Tibial geometry is associated with failure load ex vivo: a MRI, pQCT and DXA study
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- Liu, D., Manske, S.L., Kontulainen, S.A. et al. Osteoporos Int (2007) 18: 991. doi:10.1007/s00198-007-0325-0
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We studied the relations between bone geometry and density and the mechanical properties of human cadaveric tibiae. Bone geometry, assessed by MRI and pQCT, and bone density, assessed by DXA, were significantly associated with bone’s mechanical properties. However, cortical density assessed by pQCT was not associated with mechanical properties.
The primary objective of this study was to determine the contribution of cross-sectional geometry (by MRI and pQCT) and density (by pQCT and DXA) to mechanical properties of the human cadaveric tibia.
We assessed 20 human cadaveric tibiae. Bone cross-sectional geometry variables (total area, cortical area, and section modulus) were measured with MRI and pQCT. Cortical density and areal BMD were measured with pQCT and DXA, respectively. The specimens were tested to failure in a four-point bending apparatus. Coefficients of determination between imaging variables of interest and mechanical properties were determined.
Cross-sectional geometry measurements from MRI and pQCT were strongly correlated with bone mechanical properties (r2 range from 0.55 to 0.85). Bone cross-sectional geometry measured by MRI explained a proportion of variance in mechanical properties similar to that explained by pQCT bone cross-sectional geometry measurements and DXA measurements.
We found that there was a close association between geometry and mechanical properties regardless of the imaging modality (MRI or pQCT) used.
KeywordsBone strengthFractureMagnetic resonance imagingPeripheral quantitative computed tomographyTibia diaphysis
There are currently no accurate non-destructive measures of overall bone strength, and the relative contributions of properties such as density and cross-sectional geometry to bone strength are not clear. Studies using cadaveric specimens have shown that areal bone mineral density (aBMD) measured by dual-energy X-ray absorptiometry (DXA) is strongly correlated with bone strength [1–3]. However, DXA is limited by several factors, including its representation of bone density (aBMD), which is confounded by variability in bone size ; the lack of discrimination between cortical and trabecular bone compartments; and errors introduced by the variation in surrounding soft tissues and bone marrow [5–7]. These limitations inhibit our ability to understand the bone-related determinants of fracture risk. Imaging techniques such as peripheral quantitative computed tomography (pQCT) and magnetic resonance imaging (MRI) are capable of assessing bone cross-sections. Hence, these imaging outcomes may provide insight as to the relative contributions of bone cross-sectional geometry and density to bone strength.
MRI represents an attractive option to evaluate trabecular architecture [8–10] and cortical bone geometry [11–14] in vivo without exposure to ionizing radiation. In addition, assessment of total bone geometry at cortical sites with MRI is highly accurate, with less than 2.3% (SD 2.0%) error when measured with phantoms and venison femora .
In contrast to MRI, pQCT is more commonly used as it can assess cross-sectional geometry and the apparent volumetric bone mineral density of both cortical and trabecular compartments of the peripheral skeleton (radius and tibia) . The tibial diaphysis provides a relatively simple model to characterize the effects of weight bearing long bones and to monitor bone geometry and bending indices. Further, the tibia is commonly used to evaluate bone strength during growth and in the aging skeleton [16, 17], and in response to diet  and exercise interventions [19, 20]. However, to our knowledge, the relation between mechanical properties and imaging parameters has not previously been assessed in the tibia. In addition, the relative importance of geometry and cortical density (CoD) to bone strength is poorly understood.
Thus, the primary objective of this laboratory study was to determine the contribution of cross-sectional geometry (by MRI and pQCT) and density (by pQCT and DXA) to mechanical properties of the human cadaveric tibia (failure load, failure moment and stiffness). Our secondary objective was to determine whether bone geometry and density in combination enhanced the prediction of tibial mechanical properties compared with either parameter alone. Taken together, our goal was to better understand how these imaging systems predict failure at the tibia.
Materials and methods
Magnetic resonance imaging
To determine MRI accuracy, we compared CoA at the 25% site of the tibia by MRI and by histomorphometry . Using the same acquisition and analysis protocol as in the current study, we found that CoA was highly correlated between methods (r2 = 0.82). However, the mean value between methods was significantly different (−9%, 14.4 mm2; 95% CI: −27.4 to −1.4).
