Cortical bone fracture analysis using XFEM - case study

A proposal for the combined analysis of bone quantity and quality of human cortical bone by quasi-brittle fracture mechanics

Quasi-brittle fracture mechanics is used to evaluate fracture of human cortical bone in aging. The approach is demonstrated using cortical bone bars extracted from one 92-year-old human male cadaver. In-situ fracture mechanics experiments in a 3D X-ray microscope are conducted. The evolution of the fracture process zone is documented. Fully developed fracture process zone lengths at peak load are found to span about three osteon diameters. Crack deflection and arrest at cement lines is a key process to build extrinsic toughness. Strength and toughness are found as size-dependent, not only for laboratory-scale experimental specimens but also for the whole femur. A scaling law for the length fracture process zone is used. Then, size-independent, tissue fracture properties are calculated. Linear elastic fracture mechanics applied to laboratory beam specimens underestimates the tissue toughness by 60%. Tissue fracture properties are used to predict the load capacity of the femur in bending within the range of documented data. The quasi-brittle fracture mechanics approach allows for the assessment of the combined effect of bone quantity and bone quality on fracture risk. However, further work is needed considering a larger range of subjects and in the model validation at the organ length scale.

Characterization of damage mechanisms in cortical bone: Quantification of fracture resistance, critical strains, and crack tortuosity

One step towards understanding bone fragility and degenerative diseases is to unravel the links between fracture resistance and the compositional and structural characteristics of cortical bone. In this study, we explore an optical method for automatic crack detection to generate full fracture resistance curves of cortical bone. We quantify fracture toughness, critical failure strains at the crack tip, and crack tortuosity in three directions and analyze how they relate to cortical bone microstructure. A three-point bending fracture test of single-edge notched beam specimens in three directions (cracks propagating transverse, radial and longitudinal to the microstructure) from bovine cortical bone was combined with 2D-digital image correlation. Crack growth was automatically monitored by analyzing discontinuities in the displacement field using phase congruency analysis. Fracture resistance was analyzed using J-R-curves and strains were quantified at the crack tip. Post-testing, a subset of specimens was scanned using micro-tomography to visualize cracks and to quantify their tortuosity. Both fracture toughness and crack tortuosity were significantly higher in the transverse direction compared to the other directions. Similar fracture toughness was found for radial and longitudinal directions, albeit 20% higher crack tortuosity in the radial specimens. This suggests that radial crack deflections are not as efficient toughening mechanisms. Strains at crack initiation were ∼0.4% for all tissue orientations, while at fully developed damage process zones failure strains were significantly higher in the transverse direction (∼1.5%). Altogether, we present unique quantitative data including different aspects of bone damage in three directions, illustrating the importance of cortical bone microstructure.

Isolating the Role of Bone Lacunar Morphology on Static and Fatigue Fracture Progression through Numerical Simulations

Currently, the onset of bone damage and the interaction of cracks with the surrounding micro-architecture are still black boxes. With the motivation to address this issue, our research targets isolating lacunar morphological and densitometric effects on crack advancement under both static and cyclic loading conditions by implementing static extended finite element models (XFEM) and fatigue analyses. The effect of lacunar pathological alterations on damage initiation and progression is evaluated; the results indicate that high lacunar density considerably reduces the mechanical strength of the specimens, resulting as the most influencing parameter among the studied ones. Lacunar size has a lower effect on mechanical strength, reducing it by 2%. Additionally, specific lacunar alignments play a key role in deviating the crack path, eventually slowing its progression. This could shed some light on evaluating the effects of lacunar alterations on fracture evolution in the presence of pathologies.

