Load-induced changes in bone stiffness and cancellous and cortical bone mass following tibial compression diminish with age in female mice

The vertebrate skeleton is an adaptive structure that remodels to meet physiological and physical demands. Mechanical forces are important influences on skeletal growth and remodeling because of the skeleton's role in structural support. Racquet sport athletes provide an excellent example of the anabolic effects of mechanical loading on the skeleton, as bones in their dominant playing arms are larger than their non-dominant arms (Jones et al., 1977; Ruff et al., 1994; Kannus et al., 1995; Haapasalo et al., 1998; Bass et al., 2002). By contrast, bone mass in the long bones of astronauts, paralytics and patients on long-term bedrest decreases following the removal of normal functional loads on the skeleton (Lang et al., 2004; Sievanen, 2010). Thus, modeling and remodeling in the skeleton serve to increase skeletal mass to withstand increased habitual loads while also preventing an unnecessarily robust skeleton that would be metabolically costly to support relative to the mechanical forces experienced.

In vivo loading models are commonly used to understand the regulation of bone cell function and skeletal structure by mechanical stimuli. Through these models, we know that the anabolic response of cortical bone to mechanical stimuli decreases with age and through adulthood (Rubin et al., 1992; Turner et al., 1995; Srinivasan et al., 2003; Lynch et al., 2011). Similar age-related skeletal decreases in the response to exercise have been reported in humans (Kannus et al., 1995; Bass et al., 2002). Although the age-dependent cortical response to mechanical stimuli is well documented, understanding the response of cancellous tissue architecture and bone mass to physical stimuli with age is of key importance because corticocancellous sites in the skeleton, such as the femoral head, vertebrae and distal radius, are most susceptible to osteoporotic fracture (Melton et al., 2003). Developing a clear understanding of age-related changes in the whole-bone response to mechanical stimuli, including both cortical and cancellous tissues, will enable future research to focus on characterizing specific cellular mechanisms regulating anabolic processes in the skeleton.

Histomorphometric and radiological measures are the current standard to assess the skeletal response to applied load in in vivo models (Rubin et al., 1992; Robling et al., 2001; Gross et al., 2002; Fritton et al., 2005; De Souza et al., 2005). However, these techniques do not directly reflect whole -bone function during loading. Restricting post-loading assessments of the skeletal response to load to only the cortical and cancellous envelopes does not account for load-induced changes in whole-bone morphology that can have important consequences for whole-bone mechanical adaptation to applied load. For example, longitudinal bone curvature affects the moments acting on the skeleton and load transmission through the limb (Biewener, 1983b; Lanyon, 1987; Main et al., 2010; Dodge et al., 2012) and is sensitive to physical stimuli, decreasing in response to either removal or application of mechanical loads (Lanyon, 1980; Biewener and Bertram, 1994; Mosley et al., 1997). Similarly, ex vivo mechanical tests incorporating strain gauge measures are rarely used to determine changes in whole-bone mechanical behaviour following loading. Studies that have incorporated these measures examined partially dissected limbs in euthanized rodents (Robling et al., 2002; Warden et al., 2005).

However, both euthanasia and dissection of the surrounding tissues could significantly influence strain gauge-based stiffness measures (Dodge et al., 2012). No studies to date have examined functional alterations in whole -bone stiffness by measuring bone strains on the intact limbs of living rodents following adaptation to in vivo mechanical loading. Absence of these measures is significant given the load-bearing function of the skeleton and the hypothesized importance of tissue strains in modulating bone's biological response to load (Carter, 1982; Frost, 1983; Lanyon, 1987). Thus, measuring in vivo bone stiffness in relation to changes in whole-bone morphology following controlled applied loading is a crucial next step in developing anabolic loading therapies for the skeleton.

