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Patterns of strain in the macaque tibia during functional activity.

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AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 116:257–265 (2001)
Patterns of Strain in the Macaque Tibia During
Functional Activity
Brigitte Demes,1* Yi-Xian Qin,2 Jack T. Stern, Jr.,1 Susan G. Larson,1 and Clinton T. Rubin1,2,3
1
Department of Anatomical Sciences, State University of New York, Stony Brook, New York 11794-8081
Department of Biomedical Engineering, State University of New York, Stony Brook, New York 11794-2580
3
Center for Biotechnology, State University of New York, Stony Brook, New York 11794-2580
2
KEY WORDS
in vivo bone strain; cross-sectional properties; functional adaptation
ABSTRACT
The strain environment of the tibial midshaft of two female macaques was evaluated through in
vivo bone strain experiments using three rosette gauges
around the circumference of the bones. Strains were collected for a total of 123 walking and galloping steps as well
as several climbing cycles. Principal strains and the angle
of the maximum (tensile) principal strain with the long
axis of the bone were calculated for each gauge site. In
addition, the normal strain distribution throughout the
cross section was determined from the longitudinal normal strains (strains in the direction of the long axis of the
bone) at each of the three gauge sites, and at the corresponding cross-sectional geometry of the bone. This strain
distribution was compared with the cross-sectional properties (area moments) of the midshaft. For both animals,
the predominant loading regime was found to be bending
about an oblique axis running from anterolateral to posteromedial. The anterior and part of the medial cortex are
in tension; the posterior and part of the lateral cortex are
in compression. The axis of bending does not coincide with
the maximum principal axis of the cross section, which
runs mediolaterally. The bones are not especially buttressed in the plane of bending, but offer the greatest
strength anteroposteriorly. The cross-sectional geometry
therefore does not minimize strain or bone tissue. Peak
tibial strains are slightly higher than the peak ulnar
strains reported earlier for the same animals (Demes et al.
[1998] Am J Phys Anthropol 106:87–100). Peak strains for
both the tibia and the ulna are moderate in comparison to
strains recorded during walking and galloping activities
in nonprimate mammals. Am J Phys Anthropol 116:
257–265, 2001. © 2001 Wiley-Liss, Inc.
It has been known for more than a century that
bones adjust their external dimensions and internal
architecture in response to their mechanical environment (Meyer, 1867; Wolff, 1870; Roux, 1881; review in Martin et al., 1998). Although this paradigm
is undisputed in general, the exact relationship between mechanical loads and bone shape is not completely understood. Experimental evidence keeps accumulating that casts doubt on older equilibrium
models of bone adaptations, such as those of Roux
(1912), Kummer (1972), or Frost (1987), that predict
in some form or another that bone economizes its
shape in response to mechanical loads, i.e., adjusts
to minimize stresses. Long bone curvature, for example, does not seem to neutralize or reduce bending (sensu Pauwels, 1948), but instead increases
bending (Rubin, 1984; Bertram and Biewener,
1988). Long bone midshafts are also not preferentially reinforced in the plane of bending so as to
reduce bending stresses (Gross et al., 1997; Demes
et al., 1998). Similarly, the strain distribution in
long bone diaphyses is far from being uniform, as
predicted by the equilibrium models (e.g., Gross et
al. 1992; Biewener et al., 1996; Demes et al., 1998).
Bone seems to respond not only to load magnitudes,
but also to load frequency, load variability (or the
lack thereof), daily strain history, and a variety of
nonmechanical factors (reviewed in Rubin et al.,
1994). This heterogeneous adaptive pattern complicates functional interpretations of bone morphology.
