Optimization of bone growth and remodeling in response to loading in tapered mammalian limbs
1 Peabody Museum, Harvard University, 11 Divinity Avenue, Cambridge
Massachusetts 02138, USA
2 Department of Anthropology, University of New Mexico, Albuquerque, New
Mexico, 87131, USA
3 Department of Anatomical Sciences, Health Sciences Center, State
University of New York, Stony Brook, New York, 11794, USA
4 Museum of Comparative Zoology, Harvard University, 26 Oxford St.,
Cambridge, Massachusetts, 02138, USA
* Author for correspondence (e-mail: danlieb{at}fas.harvard.edu)
Accepted 27 May 2003
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Summary |
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Key words: bone, periosteal modeling, Haversian re-modeling, growth, sheep, strain
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Introduction |
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Limb tapering may save energy during swing, but may also affect bone
strength during stance. Limbs during stance are usually modeled as cylinders
subject to a combination of bending and axial compression from body mass and
ground reaction forces. At midstance, when ground reaction forces (GRFs) are
typically highest and approximately vertical, bending stress/strain at
midshaft (the likely location of maximum bending) is a function of many
factors, including the magnitude and orientation of GRF relative to the
element and the cross-sectional and the material properties of the bone
(Biewener et al., 1983).
Distal tapering, therefore, leads not only to higher compressive strains
because of smaller cortical areas, but also to potentially higher bending
strains because of decreased second moments of area (I) available to
resist the bending moments that account for a high proportion of midshaft
strains (Bertram and Biewener,
1988
).
High strains in tapered distal bones can pose structural problems,
especially because repeated high strains can lead to the generation and
propagation of fatigue damage (e.g. microcracks), which contribute to
mechanical failure (see Martin et al.,
1998; Currey,
2002
). Mammals have several potential adaptations to distal
tapering, of which the two best documented are changes in gait and element
length with increasing body mass. Larger mammals tend to orient their distal
limb bones more in line with GRFs at peak loading, thereby increasing the
proportion of axial compression relative to bending
(Gambaryan, 1974
;
Biewener, 1983
;
Biewener et al., 1988
;
Polk, 2002
). Larger mammals
also tend to compensate for geometric scaling of midshaft diameters by
shortening distal limb elements relative to total limb length l,
thereby reducing bending moments (Smith
and Savage, 1956
; Gambaryan,
1974
; Alexander,
1977
; Jungers,
1985
; Bertram and Biewener,
1992
). Other potential adaptations to limb tapering are less well
documented. While bone curvature across mammals decreases slightly but
significantly with body mass M
(
M0.09), helping to reduce bending stresses
(Biewener, 1983
), distal
elements are not straighter than proximal elements
(Bertram and Biewener, 1988
).
In addition, some studies (see MacKelvie
et al., 2002
) show a positive correlation between exercise and
bone mineral density, which increases stiffness, but also reduces post-yield
toughness (Currey, 2002
), but
no studies have found variations in bone mineral density between proximal and
distal limb midshafts (Ruff and Hayes,
1984
).
This study examines two additional and potential adaptations for limb tapering, modeling and Haversian remodeling for the following reasons. First, they are probably the most labile osteogenic responses to loading that generate phenotypically plastic variations in cortical bone shape and strength. Second, how cortical bone modulates modeling and Haversian remodeling has been a longstanding problem, especially for understanding how bones age and maintain structural variations.
Modeling
Modeling (defined here in a narrow sense as the addition of bone mass)
increases resistance to bending by augmenting I around the axes in
which applied forces generate deformation so that a given moment generates
less strain (Wainright et al.,
1976). Because I depends on the squared distance of each
unit area from the neutral axis of bending, bones should optimize I
relative to mass by adding bone periosteally and removing it endosteally
(expanding the medullary cavity), yielding a high ratio of diameter
(D) to wall thickness (t), Marrow, however, whose density is
roughly 50% of bone, limits the optimum D/t ratio in mammals
to approximately 4.6 to maximize stiffness relative to mass
(Pauwels, 1974
;
Alexander, 1981
;
Currey and Alexander, 1985
).
Among terrestrial mammals, the median ratio of D/t is
approximately 4.4, with a higher median value for the femur (5.4) and lower
values for the humerus and more distal limb elements
(Currey and Alexander, 1985
).
