Biological constraints that limit compensation of a common skeletal trait variant lead to inequivalence of tibial function among healthy young adults



Having a better understanding of how complex systems like bone compensate for the natural variation in bone width to establish mechanical function will benefit efforts to identify traits contributing to fracture risk. Using a collection of pQCT images of the tibial diaphysis from 696 young adult women and men, we tested the hypothesis that bone cells cannot surmount the nonlinear relationship between bone width and whole bone stiffness to establish functional equivalence across a healthy population. Intrinsic cellular constraints limited the degree of compensation, leading to functional inequivalence relative to robustness, with slender tibias being as much as two to three times less stiff relative to body size compared with robust tibias. Using Path Analysis, we identified a network of compensatory trait interactions that explained 79% of the variation in whole-bone bending stiffness. Although slender tibias had significantly less cortical area relative to body size compared with robust tibias, it was the limited range in tissue modulus that was largely responsible for the functional inequivalence. Bone cells coordinately modulated mineralization as well as the cortical porosity associated with internal bone multicellular units (BMU)-based remodeling to adjust tissue modulus to compensate for robustness. Although anecdotal evidence suggests that functional inequivalence is tolerated under normal loading conditions, our concern is that the functional deficit of slender tibias may contribute to fracture susceptibility under extreme loading conditions, such as intense exercise during military training or falls in the elderly. Thus, we show the natural variation in bone robustness was associated with predictable functional deficits that were attributable to cellular constraints limiting the amount of compensation permissible in human long bone. Whether these cellular constraints can be circumvented prophylactically to better equilibrate function among individuals remains to be determined. © 2011 American Society for Bone and Mineral Research


Physiological systems, like bone, tolerate many genetic and environmental factors by adjusting traits in a highly coordinated, compensatory manner to establish organ-level function. This ubiquitous process is critical for population-wide fitness and occurs at all levels of biological organization,1–3 including interactions among systems.4 Trait variants that are commonly expressed in a population are expected to be adequately compensated to have survived the pressures of natural selection.5 However, the amount of variation in system function tolerated by a population is not fully understood.6 For most systems, individual traits are nonlinearly related to organ-level function, and intrinsic boundaries on cellular activity could limit the degree to which adaptive processes can adjust traits, resulting in functional disparity or inequivalence among individuals. Functional inequivalence associated with a common trait variant could be a public health concern if system performance is limited and susceptibility to common diseases is increased for a predictable segment of the population.

We studied how biological constraints that limit compensation of a common skeletal trait variant lead to functional inequivalence among healthy, young adults. To be functional, bones must be sufficiently stiff and strong to support the loads incurred during daily activities. The adaptive process that adjusts traits to match bone stiffness with these loads occurs primarily during growth7 with continued modifications throughout life.8 This process is well understood for the population-average bone. However, two people with similar body sizes can acquire widely varying bone sizes, ranging from slender (narrow relative to length) to robust (wide relative to length) (Fig. 1). Bone robustness is a common, heritable9 morphological variant established by approximately 2 years of age.10 Because bone stiffness is proportional to the fourth power of width, small variations in width must be compensated by large, coordinated changes in other traits11, 12 to maximize stiffness while minimizing mass,13 otherwise slender bones would be weak and prone to fracturing, whereas robust bones would be bulky and metabolically expensive to maintain and move through space. Slender bones are generally assumed to be less strong than robust bones,14, 15 but just how much variation in function is tolerated among healthy individuals and whether this variation stems from limited functional compensation are not known. We hypothesized that the nonlinear relationship between bone width and whole bone stiffness is too severe for bone cells to compensate slender and robust bones equivalently. Our goals were to determine if adaptive processes establish a uniform level of skeletal function across a healthy population and to identify biological constraints that limit the ability of the skeletal system to fully compensate the normal range in robustness.

Figure 1.

Representative pQCT images of slender and robust tibial cross-sections taken at the 38% and 66% anatomical sites. Measures of morphology are shown for clarification.


Study participants

A total of 730 women (20.8 ± 3.1 years old) and men (21.4 ± 3.4 years old) from the United States and the United Kingdom volunteered to participate in this study, all with informed consent. The average BMI for those with recorded height was 23.4 ± 2.9 kg/m2 for women and 23.7 ± 2.8 kg/m2 for men. For the US cohort, 347 individuals (321 women, 26 men) were enrolled through the Naval Station Great Lakes (Great Lakes, Illinois, USA), the Physical Therapy Department at Oakland University (Rochester, Michigan, USA), and the University of Connecticut (Storrs, Connecticut, USA). Individuals were not quantitatively assessed for the amount of physical activity before enrolling in military training. Individuals recruited into the US cohort were healthy and had no prior participation in organized sports. For the UK cohort, 383 individuals were recruited through the Army Training Centre in Pirbright, Surrey, England (148 women, 100 men) and the Infantry Training Centre in Catterick, North Yorkshire, England (135 men). The UK cohort was purely voluntary and did not exclude anyone based on prior training or participation in sports. All individuals passed rigorous medical entry assessments.

The primary criteria for excluding individuals from the study was image quality. A few individuals moved during pQCT scanning, resulting in tibial cross-sections with small streaks in the image. Each image was scored for image quality by one individual (CN) before quantifying cross-sectional morphology. Those with motion artifacts near the region of interest were removed from the analysis. In addition, data for one woman from the US cohort with unusually robust bones (> 5 standard deviations from the mean) were excluded, because her traits generated excessively large residuals that affected most regression analyses. Of the total number of individuals enrolled, 696 individuals (442 women, 254 men) had valid information regarding anthropometric and morphological traits that were absent of motion artifacts from which functional equivalence was tested. Individuals were from various racial and ethnic backgrounds, but were primarily white. All data sets were combined and segregated by sex only.