Anthropologists’ interest in bone adaptations goes
beyond understanding the relationship between
loading regimes and bone shapes. An important goal
of functional morphological studies in anthropology
is the reconstruction of activity patterns of fossil
primates. Activity patterns are not equivalent to
loading patterns such as “bending,” “compression,”
or “shear,” but they translate into loading patterns
through the combined action of muscle, joint, and
gravitational forces applied to bones. Our knowledge
about this interface is limited. Ground reaction
forces and muscle activity (albeit not force) have
been measured for a number of primate species (e.g.,
Kimura et al., 1979; Stern and Susman, 1981; Reynolds, 1985; Larson and Stern, 1986, 1989; Demes et
al., 1994; Schmitt, 1999), but joint forces are unknown for primates with the exception of hip joint
©
2001 WILEY-LISS, INC.
Grant sponsor: National Science Foundation; Grant number: BCS
9806291.
*Correspondence to: Brigitte Demes, Department of Anatomical
Sciences, State University of New York, Stony Brook, NY 11794-8081.
E-mail: bdemes@mail.som.sunysb.edu
Received 3 November 2000; accepted 30 July 2001.
258
B. DEMES ET AL.
forces in orthopaedic patients (e.g., Bergmann et al.,
1993). Inferences regarding loading regimes and behavior therefore remain largely hypothetical.
In vivo strain measurements allow the direct
quantification of the deformations of bones during
functional activity, which can then be related to
activity patterns, thus bridging the gap between
behavior and morphology.
We previously characterized the strain environment of the macaque ulna (Demes et al., 1998).
Based on data from three animals, we reported a
mediolateral bending regime for the bone’s midshaft, with compressive strains in the medial cortex
and tensile strains in the lateral cortex. Mediolateral bending is not an intuitive loading regime for
quadrupeds with limb movements predominantly in
sagittal planes. However, we suggested that this
pattern of loading could be related to the orientation
of the substrate reaction resultant. The macaque
ulna is not reinforced in the plane of bending. Strain
magnitudes were moderate if compared to strains
recorded for walking gaits of nonprimate mammals.
Here we report strain recordings on the tibiae of
two of the three macaques for which we obtained
ulnar strains.1 Although ulnar and tibial data were
not collected simultaneously, when matched up for
equivalent speeds, they allowed us to address questions regarding the effects of differential weight support by the fore- and hindlimbs of primates (Kimura
et al., 1979; Demes et al., 1994). In addition, the
tibial strain data add to the small database of primate bone strain, making comparisons of patterns of
bone loading between primates and nonprimate
mammals more feasible. Such comparisons are interesting in light of the many differences in gait
kinetics and kinematics between these two groups
(review in Larson, 1998).
The specific questions we wish to address are: 1)
What are the strain environment and major loading
regime of the tibial midshaft of macaques during
functional activity? 2) How do the differences in
functional roles of the fore- and hindlimbs of macaques during locomotion impact on bone deformation? 3) How does the strain environment of the
macaque compare to that of nonprimate mammals
in the context of their documented gait differences?
4) How does the strain distribution in long bones
relate to their cross-sectional properties?
METHODS
Instrumentation and data collection followed the
protocol reported for previous experiments on the
macaque ulna (Demes et al., 1998). All procedures
were reviewed and approved by the Institutional
Animal Care and Use Committee. While subjects
were under general anesthesia, the tibiae of two
adult female macaques (Macaca mulatta) were each
instrumented with three rectangular, three-element
1
The third animal died from gastrointestinal problems unrelated to
the experimental procedures.
strain gauges (Kenkyujo, Tokyo, Japan). An approximately 6-cm-long skin incision on the anteromedial
side of the leg was made and gauges were placed on
the medial, lateral, and posterior aspects of the
bones. The gauge position, as determined from postoperative x-rays, was at 51% total length from the
proximal end in animal A, and at 40% in animal
J. Muscles were retracted, but no fibers detached
from the bone. Small areas of bone were exposed by
elevating the periosteum, and the surface was degreased and cleaned with chloroform. The gauges
were bonded to the bone with isobutyl 2-cyanoacrylate monomer. For relief of tension on wires, they
were attached to small resin blocks screwed into the
tibia at 2-cm distance from the gauges (Fig. 1). Wires
were run subcutaneously across the knee and hip
joints and surfaced on the back through a small skin
incision. Here they were soldered to a connector that
was attached to and protected by a vest worn by the
animals. A cable ran from the connector to the computer during data collection. Prior to the experiments, the animals were trained to walk with a pole
attached to a neck collar. The cable was attached to
that pole.