There is abundant evidence in juveniles that modeling increases I in
response to loading, mostly through increases in periosteal apposition
(Chamay and Tchantz, 1972
;
Goodship et al., 1979
;
Lanyon et al., 1982
;
Lanyon and Rubin, 1984
; Rubin
and Lanyon,
1984a
,b
,
1985
;
Biewener et al., 1986
;
Raab et al., 1991
;
Lieberman, 1996
;
Bass et al., 1998
;
Ruff et al., 1994
;
Lieberman and Pearson, 2001
),
and to a lesser extent through inhibition of endosteal resorption
(Woo et al., 1981
). To
evaluate modeling effects on I as a means of compensating for distal
tapering, however, more data are needed on strains in proximal versus
distal midshafts during conditions of loading that are within biologically
normal ranges and without the potentially confounding effects of surgical
intervention (see Bertram and Swartz,
1991
). Obviously distal bones do not usually model as much as
proximal bones (otherwise they would have similar cortical thickness), but it
is not known if differences in strain environments account for differences in
modeling rates.
Haversian remodeling
Another potential adaptation to limb tapering may be to increase Haversian
remodeling (HR) rates in distal versus proximal elements. During HR,
osteoclasts first resorb old bone, and osteoblasts then lay down concentric
lamellae of new bone around a central vascular channel. The function of HR is
not entirely understood (see Martin et
al., 1998; Currey,
2002
), but it is generally thought that it prevents or repairs
fatigue damage caused by high strain magnitudes and/or frequencies. Although
Haversian (secondary osteonal) bone is weaker in vitro than young
primary osteonal bone (Currey,
1959
; Carter and Hayes,
1977a
,b
;
Vincentelli and Grigorov,
1985
), it is apparently stronger than old, microcrack-damaged
primary bone (Schaffler et al.,
1989
,
1990
). Haversian systems may
also prevent or halt microfracture propagation. In addition, HR can strengthen
bone by reorienting more collagen along axes of tension
(Martin and Burr, 1982
; Riggs
et al.,
1993a
,b
).
A number of studies demonstrate that loading increases remodeling rates
(H
rt et al., 1972
;
Bouvier and Hylander, 1981
,
1996
;
Churches and Howlett, 1981
;
Rubin and Lanyon, 1984b
,
1985
;
Schaffler and Burr, 1988
;
Burr et al., 1985
;
Mori and Burr, 1993
;
Lieberman and Pearson, 2001
;
Lees et al., 2002
; for a
review, see Goodship and Cunningham,
2001
). In addition, HR preferentially occurs in older regions of
long bones that have presumably accumulated the most damage
(Frost, 1973
;
Bouvier and Hylander, 1981
;
Currey, 2002
).
The possibility that HR is an adaptation for maintaining tapered distal
limbs has been suggested but never been tested comprehensively. Lieberman and
Crompton (1998) found higher
rates of HR in distal than proximal midshafts in juvenile swine, and Lieberman
and Pearson (2001
) found
higher rates of HR in distal than proximal midshafts in juvenile sheep.
However, these studies did not relate rates of HR to differences in strain
environments, and only examined juveniles.
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The optimization model |
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The general prediction is that if bones optimize strength relative to the
cost of adding mass, and if HR repairs or prevents microdamage, then the
proportions of modeling versus HR responses to loading should vary at
different skeletal locations and ages in relation to their costs and benefits
(Fig. 1). As noted above, the
major mechanical benefit of modeling is to strengthen a bone by increasing the
second moment of area around the axes in which bending forces generate
deformation. The major long-term cost of modeling, however, is the additional
energy required to accelerate added mass during swing, a cost that should be
approximately proportional to mR2, where m is the
mass of the limb, and R is the distance from the center of mass (COM)
of the limb to the hip or shoulder joint
(Hildebrand, 1985;
Winter, 1990
). Adding bone
mass distally will not only increase the limb's mass but will also move the
limb's COM distally (increasing R). Because cost is proportional to
R2, small increases in R may have large
effects.
|
The costs and benefits of HR are less understood, but differ from those of
modeling. As noted above, proposed benefits of HR include replacing and
thereby strengthening fatigue-damaged bone, increasing elasticity, and halting
microfracture propagation without adding mass or changing shape
(Martin et al., 1998;
Schaffler et al., 1990
;
Currey, 2002
). But HR occurs
slowly, increases porosity, and incurs higher long-term metabolic costs than
modeling by leaving a bone insufficiently strong to resist further strain
damage, requiring subsequent growth or remodeling
(Martin, 1995
).
One additional issue to be considered is the effect of age. As
osteoprogenitor cells senesce, they decline in number and become less
sensitive to many epigenetic stimuli, including those from mechanical loading
(Muschler et al., 2001;
Chan and Duque, 2002
). In
vitro and comparative studies indicate that osteoblasts are less
responsive to strains in older individuals
(Erdmann et al., 1999
;
Stanford et al., 2000
;
Donahue et al., 2001
). In
addition, mechanical loading stimulates osteogenesis mostly prior to skeletal
maturity, and primarily acts to slow down the rate of bone loss in older
individuals (e.g. Ruff et al.,
1994
; Bass et al.,
1998
; Wolff et al.,
1999
; Kohrt,
2001
).
