Comparison of HR-pQCT- and microCT-based finite element models for the estimation of the mechanical properties of the calcaneus trabecular bone
The calcaneus bone is formed of extensive trabecular bone and is therefore well suited to be used as an example of loaded bone to establish the ability of combining microfinite element (microFE) technique with high-resolution peripheral quantitative computed tomography (HR-pQCT) in determining its mechanical properties. HR-pQCT is increasingly used as a tool for in vivo bone clinical research, but its use has been limited to the distal radius and tibia. The goal of this study was to determine the applicability of HR-pQCT-derived microFE models of the calcaneus trabecular bone with 82 μm voxel size with reference to higher-resolution microCT-based models taken as gold standard. By comparing the outputs of microFE models generated from both HR-pQCT and microCT images of the trabecular bone of five calcaneus cadaveric specimens, it was found that the HR-pQCT-based models predicted mechanical properties for fracture load, total reaction force and von Mises stress are considerably different from microCT-based counterparts by 33, 64 and 70%, respectively. Also, the morphological analysis showed a comprehensive geometrical difference between HR-pQCT-based microFE models and their microCT-based equivalents. The results of the HR-pQCT-based models were found to have strong dependency on the threshold value chosen to binarise the images prior to finite element modelling. In addition, it was found that the voxel size has a strong impact on accuracy of imaged-based microFE models compared to other factors such as the presence of soft tissue and image scanning integration time. Therefore, although HR-pQCT has shown to be useful to predict overall structural and biomechanical changes, it is limited in providing local accurate biomechanical properties of trabecular bone and therefore should be used with caution when assessing bone remodelling through local changes of trabecular bone apposition and resorption in disease treatment monitoring.
KeywordsIn vivo assessment Trabecular microstructure Finite element model HR-pQCT Trabecular segmentation Calcaneus
The calcaneus bone has important function within the human musculoskeletal system of bearing body weight during standing and motion. The large portion of this anatomical part consists of trabecular bone; age- and osteoporosis-related changes in calcaneal bone reflects bone strength at other skeletal sites, and the heel has been widely used to predict future fracture risk predominantly using measurements by quantitative ultrasound (McCloskey et al. 2015). The in vivo assessment of bone microstructure contributes to a better understanding of the pathophysiology of diseases such as osteoporosis as well as improving our understanding of the efficacy of therapeutic interventions (Farr and Khosla 2015; Fuller et al. 2015; Liebl et al. 2014; Paggiosi et al. 2014; Nishiyama and Shane 2013; Pialat et al. 2012). High-resolution peripheral quantitative computed tomography (HR-pQCT) is a non-invasive, low-radiation technique designed to measure bone microstructural properties at peripheral sites in vivo (Putman et al. 2014; Stein et al. 2014; Boutroy et al. 2008). Although the second-generation HR-pQCT system (XtremeCT II) has provided improved image resolution (e.g. 61 μm Manske et al. 2015 and 41 μm Enns-Bray et al. 2016), the first-generation XtremeCT I system (82 μm voxel size) is still widely used for bone mechanical analysis purposes. Many recent HR-pQCT-based studies have followed a similar microFE modelling framework, which originated from the pioneering work of van Rietbergen and colleagues (van Rietbergen and Ito 2015; Van Rietbergen et al. 1995) who developed a methodology based on microCT scans of trabecular bone. The methodology was based on three main steps: (1) low-pass image filtration, (2) global single level threshold and (3) conversion of binarised image voxels into linear hexahedron elements. Since then, this modelling protocol has been revised and improved. For example, Laib and Ruegsegger (1999) applied a 3D Laplace–Hamming high-pass filter to effectively remove trabecular-edge noises from microCT images. In another study, Ulrich et al. (1998) studied the effect of mesh smoothing on microCT-based trabecular structure by using tetrahedral elements to improve the preservation of trabecular connectivity in comparison with hexahedral mesh. In another study, a volumetric topological analysis (Saha et al. 2010) was developed to classify the trabecular microstructure into plate/rod-like components, and the hexahedral elements were replaced by beam and shell elements according to their topological classification (Wang et al. 2015; Vanderoost et al. 2011).
