Multiscale modeling of bone fracture using cohesive finite elements
Highlights
► Most effective fracture toughening resulted from lower cement line strength. ► Lower cement line strength reduced the propensity to fracture at the macroscale. ► Evaluating microscale properties improves whole bone fracture risk assessment.
Introduction
Bone is a hierarchical material that exhibits fracture mechanisms at multiple length scales ranging from nano- to macroscale [1], [2]. In order to gain a full understanding of the fracture behavior of bone and for reliable bone fracture risk assessment it is necessary to gain insight into the underlying fracture mechanisms at each length scale.
Fracture toughness and strength of bone have been shown to be influenced by microstructural parameters including size and density of osteons as well as intracortical porosity [3], [4], [5], [6], [7]. Microstructural features such as osteons and cement lines (Fig. 1) play an important role in determining the crack growth trajectory in cortical bone [8], [9], [10], [11], [12], [13], [14], [15], [16], [17]. Cracks that penetrate osteons may lead to complete failure of the bone. On the other hand, cracks that are deflected into cement lines slow down the crack propagation and increase the crack resistance of the bone. In addition, the crack deflection mechanism by cement lines becomes less effective with aging which may account for the reduction in fracture toughness of bone with age [14], [18]. These mechanisms observed at the microscale are expected to significantly affect the macroscale fracture behavior of bone. Furthermore, direction of crack growth significantly influences the fracture toughness of bone as a result of its interaction with the microstructural features during formation and growth [13], [15], [19], [20], [21], [22]. Crack growth that is perpendicular to the direction of osteons (transverse direction) leads to higher fracture toughness than parallel to the direction of osteons (longitudinal direction). The influence of the material level changes in the microstructural features of the bone and its interaction with especially transverse crack growth, which is the clinically relevant fracture mode, can provide a better understanding of the fracture behavior of bone at the macroscale.
The propensity to form a macroscale crack increases the fracture risk of individuals even during low energy falls. Recently, distal forearm has been determined as an early detection site of fracture risk based on the findings that show that distal forearm fracture is a predictor of future hip and spine fractures [23], [24]. As a result, evaluation of the influence of lower length scales on distal forearm fracture may provide new information for patient-specific fracture risk assessment.
In light of the studies presented in the literature, in the current study, we investigate the influence of bone microstructure on macroscale fracture using a computational fracture mechanics approach based on cohesive finite element modeling. Fracture mechanics has been widely used for the assessment of bone fracture in experimental evaluations [13], [15], [25], [26]. The experimental studies provide important insight into the fracture behavior of bone, however, due to the variability between donor bones used in testing, it is not possible to isolate the effect of individual factors on bone fracture. Unlike experimental studies, the use of computational approaches enables controlled evaluation of the effects of a single parameter on the fracture response of bone. This controlled evaluation makes it possible to elucidate the interaction of different length scales and how lower length scale properties can influence the higher length scales in bone fracture.
Finite element studies performed on micro- or macroscale models of bone mostly focused on either linear elastic fracture mechanics or strength-based analysis [27], [28], [29], [30], [31], [32], [33], [34]. Although cohesive modeling has been widely used in various engineering disciplines, it has recently been applied to bone fracture [35], [36], [37], [38], [39]. A fracture process zone forms during the crack formation and propagation in bone, therefore, cohesive models are appropriate for characterizing bone fracture by capturing the behavior in the process zone.
The current study focuses on the isolated effects of microstructural features of bone and provides information that cannot be directly measured by experiments. Primarily, the investigations were carried at two length scales, namely, micro- and macroscale. The simulations evaluate the influence of microstructural material properties on microscale fracture behavior and fracture toughness. In addition, we assess distal forearm fracture at the macroscale based on simulation results obtained using a representative volume at the microscale level. These investigations are carried out in three parts. The first study focuses on the two-dimensional (2D) evaluation of finite element models created based on human cortical bone microscopy images to determine the influence of cement line properties on the microcrack propagation path (Section 2.1 Microscale bone fracture modeling of 2D human microscopy images, 3.1 2D microscale human bone models). This study lays the foundation for the second part that utilizes three-dimensional (3D) finite element models to determine the effect of microscale material properties of bone on macroscale fracture toughness using a compact tension (CT) specimen incorporating a detailed bone microstructure section (Section 2.2 3D microscale CT specimen fracture modeling, 3.2 3D microscale CT specimen models). The last part of the study evaluates the distal forearm fracture using idealized models of radius bone based on the mechanical properties extracted from the microscale models (Section 2.3 Macroscale bone fracture modeling of 3D idealized human radius bone, 3.3 3D idealized human radius bone models).
Section snippets
Microscale bone fracture modeling of 2D human microscopy images
Human microscopy images with dimensions of 1.17 mm × 0.89 mm obtained from middiaphysis of tibiae of male donors (49 and 70-year-old) were utilized to create finite element models that represent varying microstructures of bone (number of osteons: 25 and 16, osteon area: 66% and 57%, respectively) (Fig. 1a and b). These models are denoted as Microstructure 1 and Microstructure 2 corresponding to 49 and 70-year-old donor bone, respectively. The images were converted to finite element models using
2D microscale human bone models
The first set of simulations investigated the effect of the cement line cohesive strength and toughness on the microscale crack growth behavior. The cohesive properties of the interstitial and osteonal bone were held constant and either the strength or fracture toughness of the cement line was varied. The relative cohesive properties of the cement line with respect to the surrounding bone altered the crack propagation path in both bone microstructures (Fig. 5a–f). When the cement line cohesive
Discussion
This study presented a multiscale approach to modeling bone fracture that related the microscale properties with macroscale fracture of bone. Two microscale studies were undertaken including crack growth in 2D human microscopy images and 3D compact tension specimen models detailing the microstructure of bone to evaluate the influence of microstructural features on crack growth in bone. The macroscale simulations evaluated the whole bone fracture load for distal forearm fracture utilizing the
Conclusions
The current study demonstrated the strength of cohesive modeling in simulating bone fracture at both micro- and macroscale. These simulations isolated individual effects of the microstructural features of bone that may contribute to bone fracture and provided information that cannot be directly measured by experiments.
The results obtained from micro and macroscale studies show that the most important mechanism that induces crack deflection mechanism in bone is the lower cement line strength
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