In this study, we examine changes in the skeleton's structural response to applied load in three age groups of female mice ranging from young, growing animals to mature adults. This ontogenetic approach provides developmental context for the discrepancies found in previous studies for the corticocancellous response to applied load and complements our previous work showing that the skeletal response to applied mechanical strain was similar in 10-week-old male and female mice and significantly reduced in mature 26-week-old female mice (Lynch et al., 2010; Lynch et al., 2011). The goals of this study were to determine: (1) cancellous and cortical adaptation to applied load in growing and adult female mice as a function of age and (2) the contribution of age-dependent changes in cortical and whole-bone morphological adaptation to bone stiffness. To address these goals, an established osteogenic loading protocol was applied to the tibiae of growing and adult female C57Bl/6 mice (6, 10 and 16 weeks old) (Fig. 1). We hypothesized that bone mass would increase in the loaded tibiae, but that the anabolic response to loading would decrease with age in cancellous and cortical bone of growing and adult female mice. Secondly, stiffness in the loaded tibiae would be greater than in the non-loaded control tibiae primarily because of load-induced increases in cortical bone geometry and decreases in longitudinal bone curvature.

Applied load had a significant anabolic effect on cancellous tissue mass in the proximal tibial metaphysis, and the relative effect of load decreased with age (Figs 2, 3, Table 1). Cancellous bone volume fraction (BV/TV) was 107, 60 and 21% greater in the loaded relative to the control tibiae in the 6-, 10- and 16-week-old mice, respectively (Fig. 3). Similarly, trabecular thickness (Tb.Th) was 68, 42 and 31% greater in the loaded relative to the control limbs in the 6-, 10- and 16-week-old groups, respectively. Trabecular separation (Tb.Sp) was greater in the loaded relative to the control tibiae (+12%), and this difference was age-independent (Table 1). Cancellous tissue mineral density (cn.TMD) was 10, 6 and 3% greater in the loaded relative to control tibiae for the 6-, 10- and 16-week-old groups, respectively. In the control limbs, BV/TV and Tb.Th increased from 6 to 10 weeks of age and were similar in the 10- and 16-week-old mice (Fig. 3, Table 2). Tb.Sp decreased from 6 to 10 weeks of age (P=0.003) and was similar between the 10- and 16-week-old mice. In the loaded tibiae, BV/TV was similar in the three age groups, while Tb.Th was greater in the 6-week-old than the 16-week-old mice. In both the loaded and control limbs, cn.TMD was greater in the 10- and 16-week-old mice than in the 6-week-old mice.

At the mid-diaphysis, mechanical loading had a strong effect on cortical geometry, and the relative effect of load decreased with age (Figs 2, 4, Table 1). Cortical cross-sectional area (Ct.Ar) was 43, 30 and 17% greater in the loaded relative to control tibiae in the 6-, 10- and 16-week-old mice. The maximum moment of inertia (I_MAX) increased in the loaded tibiae by 72, 62 and 34% compared with control tibiae, while the minimum moment of inertia (I_MIN) for the loaded tibiae was greater than that for the control tibiae by 58, 30 and 13% in the 6-, 10- and 16-week-old mice, respectively. In the control limbs, Ct.Ar, I_MAX and I_MIN increased from 6 to 10 weeks of age and were maintained from 10 to 16 weeks of age (Fig. 4, Table 2). In the loaded limbs, Ct.Ar, I_MAX and I_MIN were greatest in the 10-week-old mice and similar for the 6- and 16-week-old groups.

Cortical TMD (ct.TMD) and bone curvature were generally greater in older mice and not strongly affected by applied load (Table 1). ct.TMD changed slightly, but significantly, with applied load in 6- and 10-week-old mice (+1 and −1%, respectively), but was unaffected by load in 16-week-old mice (Fig. 4, Table 2). The anterior-posterior and medial-lateral radii of curvature (C_AP and C_ML) increased with age but were unaffected by applied load at any age (Fig. 5, Table 1).