Bone morphology and tissue-mineral density

Morphological traits were quantified for tibial diaphyses using peripheral quantitative computed tomography, pQCT (XCT 2000 or 3000; Stratec Medizintechnik, Pforzheim, Germany), as described previously.16 Although the systems were not cross-calibrated, the US and UK pQCT instruments were made by Stratec, and both were calibrated by the manufacturer and used similar manufacturer-provided calibration quality-assurance (QA) devices. Consequently, differences in instruments were corrected by converting attenuation to pQCT density using a common calibration device. A QA scan was conducted at least once every 24 hours to test for drift in the system calibration. The difference in measured and calibrated density values were less than 1%, ensuring that the system calibration did not drift over time and allowing us to compare data derived from the two systems. The XCT 2000 and 3000 were shown by others to generate equivalent trait values (total cross-sectional area, cortical area, cortical density) at multiple locations along the tibia, including the 8%, 50%, and 66% sites.17 Tibial length (Le) was measured from the distal aspect of the medial malleolus to the proximal medial joint line. This measurement requires palpation of the skin to locate the bony landmarks, and the errors associated with this measurement could be on the order of a few millimeters. This measurement error, because it is only 1% to 2% of tibial length, had a minimal effect on the calculation of robustness. Further, a validation study using cadaveric tibias compared traits measured for three adjacent images (2.5 mm apart) at the 38% and 66% sites. Traits like Ct.Ar, Ct.TMD, and Ct.Th varied between 0.3% to 2.6% across the images, indicating that bone traits were not sensitive to small positioning errors.

The non-dominant leg of each volunteer was positioned in the gantry of the pQCT system and the distal tibial end plate was identified during a scout scan. Axial scans (0.4 or 0.5 mm pixel size) were acquired at sites located 38% and 66% proximal to the distal endplate. Grayscale values were converted to cortical tissue mineral density (Ct.TMD) for each cross-section using calibration constants. Cross-sectional morphology and Ct.TMD were quantified using Matlab software (MathWorks, Natick, MA, USA), as described above.16 Images were rotated to standardize image orientation and thresholded to delineate bone voxels (800–1500 mg/cc) from nonbone voxels. Morphological traits included the total cross-sectional area (Tt.Ar), cortical area (Ct.Ar), and the area moments of inertia about the anteroposterior (IAP) and mediolateral axes (IML). Robustness was calculated as Tt.Ar/Le to reflect the biological relationship between the growth in width, which increases by area, and the growth in length. The same individual (CN) conducted all morphological analyses using BAMpack (Bone Alignment and Measurement package) software. Some of the data were reported previously.18

Functional equivalence

To test for functional equivalence, we determined whether the relationship between whole-bone bending stiffness and the applied loads depends on robustness. Whole bone stiffness and the applied loads are not directly measurable, but can be estimated from pQCT images and anthropometric traits, respectively. The loads applied to the tibia were calculated as the product of a force (body weight) and the distance about which the force acts (bone length).7, 19 By engineering convention, whole bone stiffness was calculated as the product of tissue modulus (E) and the cross-sectional area moment of inertia (I). The bending stiffness in the posteroanterior (P-A) direction was used in the functional equivalence analysis, given that tibias are loaded predominantly in this direction during ambulation.20 Whole bone stiffness (EI) was calculated from the pQCT images by converting Ct.TMD to E based on a validation study described below (see Validation Studies) and then multiplying E by IML, which is the rectangular moment of inertia about the mediolateral axis. The product EI was adjusted using the linear regression derived from the validation study (see below) that compared EI estimated from pQCT with EI measured by subjecting cadaveric tibias to conventional bending tests. To test for functional equivalence, we regressed bending stiffness, EI, against robustness after accounting for body size (BW-Le) effects by partial regression analysis. The slope of the partial regression should not be significantly different from zero if slender and robust tibias exhibit the same stiffness relative to applied loads (ie, functional equivalence).

Biological constraints limiting compensation

To identify biological constraints limiting the degree of compensation permissible in human long bone, we first determined whether individuals in our study population used a similar strategy to compensate for a common, heritable trait like robustness. In general, bone cells are expected to coordinate traits in a nonrandom manner to establish function for any given person. If all individuals were to use a similar biological strategy to compensate for robustness, then functionally related traits would correlate across a population and, because many traits are involved, these correlations would resemble a network of trait interactions.2, 21, 22 Prior work identified important interactions among robustness, relative cortical area (cortical area/total area), and tissue-stiffness for a small cohort of cadaveric tibias.22 Path Analysis was conducted to test whether our large study population exhibited a common pattern in the way traits covary and to identify the relative contribution of each trait to whole bone stiffness. A Path Model was constructed by specifying the directed paths among select bone traits. As in prior work, we postulated that relationships occur in a particular order, such that slender bones (Tt.Ar/Le) are compensated by greater tissue-modulus (E) and a proportionally greater relative cortical area (RCA = Ct.Ar/Tt.Ar), whereas robust bones are compensated by reduced E and reduced RCA. We arranged the traits and specified the direction of the arrows (interactions) among traits to provide a test of the compensatory interactions among traits and to determine how these traits together define the inter-individual variation in whole bone stiffness. The primary difference from prior Path Models is that we allow the amount of bone (Ct.Ar) to vary independently of robustness. This was based on work in mouse bone showing that Ct.Ar and robustness are regulated by independent genes.23 We found this model was sufficiently general to accommodate dimorphic growth patterns, allowing us to combine data for men and women. Path coefficients, which represent the magnitude of the direct and indirect relationships among traits, were calculated using standardized (Z-transformed) data (LISREL v.8.8; Scientific Software International, Lincolnwood, IL, USA). Structural equations were constructed using the path coefficients to specify the interconnected relationships. For traits with both direct and indirect paths, the structural equations were rederived in terms of the independent traits (BW-Le, robustness, cortical area). These are reported as the reduced form equations. Observed and model-implied covariance matrices were compared using maximum likelihood estimation. Chi-squared values with an associated p value greater than 0.05 indicate the model adequately fits the data. The root mean square error of approximation (RMSEA), which is a measure of fit that is adjusted for population size and takes the number of degrees of freedom of the model into consideration, was also reported as an additional fit index. For RMSEA, the p value represents the significance of fit with p < 0.05 indicating a close fit.24

Validation studies

Several validation studies were conducted using cadaveric tibias to confirm that whole-bone bending stiffness (EI) could be accurately estimated from pQCT images. This involved relating cortical tissue-mineral density derived from pQCT with matrix composition (mineralization), porosity, and tissue modulus, and then correlating EI derived from pQCT with EI measured directly after loading human tibias in four-point bending.

