Areal bone mineral density measurements are two-dimensional projections of a three-dimensional structure and are used as a surrogate measure of bone strength. Although this measurement provides information regarding the bone mineral content, it has limited sensitivity and specificity in fracture prediction.1 To address these limitations, efforts have been made to quantify features such as femoral neck cross-sectional area, cortical thickness, and cortical area from images acquired using dual-energy X-ray absorptiometry (DXA) or computed tomography (CT).2–9
These noninvasive imaging methods use structural analyses that often assume the femoral neck is a cylindrical tube with a uniform thickness around the perimeter of each cross-section along its length.5, 7, 10 Moreover, most methods use mean cortical thickness under the assumption that the cortical thicknesses are normally distributed even though there is large variability in cortical bone morphology. This variability in morphology is an important characteristic of cortical bone because it reflects the diverse focal modeling and remodeling along the femoral neck that is responsible for the differing size, shape, and strength of the femoral neck along its length.11
Specific regions of the femoral neck such as the superior cortex are more likely to fracture should a fall occur.12, 13 However, this specific anatomical information has not been incorporated into clinical assessment of fracture risk. The determination of the structural parameters that best predict differences in stress imposed on bone are likely to assist in the assessment of bone fragility and its treatment.
We used 457 high-resolution CT images of femoral neck cross-sections to investigate the relationship between femoral neck structure and stress. Structural parameters were measured within each cross-section and correlated to the peak bone stresses generated in a sideways fall and estimated using finite-element modeling. (The peak hip joint contact force during walking was also investigated and is included as Supplemental Material.) We hypothesized that median cortical thickness is the best determinant of peak bone stress compared to cross-sectional area, cortical fraction, cortical area, or femoral neck diameters.
Materials and Methods
Samples, image acquisition, and structural measurements
The femoral neck cross-sections from 12 postmortem specimens (left proximal femurs) were analyzed using high-resolution images. All specimens were from Caucasian females (mean age 69 years; range, 29–85 years) who died from illnesses unrelated to bone disease. The femoral specimens were stored at −20°C and thawed the day before imaging. The study was approved by the Human Research Ethics Committee of Austin Health, Melbourne.
Three-dimensional high-resolution (isotropic 63-µm voxel size, in-plane 1024 × 1024 pixel resolution) µCT data were acquired (Fig. 1A) along the femoral neck axis. The cortex was separated from the trabecular bone using an image-processing step based on an erosion/dilation algorithm previously published.14 Briefly, Minkowski functionals were computed based on Euler-characteristic descriptions of the connectivity of the cortical bone. A Euclidean distance map was used to map each voxel in its representative structural phase (cortex, background, or trabecular bone) to its nearest interface. The erosion/dilation was then performed at the different distances from the bone interface. Disconnected regions of bone were removed by cluster labeling wherein all clusters with a total size less than 200 voxels were rejected.
Every fifth slice along the length of the femoral neck was analyzed, resulting in an average of 44 slices per specimen. Within each slice, the following structural parameters were measured from the µCT images: total cross-sectional area, apparent cortical area (cortical pores included in area calculation), trabecular area, anterior-posterior diameter, superior-inferior diameter, and cortical thicknesses (Fig. 1B). The cortical fraction for each slice was calculated as the ratio of the cortical area to the total bone area (trabecular plus cortical bone). The radial distribution of cortical thicknesses for each slice was measured at every degree around the perimeter of each of the cross-sections by radiating 360 lines from the femoral neck axis within each slice. The cortical thickness was calculated as the intersecting distance of this line with the inner and outer cortical boundaries.
Finite-element analysis and strength calculations
Finite-element models were created using the segmented cortex to calculate the stress in the femoral neck as a result of the peak hip joint force generated during a sideways fall (Fig. 1C). The points delineating the cortex were assembled into surface models (stereolithography files) using reverse engineering software (Geomagic v.10; Geomagic, Bethesda, MD, USA) and converted into solid models. The solid models were imported into a finite-element software package (Abaqus v.11-1; Dassault Systemes, Velizy-Villacoubly, France) where the geometry was discretized into a finite-element mesh made of 10-node quadratic tetrahedral elements. An average of 88,249 elements were used in each model, and the cortex was assigned an isotropic Young's modulus of 16.5 GPa and a Poisson's ratio of 0.3.15
The orientation of the peak hip joint force as a result of a sideways fall was defined according to experimental simulations in which the joint reaction force was oriented 60 degrees to the femur shaft axis.16, 17 The components of the average ultimate load (1922 N and 2744 N in the proximal and lateral directions, respectively) were applied to a reference node located at the center of the femoral head, and resulted in combined loading on the femoral neck of bending, compression, and shear.16 Connector elements were used to distribute the load on the femoral neck at the neck-head junction, and the element faces at the distal end of the femoral neck were fixed. A linear stress analysis was performed to calculate the stress in the femoral neck as a result of the load conditions. All elements corresponding to each µCT cross-sectional slice within 0.1 mm were isolated and the location of the element with the maximum von Mises stress was identified. The peak von Mises stress was calculated as the average of the elements surrounding this location within a 0.1 mm radius.