Four specific hypotheses are tested. (1) While rates of periosteal growth are known to be less in distal than proximal midshafts (otherwise distal elements would not be thinner), rates of additional growth in response to loading are predicted to be less in distal than proximal elements. The null hypothesis is that rates of additional midshaft periosteal growth in response to loading are either similar between elements or vary in proportion to magnitudes of strain. (2) Because distal elements have thinner cortices than proximal elements (due to lower baseline rates of modeling), strain magnitudes should be higher in midshafts of distal elements compared to more proximal elements. The null hypothesis is that peak strain magnitudes should be similar between elements. (3) If HR is an adaptation to either prevent or repair fatigue damage caused by high strains, then rates of HR are predicted to be higher in distal than proximal elements because of increased strains in distal elements (hypothesis 2). The null hypothesis is that rates of HR at midshafts in response to loading are similar between elements. (4) If HR functions to repair or prevent fatigue damage, then rates of HR at midshafts should increase with age to compensate for decreased rates of modeling in response to mechanical loading. The null hypothesis is that HR rates at midshafts do not vary with age.
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Materials and methods |
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An additional sample of five juvenile Dorset sheep approximately 40 days old were used for strain gauge analyses. These animals were the same age and body mass (2030 kg) as the juvenile group described above prior to treatment period. The animals were trained to run on a treadmill at 1.5 m s1, a trotting gait corresponding to a Froude number of 0.5 and thus comparable to the above-described sample. Strains in these animals therefore approximate the pattern and magnitude of strain in the juvenile sample of exercised versus non-exercised Dorset sheep at the start of the exercise treatment period.
Histological analyses
For the exercised and control sheep, modeling and HR during the treatment
period were quantified post-mortem on midshaft sections of the femur,
tibia and metatarsal, stained and dehydrated in a solution of 1% basic Fuchsin
in ethanol for 7 days, embedded in poly-methyl methacrylate, and cut into two
sections. Each section was mounted to a glass slide, ground to a 100
µm-thick section, coverslips placed on top and analyzed using an Olympus
SZH-10 microscope (Olympus America, Melville, NY, USA) with epifluorescence.
Sections were digitized using a SPOT 1.3 digital camera (Diagnostic
Instruments, Sterling Heights, MI, USA).
Haversian systems formed during the fluorochrome-labeled treatment period were counted in each quadrant using Image Pro-Plus (Media Cybernetics, Silver Spring, MD, USA). We could not label the first two phases of Haversian remodeling (activation and resorption), but the dyes enabled us to determine if the onset of the third phase, formation, occurred during the treatment period. Thus Haversian systems were not counted if the outer (first) layer of Haversian bone was not labeled with fluorochome dye. Haversian systems activated before the treatment period could not be excluded, but these were assumed to be the same for both treatment groups (i.e. before the exercise treatment period). HR density was calculated as the total number of initiated Haversian systems/cross-sectional area; HR rate was calculated as the total number of initiated Haversian systems/cross-sectional area/treatment day. Periosteal area (PA) added was measured using NIH Image v1.62 (http://rsb.info.nih.gov/nih-image/) as the total area added during the treatment period from the initial Calcein line, which marked the first day of the experiment, to the outer cortex of the bone. PA added was standardized by body mass; Periosteal modeling (PM) rate was calculated as PA added/treatment day.
Strain and kinematic recordings
Rosette strain gauges were surgically attached to three locations around
the midshaft of the tibia in five juveniles and the metatarsal in three
juveniles of the strain-gauge sheep sample (see above). Prior to surgery,
subjects were sedated with ketamine (8.0 mg kg1, i.m.),
xylazine (0.05 mg kg1, i.m.) and atropine (0.05 mg
kg1, i.m.), intubated, and maintained on a surgical plane of
anaesthesia with isofluorane. The left hind limb of each animal was shaved and
sterilized, and the location of the midshaft marked. Under sterile surgical
conditions, insulated FRA-1-11 rosette strain gauges (Sokki Kenkyujo, Tokyo,
Japan) of 120±0.5 resistance were affixed to the cranial,
medial and caudal surfaces of the tibial midshaft through an incision on the
medial surface, and to the cranial, medial and lateral surfaces of the
metatarsal midshaft from incisions on the medial and lateral surfaces of the
foot (in one sheep, no. 574, the cranial gauge was positioned on the
craniomedial surface). Gauges were sealed using M-coat and D-coat
(MicroMeasurements Inc., Raleigh, NC, USA). To provide anaesthesia and
minimize inflammation, Bupivacaine (diluted 1:10 v/v) was injected
subcutaneously around each incision site. Muscles and tendons were retracted
on the posterior and anterior surface of both bones during gauge insertion,
but care was taken to ensure that these structures were not cut or damaged.