1. Correlating cortical tissue mineral density with ash content and porosity

The inter-individual variation in Ct.TMD measured using pQCT could result in part from differences in matrix mineralization and/or porosity, both of which are important determinants of tissue modulus.25 We assessed this relationship by correlating Ct.TMD with ash content and porosity using a set of unfixed, cadaveric tibias (n = 13; 8 male, 5 female; age range = 17 to 54 years). Cross-sectional morphology and Ct.TMD were quantified at sites located 25%, 38%, 50%, 66%, and 75% proximal to the distal end-plates for the cadaveric tibias using the same pQCT protocols described above. The tibias were then sectioned (2.5 mm thickness) at each of the five anatomical sites using a diamond-coated band saw (Exakt Technologies, Inc; Oklahoma City, OK, USA). The ash content (ash weight/hydrated weight) for each cross-section was measured according to previously published protocols.22

To account for the effects of porosity on Ct.TMD, a second 2.5-mm-thick cross-section was obtained at the 38% and 66% sites adjacent to the ones used for ashing for 10 of the 13 tibias (six male, four female, age 37 +/− 8 years). Each cross-section was sectioned radially into six wedges, imaged using a Skyscan 1172 µCT (SkyScan, Kontich, Belgium) with a 1-mm-thick aluminum filter, and reconstructed at a 5-µm voxel size. This procedure captured vascular spaces (including primary vascular canals, Haversian canals, Volkmann's canals, and resorption bays), while excluding osteocyte lacunae. Noise was reduced by applying a 1-pixel median filter to the image stack using ImageJ, followed by a series of despeckling and morphological processing steps (opening) using the manufacturer's software. These procedures were standardized for all blocks; however, an additional processing step was added to some samples if visual inspection showed lingering noise. A region of interest (ROI) was manually selected to exclude cancellous bone (defined visually as regions with greater than ∼50% porosity). The final ROI was shrink-wrapped to the very edge of the bone, and then eroded by 2 pixels to remove edge artifacts. Total tissue volume (Tt.V), total canal volume (Tt.Ca.V), and average 2-D pore number (Ct.Po.N) were measured. Porosity (Ct.Po, %) was calculated as canal volume normalized by total tissue-volume, and pore density (Ct.Po.Dn, 1/mm2) was calculated as Ct.Po.N normalized by cross-sectional area. Data from each of the six wedges were combined to generate an average Ct.Po and Ct.Po.Dn for each cross-section.

2. Estimating tissue modulus from cortical tissue mineral density

To verify that tissue modulus, E, can be accurately calculated from Ct.TMD measured using pQCT, we conducted traditional materials tests on bone samples machined from the intervening segments of the tibial diaphyses used to assess ash content and porosity. Diaphyseal segments greater than 40 mm in length were sectioned into regular prismatic beams using a diamond-coated wafering saw. Cortical bone samples (n = 42) from 9 cadaveric tibias were loaded to failure in four-point bending at 0.05 mm/s using a servohydraulic materials testing system (Instron model 8872, Instron Corp., Canton, MA, USA), as described previously.11 Tissue modulus was calculated from a linear regression of the initial portion of the stress-strain curve. For each bone sample, Ct.TMD assessed by pQCT was determined on a regional basis corresponding to the location of the machined bone sample. Linear regression analysis was conducted between tissue modulus and Ct.TMD to calculate the slope and y-intercept. Because tissue modulus and the associated Ct.TMD were measured in a site-specific manner rather than averaged over the entire cross-section (as is done for the study population), we used the maximum slope and y-intercept of the 95% confidence interval to convert Ct.TMD to E. We found this method was necessary to ensure that estimating E from Ct.TMD captured the full range in tissue modulus across the live human cohort. This relationship was confirmed by comparing the regressions of E (determined by pQCT) versus robustness for the live human cohort with the regression of E (determined by conventional four-point bending tests) versus robustness for the cadaveric samples. Slopes and y-intercepts were compared by ANCOVA.

3. Estimating whole-bone bending stiffness (EI) from pQCT data

To verify that EI calculated from pQCT accurately estimated whole-bone bending stiffness, intact tibias (n = 13), which were contralateral to those used for ashing and porosity, were subjected to whole bone four-point bending tests. The cadaveric tibias were imaged before mechanical testing using the same protocols described above, and EI was measured at 25%, 38%, 50%, 66%, and 75% sites proximal to the distal end-plate by calculating E from Ct.TMD and quantifying IML and IAP from the cross-sectional images. To minimize rotation of the tibias during testing, the proximal and distal metaphyses were embedded in square aluminum channels filled with Bondo (3M; Maplewood, MN, USA). Parallel guides were used to ensure the proximal and distal aluminum pots were aligned relative to each other. Once the Bondo cured, the aluminum channels were removed and the tibias were placed in a four-point bending apparatus that was customized to include two parallel aluminum guides, similar to those used for embedding. The guides, which prevented rotation of the tibias during testing, were covered with Teflon tape to minimize frictional loads being applied to the metaphyses during the bending tests.

Tibias were loaded to preyield load-levels at 0.1 mm/s in the anteroposterior (AP), posteroanterior (PA), mediolateral (ML), and lateromedial (LM) directions to obtain stiffness values for each anatomical axis. Tibias were then loaded to failure in the LM direction at 0.1 mm/s. Difficulties in loading one sample in the LM direction resulted in poor estimates of whole bone stiffness. The LM stiffness value for this sample was excluded from the analysis.

