Hz, allowing hoof contact times to be recorded and the locomotor
behavior associated with each footfall of the experimental limb to be
classified.
Behaviors
Each behavior was first classified as a walk, trot, gallop or jump. The
walks, trots and gallops that occurred on level ground were further classified
as steady gallops, steady walks/trots, accelerations or decelerations. The
rest of the walks, trots and gallops were categorized as either uphill or
downhill. The jumps were divided into high-force jumping behaviors (landing
down/jumping up) and low-force jumping behaviors (landing up/jumping down).
This yielded eight possible behavior combinations. Strain data and hoof
contact times for footfalls of the experimental limb were recorded while the
animal was performing one of these definable behaviors. Footfalls during
behaviors that did not fall into one of these categories (discontinuous,
non-forward locomotor behaviors such as slipping, backing up, stepping
sideways, shifting weight, slowly turning in place, etc) did not result in
consistent strain traces that would allow us to find meaningful peak strains,
or the strains were of such low magnitude that the signal was considered
unreliable, so these footfalls were not analyzed.
Treadmill locomotion
After the outdoor strain data collection trials, the goats were led indoors
and made to walk, trot and gallop at a range of speeds (1.1–3.8 m
s–1) on a motorized treadmill. High speed digital video
(Redlake Motionscope) was taken from a lateral aspect at 125 Hz to record the
foot-down and foot-off times of the experimental limb. Bone strains were
recorded from the radius, the metacarpus, or both bones simultaneously
(depending on the animal and bones that were instrumented with strain gauges),
while the goat ran at controlled speeds. After strain data and post-operative
GRF data were collected, the animals were euthanized by an injection of sodium
pentobarbital (150 mg kg–1; intravenous, jugular). The
instrumented bones were dissected from the limbs and the orientations of the
strain gauges relative to the long axis of the bone measured using digital
photographs of the dissected bone. The curvatures of the bones
(Fig. 2B) were measured using a
previously described technique (Bertram and
Biewener, 1992; Main and
Biewener, 2004).
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The raw strain data were analyzed using a custom MATLAB program
(Main and Biewener, 2004). Raw
data were first filtered using a fourth order Butterworth filter with a cutoff
frequency of 125 Hz. The data were then zeroed by subtracting the average
strain during swing phase (when the voltage changes are minimal) from the
filtered data, then the voltages were converted to microstrain (µ, or
strain x10–6) using the 1000 µ
shunt-calibration. For the rosette strain gauges, standard equations that
assume a uniaxial planar state of strain were used to convert the zeroed and
calibrated strains into principal tensile and compressive strains. By
convention, the principal tensile and compressive strains act perpendicular to
one another. From these equations the orientations of the principal tensile
strains relative to the long axis of the bone were also found
(Fig. 2B). These angles were
corrected for any gauge offset found after inspecting the attached gauge on
the dissected bone. Principal strains and orientations could only be
calculated from rosette strain gauges with three functioning elements;
footfalls in which the gauges had one or more non-functioning elements were
not used. The principal strains and the strains recorded from the medial
single-element gauges were multiplied by the post-operative correction factor
to adjust the strains for post-operative lameness (average correction
1.10±0.05 across animals). This post-operative reduction in limb load
probably only affected strain magnitudes and not the overall strain patterns
(Main and Biewener, 2004).
For each stance phase, the peak positive (tensile) and negative (compressive) principal strains and their orientations, along with their corresponding principal strains, were recorded for each rosette gauge on the cranial and caudal cortices of the metacarpus and radius. Peak longitudinal strains on the medial surfaces of both bones were also recorded. Because peak principal tension did not necessarily occur at the time of peak principal compression (principal tension tended to peak around 70±17% of stance phase, whereas principal compression peaked around 50±20% of stance; mean ± s.d.), we determined which of the two had the greatest average absolute magnitude for any given behavior category and used the larger and its orientation in further analyses.
