Effect of Image Resolution on the Accuracy of Trabecular Morphology and the Convergence Behavior of Micro-CT Finite Element Models of Mouse Bone

INTRODUCTION High resolution images from micro-computed tomography (microCT) have been an important tool for quantifying trabecular morphology and the mechanical behavior of bone. The accuracy of these measures are heavily dependent on image resolution [1], which determines the Nyquist frequency (highest spatial frequency encoded in the image) and translates to element size when using voxel based finite element (FE) models. An insufficient image resolution will introduce partial volume and aliasing artifacts into the image that can affect micro-structural details and thus influence FE model behavior. Similarly, the additional degrees of freedom associated with smaller elements will improve FE model accuracy, but the computation requirements may be excessive. Therefore, the purpose of this study was to determine the influence of image resolution on trabecular architectural details and the convergence behavior of micro-CT based finite element models of mouse bone. METHODS Six tibiae of C57BL/6 mice (age: 20 weeks, tibia length: 17.9±0.17mm) were imaged using a micro-CT scanner (Scanco 40Scanco Medical AG, Switzerland) with a 20 m isometric voxel size. Axial images were re-oriented along the long axis of the bone, resampled at 20m, 30m, 40m and 60m voxel-size, and segmented using Mimics 13.1 software (Materialise, Leuven, Belgium). Trabecular bone in the mouse tibia is mainly concentrated at the proximal end. Hence, the proximal 4 mm was selected for analysis. A custom written code in Matlab (The Mathworks, Inc., Natick, MA) was used to directly convert segmented images into voxel-based FE models. The models consisted of 8-node linear hexahedral elements that were assigned linearly-elastic isotropic material properties with a Young’s modulus of 18GPa and a Poisson’s ratio of 0.4 [2]. The proximal 1 mm section of the model was loaded to10 N and nodes of a 200 μm section at the distal end of the model were fully constrained. A load of 10 N was chosen to simulate in-vivo loading models used in our lab [3]. The compressive force was directed towards the centroid of the distal constrained nodes. The model was solved using Abaqus 6.10 (Simulia. Providence, RI) on an 8 core system with 16 GB of RAM. The whole bone (excluding the loaded and constrained nodes) and two 120m transverse sections that included both trabecular bone (section 1) and cortical shell (sections 1 and 2) were selected to analyze the output parameters of Von-Mises stress and strain. Apparent stiffness of the entire model was calculated as the applied load/displacement. A model was considered to be converged if the differences in output parameters were less than 5% compared to the 20 m model. Three-dimensional morphological analyses of trabecular bone were performed using BoneJ [4]. A one mm transverse section of trabecular bone was extracted immediately distal to the growth plate for all bones and voxel-sizes. Architectural parameters of interest included trabecular thickness (Tb.Th), number (Tb.N), and degree of anisotropy (DA). RESULTS Decreasing image resolution had a minor influence on the bone’s mechanical behavior. The output parameters from the FE models changed a maximum of 4% going from a 20 m voxel-size to a 60 m voxel-size (Figure 1). Since the elements were assigned linear-elastic isotropic material properties, Von Mises stresses and strains changed similarly, thus only strains are reported here. As anticipated image resolution had a large effect on the number of elements, nodes and the run time of the model simulation (Table 1). Decreasing the image resolution resulted in an increase in Tb.Th., a decrease in Tb.N and a decrease in DA (Table 2). For example, Tb.Th. increased by 7.5% for the 30 m voxel-size compared to the 20 m voxel-size.