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Research Papers

Interaction of Microcracks and Tissue Compositional Heterogeneity in Determining Fracture Resistance of Human Cortical Bone

[+] Author and Article Information
Ahmet Demirtas

Department of Mechanical Engineering,
Villanova University,
800 Lancaster Avenue,
Villanova, PA 19085
e-mail: ademirta@villanova.edu

Ani Ural

Department of Mechanical Engineering,
Villanova University,
800 Lancaster Avenue,
Villanova, PA 19085
e-mail: ani.ural@villanova.edu

1Corresponding author.

Manuscript received July 27, 2017; final manuscript received April 24, 2018; published online May 24, 2018. Assoc. Editor: Brian D. Stemper.

J Biomech Eng 140(9), 091003 (May 24, 2018) (10 pages) Paper No: BIO-17-1329; doi: 10.1115/1.4040123 History: Received July 27, 2017; Revised April 24, 2018

Recent studies demonstrated an association between atypical femoral fracture (AFF) and long-term bisphosphonate (BP) use for osteoporosis treatment. Due to BP treatment, bone undergoes alterations including increased microcrack density and reduced tissue compositional heterogeneity. However, the effect of these changes on the fracture response of bone is not well understood. As a result, the goal of the current study is to evaluate the individual and combined effects of microcracks and tissue compositional heterogeneity on fracture resistance of cortical bone using finite element modeling (FEM) of compact tension (CT) specimen tests with varying microcrack density, location, and clustering, and material heterogeneity in three different bone samples. The simulation results showed that an increase in microcrack density improved the fracture resistance irrespective of the local material property heterogeneity and microcrack distribution. A reduction in material property heterogeneity adversely affected the fracture resistance in models both with and without microcracks. When the combined changes in microcrack density and tissue material property heterogeneity representing BP treatment were evaluated, the models corresponding to BP-treated bone demonstrated reduced fracture resistance. The simulation results also showed that although microcrack location and clustering, and microstructure significantly influenced fracture resistance, the trends observed on the effect of microcrack density and tissue material property heterogeneity did not change. In summary, these results provide new information on the interaction of microcracks, tissue material property heterogeneity, and fracture resistance and may improve the understanding of the influence of mechanical changes due to prolonged BP use on the fracture behavior of cortical bone.

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Figures

Grahic Jump Location
Fig. 1

Transverse microscopy images of human cortical bone from the mid-diaphysis of the tibiae of male donors (a) 58-year-old (model A), (b) 70-year-old (model B) and (c) 81-year-old (model C). Different colors in (a)–(c) are due to staining applied to the bone for different histomorphometry analyses. The black lines on the images are tissue preparation artifacts and do not represent real cracks. Three-dimensional (3D) model of the transverse microscopy images of (d) model A, (e) model B, and (f) model C. (g) Finite element model of the CT specimen. The “x” shows the fixed boundary condition applied to the specimen and the arrows show the displacement boundary condition on loading pins. The circled region shows the location where the detailed microstructure region was inserted. The microstructure is assembled in the CT specimen such that osteons are parallel to the z-axis.

Grahic Jump Location
Fig. 2

Microcracks with different sizes and locations in (a) model A, (b) model B, and (c) model C. (d) Microcracks with identical size and location in all models demonstrated in Model A. Note that the exact same microcrack sizes and locations were also incorporated in models B and C as in model A. Blue colored lines show the location of microcracks for the models with 5 microcracks/mm2. Blue and red colored lines show the location of microcracks for models with the 10 microcracks/mm2. Clustered microcracks in model A (e) near the edge and (f) around the center. The red circles show the regions where the clustered microcracks are located.

Grahic Jump Location
Fig. 3

Traction (T)—crack opening displacement (δ) relationship defining the cohesive model. In the graph, σc, δu, and Gc correspond to the critical strength, ultimate crack opening displacement, and critical energy release rate, respectively. Note that the initial ascending line shown in dotted line is used only in the interface element formulation and is not required for the XFEM formulation.

Grahic Jump Location
Fig. 4

Total crack volume comparison of models A, B, and C with identical and different microcrack locations and sizes incorporating 5 and 10 microcracks/mm2 and homogeneous and heterogeneous material property distributions. Clustered microcrack results for model A are also presented. The values were normalized based on the highest crack volume among the models.

Grahic Jump Location
Fig. 5

Total damage energy density comparison of models A, B, and C with identical and different microcrack locations and sizes incorporating 5 and 10 microcracks/mm2 and homogeneous and heterogeneous material property distributions. Clustered microcrack results for model A are also presented. The values were normalized based on the highest crack damage energy density volume among the models.

Grahic Jump Location
Fig. 6

Representative planar view of crack growth for model A with (a) 10, (b) 5, and (c) zero microcracks with homogeneous (HM) and heterogeneous (HT) material properties and two different microcrack distributions (I, D) and (d) clustered microcracks that are near the edge (HMC1) and near the center (HMC2). The colors represent the damage accumulation in a rainbow contour where red is full crack and dark blue represents the lowest damage. The regions shown by light and dark gray elements correspond to no damage accumulation in interstitial bone and osteons, respectively. The dashed circles show the borders of damaged/fractured osteons. The crack growth direction is shown with dashed arrows.

Grahic Jump Location
Fig. 7

Comparison of (a) total crack volume and (b) damage energy density between 5HT and 10 HM models for both microcrack distributions and for all three microstructures representing non-BP treated (BP-) and BP-treated (BP+) bones, respectively

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