Anisotropic mode-dependent damage of cortical bone using the extended finite element method (XFEM)

Biomechanical properties and clinical significance of cancellous bone in proximal femur: A review

Trabecular bone plays an important role in the load-bearing capacity of the femur. Understanding the structural characteristics, biomechanics, and mechanical conduction of the trabecular bone is of great value in studying the mechanism of fractures and formulating surgical plans. The past decade has witnessed unprecedented progress in imaging, biomechanics and finite element analysis techniques, translating into a better understanding of trabecular bone. This article reviews the research progress achieved over the years regarding femoral trabecular bone, especially on factors influencing the strength of the proximal femoral cancellous bone and cancellous bone microfractures and provides a comprehensive overview of the latest findings on proximal femoral trabecular bone and their clinical significance.

Homogeneous material models can overestimate stresses in high tibial osteotomy: A finite element analysis

Although widely used numerical models can assess the stability of lateral hinges in high tibial osteotomy (HTO) and may provide acceptable results in comparative studies, accurate stress prediction may not be possible due to simplified homogeneous models of the bone. The present study aimed to investigate the effect of a heterogeneous versus four homogeneous models on the results of stress and force. Each of the four homogenized FE models utilized the same elastic modulus of 16,700 MPa for the cortical while employing a single elastic modulus varying from 155 to 5000 MPa for the cancellous. In heterogeneous model, the modulus of each element was assigned using the bone density. It was found that stresses at the hinge in homogeneous models were higher than those in the heterogeneous model. The maximum principal stress (MPS) was 437 MPa for the heterogeneous model while that was 2179, 2351, 2581, and 2637 MPa for the homogeneous models with the elastic moduli of 155, 500, 2130, and 5000 MPa, respectively. Also, the opening force was 150 N for the heterogeneous model significantly lower than 649-1534 N range predicted for the homogeneous models. The use of a homogeneous model in the FE analysis of HTO overestimated the stresses and force. Thus, in addition to casting doubt on the use of a single modulus in the numerical analysis of HTO, Future HTO studies can use our results as a benchmark for comparison purposes and highlight the use of patient-specific bone density - elastic modulus relation in simulation.

Effect of geometrical structure variations on strength and damage onset of cortical bone using multi-scale cohesive zone based finite element method

Three-dimensional multi-scale finite element models were designed to examine the effects of geometrical structure variations on the damage onset in cortical bone at multiple structural scales. A cohesive zone finite element approach, together with anisotropic damage initiation criteria, is used to predict the onset of damage. The finite element models are developed to account for the onset of microdamage from the microscopic length scales consisting of collagen fibres, to the macroscopic level consisting of osteons and the Haversian canals. Numerical results indicated that the yield strain at the initiation of microcracks is independent of variations in the local mineral volume fraction at each structural scale. Further, the yield strain and strength properties of cortical bone are dependent on its structural anisotropy and hierarchical structure. A positive correlation is observed between bone strength and mineral content at each length scale.

Biomechanical evaluation of different strain judging criteria on the prediction precision of cortical bone fracture simulation under compression

Introduction: The principal strain or equivalent strain is mainly used in current numerical studies to determine the mechanical state of the element in the cortical bone finite element model and then perform fracture simulation. However, it is unclear which strain is more suitable for judging the element mechanical state under different loading conditions due to the lack of a general strain judging criterion for simulating the cortical bone fracture. Methods: This study aims to explore a suitable strain judging criterion to perform compressive fracture simulation on the rat femoral cortical bone based on continuum damage mechanics. The mechanical state of the element in the cortical bone finite element model was primarily assessed using the principal strain and equivalent strain separately to carry out fracture simulation. The prediction accuracy was then evaluated by comparing the simulated findings with different strain judging criteria to the corresponding experimental data. Results: The results showed that the fracture parameters predicted using the principal strain were closer to the experimental values than those predicted using the equivalent strain. Discussion: Therefore, the fracture simulation under compression was more accurate when the principal strain was applied to control the damage and failure state in the element. This finding has the potential to improve prediction accuracy in the cortical bone fracture simulation.