All tests were conducted using a servohydraulic materials testing system (Instron model 8872, Instron Corp., Canton, MA, USA). The distance between the lower two supports (L) was adjusted for each tibia so the supports contacted the bone at the 25% and 75% anatomical sites. The upper-two loading points were placed at one-third and two-thirds of the lower-support span length. Load-deflection graphs were analyzed for stiffness, failure load, postyield deflection, and work-to-fracture. Deflection was corrected for system compliance. A validation study confirmed this loading procedure estimated the modulus of steel and aluminum bars to within 1% of textbook values. The bending stiffness (EI) of each tibia was calculated by correcting load and deflection for the geometry of the loading setup according to the following equation:

equation image

where, P/y = stiffness from the load-deflection curve, L = span length of the lower two supports, a = span of the upper loading points = one-third L. Linear regression analysis and the Bland Altman analysis were used to determine whether EI estimated from pQCT from one of the five anatomical sites accurately predicted whole-bone bending stiffness measured directly from four-point bending tests. Our goal was to identify an anatomical site from which the linear regression between EI derived from pQCT images and EI measured from four-point bending had a high R2 value, was significant, and had a slope close to 1. Further, this site also had to have a Bland Altman plot with a low bias regarding whether EI estimated from pQCT predicted bending stiffness consistently across all stiffness values.


Validation studies

Because whole-bone bending stiffness depends on both morphology and tissue-quality, a validation study was conducted using cadaveric tibias to determine how Ct.TMD determined by pQCT relates to matrix mineralization and porosity, both of which affect X-ray attenuation and define tissue modulus. A linear regression analysis revealed that none of the traits of interest (robustness, Tt.Ar, Ct.Ar, Ma.Ar, Ct.TMD, Le, J, E) changed significantly with age (R2 = 0.0 – 0.1, p value = 0.1 – 0.9), and this was true for the 25%, 38%, 50%, 66%, and 75% anatomical sites. Linear regression analysis showed that Ct.TMD correlated positively with ash content (R2 = 0.34, p < 0.007) and negatively with porosity (R2 = 0.51, p < 0.0004) and pore density (R2 = 0.35, p < 0.006). Pore density correlated significantly with porosity (R2 = 0.40, p < 0.003), as expected. Multiple linear regression analysis showed that 63% of the variation in Ct.TMD was explained by ash content, porosity, and pore density (Table 1). Tissue modulus determined by conventional four-point bending tests correlated positively with Ct.TMD (R2 = 0.27, p < 0.0004), as expected.

Table 1. Multiple Linear Regression Analysis
EquationR2 (adj)p Value
Ct.TMD = 668 – 7.20%Porosity + 977%Ash Content0.600.0001
Ct.TMD = 657 – 4.84%Porosity + 1046%Ash Content – 2.70 Ct.Po.N0.630.0001

Further examination revealed significant negative correlations between robustness and Ct.TMD (Fig. 2A) and ash content (Fig. 2B), as expected. Surprisingly, a significant positive correlation was observed between porosity and robustness (Fig. 2C), which remained significant after accounting for age effects by partial regression analysis (R2 = 0.42, p < 0.04). The slope of the tissue modulus versus robustness regression (Fig. 2D) was not significantly different between the live human cohort and the cadaveric data (p < 0.84, ANCOVA), confirming that our method of estimating E from Ct.TMD replicated the full range of variation in tissue modulus expected for the live human cohort. A small difference in the y-intercepts between regressions was expected because of differences in attenuation associated with imaging cadaveric tibias in water compared with acquiring images for tibias of living humans with surrounding muscle, fat, and skin.

Figure 2.

(A) Ct.TMD, (B) ash content, and (C) porosity correlated significantly with tibial robustness measured at the 66% anatomical site. (D) Tissue modulus measured directly for the cadaveric tibias correlated negatively with robustness. The slope of this line was not significantly different from that of the entire live human cohort (p < 0.84, ANCOVA), where E was estimated from Ct.TMD measured by pQCT. (E) Bending stiffness (EI), estimated from pQCT images acquired at the 38% site, accurately predicted whole-bone bending stiffness of cadaveric tibias (n = 13) loaded to failure in conventional four-point bending tests in the posteroanterior (PA) and lateromedial (LM) directions. Tissue stiffness, E, was estimated from tissue-mineral density (Ct.TMD), and I was calculated about the PA and ML axes from the pQCT images.

Finally, the whole bone four-point bending tests showed that EI measured at the 38% site correlated best (ie, slope closest to 1) with bending stiffness measured in the PA and LM directions (Fig. 2E). This was confirmed by conducting a Bland Altman analysis, which compared the difference between EI measured directly by four-point bending to EI measured by pQCT at each of the five anatomical sites. The data points for the 25% and 38% sites were on average 0.3 SD away from the average of the two methods, whereas data for the 50%, 66%, and 75% sites were on average 1.0, 2.4, and 3.4 SDs, respectively, from the average of the two methods. The regression between the difference and the average showed that the 38% site had the lowest R2 value (p < 0.1) and the p value was not significant (p < 0.11). This regression was borderline significant for the 25% site (negative slope, R2 = 0.14, p < 0.06) and highly significant (all positive slopes, R2 = 0.72–0.92, all p < 0.0001) for the 50%, 66%, and 75% sites, indicating that stiffer bones were underestimated by pQCT data measured at the 25% site and overestimated by pQCT data measured at the 50%, 66%, and 75% sites. Thus, EI measured at the 38% site was the only site to show good agreement between methods and consistent predictability across all stiffness values. Thus, we show that EI calculated from pQCT images accurately estimated whole-bone bending stiffness.

Functional equivalence

Tibial robustness (total cross-sectional area/tibial length) was normally distributed (p > 0.10, Kolmogorov-Smirnov test) and varied ∼2-fold among men and women (Fig. 3A). Further, robustness increased modestly with BW-Le (Fig. 3B), and significant differences in the y-intercept (p < 0.0001, ANCOVA) indicated the greater tibial robustness for men was independent of a measure of body size, consistent with sexually dimorphic growth patterns.

Figure 3.

