Finite Element Models Of Bone Research Articles

Elastic Modulus and Its Relation to Apparent Mineral Density in Juvenile Equine Bones of the Lower Limb.

Density-modulus relationships are necessary to develop finite element models of bones that may be used to evaluate local tissue response to different physical activities. It is unknown if juvenile equine trabecular bone may be described by the same density-modulus as adult equine bone, and how the density-modulus relationship varies with anatomical location and loading direction. To answer these questions, trabecular bone cores from the third metacarpal (MC3) and proximal phalanx (P1) bones of juvenile horses (age <1 yr) were machined in the longitudinal (n = 134) and transverse (n = 90) directions and mechanically tested in compression. Elastic modulus was related to apparent computed tomography density of each sample using power law regressions. We found that density-modulus relationships for juvenile equine trabecular bone were significantly different for each anatomical location (MC3 versus P1) and orientation (longitudinal versus transverse). Use of the incorrect density-modulus relationship resulted in increased root mean squared percent error of the modulus prediction by 8-17%. When our juvenile density-modulus relationship was compared to one of an equivalent location in adult horses, the adult relationship resulted in an approximately 80% increase in error of the modulus prediction. Moving forward, more accurate models of young bone can be developed and used to evaluate potential exercise regimens designed to encourage bone adaptation.

High performance multi-platform computing for large-scale image-based finite element modeling of bone

BackgroundImage-based finite element (FE) modeling of bone is a non-invasive method to estimate bone stiffness and strength. High-resolution imaging data as input allows for inclusion of bone microarchitecture but results in large amounts of data unsuitable for traditional FE solvers. Bone-specific mesh-free solvers have been developed over the past 20 years to improve on memory efficiency in simulated bone loading applications. The objective of this study was to provide linear performance benchmarking for a bone-specific, mesh-free solver (FAIM) using µCT and HR-pQCT image data on Mac, Linux, and Windows operating systems using both single- and multi-thread CPU and GPU processing. MethodsThe focus is on the linear gradient-descent solver using standardized uniaxial loading of bone models from µCT, and first- and second-generation HR-pQCT scans of the radius and tibia. Convergence, speedup, memory, and batch performance tests were completed using CPUs and GPUs on three laboratory-based systems with Windows, Linux, and Mac operating systems. ResultsAlthough varying by system and model size, time-per-iteration was as low as 0.03 s when an HR-pQCT-based radius model (6.45 million DOF) was solved with 3 GPUs. Strong scaling was achieved with GPU and CPU parallel processing, with strong parallel efficiencies when models were solved using 3 GPUs or ≤ 10 CPU threads. Errors in force, strain energy density, and Von Mises stress were as low as 0.1% when a convergence tolerance of 10−3 or smaller was used. ConclusionThe results of this study indicate that to maximize computational efficiency and minimize model solution times using FAIM software under the standardized tested conditions using µCT, XCT1 and XCT2 HR-pQCT image data, convergence tolerance set to 10−4, and 10 threads or 2 GPUs are sufficient for efficient solution times. Less strict convergence tolerances will improve solution times but will introduce more error in the outcome measures.

From computed tomography to finite element space: A unified bone material mapping strategy

BackgroundThe spatially varying mechanical properties in finite element models of bone are most often derived from bone density data obtained via quantitative computed tomography. The key step is to accurately and efficiently map the density given in voxels to the finite element mesh. MethodsThe density projection is first formulated in least-squares terms and then discretized using a continuous and discontinuous variant of the finite element method. Both discretization variants are compared with the nodal and element approaches known from the literature. FindingsIn terms of accuracy in the L2 norm, energy distance and efficiency, the discontinuous zero-order variant appears to be the most advantageous. The proposed variant sufficiently preserves the spectrum of density at the edges, while keeping computational cost low. InterpretationThe continuous finite element method is analogous to the nodal formulation in the literature, while the discontinuous finite element method is analogous to the element formulation. The two variants differ in terms of implementation, computational cost and ability to preserve the density spectrum. These differences cannot be described and measured by known indirect methods from the literature.

