Bone strength at the distal radius can be estimated from high-resolution peripheral quantitative computed tomography and the finite element method
Abstract
Bone strength is a fundamental contributor to fracture risk, and with the recent development of in vivo 3D bone micro-architecture measurements by high-resolution peripheral quantitative computed tomography, the finite element (FE) analysis may provide a means to assess patient bone strength in the distal radius. The purpose of this study was to determine an appropriate FE procedure to estimate bone strength by comparison with experimental data. Models based on a homogeneous tissue modulus or a modulus scaled according to computed tomography attenuation were assessed, and these were solved by linear and non-linear FE analyses to estimate strength.
The distal radius from fresh, human cadaver forearms (5 male/5 female, ages 55 to 93) was dissected free and four 9.1 mm sections were cut beginning at the subchondral plate to provide 40 test specimens. The sections were scanned using an in vivo protocol providing 3D image data with an 82 μm voxel size. All specimens were mechanically tested in uniaxial compression, and elastic and yield properties were determined. Linear FE analyses were performed on all specimens (N = 40), and non-linear analyses using an asymmetric, bilinear yield strain criteria were performed on a sub-sample (N = 10) corresponding to the normal clinical measurement site.
Experimentally determined apparent elastic properties correlated highly with ultimate stress (R2 = 0.977, p < 0.05, N = 31) for the 31 specimens tested to failure. Subsequently, a linear FE analysis estimating apparent elastic properties also correlated highly with failure, and the correlation was higher when moduli were determined from scaled CT-attenuation values than a homogeneous modulus (R2 = 0.983 vs. R2 = 0.972, p < 0.05, N = 31). A non-linear analysis based on tensile and compressive yield strains of 0.0295 and 0.0493 for homogeneous models, and 0.0127 and 0.0212 for scaled models directly estimated ultimate stress, and correlated highly (R2 = 0.951 vs. R2 = 0.937, p < 0.05, N = 5).
The linear relation between stiffness and strength may be unique to radius compressive loading. It supports the use of a linear FE analysis to determine bone strength by regression equations established here. Scaled tissue modulus models performed better than homogeneous modulus models, and the advantage of a scaled model is its potential to account for mineralization changes. The combined numerical–experimental procedure for FE model validation on the patient micro-CT technology demonstrated that bone strength can be estimated non-invasively, and this may provide important insight into fracture risk in patient populations.
Introduction
Osteoporosis is a common multi-factorial disorder of reduced bone mass and micro-architectural deterioration of bone tissue, manifesting clinically as a concurrent increase in fragility and fracture risk [1], [2], [3]. The definition of osteoporosis, according to WHO, is a hip bone mineral density (BMD) measured by dual X-ray absorptiometry (DXA) of more than 2.5 SD below the mean for young, Caucasian adult women [4]. Although DXA-based BMD is used as a surrogate measure of bone strength, it cannot account for bone micro-structure and tissue density variations, and it has limited ability to assess compartmental differences (cortical versus cancellous). Osteoporosis is a disease of low bone strength, not low bone mass as has been previously pointed out [5], therefore more direct surrogates for bone strength should be considered [6]. One promising approach is the use of patient-specific finite element (FE) analysis.
The current standard for patient-specific analysis of strength by FE is to use clinical computed tomography (CT) to provide three-dimensional (3D) data for generation of continuum-level models [7], [8]. This approach has been applied to clinical studies [9] where it was determined that upon drug treatment both the degree of density change and the density distribution affects predicted vertebral strength. Although clinical CT has the advantage that central skeletal sites can be assessed, it is limited by image resolution. The continuum models do not include micro-architectural features, and special care must be taken in the analysis of the cortical region, particularly when it is thin. Despite these limitations, a good estimate of apparent-level bone strength can be achieved.
