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.  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: firstname.lastname@example.org 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. 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