Design optimization procedure for an orthopedic insole having a continuously variable stiffness/shape to reduce the plantar pressure in the foot of a diabetic patient

Foot ulcers and lower-limb amputations are among the major problems in diabetic patients. Orthopedic insoles can reduce the risk of diabetic foot ulcers in patients through pressure redistribution on the bottom of the foot. The purpose of this study was to propose an optimization method to design the dedicated insoles for diabetic patients in order to decrease the maximum plantar pressure. At first, a three-dimensional finite element model of bones, ligaments and soft tissue of a diabetic patient's foot was created using CT scan images. Then, the foot plantar pressure was calculated by means of a finite element software. Next, the stiffness and shape of a simple flat insole were separately modified to reduce the maximum foot plantar pressure. The optimization method resulted in a dedicated insole design with a continuously variable stiffness/shape within its area that creates a smooth pressure distribution for the patient comfort. The results showed a 40% reduction in the maximum foot pressure, which we attribute to the modification of insole stiffness. In addition, the optimal shape of the proposed insole decreased the maximum plantar pressure by 25% compared to the flat insole.

On the limits of finite element models created from (micro)CT datasets and used in studies of bone-implant-related biomechanical problems

Patient-specific approach is gaining a wide popularity in computational simulations of biomechanical systems. Simulations (most often based on the finite element method) are to date routinely created using data from imaging devices such as computed tomography which makes the models seemingly very complex and sophisticated. However, using a computed tomography in finite element calculations does not necessarily enhance the quality or even credibility of the models as these depend on the quality of the input images. Low-resolution (medical-)CT datasets do not always offer detailed representation of trabecular bone in FE models and thus might lead to incorrect calculation of mechanical response to external loading. The effect of image resolution on mechanical simulations of bone-implant interaction has not been thoroughly studied yet. In this study, the effect of image resolution on the modeling procedure and resulting mechanical strains in bone was analyzed on the example of cranial implant. For this purpose, several finite element models of bone interacting with fixation-screws were generated using seven computed tomography datasets of a bone specimen but with different image resolutions (ranging from micro-CT resolution of 25 μm to medical-CT resolution of 1250 μm). The comparative analysis revealed that FE models created from images of low resolution (obtained from medical computed tomography) can produce biased results. There are two main reasons: 1. Medical computed tomography images do not allow generating models with complex trabecular architecture which leads to substituting of the intertrabecular pores with a fictitious mass; 2. Image gray value distribution can be distorted resulting in incorrect mechanical properties of the bone and thus in unrealistic or even completely fictitious mechanical strains. The biased results of calculated mechanical strains can lead to incorrect conclusion, especially when bone-implant interaction is investigated. The image resolution was observed not to significantly affect stresses in the fixation screw itself; however, selection of bone material representation might result in significantly different stresses in the screw.

The Relevance of Biomechanical Analysis in Joint Replacements: A Review

Biomechanical analysis, numerical and experimental, has been extensively used for more than 3 decades to investigate the mechanical behaviour of bone and implant–bone structures in joint replacement. In this review article, a detailed overview of the state-of-the-art techniques used for the development and pre-clinical testing of orthopaedic implants has been presented, with special focus on the hip-joint and hip implants. The efficacies of biomechanical analysis in analysing failure mechanisms in joint replacement, its clinical relevance, challenges and limitations, and future directions have been highlighted. Finite element (FE) modelling and analysis have contributed immensely towards testing of clinical hypotheses and evaluation of implant designs. Over the last few decades, the size and sophistication of the FE models have increased considerably. A critical analysis of the currently available subject-specific FE modelling techniques has been presented including, development of computed tomography-scan-based FE models of bone and implant, assignment of heterogeneous bone material properties, loading and boundary conditions. The relationship between stress–strain analysis and implant failure needs careful interpretation for clinical relevance. Verification and validation of these models are essential for assessing the validity of the predicted results. The salient features of adaptive simulations including bone remodelling and tissue differentiation and its prominence in investigating potential failure mechanisms and implant design evaluations have been discussed. The key considerations for design and development of orthopaedic implants have been suggested. It is envisaged that the FE simulations would be more holistic in nature, incorporating the complexities and variabilities of the clinical problems.

