Anisotropy of age-related toughness loss in human cortical bone: a finite element study

Simulation analysis of surgical neck fractures of the humerus related to bone degeneration

The most common type of proximal humerus fracture is surgical neck fracture. The purpose of this paper is to study the mechanical mechanism and the effect of bone degeneration on humeral surgical neck fractures. The right humerus finite element models were established based on CT computed tomography. The stress values and crack propagation process under an axial force were obtained. Three indexes (mechanical property, cortical bone thickness of diaphysis and cancellous bone volume fraction) in this article were used to describe bone degeneration. The results showed that the three models group with different index had the same conclusions. The calculation results showed that the higher the bone degeneration level, the shorter the fracture time and the lower the fracture stress. The crack initiated from the medial side of the humerus, then gradually grew toward lateral side along the both sides, and finally broke. The medial crack was flat and single like "a thin line", while the lateral fracture of the humerus was irregular and crushed into fragments. The medial humerus cracks were generated by tensile stress, while the lateral cracks were generated by compressive stress. The thickness of humerus diaphysis might be used as the index of fracture risk due to direct readability from clinical images and quantitative relation of fracture risk. This article would provide reference data for the treatment and prevention of humeral surgical neck fracture.

Advanced Modeling Methods-Applications to Bone Fracture Mechanics

PURPOSE OF REVIEW

The goal of this review is to summarize recent advances in modeling of bone fracture using fracture mechanics-based approaches at multiple length scales spanning nano- to macroscale.

RECENT FINDINGS

Despite the additional information that fracture mechanics-based models provide over strength-based ones, the application of this approach to assessing bone fracture is still somewhat limited. Macroscale fracture models of bone have demonstrated the potential of this approach in uncovering the contributions of geometry, material property variation, as well as loading mode and rate on whole bone fracture response. Cortical and cancellous microscale models of bone have advanced the understanding of individual contributions of microstructure, microarchitecture, local material properties, and material distribution on microscale fracture resistance of bone. Nano/submicroscale models have provided additional insight into the effect of specific changes in mineral, collagen, and non-collagenous proteins as well as their interaction on energy dissipation and fracture resistance at small length scales. Advanced modeling approaches based on fracture mechanics provide unique information about the underlying multiscale fracture mechanisms in bone and how these mechanisms are influenced by the structural and material constituents of bone at different length scales. Fracture mechanics-based modeling provides a powerful approach that complements experimental evaluations and advances the understanding of critical determinants of fracture risk.

Modelling of bone fracture and strength at different length scales: a review

In this paper, we review analytical and computational models of bone fracture and strength. Bone fracture is a complex phenomenon due to the composite, inhomogeneous and hierarchical structure of bone. First, we briefly summarize the hierarchical structure of bone, spanning from the nanoscale, sub-microscale, microscale, mesoscale to the macroscale, and discuss experimental observations on failure mechanisms in bone at these scales. Then, we highlight representative analytical and computational models of bone fracture and strength at different length scales and discuss the main findings in the context of experiments. We conclude by summarizing the challenges in modelling of bone fracture and strength and list open topics for scientific exploration. Modelling of bone, accounting for different scales, provides new and needed insights into the fracture and strength of bone, which, in turn, can lead to improved diagnostic tools and treatments of bone diseases such as osteoporosis.

