Fast estimation of Colles' fracture load of the distal section of the radius by homogenized finite element analysis based on HR-pQCT
Graphical Abstract
Introduction
Colles' fractures often caused by a so-called FOOSH (fall on outstretched hand) occur earlier in life than other more life threatening fractures, such as femoral neck and spine fractures [1], [2]. Therefore, it is sensible to use the noninvasive finite element (FE) analysis predictions of Colles' fracture load as an advanced, more accurate and reproducible diagnostic tool for osteoporosis and for longitudinal follow-up of pharmacological or exercise therapies.
Quantitative computed tomography-based finite element (QCT-based FE) analysis enables the in vivo prediction of the mechanical properties of bones with the highest coefficients of determination [3]. The standard FE approach in predicting bone's mechanical properties is continuum voxel-based FE models. In this technique, the QCT scan of the bone is coarsened to 1–3 mm isotropic hexahedron finite elements and the local mechanical properties of the bone, such as stiffness and yield properties are derived from the bone density of the coarsened voxel elements [4], [5]. This approach assumes isotropic properties for the bone and does not account for its trabecular micro-architecture. A more recent technique is high resolution peripheral quantitative computed tomography or HR-pQCT-based linear μFE modeling of the bone, which is the current standard to assess the fracture load of the distal section of the radius [6]. This technique converts the bone voxels of a segmented high resolution CT image into linear hexahedral or tetrahedral elements and can predict the stiffness of the bone using a linear elastic constitutive law [7], [8]. However, linear μFE does not enable direct computation of bone's failure load due to the nonlinear cracking response of bone prior to failure. These models use therefore other criteria such as strain or energy density based quantities to estimate the failure load of the bone, which are less accurate and require calibration for each specific application [6], [9]. Whereas non-linear μFE analyses are possible and predict the bone's yield properties more accurately [10], [11], [12], [13], the computational costs of such analyses are currently very high.
Alternatively, QCT-based homogenized finite element (hFE) models overcome the downsides of the isotropic voxel-based continuum and the μFE models. The hFE models homogenize the structural properties of the bone such as the bone volume over total volume (BV/TV) and the trabecular orientation (fabric anisotropy) inside a predefined volume element (VE) and map these properties to the continuum elements at the macroscopic level [14], [15], [16]. They can predict the stiffness and the failure load of the bone using nonlinear material models with less computational resources in less time [17], [18], [19] than μFE models. Recent studies showed that BV/TV and fabric anisotropy predict more than 97% of bone's elastic and yield properties [20], [21]. Keeping this in mind, HR-pQCT provides detailed insight into the inner micro-architecture of the bone at a homogeneous voxel size of 82 μm [22], [23], [24]. The second generation of the HR-pQCT scanner (XtremeCT II, SCANCO Medical AG, Switzerland) enables in vivo reconstructions of the distal section of the radius at higher resolution ( <61 μm), only slightly higher ionizing dose and reduced scan time compared to its predecessor [25]. In a previous study, Varga et al. [26] used HR-pQCT reconstructions of the distal section of the radius based on the first generation XtremeCT to validate experimentally hFE models in predicting Colles' fracture load (R2 = 0.94). The bones were scanned without the attached soft tissues, the resolution sensitivity of the numerical models as well as the reproducibility of the technique were not addressed.
The new XtremeCT II scanner enables clinical scanning of the human forearm at 61 μm, denoted as HR (high resolution) and at 82 μm, denoted as LR (low resolution) which is fully compatible with the one used in the original XtremeCT scanner. The HR protocol provides more accurate 3D reconstructions of the bone's micro-architecture than the LR protocol; however, it requires longer scan time as well as slightly higher radiation dose (5 versus 3 μSv). Although, the higher resolution is clearly beneficial for morphological analyses of trabecular bone structure, it remains unknown if it can significantly enhance the FE predictions of the bone's fracture load and improve their reproducibility compared with the LR protocol.
The major aims of this work were to:
- (1)
Validate experimentally a fast and accurate patient-specific estimation of fracture load based on XtremeCT II reconstructions of the distal section of the forearm including soft tissues,
- (2)
Calibrate the key input variables for hFE analysis, namely BV/TV and fabric, retrieved from HR-pQCT for both LR and HR protocols with respect to a high resolution (16.4 μm) μCT scan,
- (3)
Investigate the sensitivity of the μFE/hFE predictions of stiffnesses and failure loads to the alteration of the nominal voxel size of the CT reconstructions, and
- (4)
Evaluate the short term reproducibility of BV/TV, fabric and the resulting predictions of stiffness and failure loads from μFE and hFE models.
Section snippets
Materials and methods
The overall design of the study is summarized in Fig. 1 and each part is described in the next sections.
BV/TV and fabric anisotropy calibration
Strong correlations were found for BV/TV of the gray level images obtained with HR-pQCT using both HR and LR protocols, and the segmented μCT images at 16.4 μm nominal voxel size (Fig. 3). It was observed that the method proposed in [33] to calculate the BMD based bone volume fraction, namely , is a good approximation. However, the BV/TVd values of HR-pQCT systematically underestimated the BV/TV values of μCT. To account for this shift, a linear calibration was sufficient.
Discussion
A fast patient-specific hFE methodology was developed and validated to predict Colles' fracture load from the images of a second generation XtremeCT II scanner, using two scanning protocols: HR with a nominal voxel size of 61 μm and LR which is the compatibility mode of its predecessor XtremeCT with a voxel size of 82 μm. The failure load predictions obtained here with the LR protocol are very close to those reported for the first generation XtremeCT for both μFE (R2 = 0.95) and hFE (R2 = 0.94)
Conclusion
Both HR and LR scanning protocols and both μFE and hFE models showed high potential in the prediction of the ultimate load of the distal section of the radius. In comparison to the current linear μFE state-of-the-art, the nonlinear hFE exhibits comparable predictive accuracy, computes three times faster but shows slightly degraded reproducibility (2.2–2.3 % versus 1.2–1.6 % for μFE). Surprisingly, the linear hFE method is as accurate as the nonlinear hFE predictions, but is more reproducible
Acknowledgment
This research was made possible through funding (grant no 14311.1 PFLS-LS) obtained from the Swiss Commission for Technology and Innovation CTI. The authors would like to thank Mrs Jarunan Panyasantisuk for providing the material constants of the stiffness tensor and the initial yield surface and Dr Peter Varga and Mr Vimal Chandral for providing the image registration routines, used in the current work.
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