In vivo tibial stiffness changed inversely with applied load in an age-dependent manner. Stiffness was greater in the loaded relative to control tibiae for 6-week-old mice (+81%; Fig. 6, Tables 1, 2). Tibial stiffness did not differ between loaded and control tibiae in 10-week-old mice. In 16-week-old mice, tibial stiffness was reduced in the loaded relative to control limbs (−42%). The loaded tibiae of 6-week-old mice were stiffer than the loaded tibiae of the two older groups (Fig. 6, Table 2). Stiffness did not vary significantly with age in the control limbs. In all mice, tensile (positive) strains were induced on the medial midshaft during compression loading as a result of a combination of anterior-posterior and medial-lateral bending at this site.

Axial and bending stresses induced by a 9 N compressive load were less in the loaded than in the control limbs, and this difference decreased with age (Fig. 7, Table 1). In the loaded tibiae, axial stress (σ_ax) was 40, 28 and 18% lower than in the control tibiae for the 6-, 10- and 16-week-old mice, respectively. σ_ax was similar in the loaded tibiae at all ages and decreased with age in the control limbs (Fig. 7, Table 2). Anterior-posterior bending stress (σ_b,AP) in the loaded tibiae was 46, 27 and 21% less than in the control tibiae for the 6-, 10- and 16-week-old mice, respectively. σ_b,AP increased with age in the loaded tibiae and was generally similar among age groups in the control limbs. Medial-lateral bending stress (σ_b,ML) showed a general increase with age and was 33% lower in the loaded relative to the control tibiae across the three age groups (Fig. 7, Table 1).

The effects of in vivo loading on tibial length and body mass varied with age. Loaded tibiae were shorter than control tibiae in 6-week-old mice (−3%, P<0.001), but similar in length for the two older groups (P>0.75 for both groups). Body mass increased with age among the groups and increased over the 2 week loading period for the 6- and 10-week-old mice, but decreased slightly for the 16-week-old mice during the experiment.

We examined cancellous and cortical tissue adaptation to 2 weeks of applied loading in the tibiae of growing and adult female mice and related changes in functional tibial stiffness with loading to cancellous architecture, cortical cross-sectional geometry and longitudinal bone curvature. The anabolic effect of applied load on cancellous and cortical tissue in the tibia decreased with age. In vivo tibial stiffness varied inversely with age in loaded tibiae and remained similar with age in control tibiae. Bone curvature was not affected by applied loading. Changes in tibial stiffness following loading did not directly reflect changes in cross-sectional geometry and bone curvature in 10- and 16-week-old mice, suggesting a load-induced change in bone material properties in older mice. These results clearly demonstrate the importance of measuring post-loading whole-bone stiffness to assess bone adaptation to load and demonstrate the limitations of using cross-sectional geometry alone as a surrogate for whole-bone structural behaviour.

Two weeks of applied load increased cancellous bone mass in the proximal tibiae of growing and adult mice, and the relative anabolic response decreased with age (Fig. 3). Few studies have examined the effect of age on changes in cancellous tissue with applied load. Previously, cancellous tissue in the proximal tibiae of 8-week-old C57Bl/6 mice showed an anabolic response to applied load, while bone volume fraction actually decreased with loading in 12- and 20-week-old mice (De Souza et al., 2005). Although this previous study found an age-related decrease in the anabolic response to load, similar to our study, the net bone loss reported in the loaded tibiae at 12 and 20 weeks contrasts with the load-induced net gain in bone mass that we measured at 10 and 16 weeks of age. These differences may be related to disparities in the load waveform characteristics and/or the total number of load cycles applied between the two studies. Our study applied lower loads (~9 versus 13 N) at a greater frequency (4 versus 2 Hz) and for a greater number of cycles per day (1200 versus 40). The increased cancellous bone mass reported here in the loaded tibiae for the 10- and 16-week-old female C57Bl/6 mice agrees with previous tibial loading studies from our laboratory for 10-week-old male and female C57Bl/6 mice (Fritton et al., 2005; Fritton et al., 2008; Lynch et al., 2010) and with tibial loading experiments using 16- to 19-week-old female C57Bl/6 mice (Sugiyama et al., 2008; Sugiyama et al., 2010; Holguin et al., 2013). The decreased anabolic cancellous response to applied load with age from 6 to 16 weeks of age found here is consistent with our previous work showing a decrease in the cancellous response from 10 to 26 weeks of age (Lynch et al., 2011).