Tibial robustness (Tt.Ar/Le) measured at the 66% anatomical site (A) varied widely among women (solid line) and men (dashed line), and (B) increased modestly with BW-Le for women (R2 = 0.10) and men (R2 = 0.08). Differences in the y-intercept (ANCOVA, p < 0.0001) indicated that men have more robust tibias relative to BW-Le compared with women. (C) Whole-bone bending stiffness (EI) increased significantly with BW-Le for women (R2 = 0.38) and men (R2 = 0.38). (D) Whole-bone bending stiffness correlated significantly with robustness for women (R2 = 0.40) and men (R2 = 0.37) after accounting for BW-Le by partial regression analysis. All linear regressions were significant at p < 0.0001.

Whole bone stiffness increased with applied loads (Fig. 3C), and the R2 values suggested our study population tolerated a modest degree of variation in bone stiffness. Because the slope of the regressions for EI versus robustness was significantly different between men and women (p < 0.017, ANCOVA), we tested for sex-specific effects by correcting EI for BW-Le by regression analysis. When men and women were compared at a common BW-Le (260.2 kg cm), male tibias were 40.9% stiffer relative to applied loads compared with female tibias (p < 0.0001, t-test). Importantly, bone stiffness correlated significantly with robustness for both sexes after accounting for BW-Le (Fig. 3D). Tibias that were slender relative to BW-Le were as much as two to three times less stiff relative to applied loads compared with robust tibias. This analysis confirmed that the variation in robustness was not fully compensated by the underlying biology, resulting in functional inequivalence among individuals, as hypothesized.

Interactions among traits contributing to whole bone stiffness

Robustness, relative cortical area (cortical area/total area), and tissue-stiffness, which are functionally interacting traits shown previously to contribute to long bone function, exhibited a well-defined trajectory in a 3-D plot (Fig. 4A, B). Path Analysis was used to determine how this pattern of trait interactions contributed to the variation in whole bone stiffness. The significant goodness-of-fit criteria for the Path Model (chi-square test p value = 0.39; RMSEA = 0.000) confirmed that traits covaried in a highly consistent manner among individuals (Fig. 4C). Similar networks were found when analyzing the male and female data separately (not shown). Some trait-trait interactions were expected based on mathematical associations (eg, the interactions among Ct.Ar, Robustness, and RCA), whereas other interactions were indicative of biological associations (eg, the interaction between RCA and E). Removing or reversing the arrow between RCA and E resulted in loss of goodness-of-fit for the model, suggesting the interaction between the amount of bone and tissue modulus is a critical component of the functional adaptation process. The network and the reduced structural equations indicated that individuals with slender bones relative to BW-Le acquired a proportionally greater relative cortical area and tissue modulus to establish stiffness, whereas individuals with robust bones established stiffness by acquiring a proportionally lower relative cortical area and tissue modulus. The reduced form equations showed that the network of trait interactions explained 73% of the variation in whole bone stiffness and that Ct.Ar and robustness had similar relative contributions to whole-bone bending stiffness.

Figure 4.

An emergent trajectory was observed among robustness, tissue stiffness, and relative cortical area for (A) women and (B) men. Symbols: open circles = 38% anatomical site; filled circles = 66% anatomical site. (C) The Path Model, which included data for both men and women, showed significant goodness-of-fit criteria. The reduced structural equations revealed that 73% of the variation in whole bone stiffness was explained by BW-Le, robustness, and cortical area. Arrows: solid = positive association; dashed = negative association. Abbreviations: E = tissue-stiffness; Ct.Ar = cortical area; RCA = relative cortical area = Ct.Ar/Tt.Ar; Tt.Ar = total cross-sectional area.

Biological constraints limiting compensation

Because the Path Analysis indicated that individuals in our study population utilized a similar biological strategy to mechanically compensate robustness, we could identify common boundaries on cellular activity or “biological constraints” that limited the degree of compensation permissible in human long bone and that were responsible for the functional inequivalence. The two major compensatory traits contributing to function included the amount of bone (cortical area) and tissue modulus. Cortical area measured at the 38% (women R2 = 0.36, men R2 = 0.38) and 66% (women R2 = 0.25, men R2 = 0.31) anatomical sites correlated positively with BW-Le for both sexes (p < 0.0001 for all regressions). Men exhibited a significantly greater amount of bone (10% to 11%) compared with women across the full range in body size (ANCOVA, intercept p < 0.0001). After accounting for BW-Le, we found that cortical area correlated positively with robustness at both the 38% (Fig. 5A) and 66% sites (Fig. 5B), indicating that tibias that were slender relative to BW-Le were constructed with less bone tissue relative to BW-Le compared with robust tibias. To further compensate for robustness, osteoblasts and osteoclasts must also adjust tissue modulus. Both men and women showed significant negative correlations between tissue modulus and robustness (Fig. 5C), indicating that osteoblasts compensated slender tibias with greater tissue-modulus. We estimated the regression between tissue modulus and robustness required to equilibrate function among individuals by iteratively modifying the relationship between tissue modulus and Ct.TMD until the slope of the partial regression between EI and robustness was not significantly different from zero or the R2 value was less than 0.01 (ie, satisfying the null hypothesis). The regressions required to establish functional equivalence for men and women are shown in Fig. 5C. These regressions do not represent biologically realistic outcomes, because they would result in excessively large tissue-modulus values for slender bones and extremely low tissue-modulus values for robust bones.

Figure 5.

Cortical area correlated positively with robustness for both the (A) 38% (women R2 = 0.58, men R2 = 0.53) and (B) 66% (women R2 = 0.29, men R2 = 0.17) anatomical sites, after accounting for BW-Le by partial regression analysis. All linear regressions were significant at p < 0.0001. (C) Tissue-modulus estimated from pQCT correlated negatively with robustness at the 38% and 66% sites for women (R2 = 0.42) and men (R2 = 0.33). The relationship between tissue modulus and robustness required to establish functional equivalence is shown for women (short-dashed line) and men (long-dashed line). All linear regressions were significant at p < 0.0001.


