Failure modelling of trabecular bone using a non-linear combined damage and fracture voxel finite element approach

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.

2D and 3D numerical models to evaluate trabecular bone damage

The comprehension of trabecular bone damage processes could be a crucial hint for understanding how bone damage starts and propagates. Currently, different approaches to bone damage identification could be followed. Clinical approaches start from dual X-ray absorptiometry (DXA) technique that can evaluate bone mineral density (BMD), an indirect indicator of fracture risk. DXA is, in fact, a two-dimensional technology, and BMD alone is not able to predict the effective risk of fractures. First attempts in overcoming this issue have been performed with finite element (FE) methods, combined with the use of three-dimensional high-resolution micro-computed tomographic images. The purpose of this work is to evaluate damage initiation and propagation in trabecular vertebral porcine samples using 2D linear-elastic FE models from DXA images and 3D linear FE models from micro-CT images. Results show that computed values of strains with 2D and 3D approaches (e.g., the minimum principal strain) are of the same order of magnitude. 2D DXA-based models still remain a powerful tool for a preliminary screening of trabecular regions that are prone to fracture, while from 3D micro-CT-based models, it is possible to reach details that permit the localization of the most strained trabecula.

Loss of longitudinal superiority marks the microarchitecture deterioration of osteoporotic cancellous bones

Osteoporosis (OP), a skeletal disease making bone mechanically deteriorate and easily fracture, is a global public health issue due to its high prevalence. It has been well recognized that besides bone loss, microarchitecture degradation plays a crucial role in the mechanical deterioration of OP bones, but the specific role of microarchitecture in OP has not been well clarified and quantified from mechanics perspective. Here, we successfully decoupled and identified the specific roles of microarchitecture, bone mass and tissue property in the failure properties of cancellous bones, through μCT-based digital modeling and finite element method simulations on bone samples from healthy and ovariectomy-induced osteoporotic mice. The results show that the microarchitecture of healthy bones exhibits longitudinal superiority in mechanical properties such as the effective stiffness, strength and toughness, which fits them well to bearing loads along their longitudinal direction. OP does not only reduce bone mass but also impair the microarchitecture topology. The former is mainly responsible for the mechanical degradation of bones in magnitude, wherever the latter accounts for the breakdown of their function-favorable anisotropy, the longitudinal superiority. Hence, we identified the microarchitecture-deterioration-induced directional mismatch between material and loading as a hazardous feature of OP and defined a longitudinal superiority index as measurement of the health status of bone microarchitecture. These findings provide useful insights and guidelines for OP diagnosis and treat assessment.

Combined Effects of Exercise and Denosumab Treatment on Local Failure in Post-menopausal Osteoporosis-Insights from Bone Remodelling Simulations Accounting for Mineralisation and Damage

Denosumab has been shown to increase bone mineral density (BMD) and reduce the fracture risk in patients with post-menopausal osteoporosis (PMO). Increase in BMD is linked with an increase in bone matrix mineralisation due to suppression of bone remodelling. However, denosumab anti-resorptive action also leads to an increase in fatigue microdamage, which may ultimately lead to an increased fracture risk. A novel mechanobiological model of bone remodelling was developed to investigate how these counter-acting mechanisms are affected both by exercise and long-term denosumab treatment. This model incorporates Frost's mechanostat feedback, a bone mineralisation algorithm and an evolution law for microdamage accumulation. Mechanical disuse and microdamage were assumed to stimulate RANKL production, which modulates activation frequency of basic multicellular units in bone remodelling. This mechanical feedback mechanism controls removal of excess bone mass and microdamage. Furthermore, a novel measure of bone local failure due to instantaneous overloading was developed. Numerical simulations indicate that trabecular bone volume fraction and bone matrix damage are determined by the respective bone turnover and homeostatic loading conditions. PMO patients treated with the currently WHO-approved dose of denosumab (60 mg administrated every 6 months) exhibit increased BMD, increased bone ash fraction and damage. In untreated patients, BMD will significantly decrease, as will ash fraction; while damage will increase. The model predicted that, depending on the time elapsed between the onset of PMO and the beginning of treatment, BMD slowly converges to the same steady-state value, while damage is low in patients treated soon after the onset of the disease and high in patients having PMO for a longer period. The simulations show that late treatment PMO patients have a significantly higher risk of local failure compared to patients that are treated soon after the onset of the disease. Furthermore, overloading resulted in an increase of BMD, but also in a faster increase of damage, which may consequently promote the risk of fracture, specially in late treatment scenarios. In case of mechanical disuse, the model predicted reduced BMD gains due to denosumab, while no significant change in damage occurred, thus leading to an increased risk of local failure compared to habitual loading.