Data were collected shortly after the animals recovered from anesthesia. Activity was monitored
with video recordings. A superimposed image of the
output of one of the gauge elements, displayed on an
oscilloscope screen, was used to synchronize strain
data and video footage. Strains were recorded at
409.6 Hz with SX 500 amplifiers (Syminex, Inc.,
Marseille, France). The animals were anesthetized
again after data collection, and x-rays (Fig. 1) and
CT scans (Fig. 2) were taken of the instrumented leg
to determine gauge positions and orientations, and
to obtain the cross-sectional geometry of the bones
at the level of the gauge sites. Subsequently, the
gauges were removed. They were all found firmly
bonded to the bone.
Data were analyzed in a custom-written subroutine of the program Igor (WaveMetrics, Inc., Lake
Oswego, NY). Equations in this routine were derived
from a standard engineering textbook (Dally and
Riley, 1991). Principal strains and the angles of the
maximum (tensile) principal strain with the long
axis of the bone were calculated for each rosette
from the strains registered by its three elements
spaced at angles of 45°. The principal strain directions were first calculated relative to the a-element
of each rosette and subsequently, by knowing the
orientation of the a-element on the bone, relative to
the long axis of the shaft. In addition, the longitudinal normal strain was calculated for each gauge site,
i.e., the strain in the direction of the long axis of the
shaft or normal to its cross-sectional plane at the
level of the gauge sites. Interpretation of loading
regimes based solely on the strain information at the
isolated gauge sites can be spurious. The use of
three gauges allows a complete characterization of
the normal strain distribution across the entire section at the level of the gauge sites. Normal strain
distributions were calculated based on linear beam
IN VIVO STRAIN IN MACAQUE TIBIA
259
Fig. 2. CT scan of instrumented leg of animal J at level of
gauges, showing cross sections through tibia with the three
gauges (arrows) and fibula. Wires run anteromedially to the tibia.
Fig. 1. X-ray of the instrumented leg of animal J, showing the
wires and bone screws holding resin flanges attached to the wires
for strain relief. Inset: Arrows indicate soldering dots immediately distal to gauge elements.
theory (Rybicki et al., 1977; Gross et al., 1992). Using coordinate data of the three gauge sites as determined from CT scans, the normal longitudinal
strains at each gauge site, and equations provided
by Rybicky et al. (1977), the calculations of strain
distributions were performed in a subroutine of the
program PV-Wave (Visual Numerics, Inc., Houston,
TX). The maximum tension and compression along
the circumference of the shaft are reported here, as
well as the position of the neutral axis of bending
with reference to a standard anatomical plane. All
strains are reported in microstrain (␮⑀).
Element a of the posterior rosette of animal A
failed halfway through the experiment, and princi-
pal strains for walking steps could not be obtained
for this rosette. However, the b-element was aligned
with the long axis of the bone, and normal strains
are therefore available.
Strains were collected continuously. Subsequently, the peak strains at or around midstance
were identified, and these are reported here. Average speed of locomotion was determined for gait
sequences at steady speed, using the video recordings. Time was determined from the video frame
rate, and distance traveled from a scale in the animals’ path. Although an attempt was made to elicit
a range of gaits and speeds, one animal (J) did not
gallop during the experimental session.
Second moments of area were calculated for the
bone cross sections immediately adjacent to the level
of the gauges. (The gauge site level was avoided
because the metal parts obscure the bone.) The
cross-sectional geometry and dimensions were obtained from CT scans, and the calculation was performed in a subroutine of Scion Image (NIH).
Normal strains were compared between bones,
between animals, and between gaits, using analyses of variance (ANOVAs) followed by comparisons for all pairs using post hoc Tukey-Kramer
honest significant differences. Because ANOVAs
are sensitive to departures of data distributions
from normality, more conservative nonparametric
Kruskall-Wallis tests were performed prior to proceeding with the post hoc pairwise comparisons.
