Ontogenetic patterns of limb loading, in vivo bone strains and growth in the goat radius
Concord Field Station, Department of Organismic and Evolutionary Biology, Harvard University, 100 Old Causeway Road, Bedford, MA 01730, USA
* Author for correspondence (e-mail: rmain{at}oeb.harvard.edu)
Accepted 30 April 2004
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Summary |
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Key words: bone geometry, bone growth, bone strain, limb loading, ontogeny, scaling
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Introduction |
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Although these studies and the ideas they espouse have contributed greatly
to the understanding of form and function in the musculoskeletal system, they
are limited in their broad taxonomic comparison made over a large size range
of adult organisms. The strategies used to maintain bone stresses within safe
limits in the limbs of animals that vary over a smaller size range and that
are more closely related may be different from those seen in general
comparisons of more distantly related taxa. One example in which this may be
the case is during the ontogenetic growth of an animal, for which negative
allometry in the cross-sectional geometry and other linear dimensions of limb
bones has been reported (Carrier,
1983; Carrier and Leon,
1990
; Biewener and Bertram,
1994
).
In the black-tailed jack rabbit (Lepus californicus), negative
allometry of the diameter and second moment of area of the third metatarsal
allows for relatively lower stresses in the bones of younger rabbits, which
are less well mineralized and therefore not as stiff as the bones of older
rabbits (Carrier, 1983).
Carrier proposed that these features, coupled with appropriate changes in the
moment and contractile properties of the gastrocnemius, allowed younger and
older rabbits to maintain a similar capacity for accelerating and escape
velocity through much of ontogeny. Although Carrier's study argued for a
selective advantage in the departure away from the positive skeletal allometry
needed to maintain stress/strain similarity in the rabbit's limb bones, his
analysis was largely based on morphometric data and did not quantify features
of in vivo locomotor performance and mechanics that would allow the
actual stresses and strains on the musculoskeletal system of growing jack
rabbits to be determined.
Related studies examining bone strains
(Biewener et al., 1986) and
morphological scaling patterns in the chicken tibiotarsus
(Biewener and Bertram, 1994
)
during ontogenetic growth found that even though the tibiotarsus showed
negative ontogenetic allometry in both cross-sectional and second moments of
area, peak strains (assessed at 35% of maximum speed) in the tibiotarsus
remained constant during most of the animal's growth. However, in contrast to
the suggested similarity in peak bone stresses at absolute levels of locomotor
performance (e.g. peak acceleration) indicated for growing jack rabbits
(Carrier, 1983
), the results
for the chicken tibiotarsus indicate that locomotor stresses/strains were not
maintained through ontogeny at similar absolute speeds. Peak bone strains
remained similar between 4- and 17-week-old chickens at the same relative
speeds (0.48 m s1 and 1.17 m s1,
respectively). However, this suggests that if young chicks approached adult
speeds, bone strains would probably exceed adult strain levels despite younger
chicks having relatively more robust tibiotarsi. These studies focused on
linking patterns of bone strain to changes in bone geometry during skeletal
growth but did not examine how limb and bone loading patterns may be related
to locomotor performance and resulting levels of bone strain. No study to
date, therefore, has examined how bone strain patterns and ontogenetic changes
in bone size and shape relate to the locomotor forces transmitted by the limb
as an animal grows. By linking ontogenetic patterns of limb loading with
patterns of bone geometry and functional strain magnitudes, two important
questions can be addressed: (1) how is skeletal growth matched to increases in
body mass and limb loading and (2) does this interaction result in similar
patterns and magnitudes of functional bone strains during ontogeny, as has
been previously observed in the chicken tibiotarsus
(Biewener et al., 1986
)?
To answer these questions, we collected forelimb loading data and in
vivo bone strains from the goat radius through ontogeny across a range of
gaits and speeds. We also collected morphometric data to determine how the
midshaft cross-sectional geometry of the radius changed during ontogenetic
growth. We hypothesized that (1) strain magnitudes and distributions at the
midshaft of the goat radius would remain relatively constant across different
age and size groups within a given gait, similar to the chicken tibiotarsus.