Effect of CT imaging on the accuracy of the finite element modelling in bone

The finite element (FE) analysis is a highly promising tool to simulate the behaviour of bone. Skeletal FE models in clinical routine rely on the information about the geometry and bone mineral density distribution from quantitative computed tomography (CT) imaging systems. Several parameters in CT imaging have been reported to affect the accuracy of FE models. FE models of bone are exclusively developed in vitro under scanning conditions deviating from the clinical setting, resulting in variability of FE results (< 10%). Slice thickness and field of view had little effect on FE predicted bone behaviour (≤ 4%), while the reconstruction kernels showed to have a larger effect (≤ 20%). Due to large interscanner variations (≤ 20%), the translation from an experimental model into clinical reality is a critical step. Those variations are assumed to be mostly caused by different “black box” reconstruction kernels and the varying frequency of higher density voxels, representing cortical bone. Considering the low number of studies together with the significant effect of CT imaging on the finite element model outcome leading to high variability in the predicted behaviour, we propose further systematic research and validation studies, ideally preceding multicentre and longitudinal studies.

Computational investigation of ultrastructural behavior of bone using a cohesive finite element approach.

Bone ultrastructure at sub-lamellar length scale is a key structural unit in bone that bridges nano- and microscale hierarchies of the tissue. Despite its influence on bulk response of bone, the mechanical behavior of bone at ultrastructural level remains poorly understood. To fill this gap, in this study, a two-dimensional cohesive finite element model of bone at sub-lamellar level was proposed and analyzed under tensile and compressive loading conditions. In the model, ultrastructural bone was considered as a composite of mineralized collagen fibrils (MCFs) embedded in an extrafibrillar matrix (EFM) that is comprised of hydroxyapatite (HA) polycrystals bounded via thin organic interfaces of non-collagenous proteins (NCPs). The simulation results indicated that in compression, EFM dictated the pre-yield deformation of the model, then damage was initiated via relative sliding of HA polycrystals along the organic interfaces, and finally shear bands were formed followed by delamination between MCF and EFM and local buckling of MCF. In tension, EFM carried the most of load in pre-yield deformation, and then an array of opening-mode nano-cracks began to form within EFM after yielding, thus gradually transferring the load to MCF until failure, which acted as crack bridging filament. The failure modes, stress-strain curves, and in situ mineral strain of ultrastructural bone predicted by the model were in good agreement with the experimental observations reported in the literature, thus suggesting that this model can provide new insights into sub-microscale mechanical behavior of bone.

Elastic modulus varies along the bovine femur

Bone is a heterogeneous material and its mechanical properties vary within the body. Variations in the mechanical response of different bone samples taken from the body cannot be fully explained by only looking at local compositional information at the tissue level. Due to different states of the stress within bones, one might expect that mechanical properties change over the length of a bone; this has not been a matter of systematic research in previous studies. In this study, the distribution of the tissue elastic modulus along the bovine femur is investigated using three-point bending tests. Two bovine femora were split to seven and eight blocks from proximal to distal metaphysis, respectively and twenty beam shaped bone samples were extracted and tested from each block. Based on our findings, the longitudinal elastic modulus follows a gradient pattern along the bovine femur as it increases along the bone from the proximal metaphysis to mid-diaphysis and then decreases toward the distal metaphysis again. Considering long bones to be subjected to bending loads, this mechanism alters the bone structure to support load in the regions where it is needed; similar as outlined by Wolff's law. In another part of this study, microfocus X-ray computed tomography (μCT) was found unable to predict the same trend of changes for the elastic modulus via image-based or density-based elastic moduli calculations. This is insofar important as conventional finite element models of bone are often directly shaped from μCT data. Based on our findings, it seems that current computed tomography based finite element models generated in this manner may not adequately capture the local variation of material behavior of bone tissue, but this may be improved by considering the changes of the elastic modulus along the femur.