However, it is still debated whether accurate finite element (FE) predictions can be obtained from HR-pQCT-imaged trabecular bone when the same procedures defined for microCT-based FE analysis are used. Bevill and Keaveny (2009) used a simple mesh resampling technique on human cadaveric trabecular microstructures (femoral neck, greater trochanter and vertebral body), obtained from microCT scan with 20 μm voxel size. They concluded that scans with voxel size below 80 μm can accurately predict bone strength. However, they did not account for the intrinsic reduction of signal-to-noise ratio of in vivo HR-pQCT images compared to a resampled microCT image. Depalle et al. (2013) also performed a similar investigation by considering L2 human cadaveric vertebrae, and they found that voxel size and degree of element formulation are important factors which directly impact on the accuracy of stress distribution within the trabecular microstructure in the FE model. In a more recent study, Christen et al. (2016) investigated the voxel size dependency of cadaveric distal radius compressive load by using microCT and generating microstructures using multiple downscaled images (from 50 to 150 μm) where they found small voxel size dependency at 61 μm (average error in three orthogonal loading cases of 8.2% compared to 25-μm gold-standard microCT-based model) and increased dependency at larger voxel sizes (average error of 16.7% for 82 μm). MacNeil and Boyd (2008) and Varga et al. (2011) investigated the accuracy of HR-pQCT-based microFE strength predictions (Pistoia et al. 2002) by conducting cadaveric distal radius uniaxial compressive test. In these studies, good agreement was observed between FE results and experimental data derived to calculate apparent bone strength. It should be noted that in distal radius sections the presence of dense cortical shell around the trabecular region acts as mechanical stabiliser in particular when the load is applied longitudinally. As a result, the cortical part of such a specimen bears more load than the trabecular bone. On the other hand, the cortical shell is more accurately converted to microFE compared to the trabecular region which has a wider range of greyscale distribution, if a single level threshold-based method is applied. Therefore, it is hard to understand whether the local predictions of HR-pQCT-based microFE models of distal radius or tibia are accurate in their trabecular core.
To investigate the HR-pQCT-based (82 μm voxel size) FE prediction for human distal tibia by considering whole (cortex and trabecular part) and trabecular segment as well as cubic subvolumes of trabecular region, Liu et al. (2010) pioneered a direct morphological and FE mechanical comparative study where microCT-based models for each cadaveric specimen were considered as gold standard. In this study, despite the differences between HR-pQCT and microCT measurements, high correlations between the two modelling approaches were observed. To evaluate the trabecular bone behaviour more explicitly and using microCT-based models as a gold standard, Tjong et al. (2012) applied HR-pQCT imaging on cadaveric distal radius samples by considering multiple voxel sizes (41, 82 and 123 μm) and found a strong correlation between HR-pQCT model voxel sizes and the accuracy of trabecular region morphometric parameters. In the latest study, Zhou et al. (2016) had examined the accuracy of HR-pQCT (82 μm voxel size)-based microFE predictions for human cadaveric distal radius and tibia by calculating and comparing mechanical properties (bone stiffness and yield strength) and morphological parameters against gold-standard microCT-based microFE and mechanical testing results. They reported a strong correlation between HR-pQCT- and microCT-based mechanical and morphological properties, where corrective adjustment was required to achieve the accurate values for HR-pQCT-based models in the light of their microCT counterparts. To the best of the authors’ knowledge, there has not been any established systematic study on the morphological and mechanical properties of microFE models derived from calcaneum HR-pQCT scans. Therefore, by adopting the comparative analysis approach from Liu et al. (2010) study, the aim of this study was to determine the influence of global thresholding technique of HR-pQCT on the morphological and biomechanical analyses of calcaneus trabecular bone when compared with microCT-based reconstructions and models.