Consistent with this hypothesis, but in contrast to the findings of previous
ontogenetic skeletal allometry studies
(Carrier, 1983;
Biewener and Bertram, 1994
),
we (2) expected that bone growth patterns would match changes in limb loading
with positive allometry in bone cross-sectional geometry and decreased
longitudinal curvature to maintain ontogenetic strain similarity. We also
hypothesized that (3) the radius would be loaded primarily in bending during
stance throughout ontogeny at all gaits, similar to the pattern observed
previously in adult goats (Biewener and
Taylor, 1986
).
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Materials and methods |
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Ground reaction force (GRF) data were collected from six small young goats
(mass, 4.3±1.2 kg; age, 5.6±4.0 weeks; mean ±
S.D.), seven intermediate goats (mass, 8.7±1.6
kg; age, 15.2±10.4 weeks) and five large adult goats (mass,
31.7±11.3 kg; age, 3.0±2.4 years) over a range of gaits and
speeds. In vivo strain data were recorded from the midshaft radius of
the same six small and seven intermediate goats across speed and gait
(Table 1) and compared with
previously published data for three adult goats (mass, 27.0±2.65 kg;
age, >2 years; Biewener and Taylor,
1986). Similar methods to collect the strain data were used here
as in the earlier study, except that in the present study strains were
measured from the medial surface of the radius, in addition to the cranial and
caudal surfaces. Also, strains were not measured from the tibia. Bone geometry
and percentage mineral ash content data were collected from 11 small (mass,
3.7±1.5 kg; age, 5.1±5.4 weeks), eight intermediate (mass,
8.7±3.0 kg; age, 17.4±11.4 weeks) and four adult goats (mass,
20.3±5.2 kg; ages, 0.8, 0.8, 1.2 and 7.0 years). Morphological
measurements were obtained from the juvenile animals in which strains were
collected, as well as from four adult goats euthanized for other purposes and
six additional goats (1.58.8 kg) that died of natural causes.
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Ground reaction force data collection
GRF data were collected to examine how peak limb loads changed through
ontogeny between the different groups. They were also recorded before and
after the surgery to attach the strain gauges in the juvenile goats to
determine if GRFs were diminished as a result of any post-surgical lameness.
Before the GRF data were collected, both forelimbs were shaved, the centers of
joint rotation palpated and the following points marked with non-toxic white
paint: top of the scapula, shoulder, elbow, wrist, metacarpo-phalangeal joint
and hoof. The distances (segment lengths) between the markers were also
recorded.
The GRF data were recorded using a Kistler force platform (0.4 mx0.6 m; 9286A; Kistler, Amherst, NY, USA) and an A/D converter (Bioware 3.2; Kistler) sampling at 2.5 kHz. The goats were simultaneously videotaped from a lateral view (Redlake Motionscope PCI; San Diego, CA, USA) at 125 Hz to record which limbs made contact with the plate, the timing of foot contact and to ensure that only data from trials in which the goat was moving at a steady speed were analyzed. A post-trigger pulse that stopped the video camera was also recorded by the computer to synchronize the force and video data. The magnitude of the peak vertical GRF was measured and normalized by the goat's body weight (Fv/BW) to assess ontogenetic patterns of limb loading.
Surgical procedures
The day following the pre-surgical force platform and video recordings,
goats were prepped for surgery and anesthetized using a mixed injection of
xylazine (1 mg kg1) and ketamine (4 mg
kg1) into the jugular vein. After induction, goats were
intubated and maintained on a closed system anesthesia machine (Matrx, Orchard
Park, NY, USA) at 0.51.0% isoflurane. Breathing and heart rate were
monitored throughout surgery and the anesthesia was adjusted as necessary.
Strain gauges were attached under sterile surgical conditions to the cranial, caudal and medial midshaft surfaces of the left radius. A 35 cm incision was made over the medial surface of the radius. After exposing the attachment sites by retracting the skin and overlying muscles, a small 1 cm2 region of the periosteum was removed and the underlying mineralized surface lightly scraped with a periosteal elevator. The bone surface was then defatted and dried using methyl ethyl ketone (Sigma Chemical Co., St Louis, MO, USA). Once dried, the gauges were attached to each bone site using a self-catalyzing cyanoacrylate adhesive (Duro, Henkel Loctite Corp., Rocky Hill, CT, USA).