Bone micro-architecture can be incorporated into large-scale FE models when high-resolution image data is available, and those data can be obtained through the use of micro-computed tomography (μCT). The typical approach is to directly convert the 3D image data to FE meshes on a voxel-by-voxel basis [10], [11] resulting in models that have millions of degrees of freedom and require specialized FE solvers [11], [12]. Most frequently, these models are limited to a linear analysis to estimate elastic properties (i.e., elastic modulus) [13], [14], [15] because they are computationally intensive. However, non-linear analyses of these model types have been applied when model sizes were considerably smaller, for example, representing cancellous sub-volumes [16]. The advantage of a non-linear FE approach is that the bone strength properties can be predicted directly [16] when an appropriate failure criterion is used, as opposed to a linear model which must assume a relation between apparent elastic properties and failure strength. But, the reason that non-linear FE models are not used more often is because they are computationally demanding. Therefore, it has been attractive to assess strength from linear, large-scale FE models despite their intrinsic inability to model strength directly. One approach has been to approximate yield load by estimating the force required for a pre-defined tissue volume to exceed a preset strain magnitude, and this approach has been promising based on cadaver validation studies [17].
Nevertheless, a non-linear FE analysis is better suited for estimations of bone strength and post-yield behaviour than a linear model. The choice of a failure criterion is an important consideration when developing such a model, and many different failure criteria have been proposed, and each have advantages and disadvantages [18], partially depending on whether they are applied to continuum or micro-structural FE models. Some examples include the von Mises [9], maximum principal strain [19], and the Tsai-Wu [20] failure criteria, and recently criteria that incorporate damage accumulation [21]. Although there is no consensus regarding which is the most appropriate criterion, an asymmetric tissue yield strain criterion, with a ratio of principal tensile to compressive yield strains of ~ 0.6 has worked well for micro-structural models [16]. The apparent ultimate stress was not determined directly by this model; instead apparent yield properties are based on the 0.2% offset rule [16].
Another important consideration for voxel-based FE models is whether to apply a homogeneous tissue modulus for the mineralized phase, or whether to adjust the tissue modulus according to CT-based density data. A homogeneous tissue modulus works well for high-resolution image data to describe apparent-level mechanical properties [11], [22], but it cannot account for spatial variations of tissue modulus. Converting CT-attenuation data to a tissue modulus [23] can account for spatially varying moduli and performs well to predict cancellous apparent modulus [24]; however, it is sensitive to partial volume effects, and is resolution dependent [23]. When gray-scale voxel conversion is applied to continuum models (from clinical CT image data) the conversion from CT-attenuation to modulus of elasticity has resulted in good estimations of apparent strength [7] and implicitly accounts for partial volume effects. An important motivation to use a gray-scale conversion is that treatments for osteoporosis may result in changes in tissue mineralization and strength — this may be accounted for a priori by converting the CT-attenuation to moduli of elasticity.
An important drawback to assessing bone strength by FE is that critical parameters affecting the model inputs are not standardized. Failure criterion, appropriate failure parameters (i.e., yield strains), CT-attenuation to modulus conversions, and bone measurement site vary from experiment to experiment. The results of one study are unlikely to be directly applicable to others. Recently, however, a new high-resolution peripheral quantitative computed tomography scanner (HR-pQCT; XtremeCT, Scanco Medical) has been introduced that provides high-resolution 3D image data at the distal radius and tibia with an isotropic voxel size of 82 μm, and these systems have a well defined measurement protocol. Previous prototypes of this system providing a 165 μm isotropic voxel size have been used to demonstrate that bone strength predicted by a linear FE analysis corresponds well with experimental testing [17], [25], [26]. With the advent of these new micro-CT patient scanners, there is an opportunity to apply appropriate FE methods to non-invasively assess strength for patient monitoring because the scanning procedure for the HR-pQCT scanners is standardized (bone measurement site, resolution, density calibration). The development of appropriate protocols and FE model parameters can be applied more universally for all users of HR-pQCT technology with the potential prospect of accurately assessing bone strength in patients non-invasively.