The surface of the bone at each gauge site was prepared by cutting a small
window (ca. 5 mm2) in the periosteum, cauterizing any vessels, and
degreasing with 100% chloroform. Bupivacaine (diluted 1:10 v/v) was perfused
under the periosteum prior to cutting, to provide anaesthesia. Gauges were
bonded using methyl-2-cyano-acrylate glue, with continuous pressure applied
for 2 min as the glue was drying. Care was taken to align one of the elements
of the gauge with the long axis of the bone. The orientations of each gauge's
A-element (previously marked on the gauge's sealing coat using metallic ink)
relative to the long axis of the bone was recorded prior to closing the
incision with suture. Gauge leads were then passed extracutaneously underneath
flexible bandages to the hip, where they were attached to a bandage loosely
wrapped around the animal's abdomen. To provide strain relief, the leads of
each gauge were affixed tightly to a bandage wrapped around the leg near the
incision site.
Strain data were recorded 4 and 24 h after surgery, when animals were running with an apparently normal gait and showed no signs of lameness, distress or discomfort (e.g. with symmetrical limb kinematics on the operated and non-operated hind limbs and no signs of leaning or favoring one limb over another). During each recording session, the gauges were connected with insulated wire to Vishay 2120A amplifiers (MicroMeasurements Inc., Raleigh, NC, USA) to form one arm of a Wheatstone bridge in quarter-bridge mode; bridge excitation was 1 V. Voltage outputs were recorded on a TEACTM RD-145T DAT tape recorder (TEACTM Corp, Tokyo, Japan). Gauges were periodically balanced to adjust for zero offsets during the experiment, and calibrated when the animal was stationary with the instrumented leg unsupported.
To correlate strains with limb kinematics, 3-D coordinates were obtained for all hind-limb joints using an infrared motion analysis system (Qualisys Inc., East Windsor, CT, USA). Three cameras tracked the position of reflective markers (12 mm diameter) placed on the shaved skin overlying the distal interphalangeal joint, distal metatarsal, lateral malleolus, lateral epicondyle of the femur, greater trochanter and anterior superior iliac spine. Kinematic sequences captured at 60 Hz were synchronized to the strain gauge output, using a trigger that started data capture by the Qualysis system at the same time that a 2 V pulse signal was sent to the tape recorder. Limb segments were identified by connecting adjacent markers. QTools software (Qualisys Inc., East Windsor, CT, USA) was used to identify temporal midstance and measure element orientation at midstance.
Strain gauge analyses
Selected sequences of strain data were sampled from the tape recorder on a
Macintosh G4 computer using an IonetTM A-D board (GW Instruments,
Somerville, MA, USA) at 250 Hz. A Superscope 3.0TM (GW Instruments,
Somerville, MA, USA) virtual instrument (written by D.E.L.) was used to
determine the zero offset, and calculate strains (in microstrain, µ)
from raw voltage data using shunt calibration signals recorded during the
experiment. For each gauge, principal tension (
1),
compression (
2), and the orientation of principal tensile
strain (
1°) relative to the bone's long axis, were
calculated following equations in Biewener
(1992
). Igor Pro v. 4.0
(Wavemetrics Inc., Lake Oswego, OR, USA) was used to calculate these strains
at temporal midstance (when peak strain occurs) for at least 10 gait cycles
for each animal. In some cases, not all elements of the gauge were working,
but we were able to use the calibrated strain values from the element aligned
with the long axis of the bone to approximate normal strain (see below).
To characterize midshaft strain environment in the tibia and metatarsal,
digitized transverse cross-sections of each midshaft were analyzed with a
macro (written by S. Martin, University of Melbourne, Australia) for NIH Image
to calculate and graph the neutral axis (NA) and gradients of normal strain
across the section, under two assumptions: that the bone shafts are beams
loaded axially and in bending, and that the strain distribution is linear
(formulae in Rybicki et al.,
1974; Biewener,
1992
; Gross et al.,
1992
). These isoclines were used to estimate the magnitude of peak
maximum (tensile) and minimum (compressive) normal strains at the cortex of
the midshaft of the tibia and metatarsal. In several animals for which
isoclines could not be calculated for the tibia (see
Table 5), maximum strains were
estimated from the cranial gauge, and minimum strains were approximated from
the caudal gauge. Since the tibia is bent around a mediolateral axis at
midstance (see below), these approximations were considered reasonable. Strain
due to bending and axial compression was calculated following equations in
Biewener (1992
). Digitized
cross-sections in conjunction with coordinates of the experimentally
determined NA were also used to calculate the polar moment of inertia,
J, the sum of any two orthogonal second moments of area (I)
around a neutral axis through the area centroid, and Zc,
the section modulus of compression, using an additional macro for NIH Image
1.62 (written with the help of S. Martin). The macro works by calculating
IN as the sum of the areas of each pixel times its squared
distance to the neutral axis. Zc was calculated as
IN/ac, where ac is
the greatest perpendicular distance from the neutral axis to the outer
perimeter subject to compression in the plane of bending. This program was
also used to calculate J and cross-sectional areas for the juvenile,
subadult and adult sample of exercised versus control sheep.
