Elsevier

Bone

Volume 97, April 2017, Pages 65-75
Bone

Fast estimation of Colles' fracture load of the distal section of the radius by homogenized finite element analysis based on HR-pQCT

https://doi.org/10.1016/j.bone.2017.01.003Get rights and content

Highlights

  • A fast and accurate homogenized FE method for estimation of Colles' fracture load from XCT II images was validated

  • BV/TV and fabric from XCT II (61 and 82 μm) were calibrated with respect to a very high resolution μCT standard (16.4 μm)

  • The sensitivities of the predictions of failure load with respect to XCT II resolution were investigated for both μFE and hFE

  • The short term reproducibilities of BV/TV, fabric and the predictions of failure load from both hFE and μFE models were evaluated

Abstract

Fractures of the distal section of the radius (Colles' fractures) occur earlier in life than other osteoporotic fractures. Therefore, they can be interpreted as a warning signal for later, more deleterious fractures of vertebral bodies or the femoral neck. In the past decade, the advent of HR-pQCT allowed a detailed architectural analysis of the distal radius and an automated but time-consuming estimation of its strength with linear micro-finite element (μFE) analysis. Recently, a second generation of HR-pQCT scanner (XtremeCT II, SCANCO Medical, Switzerland) with a resolution beyond 61 μm became available for even more refined biomechanical investigations in vivo. This raises the question how biomechanical outcome variables compare between the original (LR) and the new (HR) scanner resolution. Accordingly, the aim of this work was to validate experimentally a patient-specific homogenized finite element (hFE) analysis of the distal section of the human radius for the fast prediction of Colles' fracture load based on the last generation HR-pQCT. Fourteen pairs of fresh frozen forearms (mean age = 77.5±9) were scanned intact using the high (61 μm) and the low (82 μm) resolution protocols that correspond to the new and original HR-pQCT systems. From each forearm, the 20 mm most distal section of the radius were dissected out, scanned with μCT at 16.4 μm and tested experimentally under compression up to failure for assessment of stiffness and ultimate load. Linear and nonlinear hFE models together with linear micro finite element (μFE) models were then generated based on the μCT and HR-pQCT reconstructions to predict the aforementioned mechanical properties of 24 sections. Precision errors of the short term reproducibility of the FE analyses were measured based on the repeated scans of 12 sections. The calculated failure loads correlated strongly with those measured in the experiments: accounting for donor as a random factor, the nonlinear hFE provided a marginal coefficient of determination (Rm2) of 0.957 for the high resolution (HR) and 0.948 for the low resolution (LR) protocols, the linear hFE with Rm2 of 0.957 for the HR and 0.947 for the LR protocols. Linear μFE predictions of the ultimate load were similar with an Rm2 of 0.950 for the HR and 0.954 for the LR protocols, respectively. Nonlinear hFE strength computation led to precision errors of 2.2 and 2.3% which were higher than the ones calculated based on the linear hFE (1.6 and 1.9%) and linear μFE (1.2 and 1.6%) for the HR and LR protocols respectively. Computation of the fracture load with nonlinear hFE demanded in average 6 h of CPU time which was 3 times faster than with linear μFE, while computation with linear hFE took only a few minutes. This study delivers an extensive experimental and numerical validation for the application of an accurate and fast hFE diagnostic tool to help in identifying individuals who may be at risk of an osteoporotic wrist fracture and to follow up pharmacological and other treatments in such patients.

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 BV/TVd=BMD1200, 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.

References (44)

  • R. Crawford et al.

    Finite element models predict in vitro vertebral body compressive strength better than quantitative computed tomography

    Bone

    (2003)
  • E. Dall’Ara et al.

    A nonlinear finite element model validation study based on a novel experimental technique for inducing anterior wedge-shape fractures in human vertebral bodies in vitro

    J. Biomech.

    (2010)
  • G. Maquer et al.

    Removal of the cortical endplates has little effect on ultimate load and damage distribution in QCT-based voxel models of human lumbar vertebrae under axial compression

    J. Biomech.

    (2012)
  • T.L. Mueller et al.

    Non-invasive bone competence analysis by high-resolution pQCT: an in vitro reproducibility study on structural and mechanical properties at the human radius

    Bone

    (2009)
  • S.L. Manske et al.

    Human trabecular bone microarchitecture can be assessed independently of density with second generation HR-pQCT

    Bone

    (2015)
  • A. Laib et al.

    Comparison of structure extraction methods for in vivo trabecular bone measurements

    Comput. Med. Imaging Graph.

    (1999)
  • P. Varga et al.

    HR-pQCT based FE analysis of the most distal radius section provides an improved prediction of Colles' fracture load in vitro

    Bone

    (2010)
  • A. Fedorov et al.

    3D Slicer as an image computing platform for the quantitative imaging network

    Magn. Reson. Imaging

    (2012)
  • P. Varga et al.

    Assessment of volume fraction and fabric in the distal radius using HR-pQCT

    Bone

    (2009)
  • H.S. Hosseini et al.

    μCT-based trabecular anisotropy can be reproducibly computed from HR-pQCT scans using the triangulated bone surface

    Bone

    (2017)
  • L.J. Melton et al.

    Fractures attributable to osteoporosis: report from the National Osteoporosis Foundation.

    J. Bone Miner. Res.

    (1997)
  • T.M. Keaveny

    Biomechanical computed tomography-noninvasive bone strength analysis using clinical computed tomography scans

    Ann. N Y Acad. Sci.

    (2010)
  • Cited by (0)

    View full text