Peripheral quantitative computed tomography
The tibiae were also scanned with pQCT (XCT 2000, Norland Corporation, Fort Atkinson, WI, USA) at the 50% site (Fig. 1). The in-plane resolution was 0.2 mm × 0.2 mm; the slice thickness was 2.3 ± 0.2 mm and the scan speed was 10 mm/min. A single investigator (DL) performed all the scans. Norland/Stratec XCT 550 software was used for analysis of pQCT scans. To identify the periosteal border and assess ToApQCT, we used Contour mode 3 with an outer threshold of 169 g/cm3. To separate cortical bone from trabecular bone and bone marrow and assess CoApQCT, we used Cort mode 4 with an outer threshold of 169 g/cm3 and an inner threshold 669 g/cm3 (Fig. 2b). We also calculated Zy pQCT (section modulus about the AP axis, defined as the y axis, mm3), and cortical volumetric bone mineral density (CoDpQCT, mg/cm3).
To determine pQCT accuracy, we compared CoA at the 25% site of the tibia by pQCT and by histomorphometry . Using similar analysis modes and thresholds as in the current study, the mean difference between methods was −0.8% (1.8 mm2; 95% CI: −9.3 to 5.8).
Dual-energy x-ray absorptiometry
Posterior-anterior (PA) scans of the whole tibiae were obtained using dual-energy X-ray absorptiometry (DXA, Hologic QDR 4500W, Waltham, MA). We used the PA lumbar spine protocol and placed rice bags under the specimens to mimic soft tissue. As the tibiae were longer than the DXA scan length, we performed two contiguous scans per tibia and marked the 50% site of each bone with a thin metal wire (diameter 0.22 mm). The first scan spanned the distal tibia to the 50% site. The second scan spanned the 50% site to the proximal tibia. We report bone mineral density (aBMD, g/cm2) based on results from the merged scans (Fig. 2c). All scans were acquired and analyzed by a single investigator (DL) using standardized procedures .
Data were analyzed using SPSS version 13.0 (SPSS Inc., Chicago, IL, USA). Means and standard deviations for all variables of interest from each imaging system and for mechanical properties were calculated. To address our primary objective, we calculated coefficients of determination (r2) to assess the relationship between bone geometry and/or density and mechanical outcomes (failure load, failure moment and stiffness).
For each regression model, the variance in failure load explained (r2) and the standard error of the estimate (SEE) are reported. In addition, for each variable in the model, we report the unstandardized B coefficient and the standardized β coefficient to demonstrate the relative importance of each variable in the model. The significance level was set at P < 0.05.
Descriptive results of MRI and pQCT at the 50% site, and DXA for the whole tibia (Mean±SD, N = 20)
482 ± 85a
243 ± 61b
929 ± 262
457 ± 79a
280 ± 58b
929 ± 267
1126 ± 28
0.84 ± 0.13
Relations between imaging outcomes and mechanical properties
Coefficient of determination (r2) between geometry and density measurements from MRI, pQCT, DXA and mechanical properties from bending tests (N = 20)
Similarly, pQCT measures of geometry (ToApQCT, CoApQCT and Zy pQCT) were strongly associated with failure load (explaining 62–77% of variance), failure moment (explaining 72–85% of variance), and stiffness (explaining 68–75% of variance). The relation between CoApQCT and failure load is illustrated in Fig. 5b (Table 2).
The magnitude of the relation between bone geometry (measured with MRI and pQCT) and mechanical properties approximated that observed for aBMD (Fig. 5c). In contrast, CoDpQCT was not significantly associated with tibial mechanical properties (Table 2).
