Integrated remodeling-to-fracture finite element model of human proximal femur behavior

The impact of the parameters of the constitutive model on the distribution of strain in the femoral head

The rapid spread of the finite element method has caused that it has become, among other methods, the standard tool for pre-clinical estimates of bone properties. This paper presents an application of this method for the calculation and prediction of strain and stress fields in the femoral head. The aim of the work is to study the influence of the considered anisotropy and heterogeneity of the modeled bone on the mechanical fields during a typical gait cycle. Three material models were tested with different properties of porous bone carried out in literature: a homogeneous isotropic model, a heterogeneous isotropic model, and a heterogeneous anisotropic model. In three cases studied, the elastic properties of the bone were determined basing on the Zysset-Curnier approach. The tensor of elastic constants defining the local properties of porous bone is correlated with a local porosity and a second order fabric tensor describing the bone microstructure. In the calculations, a model of the femoral head generated from high-resolution tomographic scans was used. Experimental data were drawn from publicly available database "Osteoporotic Virtual Physiological Human Project." To realistically reflect the load on the femoral head, main muscles were considered, and their contraction forces were determined based on inverse kinematics. For this purpose, the results from OpenSim packet were used. The simulations demonstrated that differences between the results predicted by these material models are significant. Only the anisotropic model allowed for the plausible distribution of stresses along the main trabecular groups. The outcomes also showed that the precise evaluation of the mechanical fields is critical in the context of bone tissue remodeling under mechanical stimulations.

Fracture pattern projection on 3D bone models as support for bone fracture simulations

BACKGROUND AND OBJECTIVE

Obtaining bone models that represent certain types of fractures is limited by the need for such fractures to occur in real life and to be processed from medical images. This work aims to propose a method that starts from the design of specific fracture patterns in order to be projected on 3D geometric bone models, being prepared for their subsequent geometric fracturing.

METHODS

The process of projecting expert-generated fracture patterns has been approached in such a way that they contain geometrical and topological information for the subsequent fracture of the triangle mesh representing the bone model, giving information about the validity of the fracture pattern due to the design process, the validation performed, and the relationships between the fracture lines.

RESULTS

Different 3D models of long bones have been used (femur, humerus, ulna and fibula). Also, different types of fracture patterns have been created. These patterns have been used to obtain their projection on three-dimensional bones. In this study, an expert validation of the fracture patterns projected on the bone models is performed. A forensic validation of the fracture patterns used as starting point for the projection is also performed for cases in which this fracture is produced by impact, for which there is scientific evidence based on forensic analysis. This validation also supports the experts, giving them the necessary feedback to complete or modify their fracture patterns according to criteria analyzed from a forensic point of view.

CONCLUSIONS

The patterns fit the bone models correctly, despite the irregularities of the bone models, and correspond to the expected projection. In addition, it provides us with a clear line of work, by using the topological information of the fracture pattern and the bone model, which allows us to establish a consistent basis for future guided fractures.

Mesh-independent damage model for trabecular bone fracture simulation and experimental validation

We propose in this study a two-dimensional constitutive model for trabecular bone combining continuum damage with embedded strong discontinuity. The model is capable of describing the three failure phases of trabecular bone tissue which is considered herein as a quasi-brittle material with strains and rotations assumed to be small and without viscous, thermal or other non-mechanical effects. The finite element implementation of the present model uses constant strain triangle (CST) elements. The displacement jump vector is implicitly solved through a return mapping algorithm at the local (finite element) level, while the global equilibrium equations are dealt with by Newton-Raphson method. The performance, accuracy and applicability of the proposed model for trabecular bone fracture are evaluated and validated against experimental measurements. These comparisons include both global and local aspects through numerical simulations of three-point bending tests performed on 10 single bovine trabeculae in the quasi-static regime.

Parametric investigation of the effects of load level on fatigue crack growth in trabecular bone based on artificial neural network computation

This study reports the development of an artificial neural network computation model to predict the accumulation of crack density and crack length in cancellous bone under a cyclic load. The model was then applied to conduct a parametric investigation into the effects of load level on fatigue crack accumulation in cancellous bone. The method was built in three steps: (1) conducting finite element simulations to predict fatigue growth of different three-dimensional micro-computed tomography cancellous bone specimens considering input combinations based on a factorial experimental design; (2) performing a training stage of an artificial neural network based on the results of step 1; and (3) applying the trained artificial neural network to rapidly predict the crack density and the crack length growth for cancellous bone under a cyclic loading for a given applied apparent strain, cycle frequency, bone volume fraction, bone density and apparent elastic modulus.