To determine the best measure of cortical thickness, the frequency distribution of the cortical thicknesses was evaluated for normality using a Shapiro-Wilk parametric test at a significance level of p < 0.05 (Matlab v7.9.0; Mathworks, Natwick, MA, USA). The mean is the best measure of the central tendency of data for normal distributions, whereas the median is appropriate for non-normal distributions. Two-sample Kolmogorov-Smirnov tests (p < 0.05), which make no assumptions regarding the nature of the distribution of the data, were used to determine if the mean and median cortical thickness differed. All results were expressed as mean ± 1 SD, unless otherwise stated.
The relationship between measured structural parameters and peak stress was evaluated using a multistep regression analysis. The slice position along the femoral neck was included as a variable to determine the effect of measurement location. First, a nonparametric regression was used, and breakpoint values and individual parameter slopes were calculated.18 Next, univariate parametric regression models were fit to each variable and each specimen was treated as a repeated measurement over space using generalized estimating equations.19
An independent working correlation structure was chosen, and the dependence between measurements within each specimen was taken into account in the model via empirical correlations of the peak stress. The quasi-likelihood under the independence model criterion was used with the smaller value indicating a better model.20 The robust standard error was used to control for heteroskedasticity. Finally, predictors with a p value less than 0.1 from the univariate analyses were entered into a multivariate model. The predictors with the highest p value were iteratively excluded from the model until only predictors with a p value less than 0.05 remained. All regression analyses were conducted using commercial software, STATA, and R, a publicly available statistical package.21, 22
Heterogeneity in femoral neck structure and strength
The femoral necks analyzed were irregular cylinders of varying lengths (20.3 ± 0.48 mm). In all cross-sections, the distribution of cortical thicknesses was non-normal and skewed toward smaller thicknesses (p < 0.0001) (Fig. 2A). The mean overestimated cortical thickness in 81% of the slices (p = 0.023) (Fig. 2B). The remaining slices, where the mean and median were not significantly different, were located within the third of the femoral neck near the neck-shaft junction. Based on the skewed distribution, the median represented the best measure of cortical thickness.
The structural variation within each cross-section was also found along the length of the femoral neck. Cross-sectional area, cortical area, cortical fraction, superior-inferior diameter, and median cortical thickness were largest at the femoral neck-shaft junction and decreased along the length of the femoral neck (Fig. 3). Cross-sectional area decreased to its minimum value at 65.6% ± 9.9% along the femoral neck, after which the cross-sectional area increased approaching the neck-head junction (Fig. 3A). Cortical area decreased by 1% per millimeter along the femoral neck (Fig. 3B). Cortical fraction decreased by 0.7% per millimeter along the first 40% of the femoral neck length (Fig. 3C). It then decreased by 4.6% per millimeter. Anterior-posterior diameter increased by an average of 7% along the femoral neck, whereas the superior-inferior diameter decreased by nearly one-half (approaching the femoral neck-head junction) (Fig. 3D, E). Finally, the median cortical thickness decreased modestly along the first 68% of the femoral neck, after which it decreased by 30% of its value at the femoral neck-shaft junction.
The heterogeneity in structure was matched by heterogeneity in peak bone stress along the femoral neck (Fig. 4). In general, bone stress increased with decreasing structural features. The peak stress occurred at 98% along the length of the femoral neck (159.3 ± 42 MPa) near the neck-head junction, and the minimum value was at 50% (105.2 ± 39.3 MPa) along the length of the femoral neck.
Relationship between structure and peak bone stress
Based on the R2 values, cortical area, mean cortical thickness, and median cortical thickness were the best predictors of peak stress (Table 1). The median cortical thickness was a better predictor with a higher R2 than the mean (0.59 versus 0.32, p < 0.004) in the univariate analysis. There was no correlation between peak von Mises stress and measurement location (R2 = 0.01, p = 0.12). The multivariate model combining median cortical thickness and anterior-posterior diameter better predicted peak bone stress compared to a model based on the mean cortical thickness (R2 = 0.66 versus 0.43, p < 0.02).
Table 1. Results of Univariate and Multivariate Models to Assess Effect of Structural Measurements on Maximum Stress Resulting From a Sideways Fall
Cortical area (95% CI, 163–181), mean cortical thickness (95% CI, 2.00–2.27), median cortical thickness (95% CI, 1.39–1.53).
