Validation of subject-specific automated p-FE analysis of the proximal femur

Fracture analysis of healthy and osteoporotic femora using clinical CT images, phantomless densitometry, and linear FE method

Computational fracture analysis has become a growing branch of orthopedic research. Particularly, the associated methods provide reliable tools for the analysis of 3D CT-based models of bone. This paper reports the results of such analyses for 15 human femora (healthy and osteoporotic) under different loading orientations (85 different analysis cases). A new method was developed for the calculation of the density distribution in the models from ordinary clinical CT images without calibration phantom. This method, along with a strain-energy-based linear finite element (FE) analysis scheme, was used to predict the fracture strength and pattern of 10 cadaveric femora, for which the mechanical testing results and calibrated FE models were already available. The very good agreement and consistency between different sets of results showed the reliability and accuracy of the new density calibration method, as well as the linear analysis scheme. Accordingly, the method was applied to five new clinical images, gathered from two clinics that used different scanners with different protocols. The strength and fracture pattern of each one of these specimens were analyzed under 15 different loading conditions. A consistent behavior was found for variation of the fracture load and pattern of all specimens with the loading orientations, while very clear contrasts were observed between the strength amplitudes of healthy and osteoporotic specimens. The proposed methods can be easily applied to ordinary daily (even archived) clinical CT scans to conduct fast and reliable fracture analysis of human femora for general bone research and opportunistic studies of osteoporosis and trauma.

Simulation-based prediction of bone healing and treatment recommendations for lower leg fractures: Effects of motion, weight-bearing and fibular mechanics

Despite recent experimental and clinical progress in the treatment of tibial and fibular fractures, in clinical practice rates of delayed bone healing and non-union remain high. The aim of this study was to simulate and compare different mechanical conditions after lower leg fractures to assess the effects of postoperative motion, weight-bearing restrictions and fibular mechanics on the strain distribution and the clinical course. Based on the computed tomography (CT) data set of a real clinical case with a distal diaphyseal tibial fracture, a proximal and a distal fibular fracture, finite element simulations were run. Early postoperative motion data, recorded via an inertial measuring unit system and pressure insoles were recorded and processed to study strain. The simulations were used to compute interfragmentary strain and the von Mises stress distribution of the intramedullary nail for different treatments of the fibula, as well as several walking velocities (1.0 km/h; 1.5 km/h; 2.0 km/h) and levels of weight-bearing restriction. The simulation of the real treatment was compared to the clinical course. The results show that a high postoperative walking speed was associated with higher loads in the fracture zone. In addition, a larger number of areas in the fracture gap with forces that exceeded beneficial mechanical properties longer was observed. Moreover, the simulations showed that surgical treatment of the distal fibular fracture had an impact on the healing course, whereas the proximal fibular fracture barely mattered. Weight-bearing restrictions were beneficial in reducing excessive mechanical conditions, while it is known that it is difficult for patients to adhere to partial weight-bearing recommendations. In conclusion, it is likely that motion, weight bearing and fibular mechanics influence the biomechanical milieu in the fracture gap. Simulations may improve decisions on the choice and location of surgical implants, as well as give recommendations for loading in the postoperative course of the individual patient.

[Movement analysis and musculoskeletal simulation in non-union treatment-Experiences and first clinical results]

BACKGROUND

The mechanical boundary conditions of the non-union and osteosynthetic construct are a key determinant of fracture healing after revision surgery. Aim of this study was to introduce a movement analysis and simulation workflow to determine the mechanical conditions during non-union healing in vivo.

MATERIAL AND METHODS

On an individual case basis after non-union revision surgery we performed an accelerometry-based movement analysis. The results were then used as input for a musculoskeletal simulation of the non-union, osteosynthetic construct as well as adjacent joints mechanical boundary conditions.

RESULTS

A total of 13 patients were analyzed with our new workflow. The introduced protocol allows an in vivo determination of the mechanical boundary conditions. On clinical follow-up all patients showed radiographic consolidation of the non-union.

CONCLUSION

The introduced workflow allows a clinically applicable determination of the mechanical boundary conditions of fracture and non-union healing. Further studies can now determine the effect of the introduced technique for mechanically optimized postoperative aftercare regimes as well as biomechanically adapted surgical treatment.

