Validation of a finite element model of a unilateral external fixator in a rabbit tibia defect model

In case of large segmental defects in load-bearing bones, an external fixator is used to provide mechanical stability to the defect site. The overall stiffness of the bone–fixator system is determined not only by the fixator design but also by the way the fixator is mounted to the bone. This stiffness is an important factor as it will influence the biomechanical environment to which tissue engineering scaffolds and regenerating tissues are exposed. A finite element (FE) model can be used to predict the system stiffness. The goal of this study is to develop and validate a 3D anatomical FE model of a bone–fixator system which includes a previously developed unilateral external fixator for a large segmental defect model in the rabbit tibia. It was hypothesized that the contact interfaces between bone and fixator screws play a major role for the prediction of the stiffness. In vitro mechanical testing was performed in order to measure the axial stiffness of cortical bone from mid-shaft rabbit tibiae and of the tibia–fixator system, as well as the bending stiffness of individual fixator screws, inserted in bone. μCT-based case-specific FE models of cortical bone and SCREW–BONE specimens were created to simulate the corresponding mechanical test set-ups. The Young's modulus of rabbit cortical bone as well as appropriate screw–bone contact settings were derived from those FE models. We then used the derived settings in an FE model of the tibia–fixator system. The difference between the FE predicted and measured axial stiffness of the tibia–fixator system was reduced from 117.93% to 7.85% by applying appropriate screw–bone contact settings. In conclusion, this study shows the importance of screw–bone contact settings for an accurate fixator stiffness prediction. The validated FE model can further be used as a tool for virtual mechanical testing in the design phase of new tissue engineering scaffolds and/or novel patient-specific external fixation devices.     

Validation of a finite element model of the human metacarpal

Implant loosening and mechanical failure of components are frequently reported following metacarpophalangeal (MCP) joint replacement. Studies of the mechanical environment of the MCP implant-bone construct are rare. The objective of this study was to evaluate the predictive ability of a finite element model of the intact second human metacarpal to provide a validated baseline for further mechanical studies. A right index human metacarpal was subjected to torsion and combined axial/bending loading using strain gauge (SG) and 3D finite element (FE) analysis. Four different representations of bone material properties were considered. Regression analyses were performed comparing maximum and minimum principal surface strains taken from the SG and FE models. Regression slopes close to unity and high correlation coefficients were found when the diaphyseal cortical shell was modelled as anisotropic and cancellous bone properties were derived from quantitative computed tomography. The inclusion of anisotropy for cortical bone was strongly influential in producing high model validity whereas variation in methods of assigning stiffness to cancellous bone had only a minor influence. The validated FE model provides a tool for future investigations of current and novel MCP joint prostheses.     

Compressive behaviour of bovine cancellous bone and bone analogous materials, microCT characterisation and FE analysis

Compressive behaviour of bovine cancellous bone and three open-cell metallic foams (AlSi7Mg (30 ppi and 45 ppi); CuSn12Ni2 (30 ppi)) has been studied using mechanical testing, micro-focus computed tomography and finite element modelling. Whilst the morphological parameters of the foams and the bone appear to be similar, the mechanical properties vary significantly between the foams and the bone. Finite element models were built from the CT images of the samples and multi-linear constitutive relations were used for modelling of the bone and the foams. The global responses of the bone and foam samples were reasonably well captured by the FE models, whilst the percentage of yielded elements as a measure of damage evolution during compression seems to be indicative of the micro-mechanical behaviour of the samples. The damage evolution and distribution patterns across the bone and the foams are broadly similar for the strain range studied, suggesting possible substitution of trabecular bones with appropriate foams for biomechanical studies.     

Experimental and computational models to investigate the effect of adhesion on the mechanical properties of bone-cement composites

A generic finite element approach was developed to study the effect of adhesion on the mechanical response of bone cement composites and validated against literature data. The results showed that a zero friction bone-cement (PMMA) interface conditions captured the results of the experimental testing better than assuming a fully bonded interface. An experimental model for studying the effect of interface adhesion in a bone-cement like composite was also developed in the present study. The results using this model indicate that the difference in Young's modulus and ultimate strength between a fully bonded interface and unbonded interface is approximately 30% for bone volume fraction similar to what can be found in osteoporotic vertebrae. Apart from concluding that bone to cement adhesion is a major contributor to the mechanical response of bone-cement composites, our studies based on the generic FE approach also indicate that the mechanical properties of the cement is the most important contributor to the resulting mechanical properties of the composite at bone volume fraction relevant in terms of vertebroplasty treatment.     