Prediction of mechanical properties of trabecular bone in patients with type 2 diabetes using damage based finite element method

Type-2 diabetic (T2D) and osteoporosis (OP) suffered patients are more prone to fragile fracture though the nature of alteration in areal bone mineral density (aBMD) in these two cases are completely different. Therefore, it becomes crucial to compare the effect of T2D and OP on alteration in mechanical and structural properties of femoral trabecular bone. This study investigated the effect of T2D, OP, and osteopenia on bone structural and mechanical properties using micro-CT, nanoindentation and compression test. Further, a nanoscale finite element model (FEM) was developed to predict the cause of alteration in mechanical properties. Finally, a damage-based FEM was proposed to predict the pathological related alteration of bone's mechanical response. The obtained results demonstrated that the T2D group had lower volume fraction (-18.25%, p = 0.023), young's modulus (-23.47%, p = 0.124), apparent modulus (-37.15%, p = 0.02), and toughness (-40%, p = 0.001) than the osteoporosis group. The damage-based FE results were found in good agreement with the compression experiment results for all three pathological conditions. Also, nanoscale FEM results demonstrated that the elastic and failure properties of mineralised collagen fibril decreases with increase in crystal size. This study reveals that T2D patients are more prone to fragile fracture in comparison to OP and osteopenia patients. Also, the proposed damage-based FEM can help to predict the risk of fragility fracture for different pathological conditions.

A Review on Multiscale Bone Damage: From the Clinical to the Research Perspective

The investigation of bone damage processes is a crucial point to understand the mechanisms of age-related bone fractures. In order to reduce their impact, early diagnosis is key. The intricate architecture of bone and the complexity of multiscale damage processes make fracture prediction an ambitious goal. This review, supported by a detailed analysis of bone damage physical principles, aims at presenting a critical overview of how multiscale imaging techniques could be used to implement reliable and validated numerical tools for the study and prediction of bone fractures. While macro- and meso-scale imaging find applications in clinical practice, micro- and nano-scale imaging are commonly used only for research purposes, with the objective to extract fragility indexes. Those images are used as a source for multiscale computational damage models. As an example, micro-computed tomography (micro-CT) images in combination with micro-finite element models could shed some light on the comprehension of the interaction between micro-cracks and micro-scale bone features. As future insights, the actual state of technology suggests that these models could be a potential substitute for invasive clinical practice for the prediction of age-related bone fractures. However, the translation to clinical practice requires experimental validation, which is still in progress.

High-Performance Computing Comparison of Implicit and Explicit Nonlinear Finite Element Simulations of Trabecular Bone

BACKGROUND AND OBJECTIVE

Finite element models built from micro-computed tomography scans have become a powerful tool to investigate the mechanical properties of trabecular bone. There are two types of solving algorithms in the finite element method: implicit and explicit. Both of these methods have been utilized to study the trabecular bone. However, an investigation comparing the results obtained using the implicit and explicit solvers is lacking. Thus, in this paper, we contrast implicit and explicit procedures by analyzing trabecular bone samples as a case study.