Individualized Determination of the Mechanical Fracture Environment After Tibial Exchange Nailing-A Simulation-Based Feasibility Study

Non-union rate after tibial fractures remains high. Apart from largely uncontrollable biologic, injury, and patient-specific factors, the mechanical fracture environment is a key determinant of healing. Our aim was to establish a patient-specific simulation workflow to determine the mechanical fracture environment and allow for an estimation of its healing potential. In a referred patient with failed nail-osteosynthesis after tibial-shaft fracture exchange nailing was performed. Post-operative CT-scans were used to construct a three-dimensional model of the treatment situation in an image processing and computer-aided design system. Resulting forces, computed in a simulation-driven workflow based on patient monitoring and motion capturing were used to simulate the mechanical fracture environment before and after exchange nailing. Implant stresses for the initial and revision situation, as well as interfragmentary movement, resulting hydrostatic, and octahedral shear strain were calculated and compared to the clinical course. The simulation model was able to adequately predict hardware stresses in the initial situation where mechanical implant failure occurred. Furthermore, hydrostatic and octahedral shear strain of the revision situation were calculated to be within published healing boundaries—accordingly the fracture healed uneventfully. Our workflow is able to determine the mechanical environment of a fracture fixation, calculate implant stresses, interfragmentary movement, and the resulting strain. Critical mechanical boundary conditions for fracture healing can be determined in relation to individual loading parameters. Based on this individualized treatment recommendations during the early post-operative phase in lower leg fractures are possible in order to prevent implant failure and non-union development.

Image-based finite-element modeling of the human femur

Fracture is considered a critical clinical endpoint in skeletal pathologies including osteoporosis and bone metastases. However, current clinical guidelines are limited with respect to identifying cases at high risk of fracture, as they do not account for many mechanical determinants that contribute to bone fracture. Improving fracture risk assessment is an important area of research with clear clinical relevance. Patient-specific numerical musculoskeletal models generated from diagnostic images are widely used in biomechanics research and may provide the foundation for clinical tools used to quantify fracture risk. However, prior to clinical translation, in vitro validation of predictions generated from such numerical models is necessary. Despite adopting radically different models, in vitro validation of image-based finite element (FE) models of the proximal femur (predicting strains and failure loads) have shown very similar, encouraging levels of accuracy. The accuracy of such in vitro models has motivated their application to clinical studies of osteoporotic and metastatic fractures. Such models have demonstrated promising but heterogeneous results, which may be explained by the lack of a uniform strategy with respect to FE modeling of the human femur. This review aims to critically discuss the state of the art of image-based femoral FE modeling strategies, highlighting principal features and differences among current approaches. Quantitative results are also reported with respect to the level of accuracy achieved from in vitro evaluations and clinical applications and are used to motivate the adoption of a standardized approach/workflow for image-based FE modeling of the femur.

Assessment of finite element models for prediction of osteoporotic fracture

With increasing life expectancy and mortality rates, the burden of osteoporotic hip fractures is continually on an upward trend. In terms of prevention, there are several osteoporosis treatment strategies such as anti-resorptive drug treatments, which attempt to retard the rate of bone resorption, while promoting the rate of formation. With respect to prediction, several studies have provided insights into obtaining bone strength by non-invasive means through the application of FE analysis. However, what valuable information can we obtain from FE studies that have focused on osteoporosis research, with respect to the prediction of osteoporotic fractures? This paper aims to fine studies that have used FE analysis to predict fractures in the proximal femur through a systematic search of literature using PUBMED, with the main objective of supporting the diagnosis of osteoporosis. The focus of these FE studies is first discussed, and the methodological aspects are summarized, by mainly comparing and contrasting their meshing properties, material properties, and boundary conditions. The implications of these methodological differences in FE modelling processes and propositions with the aim of consolidating or minimalizing these differences are further discussed. We proved that studies need to start converging in terms of their input parameters to make the FE method applicable to clinical settings. This, in turn, will decrease the time needed for in vitro tests. Current advancements in FE analysis need to be consolidated before any further steps can be taken to implement engineering analysis into the clinical scenario.