Numerical modelling of hip fracture patterns in human femur

BACKGROUND AND OBJECTIVE

Hip fracture morphology is an important factor determining the ulterior surgical repair and treatment, because of the dependence of the treatment on fracture morphology. Although numerical modelling can be a valuable tool for fracture prediction, the simulation of femur fracture is not simple due to the complexity of bone architecture and the numerical techniques required for simulation of crack propagation. Numerical models assuming homogeneous fracture mechanical properties commonly fail in the prediction of fracture patterns. This paper focuses on the prediction of femur fracture based on the development of a finite element model able to simulate the generation of long crack paths.

METHODS

The finite element model developed in this work demonstrates the capability of predicting fracture patterns under stance loading configuration, allowing the distinction between the main fracture paths: intracapsular and extracapsular fractures. It is worth noting the prediction of different fracture patterns for the same loading conditions, as observed during experimental tests.

RESULTS AND CONCLUSIONS

The internal distribution of bone mineral density and femur geometry strongly influences the femur fracture morphology and fracture load. Experimental fracture paths have been analysed by means of micro-computed tomography allowing the comparison of predicted and experimental crack surfaces, confirming the good accuracy of the numerical model.

Interaction of Microcracks and Tissue Compositional Heterogeneity in Determining Fracture Resistance of Human Cortical Bone

Recent studies demonstrated an association between atypical femoral fracture (AFF) and long-term bisphosphonate (BP) use for osteoporosis treatment. Due to BP treatment, bone undergoes alterations including increased microcrack density and reduced tissue compositional heterogeneity. However, the effect of these changes on the fracture response of bone is not well understood. As a result, the goal of the current study is to evaluate the individual and combined effects of microcracks and tissue compositional heterogeneity on fracture resistance of cortical bone using finite element modeling (FEM) of compact tension (CT) specimen tests with varying microcrack density, location, and clustering, and material heterogeneity in three different bone samples. The simulation results showed that an increase in microcrack density improved the fracture resistance irrespective of the local material property heterogeneity and microcrack distribution. A reduction in material property heterogeneity adversely affected the fracture resistance in models both with and without microcracks. When the combined changes in microcrack density and tissue material property heterogeneity representing BP treatment were evaluated, the models corresponding to BP-treated bone demonstrated reduced fracture resistance. The simulation results also showed that although microcrack location and clustering, and microstructure significantly influenced fracture resistance, the trends observed on the effect of microcrack density and tissue material property heterogeneity did not change. In summary, these results provide new information on the interaction of microcracks, tissue material property heterogeneity, and fracture resistance and may improve the understanding of the influence of mechanical changes due to prolonged BP use on the fracture behavior of cortical bone.

Mapping anisotropy improves QCT-based finite element estimation of hip strength in pooled stance and side-fall load configurations

Hip fractures are one of the most severe consequences of osteoporosis. Compared to the clinical standard of DXA-based aBMD at the femoral neck, QCT-based FEA delivers a better surrogate of femoral strength and gains acceptance for the calculation of hip fracture risk when a CT reconstruction is available. Isotropic, homogenised voxel-based, finite element (hvFE) models are widely used to estimate femoral strength in cross-sectional and longitudinal clinical studies. However, fabric anisotropy is a classical feature of the architecture of the proximal femur and the second determinant of the homogenised mechanical properties of trabecular bone. Due to the limited resolution, fabric anisotropy cannot be derived from clinical CT reconstructions. Alternatively, fabric anisotropy can be extracted from HR-pQCT images of cadaveric femora. In this study, fabric anisotropy from HR-pQCT images was mapped onto QCT-based hvFE models of 71 human proximal femora for which both HR-pQCT and QCT images were available. Stiffness and ultimate load computed from anisotropic hvFE models were compared with previous biomechanical tests in both stance and side-fall configurations. The influence of using the femur-specific versus a mean fabric distribution on the hvFE predictions was assessed. Femur-specific and mean fabric enhance the prediction of experimental ultimate force for the pooled, i.e. stance and side-fall, (isotropic: r²=0.81, femur-specific fabric: r²=0.88, mean fabric: r²=0.86,p<0.001) but not for the individual configurations. Fabric anisotropy significantly improves bone strength prediction for the pooled configurations, and mapped fabric provides a comparable prediction to true fabric. The mapping of fabric anisotropy is therefore expected to help generate more accurate QCT-based hvFE models of the proximal femur for personalised or multiple load configurations.