The Kruskall-Wallis statistics confirmed the F
statistics of the ANOVAs in all cases. It was therefore decided that ANOVAs and post hoc tests were
appropriate for the data.
RESULTS
Principal strains
Peak principal strains and strain angles with the
long axis of the bone at midstance are reported in
Table 1. One element of the posterior rosette of
260
B. DEMES ET AL.
TABLE 1. Peak principal strains and principal strain angles at the tibial midshaft for the stance phase of locomotion1
Lateral
Animal A
Walking steps (n ⫽ 24)
Gallops (n ⫽ 69)
Animal J
Walking steps (n ⫽ 30)
Climbing (n ⫽ 5)
Posterior
Medial
Maximum
Minimum
Angle2
Maximum
Minimum
Angle2
239 ⫾ 60
⫺448 ⫾ 72
108 ⫾ 3
211 ⫾ 83
⫺479 ⫾ 124
112 ⫾ 8
1,272 ⫾ 424
⫺1,240 ⫾ 378
80 ⫾ 2
452 ⫾ 85
⫺396 ⫾ 72
15 ⫾ 4
472 ⫾ 129
⫺474 ⫾ 126
17 ⫾ 9
Maximum
Minimum
Angle2
Maximum
Minimum
Angle2
177 ⫾ 32
⫺522 ⫾ 100
88 ⫾ 3
199 ⫾ 30
⫺548 ⫾ 122
87 ⫾ 4
168 ⫾ 36
⫺527 ⫾ 101
91 ⫾ 3
156 ⫾ 68
⫺541 ⫾ 244
92 ⫾ 2
258 ⫾ 63
⫺117 ⫾ 33
168 ⫾ 12
299 ⫾ 166
⫺177 ⫾ 88
165 ⫾ 5
Strains are given in microstrain, mean values ⫾ 1 standard deviation.
Angle of the maximum principal strain with the long axis of the bone in counterclockwise direction; 0° signifies alignment of
maximum tensile strain with the long axis of tibia; 90° signifies alignment of maximum compressive strain with the long axis of tibia.
1
2
animal A failed before the recording of walking
strains, so that principal strains could not be calculated for the posterior midshaft during walking.
Walking and galloping steps (when available) are
separated. For one animal (J), we also collected a
small number of climbing steps on a cage wall.
Strain magnitudes vary considerably, within gaits
and between gaits. The strain directions, on the
other hand, show little variation. One of the principal strains is always fairly closely aligned with the
long axis of the tibia. If the angles are close to zero,
the principal tensile strain falls along the long axis;
if they are close to 90°, the principal compressive
strain falls along the long axis. The angular deviations from either 0° or 90°, range from 1–22° (Table
1), indicating that torsion is a very minor loading
factor. Strain orientations are also very consistent
throughout stance phase (not reported here).
Normal strains
Maximum normal strains around the perimeter of
the bones are reported in Table 2. Note that Table 2
also contains comparative data on the ulna that
were recorded previously for the same animals
(Demes et al., 1998). Maximum compressive strains
in the tibial midshaft are a little bit higher than
maximum tensile strains, but this difference is significant only for the walking steps of animal J (Table
2). This pattern indicates a bending regime superimposed by compression. The normal strains, like
the principal strains, exhibit a high degree of variability in magnitude. In contrast, and with the exception of the ulna in animal J, the axis of bending is
highly consistent within animals and gaits, and
moderately varies between animals, and between
walking and galloping steps. The average bending
axis for walking steps is shown superimposed on the
bones’ cross sections in Figure 3. For the tibiae of
both animals, it runs from anterolateral to posteromedial, with the anteromedial cortex in tension and
the posterolateral cortex in compression (Fig. 3a,b).