Comparative Study of Femur Bone Having Different Boundary Conditions and Bone Structure Using Finite Element Method

Background:

Femur bone is an important part in human which basically gives stability and support to carry out all day to day activities. It carries loads from upper body to lower abdomen.

Objective:

In this work, the femur having composite structure with cortical, cancellous and bone marrow cavity is bisected from condyle region with respect to 25%, 50% and 75% of its height. There is considerable difference in the region chosen for fixing all degrees of freedom in the analysis of femur.

Methods:

The CT scans are taken, and 3D model is developed using MIMICS. The developed model is used for static structural analysis by varying the load from 500N to 3000N.

Results:

The findings for 25% bisected femur model report difference in directional deformation less than 5% for loads 2000N and less. In the study comparing fully solid bone and the composite bone, the total deformation obtained for a complete solid bone was 3.5 mm which was 18.7% less than that determined for the composite bone.

Conclusion:

The standardization for fixing the bone is developed. And it is required to fix the distal end always with considering full femur bone.

Phase-field boundary conditions for the voxel finite cell method: Surface-free stress analysis of CT-based bone structures

The voxel finite cell method uses unfitted finite element meshes and voxel quadrature rules to seamlessly transfer computed tomography data into patient-specific bone discretizations. The method, however, still requires the explicit parametrization of boundary surfaces to impose traction and displacement boundary conditions, which constitutes a potential roadblock to automation. We explore a phase-field-based formulation for imposing traction and displacement constraints in a diffuse sense. Its essential component is a diffuse geometry model generated from metastable phase-field solutions of the Allen-Cahn problem that assumes the imaging data as initial condition. Phase-field approximations of the boundary and its gradient are then used to transfer all boundary terms in the variational formulation into volumetric terms. We show that in the context of the voxel finite cell method, diffuse boundary conditions achieve the same accuracy as boundary conditions defined over explicit sharp surfaces, if the inherent length scales, ie, the interface width of the phase field, the voxel spacing, and the mesh size, are properly related. We demonstrate the flexibility of the new method by analyzing stresses in a human femur and a vertebral body.

Study of the variations of fall induced hip fracture risk between right and left femurs using CT-based FEA

Background

Hip fracture of elderly people—suffering from osteoporosis—is a severe public health concern, which can be reduced by providing a prior assessment of hip fracture risk. Image-based finite element analysis (FEA) has been considered an effective computational tool to assess the hip fracture risk. Considering the femoral neck region is the weakest, fracture risk indicators (FRI) are evaluated for both single-legged stance and sideways fall configurations and are compared between left and right femurs of each subject. Quantitative Computed Tomography (QCT) scan datasets of thirty anonymous patients’ left and right femora have been considered for the FE models, which have been simulated with an equal magnitude of load applied to the aforementioned configurations. The requirement of bilateral hip assessment in predicting the fracture risk has been explored in this study.

Results

Comparing the sideways fall and single-legged stance, the FRI varies by 64 to 74% at the superior aspects and by 14 to 19% at the inferior surfaces of both the femora. The results of this in vivo analysis clearly substantiate that the fracture is expected to initiate at the superior surface of femoral neck region if a patient falls from his/her standing height. The distributions of FRI between the femurs vary considerably, and the variability is significant at the superior aspects. The p value (= 0.02) obtained from paired sample t-Test yields p value ≤ 0.05, which shows the evidence of variability of the FRI distribution between left and right femurs. Moreover, the comparison of FRIs between the left and right femur of men and women shows that women are more susceptible to hip fracture than men.

Conclusions

The results and statistical variation clearly signify a need for bilateral hip scanning in predicting hip fracture risk, which is clinically conducted, at present, based on one hip chosen randomly and may lead to inaccurate fracture prediction. This study, although preliminary, may play a crucial role in assessing the hip fractures of the geriatric population and thereby, reducing the cost of treatment by taking predictive measure.

