Elsevier

Journal of Biomechanics

Volume 47, Issue 13, 17 October 2014, Pages 3272-3278
Journal of Biomechanics

Mapping anisotropy of the proximal femur for enhanced image based finite element analysis

https://doi.org/10.1016/j.jbiomech.2014.08.020Get rights and content

Abstract

Finite element (FE) models of bone derived from quantitative computed tomography (QCT) rely on realistic material properties to accurately predict bone strength. QCT cannot resolve bone microarchitecture, therefore QCT-based FE models lack the anisotropy apparent within the underlying bone tissue. This study proposes a method for mapping femoral anisotropy using high-resolution peripheral quantitative computed tomography (HR-pQCT) scans of human cadaver specimens. Femur HR-pQCT images were sub-divided into numerous overlapping cubic sub-volumes and the local anisotropy was quantified using a ‘direct-mechanics’ method. The resulting directionality reflected all the major stress lines visible within the trabecular lattice, and provided a realistic estimate of the alignment of Harvesian systems within the cortical compartment. QCT-based FE models of the proximal femur were constructed with isotropic and anisotropic material properties, with directionality interpolated from the map of anisotropy. Models were loaded in a sideways fall configuration and the resulting whole bone stiffness was compared to experimental stiffness and ultimate strength. Anisotropic models were consistently less stiff, but no statistically significant differences in correlation were observed between material models against experimental data. The mean difference in whole bone stiffness between model types was approximately 26%, suggesting that anisotropy can still effect considerable change in the mechanics of proximal femur models. The under prediction of whole bone stiffness in anisotropic models suggests that the orthotropic elastic constants require further investigation. The ability to map mechanical anisotropy from high-resolution images and interpolate information into clinical-resolution models will allow testing of new anisotropic material mapping strategies.

Introduction

Image-based finite element (FE) analysis of bone provides a non-invasive estimate of bone strength. FE models derived from clinical quantitative computed tomography (QCT) have been used to estimate bone mechanics, including stiffness and failure load, in physiological and non-physiological loading configurations, showing good correlation with experimental data (Dragomir-Daescu et al., 2011, Schileo et al., 2008, Keyak et al., 1998). QCT-based FE models have demonstrated superior prediction of femoral fracture compared to dual-energy x-ray absorptiometry (DXA) in both cadaver (Cody et al., 1999) and clinical studies (Orwoll et al., 2009). Patient-specific FE models are also becoming increasingly utilized for the assessment of therapeutic interventions (Keaveny et al., 2012, Lewiecki et al., 2009).

QCT-based FE models typically form a continuum of elements based on 3D image voxels that describe the bone’s geometry and density distribution. Several empirical relationships exist, summarized by Helgason et al. (2008), relating element density to isotropic tissue stiffness. However this approach does not incorporate the anisotropic behavior of the underlying microarchitecture contained within elements representing the cancellous bone compartment. The heterogeneous trabecular architecture has a varying degree of anisotropy (DA) with minimal correlation between DA and bone volume fraction (BVF) (Charlebois and Zysset, 2010, Goulet et al., 1994). Studies looking at clinically relevant loading configurations, such as a side-ways fall, have been able to explain approximately 85–90% of the variance in experimental stiffness using FE models constructed with isotropic material properties (Dragomir-Daescu et al., 2011, Koivumäki et al., 2012, Keyak et al., 1998). It is possible that the remaining variance in whole bone stiffness is partly related to unaccounted anisotropy of the microarchitecture, which is difficult to resolve in the proximal femur at clinical CT resolutions.

Incorporating anisotropic material properties into image-based FE models of the proximal femur requires properly oriented principal stiffness directions for each element, and the DA that reflects the mechanics of the microarchitecture. The orthotropic DA is intrinsically described by the nine independent orthotropic elastic constants, which have thus far been derived from modal analysis (Taylor et al., 2002), image-based fabric tensors (Zysset and Curnier, 1995), or image-based FE analysis (Yang et al., 1999). Directionality on the other hand, has been measured and applied to FE models of the proximal femur in a variety of ways. Early studies applied orthotropic material properties to their models with little account for alignment between principal stiffness direction and orientation of the underlying microarchitecture, but the resulting models showed very little change compared to isotropic models (Peng et al., 2006). Meanwhile, studies accounting for directionality only in predictable skeletal regions, such as the femoral neck and shaft, found a 13% difference in maximum von Mises stress and 15% difference in nodal displacement in certain regions of the femoral neck (Yang et al., 2010).