Cortical bone continuum damage mechanics constitutive model with stress triaxiality criterion to predict fracture initiation and pattern

A primary objective of finite element human body models (HBMs) is to predict response and injury risk in impact scenarios, including cortical bone fracture initiation, fracture pattern, and the potential to simulate post-fracture injury to underlying soft tissues. Current HBMs have been challenged to predict the onset of failure and bone fracture patterns owing to the use of simplified failure criteria. In the present study, a continuum damage mechanics (CDM) model, incorporating observed mechanical response (orthotropy, asymmetry, damage), was coupled to a novel phenomenological effective strain fracture criterion based on stress triaxiality and investigated to predict cortical bone response under different modes of loading. Three loading cases were assessed: a coupon level notched shear test, whole bone femur three-point bending, and whole bone femur axial torsion. The proposed material model and fracture criterion were able to predict both the fracture initiation and location, and the fracture pattern for whole bone and specimen level tests, within the variability of the reported experiments. There was a dependence of fracture threshold on finite element mesh size, where higher mesh density produced similar but more refined fracture patterns compared to coarser meshes. Importantly, the model was functional, accurate, and numerically stable even for relatively coarse mesh sizes used in contemporary HBMs. The proposed model and novel fracture criterion enable prediction of fracture initiation and resulting fracture pattern in cortical bone such that post-fracture response can be investigated in HBMs.

A review on experimental and numerical investigations of cortical bone fracture

This paper comprehensively reviews the various experimental and numerical techniques, which were considered to determine the fracture characteristics of the cortical bone. This study also provides some recommendations along with the critical review, which would be beneficial for future research of fracture analysis of cortical bone. Cortical bone fractures due to sports activities, climbing, running, and engagement in transport or industrial accidents. Individuals having different diseases are also at high risk of cortical bone fracture. It has been observed that osteon orientation influences cortical bone fracture toughness and fracture mechanisms. Apart from this, recent studies indicate that fracture parameters of cortical bone also depend on many factors such as age, sex, temperature, osteoporosis, orientation, location, loading condition, strain rate, and storage facility, etc. The cortical bone regains its fracture toughness due to various toughening mechanisms. Owing to these factors, several experimental, clinical, and numerical investigations have been carried out to determine the fracture parameters of the cortical bone. Cortical bone is the dense outer surface of the bone and contributes to 80%–82% of the skeleton mass. Cortical bone experiences load far exceeding body weight due to muscle contraction and the dynamics of motion. It is very important to know the fracture pattern, direction of fracture, location of the fracture, and toughening mechanism of cortical bone. A basic understanding of the different factors that affect the fracture parameters and fracture mechanisms of the cortical bone is necessary to prevent the failure and fracture of cortical bone. This review has summarized the advancement considered in the various experimental techniques and numerical methods to get complete information about the fracture mechanisms of cortical bone.

Computational homogenisation based extraction of transverse tensile cohesive responses of cortical bone tissue

The numerical assessment of fracture properties of cortical bone is important in providing suggestions on patient-specific clinical treatments. We present a generic finite element modelling framework incorporating computational fracture approaches and computational homogenisation techniques. Finite element computations for statistical volume elements (SVEs) at the microscale are performed for different sizes with random osteon packing with a fixed volume fraction. These SVEs are loaded in the transverse direction under tension. The minimal SVE size in terms of ensuring a representative effective cohesive law is suggested to be 0.6 mm. Since cement lines as weak interfaces play a key role in bone fracture, the effects of their fracture properties on the effective fracture strength and toughness are investigated. The extracted effective fracture properties can be used as homogenised inputs to a discrete crack simulation at macroscopic or structural scale. The extrinsic toughening mechanisms observed in the SVE models are discussed with a comparison against experimental observations from the literature, giving beneficial insights to cortical bone failure.

A multi-objective approach to optimize the weight and stress of the locking plates using finite element modeling

This paper aims to identify an optimum bone fracture stabilizer. For this purpose, three design variables including the ratio of the screw diameter to the plate width at three levels, the ratio of the plate thickness to the plate width at three levels, and the diameter of the bone at two levels were selected for analysis. Eighteen 3D verified finite element models were developed to examine the effects of these parameters on the weight, maximum displacement and maximum von Mises stress of the fixation structure. Considering the relations between the inputs and outputs using multivariate regression, a genetic algorithm was used to find the optimal choices. Results showed that the diameter of the bone and the amount of load applied on it did not have a significant effect on the normalized stresses on the structures. Furthermore, in all ratio of the plate thickness to the plate width, as the ratio of the screw diameter to the plate width increased, the amount of stress on the structure decreased. But, by further increasing the ratio of the screw diameter to the plate width, the amount of stress on the structure increased. On the other hand, by increasing the value of the ratio of the plate thickness to the plate width, the maximum amount of stress on the structure decreased. Finally, optimal solutions in terms of the weight and the maximum amount of stress on the structure were presented.