Once it was determined whether the peak compression or peak tension was
greater during a particular footfall, the degree to which the peak principal
strain dominated the corresponding perpendicular strain was quantified by
calculating the `fractional tensile strain ratio' (FTSR) for each footfall:
 | (1) |
1 and 2 are the principal tension and
compression, respectively. FTSR represents the ratio of the principal tension
to the sum of the principal tension and the absolute magnitude of the
corresponding principal compression. When principal tension exceeds principal
compression, the ratio is between 0.5 and 1, and when compression is greater
than tension, the ratio is between 0 and 0.5. This ratio identifies the
dominant type of strain for a particular footfall, and its relative dominance.
When principal tension equals principal compression (as for pure torsion),
FTSR=0.5. At the time of the largest peak principal strain, the tensile strain orientation (TSO) relative to the bone's long axis was also determined. This value falls between 0° and 90°: if the principal tensile strain is aligned near the long axis of the bone, the angle will fall near 0°, whereas, if the principal compressive strain is aligned close to the long axis, TSO will be closer to 90°. When the TSO associated with a given peak strain lies between 22.5° and 67.5°, then the bone is experiencing primarily off-axis loads, such as torsion, since in these cases the principal tension is acting in an orientation that is closer to 45° than to either the longitudinal or transverse axis of the bone. We plotted FTSR against TSO (Fig. 2A) to evaluate the degree of variability in loading patterns for different bone surfaces in relation to both the dominant strain type and the orientation of the strain relative to the long axis of the bone.
Axial and bending strain components were determined by using the following
equations (Main and Biewener,
2004):
 | (2) |
 | (3) |
cranial and caudal are the peak
principal strains on the cranial and caudal surfaces of the bones,
respectively.
Measures of variability
We quantified the variability in loading pattern for each bone surface in a
number of ways. The two-dimensional spread in data points was first determined
using the participation ratio (PR), which is the area occupied by data on the
2D scatterplot (Fig. 2A). PR is
calculated by dividing the 2D parameter space into a number of bins and
assessing the number of bins that contain data points, normalized by the
number of samples in order to remain robust to sample size
(Ciampaglio et al., 2001). The
value is dimensionless and can range from 1.0, for which all of the data
points lie in one bin, up to the number of bins (2500 in this case). Thus, the
lower the PR value, the more constrained the data are in the 2D parameter
space. PR gives an indication of the amount of scatter in a group of data on
the pattern graphs, and although PR values from two groups cannot be compared
statistically using a t-test, PR can be found for different
individuals and averaged. As another measure of two-dimensional spread in data
points the 2D distance to the individual mean (DIM) was determined. This was
done by dividing the TSO value of each data point by 90° to scale it from
0 to 1 (to match the FTSR value range) and then calculating the 2D distance
from each point to the individual mean for each animal. The average distance
to the DIM across the individuals sampled was then determined for each bone
surface.
To measure how constrained the loading patterns were to a certain range of
strain orientations and strain types, we calculated the percentage of
footfalls for each bone surface that landed within the expected zone for a
given surface (zone 1 for the cranial radius, zone 2 for the caudal radius,
and the cranial and caudal metacarpus; Fig.
2). The two bones were then compared using the average percentage
across the cranial and caudal surfaces, where a higher percentage meant less
variability and a lower percentage more variability. In addition to
considering these composite measures of variability in loading pattern, we
also considered the two dimensions (TSO and FTSR) separately, using their
variance as a measure of variability
(Sokal and Rohlf, 1981).
To quantify variation in strain magnitude frequency distributions, we again
used the sample variance as a measure of variability
(Sokal and Rohlf, 1981) to
compare between groups. To compare variability in axial versus
bending strain components in the metacarpus and radius, we used the
coefficient of variation (CV) of each component.
Statistical analysis
To assess differences in loading pattern variability we compared means of
the following parameters between the outdoor and steady treadmill trials: PR,
DIM, percent of footfalls in the expected bone loading zone
(Fig. 2A), variance in TSO, and
variance in FTSR. The variance in TSO and FTSR within individuals was also
compared between outdoor and treadmill conditions. To assess differences in
strain magnitude between conditions, we compared mean absolute principal
strain magnitudes for each surface, as well as the mean magnitudes for the
axial and bending strain components for both bones. To investigate strain
magnitude variability we compared the variances of the absolute principal
strain magnitude distributions and mean coefficients of variation for the
axial and bending strain magnitudes.