Finite element modelling of a unilateral fixator for bone reconstruction: Importance of contact settings

When reconstructing a large segmental bone defect by means of a porous scaffold, a fixator is used to stabilize the reconstruction. The fixator stiffness is an important factor as it will influence the biomechanical environment to which scaffold and regenerating tissues are exposed. A finite element (FE) model can be used to predict the fixator stiffness. The goal of this study was to develop and validate a detailed 3D FE model of a custom-developed unilateral external fixator. In particular, it was hypothesized that the contact interfaces between the different fixator components play a major role for the prediction of the fixator stiffness. In vitro mechanical testing of the entire fixator as well as of separate fixator components was performed in order to measure the stiffness. The mechanical test set-ups were simulated by means of detailed FE models that considered different levels of refinement of the various contact interfaces. The error on predicted fixator stiffness in comparison to measured stiffness was reduced from 121% to 16% by refining the contact settings of the FE model. The individual sources of error between the measured and predicted fixator stiffness could be quantitatively assessed as well. In conclusion, this study warrants for a careful modelling of the geometry and contact settings, when using FE models for the prediction of fixator stiffness.     

Three-Dimensional Finite Element Modeling of Human Ear for Sound Transmission

An accurate, comprehensive finite element model of the human ear can provide better understanding of sound transmission, and can be used for assessing the influence of diseases on hearing and the treatment of hearing loss. In this study, we proposed a three-dimensional finite element model of the human ear that included the external ear canal, tympanic membrane (eardrum), ossicular bones, middle ear suspensory ligaments/muscles, and middle ear cavity. This model was constructed based on a complete set of histological section images of a left ear temporal bone. The finite element (FE) model of the human ear was validated by comparing model-predicted ossicular movements at the stapes footplate and tympanic membrane with published experimental measurements on human temporal bones. The FE model was employed to predict the effects of eardrum thickness and stiffness, incudostapedial joint material, and cochlear load on acoustic-mechanical transmission through the human ossicular chain. The acoustic-structural coupled FE analysis between the ear canal air column and middle ear ossicles was also conducted and the results revealed that the peak responses of both tympanic membrane and stapes footplate occurred between 3000 and 4000 Hz.     

A finite element analysis of a T12 vertebra in two consecutive examinations to evaluate the progress of osteoporosis

Osteoporosis is a metabolic disease that causes bones to become fragile and be more likely to break. As basic clinical examinations to detect osteoporosis, dual energy X-ray absorptiometry (DXA) and quantitative computer tomography (QCT) are used. In the framework of a typical clinical examination, QCT scans were obtained from the T12 vertebra of an elderly woman and osteoporosis was diagnosed. One year later, new QCT scans were obtained in order to evaluate her clinical condition. Using both sets as primary information, two patient-specific finite element (FE) models were created and analyzed under compressive load. Vertebral bone was treated as orthotropic material and its elastic modulus was set as an indirect function of Hounsfield Units (HU). Commercial software for medical image processing and FE analysis, along with in house codes, were used for the mechanical analysis of the FE models. Alterations in the geometry/shape of the vertebra as well as in the distributions of several mechanical quantities were detected between the two FE models.As far as the volume of the vertebra is concerned, it augmented by a percentage of 9.7% while the volume of the vertebral body alone increased by 5.6%. In all the maximum values of the mechanical quantities a measurable reduction was observed (axial compressive displacement: 37.9%, von Mises stress: 23.8%, von Mises strains: 15.1%) and all the investigated distributions in the second FE model became smoother. Finally, the percentage of volume with von Mises strains greater than 4500 μstrain dropped from 8.9%, in the first examination, to 4.9% in the second one. Clinically, the prescribed medication seems to have reinforced the structural stability of the vertebra as a whole and through external remodeling the shape of the vertebra changed in a way that the majority of its volume was relieved from stresses and strains of high magnitude.     

