Finite Element Models Of Bone Research Articles

Thermal analysis of orthogonal cutting of cortical bone using finite element simulations

Bone cutting is widely used in orthopaedic, dental and neuro surgeries and is a technically demanding surgical procedure. One of the major concerns in current research is thermal damage of the bone tissue caused by high-speed power tools, which occurs when temperature rises above a certain threshold value for the tissue known as bone necrosis. Hence, optimisation of cutting parameters is necessary to avoid thermal necrosis and improve current orthopaedic surgical procedures. In this study a thermo-mechanical finite element model of bone cutting is presented that idealises cortical bone as an equivalent homogeneous isotropic material. The maximum temperature in the bone was found in the region where the thin bone layer (chip) was separated from the bone sample that was adjacent to the tool rake (i.e., front face of the tool). Temperature values were calculated with the model and compared for cutting conditions with and without a coolant (irrigation). The influence of bone's thermal properties on the depth of thermal necrosis is discussed. The simulated cutting temperatures were compared with experimental results obtained in bone drilling tests. Simulations of the cutting processes identified critical variables and cutting parameters affecting thermo-mechanics of bone cutting.

Finite element analysis of forces of plane cutting of cortical bone

Bone cutting is an essential part of orthopaedic surgery when bone is fractured or damaged by a disease and is used for pins insertion and plates fixation. A finite element model of bone cutting is developed and compared with experimental results. The model allows the interaction between the bone and cutting tool to be studied, hence enabling the evaluation and optimization of the cutting procedure. Results of finite element simulations are obtained for the cutting force as a function of cutting parameters. A strong dependence of cutting parameters on the cutting force was found and described in this paper.

The effect of the density–modulus relationship selected to apply material properties in a finite element model of long bone

Material property assignment is a critical step in developing subject-specific finite element models of bone. Inhomogeneous material properties are often applied using an equation relating density and elastic modulus, with the density information coming from CT scans of the bone. Very few previous studies have investigated which density–elastic modulus relationships from the literature are most suitable for application in long bone. No such studies have been completed for the ulna. The purpose of this study was to investigate six such density–modulus relationships and compare the results to experimental strains from eight cadaveric ulnae. Subject-specific finite element models were developed for each bone using micro-CT scans. Six density–modulus equations were trialed in each bone, resulting in a total of 48 models. Data from a previously completed experimental study in which each bone was instrumented with twelve strain gauges were used for comparison. Although the relationship that best matched experimental strains was somewhat specimen and location dependent, there were two relations which consistently matched the experimental strains most closely. One of these under-estimated and one over-estimated the experimental strain values, by averages of 15% and 31%, respectively. The results of this study suggest that the ideal relationship for the ulna may lie somewhere in between these two relations.

Multiscale modelling of the skeleton for the prediction of the risk of fracture

Background The development of a multiscale model of the human musculoskeletal system able to accurately predict the risk of bone fracture is still a grand challenge . The aim of this paper is to present the Living Human Project, to describe the final system and to review the achievements obtained so far. The Living Human musculoskeletal supermodel is conceived as the interconnection of five interdependent sub-models: the continuum, the boundary condition, the constitutive equation, the remodelling history and the failure criterion sub-models. Methods Methods are available to develop accurate subject-specific finite element models of bones that can incorporate the subject’s tissue-density distribution and empirically derived constitutive laws. Anatomo-functional musculoskeletal models can be registered with gait analysis data to predict muscle and joint forces acting on the patient’s skeleton during gait. These are the boundary conditions for the continuum models that showed an average error of 12% in the prediction of the failure load. Still, the entire supermodel is defined as a collection of procedural macros to predict the risk of fracture and should be improved. Findings Even with these limitations, the organ-level model already found some clinically relevant applications, especially in the analysis of joint prostheses. Also, the body-organ level multiscale model finds some clinical applications in paediatric skeletal oncology. The tissue- and the cell-level models are not yet fully validated. Thus, they cannot be safely used in clinical applications. Interpretation The continuum sub-model is the most mature model available. More powerful methods are needed for the generation of anatomo-functional musculoskeletal models. Muscle force prediction should be improved, investigating new probabilistic approaches to identify the neuro-motor strategy. The changes of the tissue properties in the various regions of the skeleton and predictive remodelling models should be included. An adequate information technology infrastructure should be developed to support collaborative work and integration of different sub-models.