METHODS

Micro-computed tomography-based finite element analysis of trabecular bone under a direct quasi-static compression was done using implicit and explicit methods. The differences in the predictions of mechanical properties and computational time of the two methods were studied using high-performance computing.

RESULTS

Our findings indicate that the results using implicit and explicit solvers are well comparable, given that similar problem set up is carefully utilized. Also, the parallel scalability of the two methods was similar, while the explicit solver performed about five times faster than the implicit method. Along with faster performance, the explicit method utilized significantly less memory for the analysis, which shows another benefit of using an explicit solver for this case study.

CONCLUSIONS

The comparison of the implicit and explicit methods for the simulation of trabecular bone samples should be highly valuable to the bone modeling community and researchers studying complex cellular and architectured materials.

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.

Effect of variations in tissue-level ductility on human vertebral strength

Although the ductility of bone tissue is a unique element of bone quality and varies with age and across the population, the extent to which and mechanisms by which typical population-variations in tissue-level ductility can alter whole-bone strength remains unclear. To provide insight, we conducted a finite element analysis parameter study of whole-vertebral (monotonic) compressive strength on six human L1 vertebrae. Each model was generated from micro-CT scans, capturing the trabecular micro-architecture in detail, and included a non-linear constitutive model for the bone tissue that allowed for plastic yielding, different strengths in tension and compression, large deformations, and, uniquely, localized damage once a specified limit in tissue-level ultimate strain was exceeded. Those strain limits were based on reported (mean ± SD) values from cadaver experiments (8.8 ± 3.7% strain for trabecular tissue and 2.2 ± 0.9% for cortical tissue). In the parameter study, the strain limits were varied by ±1 SD from their mean values, for a combination of nine analyses per specimen; bounding values of zero and unlimited post-yield strain were also modeled. The main outcomes from the finite element analysis were the vertebral compressive strength and the amount of failed (yielded or damaged) tissue at the overall structure-level failure. Compared to a reference case of using the mean values of ultimate strain, we found that varying both trabecular and cortical tissue ultimate strains by ±1 SD changed the computed vertebral strength by (mean ± SD) ±6.9 ± 1.1% on average. Mechanistically, that modest effect arose because the proportion of yielded tissue (without damage) was 0.9 ± 0.3% of all the bone tissue across the nine cases and the proportion of damaged tissue (i.e. tissue exceeding the prescribed tissue-level ultimate strain) was 0.2 ± 0.1%. If the types of variations in tissue-level ductility investigated here accurately represent real typical variations in the population, the consistency of our results across specimens and the modest effect size together suggest that typical variations in tissue-level ductility only have a modest impact on vertebral compressive strength, in large part because so few trabeculae are damaged at the load capacity of the bone.

Efficient materially nonlinear μ FE solver for simulations of trabecular bone failure

An efficient solver for large-scale linearμ ⁢ FE simulations was extended for nonlinear material behavior. The material model included damage-based tissue degradation and fracture. The new framework was applied to 20 trabecular biopsies with a mesh resolution of36 ⁢ μ ⁢ m . Suitable material parameters were identified based on two biopsies by comparison with axial tension and compression experiments. The good parallel performance and low memory footprint of the solver were preserved. Excellent correlation of the maximum apparent stress was found between simulations and experiments (R 2 > 0.97 ). The development of local damage regions was observable due to the nonlinear nature of the simulations. A novel elasticity limit was proposed based on the local damage information. The elasticity limit was found to be lower than the 0.2% yield point. Systematic differences in the yield behavior of biopsies under apparent compression and tension loading were observed. This indicates that damage distributions could lead to more insight into the failure mechanisms of trabecular bone.