Investigation on the Differences in the Failure Processes of the Cortical Bone under Different Loading Conditions

Cortical bone is a transversely isotropic material, and the mechanical properties may be related to the loading direction on the osteon. Therefore, analyzing the differences in the failure processes of cortical bone under different loading conditions is necessary to explore the measures for reducing the incidence of fracture. In this study, to investigate the effects of different loading directions on the fracture performance in the cortical bone, a numerical method that could simultaneously simulate the failure processes in the cortical bone structure under compression and bending loads was established based on continuum damage mechanics theory. The prediction accuracy and feasibility of the numerical method were first verified by comparing with the corresponding experimental results. Then, the differences in the failure process and fracture performance of the same cortical bone structure under compression and bending loads were investigated. The simulation results indicated that for the same structure, the slip-open failure mode appeared under compression load, and the crack propagated along a certain angle to the loading direction; the tension-open failure mode appeared under bending load, and the crack propagated along the direction perpendicular to the loading direction. Meanwhile, the fracture load was greater and the fracture time was later in the compression than in the bending condition. These phenomena stated that discrepant failure processes and fracture patterns occurred in the same cortical bone structure under different loading conditions. The main reason may be related to the tension–compression asymmetry and transversely isotropic characteristics in the cortical bone material. The fracture simulations in the cortical bone under different loading conditions could improve the prediction accuracy in bone biomechanics and provide the prevention method for cortical bone damage and fracture.

Load Eccentricity of Compressed Composite Z-Columns in Non-Linear State

The study investigated short, thin-walled Z-shaped carbon-epoxy laminate columns. Z-columns were compressed while considering the eccentric force realized from the center of gravity of the column section. The study involved performing a nonlinear analysis of the structures with implemented geometric imperfections reflecting the first buckling modes. The nonlinear analysis was performed by using the Tsai-Wu criterion to determine the effort of the composite material. The computations were run until the critical parameter was reached in the Tsai-Wu criterion, allowing for a description of the failure initiation mechanism in the composite material. The first signs of damage to the composite material were determined by using the acoustic emission method. Based on the results, postcritical equilibrium paths of the numerical models were determined. The equilibrium paths were then compared with the experimental characteristics of real structures. The numerical results and experimental findings show a satisfactory agreement. The results confirmed that the numerical models were adequate for estimating the performance of composite structures in the postcritical range, depending on the amplitude of compressive load eccentricity. The research topic undertaken is important because the thin-walled structure design relates to actual loads which, in most cases, differ from the idealized theoretical load conditions.

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.

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 new compressible hyperelastic model for the multi-axial deformation of blood clot occlusions in vessels

Mechanical thrombectomy can be significantly affected by the mechanical properties of the occluding thrombus. In this study, we provide the first characterisation of the volumetric behaviour of blood clots. We propose a new hyperelastic model for the volumetric and isochoric deformation of clot. We demonstrate that the proposed model provides significant improvements over established models in terms of accurate prediction of nonlinear stress-strain and volumetric behaviours of clots with low and high red blood cell compositions. We perform a rigorous investigation of the factors that govern clot occlusion of a tapered vessel. The motivation for such an analysis is twofold: (i) the role of clot composition on the in vivo occlusion location is an open clinical question that has significant implications for thrombectomy procedures; (ii) in vitro measurement of occlusion location in an engineered tapered tube can be used as a quick and simple methodology to assess the mechanical properties/compositions of clots. Simulations demonstrate that both isochoric and volumetric behaviours of clots are key determinants of clot lodgement location, in addition to clot-vessel friction. The proposed formulation is shown to provide accurate predictions of in vitro measurement of clot occlusion location in a silicone tapered vessel, in addition to accurately predicting the deformed shape of the clot.

A Parametric Study on Factors Influencing the Onset and Propagation of Aortic Dissection Using the Extended Finite Element Method

OBJECTIVE

Aortic dissection is a life-threatening event which starts most of the time with an intimal tear propagating along the aortic wall, while blood enters the medial layer and delaminates the medial lamellar units. Studies investigating the mechanisms underlying the initiation sequence of aortic dissection are rare in the literature, the majority of studies being focused on the propagation event. Numerical models can provide a deeper understanding of the phenomena involved during the initiation and the propagation of the initial tear, and how geometrical and mechanical parameters affect this event. In the present paper, we investigated the primary factors contributing to aortic dissection.