To test for differences in the means described above, we performed unpaired
t-tests and non-parametric Mann–Whitney U-tests when
the variances of two groups were not equal. The P values were
adjusted using the sequential Bonferroni technique to correct for multiple
comparisons (Rice, 1989). To
test for differences in variance between conditions (for TSO, FTSR and
principal strain distributions), we performed F-tests in which we
compared the ratio of the variances between two groups to the critical
F value (Rohlf and Sokal,
1981).
To determine if the strain magnitude frequency distributions fit a lognormal distribution, we performed Kolmogorov–Smirnov Lilliefors `goodness of fit' tests on the strain magnitudes from each bone surface under both outdoor and treadmill conditions. The sample distribution is considered to be not significantly different from a lognormal curve if P>0.05. All statistical tests were performed using SPSS (version 14.0 for Windows; Chicago, IL, USA), except for the goodness of fit tests, which were performed in JMP (version 4; SAS Institute Inc., Cary, NC, USA). Significance threshold was set at P<0.05 and values presented in the text are means ± standard error (s.e.m.), unless otherwise noted.
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RESULTS |
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The general bone loading patterns for outdoor footfalls were similar to those of treadmill footfalls, with the majority of loading cycles falling in the same zone for both outdoor and treadmill (Fig. 4). For example, the percentage of footfalls in the expected zone during outdoor and treadmill locomotion was 72% and 74% for the cranial surface of the metacarpus, and 53% and 51% for the caudal surface, respectively (Table 2). This was the case for the cranial and caudal surfaces of both forelimb bones (Fig. 4). For outdoor footfalls, the cranial and caudal surfaces of the metacarpus were loaded primarily in compression (FTSR: 0.26±0.01 and 0.33±0.04, respectively) with the principal compression lying closer to the long axis of the bone (TSO: 74±4° and 68±9°, respectively; Table 2). In the radius, the caudal surface was loaded similarly (FTSR: 0.33±0.02; TSO: 81±1°), but the cranial surface was loaded primarily in tension, which acted near the bone's long axis (FTSR: 0.62±0.02; TSO: 14±3°; Table 2).
During treadmill activity (Fig. 4), the metacarpus experienced generally similar loading patterns as observed for the outdoor activities, with the cranial and caudal surfaces experiencing compression (FTSR: 0.28±0.01 and 0.30±0.02, respectively) that acted close to the bone's long axis (TSO: 72±5° and 68±11°, respectively; Table 2). The overall loading pattern of the radius was also similar to that recorded for the outdoor activities, with the caudal surface loaded predominantly in axial compression (FTSR: 0.31±0.02; TSO: 81±1°) and the cranial surface loaded mostly in tension (FTSR: 0.63±0.02; TSO: 10±3°), with both principal strains acting close to the bone's long axis.
Variability in strain pattern
Outdoor versus treadmill
The variability in loading pattern, or the two-dimensional spread of the
data, was greater during outdoor behaviors than during treadmill locomotion.
This was true for the cranial and caudal surfaces of both bones, using
participation ratio (PR; Fig.
5A) or distance to the individual mean (DIM,
Fig. 5B) to evaluate the data
spread (both yielded similar results). The difference between outdoor and
treadmill PR within each surface was significant in three of the four
comparisons (caudal metacarpus and cranial/caudal radius; Mann–Whitney
U-tests, P<0.05), and the cranial radius had
significantly higher DIM during outdoor than treadmill locomotion
(P<0.05). All four surfaces had approximately the same PR for both
outdoor (mean across the four surfaces: 62.6±9.9;
Fig. 5A) and treadmill
locomotion (mean: 12.8±3.0; Fig.
5A).
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The percentage of footfalls landing in the expected bone loading zone was not significantly different between outdoor and treadmill conditions for any of the four surfaces (Fig. 5C). The variance in tensile strain orientation (TSO, normalized to 90°) was significantly greater during outdoor trials compared to treadmill trials in 11 of the 14 individual comparisons (Fig. 6A). Variance in FTSR was significantly greater during outdoor trials than during treadmill trials in 12 of 14 comparisons (Fig. 6B).