Similar to our cancellous results, applied load increased cortical bone mass at all three ages, and the relative adaptive response decreased with age. These results agree with previous studies reporting decreased cortical adaptation with age to a given applied strain magnitude (Rubin et al., 1992; Turner et al., 1995; Srinivasan et al., 2003; Lynch et al., 2011). In cancellous tissue, all three age groups achieved similar values for BV/TV and Tb.Th in the loaded limbs. In cortical bone, the relative anabolic response was greatest in 6-week-old mice, but the greatest cortical geometries were achieved in the loaded tibiae of 10-week-old mice. Although the absolute magnitude of the cortical area increase in the tibial midshaft was less in 10-week-old than in 6-week-old mice, the larger cortical area in the 10-week-old mice at the start of the experiment (Main et al., 2010) led to a larger cortical cross-section in the 10-week-old mice following loading. Further studies are needed to verify the long-term effects of tissue adaptation on cortical and cancellous bone mass in the different age groups examined in this study. The positive effects of exercise during growth on adult bone mass, even following cessation of activity, has been shown in human athletes and rodent loading models (Warden et al., 2007; Erlandson et al., 2012).

Two weeks of applied load altered tibial stiffness in an age-dependent manner. In the 6-week-old mice, stiffness increased in the loaded relative to the control tibiae, while stiffness was similar and decreased in the loaded relative to control tibiae in 10- and 16-week-old mice, respectively. While tibial stiffness was independent of age in the control limbs, the loaded tibiae of 6-week-old mice were stiffer than either the loaded or control tibiae of the 10- or 16-week-old mice. Increased stiffness in the loaded tibiae of 6-week-old mice is consistent with this group having the greatest load-induced increase in cortical geometry and largest decrease in load-induced stress. The increased cortical geometry and reduced stresses with loading in 10-week-old mice may have been insufficient to produce a measurable increase in tibial stiffness following loading. Given the load-induced increase in cortical geometry in 16-week-old mice, reduced stiffness in the loaded tibiae for this group must reflect decreased tissue material properties at the level of gauge attachment.

The midshaft cortical tissue was examined for microcracks in the three age groups, using basic fuchsin, to verify that decreased stiffness in the loaded tibiae of 16-week-old mice was not caused by load-induced damage. Microcracks were not present in the diaphyseal cortices of the loaded tibiae at any age (data not shown). Thus, the decreased stiffness in the loaded tibiae at 16 weeks of age must reflect altered material properties in the bone tissue itself at the site of the stiffness measures. Target strain levels in the present study were chosen based upon in vivo studies showing that 1200 με corresponds to moderate levels of activity in many vertebrates (Rubin and Lanyon, 1982; Biewener, 1993), including mice (Lee et al., 2002; Sugiyama et al., 2012). Previously, even greater compressive loads than those used in this study (13 N), which induced 1500 με on the medial tibia, did not cause microdamage in 12-week-old mice (De Souza et al., 2005). Although in vivo loading can have clear anabolic effects on skeletal geometry, the influence of long-term loading protocols on mineral and collagen physiochemical properties have not been well characterized. Using Raman microspectroscopy, two related studies found increased mineral:matrix ratios in growing and adult male mice following 21 days of treadmill exercise (Kohn et al., 2009; Wallace et al., 2010). Collagen cross-linking also increased in C3H mice, but not B6/129 mice (Wallace et al., 2010). The greater mechanical stimulus provided by tibial loading in our study, relative to these exercise studies, may have produced age-related changes in tissue properties, such as the degree of mineralization or collagen cross-linking, that were detrimental to tissue material properties in the older mice. Changes in these tissue properties might not be detectable by microcomputed tomography (microCT).