Cross-sectional properties were standardized by body mass and element
length.
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Results |
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Table 2 and Fig. 2 also indicate that HR densities and HR rates at the midshaft vary inversely with modeling rates. All age groups show a marked increase in HR density and HR rate in distal versus proximal midshafts, but with considerably higher HR rates in adults than juveniles (P<0.05). Exercise effects on HR are greatest in juveniles, and decline during ontogeny. No statistically significant effect of exercise on HR density was found in adults in any midshaft. In the femur and tibia of the control animals, Haversian systems were absent or rare in juveniles and subadults, and at low densities in adults. Haversian densities were higher in the metatarsals than the tibia or femur at all ages, particularly in the adult controls. Thus, at least in immature animals, exercise exaggerated an existing trend of higher HR rates in distal versus proximal midshafts. The spatial distribution of Haversian systems (by quadrant) differed between bones, but was not significantly different between runners and controls. In the juveniles, 100% of added Haversian systems in the femur were in the caudal quadrant; in the tibia, 98% were in the cranial and medial quadrants; and in the metatarsal, 52% were in the cranial quadrant, and 18% and 20% in the medial and lateral quadrants, respectively.
Table 3 summarizes some
effects of periosteal modeling rates on bone cross-sectional properties during
ontogeny in the control versus exercised sheep sample (endosteal
resorption rates could not be measured in this study). Cortical area
CA, standardized by body mass, which indicates bone strength in
compression, is greater in proximal than distal midshafts. Mass- and
length-standardized measurements of the polar moment of inertia, J,
an indicator of overall resistance to bending and torsion in fairly
symmetrical cross-sections such as these
(Wainright et al., 1976), is
approximately 15% smaller in the metatarsal versus tibia, and
approximately 50% smaller in the tibia versus femur.
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Midshaft strains
Tables 4 and
5 summarize normal strains and
the orientation of principal strains from gauge sites at midstance, along with
calculated maximum and minimum normal strains on the cortex and total bending
strain for 10 typical strides at 1.5 m s1 from the
metatarsal and tibia (no strain data were obtained for the femur). Not all
elements were working in several gauges, as noted in Tables
4 and
5, in which case longitudinal
strains (strains from the element aligned with the bone's long axis) were
substituted for normal strains (no calculations of the orientation of tension
are possible for these gauges). Note that in the metatarsal of one animal (no.
539), the medial gauge was located on the tensile side of the NA, whereas in
the other two individuals (nos. 574 and 616), the medial gauge was located
more cranially, on the compressive side of the NA. In addition, all the tibial
gauges worked simultaneously in only one animal (no. 600). However, of the
five animals with tibial strain data, at least three gauges worked from each
site, and the results are similar between individuals (see
Table 5). In particular, all
gauges on the caudal and medial cortices experienced compressive normal
strains, with much higher values on the caudal cortex; all gauges on the
cranial cortex experienced tensile normal strains; and measurements of maximum
principal strain angle at each site do not vary greatly. The relative
magnitudes of normal strain between all gauge sites are approximately similar,
indicating a strain regime of bending in the sagittal plane combined with
axial compression (which shifts the neutral axis towards the cortex subject to
tension). Fig. 3 illustrates
typical cross-sectional strain isoclines for both midshafts using mean normal
strains calculated for each gauge site and representative cross sections (nos.
600 for the tibia, 539 for the metatarsal).