Understanding Bone Strength from Finite Element Models: Concepts for Non-engineers

Recent clinical studies have reported not only changes in bone mineral density in patient populations but also changes in bone strength determined using finite element modeling. Finite element modeling is a technique well established in engineering but unfamiliar to many clinicians and basic biologists. Here, we provide a conceptual introduction to finite element modeling and its clinical applications to bone that is written for individuals without any background in engineering. Finite element modeling of bone is the net result of over 60 years of effort in the engineering community and over 40 years of effort in the field of bone biomechanics. We discuss the mathematical and theoretical basis for finite element modeling, how finite element models are created from clinical images and the assumptions made in using finite element models to estimate whole bone strength. In addition, we discuss the limitations of finite element modeling in patient populations with altered bone tissue quality. Clinical studies have shown that prediction of fracture risk using finite element modeling is as effective, and in some cases superior, to simple measures of bone mineral density. Further application of finite element modeling to clinical studies has the potential to improve fracture risk assessment beyond what is currently possible with bone mineral density.

Quantifying trabecular bone material anisotropy and orientation using low resolution clinical CT images: A feasibility study

Accounting for spatial variation of trabecular material anisotropy and orientation can improve the accuracy of quantitative computed tomography-based finite element (FE) modeling of bone. The objective of this study was to investigate the feasibility of quantifying trabecular material anisotropy and orientation using clinical computed tomography (CT). Forty four cubic volumes of interest were obtained from micro-CT images of the human radius. Micro-FE modeling was performed on the samples to obtain orthotropic stiffness entries as well as trabecular orientation. Simulated computed tomography images (0.32, 0.37, and 0.5mm isotropic voxel sizes) were created by resampling micro-CT images with added image noise. The gray-level structure tensor was used to derive fabric eigenvalues and eigenvectors in simulated CT images. For ‘best case’ comparison purposes, Mean Intercept Length was used to define fabric from micro-CT images. Regression was used in combination with eigenvalues, imaged density and FE to inversely derive the constants used in Cowin and Zysset–Curnier fabric-elasticity equations, and for comparing image derived fabric-elasticity stiffness entries to those obtained using micro-FE. Image derived eigenvectors (which indicated trabecular orientation) were then compared to orientation derived using micro-FE. When using clinically available voxel sizes, gray-level structure tensor derived fabric combined with Cowin's equations was able to explain 94–97% of the variance in orthotropic stiffness entries while Zysset–Curnier equations explained 82–88% of the variance in stiffness. Image derived orientation deviated by 4.4–10.8° from micro-FE derived orientation. Our results indicate potential to account for spatial variation of trabecular material anisotropy and orientation in subject-specific finite element modeling of bone using clinically available CT.

Singularity-free finite element model of bone through automated voxel-based reconstruction

Computed tomography (CT) provides both anatomical and density information about tissues. Bone is segmented by raw images and Finite Element Method (FEM) voxel-based meshing technique is achieved by matching each CT voxel to a single finite element (FE). As a consequence of the automated model reconstruction, unstable elements – i.e. elements insufficiently anchored to the whole model and thus potentially involved in partial rigid body motion – can be generated, a crucial problem in obtaining consistent FE models, hindering mechanical analyses. Through the classification of instabilities on topological connections between elements, a numerical procedure is proposed in order to avoid unconstrained models.

Constructing anisotropic finite element model of bone from computed tomography (CT).

Image-based finite element (FE) modeling of human bones has been increasingly applied as a useful tool in biomedical engineering. However, most existing image-based FE models assume isotropic mechanical properties for bones, although bones are typically anisotropic material. In this study, we attempted to construct anisotropic FE models from medical computed tomography (CT) scans by modifying the existing empirical relations of bone elasticity-density. The hypothesis adopted in the study is that bone anisotropy is generated by the variations of bone density and the proposed anisotropic relations should degenerate to the isotropic ones if bone density variation is taken zero. The effect of considering bone anisotropy in FE models was investigated by numerical studies. The obtained numerical results showed that the relative error in the finite element solutions produced respectively by the isotropic and anisotropic FE models can be as large as 50%. We concluded from this preliminary study that the consideration of anisotropy in bone FE models has a significant effect on the accuracy of bone behavior predicted by the FE models. However, well-designed bone tests have to be conducted to validate the anisotropic bone elasticity-density relation proposed in this study.