The bending axis is closer to the mediolateral plane
of the bone in animal A and approaches it more
TABLE 2. Greatest normal strains in midshaft cross section of
the tibia and ulna and direction of bending1
Tibia data
Animal A
Walking
steps
Gallops
Animal J
Walking
steps
Climbing
Ulna data
Animal A
Walking
steps
Animal J
Walking
steps
Gallops
n
Tension
Compression
Angle2
24
1,142 ⫾ 203
⫺1,150 ⫾ 203
⫺57 ⫾ 4
69
1,914 ⫾ 573
⫺1,968 ⫾ 578
⫺71 ⫾ 3
30
438 ⫾ 65
⫺693 ⫾ 116
⫺45 ⫾ 6
5
481 ⫾ 117
⫺747 ⫾ 180
⫺44 ⫾ 21
17
703 ⫾ 84
18
601 ⫾ 235
⫺604 ⫾ 332
23 ⫾ 16
6
456 ⫾ 128
⫺570 ⫾ 150
36 ⫾ 9
⫺1,002 ⫾ 133
6⫾2
Strains are given in microstrain, mean values ⫾ 1 standard
deviation; ulna data are from Demes et al. (1998).
2
Angle of the neutral axis of bending with the anteroposterior
plane; 0° signifies an axis in the sagittal plane; negative angles
indicate axes running from anterolateral to posteromedial; positive angles indicate axes running from anteromedial to posterolateral.
1
closely during the gallops (Table 2). Bending of the
ulna is around axes that are closer to anteroposterior, and the lateral aspect of the bone is in tension,
and the medial in compression (Fig. 3c,d; see also
Demes et al., 1998).
Figure 3 also shows the maximum principal axes
of the bone cross sections at the level of the gauge
sites, as calculated from their geometric properties.
The two tibiae offer the greatest strength in bending
anteroposteriorly, which is not surprising, given
their elliptical cross sections (Fig. 3a,b). The maximum and minimum second moments of area for the
cross sections through the tibia at the level of the
gauges are 0.0327 and 0.0142 cm4 for animal A, and
0.0906 and 0.0353 cm4 for animal J. The maximum
principal axes form angles of 30 – 40° with the planes
of bending, i.e., the planes in which the bones are
bent during walking and the planes in which they
IN VIVO STRAIN IN MACAQUE TIBIA
261
Fig. 3. Cross sections through tibiae and ulnae of two macaques, drawn from CT scans. Outlines were traced in immediate vicinity
of gauges to avoid disturbances due to “bleeding” of the metal. Solid lines indicate axes about which bones are bent during walking;
dashed lines indicate maximum principal axes as determined from area properties calculation. Numbers indicate maximum (tensile)
and minimum (compressive) longitudinal strains; their position indicates approximately where they occur in the cross section. a: Tibia,
animal A. b: Tibia, animal J. c: Ulna, animal A. d: Ulna, animal J. Site has been adjusted so that all bones have the same
anteroposterior diameter.
offer greatest resistance to bending do not coincide.
The two ulnae, which have more circular cross sections, offer slightly greater strength in bending anteroposteriorly than mediolaterally (Fig. 3c,d). However, they are being bent in a plane perpendicular to
that plane. The maximum and minimum second moments of area for the ulna cross sections at the level
of the gauge sites are 0.0094 and 0.0082 cm4 for
animal A, and 0.0194 and 0.0132 cm4 for animal J.
Peak normal strains are displayed as a function of
speed in Figure 4a,b. Each data point in these figures represents the average peak strain magnitudes
for a gait sequence consisting of several steps. The
trend lines through the data points indicate that
262
B. DEMES ET AL.
Average peak normal strains at midstance were
compared statistically between animals, between
bones, and between gaits (Table 3). Direct comparisons were limited, as animal A did not gallop in the
ulna experiment, and animal J did not gallop in the
tibia experiment. With the exception of the peak
tensile strain for the walking steps of animal J, peak
tibial normal strains tend to be higher than peak
ulnar normal strains. However, this difference in
strain magnitudes between the hindlimb and forelimb bone is significant only for tensile strains in
animal A (Table 3). A comparison of strain magnitudes for the two bones for the stance phase of galloping is possible only across animals. The galloping
strains for the tibia of animal A are almost four
times higher than the galloping strains for the ulna
of animal J. Within bones and animals, data were
available to compare strain magnitudes between
gaits for the tibia of animal A and the ulna of animal
J. Both tensile and compressive strains are significantly higher in the tibia of animal A while galloping
than while walking. The strain magnitudes in the
ulna of animal J while galloping are similar to the
walking strains (Table 3). Strains for animal A are
higher than strains for animal J when compared for
the same bone and gait, but significantly so only for
the tibia.