Recent studies have turned to computational methods in order to develop a robust measurement of bone directionality. Stiffness directions have been approximated as the principal stress directions calculated on a per element basis after simulating complex physiological loads during gait, including joint contact and muscle attachment forces (San Antonio et al., 2012). Alternatively, directionality can be described with fabric tensor derived from mean intercept length (MIL) analysis of micro-CT images (Harrigan and Mann, 1984). In bone mechanics, fabric provides a description of local anisotropy (Cowin, 1985), which can be combined with the element density to determine the compliance tensor for each element (Zysset and Curnier, 1995). Anisotropic femur models constructed using information from numerous local fabric measurements, has shown improved whole-bone stiffness prediction compared to isotropic models relative to a micro-CT gold standard for two specimens (Marangalou et al., 2012). Methods have also been developed for assessing structural anisotropy directly from clinical resolution images using gradient structure tensors (Tabor et al., 2013). While this technique has demonstrated good directionality agreement with fabric tensors in tissue samples from vertebral (Wolfram et al., 2009) and femoral (Kersh et al., 2013) specimens, the resulting DA measured in these studies has only shown weak correlation with fabric tensors thus far.

This study proposes a new method for quantifying and mapping anisotropy of the proximal femur using the direct mechanics (DM) method (van Rietbergen et al., 1996). This approach provides a direct computational assessment of mechanical anisotropy by deriving directionality and DA of trabecular bone from FE-based stiffness tensors. This provides a robust measurement of mechanical anisotropy, which served as the original gold standard to validate other anisotropy measurements, such as MIL (Odgaard et al., 1997). The goal of this research was to develop a DM mapping methodology followed by interpolation of anisotropic data into clinical resolution, QCT-based models of the proximal femur. We hypothesize that the addition of anisotropic information will lead to a significant change in FE model behavior and improve correlation with experimental data, when compared to isotropic models.

Section snippets

Methods

Seven cadaveric proximal femur specimens were fresh frozen, with all soft tissue removed, and stored in saline solution prior to scanning in DXA, QCT, and High Resolution-peripheral Quantitative Computed Tomography (HR-pQCT). The heterogeneous sample set included both healthy and osteoporotic femurs, with a wide range of reported T-scores as determined from the DXA scans (Table 1). After QCT scanning (GE Discovery CT750HD, GE Healthcare; 120 kVp, 60 mAs, 512×512 matrix size) periosteal surfaces

Results

The processes of subdivision required approximately 5 days of computation time per bone using a single thread on an OpenVMS machine running IPL (Scanco Medical). This lengthy processing time can be attributed to the lack of parallelization of operations within the IPL framework. Subdivision of each femur specimen with 50% sub-volume overlap resulted in approximately 1.3×104 cubes. DM analysis of an entire set of cube required approximately 24 h, using three GPU cores. Comparing a frontal slice

Discussion

This study implemented a novel approach for quantitatively mapping the anisotropy of the proximal femur, and interpolating directionality from this map into the material properties of QCT-based FE models. This was achieved by subdividing HR-pQCT images into numerous cubic sub-volumes for local anisotropy measurements using DM analysis. Qualitatively, the directionality visualized by this mapping methodology displayed good alignment with the general trabecular alignment observable from the

Conflict of interest statement

None of the authors have a conflict of interest related to this work.

Acknowledgements

We would like to thank Mr. Eric Nodwell for technical programming assistance and development of the FAIM software for this project, and Dr. Yves Pauchard for his assistance in developing image registration software. This work was funded by the Natural Sciences and Engineering Research Council of Canada (NSERC).

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