Strain in the ostrich mandible during simulated pecking and validation of specimen-specific finite element models

Finite element (FE) analysis is becoming a frequently used tool for exploring the craniofacial biomechanics of extant and extinct vertebrates. Crucial to the application of the FE analysis is the knowledge of how well FE results replicate reality. Here I present a study investigating how accurately FE models can predict experimentally derived strain in the mandible of the ostrich Struthio camelus, when both the model and the jaw are subject to identical conditions in an in‐vitro loading environment. Three isolated ostrich mandibles were loaded hydraulically at the beak tip with forces similar to those measured during force transducer pecking experiments. Strains were recorded at four gauge sites at the dorsal and ventral dentary, and medial and lateral surangular. Specimen‐specific FE models were created from computed tomography scans of each ostrich and loaded in an identical fashion as in the in‐vitro test. The results show that the strain magnitudes, orientation, patterns and maximum : minimum principal strain ratios are predicted very closely at the dentary gauge sites, even though the FE models have isotropic and homogeneous material properties and solid internal geometry. Although the strain magnitudes are predicted at the postdentary sites, the strain orientations and ratios are inaccurate. This mismatch between the dentary and postdentary predictions may be due to the presence of intramandibular sutures or the greater amount of cancellous bone present in the postdentary region of the mandible and requires further study. This study highlights the predictive potential of even simple FE models for studies in extant and extinct vertebrates, but also emphasizes the importance of geometry and sutures. It raises the question of whether different parameters are of lesser or greater importance to FE validation for different taxonomic groups.     

具有解剖基下颌的人体头部有限元模型的建立

根据人体下颌骨的螺旋 CT扫描图像 ,利用三维重建、图像处理和网格划分技术 ,建立了人体下颌骨的三维有限元模型。根据颞下颌关节的解剖结构及其力学特点 ,将已建立的下颌骨模型通过关节和经过修改的Hybrid 假人头部模型相连接 ,从而建立一个具有解剖基下颌的人体头部有限元模型。根据已有的尸体实验结果 ,验证了模型的可靠性。本模型可用于钝物撞击颌面伤害机理的研究和伤害程度的评估     

Patient-specific finite element modeling for femoral bone augmentation

The aim of this study was to provide a fast and accurate finite element (FE) modeling scheme for predicting bone stiffness and strength suitable for use within the framework of a computer-assisted osteoporotic femoral bone augmentation surgery system. The key parts of the system, i.e. preoperative planning and intraoperative assessment of the augmentation, demand the finite element model to be solved and analyzed rapidly. Available CT scans and mechanical testing results from nine pairs of osteoporotic femur bones, with one specimen from each pair augmented by polymethylmethacrylate (PMMA) bone cement, were used to create FE models and compare the results with experiments. Correlation values of R² = 0.72–0.95 were observed between the experiments and FEA results which, combined with the fast model convergence (～3 min for ～250,000 degrees of freedom), makes the presented modeling approach a promising candidate for the intended application of preoperative planning and intraoperative assessment of bone augmentation surgery.     

Effect of specimen conditioning on the microarchitectural parameters of trabecular bone assessed by micro-computed tomography

The best way to preserve the mechanical properties of bone specimens is hydration in NaCl, whereas the reference process in microCT analysis is defatting. However, for finite element modelling (FEM) it is necessary to use the same bone specimens for biomechanical testing and 3D imaging. This study aimed to evaluate the effect of sample conditioning on trabecular bone microarchitectural parameters. Trabecular bones were analysed by microCT under three successive conditions: first, the fatted samples were analysed immersed in NaCl (process N); second, they were hydrated for 24 h then imaged without immersion (process H); third, the samples were defatted before analysis (process D). The microarchitectural parameters bone volume/tissue volume (BV/TV), trabecular spacing (Tb.Sp), number (Tb.N) and thickness (Tb.Th) were calculated. Except for BV/TV, there was no significant difference between the processes N and D. In process H, BV/TV, Tb.Th and Tb.N were higher and BS/BV and Tb.Sp were lower than in process D. Results showed that the process D may be replaced by the process N. The process H induced significant differences in microarchitectural parameters when compared to process D. Nevertheless, this sample conditioning should be used to develop FEM when microCT images are to be acquired during compressive testing.     