A novel phase field method for modeling the fracture of long bones

A proximal humerus fracture is an injury to the shoulder joint that necessitates medical attention. While it is one of the most common fracture injuries impacting the elder community and those who suffer from traumatic falls or forceful collisions, there are almost no validated computational methods that can accurately model these fractures. This could be due to the complex, inhomogeneous bone microstructure, complex geometries, and the limitations of current fracture mechanics methods. In this paper, we develop a novel phase field method to investigate the proximal humerus fracture. To model the fracture in the inhomogeneous domain, we propose a power-law relationship between bone mineral density and critical energy release rate. The method is validated by an in vitro experiment, in which a human humerus is constrained on both ends while subjected to compressive loads on its head, in the longitudinal direction, that lead to fracture at the anatomical neck. CT scans are employed to acquire the bone geometry and material parameters, from which detailed finite element meshes with inhomogeneous Young modulus distributions are generated. The numerical method, implemented in a high performance computing environment, is used to quantitatively predict the complex 3D brittle fracture of the bone and is shown to be in good agreement with experimental observations. Furthermore, our findings show that the damage is initiated in the trabecular bone-head and propagates outward towards the bone cortex. We conclude that the proposed phase field method is a promising approach to model bone fracture.

An explicit micro-FE approach to investigate the post-yield behaviour of trabecular bone under large deformations

Homogenised finite element (FE) analyses are able to predict osteoporosis-related bone fractures and become useful for clinical applications. The predictions of FE analyses depend on the apparent, heterogeneous, anisotropic, elastic, and yield material properties, which are typically determined by implicit micro-FE (μFE) analyses of trabecular bone. The objective of this study is to explore an explicit μFE approach to determine the apparent post-yield behaviour of trabecular bone, beyond the elastic and yield properties. The material behaviour of bone tissue was described by elasto-plasticity with a von Mises yield criterion closed by a planar cap for positive hydrostatic stresses to distinguish the post-yield behaviour in tension and compression. Two ultimate strains for tension and compression were calibrated to trigger element deletion and reproduce damage of trabecular bone. A convergence analysis was undertaken to assess the role of the mesh. Thirteen load cases using periodicity-compatible mixed uniform boundary conditions were applied to three human trabecular bone samples of increasing volume fractions. The effect of densification in large strains was explored. The convergence study revealed a strong dependence of the apparent ultimate stresses and strains on element size. An apparent quadric strength surface for trabecular bone was successfully fitted in a normalised stress space. The effect of densification was reproduced and correlated well with former experimental results. This study demonstrates the potential of the explicit FE formulation and the element deletion technique to reproduce damage in trabecular bone using μFE analyses. The proper account of the mesh sensitivity remains challenging for practical computing times.

Assessment of mechanical properties of human head tissues for trauma modelling

Many discrepancies are found in the literature regarding the damage and constitutive models for head tissues as well as the values of the constants involved in the constitutive equations. Their proper definition is required for consistent numerical model performance when predicting human head behaviour, and hence skull fracture and brain damage. The objective of this research is to perform a critical review of constitutive models and damage indicators describing human head tissue response under impact loading. A 3D finite element human head model has been generated by using computed tomography images, which has been validated through the comparison to experimental data in the literature. The threshold values of the skull and the scalp that lead to fracture have been analysed. We conclude that (1) compact bone properties are critical in skull fracture, (2) the elastic constants of the cerebrospinal fluid affect the intracranial pressure distribution, and (3) the consideration of brain tissue as a nearly incompressible solid with a high (but not complete) water content offers pressure responses consistent with the experimental data.