Sterilized rectangular rosette strain gauges (FRA-1-11; Tokyo Sokki
Kenkyujo Co., Ltd, Tokyo, Japan) were attached to both the cranial and caudal
surfaces of the radius while a single element gauge (FLA-1-11) was attached
medially. Rosette strain gauges are three-element gauges that allow the
maximum (tensile) and minimum (compressive) principal strains, and their
angles () relative to the bone's longitudinal axis to be determined. The
rosette gauges were attached so that the central element of the gauge was
aligned closely parallel to the bone's longitudinal axis at each site. The
actual position and angular orientation of the strain gauges were determined
post-mortem using a clear protractor and ruler. On average, alignment of the
gauges was within ±3° (range, 015°) to the bone's
longitudinal axis, with the gauges' proximo-distal position at the midshaft
varying by less than 6±5% of the bone's length.
After the strain gauges were bonded to the bone's three midshaft surfaces, the medial incision was sutured and the wire leads (36-gauge, etched Teflon insulation; Micromeasurements, Raleigh, NC, USA) passed through the distal end of the sutured incision. The lead wires were then wrapped laterally around the limb and the pre-soldered epoxy-mounted miniature connector (3xGM-6; Microtech, Inc., Boothwyn, PA, USA) sutured to the skin to provide strain relief to the wires. The incision and the connector were then wrapped in sterile gauze and elastic bandaging tape.
Strain data collection
The goats were given 12 days to recover following surgery. If they
showed any visible signs of lameness during recovery, an intramuscular
injection of flunixin (1 mg kg1) was administered every 12 h
to relieve soreness in the limb. The lead wire connector for the strain gauges
was connected to a 5.5 m shielded cable (NMUF6/30-4046SJ; Cooner Wire,
Chatsworth, CA, USA) that was secured with surgical tape to the upper part of
the forelimb and to a collar around the goat's neck. The cable connected to a
bridge amplifier (Vishay 2120; Micromeasurements), from which the raw strain
signals were sampled by an A/D converter (Axon Instruments, Union City, CA,
USA) at either 1.0 or 2.5 kHz. The goat's joint centers and hoof were again
marked, and lateral-view video was collected at 125 Hz and synchronized to the
strain data using a trigger pulse to relate the timing of foot contact, stride
length, stride frequency and duty factor to the bone strain recordings.
Data were collected while the goats were run down a hallway (small, N=4; intermediate, N=6) or on a motorized treadmill (small, N=3; intermediate, N=2). For the hallway trials, speed was determined by digitizing the eye of the animal as it moved through the field of view. Hallway over-ground recordings provided an assessment of bone strain patterns recorded under equivalent circumstances as our force platform recordings. However, treadmill recordings provided steadier speeds and allowed a larger number of strides over a wider range of speeds and gaits to be collected. No significant differences in strains were found at any site for any speed or gait during treadmill versus over-ground locomotion in the two goats for which equivalent recordings were made (Student's paired t-test, P>0.05). After in vivo bone strain and post-surgical GRF data collection was completed, each goat was euthanized by an injection of sodium pentobarbital (150 mg kg1; intravenous, jugular), and their limb bones dissected for morphological and histological analysis.
Strain data analysis
Raw strain data were filtered using a 4th order zero lag Butterworth filter
with a cutoff frequency of 125 Hz toattenuate noise in the signal. Data from
35 consecutive foot contacts were chosen for both the over-ground and
treadmill trials in which the goat moved at a steady pace using a single gait.
Typically, data from 5060 strides were collected for each goat over the
three gaits. The raw strain data were analyzed using a custom MATLAB program
(The Mathworks, Inc., Natick, MA, USA) that zeroed and calibrated the data,
converting voltages to microstrain (µ, or strain
x106) based on a 1000 µ
shunt-calibration of
the Vishay bridge amplifier. Zero strain levels were determined during the
swing phase of the limb when the voltage change in the signal was minimal.
