Introduction: In the present work, the fracture in microstructure of cortical bone with a high level of AGEs under cyclic loading is studied using phase-field method. We consider that the material properties of bone are subjected to change due to the high content of AGEs by reducing the fracture toughness of bone.
Materials and
Methods: Using two cadaveric female human tibias (ages: 60 and 81), we cut the cross-section at 50% of the mid-shaft length in each tibia to extract samples. The sample collection and preparation can be found in [1]. Through microscopy images and manual segmentation, twelve 2D plane strain models were created. With aging, AGEs levels in human cortical bone can be elevated, where a relationship with the decreased energy release rate (Gc) is suggested [2]. The cyclic loading condition is with a minimum load (Umin) of -0.002 mm and a maximum load (Umax) of 0.002 mm with a period of 2 seconds. We also assume three possible cases for the reduction in Gc for osteons and interstitial tissue of bone with an increase in AGE concentration as below: R_g=(G_ost-G_int)/G_ost x100% (1) where R_g can have the values 70, 50, and 15%.
Results, Conclusions, and Discussions: The activation or deactivation of toughening mechanisms in the cortical bone samples with increasing mismatch ratio due to elevated AGEs is reported (Fig. 1), and the fracture responses of the 60- and 81-year-old models under cyclic loading are compared (Fig. 2). Another finding in the study is that for some models (such as model 1), changes in the mismatch ratio do not significantly affect the crack growth trajectories. However, some other models (e.g. model 3) show the formation of the crack is dependent on changes in the mismatch ratio by increasing or decreasing the accumulation of damaged cement lines (Fig. 3).
Moreover, Fig.4 presents the changes in the lifetime of Model 1 by decreasing the amount of the cyclic load. As it can be seen and as expected, there is an increase in the number of cycles for Model 1 with decreasing the applied load.
The results of this study show that the activation and deactivation of toughening mechanisms can be dependent on the mismatch ratio between the fracture properties of cortical features due to high AGEs content. In addition, in studies on fatigue fracture of cortical bone with increased AGEs, the configuration of the microstructural features (e.g., shape and size of osteons) should be included in the fracture analyses. Furthermore, the fatigue lifetime of cortical samples can depend on the Haversian canals size and the degraded materials properties due to increased AGEs.
The current framework enables us to investigate the fracture response of bone under cyclic loading. This way we can get a perspective about parameters, such as toughening mechanisms in the microstructural scale, as well as stress fields, which are either not feasible to be done through experiments or if possible, they would be costly and time consuming. Additionally, a relation can be drawn between bone properties and damage parameters, such as post-yield absorbed energy, as medical diagnostics largely rely on bone mass density in evaluating the susceptibility of fracture.
Acknowledgements (Optional): The authors acknowledge the computing resources and support at Drexel University. We thank Mr. Josephson and Moore for the imaging of bone samples. We also thank Dr. L. Karim, Ms. T. Rezaee, Dr. T. A. Freeman for providing the cortical bone samples and the laboratory.
References: 1. Maghami E et al., Jour of Biom 2021;125:110600. 2. Tang S, et al.. Jour of Biom 2011;44(2):330–6.