Histomorphometric and microCT analyses are used in many applied loading studies to measure adaptive increases in bone mass (Rubin et al., 1992; Robling et al., 2001; Gross et al., 2002; Fritton et al., 2005; De Souza et al., 2005) and/or estimate changes in load-induced bone strains (Turner et al., 1995; Akhter et al., 1998; Robling and Turner, 2002), often without accompanying structural or material tests. However, as shown in the present study, increased mid-diaphyseal cross-sectional geometry does not necessarily increase whole-bone stiffness during axial compression loading in the tibia, illustrating the importance of structural or material tests to more fully assess bone adaptation to load. Geometric analyses alone do not provide information regarding changes in tissue composition or material properties (van der Meulen et al., 2001). A previous comparison of ulnar strains measured in baseline rats and following applied loading found decreased ex vivo bone strains and increased bone strength in adult rat ulnae post-loading (Robling et al., 2002), in contrast to the decreased tibial stiffness with loading found here for adult mice tibiae. However, greater absolute strains were induced during loading (−3300 versus 1200 με) for a longer period of time (16 versus 2 weeks) than in the present study, resulting in I_MIN increases of 70–100% in the loaded relative to the control limbs compared with a 13% increase in I_MIN here. The conflicting stiffness results, despite load-induced increases in bone geometry in both studies, highlight the value of measuring whole-bone mechanical function following loading through whole-bone stiffness tests, when the goal is to investigate physical methods for increasing bone mass and strength or stiffness.

The ‘whole-bone’ stiffness measures made in this study are from in vivo mechanical tests incorporating the length of the entire bone, not the diaphysis of excised bones. In this study, stiffness was measured at a single site on the medial surface of the tibia near the midshaft. Measuring stiffness at different sites on the tibia could produce different post-loading results given regional differences in the anabolic response to load and the complex geometry of the tibia. Differential changes in post-loading stiffness may even occur at different sites on the midshaft where the periosteal anabolic response to applied loads is likely non-uniform. More comprehensive measures of stiffness, such as finite element modeling approaches, could potentially address these limitations.

Recently, load-induced strains in experimentally loaded and contralateral mouse tibiae were compared using a digital image correlation method (Sztefek et al., 2010). Two weeks of tibial loading in 8-week-old male mice subjected to 12 N compressive loads did not significantly decrease average peak strains on the medial surface of the tibia, similar to our results in 10-week-old female mice. However, the load-induced changes in bone geometry or curvature were not reported for this study, so the structural or material causes for these results cannot be evaluated. Given the decreased stiffness with load reported here in 16-week-old mice, despite increased cortical geometry, the lack of tissue material property analyses is a limitation of our study. At the tissue level, nanoindentation, FTIR or Raman analyses could identify the time course of material property and compositional changes in newly formed and existing bone tissue to further understand changes in bone structural stiffness or strength with age and load (Busa et al., 2005; Gourion-Arsiquaud et al., 2009; Kohn et al., 2009; Donnelly et al., 2010).

Bone curvature is an important determinant of bone stress and, ultimately, stiffness during skeletal loading. Increased curvature with age is responsible for maintenance of functional tibial stiffness despite age-related increases in bone geometry in the control limbs, similar to previous findings for mice between 6 and 16 weeks of age (Main et al., 2010). Two weeks of applied load did not significantly alter tibial curvature, and thus did not contribute to the changes in functional stiffness measured for the loaded tibiae. The maintenance of bone curvature following loading in our study contrasts with the decreased curvature following applied loading found in rat ulnae (Mosley et al., 1997). The differential effects of applied load on bone curvature in these two studies may be related to differences in the biological response of the rat ulna and mouse tibia to load, the magnitudes of the induced strains (−2000 versus 1200 με), or the methods for measuring curvature. Cortical geometry and whole-bone morphology are important determinants of functional bone stiffness and the loading environment engendered in the tissue (Lanyon, 1987) and should be considered more widely in functional adaptation and comparative skeletal biomechanics studies.