Identifying Novel Clinical Surrogates to Assess Human Bone Fracture Toughness

Fracture risk does not solely depend on strength but also on fracture toughness; ie, the ability of bone material to resist crack initiation and propagation. Because resistance to crack growth largely depends on bone properties at the tissue level, including collagen characteristics, current X-ray based assessment tools may not be suitable to identify age-related, disease-related, or treatment-related changes in fracture toughness. To identify useful clinical surrogates that could improve the assessment of fracture resistance, we investigated the potential of (1)H nuclear magnetic resonance spectroscopy (NMR) and reference point indentation (RPI) to explain age-related variance in fracture toughness. Harvested from cadaveric femurs (62 human donors), single-edge notched beam (SENB) specimens of cortical bone underwent fracture toughness testing (R-curve method). NMR-derived bound water showed the strongest correlation with fracture toughness properties (r = 0.63 for crack initiation, r = 0.35 for crack growth, and r = 0.45 for overall fracture toughness; p < 0.01). Multivariate analyses indicated that the age-related decrease in different fracture toughness properties were best explained by a combination of NMR properties including pore water and RPI-derived tissue stiffness with age as a significant covariate (adjusted R(2)  = 53.3%, 23.9%, and 35.2% for crack initiation, crack growth, and overall toughness, respectively; p < 0.001). These findings reflect the existence of many contributors to fracture toughness and emphasize the utility of a multimodal assessment of fracture resistance. Exploring the mechanistic origin of fracture toughness, glycation-mediated nonenzymatic collagen crosslinks and intracortical porosity are possible determinants of bone fracture toughness and could explain the sensitivity of NMR to changes in fracture toughness. Assuming fracture toughness is clinically important to the ability of bone to resist fracture, our results suggest that improvements in fracture risk assessment could potentially be achieved by accounting for water distribution (quantitative ultrashort echo time magnetic resonance imaging) and by a local measure of tissue resistance to indentation, RPI.

Crack propagation in bone on the scale of mineralized collagen fibrils: role of polymers with sacrificial bonds and hidden length

Sacrificial bonds and hidden length (SBHL) in structural molecules provide a mechanism for energy dissipation at the nanoscale. It is hypothesized that their presence leads to greater fracture toughness than what is observed in materials without such features. Here, we investigate this hypothesis using a simplified model of a mineralized collagen fibril sliding on a polymeric interface with SBHL systems. A 1D coarse-grained nonlinear spring-mass system is used to model the fibril. Rate-and-displacement constitutive equations are used to describe the mechanical properties of the polymeric system. The model quantifies how the interface toughness increases as a function of polymer density and number of sacrificial bonds. Other characteristics of the SBHL system, such as the length of hidden loops and the strength of the bonds, are found to influence the results. The model also gives insight into the variations in the mechanical behavior in response to physiological changes, such as the degree of mineralization of the collagen fibril and polymer density in the interfibrillar matrix. The model results provide constraints relevant for bio-mimetic material design and multiscale modeling of fracture in human bone.

Insights into reference point indentation involving human cortical bone: sensitivity to tissue anisotropy and mechanical behavior

Reference point indentation (RPI) is a microindentation technique involving 20 cycles of loading in "force-control" that can directly assess a patient׳s bone tissue properties. Even though preliminary clinical studies indicate a capability for fracture discrimination, little is known about what mechanical behavior the various RPI properties characterize and how these properties relate to traditional mechanical properties of bone. To address this, the present study investigated the sensitivity of RPI properties to anatomical location and tissue organization as well as examined to what extent RPI measurements explain the intrinsic mechanical properties of human cortical bone. Multiple indents with a target force of 10N were done in 2 orthogonal directions (longitudinal and transverse) per quadrant (anterior, medial, posterior, and lateral) of the femoral mid-shaft acquired from 26 donors (25-101 years old). Additional RPI measurements were acquired for 3 orthogonal directions (medial only). Independent of age, most RPI properties did not vary among these locations, but they did exhibit transverse isotropy such that resistance to indentation is greater in the longitudinal (axial) direction than in the transverse direction (radial or circumferential). Next, beam specimens (~2mm×5mm×40mm) were extracted from the medial cortex of femoral mid-shafts, acquired from 34 donors (21-99 years old). After monotonically loading the specimens in three-point bending to failure, RPI properties were acquired from an adjacent region outside the span. Indent direction was orthogonal to the bending axis. A significant inverse relationship was found between resistance to indentation and the apparent-level mechanical properties. Indentation distance increase (IDI) and a linear combination of IDI and the loading slope, averaged over cycles 3 through 20, provided the best explanation of the variance in ultimate stress (r(2)=0.25, p=0.003) and toughness (r(2)=0.35, p=0.004), respectively. With a transverse isotropic behavior akin to tissue hardness and modulus as determined by micro- and nano-indentation and a significant association with toughness, RPI properties are likely influenced by both elastic and plastic behavior of bone tissue.