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The percentage of footfalls in the expected bone-loading zone, averaged across the cranial and caudal surfaces, was significantly higher in the radius than the metacarpus for both outdoor locomotion (88.6±3.7% radius versus 61.2±13.5% metacarpus; P=0.046) and treadmill locomotion (96.5±1.6% radius versus 60.1±18.2% metacarpus; P=0.013; Table 2). During outdoor locomotion (grey bars), although the variance in TSO averaged across the cranial and caudal surfaces was similar between the bones (Fig. 6C), the variance in FTSR averaged across cranial and caudal surfaces was significantly greater in the metacarpus than the radius (Fig. 6D). During treadmill locomotion (black bars) the average variance in TSO was larger in the metacarpus than the radius (Fig. 6C), but the average variance in FTSR across these midshaft surfaces was not significantly different between the two bones (Fig. 6D).
Variability in local bone strain magnitude
Outdoor versus treadmill
Out of 22 individual bone surface comparisons of the variance in strain
magnitude between outdoor and treadmill locomotion for the seven goats, the
variance in strain magnitude for outdoor, non-steady locomotion was greater in
all but two cases. However, the difference in variance between outdoor and
treadmill was significant in only half of those comparisons according to
F-tests (4 of 8 metacarpus, 7 of 14 radius).
Radius versus metacarpus
Mean peak strain magnitudes during outdoor behaviors were not significantly
different from those experienced during treadmill locomotion. This was true on
the three midshaft surfaces of both the metacarpus and the radius
(Table 3). The similarity
between conditions is illustrated by the frequency distributions for the
metacarpus (Fig. 7) and radius
(Fig. 8), comparing outdoor and
treadmill conditions. During outdoor locomotion, the cranial and caudal
surfaces of the metacarpus experienced mean absolute magnitudes that were
similar to each other (256±54 µ and 281±43 µ,
respectively; Table 3) and to
the cranial surface of the radius (281±95 µ). However, the
caudal surface of the radius experienced a greater absolute mean peak strain
magnitude (581±67 µ). The medial surfaces of the metacarpus
and radius also experienced absolute peak strain magnitudes in this range
(567±77 µ and 656±111 µ, respectively;
Table 3).
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Axial and bending strains
During outdoor locomotion, the mean bending strain in the radius was 5.3
times greater than that of the metacarpus (446±82 µ and
84±24 µ, respectively, P=0.015;
Fig. 9A;
Table 4), while the axial
strains were not different (–167±41 µ radius and
–210±39 µ metacarpus, P>0.05;
Fig. 9A;
Table 4). The metacarpus showed
more variability in bending strain than did the radius (CV=1.06 in the
metacarpus versus 0.33 in the radius), but the two bones had a
similar CV for axial strains (–0.66 metacarpus, –0.59 radius;
Fig. 9B;
Table 4). Bending strains in
the straighter metacarpus were lower than the axial strains (bending to axial
strain ratio=0.40), but this difference was not significant
(P=0.051). By contrast, the bending strains in the radius were
significantly greater than the axial strains (bending to axial strain
ratio=2.67; P=0.023).
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During treadmill locomotion, the mean bending strain in the radius was 11.4
times greater than in the metacarpus (493±68 µ and
43±31 µ, respectively, P=0.012;
Fig. 9C;
Table 4), whereas axial strains
were again not different (–123±70 µ radius and
–194±8 µ metacarpus, P>0.05;
Fig. 9C;
Table 4). The metacarpus also
showed more variability in bending strain than the radius during treadmill
locomotion (CV=0.65 in the metacarpus versus 0.23 in the radius), but
the CVs for axial strains were similar (–0.35 metacarpus, –0.24
radius; Fig. 9D;
Table 4). Bending strains in
the metacarpus were lower than the axial strains (bending to axial strain
ratio=0.22), but we could not test the significance of this difference because
of a low sample size. The bending strain of the radius was significantly
larger than its axial strain (bending to axial strain ratio=4.02;
P=0.003).