2 Materials and methods
2.1 Specimen preparation
The extracted calcaneus specimens (fully dissected with removed soft tissues) were then scanned with a microCT system (SkyScan 1172, Bruker, Belgium) with the following parameters: 17.41 μm isotropic voxel size, 2950 ms integration time, 100 kV voltage, 100 μA current, 180° total rotation, 0.7° rotation step, 2 × averaging. The microCT images of parallelepiped portion of calcaneus and HR-pQCT images of full feet (acquired with 100 ms integration time or 200 ms integration time, independent registrations) were rigidly registered using AMIRA 6.0.1 in order to select the same region of interest between the low- and high-resolution images.
To construct microCT-based trabecular models, 301 × 301 × 301 voxel cubic subvolumes were considered from the central region of the registered microCT data, where also the equivalent volumes were extracted from their corresponding HR-pQCT sets (65 × 65 × 65 voxels, one extra voxel size was considered on each side to fully capture the boundary geometry). Initially, the uint16 microCT image slices were converted into uint8 format and then filtered by applying low-pass Gaussian filter (0.5,5). The gold standards for both the morphological parameters and the mechanical properties in this study were derived from the segmentations of the microCT images which were used to generate the microCT-based models. For a high-resolution microCT images, adopting a single level threshold method is an adequate technique to separate the pixels which represent bone from surrounding marrow/air (Ding et al. 1999). To select the right threshold, the BV/TV values were initially computed at different threshold ranges. Then, by differentiating the BV/TV and threshold curve, the threshold value corresponding to the steepest curve gradient was chosen as the right input that was equal to 90 for all the specimens (Scanco Medical AG 1997). To study the effect of resampling method (similar to Bevill and Keaveny 2009), additional microstructures were also generated by resampling the original binarised microCT-based model using MATLAB-written resize function (k-wave 2015; That is, the model is downsampled by a factor of 17.41/82 ≈ 0.2) and a single value thresholding was applied to achieve BV/TV similar to the gold-standard microCT model (referred to as microCTRes).
2.3 FE computation
2.4 Output processing
von Mises stress (Stressvm), total applied force (Ftot) and estimated failure load (Ffrct) were computed from each FE simulation for each loading case (Vilayphiou et al. 2010, 2011; Wegrzyn et al. 2010). To predict Ffrct, the Pistoia et al. (2002) criteria were used by assuming that bone failure would happen when at least 2% of the total volume of elements are loaded beyond 7000 μ strain. At the end of each FE simulation, the elemental Straineqv values and the total applied reaction force, Ftot, were extracted and imported to the MATLAB-based program to evaluate the Ffrct.
2.5 Microstructural classification
3.1 Morphological analysis
On average, the specimens 1–4 had DA = 0.66 ± 0.03, whereas for specimen 5 (highly osteoporotic) DA was equal to 0.99. Also, the averaged angular difference between the main trabecular direction and the x-axis (see Fig. 3) was 13.57 ± 3.80° for specimens 1–4 and 72.24° for specimen 5.
3.2 Mechanical analysis
Ex vivo mechanical finite element and microstructural analyses were conducted on HR-pQCT scans of calcaneum trabecular subvolumes with microCT-based models used as gold standard. For these five sample cases, the local structural thickness, Sthick, of generated microCTRes and HR-pQCTTH1/TH2 models is significantly different from the gold-standard microCT model, whereas this difference is lower for microCTRes models. The inaccurate estimation of trabecular thickness by using XtremeCT I system is consistent with the results from Manske et al. (2015) for human cadaveric radii samples. It was found that increasing the integration time for HR-pQCT scans does not noticeably improve the geometrical quality of generated microstructures; as a result, their mechanical properties were also less improved. Also, Cr curves similarities between HR-pQCTTH1 and microCTRes models highlight the dominant role of voxel sizes on the accuracy of morphological properties, since the microCTRes is generated purely through downsampling method. A similar trend was observed between HR-pQCTTH1 and microCTRes FE results, which again shows a principal influence of voxel size on the quality of image-based microFE models.