Nonlinear micro-CT based FE modeling of trabecular bone-Sensitivity of apparent response to tissue constitutive law and bone volume fraction

In this study, the sensitivity of the apparent response of trabecular bone to different constitutive models at the tissue level was investigated using finite element (FE) modeling based on micro-computed tomography (micro-CT). Trabecular bone specimens from porcine femurs were loaded under a uniaxial compression experimentally and computationally. The apparent behaviors computed using von Mises, Drucker-Prager, and Cast Iron plasticity models were compared. Secondly, the effect of bone volume fraction was studied by changing the bone volume fraction of a trabecular bone sample while keeping the same basic architecture. Also, constitutive models' parameters of the tissue were calibrated for porcine bone, and the effects of different parameters on resulting apparent response were investigated through a parametric study. The calibrated effective tissue elastic modulus of porcine trabecular bone was 10±1.2 GPa, which is in the lower range of modulus values reported in the literature for human and bovine trabecular bones (4-23.8 GPa). It was also observed that, unlike elastic modulus, yield properties of tissue could not be uniquely calibrated by fitting an apparent response from simulations to experiments under a uniaxial compression. Our results demonstrated that using these 3 tissue constitutive models had only a slight effect on the apparent response. As expected, there was a significant change in the apparent response with varying bone volume fraction. Also, both apparent modulus and maximum stress had a linear relation with bone volume fraction.

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.

Micro Finite Element models of the vertebral body: Validation of local displacement predictions

The estimation of local and structural mechanical properties of bones with micro Finite Element (microFE) models based on Micro Computed Tomography images depends on the quality bone geometry is captured, reconstructed and modelled. The aim of this study was to validate microFE models predictions of local displacements for vertebral bodies and to evaluate the effect of the elastic tissue modulus on model’s predictions of axial forces. Four porcine thoracic vertebrae were axially compressed in situ, in a step-wise fashion and scanned at approximately 39μm resolution in preloaded and loaded conditions. A global digital volume correlation (DVC) approach was used to compute the full-field displacements. Homogeneous, isotropic and linear elastic microFE models were generated with boundary conditions assigned from the interpolated displacement field measured from the DVC. Measured and predicted local displacements were compared for the cortical and trabecular compartments in the middle of the specimens. Models were run with two different tissue moduli defined from microindentation data (12.0GPa) and a back-calculation procedure (4.6GPa). The predicted sum of axial reaction forces was compared to the experimental values for each specimen. MicroFE models predicted more than 87% of the variation in the displacement measurements (R² = 0.87–0.99). However, model predictions of axial forces were largely overestimated (80–369%) for a tissue modulus of 12.0GPa, whereas differences in the range 10–80% were found for a back-calculated tissue modulus. The specimen with the lowest density showed a large number of elements strained beyond yield and the highest predictive errors. This study shows that the simplest microFE models can accurately predict quantitatively the local displacements and qualitatively the strain distribution within the vertebral body, independently from the considered bone types.

Micro-CT based finite element models of cancellous bone predict accurately displacement once the boundary condition is well replicated: A validation study

Non-destructive 3D micro-computed tomography (microCT) based finite element (microFE) models are used to estimate bone mechanical properties at tissue level. However, their validation remains challenging. Recent improvements in the quantification of displacements in bone tissue biopsies subjected to staged compression, using refined Digital Volume Correlation (DVC) techniques, now provide a full field displacement information accurate enough to be used for microFE validation. In this study, three specimens (two humans and one bovine) were tested with two different experimental set-ups, and the resulting data processed with the same DVC algorithm. The resulting displacement vector field was compared to that predicted by microFE models solved with three different boundary conditions (BC): nominal force resultant, nominal displacement resultant, distributed displacement. The first two conditions were obtained directly from the measurements provided by the experimental jigs, whereas in the third case the displacement field measured by the DVC in the top and bottom layer of the specimen was applied. Results show excellent relationship between the numerical predictions (x) and the experiments (y) when using BC derived from the DVC measurements (U_X: y=1.07x-0.002, RMSE: 0.001mm; U_Y: y=1.03x-0.001, RMSE: 0.001mm; U_Z: y=x+0.0002, RMSE: 0.001 mm for bovine specimen), whereas only poor correlation was found using BCs according to experiment set-ups. In conclusion, microFE models were found to predict accurately the vectorial displacement field using interpolated displacement boundary condition from DVC measurement.