Strain data for the rosette strain gauges were converted into principal
strains, and their orientations determined using standard equations that
assume a uniaxial planar state of strain
(Biewener, 1992
). Principal
strains and strains recorded by the medial single element gauge were then
adjusted (=
Fv pre-surgery/Fv
post-surgery) to correct for any post-surgical lameness in the limb, assuming
that changes in strain were proportional to changes in limb loading.
Post-operative forces were 80±9% (mean ±
S.D.) of the pre-operative forces at a gallop (range,
6395%), the gait for which the greatest post-operative sample sizes
were obtained. Post-operative reductions in GRF of this magnitude are typical
of strain gauge experiments examining mammalian forelimb bones
(Biewener et al., 1983
;
Biewener and Taylor, 1986
)
and, although significant, the goats' gaits were not significantly altered.
Thus, the reduction in limb load probably only affected strain magnitudes and
not overall patterns or distributions of strain.
Peak positive (tensile) and negative (compressive) principal strains and
their orientations, as well as peak tensile and compressive medial
longitudinal strains and the percentage of stance phase when they occurred
were determined. In keeping with previous studies
(Rubin and Lanyon, 1982;
Biewener and Taylor, 1986
),
the largest principal strains on the cranial and caudal surfaces, which were
tensile and compressive, respectively, are those that we report and focus on
in this study. The largest strains on the medial surface were compressive.
Peak axial and bending strains were determined using the following
equations:
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To gain a more detailed understanding of the strain environment in the
midshaft of the radius and the position and orientation of the neutral axis of
bending throughout the swing and stance phases, recordings from the central
gauge axis of the cranial and caudal rosette gauges were used, together with
longitudinal strains recorded by the single element gauge at the medial
midshaft site, to determine the planar distribution of axial strains at the
bone's midshaft (Biewener,
1992). This was mapped on the cross-section of the bone using a
custom-written MATLAB program.
Bone geometry and percentage mineral content
Upon euthanization, both the left and right radii were removed from the
limbs and cleaned of any muscle and connective tissue. The radii were then
left to dry at room temperature for at least one week. Both the cranio-caudal
(C-C) and medio-lateral (M-L) curvatures were measured from the
non-instrumented (right) limb by dividing the radius of curvature for each
direction by half the C-C or M-L diameter of the bone, respectively. The
radius of curvature was measured as the orthogonal distance from the C-C or
M-L midpoint of the bone at its midshaft to a line bisecting the proximal and
distal articular ends of the bone (Bertram
and Biewener, 1992).
The right radius was also used to determine the percentage mineral ash content. One-third of the bone's length, centered about the midshaft, was cut, and the periosteum, marrow and adjacent ulna removed and allowed to dry thoroughly. The bone section was weighed (Sartorius 1800; Goettingen, Germany), placed in a small aluminum dish, weighed again, and placed in an oven (Huppert Model 2 Deluxe; Chicago, IL, USA) for 12 h at 400°C. Immediately upon removal from the oven, the ashed bone and dish were weighed again. The percentage mineral ash content of the section of bone was determined as: post-ashed mass/pre-ashed mass x 100. Because adult goat ash specimens were limited, each middle third section of bone selected for ashing was cut in two and ashed separately. The mean of the two ash values was used in the analysis.
After measuring the alignment of the strain gauges and their placement relative to the bone's midshaft, the instrumented (left) radius and adjacent ulna were embedded in fiberglass resin (Bondo-Mar-Hyde Corp.; Atlanta, GA, USA). A 330 µm section was taken at the midshaft using a diamond annular saw (Microslice II; Cambridge Instruments, Ltd, Cambridge, UK). After affixing the section to a microscope slide, a magnified digital picture of the cross-section was taken using a video camera (Sony XC-75; Cypress, CA, USA). From this magnified cross-section, the cross-sectional area and C-C and M-L second moments of area (ICC and IML, respectively) were calculated using a custom macro for NIH Image 1.61 (Bethesda, MD, USA). These measurements were also made including the ulna to determine to what extent it contributed to the forelimb skeleton's overall cross-sectional properties.