In summary, in vivo tibial loading is anabolic in both cancellous and cortical compartments in the mouse tibia and increases functional in vivo stiffness in 6-week-old mice. Two weeks of applied loading to induce 1200 με tissue deformations at the medial tibial mid-diaphysis increased cancellous bone mass and cortical geometry and decreased tissue stresses more in growing than adult female mice. Post-adaptation in vivo stiffness measurements showed that increased cortical geometry with loading increased tibial stiffness in young mice, but decreased stiffness in adult mice. As load-induced damage was not present in the loaded tibiae at any age, the decrease in stiffness with loading in 16-week-old mice may be due to alterations in tissue material properties that will be explored further in future studies. Measures of whole-bone stiffness and morphology in conjunction with histological and material property assessments of the bone's response to load are important in understanding the transmission of load through the skeleton and the functional adaptation of bones to mechanical loads.

Dynamic compressive loads were applied to the left tibiae of 6- (N=16), 10- (N=6) and 16-week-old (N=18) female C57Bl/6 mice (Mus musculus, Linnaeus; Jackson Labs, Bar Harbor, ME, USA). At the start of the experiment, the average body masses of the separate 6-, 10- and 16-week-old experimental groups were 15.7, 18.6 and 21.6 g, respectively. At 6 weeks of age, mice are rapidly growing and post-pubescent (Sheng et al., 1999; Richman et al., 2001; Somerville et al., 2004). Female C57Bl/6 mice are considered mature adults by 16 weeks of age (Flurkey et al., 2007), active growth has decreased, and peak bone mass is achieved (Beamer et al., 1996; Sheng et al., 1999; Somerville et al., 2004). Ten weeks is an intermediate age that was used in our previous loading experiments (Fritton et al., 2005; Fritton et al., 2008; Lynch et al., 2010). The 10-week-old mice were included in this study primarily to measure changes in tibial stiffness following loading that were not examined in our previous studies focusing on the morphologic response of the tibia to applied load (Lynch et al., 2010) or examining age-related changes in the morphologic determinants of tibial stiffness (Main et al., 2010). Previous work from our group has shown that age-related differences in tibial stiffness can be determined using five mice per experimental group (Lynch et al., 2010; Lynch et al., 2011). Despite the smaller sample size for the 10-week-old group, their morphometric data are also included for comparison with the 6- and 16-week-old mice.

Compressive loads were applied to the left tibia of each mouse for 2 weeks using a custom loading device (Fritton et al., 2005; Main et al., 2010). Briefly, the loading device holds the knee in a small brass cup while applying dynamic compressive loads at the foot by displacement of an electromagnetic linear actuator (Fig. 1), controlled by force feedback using custom-written software (LabView, v.8.5, National Instruments, Austin, TX, USA). The force transmitted through the tibia to the knee is measured using a load cell placed in line with the knee cup (ELFS-T3E-20L, Measurement Specialties, Inc., Hampton, VA, USA). Using an osteogenic protocol validated in previous studies from our group (Lynch et al., 2010; Lynch et al., 2011), triangle waveform loads were applied 5 days week⁻¹ (days 1–5, 8–12) for 1200 cycles day⁻¹ at 4 Hz while the animals were anesthetized (2% isoflurane, 1.0 l O₂ min⁻¹). The loading waveform was characterized by 0.15 s of loading/unloading with a 0.10 s ‘rest phase’ between load cycles (Fig. 1) (Lynch et al., 2010). Based upon previously established age-related differences in tibial stiffness in these age groups (Main et al., 2010), peak applied loads were adjusted for each age group at the start of the experiments to induce 1200 με on the medial surface of the tibial midshaft. This strain level is characteristic of moderate activity levels in rodents and a variety of vertebrates (Rubin and Lanyon, 1982; Biewener, 1993; Mosley et al., 1997; Rabkin et al., 2001). Peak loads of −9.1, −9.1 and −8.8 N and ‘rest phase’ loads of −1.5, −1.7 and −1.7 N were applied to the tibiae of the 6-, 10- and 16-week-old mice, respectively. The timing of the loading cycle was maintained across the three age groups. The right tibia served as a non-loaded control. Mice were housed four to five per cage and maintained on a 12 h:12 h light:dark cycle. Mice were allowed normal cage activity and ad libitum access to commercial rodent diet and water between loading sessions.