Relative contributions of bone cross-sectional geometry and density to failure load
Hierarchical linear regression model summary for Model a (N = 20) and Model b (N = 20), including the coefficient of determination (r2) and standard error of the estimate (SEE) for each model, and the unstandardized regression coefficient (B), the standardized regression coefficient (β) and the P-value for each variable included in the final models
Final model aa
Final model bb
We utilized novel technologies, including MRI and pQCT, to assess bone geometry at the tibial diaphysis. We found that bone geometry thus obtained explained a similar proportion of the variance in mechanical properties as aBMD assessed by DXA. The strength of these associations were similar to those reported in cadaveric studies of the distal radius tested in three-point bending [1, 28]. Further, MRI findings in the current study are in keeping with our recent reports at the femoral neck that showed a strong relation between cortical geometry (by MRI) and proximal femur failure load . However, we observed a slightly stronger association between bone geometry and failure moment than between bone geometry and failure load. This reflects the contribution of tibial bone length to failure moment, demonstrated by the strong association between bone length and total (r2 = 0.53) and cortical (r2 = 0.61) bone cross-sectional area.
Bone shape, and therefore properties related to the bone cross-section, vary along the length of the tibia . Although the focus of the current study was the 50% site of the tibia, we also assessed the 66% site (assessed from the distal tibial articulating surface). Although we observed similar relationships between imaging properties (geometry and cortical density) and mechanical properties, the magnitude of the relationships were lower (data not shown).
Cortical density represents a combination of the porosity and the mineral content of bone. We observed low variability (1126 ± 28 mg/cm3) in cortical density. This is not surprising given the relatively narrow age range of human specimens in the current study (68 to 80 years) and the highly cortical site we examined (tibial diaphysis). When the material is relatively homogenous (as in the human tibial diaphysis), the mechanical properties of the structure will be influenced solely by the distribution of that material. Thus, we found no association between CoDpQCT and mechanical properties and, not surpringly, CoDpQCT did not contribute significantly to the bone failure prediction model after accounting for CoAMRI or CoApQCT. That said, within a species, we would expect a larger range in cortical density based on differences in cortical porosity if we evaluated specimens across the entire lifespan . Similarly, across species where there is greater variability in cortical density, density explained a considerable amount of the variation in failure of cortical bone (tested in bending at the materials level) .
As in previous studies of the proximal femur and radius, aBMDDXA was strongly associated with mechanical properties [28, 33, 34]. However, to our knowledge, this has never before been evaluated at the tibia. Regardless, this is not surprising as aBMD is an integral measure of both bone size and density  and, as such, it captures the variability in bone size between specimens. Indeed, cortical cross-sectional area explained 82% to 87% of the variance in aBMDDXA. This “size artefact” in measurement of aBMD is eliminated with pQCT, which discriminates between bone size and apparent tissue density so that the relevant contribution of each to bone strength can be ascertained.
We acknowledge that our study has a number of limitations. First, the relatively small sample size limited our ability to compare the strength of the geometry-mechanical property associations between imaging systems. Second, the analysis was conducted on a small number of older adult human specimens. The results are therefore not generalizable to other human populations or to other species. They may also be generalizable only to weight-bearing long bones tested in four-point bending. Third, the coefficients of determination we report are based on normal linear regression despite the fact that our samples are not all independent (20 samples came from 10 donors). To determine the effect of the paired samples, we ran mixed effects models for CoAMRI and CoApQCT (independent variables) and failure load (dependent variable) with ‘donor’ as a random effect (data not shown). We found that results did not differ from those we report for normal linear regression. Finally, image resolution for pQCT was superior to the image resolution for MRI. The improved pQCT resolution likely enhanced its accuracy , compared with MRI . However, we found that there was a close association between geometry and mechanical properties regardless of the imaging modality (MRI or pQCT) used. As the inaccuracy in MRI reflected a tendency towards a systematic rather than random error, this is not surprising.
In closing, we extend previous findings by utilizing novel imaging technologies to assess the contribution of bone geometry to failure at a primarily cortical site in a long bone. Future studies might assess more clinically relevant trabecular bone sites to determine the contribution of both cortical and trabecular bone to bone strength and failure.
We thank Sylvia Renneberg and Jennifer McCord for conducting the MRI measurements. We also thank Dr. David ML Cooper for his review of the manuscript. Financial support to conduct the study was provided by the Canadian Institutes of Health Research, Natural Science and Engineering Council of Canada and the Michael Smith Foundation for Health Research to whom we are grateful.