Individualised, micro CT-based finite element modelling as a tool for biomechanical analysis related to tissue engineering of bone

Load-bearing tissues, like bone, can be replaced by engineered tissues or tissue constructs. For the success of this treatment, a profound understanding is needed of the mechanical properties of both the native bone tissue and the construct. Also, the interaction between mechanical loading and bone regeneration and adaptation should be well understood. This paper demonstrates that microfocus computer tomography (microCT) based finite element modelling (FEM) can have an important contribution to the field of functional bone engineering as a biomechanical analysis tool to quantify the stress and strain state in native bone tissue and in tissue constructs. Its value is illustrated by two cases: (1) in vivo microCT-based FEM for the analysis of peri-implant bone adaptation and (2) design of biomechanically optimised bone scaffolds. The first case involves a combined animal experimental and numerical study, in which the peri-implant bone adaptive response is monitored by means of in vivo microCT scanning. In the second case microCT-based finite element models were created of native trabecular bone and bone scaffolds and a mechanical analysis of both structures was performed. Procedures to optimise the mechanical properties of bone scaffolds, in relation to those of native trabecular bone are discussed.     

Comparison of an inhomogeneous orthotropic and isotropic material models used for FE analyses

Finite element (FE) analysis has been widely used to study the behaviour of bone or implants in many clinical applications. One of the main factors in analyses is the realistic behaviour of the bone model, because the behaviour of the bone is strongly dependent on a realistic bone material property assignment. The objective of this study was to compare isotropic and orthotropic inhomogeneous material models used for FE analyses of the "global" proximal femur and "small" specimens of the bone (cancellous and cortical). Our hypothesis was that realistic material property assignment (orthotropy) is very important for the FE analyses of small bone specimens, whereas in global FE analyses of the proximal femur, this assignment can be omitted, if the inhomogeneous material model was used. The three-dimensional geometry of the "global" proximal femur was reconstructed using CT scans of a cadaveric femur. This model was implemented into an FE simulation tool and various bone material properties, dependant on bone density, were assigned to each element in the models. The "small" specimens of cortical and cancellous bone were created in the same way as the model of the proximal femur. The results obtained from FE analyses support our above described hypothesis.     

Vibrational testing of trabecular bone architectures using rapid prototype models

The purpose of this study was to investigate if standard analysis of the vibrational characteristics of trabecular architectures can be used to detect changes in the mechanical properties due to progressive bone loss. A cored trabecular specimen from a human lumbar vertebra was microCT scanned and a three-dimensional, virtual model in stereolithography (STL) format was generated. Uniform bone loss was simulated using a surface erosion algorithm. Rapid prototype (RP) replicas were manufactured from these virtualised models with 0%, 16% and 42% bone loss. Vibrational behaviour of the RP replicas was evaluated by performing a dynamic compression test through a frequency range using an electro-dynamic shaker. The acceleration and dynamic force responses were recorded and fast Fourier transform (FFT) analyses were performed to determine the response spectrum. Standard resonant frequency analysis and damping factor calculations were performed. The RP replicas were subsequently tested in compression beyond failure to determine their strength and modulus. It was found that the reductions in resonant frequency with increasing bone loss corresponded well with reductions in apparent stiffness and strength. This suggests that structural dynamics has the potential to be an alternative diagnostic technique for osteoporosis, although significant challenges must be overcome to determine the effect of the skin/soft tissue interface, the cortex and variabilities associated with in vivo testing.     

Numerical Modelling of Femur Fracture and Experimental Validation Using Bone Simulant

Bone fracture pattern prediction is still a challenge and an active field of research. The main goal of this article is to present a combined methodology (experimental and numerical) for femur fracture onset analysis. Experimental work includes the characterization of the mechanical properties and fracture testing on a bone simulant. The numerical work focuses on the development of a model whose material properties are provided by the characterization tests. The fracture location and the early stages of the crack propagation are modelled using the extended finite element method and the model is validated by fracture tests developed in the experimental work. It is shown that the accuracy of the numerical results strongly depends on a proper bone behaviour characterization.     

