PSI - Issue 28

Juan Du et al. / Procedia Structural Integrity 28 (2020) 577–583 J. Du et al./ Structural Integrity Procedia 00 (2019) 000–000

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extensively used to predicting the change of bone structure and density. Still, mechanical properties of trabecular bone are needed as an input for FE models. These properties were correlated with bone mineral density (BMD), which can be estimated from an average Hounsfield unite in the CT scans. Anisotropy of bone has also a strong influence on its elastic behaviour, therefore, an approximate and simple way of obtaining a BMD distribution from CT scans was used in the bone remodelling model [5]. Simulations of bone remodelling resulted in a map of BMD, obtained from the loads applied. Some studies demonstrated that the resorption of bone mineral was effectively inhibited due to new bone formation at the site with peak strain magnitude [6][7]. So, normal strain was implemented as a feedback mechanism stimulus into computational models, gradually evolving the bone density in anatomically discretised regions of a single cortical bone shaft based on the unique regional strain stimuli [8]. Such simulations used to start from a homogenous distribution, but a trend of using inhomogeneous material distributions claimed to be more realistic. Several simulation studies employed the density distribution rather than the traditional homogenous material to predict the bone remodelling process. The inhomogeneous BMD distribution is in turn, a result of the related loading environment [9]. However, the effect of initial distribution of BMD on the simulation of trabecular bone remodelling is still unknown. To achieve this, an inhomogeneous (multi-material) model based on GV distribution of the CT scan data was proposed to evaluate the effect of initial material distribution on the local remodelling process in trabecular bone. The aim of this study was to investigate the effect of different initial density distributions as an input in the finite-element model on the structural-functional relationship of trabecular bone. The focus of this work was to evaluate the importance of using inhomogeneous material property distribution in the bone remodelling simulation, rather than to obtain a more realistic bone density distribution in the femur. 2. Materials and Methods 2.1. Model Development A bovine femoral head was scanned at 60 µm resolution using a micro-computed tomography (µ-CT) XT-H-160Xi scanner (Nikon metrology). A region of interest with a side length of 5 mm was extracted digitally from the trabecular region of a CT scan. A FE model was constructed based on our recently published two-phase finite-element model [3]. Briefly, a 60 µm voxel mesh was resampled, with a number of elements of 663,264 while maintaining the accuracy and morphological features of trabeculae (Table 1). Inhomogeneous material properties such as the Young’s modulus and BMD were calculated according to the GV distribution. BMD of the bone region was given ranging from 1.35 g/cm 3 to 1.47 g/cm 3 [10] , with the relative Young’s modulus based on the relationship proposed by Currey [11]: (1) Here, � � is BMD in element i at simulation time t , the exponent parameter b was set to 1.54, and C e (MPa) is a constant governing the relationship between the elastic modulus and density set at 4621.84. The processes for image segmentation and assigning inhomogeneous material properties were accomplished using Materialise Mimics Innovation Suite 19 (Materialise, Leuven, Belgium). The non-bone region was assigned to have a very low module of elasticity - 3 MPa - with the Poisson's ratio of 0.17, respectively, which had a negligible effect on the overall structural integrity of the trabecular structure. The load applied to the model was uniaxial compressive strain of 1% at the top surface of the bone region, (Fig. 1) and the encastre constraint was applied at the bottom surface. Abaqus 6.14 software (Dassault Systems Simulia Crop, Providence, RI, USA) was used for the simulation on a desktop workstation (HP Z440). 2.2. Mechanostat Model for Bone Remodelling The remodelling algorithm used in this study was adapted from the well-known and widely used mechano-state theory [13]. This theory describes the adaptation process of bone with a trilinear curve based on different levels of ( ) i i b E C  e t  .