Stiffness and strength of bone in osteoporotic patients treated with varying durations of oral bisphosphonates

Apparent modulus and failure stress of trabecular bone structure from 45 women with osteoporosis treated with bisphosphonates for varying durations were studied using finite element analyses and statistical modeling. Following adjustments for patient age and bone volume, increasing bisphosphonate treatment duration for up to 7.3 years was associated with treatment-time-dependent increases in bone apparent modulus and failure stress. Treatment durations exceeding 7.3 years were associated with time-dependent decreases in apparent modulus and failure stress from the peak values observed.

INTRODUCTION

The purpose of this study was to clarify the relationship between bisphosphonate (BP) treatment duration and human bone quality. This study quantified changes in the apparent modulus and failure stress of trabecular bone biopsied from patients with osteoporosis who were treated with BPs for widely varying durations.

METHODS

Forty-five iliac crest bone samples were obtained from women with osteoporosis who were continuously treated with oral BPs for varying periods of up to 16 years. Micro-CT imaging was used to develop three-dimensional virtual models of the trabecular bone from these samples. Apparent modulus and failure stress of these virtual models were determined using finite element analyses (FEA). Polynomial regression and cubic splines, adjusted for relevant (age and BV/TV) covariates, were used to statistically model the data and quantify the relationships between BP treatment duration and apparent modulus or failure stress.

RESULTS

Second-order polynomial models were needed to relate apparent modulus or failure stress to BP treatment duration. These models showed that these bone quality parameters (a) increased with increasing BP treatment duration up to approximately 7.3 years, (b) reached a maximum at this (~7.3 years) time, and then (c) declined with BP treatment durations exceeding ~7.3 years. A similar result was obtained by modeling with cubic splines.

CONCLUSIONS

Changes in FEA-derived apparent stiffness and failure stress are attributable to changes in trabecular bone structure, which in turn are related to the duration of BP treatment. These relationships are evident even after adjustments are made in the statistical models for changes in age and BV/TV. According to these models, increases in trabecular bone apparent stiffness and failure stress linked to BPs cease and appear to reverse after approximately 7.3 years of treatment. Conclusions regarding optimal BP therapy duration await study of additional bone quality parameters.

Effect of thermodisinfection on mechanic parameters of cancellous bone

Revision surgery of joint replacements is increasing and raises the demand for allograft bone since restoration of bone stock is crucial for longevity of implants. Proceedings of bone grafts influence the biological and mechanic properties differently. This study examines the effect of thermodisinfection on mechanic properties of cancellous bone. Bone cylinders from both femoral heads with length 45 mm were taken from twenty-three 6-8 months-old piglets, thermodisinfected at 82.5 °C according to bone bank guidelines and control remained native. The specimens were stored at -20 °C immediately and were put into 21 °C Ringer's solution for 3 h before testing. Shear and pressure modulus were tested since three point bending force was examined until destruction. Statistical analysis was done with non-parametric Wilcoxon, t test and SPSS since p < 0.05 was significant. Shear modulus was significantly reduced by thermodisinfection to 1.02 ± 0.31 GPa from 1.28 ± 0.68 GPa for unprocessed cancellous bone (p = 0.029) since thermodisinfection reduced pressure modulus not significantly from 6.30 ± 4.72 GPa for native specimens to 4.97 ± 2.23 GPa and maximum bending force was 270.03 ± 116.68 N for native and 228.80 ± 70.49 N for thermodisinfected cancellous bone. Shear and pressure modulus were reduced by thermodisinfection around 20 % and maximum bending force was impaired by about 15 % compared with native cancellous bone since only the reduction of shear modulus reached significance. The results suggest that thermodisinfection similarly affects different mechanic properties of cancellous bone and the reduction of mechanic properties should not relevantly impair clinical use of thermodisinfected cancellous 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.

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.