Modelling and static analysis of femur bone by using different implant materials

Femur is leg bone of the human body Undergoing more deformation. Biomechanics is the theory of how tissues, cells, muscles, bones, organs and the motion of them and how their form and function are regulated by basic mechanical properties. The aim of this study is to create a model of real proximal human femur bone and the behavior of femur bone is analyzed in ANSYS under physiological load conditions. A finite element model of bones is generated by using CT scan data are being widely used to make realistic investigations on the mechanical behavior of bone structures. . Orthopedic implantation is done in case of failure. Before implantation it is necessary to analyze the perfectness in case of its material property, size and shape, surface treatment, load resistance and chances of failure. Analysis is done for the stresses formed in different femur implant materials under static loading condition using ANSYS software. Analysis is done on different materials like structural steel, and Ti-6Al-4V implant materials. Since each femur carries 1/2 the body weight , analysis is done for 550kg,650kg, 750kg load, including the cases of patient carrying certain weight. And based on the analysis it can be concluded that, while comparing these two implant materials Ti-6Al-4V gave less deformation on static load conditions. TI-6AL4V is a low density material, which has excellent bio compatible and mechanical properties, it is ideal for the use of an implant in surgeries. Finally the success of implantation depends on implant material and size, implantation method and its handling by the patient.

Biomechanical modeling of knee for specific patients with chronic anterior cruciate ligament injury

In this study we modeled a patient specific 3D knee after anterior cruicate ligament (ACL) reconstruction. The purpose of the ACL reconstruction is to achieve stability in the entire range of motion of the knee and the establishment of the normal gait pattern. We present a new reconstruction technique that generates patient-specific 3D knee models from patient?s magnetic resonant images (MRIs). The motion of the ACL reconstruction patients is measured by OptiTrack system with six infrared cameras. Finite element model of bones, cartilage and meniscus is used for determination stress and strain distribution at different body postures during gait analysis. It was observed that the maximum effective von Mises stress distribution up to 8 MPa occurred during 30% of the gait cycle on the meniscus. The biomechanical model of the knee joint during gait analysis can provide insight into the underlying mechanisms of knee function after ACL reconstruction.

Can a partial volume edge effect reduction algorithm improve the repeatability of subject-specific finite element models of femurs obtained from CT data?

The reliability of patient-specific finite element (FE) modelling is dependent on the ability to provide repeatable analyses. Differences of inter-operator generated grids can produce variability in strain and stress readings at a desired location, which are magnified at the surface of the model as a result of the partial volume edge effects (PVEEs). In this study, a new approach is introduced based on an in-house developed algorithm which adjusts the location of the model's surface nodes to a consistent predefined threshold Hounsfield unit value. Three cadaveric human femora specimens were CT scanned, and surface models were created after a semi-automatic segmentation by three different experienced operators. A FE analysis was conducted for each model, with and without applying the surface-adjustment algorithm (a total of 18 models), implementing identical boundary conditions. Maximum principal strain and stress and spatial coordinates were probed at six equivalent surface nodes from the six generated models for each of the three specimens at locations commonly utilised for experimental strain guage measurement validation. A Wilcoxon signed-ranks test was conducted to determine inter-operator variability and the impact of the PVEE-adjustment algorithm. The average inter-operator difference in stress values was significantly reduced after applying the adjustment algorithm (before: 3.32 ± 4.35 MPa, after: 1.47 ± 1.77 MPa, p = 0.025). Strain values were found to be less sensitive to inter-operative variability (p = 0.286). In summary, the new approach as presented in this study may provide a means to improve the repeatability of subject-specific FE models of bone obtained from CT data.