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As shown in Fig. 3, at
midstance, both the metatarsal and the tibia are primarily bent around a
neutral axis that is oriented within 10° of a mediolateral axis, but is
shifted towards the caudal aspect of the metatarsal and the cranial aspect of
the tibia. Both the tibia and metatarsal have higher compressive than tensile
strains, as one would expect for a loading regime that combines bending with
axial compression (Wainright et al.,
1976). The maximum and minimum normal strains in the metatarsals
are 5070% higher than maximum and minimum strains in the tibia. The
metatarsal not only experiences substantially higher strains, but also appears
to experience relatively more compression (more tibial data are needed to
confirm this). Relative to the (assumed vertical) ground reaction force in the
sagittal plane at midstance, mean orientation of the tibia is
29±4.5° (proximal end angled cranially), and mean orientation of
the metatarsal is 14±2.7° (proximal end angled caudally). Principal
strain orientations (
1°) correspond with a loading regime
characterized primarily by bending. Principal tension on the cortices in
compression (cranial in the metatarsal, caudal in the tibia) is within 15°
of the expected 90° (Tables
3 and
4). Principal tension on the
cranial (tensile) cortex of the tibia is within a maximum of 26° of the
expected 0° (Table 5). In
addition, the orientation of tension on the medial cortex of the tibia is
within 10° of the expected 45° angle at which it should cross the
neutral axis under bending (Table
5); however, the angles of
1° on the medial
and lateral cortices of the metatarsal are more variable
(Table 4), possibly reflecting
variations in gauge positions relative to the neutral axis in this bone.
Table 6 summarizes the section moduli of compression (ZC) calculated around the experimentally determined neutral axis, the polar moment of inertia (J), and cortical area (CA) along with data on body mass and element length for the juveniles for which cross-sectional strains normal to the midshaft (Tables 4 and 5) could be calculated (note that these sheep are 90 days younger and roughly half the body mass of the post-treatment juveniles summarized in Table 1). Although complete data are available for only one tibia (no. 600), the consistency of strain results among gauges from Table 5 suggests that this is a reasonable, representative tibia (a hypothesis that needs further testing). The cross-sectional properties accord with the differences in strain documented above for the tibia and metatarsal in several respects. First, CA standardized by body mass is roughly 1.5 times greater in the tibia, causing greater resistance to axial compression; axial compression is also expected to be less in the tibia because it is loaded less vertically at midstance (see above). In addition, although section moduli of compression (Zc, standardized by element length and body mass) are comparable between the tibia and metatarsal, the tibia has a 20% greater overall strength than the metatarsal as indicated by J (standardized by element length and body mass). These differences are similar in pattern (although slightly different in value) to comparisons of length and mass standardized J for the exercised versus control samples summarized above in Table 3.
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Discussion |
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The juvenile results also support the hypothesis that HR rate in response to loading is higher in distal than proximal element midshafts. HR rate in the controls is higher in proximal than distal midshafts at all ages, with essentially no activation of HR in femoral midshafts, and several times higher HR rates in the tibia and metatarsal midshafts. In the juveniles, HR rate in response to exercise increases significantly in the tibia and metatarsal, but not in the femur. The effect of exercise is less in the subadult sample and non-existent in the adult sample. Viewed together, the data for HR and PM rates from the juvenile sample indicate the existence of a trade-off in which modeling rates decrease from proximal to distal midshafts, while HR rates increase from proximal to distal midshafts. Mechanical loading exaggerates this trade-off, stimulating proportionate increases of periosteal growth in the proximal midshafts and of HR in the distal midshafts.
A related hypothesis is that strain magnitudes should be higher in distal than proximal midshafts, since they have smaller cross-sections, and because HR may repair bone but does not augment cross-sectional strength. This is supported by the data from the strain-gauged juveniles. No femoral strains were measured, but the sum of bending and compressive strain in the metatarsal is approximately twice that in the tibia at midstance. While the metatarsal is loaded more axially than the tibia (at midstance it is inclined approximately 15° closer to vertical), the higher metatarsal strains are most likely to be attributable to smaller cross-sectional areas and second moments of areas (further research is necessary to test for effects of muscle loads exerted on these midshafts, such as the metatarsalphalangeal joint extensors). The trade-off between periosteal modeling and HR, in combination with higher metatarsal strains, therefore suggests that distal midshafts are adapted to be lighter at the expense of strength. This hypothesis, however, needs to be further tested with femoral strain data, which we predict to be even lower than in the tibia because of the femur's much greater cross-sectional strength (Table 3). Strain data from animals at later ontogenetic stages are also needed.
The results also support the fourth hypothesis, that HR rate increases with
age to compensate for decreased rates of modeling in response to loading. In
the sheep studied here, periosteal modeling rates decline with age, whereas HR
rates increase with age. However, while exercise effects on modeling decline
with age, it is interesting that exercise effects on HR also decline with age.
There are several potential explanations for this finding. One possibility is
that HR fails to be stimulated at an increased rate by loading in older
animals, but acts as a preventative mechanism to halt microcrack propagation.