Statistical analyses
The means and standard deviations for the kinematic and strain data
reported in the tables and throughout the text represent all the goats in a
given size group for whom data were collected, based on individual mean values
obtained from multiple trials (typically five) for each goat at a particular
gait. The mean value for each trial was taken from the 35 foot contacts
analyzed for that trial. Comparisons among different size groups and different
gaits were analyzed using two-way analysis of variance (ANOVA;
P<0.05; StatView 4.1; Abacus Concepts, Inc., Berkeley, CA, USA).
Similarly, statistical comparisons testing for differences in limb loading
through ontogeny were carried out using two-way ANOVA.
Least-squares regressions (KaleidaGraph 3.6; Synergy Software, Reading, PA, USA) were used to examine ontogenetic patterns of axial and bending strains versus speed and cross-sectional geometry, and percentage mineral ash content versus body mass. Significant differences in slope were based on 95% confidence intervals derived from the regressions.
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Results |
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Peak bone strains versus size
Peak midshaft bone strains in the radii of the two smaller groups were
similar in distribution and alignment to those previously reported for the
radius of adult goats. The dominant principal strain on the cranial surface
(CR) was tensile (Table 2; Figs
1,
2A) and aligned primarily along
the long axis of the bone in all gaits. On the caudal midshaft surface (CD),
the larger principal strain was compressive
(Table 2; Figs
1,
2B) and, despite greater
variability among animals, was also generally aligned close to the long axis
of the bone. Axial strains on the medial surface (MED) of the radius measured
from single element strain gauges in the two smaller groups (but not
previously in the adults; Biewener and
Taylor, 1986) were also compressive
(Table 2; Figs
1,
2C). In terms of absolute
magnitude, strains measured in the small and intermediate animals were
typically smallest at the cranial surface of the radius, larger at the caudal
surface and largest at the medial surface.
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Peak strains within the radius increased with an ontogenetic increase in body mass at all gauge locations across the three gaits. However, due to high inter-individual variation (Table 3), increases in peak strains within a gait between the small and intermediate groups were only significant on the cranial surface (CR, P<0.01; CD, P=0.08; MED, P=0.36). Peak strains in the adult radius, however, were significantly greater than those in the small and intermediate groups (CR and CD, P<0.0001).
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Peak bone strains versus gait
Strains increased with speed and a change of gait at all three gauge
locations (Table 2;
Fig. 2) in the three groups.
However, large inter-individual variation within the two smaller groups again
resulted in the change in strain generally being insignificant between gaits
(CR, P=0.03; CD, P=0.11; MED, P=0.09). In the adult
goats, peak bone strains during trotting and galloping were significantly
greater than those during walking, but no significant difference in peak
strain was observed during trotting versus galloping
(Biewener and Taylor,
1986).
Strains increased between 1.5- and 2-fold from a walk to a gallop at all three gauge sites in each size group, except on the cranial surface of the smallest group, where strains increased threefold from a walk to a gallop.
Axial versus bending strain distributions in the radius
Consistent with the overall increase in peak strain magnitude, both the
axial (Fig. 3A) and bending
(Fig. 3B) components of strain
also increased with speed and change of gait. For axial compressive strains,
this trend was significant in the smallest size group (slope,
60.8±22.5; 95% CI; r2=0.48) but was not
significant in the intermediate group due to the large variation among
individuals (slope, 48.6±89.7; r2=0.04; CV,
1.65±0.56). Nevertheless, the slopes of the regressions of axial
compressive strain versus speed in the two groups were not
significantly different from one another (based on their overlapping 95% CI).
For strains due to bending, the slopes of the regressions describing the
increase in bending across speed in the two groups were significant but again
did not differ from one another (small, 241.3±58.8,
r2=0.68; intermediate, 147.2±53.0,
r2=0.54).
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In all three size/age groups, bending constituted the major component of
strain in the radius midshaft (Fig.
3C). This trend remained consistent across speed and gait
(regression slopes of % bending strain were not significantly different from
zero: small, 2.4±3.7, r2=0.05; intermediate,
2.3±6.5, r2=0.02; adult, see table 1 in
Biewener and Taylor, 1986). In
general, the radius of adult goats experienced the greatest amount of strain
due to bending (mean, 89%; Biewener and
Taylor, 1986
), followed by the small group (73±9%) and then
the intermediate group (70±18%).