Study of stress variations in single-stance and sideways fall using image-based finite element analysis

Image-based finite element analysis (FEA) has been considered an effective computational tool to predict hip fracture risk. The patient specific FEA gives an insight into the inclusive effect of three-dimensional (3D) complex bone geometry, and the distribution of inhomogeneous isotropic material properties in conjunction with loading conditions. The neck region of a femur is primarily the weakest in which fracture is likely to happen, when someone falls. A sideways fall results in the development of greater tensile and compressive stresses, respectively, in the inferior and superior aspects of the femoral neck, whereas the state of stress is reversed in usual gait or stance configuration. Herein, the variations of stresses have been investigated at the femoral neck region considering both single-stance and sideways fall. Finite element models of ten human femora have been generated using Quantitative Computed Tomography (QCT) scan datasets and have been simulated with an equal magnitude of load applied to the aforementioned configurations. Fracture risk indicator, defined as the ratio of the maximum compressive or tensile stress computed at the superior and inferior surfaces to the corresponding yield stress, has been used in this work to measure the variations of fracture risk between single-stance and sideways fall. The average variations of the fracture risk indicators between the fall and stance are at least 24.3% and 8% at the superior and inferior surfaces, respectively. The differences may interpret why sideways fall is more dangerous for the elderly people, causing hip fracture.

Uncertainty quantification for personalized analyses of human proximal femurs

Computational models for the personalized analysis of human femurs contain uncertainties in bone material properties and loads, which affect the simulation results. To quantify the influence we developed a probabilistic framework based on polynomial chaos (PC) that propagates stochastic input variables through any computational model. We considered a stochastic E-ρ relationship and a stochastic hip contact force, representing realistic variability of experimental data. Their influence on the prediction of principal strains (ϵ1 and ϵ3) was quantified for one human proximal femur, including sensitivity and reliability analysis. Large variabilities in the principal strain predictions were found in the cortical shell of the femoral neck, with coefficients of variation of ≈40%. Between 60 and 80% of the variance in ϵ1 and ϵ3 are attributable to the uncertainty in the E-ρ relationship, while ≈10% are caused by the load magnitude and 5-30% by the load direction. Principal strain directions were unaffected by material and loading uncertainties. The antero-superior and medial inferior sides of the neck exhibited the largest probabilities for tensile and compression failure, however all were very small (pf<0.001). In summary, uncertainty quantification with PC has been demonstrated to efficiently and accurately describe the influence of very different stochastic inputs, which increases the credibility and explanatory power of personalized analyses of human proximal femurs.

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.

QCT-based failure analysis of proximal femurs under various loading orientations

In this paper, the variations of the failure strength and pattern of human proximal femur with loading orientation were analysed using a novel quantitative computed tomography (QCT)-based linear finite element (FE) method. The QCT images of 4 fresh-frozen femurs were directly converted into voxel-based finite element models for the analyses of the failure loads and patterns. A new geometrical reference system was used for the alignment of the mechanical loads on the femoral head. A new method was used for recognition and assortment of the high-risk elements using a strain energy-based measure. The FE results were validated with the experimental results of the same specimens and the results of similar case studies reported in the literature. The validated models were used for the computational investigation of the failure loads and patterns under 15 different loading conditions. A consistent variation of the failure loads and patterns was found for the 60 different analysed cases. Finally, it was shown that the proposed procedure can be used as a reliable tool for the failure analysis of proximal femurs, e.g. identification of the relevant loading directions for specific failure patterns, or determination of the loading conditions under which the proximal femurs are failure-prone.

Predicting the stiffness and strength of human femurs with real metastatic tumors

BACKGROUND

Predicting patient specific risk of fracture in femurs with metastatic tumors and the need for surgical intervention are of major clinical importance. Recent patient-specific high-order finite element methods (p-FEMs) based on CT-scans demonstrated accurate results for healthy femurs, so that their application to metastatic affected femurs is considered herein.

METHODS

Radiographs of fresh frozen proximal femur specimens from donors that died of cancer were examined, and seven pairs with metastatic tumor were identified. These were CT-scanned, instrumented by strain-gauges and loaded in stance position at three inclination angles. Finally the femurs were loaded until fracture that usually occurred at the neck. Histopathology was performed to determine whether metastatic tumors are present at fractured surfaces. Following each experiment p-FE models were created based on the CT-scans mimicking the mechanical experiments. The predicted displacements, strains and yield loads were compared to experimental observations.