Alternatively, the loads in this experiment may have been too low to stimulate
HR, a possibility suggested by the results of Lees et al.
(2002), in which ulnar
osteotomies in adult sheep induced higher microcrack rates and higher HR rates
in the proximal radius. Lees et al.
(2002
), however, did not
measure in vivo strains.
Finally, the results also test the mechanostat hypothesis (Frost,
1987,
1990
), which predicts that HR
is inhibited when modeling is stimulated (and vice versa), and that
rates of HR should be lower in midshafts subject to higher strain magnitudes,
and higher in midshafts subject to lower strains. The above results do
indicate a trade-off between modeling and HR in response to loading, but in
the opposite direction predicted by the mechanostat (higher modeling rates in
the metatarsal, subjected to higher strains, and higher rates of HR in the
tibia, subjected to lower strains).
We conclude that in comparisons of midshafts, cortical bone in the juvenile
limb optimizes strength relative to the cost of adding mass by trading-off
growth versus remodeling. Distal midshafts grow less than more
proximal midshafts, saving energy costs associated with accelerating the limbs
during the swing phase (Hildebrand,
1985; Myers and Steudel,
1985
). The amount of energy saved by distal tapering is difficult
to estimate accurately, but should be proportional to the reduction in
skeletal mass in distal versus proximal elements. The periosteal
growth rate in response to loading is lower for the metatarsal than the tibia,
causing the metatarsal to have a thinner cortex and lower section moduli to
resist bending. To estimate how much metatarsal mass was saved through reduced
growth, we calculated the increase in area and compressive section modulus
that is necessary to reduce the compressive strains due to axial compression
and bending in the metatarsal to the same magnitudes as in the tibia (approx.
40% lower). This effect of tapering was calculated using basic engineering
proportionalities for compression and bending:
c
F/A and
Mb/
c
IN/ac
(Hibbeler, 1999
), where
c is compressive strain, F is the axial force,
A is the cross-sectional area, Mb is the bending
moment, IN is the second moment of area relative to the
neutral axis, and ac is the perpendicular distance from
the neutral axis to the location of peak compression on the periosteal cortex.
For a given axial force, a reduction in compressive strain by 40% requires an
increase in cross-sectional area by 40%; for a given bending moment, a
reduction in compressive strain due to this bending moment requires an
increase of IN/ac (which is equal to
Zc) by 40%. Assuming the metatarsal is a hollow cylinder
and its area and section modulus increase by periosteal apposition (with no
endosteal expansion), the requisite increase in area and section modulus as
well as the associated increase in volume/mass can be calculated from standard
geometric formulae:
![]() |
![]() |
In order to augment the area of the juvenile sheep metatarsal sufficiently to decrease compressive strains from axial compression to the same magnitude as in the tibia, the diameter of the metatarsal would have to increase by 12%, which leads to an increase in volume/mass by 38%. In order to reduce compressive strains due to bending to tibia strain levels, the diameter of the metatarsal would have to increase by 10%, increasing the volume/mass of the metatarsal shaft by 33%. An alternative way to estimate the mass saved by distal tapering is to compare growth rates in response to loading. If one models the metatarsal as a cylinder, then its mass would have increased by approximately 12% if it grew at the same rate as the tibia in response to loading during the experiment (90 days). Over the same time period, its mass would have increased 30% if it grew at the same rate as the femur in response to loading.
The results of this study are therefore consistent with the hypothesis that
limb bones initially trade-off the rate of growth versus HR responses
to loading, thereby adapting bones to dissimilar strain environments. In
particular, lighter, thinner distal limb bones apparently adapt to higher
strains, and may do so in part with higher rates of HR. However, the results
of this study have several limitations with regard to the hypothesis of
optimization. Most importantly, while the trade-off between growth and HR
accords with the predictions of optimization of strength relative to the cost
of swinging mass, the differences evident between hind-limb midshafts may
simply reflect variable osteogenic responses to different stimuli. We think
this explanation can only be partially true. While higher rates of HR in the
metatarsal versus tibial or femoral midshafts are probably a function
of higher strains, HR alone is unlikely to increase midshaft strength in
response to strains. The finding that higher strains in the metatarsal elicit
lower rather than higher rates of modeling than in the tibia supports previous
findings that distal bones are adapted to a higher point on the
stressstrain curve and have lower safety factors
(Vaughan and Mason, 1975;
Alexander, 1981
). Thus, if
modeling alone maintains equilibrium at particular sites
(Rubin and Lanyon, 1984a
;
Biewener et al., 1986
;
Carter and Beaupré,
2001
), then it is possible that equilibrium thresholds vary
between elements in order to optimize strength relative to the cost of adding
mass. This hypothesis, however, needs to be tested further with data on strain
magnitudes at multiple skeletal elements throughout ontogeny.