Figure 5 highlights and summarizes the comparative results for the compressive strains. In this box
plot, average maximum compressive strain magnitudes are ranked by means. Strain magnitudes are
consistently higher for animal A than animal J, and
within animals, the tibia strains are higher than the
ulna strains. The average maximum tensile strain
magnitudes (not shown here) have an identical
ranking order.
DISCUSSION
Fig. 4. Peak tensile (a) and compressive (b) strains as a
function of speed. Each data point represents several steps in a
locomotor sequence, and speeds are average speeds for those
sequences. Large symbols, gallops; small symbols, walks.
strains increase with speed. However, there is considerable variation in strain magnitude that is not
explained by speed. At overlapping speeds, strains
in the tibia midshaft (triangles in Fig. 4) tend to be
higher than ulnar strains (squares in Fig. 4), and
strains in the tibia and ulna of animal A (solid
symbols in Fig. 4) tend to be higher than strains in
the corresponding bones of animal J (open symbols
in Fig. 4). The greatest amount of strain data comes
from animal A during the tibia experiment (n ⫽ 69),
and these include walks and gallops. Although the
galloping strains are on average higher than the
walking strains, the lowest galloping strains are of
the same magnitude as the walking strains, but at
about twice the speed.
The data set presented here is suboptimal in that
it does not represent a comparable range of gaits
and speeds for the two animals and for the forelimb
and hind limb experiment for each animal. This, in
combination with considerable variation in strain
magnitudes, accounts for the few statistically significant comparisons in this data set. Nevertheless,
several consistent results lead to interesting comparisons and conclusions.
The major loading regime for the tibia is bending,
and this confirms prior results showing that bending
is the predominant source of deformation for most
measured long bones in mammals (e.g., Rubin and
Lanyon, 1982; Biewener and Taylor, 1986; Demes et
al., 1998). The direction of bending is very consistent, and major variation is evident only for the few
climbing cycles recorded for one animal. The macaque tibia is curved posteriorly concave, and this
curvature, in conjunction with external forces, determines the bending regime. Compression is found
on the concave side of the curvature, and tension on
the convex side. However, the axis of bending is
oblique, and this seems to indicate that either the
ground reaction force vector passes lateral to the leg,
263
IN VIVO STRAIN IN MACAQUE TIBIA
TABLE 3. Results of statistical comparisons of normal strain magnitudes between bones, between animals, and between gaits1
Tibia
Ulna
A
Walk
Tibia A
Walk
Gallop
Tibia J
Walk
Gallop
Ulna A
Walk
Gallop
Ulna J
Walk
Gallop
J
Gallop
Walk
s
s
A
Gallop
s
Walk
Gallop
nd
nd
nd
Walk
s
nd
s
J
Gallop
ns
nd
nd
ns
nd
nd
ns
nd
ns
ns
ns
nd
ns
nd
ns
s and ns indicate significant differences (at P ⬍ 0.05) in strain magnitudes in Tukey-Kramer HSD post hoc tests or the lack thereof,
respectively; nd, no data; empty cells indicate that no comparison was made (across gaits). Entries in the upper right sector are for
tensile strain comparisons, those in the lower left sector for compressive strain comparisons.
1
Fig. 5. Box plot of average peak compressive strains, sorted
by animal, bone, and gait. Means, medians, interquartiles, and
10 –90% ranges are represented by squares, lines, boxes, and
whiskers, respectively.
compressing the lateral cortex and tensing the medial one, or that muscle forces are an additional
source of bending. As the substrate reaction force
vector during terrestrial quadrupedalism is inclined
medially in macaques (Kimura et al., 1979) and
therefore probably passes on the medial side of the
leg, muscle forces are more likely to influence the
overall bending pattern. Strain recordings on the
human distal tibia measured in vitro in a gait simulator, exposing legs to ground reaction forces and
muscle forces as experienced during the stance
phase of walking, demonstrated a bending regime
very similar to that of the macaque tibia, with the
posterolateral cortex in compression and the anteromedial cortex in tension (Peterman et al., 2001).