RESULTS

The predicted strains and displacements showed an excellent agreement with the experimental observations with a linear regression slope of 0.95 and a coefficient of regression R(2)=0.967. A good correlation was obtained between the predicted yield load and the experimental observed yield, with a linear regression slope of 0.80 and a coefficient of regression R(2)=0.78.

DISCUSSION

CT-based patient-specific p-FE models of femurs with real metastatic tumors were demonstrated to predict the mechanical response very well. A simplified yield criterion based on the computation of principal strains was also demonstrated to predict the yield force in most of the cases, especially for femurs that failed at small loads. In view of the limited capabilities to predict risk of fracture in femurs with metastatic tumors used nowadays, the p-FE methodology validated herein may be very valuable in making clinical decisions.

Low-dose three-dimensional reconstruction of the femur with unit free-form deformation

PURPOSE

This paper describes a low-dose method for reconstructing three-dimensional models of femur, using a standard shape model (SSM) and two conventional x-ray images.

METHODS

The x-ray images were taken in two orthogonal directions. The x-ray source and sensor configurations were documented. An optimized algorithm was employed to align the x-ray image to the three-dimensional model. A method of direct correspondence building is proposed for linking two-dimensional images with three-dimensional projections of a SSM. The reconstruction method proposed in this paper is based on a SSM, which was adapted for x-ray images of individual bones. The adaption was executed by deforming the template bone shape until its silhouette boundary exactly matched the x-ray image of the individual bone. A silhouette-based unit free-form deformation method was evaluated for its suitability in the adaption of the SSM for x-ray images. Comprehensive experiments were designed and conducted for 35 specimens.

RESULTS

The validity of the low-dose reconstruction method was demonstrated for the femur, with good results for accuracy (mean error of 1.1 mm, root-mean-square error of 2.1 mm), reproducibility (intraobservation coefficient of variation of 1.1%, interobservation coefficient of variation of 1.4%), and time consumption (mean of 5 min for a full femur).

CONCLUSIONS

Once this approach has been validated in vivo, it should be suited to multiple applications of routine clinical and research practices.

How accurately can we predict the fracture load of the proximal femur using finite element models?

BACKGROUND

Current clinical methods for fracture prediction rely on two-dimensional imaging methods such as dual-energy X-ray absorptiometry and have limited predictive value. Several researchers have tried to integrate three-dimensional imaging techniques with the finite element (FE) method to improve the accuracy of fracture predictions. Before FE models could be used in clinical settings, a thorough validation of their accuracy is required. In this paper, we try to evaluate the current state of accuracy of subject-specific FE models that are used for prediction of the fracture load of proximal femora.

METHODS

All the studies that have used FE for prediction of fracture load and have compared the predicted fracture load with experimentally measured fracture loads in vitro are identified through a systematic search of the literature. A quantitative analysis of the results of those studies has been carried out to determine the absolute prediction error, percentage error, and linear correlations between predicted and measured fracture loads.

FINDINGS

The reported coefficients of determination (R(2)) vary between 0.773 and 0.96 while the percentage error in prediction of fracture load varies between 5 and 46% with most studies reporting percentage errors between 10 and 20%.

INTERPRETATION

We conclude that FE models, which are currently used only experimentally, are in general more accurate than clinically used fracture risk assessment techniques. However, the accuracy of FE models depends on the details of their modeling methodologies. Therefore, modeling procedures need to be optimized and standardized before FE could be used in clinical settings.

Total hip arthroplasty by using a cementless ultrashort stem: A subject-specific finite element analysis for a young patient clinical case

In this article, a subject-specific finite element analysis has been developed to study a clinical case of a surgically misaligned hip prosthesis with an ultrashort stem. It was set out to study the strain energy density pattern, comparing the results obtained with computed tomography images. The authors developed two other numerical models: the first one analyzes the stress and strain distributions in the healthy femur (without prosthesis) and the second one analyzes the same boneimplant biomechanical system of the clinical case but assuming the prosthesis in the proper position. The misaligned prosthesis produced an overload at the proximal posterior plane of the femur, as confirmed by computed tomography images, which detect the formation of new bone. The numerical model of the correctly positioned prosthesis demonstrated that the bone is not overloaded and that the position of neutral axis does not significantly shift from the physiological condition.