Strain magnitude distributions
The distribution of strain magnitudes for the natural, outdoor behaviors
was right skewed and appeared to fit a lognormal distribution for the cranial
and caudal surfaces of both the metacarpus
(Fig. 7A,C) and radius
(Fig. 8A,C). This fit was
significant on the caudal surfaces (P=0.056 metacarpus,
P=0.15 radius; Table
3) but not on the cranial surfaces (P=0.01 for both
metacarpus and radius). The strain magnitudes also appeared to be lognormally
distributed on the medial surfaces for both bones
(Fig. 7E,F and
Fig. 8E,F), but the fits were
not significant. During treadmill locomotion the strain magnitude
distributions on the cranial and caudal surfaces of both bones did not fit a
lognormal distribution. However, the medial surfaces of both bones showed
significant lognormal distributions (P=0.125 metacarpus,
P=0.15 radius; Table
3). The D-statistic of the KSL goodness of fit test gives a
measure of the greatest deviation from the standard lognormal distribution. On
each surface of both bones this value was lower for outdoor versus
treadmill conditions (Figs 7,
8). Consequently, outdoor
strain magnitude distributions deviated less from lognormal than the treadmill
distributions.
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DISCUSSION |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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Bone strain variability during steady versus non-steady locomotion
We hypothesized that strain patterns measured during outdoor locomotion
would be more variable because non-steady behaviors may cause the forelimbs to
contact the ground in unusual positions or angles, resulting in variable
ground reaction force orientations relative to the limb and, as a consequence,
more varied strain orientations (TSO) and dominant strain types (FTSR;
Fig. 4). The softer, uneven
substrate of the outdoor arena compared to the treadmill may be another factor
causing unpredictable limb loading events. Our composite measures of the
variability of midshaft bone loading pattern, participation ratio (PR) and
distance to the individual mean (DIM), support this hypothesis
(Fig. 5A,B), as does the
variability in the two separate dimensions of loading pattern: tensile strain
orientation (TSO) and fractional tensile strain ratio (FTSR). Given the
differences in variance of these parameters between outdoor and treadmill
locomotion, it is interesting that the proportion of footfalls in the expected
bone loading zone is nearly the same for both conditions
(Fig. 5C) suggesting that the
general loading pattern for the cranial and caudal surfaces of both forelimb
bones is predictable, even during non-steady behaviors. This is consistent
with previous studies in which surface midshaft strains recorded in the long
bones of a number of species over a range of speeds and gaits showed uniform
strain patterns (Lanyon and Baggott,
1976; Rubin and Lanyon,
1982; Biewener and Taylor,
1986). Additionally, the mean values for FTSR and TSO were nearly
identical for the treadmill and outdoor activities. Although treadmill
locomotion does not entirely capture the variability in loading orientations
and dominant strain types that result from outdoor, non-steady locomotor
behaviors, the results for these goat forelimb bones indicate that treadmill
locomotion can serve as a reasonable approximation for some natural locomotor
activities.
We expected both bones would experience higher peak principal strains
during outdoor behaviors because these can include more high-intensity
activities such as jumping down or sudden decelerations, based on previous
work showing that strains increase when non-steady behaviors such as jumping
(Biewener et al., 1983a;
Biewener et al., 1988) and
accelerations (Biewener et al.,
1983b) are examined. Consistent with this, the tails of the
outdoor frequency distributions of peak principal strains (cranial and caudal
surfaces) and peak compressive strains (medial surface) extended further to
the right than the corresponding treadmill distributions (Figs
7,
8). Hence, a relatively few
high magnitude loading events recorded during outdoor activity produced
greater peak strains than the most vigorous gallops recorded on the treadmill.
However, these less frequent high magnitude events were insufficient to
significantly affect the overall mean peak strain magnitudes of the
distributions, as these were similar on all three surfaces of both bones for
outdoor and treadmill locomotion (Table
3).
