The influence of microstructure on crack propagation in cortical bone at the mesoscale.

The microstructure of cortical bone is key for the tissue's high toughness and strength and efficient toughening mechanisms have been identified at the microscale, for example when propagating cracks interact with the osteonal microstructure. Finite element models have been proposed as suitable tools for analyzing the complex link between the local tissue structure and the fracture resistance of cortical bone. However, previous models that could capture realistic crack paths in cortical bone were due to the required computational effort limited to idealized osteon geometries and small (<1 mm2) model domains. The objective of this study was therefore to bridge the gap between experimental and numerical analysis of crack propagation in cortical bone by introducing image-based models at the mesoscale. Tissue orientation maps from high-resolution micro-CT images were used to define the distribution and orientation of weak interfaces in the models. Crack propagation was simulated using the extended finite element method in combination with an interface damage model, previously developed to simulate crack propagation in microstructural osteon models. The results showed that image-based mesoscale models can be used to capture interactions between cracks and microstructure. The simulated crack paths predicted the general trends seen in experiments with more irregular patterns for cracks propagating perpendicular compared to parallel to the osteon orientation. In all, the proposed method enabled an efficient description of the tissue level microstructure, which is a necessity to predict realistic crack paths in cortical bone and is an important step towards simulating crack propagation in bone models in 3D.

Age-related properties at the microscale affect crack propagation in cortical bone.

The increased risk for fracture with age is associated not only with reduced bone mass but also with impaired bone quality. At the microscale, bone quality is related to porosity, microstructural organization, accumulated microdamage and intrinsic material properties. However, the link between these characteristics and fracture behavior is still missing. Bone tissue has a complex structure and as age-related compositional and structural changes occur at all hierarchical length scales it is difficult to experimentally identify and discriminate the effect of each mechanism. The aim of this study was therefore to use computational models to analyze how microscale characteristics in terms of porosity, intrinsic toughness properties and microstructural organization affect the mechanical behavior of cortical bone. Tensile tests were simulated using realistic microstructural geometries based on microscopy images of human cortical bone. Crack propagation was modelled using the extended finite element method where cement lines surrounding osteons were modelled with an interface damage law to capture crack deflections along osteon boundaries. Both increased porosity and impaired material integrity resulted in straighter crack paths with cracks penetrating osteons, similar to what is seen experimentally for old cortical bone. However, only the latter predicted a more brittle failure behavior. Furthermore, the local porosity influenced the crack path more than the macroscopic porosity. In conclusion, age-related changes in cortical bone affect the crack path and the mechanical response. However, increased porosity alone was not driving damage in old bone, but instead impaired tissue integrity was required to capture brittle failure in aging bone.

Crack propagation in cortical bone is affected by the characteristics of the cement line: a parameter study using an XFEM interface damage model.

Bulk properties of cortical bone have been well characterized experimentally, and potent toughening mechanisms, e.g., crack deflections, have been identified at the microscale. However, it is currently difficult to experimentally measure local damage properties and isolate their effect on the tissue fracture resistance. Instead, computer models can be used to analyze the impact of local characteristics and structures, but material parameters required in computer models are not well established. The aim of this study was therefore to identify the material parameters that are important for crack propagation in cortical bone and to elucidate what parameters need to be better defined experimentally. A comprehensive material parameter study was performed using an XFEM interface damage model in 2D to simulate crack propagation around an osteon at the microscale. The importance of 14 factors (material parameters) on four different outcome criteria (maximum force, fracture energy, crack length and crack trajectory) was evaluated using ANOVA for three different osteon orientations. The results identified factors related to the cement line to influence the crack propagation, where the interface strength was important for the ability to deflect cracks. Crack deflection was also favored by low interface stiffness. However, the cement line properties are not well determined experimentally and need to be better characterized. The matrix and osteon stiffness had no or low impact on the crack pattern. Furthermore, the results illustrated how reduced matrix toughness promoted crack penetration of the cement line. This effect is highly relevant for the understanding of the influence of aging on crack propagation and fracture resistance in cortical bone.

An interface damage model that captures crack propagation at the microscale in cortical bone using XFEM.

Reliable tools for fracture risk assessment are necessary to handle the challenge with an aging population and the increasing occurrence of bone fractures. As it is currently difficult to measure local damage parameters experimentally, computational models could be used to provide insight into how cortical bone microstructure and material properties contribute to the fracture resistance. In this study, a model for crack propagation in 2D at the microscale in cortical bone was developed using the extended finite element method (XFEM). By combining the maximum principal strain criterion with an additional interface damage formulation in the cement line, the model could capture crack deflections at the osteon boundaries as observed in experiments. The model was used to analyze how the Haversian canal and the interface strength of the cement line affected the crack trajectory in models depicting osteons with three different orientations in 2D. Weak cement line interfaces were found to reorient the propagating cracks while models with strong interfaces predicted crack trajectories that penetrated the cement line and propagated through the osteons. The presented model is a promising tool that could be used to analyze how local, age-related material changes influence the crack trajectory and fracture resistance in cortical bone.