Prediction of fracture initiation and propagation in pelvic bones

The objective is developing an XFEM model that is capable of predicting different types of fracture in the pelvic bone under various loading conditions. Previously published mechanical and failure characteristics of cortical and cancellous tissues were implemented and assigned to an intact pelvic bone with specified cortical and cancellous tissues. Various loading conditions, including combined load directions, were applied to the acetabulum to model different types of fracture (e.g., anterior/posterior wall fracture and transverse fracture) in the pelvic bone. The predicated types of fracture and the maximum force at fracture were compared to those acquired from previously published experimental tests. Anterior/posterior wall fracture and transverse fracture were the most common types of fractures determined in the simulations. The XFEM simulations were able to predict similar fractures to those reported in the experimental tests. The maximum fracture force in the XFEM model was found to be 18.6 kN compared to 8.85 kN reported in the previous experimental tests. The results revealed that different types of fracture in the pelvic bones can be caused by the various loading conditions in unstable high-rate impact loads. Using proper mechanical and failure behaviors of cortical and cancellous tissues, XFEM modeling of pelvic bone is capable of predicting bone fracture. In future work, the XFEM models of cancellous and cortical tissues can be assigned to other bones in human body skeleton so that the failure mechanism in such bones can be investigated.

Effect of hinge length on the lateral cortex fracture in high tibia osteotomy: an XFEM study

The main disadvantage of high tibial osteotomy (HTO) is the fracture of the lateral hinge during surgery. Therefore, the present study was designed to investigate the effect of different hinge lengths on the fracture type of the lateral hinge during the opening in HTO. For this purpose, extended finite element method (XFEM) was used to predict the crack initiation and growth in bone cortex in twelve models, each with different hinge lengths and medial start points. It was shown that extending the hinge length from 5 to 10, 16 and 22 mm increased the maximum principal stress around the hinge, and thus the fracture probability. A minimal effect on the results was observed by changing medial starting point of the cut from 30 to 35 and 40 mm. As a result, the extended finite element analyses confirmed the hypothesis that the extension of hinge segment increases the likelihood of a type II and type III fractures.

Effect of ageing on microstructure and fracture behavior of cortical bone as determined by experiment and Extended Finite Element Method (XFEM)

Bone fracture is a severe health concern; therefore, understanding the causes of bone fracture are crucial. This paper investigates the microstructure and fracture behaviour of cadaveric cortical bone of two different groups (Young, n= 6; Aged, n=7). The microstructure is obtained from µ-CT images, and the material parameters are measured with nanoindentation. Fracture behaviour in transverse and longitudinal orientations is investigated experimentally and numerically. The results show that the Haversian canal (HC) size increases and the osteon wall thickness (OWT) decreases significantly in the aged group, whereas a nonsignificant difference is found in tissue properties. The crack initiation (J_ic) and crack growth (J_grow) toughness of the aged group are found to be significantly lower (p<0.01) than the young group in the transverse orientation; however, for the longitudinal orientation, only the value of J_ic in the aged group is found significantly lower. Further, a 4-phase XFEM (based on micro-CT image) model is developed to investigate the crack propagation behaviour in both orientations. For the transverse orientation, results show that in the aged group, the crack initially follows the cementline and then penetrates the osteon, whereas, in the young group, it propagates along the cementline. These results are in agreement with experimental results where the decrease in J_grow is more significant than the J_ic in the aged group. This study suggests that ageing leads to a larger HC and reduced OWT, which weakens the crack deflection ability and causes fragility fracture. Further, the XFEM results indicate that the presence of a small microcrack in the vicinity of a major crack tip causes an increase in the critical stress intensity factor.