METHODS

A two-layer arterial model with an initial tear was developed, representing three different possible configurations depending on the initial direction of the tear. Anisotropic damage initiation criteria were developed based on uniaxial and shear experiments from the literature to predict the onset and the direction of crack propagation. We used the XFEM-based cohesive segment method to model the initiation and the early propagation of the tear along the aorta. A design of experiment was used to quantify the influence of 7 parameters reflecting crack geometry and mechanics of the wall on the critical pressure triggering the dissection and the directions of propagation of the tear.

RESULTS

The results showed that the obtained critical pressures (mean range from 206 to 251 mmHg) are in line with measurement from the literature. The medial tensile strength was found to be the most influential factor, suggesting that a medial degeneration is needed to reach a physiological critical pressure and to propagate a tear in an aortic dissection. The geometry of the tear and its location inside the aortic wall were also found to have an important role not only in the triggering of tear propagation, but also in the evolution of the tear into either aortic rupture or aortic dissection. A larger and deeper initial tear increases the risk of aortic dissection.

CONCLUSION

The numerical model was able to reproduce the behaviour of the aorta during the initiation and propagation of an aortic dissection. In addition to confirm multiple results from the literature, different types of tears were compared and the influence of several geometrical and mechanical parameters on the critical pressure and direction of propagation was evaluated with a parametric study for each tear configuration.

SIGNIFICANCE

Although these results should be experimentally validated, they allow a better understanding of the phenomena behind aortic dissection and can help in improving the diagnosis and treatment of this disease.

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.

Subject-specific FE models of the human femur predict fracture path and bone strength under single-leg-stance loading

Hip fractures are a major health problem with high socio-economic costs. Subject-specific finite element (FE) models have been suggested to improve the fracture risk assessment, as compared to clinical tools based on areal bone mineral density, by adding an estimate of bone strength. Typically, such FE models are limited to estimate bone strength and possibly the fracture onset, but do not model the fracture process itself. The aim of this study was to use a discrete damage approach to simulate the full fracture process in subject-specific femur models under stance loading conditions. A framework based on the partition of unity finite element method (PUFEM), also known as XFEM, was used. An existing PUFEM framework previously used on a homogeneous generic femur model was extended to include a heterogeneous material description together with a strain-based criterion for crack initiation. The model was tested on two femurs, previously mechanically tested in vitro. Our results illustrate the importance of implementing a subject-specific material distribution to capture the experimental fracture pattern under stance loading. Our models accurately predicted the fracture pattern and bone strength (1% and 5% error) in both investigated femurs. This is the first study to simulate complete fracture paths in subject-specific FE femur models and it demonstrated how discrete damage models can provide a more complete picture of fracture risk by considering both bone strength and fracture toughness in a subject-specific fashion.

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.

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.

Finite element investigation into the use of carbon fibre reinforced PEEK laminated composites for distal radius fracture fixation implants

Carbon fibre reinforced PEEK (CF/PEEK) laminates provide mechanical advantages over homogenous metal osteo-synthesis implants, e.g. radiolucency, fatigue strength and strength to weight ratio. Implants can be designed with custom anisotropic material properties, thus enabling the engineer to tailor the overall stiffness of the implant to the specific loading conditions it will experience in vivo. In the current study a multi-scale computational investigation of idealised distal radius fracture fixation plate (DRP) is conducted. Physiological loading conditions are applied to macro-scale finite element models of DRPs. The mechanical response is compared for several CF/PEEK laminate layups to examine the effect of ply layup design. The importance of ply orientation in laminated DRPs is highlighted. A high number of 0° plies near the outer surfaces results in a greater bending strength while the addition of 45° plies increases the torsional strength of the laminates. Intra-laminar transverse tensile failure is predicted as the primary mode of failure. A micro-mechanical analysis of the CF/PEEK microstructure uncovers the precise mechanism under-lying intra-laminar transverse tensile crack to be debonding of the PEEK matrix from carbon fibres. Plastic strains in the matrix material are not sufficiently high to result in ductile failure of the matrix. The findings of this study demonstrate the significant challenge in the design and optimisation of fibre reinforced laminated composites for orthopaedic applications, highlighting the importance of multi-scale modelling for identification of failure mechanisms.