Fracture analysis for biological materials with an expanded cohesive zone model

In this study, a theoretical framework for simulation of fracture of bone and bone-like materials is provided. An expanded cohesive zone model with thermodynamically consistent framework has been proposed and used to investigate the crack growth resistance of bone and bone-like materials. The reversible elastic deformation, irreversible plastic deformation caused by large deformation of soft protein matrix, and damage evidenced by the material separation and crack nucleation in the cohesive zone, were all taken into account in the model. Furthermore, the key mechanisms in deformation of biocomposites consisting of mineral platelets and protein interfacial layers were incorporated in the fracture process zone in this model, thereby overcoming the limitations of previous cohesive zone modeling of bone fracture. Finally, applications to fracture of cortical bone and human dentin were presented, which showed good agreement between numerical simulation and reported experiments and substantiated the effectiveness of the model in investigating the fracture behavior of bone-like materials.

Linear Elastic Analysis of Bovine Cortical Bone under Compression Loading

Linear elastic response of the bovine cortical bone has been examined under compression load. Experimental and computational methods were used to observe and predict the response of cortical bone. In computational method, two mechanical behaviors of isotropic and orthotropic were considered to simulate the cortical bone deformation. In experimental process, the specimens were designed to show maximum stiffness and strength by specifying osteon direction along loading axis during tests. The tests were controlled by displacement rate of 0.5 mm/minute and the overall stiffness responses of the structures were recorded to extract mechanical properties and also for validation aims. Finite Element Method (FEM) was used to model the linear response of the structure by using ABAQUS6.9EF. The FE results using orthotropic definition shows a good correlation with experimental data. A discussion was given based on overall stiffness and effective stress variation for both mechanical behaviors. In order to design the optimal implant structure, the presented study was proposed for prediction of bone structure deformation that attached to the orthopedic implants.

Micro-CT finite element model and experimental validation of trabecular bone damage and fracture

Most micro-CT finite element modeling of human trabecular bone has focused on linear and non-linear analysis to evaluate bone failure properties. However, prediction of the apparent failure properties of trabecular bone specimens under compressive load, including the damage initiation and its progressive propagation until complete bone failure into consideration, is still lacking. In the present work, an isotropic micro-CT FE model at bone tissue level coupled to a damage law was developed in order to simulate the failure of human trabecular bone specimens under quasi-static compressive load and predict the apparent stress and strain. The element deletion technique was applied in order to simulate the progressive fracturing process of bone tissue. To prevent mesh-dependence that generally affects the damage propagation rate, regularization technique was applied in the current work. The model was validated with experimental results performed on twenty-three human trabecular specimens. In addition, a sensitivity analysis was performed to investigate the impact of the model factors' sensitivities on the predicted ultimate stress and strain of the trabecular specimens. It was found that the predicted failure properties agreed very well with the experimental ones.

Extended Finite Element models of introcortical porosity and heterogeneity in cortical bone

Due to changes in the bone quality during ageing the fracture risk increases. The influence of the different parameters affecting bone quality is not well understood. The Finite Element method offers the opportunity to determine the individual contribution of a parameter by changing single parameters. In this study, the ABAQUS extended Finite Elements Method (xFEM) was applied to simulate the crack propagation in compact bone samples using the quadratic nominal stress as crack criterion. Micro computed tomography images of compact-tension samples machined from a 19 and an 81 years old donor were used to generate Finite Element meshes consisting of linear tetrahedrons via Mimics. Cavities were modelled only in the estimated crack area to avoid a high number of degrees of freedom. Crack area was meshed with a higher number of smaller elements. The other areas were meshed with a small number of larger elements. The changes in the material constants due to the simplification of the model were taken into account by using effective material parameters in these partitions. Our results show that age-related loss in bone toughness results from increased porosity and loss in heterogeneity of material level properties.