Functional compensation is a biological process critical for system health and homeostasis, because it allows individuals to tolerate many genetic and environmental factors leading to variation in one trait through coordinated, compensatory changes in other traits. Approximately 70 years ago, Waddington proposed that functional compensation or “buffering” suppresses phenotypic variation and establishes functional equivalence, or “constancy of the wild type,” across a population.5 However, we now know this concept cannot be generalized to all physiological systems, as inter-individual variation in lung size,4, 26 heart size,27 and arterial morphology28, 29 are associated with disparity in system performance, overall fitness, and disease risk. The current results were consistent with these studies, showing that compensation of tibial robustness, a common, heritable morphological variant, was imperfect and led to functional inequivalence among nearly 700 young adult women and men, as hypothesized. In contrast to prior studies showing functional equivalence of mastication among different species of soricid shrews expressing variable mandibular morphologies,30 herein we found functional inequivalence when studying the inter–individual variation in morphology of long bones within a single species.

The functional inequivalence was predictable based on robustness and the amount of disparity among individuals was substantial; tibias that were slender for BW-Le were as much as two to three times less stiff relative to BW-Le compared with tibias that were robust relative to BW-Le. The relationship between whole bone stiffness and the applied loads is important because it defines tissue–level strains, which are thought to drive functional adaptation. 31 Although BW-Le is traditionally used as a measure of the loads applied to bone,19, 32 other aspects of activity (eg, type, intensity, duration, age of onset of training) that are thought to be involved in the functional adaptation process during growth are expected to vary among individuals. Whether activity levels during growth varied predictably with bone robustness for members of our study population and would explain a portion of the functional inequivalence observed here, however, remains unclear. Functional inequivalence relative to robustness means that bone cells could not adjust traits like cortical area and tissue-modulus to the degree needed to fully compensate the nonlinear relationship between bone width and whole-bone bending stiffness. The functional inequivalence reported in Fig. 3D was not limited to bending loads, but was also found when assuming tibias were loaded in compression (data not shown). Although long bones of modern populations are comparatively more slender and weaker than archaeological populations,33, 34 it is unclear if the degree of functional inequivalence has changed over time and whether modern diets and exercise habits contributed to the substantial disparity in function observed for the young adult population examined here. Further, the vast majority of individuals in our study population were white, and it remains to be determined if the degree of functional inequivalence varies with race or ethnic background. Future work could also include measuring the amount of subcortical bone and determining whether this compartment varies in a predictable way with robustness and may reduce some of the functional equivalence reported here.

The results provided important insight into the biological constraints that limited the degree of compensation. The disparity in cortical area relative to robustness (Fig. 5A, B) may affect measures like BMD, but would contribute only modestly to the functional inequivalence because further addition of mineralized tissue to the inner surface of slender tibias would have minimal mechanical benefits. The limited range in tissue modulus (range/average = 36.7%) did not fully compensate for the wide range in moment of inertia (279%) and thus was an important determinant of the functional inequivalence reported here (Fig. 5C). Limited compensation at this level of biological organization may be a public health concern, not only because it means a predictable segment of the population has a functional deficit, but also because it remains to be determined to what extent prophylactic treatments can circumvent these intrinsic cellular constraints to establish a higher degree of functional equivalence among individuals.

Our analysis indicated that bone cells adjusted tissue modulus to compensate for robustness, but only within a very narrow range compared with that observed for bones from different species with widely varying loading demands.35 This constraint, however, may be advantageous, because extracellular matrix modifications that increase tissue modulus (eg, mineralization) generally occur at the expense of increased tissue brittleness. Slender tibias would be extremely brittle if mineralized to the degree needed to establish the same level of functionality as robust tibias (Fig. 5C). Thus, the skeletal system may have evolved to tolerate a modest degree of functional inequivalence relative to robustness, possibly to avoid developing an excessively fragile bone that is prone to fracturing under daily activities and that would decrease individual fitness and survival. This biomechanical trade-off may be an important factor defining the range in robustness values and the degree of functional inequivalence tolerated by a modern population.

The significant correlation between EI derived from pQCT and EI measured directly from four-point bending of cadaveric tibias (Fig. 2E) confirmed that we accurately estimated whole-bone bending stiffness for our study population. We used EI as the measure of bending stiffness, rather than the more commonly used strength-related parameters like bone mineral density (BMD), section modulus, the bone strength index (BSI), and the strength-strain index (SSI). BMD is useful clinically for diagnosing osteoporosis, but does not provide the details of structure and tissue quality required to assess functional inequivalence. Morphological indices like section modulus do not consider the variation in tissue quality, which we show in the current study and in prior work11, 12 is a critical component of the functional adaptation process. Both BSI and SSI incorporate Ct.TMD as a measure of tissue-quality. However, because small changes in bone density correspond to large changes in tissue modulus,25 it was important to use EI as a measure of bending stiffness to test whether the variation in E was sufficiently large to compensate the variation in moment of inertia. We found that EI measured at the 38% site was an accurate predictor of whole-bone bending stiffness (Fig. 2E), which is consistent with prior work showing that tibial architecture at the 33% site was well adapted to anterior-posterior bending loads.36 Although further work is needed to establish a standard conversion between Ct.TMD and E, our method replicated the range in E for the live human cohort and confirmed the relationship between robustness and E was accurately estimated from pQCT (Fig. 2D). The small difference in the y-intercept between the regressions for the cadaveric data and the live human cohort did not affect the outcome of our study, because the partial regression analysis and the Path Analysis relied on the variation in E relative to robustness, not the magnitude of E.