Notably, the plane of bending was not static but typically shifted its orientation throughout stance (Fig. 4). The axial and bending strains reported in Fig. 3 occurred at the time of peak compressive and tensile strains on the caudal and cranial surfaces of the radius (73% of stance for the small group and 75% of stance for the intermediate group). At this time, the orientation of bending was primarily in the cranio-caudal (C-C) direction with the neutral axis oriented in the medio-lateral (M-L) plane (Fig. 4D). However, at midstance, peak strains on the medial surface were typically, although not significantly, greater than those on the caudal surface, corresponding to a shift in the orientation of bending at this point in stance to the M-L direction (Fig. 4C). Because peak strains recorded on the medial surface were higher than those recorded on the cranial and caudal surfaces, M-L bending strains probably represented the maximum bending that the radius of the younger and smaller goats experienced.
|
Ontogenetic changes in limb loading
As expected, all three size/age groups showed a significant increase in the
normalized vertical GRF exerted on the forelimb as animals increased speed and
changed gait (Fig. 5;
P=0.0001). However, no significant difference in normalized vertical
limb load was observed over the speeds recorded within each gait among the
three size classes (P=0.33). Consequently, within a given gait, the
radius transmitted limb forces associated with the same relative ground
reaction load regardless of size.
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Bone curvature during ontogenetic growth
Both M-L and C-C normalized longitudinal curvatures of the radius did not
change significantly throughout ontogeny
(Fig. 6; regression slopes;
M-L, 0.05±0.18, r2=0.02; C-C, 0.12±0.14,
r2=0.13). Thus, the goat radius maintained its caudal and
lateral concave curvatures during growth, with the C-C curvature exceeding the
M-L curvature throughout ontogeny (1.04±0.25 versus
0.36±0.11, respectively; mean ± S.D.).
|
Ontogenetic changes in cross-sectional geometry
Strong patterns of negative allometry were observed in the ontogenetic
scaling of the cross-sectional and second moments of area. Midshaft
cross-sectional area of the radius scaled proportional to (body
mass)0.53±0.07 (M0.53±0.07,
r2=0.92; Fig.
7A). In goats, the ulna is closely associated with the radius,
contributing 10.6% to the total cross-sectional area of these two skeletal
elements of the forearm at the level of the midshaft of the radius. Although
the ulna might, therefore, compensate for the relative decrease in
cross-sectional area of the radius, the growth trajectory of the combined
cross-sectional area of the radius and ulna at the level of the radial
midshaft exhibited the same negatively allometric scaling pattern
(
M0.52±0.07, r2=0.91).
Thus, both bone elements became reduced in size relative to the increase in
body mass during ontogenetic growth.
|
Negative allometry of midshaft second moment of area of the radius scaled
M1.03±0.12 (r2=0.94) in
the medio-lateral (IML) direction and
M0.84±0.16 (r2=0.85) in
the cranio-caudal (ICC) direction
(Fig. 7B). As a result, the
bone's resistance to bending, particularly in the cranio-caudal direction, was
substantially reduced during growth. Once again, accounting for the ulna's
contribution to bending resistance in the forearm resulted in only a slight
change in the overall scaling of second moment of area for the two bone
elements combined
(IML
M1.05±0.13,
r2=0.93;
ICC
M0.80±0.16,
r2=0.83).
Ontogenetic changes in percentage mineral ash content
A small but significant increase in the percentage mineral ash content of
the radial midshaft was observed through ontogeny (1 day to 7 years of age;
Fig. 8; slope,
0.21±0.07, r2=0.68), averaging 56.3±0.80%
(N=10) in the smallest group, 57.3±1.21% (N=8) in the
intermediate group and 59.1±1.29% (N=3) in the adult
group.
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Discussion |
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Counter to our second hypothesis that ontogenetic changes in bone shape
would match ontogenetic changes in limb loading to maintain strain similarity,
we found that the relative size and shape of the goat radius supporting these
loads actually decreased. Strong negative allometry of cross-sectional area
(M0.53) and second moments of area
(ICC
M0.84;
IML
M1.03) of the radius clearly
indicates a significant decrease in the capacity of the bone to support
body-weight-related forces in both bending and axial compression. These forces
probably remained uniform relative to the animal's size within each gait
during ontogenetic growth. As a consequence, peak strain magnitudes increased
with age and size when compared at dynamically similar gait speeds.