Interaction of microstructure and microcrack growth in cortical bone: a finite element study

Microstructural features including osteons and cement lines are considered to play an important role in determining the crack growth behaviour in cortical bone. This study aims to develop a computational mechanics approach to evaluate microscale fracture mechanisms in bone. In this study, finite element models based on actual human cortical bone images that allow for arbitrary crack growth were utilised to determine the crack propagation behaviour. The simulations varied the cement line and osteon strength and fracture toughness in different bone microstructures to assess the crack propagation trajectory, stress-strain relationship and nonlinear strain energy density. The findings of this study provide additional insight into the individual influence of microstructural features and their properties on crack growth behaviour in bone using a computational approach.

The effect of strain rate on fracture toughness of human cortical bone: a finite element study

Evaluating the mechanical response of bone under high loading rates is crucial to understanding fractures in traumatic accidents or falls. In the current study, a computational approach based on cohesive finite element modeling was employed to evaluate the effect of strain rate on fracture toughness of human cortical bone. Two-dimensional compact tension specimen models were simulated to evaluate the change in initiation and propagation fracture toughness with increasing strain rate (range: 0.08-18 s(-1)). In addition, the effect of porosity in combination with strain rate was assessed using three-dimensional models of micro-computed tomography-based compact tension specimens. The simulation results showed that bone's resistance against the propagation of a crack decreased sharply with increase in strain rates up to 1 s(-1) and attained an almost constant value for strain rates larger than 1 s(-1). On the other hand, initiation fracture toughness exhibited a more gradual decrease throughout the strain rates. There was a significant positive correlation between the experimentally measured number of microcracks and the fracture toughness found in the simulations. Furthermore, the simulation results showed that the amount of porosity did not affect the way initiation fracture toughness decreased with increasing strain rates, whereas it exacerbated the same strain rate effect when propagation fracture toughness was considered. These results suggest that strain rates associated with falls lead to a dramatic reduction in bone's resistance against crack propagation. The compromised fracture resistance of bone at loads exceeding normal activities indicates a sharp reduction and/or absence of toughening mechanisms in bone during high strain conditions associated with traumatic fracture.

The relative contributions of non-enzymatic glycation and cortical porosity on the fracture toughness of aging bone

The risk of fracture increases with age due to the decline of bone mass and bone quality. One of the age-related changes in bone quality occurs through the formation and accumulation of advanced glycation end-products (AGEs) due to non-enzymatic glycation (NEG). However as a number of other changes including increased porosity occur with age and affect bone fragility, the relative contribution of AGEs on the fracture resistance of aging bone is unknown. Using a high-resolution nonlinear finite element model that incorporate cohesive elements and micro-computed tomography-based 3d meshes, we investigated the contribution of AGEs and cortical porosity on the fracture toughness of human bone. The results show that NEG caused a 52% reduction in propagation fracture toughness (R-curve slope). The combined effects of porosity and AGEs resulted in an 88% reduction in propagation toughness. These findings are consistent with previous experimental results. The model captured the age-related changes in the R-curve toughening by incorporating bone quantity and bone quality changes, and these simulations demonstrate the ability of the cohesive models to account for the irreversible dynamic crack growth processes affected by the changes in post-yield material behavior. By decoupling the matrix-level effects due to NEG and intracortical porosity, we are able to directly determine the effects of NEG on fracture toughness. The outcome of this study suggests that it may be important to include the age-related changes in the material level properties by using finite element analysis towards the prediction of fracture risk.