The calculated stiffness of the selected regions of interest in calcaneus parts has an anisotropic property with highest and lowest stiffness in loading directions 3 and 2, respectively (see Fig. 3). It was also found that the averaged angular difference between the main trabecular direction and the x-axis is 13.57 ± 3.80° which is fairly alongside the third loading direction, resulting in maximum stiffness compared to the other loading cases. It is noteworthy that this anisotropic mechanical response is also observed in HR-pQCT and resampled-based microstructures as well. Therefore, it can be stated that the HR-pQCTTH1 models are potentially able to catch anisotropic mechanical response, according to the trabecular orientations.
One of the main objectives of this work was to perform comparative study on failure load prediction, Ffrct, in the light of the imaging/modelling technique. From both geometrical analysis and FE results, it was found that the single value threshold technique does not provide accurate image-based trabecular microFE model with voxel size of 82 μm. Using HR-pQCT-based microstructure with overestimated BV/TV value (i.e. HR-pQCTTH2), the Stressvm was similar to the microCT model. However, it overestimated the apparent stiffness (measured as Ftot). It should be pointed out however, it was assumed that the bone elastic modulus is identical for all the samples and independent from the structural and physiological properties.
The microCT models have different Sthick to HR-pQCT. This means, for microFE models which are generated from 82 μm voxel size images, there is a wide image greyscale distribution. In contrast, for higher-resolution microCT images, the smaller voxel size will result in narrower greyscale distribution. Therefore, using single value threshold technique is more efficient for images with narrow intensity distribution such as cases with small voxel size or homogenous geometry (e.g. cortical bone). It is important to note that the (Pistoia et al. 2002) criteria have been established based on axial loading on the distal radius where cortical bone encloses the trabecular region. From several FE analyses on distal radius fracture (e.g. HR-pQCT with 82 μm resolution, Vilayphiou et al. 2010), it is reported that the cortical part of the distal radius bears more load (i.e. stress) than the trabecular region and therefore acts as mechanical stabiliser by transmitting force into applied loading direction. Also, due to almost homogenous geometry of cortical bone, this region has narrow image greyscale distribution where using single value threshold technique results in accurate cortical microFE. Therefore, potential inaccurate mechanical predictions resulting from the impact of large voxel size on trabecular microFE were masked by the cortical dominance. In our study, the use of purely trabecular calcaneus microFE models confirms that HR-pQCTTH1 models do not sufficiently represent the accurate microstructure geometry, especially for specimens with low BV/TV (e.g. sample 5). In particular for such low-BV/TV samples, there were weak trabecular connectivities due to their insufficient voxel resolution; therefore, performing the single level threshold method resulted in the elimination of large amounts of microstructure that were visually realised (for example, see Fig. 4).
Although only five calcaneum cadaveric samples were used in this study, high variability in terms of architecture was found from one sample to another and yet the mechanical analysis was fairly consistent for all samples providing confidence that the main outcomes of this study are valid for any calcaneum trabecular bones.
Overall it was found that the morphology of XtremeCT I HR-pQCTTH1 models for calcaneus trabecular bone is significantly different to their corresponding microCT models. Due to wide greyscale distribution of HR-pQCT images, the final HR-pQCT-based microFE is very sensitive to single level threshold technique where the whole morphology and BV/TV can be affected by the chosen threshold. By analysing microCTRes and HR-pQCTTH1 models and both morphological and mechanical similarities between the two, it was found that voxel size has a dominant effect on the microFE quality when the single value threshold method is used for generating voxel-based microstructure. The mechanical simulation results showed significant difference between the predictions of gold-standard microCT and XtremeCT I HR-pQCTTH1 models that in average are 70% lower for von Mises stress, 64% lower for apparent stiffness and 33% lower for failure load prediction.