Negative allometry of the cross-sectional area of the radius was
specifically correlated with increased axial compressive strains. It is not
surprising based upon this trend alone that strains in the goat radius
increased through ontogeny. However, in most tetrapod limb bones measured to
date, which include the goat radius, bending strains are typically the major
component of the total strain developed within the midshaft of a bone
(Rubin and Lanyon, 1982;
Biewener and Taylor, 1986
;
Biewener, 1991
). Thus, the
strong negative allometry of the second moments of area in the goat radius,
which substantially reduced its capacity for resisting bending moments in the
C-C and M-L directions, explains most of the observed increase in locomotor
strains as the goats grew in size and weight. The bone's greater negative
allometry and increased susceptibility to bending in the C-C direction
relative to the M-L direction is somewhat surprising, given its greater C-C
curvature and the parasagittal motion of the limb during locomotion.
Increased load predictability in the radius through ontogeny
Engineered structures are typically built to minimize deflection or bending
under a habitual load, so it is counterintuitive that the goat radius is
predisposed throughout ontogeny to be bent in the C-C direction. The
interaction between bone curvature and asymmetric cross-sectional geometry
favoring a preferential bending direction has been hypothesized to improve a
bone's `load predictability' (Bertram and
Biewener, 1988). According to this hypothesis, a long bone's form
evolves to meet the conflicting demands for strength versus strain
predictability as animals subject their bones to variable loading conditions.
This seems to reflect the growth pattern and increased cross-sectional shape
asymmetry of the goat radius. Its relative decrease in second moment of area
in the C-C direction, combined with its greater curvature in this direction,
favors an increase in bending-induced strains in the C-C cortices during
growth, as was generally observed. At the same time, this may provide the bone
with increased loading predictability
(Lanyon, 1987
;
Bertram and Biewener,
1988
).
Consistent with preferential C-C bending, the muscles that span and
transmit loads via the radius lie mainly in the C-C plane of the
bone. Depending on when certain muscle groups are active, this musculoskeletal
organization could either augment or attenuate the C-C bending moments imposed
upon the limb by the GRF (Pauwels,
1980). Although strains were not measured on either the medial or
lateral surfaces of the adult goat radius
(Biewener and Taylor, 1986
),
in the younger groups examined here strains recorded on the medial surface
were largest, despite the bone's greater resistance to bending in the M-L
direction. This suggests that, whereas muscles arranged along the C-C surfaces
of the radius could serve to control and attenuate strains in these cortices,
resistance to bending in the M-L plane is wholly reliant upon the bone's
inherent flexural stiffness.
Ontogenetic changes in bone material properties
The flexural stiffness of a bone is not only dependent upon its second
moment of area but also its elastic modulus (E). Elastic modulus
depends on the degree of bone mineralization, with older, more highly
mineralized bone tissue typically having a higher modulus
(Currey and Pond, 1989;
Brear et al., 1990
;
Currey, 1999
). Using simple
beam theory,
b=By/EI, where B is
the applied bending moment and y is the bone's radius
(Wainwright et al., 1976
), we
predict that E would need to increase by 1.77 times from small to
adult goats to maintain uniform C-C bending strains in the radius during
ontogeny. Lanyon et al. (1979
)
found that, in the sheep radius, E increased by 1.27 times for a 2.1%
increase in percent ash content from 17 weeks to >4 years of age,
suggesting that the 2.8% ash increase we observed in the goat radius, although
providing some increase in bending resistance, did not increase E
sufficiently to maintain peak strain levels uniform during ontogeny.
Although the small increase in mineralization (and, by extension, elastic
modulus) and strong negative allometry suggest that the adult goat radius may
be increasingly under-built as it grows, peak strains developed in the adult
radius at a gallop (1850 µ;
Biewener and Taylor, 1986
) are
no larger than those reported for most other vertebrates measured to date,
which usually range between 1800 µ
and 3000 µ
(Rubin and Lanyon, 1982
).