A mechanobiological approach to find the optimal thickness for the locking compression plate: Finite element investigations

This study aimed at finding the acceptable range, and the optimal value for the locking compression plate (LCP) thickness (THK), through simulating the osteogenic pathway of bone healing, and by checking bone-plate construct's strength and stability. To attain the goals of this research, a multi-objective approach was adopted, which should trade-off between some conflicting objectives. A finite element model of the long bone-plate construct was made first, and validated against an experimental study. The validated model was then employed to determine the initial strength and stability of the bone-plate construct, for the time right after surgery, for various thicknesses of the LCP. Afterward, coupling with a mechano-regulatory algorithm, the iterative process of bone healing was simulated, and follow up was made for each LCP thickness, over the first 16 post-operative weeks. Results of this study regarding the sequence of tissue evolution inside the fracture gap, showed a similar trend with the existing in-vivo data. For the material and structural properties assigned to the bone-plate construct, in this study, an optimal thickness for the LCP was found to be 4.7 mm, which provides an enduring fixation through secondary healing, whereas for an LCP with a smaller or greater thickness, either bone-implant failure, unstable fixation, impaired fracture consolidation, or primary healing may occur. This result is in agreement with a recent study, that has employed a comprehensive optimization approach to find the optimal thickness.

An Equivalent Constitutive Model of Cancellous Bone With Fracture Prediction

To simulate the mechanical and fracture behaviors of cancellous bone in three anatomical directions and to develop an equivalent constitutive model. Microscale extended finite element method (XFEM) models of a cancellous specimen were developed with mechanical behaviors in three anatomical directions. An appropriate abaqus macroscale model replicated the behavior observed in the microscale models. The parameters were defined based on the intermediate bone material properties in the anatomical directions and assigned to an equivalent nonporous specimen of the same size. The equivalent model capability was analyzed by comparing the micro- and macromodels. The hysteresis graphs of the microscale model show that the modulus is the same in loading and unloading; similar to the metal plasticity models. The strength and failure strains in each anatomical direction are higher in compression than in tension. The microscale models exhibited an orthotropic behavior. Appropriate parameters of the cast iron plasticity model were chosen to generate macroscale models that are capable of replicating the observed microscale behavior of cancellous bone. Cancellous bone is an orthotropic material that can be simulated using a cast iron plasticity model. This model is capable of replicating the microscale behavior in finite element (FE) analysis simulations without the need for individual trabecula, leading to a reduction in computational resources without sacrificing model accuracy. Also, XFEM of cancellous bone compared to traditional finite element method proves to be a valuable tool to predict and model the fractures in the bone specimen.

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.

Prediction of failure in cancellous bone using extended finite element method

The objective of our study is to develop extended finite element method models of cancellous bone specimens that are capable of accurately predicting the onset and propagation of cracks under mechanical loading. In order to do so, previously published three-point bending test results of a single trabecula were replicated using two different extended finite element method approaches, namely, elastic-plastic-fracture and elastic-fracture that considered different configurations of the elasto-plastic properties of bone from which the best approach to fit the experimental data was identified. The behavior of a single trabecula was then used in 2D extended finite element method models to quantify the strength of the trabecular tissue of the forearm along three perpendicular anatomical axes. The results revealed that the elastic-plastic-fracture model better represented the experimental data in the model of a single trabecula. Considering the 2D trabecular specimens, the elastic fracture model predicted higher strength than the elastic-plastic-fracture model and there was no difference in stiffness between the two models. In general, the specimens exhibited higher failure strain and more ductile behavior in compression than in tension. In addition, strength and stiffness were found to be higher in tension than compression on average. It can be concluded that with proper parameters, extended finite element method is capable of simulating the ductile behavior of cancellous bone. The models are able to quantify the tensile strength of trabecular tissue in the various anatomical directions reporting an increased strength in the longitudinal direction of forearm cancellous bone tissue. Extended finite element method of cancellous bone proves to be a valuable tool to predict the mechanical characteristics of cancellous bones as a function of the microstructure.