Age-related mechanical strength evolution of trabecular bone under fatigue damage for both genders: Fracture risk evaluation

Bone tissue is a living composite material, providing mechanical and homeostatic functions, and able to constantly adapt its microstructure to changes in long term loading. This adaptation is conducted by a physiological process, known as "bone remodeling". This latter is manifested by interactions between osteoclasts and osteoblasts, and can be influenced by many local factors, via effects on bone cell differentiation and proliferation. In the current work, age and gender effects on damage rate evolution, throughout life, have been investigated using a mechanobiological finite element modeling. To achieve the aim, a mathematical model has been developed, coupling both cell activities and mechanical behavior of trabecular bone, under cyclic loadings. A series of computational simulations (ABAQUS/UMAT) has been performed on a 3D human proximal femur, allowing to investigate the effects of mechanical and biological parameters on mechanical strength of trabecular bone, in order to evaluate the fracture risk resulting from fatigue damage. The obtained results revealed that mechanical stimulus amplitude affects bone resorption and formation rates, and indicated that age and gender are major factors in bone response to the applied loadings.

PERSONALIZED FINITE ELEMENT MODELING ANALYSIS OF FEMUR BONE HEALING AFTER INTRAMEDULLARY NAILING

Purpose: Based on rapid modeling 1 year after intramedullary nailing, personalized finite element modeling analysis was performed to predict whether the broken ends of fractured bones would break again after nail dislodgement. Methods: A total of 10 male volunteers with femur fractures who had undergone intramedullary nailing were selected 1 year after fixation and were divided into healing ([Formula: see text][Formula: see text]5) and non-healing ([Formula: see text][Formula: see text]5) groups based on X-ray analysis. We modeled each femoral fracture and performed finite element analyses after the intramedullary nail was dislodged. Static loads and constraints were applied to each model to simulate a person standing on one leg. Results: In the healing group, the von Mises stress concentrations and stress concentration point distribution were located outside the bone healing area, indicating that the stress was not concentrated at the fracture site. In the non-healing group, the maximum von Mises stress for various materials was located in the broken ends of the fractured bone, indicating that the stress was concentrated at the fracture site. Conclusion: Personalized modeling can be used to analyze bone healing before removal of a fixator to predict the stability of the fractured bone after fixator removal and to rapidly decide whether slow walking could refracture the broken ends.

ASSESSMENT OF OSTEOPOROTIC FEMORAL FRACTURE RISK: FINITE ELEMENT METHOD AS A POTENTIAL REPLACEMENT FOR CURRENT CLINICAL TECHNIQUES

Femoral fracture risk prediction is a necessary step preceding effective pharmacological intervention or pre-operative planning. Current clinical methods for fracture risk prediction rely on 2D imaging methods and have limited predictive value. Researchers are therefore trying to find improved methods for fracture prediction. During last few decades, many studies have focused on integration of 3D imaging techniques and the finite element (FE) method to improve the accuracy of fracture assessment techniques. In this paper, we review the recent advances in FE and other techniques for predicting the risk of femoral fractures. Based on a number of selected studies, the different steps that are involved in generation of patient-specific FE models are reviewed with particular emphasis on the fracture criteria. The inaccuracies that might arise due to the imperfections of the involved steps are also discussed. It is concluded that compared to image- and geometry-based techniques, FE is a more promising approach for prediction of fracture loads. However, certain technological advancements in FE modeling protocols are required before FE modeling can be recruited in clinical settings.

3D patient-specific model of the tibia from CT for orthopedic use

OBJECTIVES

3D patient-specific model of the tibia is used to determine the torque needed to initialize the tibial torsion correction.

METHODS

The finite elements method is used in the biomechanical modeling of tibia. The geometric model of the tibia is obtained from CT images. The tibia is modeled as an anisotropic material with non-homogeneous mechanical properties.

CONCLUSIONS

The maximum stress is located in the shaft of tibia diaphysis. With both meshes are obtained similar results of stresses and displacements. For this patient-specific model, the torque must be greater than 30 Nm to initialize the correction of tibial torsion deformity.