We also hypothesized that many of these high-intensity events would occur during the outdoor activities, causing greater variability in the frequency distribution of peak strain magnitudes compared to treadmill locomotion. This hypothesis was partially supported, as half of the within-individual comparisons showed a significant difference in variance between outdoor and treadmill locomotion (figure not shown). The variability (CV) of bending strain in the radius was also significantly greater during outdoor versus treadmill locomotion. The same is probably true for the metacarpus; however, a less robust sample size prevented a statistical comparison for this bone (Table 4). These findings suggest that the variable nature of outdoor behaviors may increase the risk of failure compared to steady state, not because the mean principal strains are higher than in treadmill behaviors but because of occasional extreme principal strains and because these outdoor behaviors can engender more variable bending strains than treadmill behaviors. The extent to which more variable bending increases the overall peak strain magnitude within a bone, therefore, may increase a bone's risk of failure.
Effect of bone curvature on the variability of strain pattern and magnitude
Strain pattern variability
During both outdoor and treadmill locomotion, the two goat forelimb bones
are dominated by axial loads that induce intrinsic bending in proportion to
their longitudinal curvature. Whereas the straight metacarpus experiences
compression on the cranial, caudal and medial surfaces, reflecting overall
axial compression, the radius experiences compression on its concave caudal
surface, as well as its medial cortex, and tension on its convex cranial
surface, reflecting bending that results primarily from axial loading about
the bone's longitudinal curvature, rather than extrinsic bending loads
(Fig. 2A, Figs
3,
4). These strain distributions
are consistent with previous findings in which the predominant loading mode in
the ungulate radius was axial compression with superimposed cranio-caudal
bending (Lanyon and Baggott,
1976; Goodship et al.,
1979; Lanyon et al.,
1982; Rubin and Lanyon,
1982; Biewener et al.,
1983a; Biewener and Taylor,
1986; Bertram and Biewener,
1988; Bertram and Biewener,
1992).
We hypothesized that during outdoor locomotion, the radius would be more
predictable in terms of overall midshaft strain pattern than the metacarpus
because the curvature of the radius, and probably the surrounding musculature,
would restrict the strain orientations and nature of the strains (tensile
versus compressive) to predictable ranges, whereas the patterns in
the straighter metacarpus would be more variable. This was based on previous
work showing that variation in loading orientation during jumping is greater
in straighter bones, such as the metacarpus
(Biewener et al., 1983a) and
metatarsus (Biewener et al.,
1988). The greater variability in these bones likely results from
having little longitudinal curvature, which diminishes their ability to
restrict bending to a fixed direction
(Bertram and Biewener, 1988).
Consistent with this, our data show that the percentage of footfalls in the
expected bone loading zone is significantly higher for the radius than the
metacarpus for both outdoor and treadmill locomotion
(Fig. 4 and
Table 2). This suggests that
the curved radius restricts the overall loading distribution of
midshaft strains more than the straighter metacarpus, such that a larger
proportion of footfalls are constrained to within a more predictable range of
strain patterns.
However, variability in loading pattern, as assessed by the average PR and
DIM for the cranial and caudal surfaces, was not different between the
metacarpus and radius for within location comparisons
(Fig. 5A,B;
Table 2). Examining the
separate dimensions that make up these measures of pattern variability reveals
why they do not differ. Although the variance in FTSR
(Fig. 6D) for the metacarpus is
significantly greater than that of the radius, the variance in TSO is almost
identical for the two bones (Fig.
6C). Since PR and DIM comprise both of these dimensions, it is not
surprising that similarity in one of these dimensions results in no
significant difference in the composite measures of loading pattern
variability. Additionally, these findings indicate that during outdoor,
natural behaviors, the curved radius is able to constrain the strain ratios
(FTSR) more than the straighter metacarpus, but does not constrain the
variability in orientation of the principal strain (TSO) more than in the
metacarpus. This suggests that under variable locomotor conditions a curved
bone will not see remarkably less varied principal strain orientations than a
straight bone, but the curved bone will restrict the ratio of tension to
compression to within a more predictable range for any given footfall, whereas
a straight bone will experience more variable tension-to-compression ratios.
In this case, a critical factor for preventing failure during non-steady
activities may be the specific bone microstructure and collagen fiber
orientation in the cortices of straight bones compared with curved bones
(Skedros et al., 2006), which
is a level of detail not examined in our study.
