Research paper
Deformable image registration and 3D strain mapping for the quantitative assessment of cortical bone microdamage

https://doi.org/10.1016/j.jmbbm.2011.12.009Get rights and content

Abstract

The resistance to forming microcracks is a key factor for bone to withstand critical loads without fracturing. In this study, we investigated the initiation and propagation of microcracks in murine cortical bone by combining three-dimensional images from synchrotron radiation-based computed tomography and time-lapsed biomechanical testing to observe microdamage accumulation over time. Furthermore, a novel deformable image registration procedure utilizing digital volume correlation and demons image registration was introduced to compute 3D strain maps allowing characterization of the mechanical environment of the microcracks. The displacement and strain maps were validated in a priori tests. At an image resolution of 740 nm the spatial resolution of the strain maps was 10 μm (MTF), while the errors of the displacements and strains were 130 nm and 0.013, respectively. The strain maps revealed a complex interaction of the propagating microcracks with the bone microstructure. In particular, we could show that osteocyte lacunae play a dual role as stress concentrating features reducing bone strength, while at the same time contributing to the bone toughness by blunting the crack tip. We conclude that time-lapsed biomechanical imaging in combination with three-dimensional strain mapping is suitable for the investigation of crack initiation and propagation in many porous materials under various loading scenarios.

Graphical abstract

Highlights

Initiation and propagation of microcracks in murine cortical bone was investigated. ► Synchrotron radiation-based CT and time-lapsed biomechanical testing were combined. ► 3D strain maps based on an image registration procedure were introduced and validated. ► Osteocyte lacunae contribute to bone toughness by blunting the crack tip. ► This method can be used in many porous materials under various loading scenarios.

Introduction

As a precursor to bone fractures, the accumulation of microdamage strongly impacts bone mechanical competence in terms of both bone strength and toughness and its ability to withstand fractures (Launey et al., 2010). While the resistance of bone to microcracks primarily depends on ageing and metabolic diseases (Mori et al., 1997, Schaffler et al., 1995, Zimmermann et al., 2011), the exact mechanisms involved are unclear and subject to current research.

The initiation and propagation of microdamage in cortical bone can be investigated using a combination of nondestructive time-lapsed three-dimensional (3D) imaging and suitable biomechanical testing scenarios (Nazarian and Muller, 2004, Thurner et al., 2006). In particular, synchrotron radiation-based computed tomography (SR CT) can overcome the intrinsic limitations of two-dimensional imaging methods while achieving resolutions of 1 μm (Stampanoni et al., 2002) and beyond (Snigireva and Snigirev, 2006) to assess microcracks (Voide et al., 2009). Previous studies by Voide et al., 2011, Voide et al., 2009 were able to a describe microcrack initiation and propagation, while the quantification of displacements and strains has not been investigated.

In this study, we present a multi-stage procedure combining digital volume correlation (DVC) (Bay et al., 1999, Verhulp et al., 2004) to align regions in the images and demons deformable image registration (Thirion, 1998) to increase the localization (i.e. spatial resolution) of the strain maps, which allows for the analysis of the very local deformations around microcracks. In order to validate the procedure, the accuracy, precision and spatial resolution of the deformations and strains were assessed. Combined with time-lapsed imaging during the mechanical experiment, this method allows quantification of the 3D strain and deformation fields at initiation and during microcrack propagation. In particular, this study investigates the role of the cortical bone microstructure, such as osteocyte lacunae and larger canals, in the initiation and propagation of microcracks by measuring the local deformations and strains, and it addresses the validation of the strain mapping technique.

Section snippets

Materials

The left femurs from three mature female mice of the inbred strain C3H/He (C3H) were used in this study. At an age of 19 weeks the animals were sacrificed. The animals were stored at −20 °C and thawed at room temperature just before dissection of the femora. All animal procedures were reviewed and approved by the local authorities.

The femurs were prepared and imaged as previously described (Voide et al., 2009). In brief, the ends of the femurs were embedded in polymethyl methacrylate cement

Results

The validation of the strain maps quantified the precision of the displacement and strain maps as well as their respective resolutions. From the registration of the images that were homogenously displaced by 0.5 voxels, we found that the accuracy of the displacement map was 0.0006 voxels (0.4 nm) and the precision was 0.176 voxels (130 nm) as determined from the root-mean-square error (RMSE) of the displacements. The strain maps computed for imposed strains between 0.00 and 0.05 did show a

Discussion

In the present study, for the first time, deformable image registration was used to compute a 3D strain map for cortical bone microstructure. A novel procedure to calculate the 3D deformation and strain maps with a high spatial resolution was established to analyze time-lapsed tomographic images of the cortical bone microstructure. The method was validated and we found that at a nominal image resolution of 740 nm the spatial resolution of the strain maps was 10 μm (MTF), while the errors of the

Acknowledgment

Funding from the European Union for the osteoporotic virtual physiological human project (VPHOP FP7-ICT2008-223865) is gratefully acknowledged.

References (42)

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