Therefore, it seems more likely that the radii of adult goats are not
under-built but, rather, the radii of young goats are over-built.
Ecological and evolutionary factors influencing the growth trajectory of the goat radius
Goats are precocial animals that live in herds that include both adult and
juvenile individuals. Their collective movements therefore require that young
animals, with shorter legs, take many more steps and maintain a relatively
faster speed to keep up with the adults in the herd. In the present study, we
observed that adult goats had a stride length of 0.76 m when they walked at a
speed of 1.21 m s1 (Table
1). At this speed, a young goat corresponding to our small size
group would need to trot slowly to keep up with an adult, subjecting its limbs
to a higher frequency of greater loads and strains. To maintain pace with a
trotting adult (2.27 m s1), a young goat would have to
gallop (2.34 m s1; Table
1). Given that peak strains in the radius of the young goats at a
gallop were only about 70% of those in a walking adult goat, there is
therefore no substantial mechanical detriment for a young goat having to
gallop to keep up with the adults. Even though the radius of the young goats
at a gallop supports 1.7BW while the adult radius at a walk supports
only 0.7BW, the relatively greater cross-sectional area and second
moments of area of the younger goat radius maintain strains at comparably safe
levels, even when the young goats move quickly for their size.
The `over-design' of the radius at a young age may not only help young goats to literally `keep up with the herd' but may also provide a greater safety factor during their first days following birth, when their movements may be less well coordinated and unstable. This might produce more variable patterns of bone loading, consistent with the generally greater within-individual variation in peak strains that we observed in younger goats (Table 3). With growth, the need for an enhanced safety factor diminishes as an older goat's stride length increases and they become more adept at walking and running. At this stage, the cost of maintaining a relatively `over-built' radius may outweigh the risk of mechanical failure in the radius, which becomes loaded in a more predictable manner as the goats grow and mature. Thus, the ontogenetic growth patterns in the radius seem to correspond well to changing mechanical demands in the goat's life history.
Finally, the terrain itself may present a more variable substrate for a younger, smaller goat, possibly causing them to encounter a wider variety of limb and bone loading. The less eccentric cross-sectional geometry and increased area and second moments of area of the radius of young relative to adult goats seem consistent with this. This would favor the much lower, but more variable, strains that we observed during steady level locomotion. Under less steady conditions and more varied terrain, bone strain levels might be even more variable and of greater magnitude.
Ontogenetic strain patterns in the goat radius versus the chicken tibiotarsus
In the only other study that has examined ontogenetic patterns of bone
strain, Biewener et al. (1986)
found that locomotor strains in the chicken tibiotarsus generally remained
uniform throughout ontogeny. Chickens are also precocial animals and are
capable of body support and locomotor movement soon after hatching. Similar to
the pattern of ontogenetic growth observed for the goat radius, the
cross-sectional area (
M0.55) and second moment of
area (
M1.22) of the tibiotarsus also scaled with
negative allometry, well below what would be expected to maintain strains at
similar levels (Biewener and Bertram,
1994
). However, because this earlier study did not examine
patterns of limb loading, it is difficult to assess the basis for strain
similarity observed during growth of the chicken tibiotarsus. These
observations would appear to suggest that older chickens experience lower
relative limb loads at functionally equivalent speeds.
The results obtained for the goat radius in comparison with the chicken
tibiotarsus show that similar ontogenetic patterns of bone growth can result
in varying ontogenetic patterns of bone strain. This suggests that differences
in a species' ontogeny and locomotor capability can have important influences
on bone growth and bone loading, which may allow juvenile animals to achieve
absolute performance levels similar to those of adults
(Carrier, 1983). Further
examination of limb bone growth patterns in a wider diversity of taxa is
needed to better understand the interplay among ontogenetic patterns of bone
growth, limb loading and locomotor capacity in relation to a species' ecology
and evolutionary history. Studies of in vivo bone strain patterns
under more variable, natural conditions are also needed to evaluate how
variation in locomotor activity affects the distribution and pattern of strain
within a bone, as well as how the magnitude and pattern of strain change
during growth.
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