PSI - Issue 42

Aleksandr Shalimov et al. / Procedia Structural Integrity 42 (2022) 1153–1158 A. Shalimov et al. / Structural Integrity Procedia 00 (2019) 000 – 000

1154

2

1. Introduction Trabecular bone is a cancellous porous tissue usually found at the ends of tubular bones; it performs supportive and load-bearing functions (Rincón-Kohli and Zysset, 2009), (Keaveny et al., 2001). Trabecular bone can be categorized as a bicontinuous open-cell material (Peña Fernández et al., 2021), in which a solid phase represents an interconnected network of hard plates and strands (ligaments). These ligaments form a strong and rigid skeleton, preventing bone damage at the attachment points of the tubular bones. Aging and human diseases related to low bone mass (e.g., osteopenia and osteoporosis) are characterized by a significant decrease in bone mineral density (BMD) and a transition from lamellar to rod-like trabecular microstructure as reported by Li et al. (2013).To reduce these risks and provide timely care, it is essential to fully understand the specific behavior of trabecular-bone fracture. The geometry of the bone structures was obtained using scans of human trabecular bones using the HR-pOCT (High-Resolution Peripheral Quantitative Computed Tomography) imaging technique. The results obtained in the previous modeling based on HR-pQCT data confirmed the validity of this approach to quantitative assessment of mechanical properties of bone tissue. However, less attention was given to the effect of mechanical material properties on simulated human trabecular bone fracture. The aim of this study is to evaluate the effect of tensile and compressive loads on the deterioration of bone properties using an elastic property degradation model, taking into account real morphological structure of bone tissue. For this purpose, a three-dimensional unit cell models of trabecular lattice were derived from HR-pQCT scans of the human distal tibia. The finite-element analysis (FEA) was implemented for these models, which were subject to tensile and compressive loading in elastic strain regime to predict the onset of damage accumulation and fracture in trabeculae. 2. Methodology 2.1. Processing HR-pQCT scans Unit cells replicating the structure of trabecular bone from the human distal tibia were considered (Smotrova et al., 2021). HR-pQCT is a technique that allows imaging of individual trabeculae with 82 μm resolution , providing an adequate assessment of microstructural parameters of trabecular bone. The trabecular-bone section was separated from other sections (such as cortical bone and bone marrow) by filtering to obtain a porous structure. The overall dimensions of the unit cells were 4 mm x 4 mm x 4 mm. Five different geometric models with nonrepeatable morphology were considered for analysis. The volume fraction of the porous phase for all the developed models lies within the range of 46% to 64%. 2.2. Model development The trabecular model was meshed employing a Dual Marching Cubes algorithm according to (Cohen-Or et al., 2000), with a global mesh element size of 0.06 mm using Mathematica software (Wolfram Research, Inc., Champaign, IL, USA) (Fig. 1). As a result, depending on the model, each model was meshed with approximately 600-700 thousand tetrahedral elements of C3D4 type (Table 1). The trabecular bone was modeled as an isotropic elastic material. The elastic parameters were assigned based on the data on mechanical properties obtained for individual trabeculae: Young's modulus E = 7600 MPa (Frank et al., 2017), Poisson's ratio ν = 0.3 (Gillard et al., 2014). Geometric models of the trabecular bone structure were converted into a finite-element analogue using a two-step discretization procedure (Fig. 1). The first step presumed transformation of geometrical model into a voxel finite element model; in the second step, the voxel model was transformed into a mesh of C3D4-type tetrahedral elements.

Table 1. Number of finite elements in studied FE models of structures

Structure Number of elements

1

2

3

4

5

690476

628556

643327

593276

631122