Although functional inequivalence was observed for both sexes, we also found functional disparity between men and women (Fig. 3C), consistent with prior work.36 The stiffness of tibias relative to BW-Le was 40.9% lower for women compared with men, indicating that the 14.8% reduction in robustness of female tibias was not compensated to the same degree as male tibias, despite a 7% greater tissue-modulus for female tibias (Fig. 5C; p < 0.0001, t-test). Consistent with the results of others,37 our study found that women showed 10% to 11% less Ct.Ar relative to BW-Le compared with men, which contributed in part to the functional disparity between sexes. This disparity in tibial stiffness relative to body size may help explain why women sustain approximately five times more stress fractures than men during gender-integrated military training regimens,38 and why fracture incidence is greater for elderly women compared with men.39 Prior work by others showed that sex-differences in strength-related morphological parameters are not fully eliminated even after adjusting for body size.37, 40

Anecdotally, young adult men and women expressing the full range in bone robustness successfully perform daily activities (eg, walk, run, stand), indicating that functional inequivalence is generally tolerated, probably because bone has large safety factors that minimize fracture risk under normal loading conditions.41 However, our concern is that safety factors are often exceeded under extreme loading conditions, such as falls in the elderly and the intense, repetitive exercise combined with prolonged load carriage typical of military training. Young adults with reduced stiffness relative to body size have proportionally weaker bones that would be expected to experience greater tissue strains during intense exercise, increasing matrix damage and the probability of developing a stress fracture.42 This functional inequivalence may help explain why having a slender tibia relative to body size is an important risk factor for stress fractures in military recruits14, 15 and athletes.43 Although slender bones are generally assumed to be weaker than robust bones,14, 15 it was important to formally test this assumption in the context of the skeletal system's ability to compensate a common trait variant. Prior work did not consider the compensatory changes in morphology and tissue quality that accompany the natural variation in robustness. Functional inequivalence may also be problematic in the ever-growing elderly population, because it means individuals begin the aging process at different starting points. Individuals with slender bones relative to body size would be expected to reach a fracture-risk threshold earlier in life if they lose bone mass on a structure with a pre-existing functional deficit. To the extent that functional inequivalence in the tibial diaphysis extends to other skeletal sites, our results may help explain why bone slenderness is a consistent indicator of fracture risk in the elderly.44, 45 However, to generalize the results of this study to the hip, which shows a high incidence of age-related fragility fractures, would require testing how cortical and trabecular traits are adjusted to compensate for the natural variation in femoral neck width, whether proximal femora with slender and robust necks have the same strength during a fall to the side, and whether proximal femora with slender necks show the same age-related bone loss pattern as proximal femora with robust necks.

Our analysis also showed that nearly 700 young adult men and women with different genetic backgrounds and life histories exhibited highly significant functional trait interactions. The network of trait interactions shown in the Path Model (Fig. 4C) highlighted the biological complexity of a relatively simple, tubular system. Unlike multivariate approaches such as multiple regression or principal components analysis, which make no specific assumption about the underlying biology, we used Path Analysis to test whether traits that are functionally related during growth would show correlations among adult structures consistent with the idea that bone maximizes stiffness using minimum mass.13 The network, which explained 79% of the variation in whole bone stiffness and was consistent with that reported for a small cadaveric cohort,22 indicated that young adult men and women in our study population acquired highly predictable trait sets during growth and thus shared important aspects of a negative feedback control mechanism responsible for coordinating traits to establish function. In contrast to man-made systems, where highly variable morphologies and materials are combined to establish function, biological systems like bone work with limited resources and must adjust the amount, location, and organization of a narrow range of building blocks (eg, mineral, collagen, proteoglycan, water) to achieve the degree of variation in morphology and tissue quality required to establish function across a population. These cellular constraints, which were responsible for functional inequivalence, also appear to limit the number of possible functional trait sets that can be acquired during growth. That is, individuals with slender bones coordinated Ct.Ar and tissue modulus in fairly similar ways to establish function; likewise, the same can be said for individuals with robust bones. The limited range in functional trait sets acquired during growth explained why we saw a consistent pattern in the way traits covaried across a young adult population. Although the larger number of traits in corticocancellous structures increases the possibility that compensation of robustness can occur using a wider range of trait sets, relatively similar functional trait-interactions have been observed for the human femoral neck46 and mouse vertebral body.47

The Path Model also showed that variation in compensatory traits were superimposed on the variation in robustness. This is an important outcome of this study and one worth illustrating to better convey the concept. Fig. 6 was constructed to illustrate how cortical area varied among individuals. A similar diagram could be constructed for tissue modulus. First, cortical area varied relative to robustness, with slender tibias having less Ct.Ar compared with robust tibias. Second, there was inter-individual variation in Ct.Ar for any given robustness value. This is important because it means that traits like Ct.Ar should be adjusted for body size and robustness to identify genetic factors, environmental factors, or both affecting the inter-individual variation in measures related to bone mass.23 Although the Path Analysis revealed a highly predictable pattern for nearly 700 individuals, additional data from a more diverse population would be required to establish norms for these compensatory relationships. It is important to note that having slender bones does not necessarily indicate a failure to adapt. Although periosteal expansion during early growth may be modified by extreme loading conditions,48 it is unclear to what extent variation in the normal range of loading affects an individual's skeletal robustness. Based on our data, we would argue that genetic variants, environmental variants, or both that impair the functional adaptation process may affect robustness, but would primarily affect the compensatory traits that accompany robustness, that is, Ct.Ar and E. Thus, a poorly adapted bone, whether slender or robust, would have reduced Ct.Ar and reduced E compared with the population mean for that particular robustness value. Identifying individuals with poorly adapted bones would require establishing population norms for how traits covary relative to external size and then adjusting an individual's acquired trait set for their robustness.

Figure 6.

A schematic diagram was constructed based on the results of the Path Model (Fig. 4C) and the association between Ct.Ar and robustness (Fig. 5A, B) to illustrate how variation in cortical area is superimposed on the variation in robustness. Tibial diaphyses are represented as idealized circular cross-sections, with gray values representing the variation in tissue modulus. With body size effects removed, cortical area varies with robustness, with slender tibia showing lower Ct.Ar than robust tibia. In addition, there is variation in Ct.Ar for any given robustness value. These relationships hold for men and women, despite sex-specific differences in robustness and Ct.Ar. Thus, the natural variation in robustness is associated with specific changes in cortical area and tissue-modulus that need to be considered when seeking genomic factors, and environmental factors, or both regulating bone function.