Isotropic Failure Criteria Are Not Appropriate for Anisotropic Fibrous Biological Tissues

The von Mises (VM) stress is a common stress measure for finite element models of tissue mechanics. The VM failure criterion, however, is inherently isotropic, and therefore may yield incorrect results for anisotropic tissues, and the relevance of the VM stress to anisotropic materials is not clear. We explored the application of a well-studied anisotropic failure criterion, the Tsai–Hill (TH) theory, to the mechanically anisotropic porcine aorta. Uniaxial dogbones were cut at different angles and stretched to failure. The tissue was anisotropic, with the circumferential failure stress nearly twice the axial (2.67 ± 0.67 MPa compared to 1.46 ± 0.59 MPa). The VM failure criterion did not capture the anisotropic tissue response, but the TH criterion fit the data well (R2 = 0.986). Shear lap samples were also tested to study the efficacy of each criterion in predicting tissue failure. Two-dimensional failure propagation simulations showed that the VM failure criterion did not capture the failure type, location, or propagation direction nearly as well as the TH criterion. Over the range of loading conditions and tissue geometries studied, we found that problematic results that arise when applying the VM failure criterion to an anisotropic tissue. In contrast, the TH failure criterion, though simplistic and clearly unable to capture all aspects of tissue failure, performed much better. Ultimately, isotropic failure criteria are not appropriate for anisotropic tissues, and the use of the VM stress as a metric of mechanical state should be reconsidered when dealing with anisotropic tissues.

Mechanics of linear microcracking in trabecular bone

Microcracking in trabecular bone is responsible both for the mechanical degradation and remodeling of the trabecular bone tissue. Recent results on trabecular bone mechanics have demonstrated that bone tissue microarchitecture, tissue elastic heterogeneity and tissue-level mechanical anisotropy all should be considered to obtain detailed information on the mechanical stress state. The present study investigated the influence of tissue microarchitecture, tissue heterogeneity in elasticity and material separation properties and tissue-level anisotropy on the microcrack formation process. Microscale bone models were executed with the extended finite element method. It was demonstrated that anisotropy and heterogeneity of the bone tissue contribute significantly to bone tissue toughness and the resistance of trabecular bone to microcrack formation. The compressive strain to microcrack initiation was computed to increase by a factor of four from an assumed homogeneous isotropic tissue to an assumed anisotropic heterogenous tissue.

Determination of a tissue-level failure evaluation standard for rat femoral cortical bone utilizing a hybrid computational-experimental method

Macro-level failure in bone structure could be diagnosed by pain or physical examination. However, diagnosing tissue-level failure in a timely manner is challenging due to the difficulty in observing the interior mechanical environment of bone tissue. Because most fractures begin with tissue-level failure in bone tissue caused by continually applied loading, people attempt to monitor the tissue-level failure of bone and provide corresponding measures to prevent fracture. Many tissue-level mechanical parameters of bone could be predicted or measured; however, the value of the parameter may vary among different specimens belonging to a kind of bone structure even at the same age and anatomical site. These variations cause difficulty in representing tissue-level bone failure. Therefore, determining an appropriate tissue-level failure evaluation standard is necessary to represent tissue-level bone failure. In this study, the yield and failure processes of rat femoral cortical bones were primarily simulated through a hybrid computational-experimental method. Subsequently, the tissue-level strains and the ratio between tissue-level failure and yield strains in cortical bones were predicted. The results indicated that certain differences existed in tissue-level strains; however, slight variations in the ratio were observed among different cortical bones. Therefore, the ratio between tissue-level failure and yield strains for a kind of bone structure could be determined. This ratio may then be regarded as an appropriate tissue-level failure evaluation standard to represent the mechanical status of bone tissue.

Understanding the Basics of Computational Models in Orthopaedics: A Nonnumeric Review for Surgeons

Computational models represent more than just finite element analysis, a term that many clinicians may know and globally apply. Over the past 30 years, many published studies have addressed clinically relevant orthopaedic questions with speed and precision by using a wide variety of computational approaches. Given such a wide spectrum of techniques, clinicians often do not have a full understanding of the methods used to create models and therefore do not appreciate the strengths, weaknesses, and potential pitfalls of published results. The short, nonnumeric summaries of the methodologies employed for various computational approaches presented here can help address this issue.