In vivo tibial stiffness was measured at the end of the 2 weeks of loading (day 15) for the loaded and control tibiae in a randomly chosen subset of mice from the 6 and 16 week age groups and the entire 10 week group (N=6 per group). While mice were anesthetized, tibial stiffness was measured using a single element strain gauge attached to the midshaft of the medial surface of the tibia following methods detailed previously (Main et al., 2010). Stiffness was measured over a range of compressive loads (Main et al., 2010) and was calculated as the change in load over the change in strain (Δμε; ε × 10⁻⁶) during the loading portion of the waveform and averaged across four consecutive load cycles. Stiffness data were excluded if the strain gauge was placed greater than 6% of the tibia's length from the midshaft, leaving N=3, 3 and 4 mice for the 6-, 10- and 16-week-old groups, respectively. Both strain gauge location and tibial length were determined by microCT (see below). These sample sizes are similar to or greater than those used to establish load–strain stiffness relationships in other in vivo loading studies (De Souza et al., 2005; Fritton et al., 2005; Gross et al., 2002; Hsieh et al., 2001; Lee et al., 2002; Robling and Turner, 2002; Warden et al., 2007). On day 15, the mice weighed 16.3, 19.1 and 21.0 g on average for the three age groups, respectively. Mice were euthanized by carbon dioxide inhalation. The tibiae were dissected free of soft tissue, fixed in 10% neutral buffered formalin for 24 h, and then stored in 70% ethanol at room temperature. All experimental procedures were approved by the Cornell University IACUC.

Post-loading morphometric analyses were conducted for the loaded and control tibiae in the 6- (N=10), 10- (N=6) and 16-week-old (N=12) mice by microCT. In the 10-week-old mice, the solder leads were removed from the strain gauge-instrumented tibiae prior to scanning. Two pairs of loaded and control tibiae were scanned together in phosphate-buffered saline (μCT 35, Scanco Medical, Brüttisellen, Switzerland; 55 kVp, 145 μA, 600 ms integration time, no frame averaging). A 0.5 mm aluminum filter reduced the effects of beam hardening (Meganck et al., 2009). Scans of the proximal tibial metaphyses and cortical mid-diaphyses were made at a 15 μm isotropic voxel resolution. Whole tibiae from the experimental loading group and the strain-gauged tibiae from the mice used for tibial stiffness measures were scanned with a voxel resolution of 20 μm using similar settings. Following scanning, whole bone and diaphyseal cortical segments were aligned using anatomical landmarks. Specifically, the point at which the fibular marrow canal bifurcates from the tibial marrow canal was digitally aligned with the tibiofibular junction along the z-axis of the scan using a custom script in the manufacturer's software (Main et al., 2010). A hydroxyapatite (HA) calibration phantom provided by the manufacturer was used to convert the linear attenuation for each voxel to g HA cm⁻³ for all scans.