β = standardized coefficient; R2 = coefficient of determination; QIC = quasi-likelihood independence criterion; AP = anterior-posterior; SI = superior-inferior; CI = confidence interval.
QIC values normalized to lowest variable QIC.
Mean cortical thickness
Median cortical thickness
Median cortical thickness model
Median cortical thickness
Mean cortical thickness model
Mean cortical thickness
The spatial organization of cortical bone within a cross-section and along the femoral neck is heterogeneous, and this configuration of bone determines femoral neck structural strength as estimated using finite-element analyses. Within any cross-section, the periosteal and medullary diameters at each of the 360-degree points around the perimeter differed, so that the shape of the femoral neck cross-section varied from elliptical to circular. Cortical thicknesses around the perimeter of the cross-section were not normally distributed; they were skewed toward the larger number of thin cortices. The median was the more accurate measure of the central tendency of cortical thickness and best predicted bone stress.
Thus, median cortical thickness is a more appropriate measure to understand the effects of ageing, disease, and therapy on bone strength. This has been achieved in other areas such as oncology, where the median is a better measure of survival and treatment response because the mean survival time in oncology is unduly influenced by few individuals living longer.23 Fewer thick cortices disproportionately increased the central tendency value of cortical thicknesses when the mean was used, and flawed inferences may result if the skewed distribution of cortical thicknesses is ignored. For example, erroneous reporting of a greater mean cortical thickness implies that periosteal apposition has been greater or that endocortical resorption has been less in association with age or drug therapy, when no such change has occurred.3–6, 8, 9
Under the extreme loading condition of a fall, the entire femoral neck undergoes a significant amount of stress. The uniform distribution of peak stress along the femoral neck likely obscured any differing effect of slice location. However, there was an inverse relationship between cortical structure and stress: as the structural features decreased along the neck, peak bone stress increased. This is most likely attributable to differences in the amount and configuration of cortical bone along the femoral neck. The distal femoral neck has the largest cross-section with an ellipse-like shape and thick cortices, especially inferiorly; fractures are uncommon in this region. Cross-sections in the proximal region were larger and more circular compared to the narrow neck, reflecting a shape optimized to accommodate load.24 This optimized shape is limited by the thin cortices more proximally and may explain the increased incidence of proximal femoral neck fractures. The narrow-neck and mid-femoral neck are not within regions having the highest stress, yet these areas are commonly used for assessing bone fragility.
Surrogate measures of bone strength, such as section modulus, are based on simplified geometries that do not reflect the heterogeneity of the femoral neck. Thus, differences in estimated section modulus between individuals, or changes in section modulus during follow-up, is used to evaluate the effect of age, disease, sex, or ethnic group differences on bone strength.6, 8 The results of this study suggest that the two most important structural measurements are the median cortical thickness and the anterior-posterior diameter and should be included in software designed to evaluate bone strength.
Several investigators report that the assessment of femoral neck structure is a better predictor of its strength than measures of its mass. For example, decreases in cortical thickness contribute more to femoral neck fragility than decreases in its mass.25, 26 A decrease in cortical thickness in the proximal region of the femoral neck was reported to be the most significant predictor of hip fracture compared to cortical thickness measured in the distal region of the femoral neck.27, 28 Increased stress and yield in the proximal femur has also been reported using beam theory and finite element models.29–35
This study has several limitations. The thickness of thin cortices may be overestimated due to partial volume effects. The use of isotropic, homogeneous material properties to model the cortex in the finite-element analysis may still be an oversimplification. Variation in the mechanical properties of cortical bone produced by variation in tissue mineralization and porosity has not been evaluated. The peak stress distribution reported here is therefore largely a function of macrostructure. In the future, inclusion of measures of the variation in the material properties of bone, variation in cortical porosity and larger sample numbers will allow further specification of bone microstructure and strength.
In conclusion, the diversity in femoral neck size, shape, and mass distribution from cross-section to cross-section and point-by-point around the perimeter of a cross section is the result of differing periosteal and endosteal modeling and remodeling throughout life.3 This heterogeneity is unlikely to be captured using a single diameter, cortical thickness, or cortical area derived from a single cross-section. If single measurements are used, we propose that the median cortical thickness in the proximal region of the femoral neck should be used, because it better estimates femoral neck strength.
All authors state that they have no conflicts of interest.
This work was supported by grants from the Australia National Health and Medical Research Council (Project Grant 400139) and the Australian Research Council (Discovery Project Grant DP1095366).
Authors' roles: MEK and RZ contributed equally to this work. Study design: MEK and RZ. Data collection: MEK, AJ, CA, and MAK. Data analysis: MEK and QB. Drafting and revising manuscript content: MEK, RZ, MP, QB, and ES. Approving final version of manuscript: MEK, RZ, MP, QB, CA, and ES. MEK and QB take responsibility for the integrity of the data analysis.