Patient-specific finite element modeling of bones

Finite element modeling is an engineering tool for structural analysis that has been used for many years to assess the relationship between load transfer and bone morphology and to optimize the design and fixation of orthopedic implants. Due to recent developments in finite element model generation, for example, improved computed tomography imaging quality, improved segmentation algorithms, and faster computers, the accuracy of finite element modeling has increased vastly and finite element models simulating the anatomy and properties of an individual patient can be constructed. Such so-called patient-specific finite element models are potentially valuable tools for orthopedic surgeons in fracture risk assessment or pre- and intraoperative planning of implant placement. The aim of this article is to provide a critical overview of current themes in patient-specific finite element modeling of bones. In addition, the state-of-the-art in patient-specific modeling of bones is compared with the requirements for a clinically applicable patient-specific finite element method, and judgment is passed on the feasibility of application of patient-specific finite element modeling as a part of clinical orthopedic routine. It is concluded that further development in certain aspects of patient-specific finite element modeling are needed before finite element modeling can be used as a routine clinical tool.

Experimental evaluation of new concepts in hip arthroplasty

In this thesis we evaluated two different hip arthroplasty concepts trough in vitro studies and numerical analyses. The cortical strains in the femoral neck area were increased by 10 to 15 % after insertion of a resurfacing femoral component compared to values of the intact femur, shown in an in vitro study on human cadaver femurs. There is an increased risk of femoral neck fracture after hip resurfacing arthroplasty. An increase of 10 to 15 % in femoral neck strains is limited, and cannot alone explain these fractures. Together with patient specific and surgical factors, however, increased strain can contribute to increased risk of fracture. An in vitro study showed that increasing the neck length in combination with retroversion or reduced neck shaft angle on a standard cementless femoral stem does not compromise the stability of the stem. The strain pattern in the proximal femur increased significantly at several measuring sites when the version and length of neck were altered. However, the changes were probably too small to have clinical relevance. In a validation study we have shown that a subject specific finite element analysis is able to perform reasonable predictions of strains and stress shielding after insertion of a femoral stem in human cadaver femurs. The usage of finite element models can be a valuable supplement to in vitro tests of femoral strain pattern around hip arthroplasty. Finally, a patient case shows that bone resorption around an implant caused by stress shielding can in extreme cases lead to periprosthetic fracture.

Analysis of bone demineralization due to the use of exoprosthesis by comparing Young's modulus of the femur in unilateral transfemoral amputees

BACKGROUND

There is a relation between Hounsfield units obtained from computed tomography (CT) scans and bone density. The density of the bones can be used to establish its mechanical properties and therefore to assess the bone mechanical condition using CT images.

OBJECTIVES

To identify the effect of the transfemoral amputation and the use of external lower limb prosthesis in the bone properties, by comparing Young's modulus.

STUDY DESIGN

Young's modulus comparison.

METHODS

Comparison of bone density between the healthy femur and the amputated bone of 20 unilateral transfemoral amputees was done by generating three histograms of the Hounsfield units at different parts of the femur. The histograms were created based on images obtained by CT and the Hounsfield units were translated to Young's modulus to establish the comparison.

RESULTS

The results show a significant difference (p-value <0.05) between the mean value of Young's modulus of healthy and amputated bone.

CONCLUSIONS

There is clearly a direct association between the use of external prosthesis and the bone demineralization due the stress shielding phenomenon. The Young's modulus comparison using information from CT images can be a suitable tool to analyze the bone demineralization due to the use of exoprosthesis.

2D and 3D finite element analysis of central incisor generated by computerized tomography

The purpose of this study was to compare the results of different hierarchical models in engineering analysis applied to dentistry with 2D and 3D models of a tooth and its supporting structures under 100 N occlusal loading at 45° and examine the reliability of simplified 2D models in dental research. Five models were built from computed-tomography scans: four 2D models with Plane Strain and Plane Stress State with linear triangular and quadratic quadrilateral elements and one 3D model. The finite element results indicated that the stress distribution was similar qualitatively in all models but the stress magnitude was quite different. It was concluded that 2D models are acceptable when investigating the biomechanical behavior of upper central incisor qualitatively. However, quantitative stress analysis is less reliable in 2D-finite element analysis, because 2D models overestimate the results and do not represent the complex anatomical configuration of dental structures. Therefore 3D finite element analyses of dental biomechanics cannot be simplified.