A rate-independent continuum model for bone tissue with interaction of compressive and tensile micro-damage

Low bone strength is a major risk factor for osteoporotic fractures and is only partially determined by clinical densitometry. Accumulated micro-damage induces residual strains, degrades elastic modulus and reduces bone strength independently of bone mineral density. Histologically, overloading of bone in compression and tension leads to distinct crack size, distribution and orientation which interact during combined loading scenarios. Statistics of rheological models can describe this process and reproduce experimental stress-strain curves with an unprecedented realism, but are computationally expensive and therefore difficult to generalize to 3D. Accordingly, the aim of this work is to formulate a continuum damage model that describes the key features of bone micro-damage, namely the accumulation of residual strains, the degradation of elastic modulus and the reduction of strength in compression, tension and especially in their sequential application. The promising qualitative agreement of the model with the experiments will motivate a generalization to 3D and allow the biomechanical investigation of bones and bone-implant systems subjected to cyclic overloading in tension and/or compression.

Cortical bone fracture analysis using XFEM - case study

We aim to achieve an accurate simulation of human cortical bone fracture using the extended finite element method within a commercial finite element software abaqus. A two-dimensional unit cell model of cortical bone is built based on a microscopy image of the mid-diaphysis of tibia of a 70-year-old human male donor. Each phase of this model, an interstitial bone, a cement line, and an osteon, are considered linear elastic and isotropic with material properties obtained by nanoindentation, taken from literature. The effect of using fracture analysis methods (cohesive segment approach versus linear elastic fracture mechanics approach), finite element type, and boundary conditions (traction, displacement, and mixed) on cortical bone crack initiation and propagation are studied. In this study cohesive segment damage evolution for a traction separation law based on energy and displacement is used. In addition, effects of the increment size and mesh density on analysis results are investigated. We find that both cohesive segment and linear elastic fracture mechanics approaches within the extended finite element method can effectively simulate cortical bone fracture. Mesh density and simulation increment size can influence analysis results when employing either approach, and using finer mesh and/or smaller increment size does not always provide more accurate results. Both approaches provide close but not identical results, and crack propagation speed is found to be slower when using the cohesive segment approach. Also, using reduced integration elements along with the cohesive segment approach decreases crack propagation speed compared with using full integration elements. Copyright © 2016 John Wiley & Sons, Ltd.

Modeling the Mechanical Consequences of Age-Related Trabecular Bone Loss by XFEM Simulation

The elderly are more likely to suffer from fracture because of age-related trabecular bone loss. Different bone loss locations and patterns have different effects on bone mechanical properties. Extended finite element method (XFEM) can simulate fracture process and was suited to investigate the effects of bone loss on trabecular bone. Age-related bone loss is indicated by trabecular thinning and loss and may occur at low-strain locations or other random sites. Accordingly, several ideal normal and aged trabecular bone models were created based on different bone loss locations and patterns; then, fracture processes from crack initiation to complete failure of these models were observed by XFEM; finally, the effects of different locations and patterns on trabecular bone were compared. Results indicated that bone loss occurring at low-strain locations was more detrimental to trabecular bone than that occurring at other random sites; meanwhile, the decrease in bone strength caused by trabecular loss was higher than that caused by trabecular thinning, and the effects of vertical trabecular loss on mechanical properties were more severe than horizontal trabecular loss. This study provided a numerical method to simulate trabecular bone fracture and distinguished different effects of the possible occurrence of bone loss locations and patterns on trabecular bone.

Quantification of Age-Related Tissue-Level Failure Strains of Rat Femoral Cortical Bones Using an Approach Combining Macrocompressive Test and Microfinite Element Analysis

Bone mechanical properties vary with age; meanwhile, a close relationship exists among bone mechanical properties at different levels. Therefore, conducting multilevel analyses for bone structures with different ages are necessary to elucidate the effects of aging on bone mechanical properties at different levels. In this study, an approach that combined microfinite element (micro-FE) analysis and macrocompressive test was established to simulate the failure of male rat femoral cortical bone. Micro-FE analyses were primarily performed for rat cortical bones with different ages to simulate their failure processes under compressive load. Tissue-level failure strains in tension and compression of these cortical bones were then back-calculated by fitting the experimental stress–strain curves. Thus, tissue-level failure strains of rat femoral cortical bones with different ages were quantified. The tissue-level failure strain exhibited a biphasic behavior with age: in the period of skeletal maturity (1–7 months of age), the failure strain gradually increased; when the rat exceeded 7 months of age, the failure strain sharply decreased. In the period of skeletal maturity, both the macro- and tissue-levels mechanical properties showed a large promotion. In the period of skeletal aging (9–15 months of age), the tissue-level mechanical properties sharply deteriorated; however, the macromechanical properties only slightly deteriorated. The age-related changes in tissue-level failure strain were revealed through the analysis of male rat femoral cortical bones with different ages, which provided a theoretical basis to understand the relationship between rat cortical bone mechanical properties at macro- and tissue-levels and decrease of bone strength with age.