An Efficient Method of Modeling Material Properties Using a Thermal Diffusion Analogy: An Example Based on Craniofacial Bone

The ability to incorporate detailed geometry into finite element models has allowed researchers to investigate the influence of morphology on performance aspects of skeletal components. This advance has also allowed researchers to explore the effect of different material models, ranging from simple (e.g., isotropic) to complex (e.g., orthotropic), on the response of bone. However, bone's complicated geometry makes it difficult to incorporate complex material models into finite element models of bone. This difficulty is due to variation in the spatial orientation of material properties throughout bone. Our analysis addresses this problem by taking full advantage of a finite element program's ability to solve thermal-structural problems. Using a linear relationship between temperature and modulus, we seeded specific nodes of the finite element model with temperatures. We then used thermal diffusion to propagate the modulus throughout the finite element model. Finally, we solved for the mechanical response of the finite element model to the applied loads and constraints. We found that using the thermal diffusion analogy to control the modulus of bone throughout its structure provides a simple and effective method of spatially varying modulus. Results compare favorably against both experimental data and results from an FE model that incorporated a complex (orthotropic) material model. This method presented will allow researchers the ability to easily incorporate more material property data into their finite element models in an effort to improve the model's accuracy.

Finite element analysis of a novel pin-sleeve system for external fixation of distal limb fractures in horses

The transfixation pin cast (TPC) is an external skeletal fixation technique used to treat horses with distal limb fractures, but its use is often associated with pin-loosening and an increased risk of treatment failure. To address implant loosening, the pin sleeve cast system (PSC) was recently designed and consists of a pin-sleeve unit inserted into the bone. Each pin runs through a sleeve placed in the bone, making contact at two fixed points only within the sleeve. Each pin is attached to a ring embedded in a resin cast. In this report, the mechanical performance of a traditional TPC pin arrangement was compared with that of the PSC using validated finite element models of bone substitutes previously tested in vitro. The PSC resulted in a marked reduction in peak strain magnitude around the pins and a more even distribution of strain across the bone cortex. The two systems resulted in comparable proximal fragment displacement and had a similar stress concentration around bone defects during implant removal. The findings suggest that the PSC load transfer mechanism is effective even in geometrically complex structures like equine bones.

Multiscale modelling and nonlinear finite element analysis as clinical tools for the assessment of fracture risk

The risk of osteoporotic fractures is currently estimated based on an assessment of bone mass as measured by dual-energy X-ray absorptiometry. However, patient-specific finite element (FE) simulations that include information from multiple scales have the potential to allow more accurate prognosis. In the past, FE models of bone were limited either in resolution or to the linearization of the mechanical behaviour. Now, nonlinear, high-resolution simulations including the bone microstructure have been made possible by recent advances in simulation methods, computer infrastructure and imaging, allowing the implementation of multiscale modelling schemes. For example, the mechanical loads generated in the musculoskeletal system define the boundary conditions for organ-level, continuum-based FE models, whose nonlinear material properties are derived from microstructural information. Similarly microstructure models include tissue-level information such as the dynamic behaviour of collagen by modifying the model's constitutive law. This multiscale approach to modelling the mechanics of bone allows a more accurate characterization of bone fracture behaviour. Furthermore, such models could also include the effects of ageing, osteoporosis and drug treatment. Here we present the current state of the art for multiscale modelling and assess its potential to better predict an individual's risk of fracture in a clinical setting.

Comparative analysis of bone remodelling models with respect to computerised tomography-based finite element models of bone

Subject-specific finite element models are an extensively used tool for the numerical analysis of the biomechanical behaviour of human bones. However, bone modelling is not an easy task due to the complex behaviour of bone tissue, involving non-homogeneous and anisotropic mechanical properties. Moreover, bone is a living tissue and therefore its microstructure and mechanical properties evolve with time in a known process called bone remodelling. This phenomenon has been widely studied, many being the numerical models that have been formulated to predict density distribution and its evolution in several bones. The aim of the present study is to assess the capability of a bone remodelling model to predict the bone density distribution of different types of human bone (femur, tibia and mandible) comparing the obtained results with the bone density estimated by means of computerised tomography. Good accuracy was observed for the bone remodelling predictions including the thickness of the cortical layer.