Cortical and cancellous volumes of interest (VOIs) were analyzed. The purely cancellous VOIs in the proximal tibial metaphysis began distal to the growth plate, excluding the primary spongiosa and cortical shell, and extended 10% of the total tibial length. Age-specific thresholds were used to segment mineralized tissue from water and soft tissue (0.25, 0.26 and 0.27 g HA cm⁻³ for the 6-, 10- and 16-week-old groups, respectively) (Halloran et al., 2002; Miller et al., 2007). Cancellous measures included bone volume fraction (BV/TV), cancellous tissue mineral density (cn.TMD; mg HA cm⁻³), and trabecular thickness and separation (Tb.Th and Tb.Sp; μm). Cortical VOIs were centered at the midshaft and extended proximal-distally a total of 2.5% of the bone's length. Age-specific thresholds were set at one-third of the bone peak of the X-ray attenuation histogram, resulting in 0.28, 0.30 and 0.31 g HA cm⁻³ for the 6-, 10- and 16-week-old groups, respectively, which are similar to the threshold values used previously for these age groups (Main et al., 2010). Cortical measures included cortical area (Ct.Ar; mm²), principal moments of inertia (I_MAX, I_min; mm⁴) and cortical tissue mineral density (ct.TMD; g HA cm⁻³). The relative lengths of the cancellous and cortical VOIs are consistent with the VOIs used by our group previously (Fritton et al., 2005; Lynch et al., 2010; Main et al., 2010; Lynch et al., 2011). Different threshold values for cortical and cancellous volumes have been used previously (Halloran et al., 2002; Lynch et al., 2011).

The anterior-posterior and medial-lateral radii of curvature (C_AP and C_ML; mm) were measured on whole-bone scans of the instrumented tibiae using previously published methods (Main et al., 2010). Briefly, C_AP and C_ML were measured as the perpendicular distances between reference lines passing through the midpoints of the proximal and distal ends of each tibia and the anterior-posterior and medial-lateral midpoints of the bone at mid-gauge level. Positive values for C_AP and C_ML represent anterior and medial convexities, respectively. Bone length and anterior-posterior and medial-lateral bone diameters at the level of the strain gauge were also measured using the 20 μm resolution scans.

Axial and bending stresses induced by a 9 N compressive axial load were calculated for the instrumented tibiae at the level of the strain gauge to provide insight into how morphological changes with age and loading influence the measured tibial stiffness (N=3, 3 and 4 for the 6-, 10- and 16-week-old mice, respectively). Although the three age groups received slightly different peak loads during the in vivo loading experiments, a single average load was used for the stress calculations to facilitate comparison of the effects of bone morphology on load-induced stresses. The axial (σ_ax; MPa) and anterior-posterior and medial-lateral bending stresses (σ_b,AP and σ_b,ML; MPa) induced by the compressive load were calculated using beam theory (Biewener, 1983a; Main et al., 2010). Because of the typically convex anterior and medial curvatures of the tibiae at the gauge site, σ_b is positive (tensile) on the anterior and medial bone surfaces. This stress and strain distribution for the tibial diaphysis is confirmed by previous combined finite element and strain gauge analyses of the tibia under compressive load (Stadelmann et al., 2009; Moustafa et al., 2012; Patel et al., 2014; Willie et al., 2013). The tibia experiences a combination of axial compression and medial-lateral and anterior-posterior bending that places the medial and anterior regions of the bone in tension and the lateral and posterior regions of the bone in compression.

The effects of age and loading and the interaction of these factors on tibial stiffness and cancellous and cortical morphology were examined using a linear mixed model with repeated measures. The between-subject factor was age (6, 10 or 16 weeks old) and the within-subject factor was limb (loaded or control). When the interaction term was significant, specific differences between the limbs and/or age groups were tested by pair-wise comparisons with a Bonferroni correction for multiple comparisons (PASW Statistics, v.18, SPSS). Percent differences between the loaded and control tibiae were calculated as: [(loaded–control)/control×100]. Data are presented as means ± s.d. Statistical significance is indicated at P<0.05. Only significant results are reported unless otherwise stated.

We thank Thomas Schmicker, Daniel Walsh, Casey Boyle, Sarah Yagerman and Frank Ko for their help in conducting the experiments and analyses, and Dr Mitch Schaffler for conducting the cortical microcrack analyses.