Specimen-specific vertebral fracture modeling: a feasibility study using the extended finite element method

Osteoporotic vertebral body fractures are an increasing clinical problem among the aging population. Specimen-specific finite element models, derived from quantitative computed tomography (QCT), have the potential to more accurately predict failure loads in the vertebra. Additionally, the use of extended finite element modeling (X-FEM) allows for a detailed analysis of crack initiation and propagation in various materials. Our aim was to study the feasibility of QCT/X-FEM analysis to predict fracture properties of vertebral bodies. Three cadaveric specimens were obtained, and the L3 vertebrae were excised. The vertebrae were CT scanned to develop computational models and mechanically tested in compression to measure failure load, stiffness and to observe crack location. One vertebra was used for calibration of the material properties from experimental results and CT gray-scale values. The two additional specimens were used to assess the model prediction. The resulting QCT/X-FEM model of the specimen used for calibration had 2 and 4% errors in stiffness and failure load, respectively, compared with the experiment. The predicted failure loads of the additional two vertebrae were larger by about 41-44% when compared to the measured values, while the stiffness differed by 129 and 40%. The predicted fracture patterns matched fairly well with the visually observed experimental cracks. Our feasibility study indicated that the QCT/X-FEM method used to predict vertebral compression fractures is a promising tool to consider in future applications for improving vertebral fracture risk prediction in the elderly.

Self-tapping ability of carbon fibre reinforced polyetheretherketone suture anchors

An experimental and computational investigation of the self-tapping ability of carbon fibre reinforced polyetheretherketone (CFR-PEEK) has been conducted. Six CFR-PEEK suture anchor designs were investigated using PEEK-OPTIMA® Reinforced, a medical grade of CFR-PEEK. Experimental tests were conducted to investigate the maximum axial force and torque required for self-taping insertion of each anchor design. Additional experimental tests were conducted for some anchor designs using pilot holes. Computational simulations were conducted to determine the maximum stress in each anchor design at various stages of insertion. Simulations also were performed to investigate the effect of wall thickness in the anchor head. The maximum axial force required to insert a self-tapping CFR-PEEK suture anchor did not exceed 150 N for any anchor design. The maximum torque required to insert a self-tapping CFR-PEEK suture anchor did not exceed 0.8 Nm. Computational simulations reveal significant stress concentrations in the region of the anchor tip, demonstrating that a re-design of the tip geometry should be performed to avoid fracture during self-tapping, as observed in the experimental component of this study. This study demonstrates the ability of PEEK-OPTIMA Reinforced suture anchors to self-tap polyurethane foam bone analogue. This provides motivation to further investigate the self-tapping ability of CFR-PEEK suture anchors in animal/cadaveric bone. An optimised design for CFR-PEEK suture anchors offers the advantages of radiolucency, and mechanical properties similar to bone with the ability to self-tap. This may have positive implications for reducing surgery times and the associated costs with the procedure.

Are plasticity models required to predict relative risk of lag screw cut-out in finite element models of trochanteric fracture fixation?

Using a finite element model of unstable trochanteric fracture stabilized with a sliding hip screw, the benefits of two plasticity-based formulations, Drucker-Prager and crushable foam, were evaluated and compared to the commonly used linear elastic model of trabecular bone in order to predict the relative risk of lag screw cut-out for five distinct load cases. The crushable foam plasticity formulation leads to a much greater strain localization, in comparison to the other two models, with large plastic strains in a localized region. The plastic zone predicted with Drucker-Prager is relatively more diffuse. Linear elasticity associated with a minimum principal strain criterion provides the smallest volume of elements susceptible to yielding for all loading modes. The region likely to undergo plastic deformation, as predicted by the linear elastic model, is similar to that obtained from plasticity-based formulations, which indicates that this simple criterion provides an adequate estimate of the risk of cut-out.