In conclusion, a single threshold value cannot predict both morphological structures (BV/TV) and biomechanical analyses (stress, apparent stiffness and failure load prediction) correctly. Since the resolution of XtremeCT I is not sufficient to resolve trabecular thickness, caution should be made to use it to monitor the effect of the progression of the disease or the effect of a bone drug if the target is, for example, bone remodelling since accurate trabecular thickness will not be achieved. Alternatively, employing more advanced segmentation strategies (e.g. local adaptive threshold method Burghardt et al. 2007) may improve the accuracy of HR-pQCT-based microstructures; nevertheless, a comprehensive geometrical and mechanical evaluation study is still required, in particular for the trabecular regions with small BV/TV values.
The authors acknowledge Margaret Paggiosi for operating the HR-pQCT scanner and the Skelet.Al Lab (in particular Kirsty Nicholson) for the help with the MicroCT scans. Funding from EPSRC (EP/K03877X/1), MRC and Arthritis Research UK as part of the MRC-Arthritis Research UK Centre for Integrated Research into Musculoskeletal Ageing (CIMA) and HEFCE Catalyst fund are acknowledged.
This study was funded by EPSRC (EP/K03877X/1).
Compliance with ethical standards
Conflict of interest
The authors declare that they have no conflict of interest.
- k-Wave: a MATLAB toolbox for the time-doamin simulation of acoustic wave fields (2015). http://www.k-wave.org. Accessed 18 Nov 2015
- Liu XS, Zhang XH, Sekhon KK, Adams MF, McMahon DJ, Bilezikian JP et al (2010) High-resolution peripheral quantitative computed tomography can assess microstructural and mechanical properties of human distal tibial bone. J Bone Miner Res 25(4):746–756Google Scholar
- Manzanera A, Bernard T, Preteux F, Longuet B (1999) Medial faces from a concise 3D thinning algorithm. In: IEEE international conference on computer vision (ICCV’99), pp 337–343Google Scholar
- McCloskey EV, Kanis JA, Oden A, Harvey NC, Bauer D, Gonzalez-Macias J, Hans D, Kaptoge S, Krieg MA, Kwok T, Marin F, Moayyeri A, Orwoll E, Gluer C, Johansson H (2015) Predictive ability of heel quantitative ultrasound for incident fractures: an individual-level meta-analysis. Osteoporos Int 26:1979–1987CrossRefGoogle Scholar
- Moisy F (2008) http://www.fast.u-psud.fr/~moisy/ml/. Accessed 18 Nov 2015
- Scanco Medical AG (1997) MicroCT 20 user’s guide, Software Revision 2.1, pp 54–55Google Scholar
- Stein EM, Kepley A, Walker M, Nickolas TL, Nishiyama K, Zhou B, Liu XS, McMahon DJ, Zhang CY, Boutroy S, Cosman F, Nieves J, Guo XE, Shane E (2014) Skeletal structure in postmenopausal women with osteopenia and fractures is characterized by abnormal trabecular plates and cortical thinning. J Bone Miner Res 29(5):1101–1109CrossRefGoogle Scholar
- Van Rietbergen B, Weinans H, Huiskes R, Odgaard A (1995) A new method to determine trabecular bone elastic properties and loading using micromechanical finite-element models. J Biomech 28:69–81Google Scholar
- Zhou B, Wang J, Yu EY, Zhang Z, Nawathe S, Nishiyama KK, Rey Rosete F, Keaveny TM, Shane E, Guo XE (2016) High-resolution peripheral quantitative computed tomography (HR-pQCT) can assess microstructural and biomechanical properties of both human distal radius and tibia: ex vivo computational and experimental validations. Bone 86:58–67CrossRefGoogle Scholar
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