Osteoporosis International

, Volume 18, Issue 7, pp 991–997

Tibial geometry is associated with failure load ex vivo: a MRI, pQCT and DXA study


  • D. Liu
    • Department of OrthopaedicsUniversity of British Columbia
  • S. L. Manske
    • Department of OrthopaedicsUniversity of British Columbia
    • Faculty of KinesiologyUniversity of Calgary
  • S. A. Kontulainen
    • Department of OrthopaedicsUniversity of British Columbia
    • College of KinesiologyUniversity of Saskatchewan
  • C. Tang
    • Department of OrthopaedicsUniversity of British Columbia
  • P. Guy
    • Department of OrthopaedicsUniversity of British Columbia
  • T. R. Oxland
    • Department of OrthopaedicsUniversity of British Columbia
    • Department of Mechanical EngineeringUniversity of British Columbia
    • Department of OrthopaedicsUniversity of British Columbia
    • Department of Family PracticeUniversity of British Columbia
Original Article

DOI: 10.1007/s00198-007-0325-0

Cite this article as:
Liu, D., Manske, S.L., Kontulainen, S.A. et al. Osteoporos Int (2007) 18: 991. doi:10.1007/s00198-007-0325-0



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.


Bone 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 [13]. However, DXA is limited by several factors, including its representation of bone density (aBMD), which is confounded by variability in bone size [4]; the lack of discrimination between cortical and trabecular bone compartments; and errors introduced by the variation in surrounding soft tissues and bone marrow [57]. 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 [810] and cortical bone geometry [1114] 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 [13].

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) [15]. 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 [18] 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

Study sample

Twenty unembalmed human cadaveric tibiae (from five male and five female donors) were obtained from the Department of Anatomy at the University of British of Columbia. Age at death ranged from 68 to 80 years (mean ± SD = 74 ± 6 years). The specimens were kept frozen (−20°C) until their use. We obtained antero-posterior (AP) and lateral-medial (LM) digital radiographs of all specimens. An orthopaedic surgeon (PG) screened the specimens and radiographs for defects and previous fracture. Tibial lengths, measured from the proximal articulating surface to the distal articulating surface, ranged from 323 mm to 412 mm; mean length was 363 ± 30 mm. We identified a standard measurement site as a percentage of the length from the distal articulating surface of the tibia (Fig. 1). The Clinical Research Ethics Review Board at the University of British Columbia approved this study.
Fig. 1

Tibia x-ray image with reference co-ordinates and four-point bending test set-up. The distal tibial articulating surface serves as the reference line (0%). The distal part of the tibia was cut at the site 25% of the length of the tibia. The bone was loaded from the lateral side. The bars applying load downwards were positioned at the 50% and 66% sites of the tibia. The ratio of the bending span to the outer diameter in the lateral-medial direction L/D ≈ 6; the distance between the bars applying load downwards was one-third of the total bending span l = 1/3 L

Magnetic resonance imaging

The tibiae were submerged in water and scanned with a 1.5 T MRI system (GE Medical Systems, Milwaukee, WI, USA) using a quadrature head coil. We obtained axial scans using a T1-weighted (repetition time TR = 600 ms, echo time TE = 14 ms) spin-echo sequence to acquire 85 contiguous images with no gap (Fig. 2a). The in-plane resolution was 0.5 mm × 0.5 mm, derived from a field of view of 25 cm2 and a matrix size of 512 × 256 (interpolated to 512 × 512). The slice thickness was 3.0 mm. Two trained technologists performed all scans. One 3.0 mm slice at the 50% site of the tibia length was analyzed by a single investigator (SLM). Periosteal and endosteal borders were segmented using a threshold-driven region-growing algorithm (Analyze 6.0, Mayo Clinic, Lenexa, KS). Total cross-sectional area (ToAMRI, mm2) was defined as the area within the periosteal border. Cortical cross-sectional area (CoAMRI, mm2) was defined as the area between the periosteal and endosteal borders. Section modulus (ZyMRI, mm3) was calculated about the AP axis, defined here as the y axis.
Fig. 2

Imaging measurement areas of (a) MRI, (b) pQCT and (c) DXA. Total area includes cortical area, trabecular area and bone marrow. The cortical bone is the black area in (a) and white area in (b). The thin white line in the middle of image (c) shows the metal wire used as a reference point (50% of total length) to merge two contiguous scans

To determine MRI accuracy, we compared CoA at the 25% site of the tibia by MRI and by histomorphometry [21]. 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 [22]. 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 [23].