Patient-Specific Bone Multiscale Modelling, Fracture Simulation and Risk Analysis-A Survey

This paper provides a starting point for researchers and practitioners from biology, medicine, physics and engineering who can benefit from an up-to-date literature survey on patient-specific bone fracture modelling, simulation and risk analysis. This survey hints at a framework for devising realistic patient-specific bone fracture simulations. This paper has 18 sections: Section 1 presents the main interested parties; Section 2 explains the organzation of the text; Section 3 motivates further work on patient-specific bone fracture simulation; Section 4 motivates this survey; Section 5 concerns the collection of bibliographical references; Section 6 motivates the physico-mathematical approach to bone fracture; Section 7 presents the modelling of bone as a continuum; Section 8 categorizes the surveyed literature into a continuum mechanics framework; Section 9 concerns the computational modelling of bone geometry; Section 10 concerns the estimation of bone mechanical properties; Section 11 concerns the selection of boundary conditions representative of bone trauma; Section 12 concerns bone fracture simulation; Section 13 presents the multiscale structure of bone; Section 14 concerns the multiscale mathematical modelling of bone; Section 15 concerns the experimental validation of bone fracture simulations; Section 16 concerns bone fracture risk assessment. Lastly, glossaries for symbols, acronyms, and physico-mathematical terms are provided.

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.

Investigation on distal femoral strength and reconstruction failure following curettage and cementation: In-vitro tests with finite element analyses

Cement augmentation following benign bone tumor surgery, i.e. curettage and cementation, is recommended in patients at high risk of fracture. Nonetheless, identifying appropriate cases and devices for augmentation remains debatable. Our goal was to develop a validated biomechanical tool to: predict the post-surgery strength of a femoral bone, assess the precision and accuracy of the predicted strength, and discover the mechanisms of reconstruction failure, with the aim of finding a safe biomechanical fixation. Tumor surgery was mimicked in quantitative-CT (QCT) scanned cadaveric human distal femora, and subsequently tested in compression to measure bone strength (F_Exp). Finite element (FE) models considering bone material non-homogeneity and non-linearity were constructed to predict bone strength (F_FE). Analyses of contact, damage, and crack initiation at the bone-cement interface (BCI) were completed to investigate critical failure locations. Results of paired t-tests did not show a significant difference between F_Exp and F_FE (P > 0.05); linear regression analysis resulted in good correlation between F_Exp and F_FE (R² = 0.94). Evaluation of the models precision using linear regression analysis yielded R² = 0.89, with the slope = 1.08 and intercept = -324.16 N. FE analyses showed the initiation of damage and crack and a larger cement debonding area at the proximal end and most interior part of BCI, respectively. Therefore, we speculated that devices that reinforce critical failure locations offer the most biomechanical advantage. The QCT-based FE method proved to be a reliable tool to predict distal femoral strength, identify some causes of reconstruction failure, and assist in a safer selection of fixation devices to reduce post-operative fracture risk.

Experimental and numerical comparisons between finite element method, element-free Galerkin method, and extended finite element method predicted stress intensity factor and energy release rate of cortical bone considering anisotropic bone modelling

Stress intensity factor and energy release rate are important parameters to understand the fracture behaviour of bone. The objective of this study is to predict stress intensity factor and energy release rate using finite element method, element-free Galerkin method, and extended finite element method and compare these results with the experimentally determined values. For experimental purpose, 20 longitudinally and transversely fractured single-edge notched bend specimens were prepared and tested according to ASTM standard. All specimens were tested using the universal testing machine. For numerical simulations (finite element method, element-free Galerkin method, and extended finite element method), two-dimensional model of cortical bone was developed by assuming plane strain condition. Material properties of the cortical bone were considered as anisotropic and homogeneous. The values obtained through finite element method, element-free Galerkin method, and extended finite element method are well corroborated to experimentally determined values and earlier published data. However, element-free Galerkin method and extended finite element method predict more accurate results as compared to finite element method. In the case of the transversely fractured specimen, the values of stress intensity factor and energy release rate were found to be higher as compared to the longitudinally fractured specimen, which shows consistency with earlier published data. This study also indicates element-free Galerkin method and extended finite element method predicted stress intensity factor and energy release rate results are more close to experimental results as compared to finite element method, and therefore, these methods can be used in the different field of biomechanics, particularly to predict bone fracture.