The material mapping strategy influences the accuracy of CT-based finite element models of bones: An evaluation against experimental measurements

Aim of the present study was to evaluate the influence on the global model's accuracy of the strategy adopted to define the average element Young's modulus in subject-specific finite element models of bones from computed tomography data. The classic strategy of calculating the Young's modulus from an average element density and the one that averages the Young's moduli directly derived from each voxel Hounsfield Unit were considered. These strategies were applied to the finite element model of a real human femur. The accuracy of the superficial stress and strain predictions was evaluated against experimentally measured values in 13 strain-gauge locations for five different loading conditions. The results obtained for the two material distributions were statistically different. Both models predicted very accurately the superficial stresses, with regression coefficients higher than 0.9 and slopes not significantly different from unity. The second strategy definitely improved the strains prediction accuracy: the regression coefficient raised from 0.69 to 0.79; the average and peak errors decreased from 45.1% to 31.3% and from 228% to 134% of the maximum measured strain, respectively. The stress fields predicted inside the bone were also significantly different. A new software implementing the second strategy was made available in the public domain.

Establishment of an architecture-specific experimental validation approach for finite element modeling of bone by rapid prototyping and high resolution computed tomography

A new experimental validation method for assessing the accuracy of large-scale finite element (FE) models of bone micro-structure at the apparent and tissue level was developed. Augmented scaled bone replicas were built using rapid prototype machines based on micro-computed tomography (micro-CT) data. The geometric accuracy of the model was evaluated by comparing experimental tests with the replicas to the FE solution based on the same micro-CT data. A new version of the large-scale FE solver was developed to incorporate orthotropic material properties, hence the experimentally determined properties of the rapid prototype material were input into the FE models. The modified FE solver predicted the experimental apparent level stiffness within less than 1%, and the difference between experimental strain gauge measurements and FE-calculated surface stresses was 7% and 49% on a flat and curved surface region, respectively. While absolute error estimates of surface stresses were limited due to strain gauge errors, the relatively larger difference on the curved surface is indicative of the limitations of a hexahedron FE model for representing such geometries. Although the validation approach is applied here for hexahedron based meshes, the method is flexible for varying bone architectures and will be important for validation of future large-scale FE modeling developments that utilize techniques such as mesh smoothing and tetrahedron elements.

Subject-specific finite element models of long bones: An in vitro evaluation of the overall accuracy

The determination of the mechanical stresses induced in human bones is of great importance in both research and clinical practice. Since the stresses in bones cannot be measured non-invasively in vivo, the only way to estimate them is through subject-specific finite element modelling. Several methods exist for the automatic generation of these models from CT data, but before bringing them in the clinical practice it is necessary to assess their accuracy in the predictions of the bone stresses. Particular attention should be paid to those regions, like the epiphyseal and metaphyseal parts of long bones, where the automatic methods are typically less accurate. Aim of the present study was to implement a general procedure to automatically generate subject-specific finite element models of bones from CT data and estimate the accuracy of this general procedure by applying it to one real femur. This femur was tested in vitro under five different loading scenarios and the results of these tests were used to verify how the adoption of a simplified two-material homogeneous model would change the accuracy with respect to the density-based inhomogeneous one, with special attention paid to the epiphyseal and metaphyseal proximal regions of the bone. The results showed that the density-based inhomogeneous model predicts with a very good accuracy the measured stresses ( R 2 = 0.91 , RMSE=8.6%, peak error=27%), while the two-material model was less accurate ( R 2 = 0.89 , RMSE=9.6%, peak error=35%). The results showed that it is possible to automatically generate accurate finite element models of bones from CT data and that the strategy of material properties mapping has a significant influence on its accuracy.

MULTIMODAL DISPLAY INTERFACE FOR PLANNING AND MONITORING COMPLEX SKELETAL RECONSTRUCTIONS

The aim of the present work is to present the new software Multimod Data Manager and to show applications in the planning and monitoring of complex skeletal reconstructions in orthopedic oncology. The DataManager allows the full integration of different kind of data, particularly medical imaging data, both static as CT, SPECT or MRI, or time-varying as fluoroscopy or dynamic MRI, with motion analysis data, but also 3D computer and finite element models of bones, joints and also soft tissues. All the data can be visualized with highly interactive and specialized modalities and can be integrated to offer a complete representation of the patient anatomy. Several algorithms are implemented to allow registration and synchronization of the data. A fully 3D environment is offered to the surgeon to navigate inside the medical imaging dataset. To exemplify the use of the software we document in this paper the data processing used to investigate different specific clinical cases in the field of orthopedic oncology.