Strains on the anterior and posterior cortices were
found to be closely coupled to triceps surae activation. In macaques, the two heads of the gastrocnemius are moderately active during quadrupedal
walking (Jouffroy et al., 1999). Soleus activity is of
higher amplitude, but unlike in humans, the soleus
does not originate from the tibia. We conclude from
this that loading regimes cannot be deduced reliably
from locomotor kinematics. Bone curvature and all
forces applied to the bone must be taken into consideration.
The shafts of the two tibiae as well as the two
ulnae analyzed previously (Demes et al., 1998) are
not particularly reinforced in the planes where they
are bent. Traditional models of bone adaptation that
assume minimizing bone tissue or stresses and
strains are not in accordance with these results.
Like other studies (e.g., Gross et al., 1992; Biewener
and Taylor, 1986; Blob and Biewener, 1999), our
data indicate considerable strain gradients, with regions of high strain and low strain. Controlled loading of functionally isolated turkey ulnae also demonstrates that bone deposition is minimally related
to maximum strain magnitudes, and instead is associated with the strain gradient (Gross et al., 1997).
Gies and Carter (1982) showed that experimentally
determined axes about which there is bending or
rotation in the canine radius do not coincide with
area cross-sectional properties. Cubo and Casinos
(1998) arrived at similar conclusions when contrasting the axis of bending determined experimentally
by Biewener and Dial (1995) for the humerus of
pigeons during flight with the principal axes of humeri of 39 species of birds, including pigeons. Bone
cross sections therefore do not seem to reflect functional loading in the straightforward way the optimization models suggest. This should be taken into
account in attempts to infer loading patterns and
locomotor modes from cross-sectional properties.
Although tibial strains tend to be higher than
ulnar strains, the difference in peak strain magnitudes is not very pronounced. Macaques carry
slightly more weight on their hindlimbs than on the
forelimbs (Kimura et al., 1979), but the difference in
peak vertical forces may be too subtle to be reflected
in strain magnitudes. In addition, the tibia is also
more robust than the ulna and therefore (assuming
264
B. DEMES ET AL.
similar material properties) deforms less for any
given force or moment.
The consistently higher strains for animal A in
comparison to animal J are likely related to differences in bone robustness. Both the tibia and the
ulna of animal A offer less resistance against bending. The second moments of area for the bones of
animal A are considerably smaller that those of the
corresponding bones of animal J. Bone lengths are
similar for the two animals, and body weights fluctuated, with animal J being heavier than A at the
time of the ulna experiments, and similar in weight
at the time of the tibia experiments. Alternatively,
differences in gauge position could be responsible for
the difference in strain magnitudes. The tibia
gauges were positioned at midshaft in animal A, and
proximal to midshaft in animal J. It was demonstrated with three strain gauges, aligned linearly
along the caudal aspect of the radius and tibia of
goats, that maximum strains act at midshaft (Biewener and Taylor, 1986). However, in the ulna experiments, the gauges were closer to midshaft in
animal J that had the lower strain magnitudes.
Strain gauge analyses of the primate locomotor
system are very limited in number. Fleagle et al.