Mechanical testing

Once imaging was completed, the specimens were prepared for testing to determine the mechanical properties of the tibia structure. The tibiae were cut at the 25% site with an EXAKT310 low speed diamond band saw (EXAKT, Norderstedt, Germany). The specimens were cleaned of all soft tissue prior to mechanical testing and were kept moist throughout the procedure. We performed four-point bending structural testing on the tibia diaphysis to determine the mechanical properties at the weakest point in the span between the 50% and 66% sites. We used a standard test method for engineering materials, described in ASTM D790M-86 [24], with a bending fixture specifically designed for this procedure [25, 26]. The distal cut end of the specimen was embedded in a square polymethylmethacrylate (PMMA) pot. We used an Instron mechanical testing system (model 8874, Instron Corp., Canton, MA) to perform the four-point bending tests. The tibiae were loaded in the lateral-medial direction with compression stress applied to the lateral side (Fig. 1). The top supports were located at the 50% and 66% sites of the tibia (Fig. 1), and the distance between the loading upper bars was one-third of the total bending span. The ratio of the bending span to the outer diameter in the lateral-medial direction was held constant (6:1). The mean span length between the lower supports was 173.9 mm (range 155.0 mm to 197.8 mm, SD 13.5 mm). The proximal end of the specimen was placed on a custom-made PMMA cup at the proximal side of the bottom support to stabilize and prevent the specimen from rotating without medial-lateral constraint. The specimens were loaded to failure at a rate of 0.1 mm/s. The load and crosshead position data were recorded at 1 kHz. We calculated failure load (N) and stiffness (N/mm) from the load-displacement curve (Fig. 4). Failure load was defined as the maximum load on the load-displacement curve. Stiffness was defined in the linear region of the load-displacement curve after passing the toe region. The linear region for the stiffness calculation was identified by visual inspection, and confirmed by fitting a linear regression (r2 > 0.99) to the load-displacement curve. We also calculated failure moment (Nm) with the following equation [27]:
$$ M = {{\left( {F_{{Failure}} \cdot L} \right)}} \mathord{\left/ {\vphantom {{{\left( {F_{{Failure}} \cdot L} \right)}} 6}} \right. \kern-\nulldelimiterspace} 6 $$
where M is the failure moment (Nm), FFailure is the failure load (N), and L is the span of lower supports (m, see Fig. 1).

Statistical analyses

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).

To address our secondary objective, we constructed two-level hierarchical linear regression models to determine the relative contributions of geometry and bone density to failure load:
$$ Model{\text{ }}\;a:{\text{ }}CoA_{{MRI}} + CoD_{{pQCT}} ; $$
$$ Model{\text{ }}\;b:{\text{ }}CoA_{{pQCT}} + CoD_{{pQCT}}. $$

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.


All 20 tibiae fractured within the testing length (within the lower supports), and were included for statistical analyses. We illustrate a typical load-displacement curve (Fig. 3), and provide the failure load for all 20 specimens (Fig. 4). The mean failure load was 4688 ± 1262 N (mean ± SD); mean failure moment was 138 ± 43 Nm; and mean stiffness in the medial-lateral direction was 931 ± 244 N/mm. ToAMRI was significantly greater than ToApQCT (t = 4.37, P < 0.001) (Table 1). CoAMRI was significantly smaller than CoApQCT (t = −6.00, P < 0.001). There was no significant difference between Zy MRI and Zy pQCT (t = −0.13, P = 0.99).
Fig. 3

Typical load-displacement curve of tibia sample. Stiffness was calculated from the linear region between the two horizontal bars. Failure load is the maximum load in the curve

Fig. 4

Failure loads for each tibia specimen. The white bars represent the right tibiae; and the grey bar represents the left tibiae

Table 1

Descriptive results of MRI and pQCT at the 50% site, and DXA for the whole tibia (Mean±SD, N = 20)


ToA, mm2

CoA, mm2

Zy, mm3

CoD, mg/cm3

aBMD, g/cm2


482 ± 85a

243 ± 61b

929 ± 262



457 ± 79a

280 ± 58b

929 ± 267

1126 ± 28




0.84 ± 0.13

aMeasurements were significantly different between instruments (t = 4.37, P < 0.001).

bMeasurements were significantly different between instruments (t = −6.00, P < 0.001).

Relations between imaging outcomes and mechanical properties

For MRI outcomes, ToAMRI, CoAMRI, and Zy MRI were strongly associated with bone failure load (explaining 61% to 72% of variance), failure moment (explaining 72% to 75% of variance) and stiffness (explaining 55% to 70% of variance) (Table 2). The close relationship between CoAMRI and failure load is illustrated in Fig. 5a.
Table 2

Coefficient of determination (r2) between geometry and density measurements from MRI, pQCT, DXA and mechanical properties from bending tests (N = 20)

Imaging methods

Independent variables

Failure load

Failure moment





































aP < 0.0001

Fig. 5

Scatter plots of cortical area measured with MRI (a) and pQCT (b) versus failure load; aBMD with DXA versus failure load (c)

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

Models that included both density and geometry did not improve the prediction of failure load after accounting for CoAMRI and CoApQCT, respectively (Model a, F-change = 0.03, P = 0.87 for 1, 17 df; Model b, F-change = 0.13, P = 0.91 for 1, 17 df, Table 3). In both final models, CoA was the only significant predictor of failure load (β = 0.84 for CoAMRI in Model a and β = 0.87 for CoApQCT in Model b, P < 0.001, compared with β = 0.02 and 0.01 for CoDpQCT in Model a and Model b, respectively, NS).
Table 3

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

Independent variable



B (SE)



Final model aa











0.975 (5.88)



Final model bb






18.75 (2.69)





0.633 (5.51)



aModel a: CoAMRI was added in the first step. CoDpQCT was added in the second step.

bModel b: CoApQCT was added in the first step. CoDpQCT was added in the second step.


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 [29]. 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 [30]. 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 [31]. 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) [32].

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 [4] 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 [22], compared with MRI [21]. 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.

Copyright information

© International Osteoporosis Foundation and National Osteoporosis Foundation 2007