The purpose of this study is to explore the use of both linear and non-linear FE models for predicting bone strength, and whether to base those models on homogeneous versus scaled elastic moduli. Experimental testing of human cadaver bones will be used to evaluate the selection of these FE modeling approaches and appropriate FE parameters for measuring bone strength.
Section snippets
Methods
The study includes both experimental and computational analysis of bone specimens from the distal radius. The finite element models were generated from the 3D image data with either homogeneous or scaled tissue elastic moduli (based on CT-attenuation), and subsequently solved using linear and non-linear FE analyses and compared to experimental results.
Results
Average morphological indices were determined for each of the four measurement sites (N = 10/site) (Table 1). The physical size, volumetric density and cortical thickness varied considerably among the four sites providing a wide range of specimen morphology (and strength).
Experimental testing data provided apparent modulus for all 40 specimens. Failure data was obtained for 31 of those specimens from which the ultimate stress (ultimate strength) was determined. The nine specimens could not be
Discussion
This study demonstrated that finite element models based on 3D measurements from HR-pQCT can estimate bone strength in the human distal radius. Strength is a fundamental determinant of fracture risk, and the results here suggest that the finite element method is a good surrogate measure for bone strength. Based on experimental testing with the cadaver data, it was demonstrated that stiffness is highly correlated with strength at the distal radius under uniaxial compression. This finding
Acknowledgments
The authors wish to acknowledge the excellent technical support of Ms. Shannon Boucousis and Mr. Lukasz Trzcinka, and the Western Canada Research Grid (www.Westgrid.ca) for providing the computing resources. This project was funded through support from the Natural Sciences and Engineering Research Council of Canada, the Canadian Institutes of Health Research, the Alberta Heritage Foundation for Medical Research, and the Canada Foundation for Innovation.
References (38)
Is a change in bone mineral density a sensitive and specific surrogate of anti-fracture efficacy?
Bone
(2007)- et al.
Finite element models predict in vitro vertebral body compressive strength better than quantitative computed tomography
Bone
(2003) - et al.
Femoral strength is better predicted by finite element models than QCT and DXA
J Biomech
(1999) - et al.
Three-dimensional finite element modelling of non-invasively assessed trabecular bone structures
Med Eng Phys
(1995) - et al.
A new method to determine trabecular bone elastic properties and loading using micromechanical finite-element models
J Biomech
(1995) - et al.
A homogenization sampling procedure for calculating trabecular bone effective stiffness and tissue level stress
J Biomech
(1994) - et al.
Direct mechanics assessment of elastic symmetries and properties of trabecular bone architecture
J Biomech
(1996) - et al.
High-resolution finite element models with tissue strength asymmetry accurately predict failure of trabecular bone
J Biomech
(2000) - et al.
Prediction of femoral fracture load using finite element models: an examination of stress- and strain-based failure theories
J Biomech
(2000) - et al.
Introduction and evaluation of a gray-value voxel conversion technique
J Biomech
(2001)
Finite element models predict cancellous apparent modulus when tissue modulus is scaled from specimen CT-attenuation
J Biomech
Estimation of distal radius failure load with micro-finite element analysis models based on three-dimensional peripheral quantitative computed tomography images
Bone
Image-based micro-finite-element modeling for improved distal radius strength diagnosis: moving from bench to bedside
J Clin Densitom
Accuracy of high-resolution peripheral quantitative computed tomography for measurement of bone quality
Med Eng Phys
Comparison of the elastic and yield properties of human femoral trabecular and cortical bone tissue
J Biomech
The elastic and ultimate properties of compact bone tissue
J Biomech
The use of ultrasound in vivo to determine acute change in the mechanical properties of bone following intense physical activity
J Biomech
Osteoporosis prevention, diagnosis, and therapy
Jama
Perspective. How many women have osteoporosis?
J Bone Miner Res
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