(1981) qualitatively reported strains from a single
element gauge on the spider monkey ulna during
walking and climbing. Swartz et al. (1989) recorded
peak strain magnitudes of around 1,500 ␮⑀ for the
three long bones of the forelimb of brachiating gibbons, using two rosette gauges on each bone. Two
studies address strain magnitudes in the human
tibia. Lanyon et al. (1975), who used a single-element gauge, reported strains below 500 ␮⑀ for the
anteromedial aspect of the tibia parallel to the bone
shaft. Burr et al. (1996) recorded higher strains from
two rosette gauges on the medial tibia during vigorous activities. Only during the most strenuous activities did strains reach nearly 2,000 ␮⑀. Put into
the context of mammalian strain data, these data as
well as our own data on the macaque ulna and tibia
suggest that primate long bones experience strain
magnitudes that are at the low end of the range of
peak strain magnitudes for mammals (Rubin and
Lanyon, 1982). Only the highest strains recorded
here (tibia strains for animal A galloping, Table 2)
fall inside the strain range of 2,000 –3,000 ␮⑀ that is
considered beneficiary for bone maintenance (Rubin
and Lanyon, 1984; Rubin et al., 1994). The ulna
strains reported earlier (Demes et al., 1998) are
similarly moderate in magnitude. Comparisons like
this are hampered by the fact that the majority of in
vivo strain studies do not completely characterize
the strain environment of a bone, but report strains
from individual gauges that may not capture the
maximum strains experienced by the bone around
its entire circumference. As we report maximum
strains around the circumference here, we believe
that the rather low strain magnitudes in the macaques are not an artifact.
Kinematic studies suggest that primates, being an
arboreal radiation, employ more compliant gaits
than do terrestrial nonprimate mammals (Demes et
al., 1990; Larson, 1998; Schmitt, 1995, 1999). However, peak substrate reaction forces for quadrupedal
primates (including macaques) are not different in
magnitude from those of quadrupdal nonprimate
mammals (Demes et al., 1998). Primates (including
macaques) also do not differ from nonprimate mammals in bending rigidity of their long bones in comparisons standardized for body mass and bone
length (Polk et al., 2000). The moderate strain magnitudes could result from greater yield and shock
absorption in the foot and ankle and hand and wrist
of macaque limbs. Alternatively, they could simply
be related to the speed range sampled here.
Although an actual gait change has not been recorded, comparison of the tibia strains of animal A
walking and galloping strongly indicates that
strains for gallops at low speeds are similar in magnitude to those of walks (Fig. 4); as with the ulna
(Demes et al., 1998), there is probably no incremental change in strain at the gait change. Macaques
and other quadrupedal primates start galloping at
low speeds and do not use a trot as an intermediate
gait between walking and galloping. The walk-totrot transition of nonprimate mammals, on the other
hand, is characterized by an increase in strain (Rubin and Lanyon, 1982; Biewener et al., 1983, 1988;
Biewener and Taylor, 1986). Ground reaction forces
also do not change much at the primate gait transition (Demes et al., 1994).
CONCLUSIONS
The tibia (like the ulna) of macaques is loaded in
bending during functional activity, with the anterior
and part of the medial cortex in tension, and the
posterior and part of the lateral cortex in compression. The bending plane does not show much variation, i.e., the loading regime is fairly stereotypic.
Strain magnitudes, on the other hand, are highly
variable, and only part of this variation is related to
speed.
The tibia midshafts of the two animals are elliptical in cross section, offering the greatest strength
in anteroposterior bending. The maximum principal
axis and the bending plane form angles of 30 – 40°,
i.e., the tibia is not especially reinforced in the plane
in which it is bent. A similar result was obtained for
the ulna. These data add to the accumulating evidence contra adaptationist models of bone optimization that assume minimization of bone or functional
strain. They caution against broad behavioral conclusions derived from long bone cross-sectional
shapes.
Peak strains in the tibia are only slightly higher
than in the ulna at comparable speeds, suggesting
that the more robust hindlimb bones effectively
moderate strains due to higher substrate reaction
force acting on the hindlimbs.
Strain magnitudes are low in comparison to
strains experienced by long bones of nonprimate
mammals, and the gait transition from walking to
galloping is not characterized by an incremental
IN VIVO STRAIN IN MACAQUE TIBIA
increase in strain that is typical for the nonprimate
mammalian gait transition from walking to trotting.
This result offers additional support to the notion that
primates as an arboreal radiation use compliant gaits.
ACKNOWLEDGMENTS
We thank Xinbin Chen who wrote part of the
program used for data analysis, Wei Lin who helped
with data collection, Terry Button for his assistance
with x-rays and CT scans, and the staff of the Division of Laboratory Animal Research for their assistance in surgery and animal care.
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