Finite element modeling of the influence of hand position and bone properties on the Colles' fracture load during a fall

Distal forearm fracture is one of the most frequently observed osteoporotic fractures, which may occur as a result of low energy falls such as falls from a standing height and may be linked to the osteoporotic nature of the bone, especially in the elderly. In order to prevent the occurrence of radius fractures and their adverse outcomes, understanding the effect of both extrinsic and intrinsic contributors to fracture risk is essential. In this study, a nonlinear fracture mechanics-based finite element model is applied to human radius to assess the influence of extrinsic factors (load orientation and load distribution between scaphoid and lunate) and intrinsic bone properties (age-related changes in fracture properties and bone geometry) on the Colles' fracture load. Seven three-dimensional finite element models of radius were created, and the fracture loads were determined by using cohesive finite element modeling, which explicitly represented the crack and the fracture process zone behavior. The simulation results showed that the load direction with respect to the longitudinal and dorsal axes of the radius influenced the fracture load. The fracture load increased with larger angles between the resultant load and the dorsal axis, and with smaller angles between the resultant load and longitudinal axis. The fracture load also varied as a function of the load ratio between the lunate and scaphoid, however, not as drastically as with the load orientation. The fracture load decreased as the load ratio (lunate/scaphoid) increased. Multiple regression analysis showed that the bone geometry and the load orientation are the most important variables that contribute to the prediction of the fracture load. The findings in this study establish a robust computational fracture risk assessment method that combines the effects of intrinsic properties of bone with extrinsic factors associated with a fall, and may be elemental in the identification of high fracture risk individuals as well as in the development of fracture prevention methods including protective falling techniques. The additional information that this study brings to fracture identification and prevention highlights the promise of fracture mechanics-based finite element modeling in fracture risk assessment.

Aging and the reduction in fracture toughness of human dentin

An evaluation of the crack growth resistance of human coronal dentin was performed on tissue obtained from patients between ages 18 and 83. Stable crack extension was achieved over clinically relevant lengths (0< or = a < or =1mm) under Mode I quasi-static loading and perpendicular to the nominal tubule direction. Results distinguished that human dentin exhibits an increase in crack growth resistance with extension (i.e. rising R-curve) and that there is a significant reduction in both the initiation (K(o)) and plateau (K(p)) components of toughness with patient age. In the young dentin (18< or =age< or =35) there was a 25% increase in the crack growth resistance from the onset of extension (K(o)=1.34 MPa m(0.5)) to the maximum or "plateau" toughness (K(p)=1.65 MPa m(0.5)). In comparison, the crack growth resistance of the old dentin (55< or =age) increased with extension by less than 10% from K(o)=1.08 MPa m(0.5) to K(p)=1.17 MPa m(0.5). In young dentin toughening was achieved by a combination of inelastic deformation of the mineralized collagen matrix and microcracking of the peritubular cuffs. These mechanisms facilitated further toughening via the development of unbroken ligaments of tissue and posterior crack-bridging. Microstructural changes with aging decreased the capacity for near-tip inelastic deformation and microcracking of the tubules, which in turn suppressed the formation of unbroken ligaments and the degree of extrinsic toughening.

Prediction of Colles' fracture load in human radius using cohesive finite element modeling

Osteoporotic and age-related fractures are a significant public health problem. One of the most common osteoporotic fracture sites in the aging population is distal radius. There is evidence in the literature that distal radius fractures (Colles' fracture) are an indicative of increased risk of future spine and hip fractures. In this study, a nonlinear fracture mechanics-based finite element method is applied to human radius to assess its fracture load as a function of cortical bone geometry and material properties. Seven three-dimensional finite element models of radius were created and the fracture loads were determined by using cohesive finite element modeling which explicitly represents the crack and the fracture process zone behavior. The fracture loads found in the simulations (731-6793 N) were in the range of experimental values reported in the literature. The fracture loads predicted by the simulations decreased by 4-5% per decade based only on material level changes and by 6-20% per decade when geometrical changes were also included. Cortical polar moment of inertia at 15% distal radius showed the highest correlation to fracture load (r(2)=0.97). These findings demonstrate the strength of fracture mechanics-based finite element modeling and show that combining geometrical and material properties provides a better assessment of fracture risk in human radius.