Comparison of Dentoalveolar Morphology in WT and P2X7R KO Mice for the Development of Biomechanical Orthodontic Models

It has been suggested that the absence of the P2X7 receptor affects long bone morphology, and that one of the cytokines dependent on its activation may also affect tooth morphology. P2X7R KO (knockout) were compared with C57B/6 WT mice (background strain) to identify differences in a maxillary molar and surrounding bone. Nineteen WT and 12 KO mouse maxillae were scanned and 3D‐reconstructed using microCT. Tooth dimensions were measured and 3D bone morphometry was conducted. A finite element model was constructed based on the results. No statistically significant differences were found in dentoalveolar characteristics between the two mouse types. A single finite element model of the tooth can be used to mechanically represent both strains. P2X7R does not have a major effect on alveolar bone or tooth morphology. The P2X7R effects are site‐specific. Anat Rec, 2009. © 2008 Wiley‐Liss, Inc.     

Composite time-lapse computed tomography and micro finite element simulations: A new imaging approach for characterizing cement flows and mechanical benefits of vertebroplasty

Vertebroplasty has been shown to reinforce weak vertebral bodies and reduce fracture risks, yet cement leakage is a major problem that can cause severe complications. Since cement flow is nearly impossible to control during surgery, small volumes of cement are injected, but then mechanical benefits might be limited. A better understanding of cement flows within bone structure is required to further optimize vertebroplasty and bone augmentation in general. We developed a novel imaging method, composite time-lapse CT, to characterize cement flow during injection.In brief, composite-resolution time-lapse CT exploits the qualities of microCT and clinical CT. The method consists in overlaying low-resolution time-lapse CT scans acquired during injection onto pre-operative high-resolution microCT scans, generating composite-resolution time-lapse CT series of cement flow within bone.In this in vitro study, composite-resolution time-lapse CT was applied to eight intact and five artificially fractured cadaveric vertebrae during vertebroplasty. The time-lapse scans were acquired at one-milliliter cement injection steps until a total of 10 ml cement was injected. The composite-resolution series were then converted into micro finite element models to compute strains distribution under virtual axial loading. Relocation of strain energy density within bone structure was observed throughout the progression of the procedure. Interestingly, the normalized effect of cement injection on the overall stiffness of the vertebrae was similar between intact and fractured specimens, although at different orders of magnitude.In conclusion, composite time-lapse CT can picture cement flows during bone augmentation. The composite images can also be easily converted into finite element models to compute virtual strain distributions under loading at every step of an injection, providing deeper understanding on the biomechanics of vertebroplasty.     

基于骨骼自适应理论优化模型的骨重建数值模拟

我们根据骨重建的自适应理论以及结构优化方法,建立了骨重建数值模拟的反问题求解模型和算法.由材料密度分布描述骨内部重建,材料密度的变化通过优化方法求解.股骨、长骨干和腰椎体冠状面(外部形状和内部结构)重建模拟的计算结果,符合实际情况,反映了骨结构对荷载环境的自适应特征,表明本文方法是骨重建研究的一种有效数值方法.     

Image-based vs. mesh-based statistical appearance models of the human femur: Implications for finite element simulations

Statistical appearance models have recently been introduced in bone mechanics to investigate bone geometry and mechanical properties in population studies. The establishment of accurate anatomical correspondences is a critical aspect for the construction of reliable models. Depending on the representation of a bone as an image or a mesh, correspondences are detected using image registration or mesh morphing. The objective of this study was to compare image-based and mesh-based statistical appearance models of the femur for finite element (FE) simulations. To this aim, (i) we compared correspondence detection methods on bone surface and in bone volume; (ii) we created an image-based and a mesh-based statistical appearance models from 130 images, which we validated using compactness, representation and generalization, and we analyzed the FE results on 50 recreated bones vs. original bones; (iii) we created 1000 new instances, and we compared the quality of the FE meshes. Results showed that the image-based approach was more accurate in volume correspondence detection and quality of FE meshes, whereas the mesh-based approach was more accurate for surface correspondence detection and model compactness. Based on our results, we recommend the use of image-based statistical appearance models for FE simulations of the femur.