This difference in the effect of longitudinal bone curvature on TSO versus FTSR helps explain why a small percentage of outdoor footfalls are scattered outside the expected loading zones (Fig. 4, grey diamonds). Recorded strains have similar ranges of TSO values for the two forelimb bones, but more constrained FTSR values for the radius (Fig. 4C,D) than the metacarpus (Fig. 4A,B). As an ad hoc experimental analysis, we hypothesized that the outlying footfalls might be of lower magnitude, such that the eccentric loading orientations were not as consequential to the integrity of the bone (lower risk of failure). This analysis is discussed further below.
In addition to longitudinal curvature, two other anatomical features that
are likely to affect loading predictability are the organization of
surrounding musculature and the cross-sectional geometry of each bone
(Bertram and Biewener, 1988).
The radius has an array of digital flexors and extensors originating from its
proximal end, whereas the metacarpus has only the interosseous muscle on its
palmar surface, with flexor and extensor tendons passing over both ends of the
bone. Based on the fixed attachment points of the muscles associated with the
radius, it is possible that its loading environment is dominated by muscular
forces more than in the metacarpus, contributing to the greater loading
predictability of the radius. Additionally, the two bones have different
cross-sectional geometries, with the metacarpus more circular and the radius
more elliptical. The more elliptical cross-sectional shape of the radius,
therefore, also likely contributes to a more restricted cranio-caudal bending.
However, neither of these factors were quantified and explored in this study.
Nevertheless, analysis of cross-sectional strain distributions and bending
orientation with respect to bone shape and muscle–tendon organization is
deserving of future study.
Peak strain magnitudes and variability
We hypothesized that during outdoor locomotion the radius would experience
greater peak strains compared to the metacarpus based on the prediction that
the radius would experience greater bending compared to the metacarpus
(Biewener et al., 1983a;
Lanyon, 1987). We evaluated
this for the caudal midshaft cortex of each bone because compression due to
bending of this cortex in the radius is augmented by axial compression,
resulting in greater net strain. By contrast, bending-induced tension of the
cranial cortex is offset by axial compression, resulting in smaller net
tensile strains. Consistent with our hypothesis and previous work
(Biewener et al., 1983b;
Lanyon, 1987;
Bertram and Biewener, 1988;
Biewener et al., 1988), the
cranial surface of the radius experienced similar tensile principal strain
magnitudes as the compressive principal strains recorded in the cranial and
caudal metacarpus (Fig. 9A),
whereas the caudal radius experienced higher peak compressive strains than the
metacarpus. As expected, we also found significantly greater bending strains
in the radius than the metacarpus (Fig.
9A). Although greater strains due to bending were measured in the
radius, the coefficient of variation (CV) of this strain component was lower
for the radius than the metacarpus (Fig.
9B). This result strongly supports the hypothesis that
longitudinal bone curvature induces a trade-off between load predictability
and strain magnitude (Bertram and Biewener,
1988; Bertram and Biewener,
1992). There was no difference in axial strain magnitudes between
the two bones, and the CV for axial strain components is the same for both
bones, suggesting that differences in bone curvature and the bending strains
that are engendered are more important for understanding functional design of
these two forelimb bones.
|
;
Biewener, 1993). The balance
between these conflicting demands results in the final architecture of the
bone, which strongly influences the nature of the stresses (and strains) that
the bone experiences.
It has been suggested that different limb bones may be expected to have
different safety factors, probably related to differences in their
architecture (Alexander, 1981;
Biewener et al., 1983a;
Currey, 2002). As discussed
above, a limb bone with substantial longitudinal curvature may have greater
predictability of loading direction
(Bertram and Biewener, 1988;
Bertram and Biewener, 1992),
which allows the bone to adjust its form and mass via remodeling to
better maintain functional integrity during natural activities
(Lanyon, 1987;
Biewener and Bertram, 1993).
This process can reduce the probability that a loading event from an
especially vigorous behavior will cause a stress that approaches the bone's
breaking strength, due to the reduced likelihood of overlap between the
positive tail of the frequency distribution of functional bone stresses and
the distribution of breaking (or failure) strengths
(Alexander, 1981). By reducing
loading variability, the mean breaking strength can safely be decreased,
allowing more economical costs of maintenance and transport, despite the
trade-off of greater stress (or strain).