Inverse finite element modeling for characterization of local elastic properties in image-guided failure assessment of human trabecular bone

The local interpretation of microfinite element (μFE) simulations plays a pivotal role for studying bone structure–function relationships such as failure processes and bone remodeling.In the past μFE simulations have been successfully validated on the apparent level,however, at the tissue level validations are sparse and less promising. Furthermore,intra trabecular heterogeneity of the material properties has been shown by experimental studies. We proposed an inverse μFE algorithm that iteratively changes the tissue level Young's moduli such that the μFE simulation matches the experimental strain measurements.The algorithm is setup as a feedback loop where the modulus is iteratively adapted until the simulated strain matches the experimental strain. The experimental strain of human trabecular bone specimens was calculated from time-lapsed images that were gained by combining mechanical testing and synchrotron radiation microcomputed tomography(SRlCT). The inverse μFE algorithm was able to iterate the heterogeneous distribution of moduli such that the resulting μFE simulations matched artificially generated and experimentally measured strains.

Predicting mouse vertebra strength with micro-computed tomography-derived finite element analysis

As in clinical studies, finite element analysis (FEA) developed from computed tomography (CT) images of bones are useful in pre-clinical rodent studies assessing treatment effects on vertebral body (VB) strength. Since strength predictions from microCT-derived FEAs (μFEA) have not been validated against experimental measurements of mouse VB strength, a parametric analysis exploring material and failure definitions was performed to determine whether elastic μFEAs with linear failure criteria could reasonably assess VB strength in two studies, treatment and genetic, with differences in bone volume fraction between the control and the experimental groups. VBs were scanned with a 12-μm voxel size, and voxels were directly converted to 8-node, hexahedral elements. The coefficient of determination or R (2) between predicted VB strength and experimental VB strength, as determined from compression tests, was 62.3% for the treatment study and 85.3% for the genetic study when using a homogenous tissue modulus (E t) of 18 GPa for all elements, a failure volume of 2%, and an equivalent failure strain of 0.007. The difference between prediction and measurement (that is, error) increased when lowering the failure volume to 0.1% or increasing it to 4%. Using inhomogeneous tissue density-specific moduli improved the R (2) between predicted and experimental strength when compared with uniform E t=18 GPa. Also, the optimum failure volume is higher for the inhomogeneous than for the homogeneous material definition. Regardless of model assumptions, μFEA can assess differences in murine VB strength between experimental groups when the expected difference in strength is at least 20%.

Theoretical effects of fully ductile versus fully brittle behaviors of bone tissue on the strength of the human proximal femur and vertebral body

The influence of the ductility of bone tissue on whole-bone strength represents a fundamental issue of multi-scale biomechanics. To gain insight, we performed a computational study of 16 human proximal femurs and 12 T9 vertebral bodies, comparing the whole-bone strength for the two hypothetical bounding cases of fully brittle versus fully ductile tissue-level failure behaviors, all other factors, including tissue-level elastic modulus and yield stress, held fixed. For each bone, a finite element model was generated (60-82 μm element size; up to 120 million elements) and was virtually loaded in habitual (stance for femur, compression for vertebra) and non-habitual (sideways fall, only for femur) loading modes. Using a geometrically and materially non-linear model, the tissue was assumed to be either fully brittle or fully ductile. We found that, under habitual loading, changing the tissue behavior from fully ductile to fully brittle reduced whole-bone strength by 38.3±2.4% (mean±SD) and 39.4±1.9% for the femur and vertebra, respectively (p=0.39 for site difference). These reductions were remarkably uniform across bones, but (for the femur) were greater for non-habitual (57.1±4.7%) than habitual loading (p<0.001). At overall structural failure, there was 5-10-fold less failed tissue for the fully brittle than fully ductile cases. These theoretical results suggest that the whole-bone strength of the proximal femur and vertebra can vary substantially between fully brittle and fully ductile tissue-level behaviors, an effect that is relatively insensitive to bone morphology but greater for non-habitual loading.