Although the limited range in E was an important determinant of the functional inequivalence (Fig. 5C), the Path Model showed that E was not a major determinant of the inter-individual variation in whole-bone bending stiffness. This is probably because the variation in E at a single anatomical site is small compared with the variation in cortical area. Further, prior work in mouse bone showed that E covaries closely with periosteal expansion rate early in life.49 Consequently, the contribution of E to the variation in whole bone stiffness may be masked in the multivariate model by its association with robustness. In contrast, Ct.Ar develops throughout growth and may be more susceptible to environmental perturbations, thereby showing greater inter-individual variation relative to robustness and making a dominant contribution to the variation in whole bone stiffness.50, 51

The validation study provided important insight into the manner by which the skeletal system adjusts tissue quality to compensate for robustness. Variation in Ct.TMD depended on both mineralization and porosity, consistent with expectations of acquiring pQCT images with a 0.4- to 0.5-mm pixel size. Although 63% of the variation in Ct.TMD was explained by ash content, porosity, and pore density (Table 1), we suspect the 37% unexplained variance could result in part from measurement error, particularly for ash content and Ct.TMD. Although these two particular traits vary predictably with bone size, they show little variation among individuals. Consequently, small measurement errors would contribute substantially to the unexplained variance. The unexplained variance could also be explained by properties that were not measured. In addition to ash content and porosity, X-ray attenuation could be affected by material heterogeneity, components of mineralization not accounted for by traditional ash content measures, and possibly the organic component of bone tissue. The negative correlations between robustness and Ct.TMD (Fig. 2A,B) and between robustness and E (Fig. 2D, 5C) are consistent with prior work.11, 12, 22 A surprising outcome was finding that porosity was also highly significantly correlated with robustness (Fig. 2C). Unlike prior work,22, 52 we assessed porosity and robustness at the same anatomical site in the current study, enabling us to see a strong association between these two traits that remained significant after correcting for age. Thus, the higher tissue-modulus of slender bones resulted from increased mineralization and reduced porosity, whereas at the other extreme the reduced tissue-modulus of robust bones resulted from reduced mineralization and increased porosity. This suggested that bone cells coordinately modulate both mineralization and porosity to regulate tissue modulus, thereby expanding the range of variation in E that can be achieved across a population beyond a strict dependence on varying matrix mineralization alone. Because tissue density correlated positively with ash content (not shown), modulating tissue quality by varying mineralization and porosity would have the added benefit of increasing the mass of slender bones while minimizing the mass of robust bones.13 It is unclear from our current study if there are additional levels of compensation that modulate tissue modulus, such as collagen orientation53, 54 and cross-linking,55 but certainly these factors should be examined in future work. The validation study was limited to available young adult and middle-aged tibias, which are difficult to acquire. The limited number of samples did not allow us to test for a sex-specific effect.

Because our analysis purposely selected vascular pores from within the cortex, the positive correlation between porosity and robustness (Fig. 2C) suggested that internal BMU-based remodeling may be suppressed in slender bones and stimulated in robust bones. These results suggested that internal remodeling may not only be regulated locally by factors such as matrix damage,56 but also globally by factors associated with the compensation of bone robustness. This intriguing outcome is worth confirming with a larger collection of tibias combined with histological techniques that provide dynamic measures of bone turnover.57 Whether the internal remodeling of slender tibias is suppressed during the intense physical exercise typical of military training and contributes to stress fracture incidence has yet to be tested.

Although individuals who enroll into the military are from the general population and are thus expected to represent the diverse range in physical fitness and general health expected for the US and the UK populations, these individuals must pass a rigorous medical screening to be permitted into military training. Thus, our results do not incorporate skeletal traits for individuals with poor health. We suspect the functional adaptation process would be impaired in these later individuals, and consequently, a randomized study of the general population would result in greater variation in the degree to which bone traits are adapted relative to an individuals robustness value. However, excluding individuals with poor health would not be expected to affect the concept of functional inequivalence. Rather, we suspect that inclusion of individuals with poorly adapted trait sets may exaggerate the degree of functional inequivalence across the population.

In conclusion, intrinsic limitations on cellular activity and biomechanical trade-offs established boundaries on tissue modulus and cortical area that prevented adaptive processes from fully compensating the nonlinear relationship between tibial width and whole-bone bending stiffness. The limited variation in trait values constrained the range of functional trait sets that could be acquired by individuals with diverse genetic backgrounds and life histories, resulting in an emergent network of trait interactions. Susceptibility to common, heritable diseases is generally thought to originate at the genetic level, and most studies seek genomic variants or altered molecular networks to develop novel diagnostics and treatments to reduce disease risk.58 Herein, we showed that predictable functional deficits may also arise at a higher level of biological organization, a phenomenon that may be difficult to predict from genetic information alone, because it involved biomechanical trade-offs, constraints on cellular activity, regulation of internal remodeling, and a network of compensatory trait interactions defining organ-level function. Limited compensation at this level of biological organization may be a public health concern, and it remains to be determined how the functional inequivalence reported in this study relates to fracture susceptibility.


All the authors state that they have no conflicts of interest.


We are grateful to D Catrambone, P Nasser, N Gendron, R Ghillani, B Spiering, H Isome, M Lester, N Andarawis-Puri, M Faillace, and CJ Terranova for materials and discussion. This work was supported by grants from the US Department of Defense (W81XWH-09-2-0113, W81XWH-07-C-0097). The opinions or assertions contained herein are the private views of the authors and are not to be construed as official or as reflecting the views of the U.S. Army or the Department of Defense.

Authors' roles: K Jepsen, C Negus, and R Evans were responsible for establishing the hypotheses. K Jepsen was responsible for analyzing the data and writing the manuscript. GF Duarte conducted the validation study. H Goldman and N Hampson were responsible for analyzing the porosity data for the cadaveric tibias validation study. A Centi, BC Nindl, WJ Kraemer, K Galloway, J Lappe, D Cullen, and R Evans were responsible for recruiting subjects and acquiring pQCT data for the US cohort. J Greeves and R Izard were responsible for recruiting subjects and acquiring pQCT data for the UK cohort. C Negus was responsible for analyzing the pQCT images using the BAMpack software that he designed.