Our results do not completely support this hypothesis for natural, outdoor locomotor behaviors. We found that while the curved radius has higher bending strains than the straighter metacarpus, it does not have greater predictability of loading orientation (TSO; Fig. 6C). However, in the radius the variability of the dominant strain type (FTSR; Fig. 6D) and the variability in bending strain (CV; Table 4) are indeed less than those of the metacarpus. It is possible that eccentric loading events during outdoor locomotion can produce loading orientations in the medio-lateral direction that are not highly constrained by the cranio-caudal curvature of the radius.
Relationship between strain magnitude and variability in strain pattern
To help explain why a percentage of footfalls are scattered outside the
expected bone loading zones, and to address the finding that the curved radius
does not constrain loading orientation (TSO) more than the metacarpus, we
investigated the relationship between strain magnitude and variability in
loading pattern in both bones. Our hypothesis was that higher magnitude
loading events would be more constrained in loading pattern, which would
reduce the likelihood that high magnitude loads occur substantially off-axis
(or with unexpected ratios of tension to compression) and thereby increase the
potential risk for damage and/or failure. Accordingly, the strain pattern
associated with very low magnitude loading cycles would not be as constrained
because they would pose less of a failure risk to the bone.
To explore this hypothesis, we removed loading events with magnitudes below the pooled median magnitude from all of the outdoor footfalls. Plotting TSO against FTSR for the remaining data shows that most of the footfalls with eccentric, off-axis loads that would have landed far from the expected loading zone have been eliminated (compare Fig. 4 with Fig. 10). This indicates that footfalls with highly unexpected TSO or FTSR values were of relatively low magnitude (below the median value for each goat), whereas all of the higher magnitude footfalls (near the median and higher) generally clustered within the expected loading zones (Fig. 10A–D). This finding supports our hypothesis that very low magnitude loading cycles are not as constrained in pattern as higher magnitude loading cycles.
To test this hypothesis further, we grouped the remaining high magnitude events within bins of strain normalized to the individual maximum magnitude (Fig. 10A–D). We then calculated the distance to the bin mean (DBM) for each data point and computed the average DBM as a measure of variability for each midshaft surface of both bones. We regressed DBM against relative strain magnitude (Fig. 10E) and found a strong negative correlation between variability in pattern and magnitude for the metacarpus (R2=0.95, slope=–0.009, P<0.001), but no correlation for the radius (R2=0.22, slope=–0.002, P=0.28). This result suggests a difference between the two bones in terms of the degree to which they constrain the loading pattern of footfalls with different magnitudes. Although the radius shows low variability in loading pattern magnitudes near the median and at the highest magnitudes, the metacarpus shows higher variability in loading pattern at magnitudes near the median and less variability at the highest magnitudes. In fact, at the highest magnitudes the variability in loading pattern of the metacarpus is nearly the same as in the radius. Our interpretation is that the curvature of the radius, or other features of its architecture, does not constrain the eccentric, very low magnitude footfalls (below the median; outliers from Fig. 4 not included in Fig. 10) any better than the metacarpus (hence the same PR and DIM) because these footfalls have low risk of causing failure, but it does constrain the TSO and FTSR of loading cycles with magnitudes near the relative median more than the metacarpus. Once the magnitudes are near the maximum, then both bones show constrained loading patterns on those footfalls.
This explains the seemingly conflicting findings that predictability in general loading pattern expressed as a percentage in the expected loading zone (Fig. 5C) differs between the bones (the radius has a higher percentage of footfalls in the expected loading zones than the metacarpus) but PR and DIM do not (Fig. 5A,B). The lowest magnitude footfalls were more likely to occur with extreme loading patterns, and hence, they increased PR and DIM for both bones similarly. The medium magnitude footfalls were more constrained in the radius than in the metacarpus, so this probably was t
) between the principal tensile
strain and the longitudinal axis. All illustrations are drawn to scale.