The finite cell method for bone simulations: verification and validation

Standard methods for predicting bone's mechanical response from quantitative computer tomography (qCT) scans are mainly based on classical h-version finite element methods (FEMs). Due to the low-order polynomial approximation, the need for segmentation and the simplified approach to assign a constant material property to each element in h-FE models, these often compromise the accuracy and efficiency of h-FE solutions. Herein, a non-standard method, the finite cell method (FCM), is proposed for predicting the mechanical response of the human femur. The FCM is free of the above limitations associated with h-FEMs and is orders of magnitude more efficient, allowing its use in the setting of computational steering. This non-standard method applies a fictitious domain approach to simplify the modeling of a complex bone geometry obtained directly from a qCT scan and takes into consideration easily the heterogeneous material distribution of the various bone regions of the femur. The fundamental principles and properties of the FCM are briefly described in relation to bone analysis, providing a theoretical basis for the comparison with the p-FEM as a reference analysis and simulation method of high quality. Both p-FEM and FCM results are validated by comparison with an in vitro experiment on a fresh-frozen femur.

Patient-Specific Finite-Element Analyses of the Proximal Femur with Orthotropic Material Properties Validated by Experiments

Patient-specific high order finite-element (FE) models of human femurs based on quantitative computer tomography (QCT) with inhomogeneous orthotropic and isotropic material properties are addressed. The point-wise orthotropic properties are determined by a micromechanics (MM) based approach in conjunction with experimental observations at the osteon level, and two methods for determining the material trajectories are proposed (along organs outer surface, or along principal strains). QCT scans on four fresh-frozen human femurs were performed and high-order FE models were generated with either inhomogeneous MM-based orthotropic or empirically determined isotropic properties. In vitro experiments were conducted on the femurs by applying a simple stance position load on their head, recording strains on femurs’ surface and head’s displacements. After verifying the FE linear elastic analyses that mimic the experimental setting for numerical accuracy, we compared the FE results to the experimental observations to identify the influence of material properties on models’ predictions. The strains and displacements computed by FE models having MM-based inhomogeneous orthotropic properties match the FE-results having empirically based isotropic properties well, and both are in close agreement with the experimental results. When only the strains in the femoral neck are being compared a more pronounced difference is noticed between the isotropic and orthotropic FE result. These results lay the foundation for applying more realistic inhomogeneous orthotropic material properties in FEA of femurs.

Evaluation of the generality and accuracy of a new mesh morphing procedure for the human femur

Various papers described mesh morphing techniques for computational biomechanics, but none of them provided a quantitative assessment of generality, robustness, automation, and accuracy in predicting strains. This study aims to quantitatively evaluate the performance of a novel mesh-morphing algorithm. A mesh-morphing algorithm based on radial-basis functions and on manual selection of corresponding landmarks on template and target was developed. The periosteal geometries of 100 femurs were derived from a computed tomography scan database and used to test the algorithm generality in producing finite element (FE) morphed meshes. A published benchmark, consisting of eight femurs for which in vitro strain measurements and standard FE model strain prediction accuracy were available, was used to assess the accuracy of morphed FE models in predicting strains. Relevant parameters were identified to test the algorithm robustness to operative conditions. Time and effort needed were evaluated to define the algorithm degree of automation. Morphing was successful for 95% of the specimens, with mesh quality indicators comparable to those of standard FE meshes. Accuracy of the morphed meshes in predicting strains was good (R(2)>0.9, RMSE%<10%) and not statistically different from the standard meshes (p-value=0.1083). The algorithm was robust to inter- and intra-operator variability, target geometry refinement (p-value>0.05) and partially to the number of landmark used. Producing a morphed mesh starting from the triangularized geometry of the specimen requires on average 10 min. The proposed method is general, robust, automated, and accurate enough to be used in bone FE modelling from diagnostic data, and prospectively in applications such as statistical shape modelling.