Effects of Different Loading Patterns on the Trabecular Bone Morphology of the Proximal Femur Using Adaptive Bone Remodeling

In this study, the changes in the bone density of human femur model as a result of different loadings were investigated. The model initially consisted of a solid shell representing cortical bone encompassing a cubical network of interconnected rods representing trabecular bone. A computationally efficient program was developed that iteratively changed the structure of trabecular bone by keeping the local stress in the structure within a defined stress range. The stress was controlled by either enhancing existing beam elements or removing beams from the initial trabecular frame structure. Analyses were performed for two cases of homogenous isotropic and transversely isotropic beams. Trabecular bone structure was obtained for three load cases: walking, stair climbing and stumbling without falling. The results indicate that trabecular bone tissue material properties do not have a significant effect on the converged structure of trabecular bone. In addition, as the magnitude of the loads increase, the internal structure becomes denser in critical zones. Loading associated with the stumbling results in the highest density; whereas walking, considered as a routine daily activity, results in the least internal density in different regions. Furthermore, bone volume fraction at the critical regions of the converged structure is in good agreement with previously measured data obtained from combinations of dual X-ray absorptiometry (DXA) and computed tomography (CT). The results indicate that the converged bone architecture consisting of rods and plates are consistent with the natural bone morphology of the femur. The proposed model shows a promising means to understand the effects of different individual loading patterns on the bone density.

A higher-order mathematical modeling for dynamic behavior of protein microtubule shell structures including shear deformation and small-scale effects

Microtubules in mammalian cells are cylindrical protein polymers which structurally and dynamically organize functional activities in living cells. They are important for maintaining cell structures, providing platforms for intracellular transport, and forming the spindle during mitosis, as well as other cellular processes. Various in vitro studies have shown that microtubules react to applied mechanical loading and physical environment. To investigate the mechanisms underlying such phenomena, a mathematical model based on the orthotropic higher-order shear deformation shell formulation and Hamilton's principle is presented in this paper for dynamic behavior of microtubules. The numerical results obtained by the proposed shell model are verified by the experimental data from the literature, showing great consistency. The nonlocal elasticity theory is also utilized to describe the nano-scale effects of the microtubule structure. The wave propagation and vibration characteristics of the microtubule are examined in the presence and absence of the cytosol employing proposed formulations. The effects of different system parameters such as length, small scale parameter, and cytosol viscosity on vibrational behavior of a microtubule are elucidated. The definitions of critical length and critical viscosity are introduced and the results obtained using the higher order shell model are compared with those obtained employing a first-order shear deformation theory. This comparison shows that the small scale effects become important for higher values of the wave vector and the proposed model gives more accurate results for both small and large values of wave vectors. Moreover, it is shown that for higher circumferential wave number, the torsional wave velocity obtained by the higher-order shell model tend to be higher than the one predicted by the first-order shell model.

Finite element prediction with experimental validation of damage distribution in single trabeculae during three-point bending tests

There is growing evidence that information on trabecular microarchitecture can improve the assessment of fracture risk. One current strategy is to exploit finite element (FE) analysis applied to experimental data of mechanically loaded single trabecular bone tissue obtained from non-invasive imaging techniques for the investigation of the damage initiation and growth of bone tissue. FE analysis of this type of bone has mainly focused on linear and non-linear analysis to evaluate the bone's failure properties. However, there is a lack of experimentally validated FE damage models at trabecular bone tissue level allowing for the simulation of the progressive damage process (initiation and growth) till complete fracture. Such models are needed to perform enhanced prediction of the apparent failure mechanical properties needed to assess the fracture risk of bone organs. In the current study, we develop a FE model based on a continuum damage mechanics (CDM) approach to simulate the damage initiation and propagation of a single trabecula till complete facture in quasi-static regime. Three-point bending experiments were performed on single bovine trabeculae and compared to FE results. In order to validate the proposed FE mode, (i) the force displacement curve was compared to the experimental one and (ii) the damage distribution was correlated to the measured one obtained by digital image correlation based on stress whitening in bone, reported to be correlated to microdamage. A very good agreement was obtained between the FE and experimental results, indicating that the proposed damage investigation protocol based on FE analysis and testing is reliable to assess the damage behavior of bone tissue and that the current damage model is able to accurately simulate the damaging and fracturing process of single trabeculae under quasi static load.

Computational simulation of the bone remodeling using the finite element method: an elastic-damage theory for small displacements

Background

The resistance of the bone against damage by repairing itself and adapting to environmental conditions is its most important property. These adaptive changes are regulated by physiological process commonly called the bone remodeling. Better understanding this process requires that we apply the theory of elastic-damage under the hypothesis of small displacements to a bone structure and see its mechanical behavior.

Results

The purpose of the present study is to simulate a two dimensional model of a proximal femur by taking into consideration elastic-damage and mechanical stimulus. Here, we present a mathematical model based on a system of nonlinear ordinary differential equations and we develop the variational formulation for the mechanical problem. Then, we implement our mathematical model into the finite element method algorithm to investigate the effect of the damage.

Conclusion

The results are consistent with the existing literature which shows that the bone stiffness drops in damaged bone structure under mechanical loading.