A second issue is that the optimization hypothesis tested here should not only apply to variations between bones but also within bones. Many (but not all) limb diaphyses are tapered (excluding the portions closest to distal epiphyses), and future analyses need to test for a trade-off between modeling and HR between proximal and distal portions of the shaft in such bones. A difficulty with testing this hypothesis is the challenge of characterizing the diaphyseal strains away from midshafts, especially toward the proximal ends, which tend to be heavily muscled, and are thus presumably subject to high local muscle forces (as well as difficult to instrument with strain gauges).
A third problem is that while higher HR rates in distal midshafts appear to
correlate with higher magnitudes of strain, the above results do not test the
presumed adaptive function of HR to repair, halt or possibly prevent
load-induced microdamage. We are studying these possibilities further by
quantifying rates of midshaft microdamage. A recent study of adult sheep
(Lees et al., 2002) found
increases in both microfracture and HR densities in the proximal radius
following ulnar osteotomies, with peak HR density after 10 weeks. These data
do not address whether microdamage is necessary to stimulate HR.
A final issue is that the effects of age on the apparent trade-off between
periosteal modeling and HR observed here cannot be explained by optimization.
Most notably, the results presented above indicate that while periosteal
modeling rates decline with age in all limb midshafts, HR rates increase, but
eventually level off. These observations accord with previously published data
on bone growth rates and HR density in various adult mammals, including humans
(e.g. Kerley, 1965;
Ruff et al., 1994
;
Martin et al., 1998
), and with
evidence for reduced sensitivity to mechanical stimuli with age
(Rubin et al., 1992
;
Turner et al., 1995
). However,
the effects of exercise in this study correlate with slight but
non-significant differences in periosteal modeling and HR rates in the
subadult sheep sample, and stimulated neither process in the young adult
sheep. This interaction between age and exercise is difficult to explain with
the data we collected. One possibility, which needs to be tested by
quantifying microcrack density, is that levels of loading examined in this
study were too low to stimulate HR. If so, increased rates of HR observed in
adult sheep relative to juvenile sheep may be a preventative mechanism to halt
microcrack propagation rather than an adaptive response to repair microcracks.
This hypothesis could be tested by analyzing HR rates along with microcrack
damage in adult sheep subjected to more vigorous loading. An additional
possibility is that the lack of any significant HR or periosteal modeling
response to exercise in adult sheep is a mechanobiological constraint caused
by skeletal senescence. Older bone tissue may not be able to respond to
strains, perhaps because osteoblasts are less responsive to strain stimuli
(Rubin et al., 1992
;
Turner et al., 1995
;
Muschler et al., 2001
;
Chan and Duque, 2002
), and
because older bone cells (probably osteocytes) may be less able to transduce
strain signals. Analyses of midshafts in humans and beagles indicate that the
density of microcracks increases with age, while the HR activation frequency
declines, along with osteocyte density
(Vashishth et al., 2000
;
Frank et al., 2002
).
These results also have implications for efforts to reconstruct habitual
behaviors from variations in cross-sectional bone geometry in humans and other
vertebrates, based on the principle that second moments of area quantify
cross-sectional resistance to loading (see
Lieberman et al., in press).
Cross-sectional shape responses to loading vary by skeletal location, and
primarily reflect stimuli prior to skeletal maturity. In addition, since
distal midshafts respond less to mechanical loading than proximal midshafts,
proximal elements such as the femur or humerus may be more sensitive
indicators of mechanical loading than more distal elements such as the
metapodia.
Finally, variable cortical bone responses to loading have several important
evolutionary and clinical implications. From an evolutionary perspective, the
trade-off between growth and remodeling provides support for the hypothesis
that natural selection tends to drive physiological systems towards more
efficient use of energy (Weibel et al.,
1991; Alexander,
1996
). Ontogenetic changes in the trade-off between cortical bone
growth versus remodeling are also clinically significant for
evaluating the role of load-bearing exercise in osteoporosis. The ontogenetic
shift documented here supports studies (e.g.
Turner et al., 1995
;
Stanford et al., 2000
),
showing that mechanical usage prior to skeletal maturity results in
permanently stronger bones; after skeletal maturity, moderate load-bearing
exercise appears to have little measurable effect on activating periosteal
modeling or HR, but may make the remodeling process more efficient by
generating osteons with smaller Haversian channels and less porous bone
(Thompson, 1980
). Future work,
therefore, is needed to address what stimuli elicit HR, and how intermediary
mechanisms modulate variable osteogenic responses to loading.
List of symbols and abbreviations
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Acknowledgments |
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References |
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