Comparison of isotropic and orthotropic material property assignments on femoral finite element models under two loading conditions

CT data has been widely used in the finite element modeling of bone. It can provide useful information on the geometrical topology and material properties of bone. Based on CT data, the assignment of bone material properties to finite element meshes is a fundamental step in the model generation. Most work done in this area has adopted isotropic assignment strategy due to its simplicity. However, bone material has been recognized as an orthotropic material. This work is aimed to investigate the effects of orthotropic material property assignment on femoral finite element model by comparing with isotropic material property assignment on the same model. There were 72 finite element models obtained from the frozen CT male dataset of visible human project. Based on the analysis results of the maximum equivalent Von Mises stress and the maximum nodal displacement, three parameters were defined to achieve this comparison. The results have shown that the differences between the two material property assignments are small under two loading conditions (double-leg standing and single-leg standing) investigated in this work.

Automatic generation of accurate subject-specific bone finite element models to be used in clinical studies

Most of the finite element models of bones used in orthopaedic biomechanics research are based on generic anatomies. However, in many cases it would be useful to generate from CT data a separate finite element model for each subject of a study group. In a recent study a hexahedral mesh generator based on a grid projection algorithm was found very effective in terms of accuracy and automation. However, so far the use of this method has been documented only on data collected in vitro and only for long bones. The present study was aimed at verifying if this method represents a procedure for the generation of finite element models of human bones from data collected in vivo, robust, accurate, automatic and general enough to be used in clinical studies. Robustness, automation and numerical accuracy of the proposed method were assessed on five femoral CT data sets of patients affected by various pathologies. The generality of the method was verified by processing a femur, an ileum, a phalanx, a proximal femur reconstruction, and the micro-CT of a small sample of spongy bone. The method was found robust enough to cope with the variability of the five femurs, producing meshes with a numerical accuracy and a computational weight comparable to those found in vitro. Even when the method was used to process the other bones the levels of mesh conditioning remained within acceptable limits. Thus, it may be concluded that the method presents a generality sufficient to cope with almost any orthopaedic application.

Validation of an automated method of three-dimensional finite element modelling of bone

This study validated an automated method of finite element modelling of bone from CT scan data. After a fresh-frozen cadaveric femur was modelled, strain gauges were attached to the bone at 11 locations and the femur was mechanically tested by applying a load to the femoral head. Linear regression analysis was used to correlate the strains predicted by the model with the experimentally measured strains. The regression results were significant ( P < 0.001), indicating that the strain calculated by the FE model is a valid predictor of the measured strain. Verification of the surface strains also supports the validity of the strains and stresses predicted inside the bone. The present study provides a strong rationale for use of this modelling method as a research tool and in possible clinical applications.

The use of strain energy as a convergence criterion in the finite element modelling of bone and the effect of model geometry on stress convergence

Keyak and Skinner 1 state that the adequacy of a finite element mesh may be verified by confirming that convergence of strain energy has been achieved. The paper concludes by stating that convergence of strain energy does not ensure that a particular mesh is adequate for producing accurate stress/strain results, and that only qualitative results can be achieved from 3D models of bone. This conclusion is challenged and the effect of element size on stress convergence is clarified. The influence of element size on stress convergence in regions of surface irregularity is studied and current methods are discussed that facilitate convergence.

Three-dimensional finite element modelling of bone: effects of element size

This study quantifies the effects of element size on the stress/strain results of finite element (FE) models of bone that are generated with a previously described automated method. This method uses cube-shaped hexahedral elements, which enabled element shape and aspect ratio to be held constant while the effects of element size were studied. Three models of a human proximal femur, each with a different element size (3.1 mm, 3.8 mm and 4.8 mm), were analysed. Convergence in strain energy of the models had been verified in previous work. The stresses and strains predicted by the models were compared on a pointwise basis using linear regression analysis. There was a general decrease in the level of stress and strain when element size was increased, even though convergence in strain energy had been achieved. An increase in element width from 3.1 mm to 3.8 mm decreased the predicted stresses by 13% to 29% overall; the predicted strains decreased by 4% to 20% for the same increase in element size. These results indicate that linear cube-shaped hexahedral elements must be very small (3 mm on a side or smaller) to represent the sharp variations in mechanical properties that exist in bone, and that use of larger elements decreases the predicted stresses and strains. The elements used in this study are similar to those typically used to represent trabecular bone in conventional (non-automated) FE modelling methods. Therefore, the sensitivity of the stress/strain results to element size that was found for trabecular bone also applies to conventional modelling of such bone. This sensitivity to element size implies that quantitative comparisons of the stresses/strains predicted in trabecular bone by different FE models may not be meaningful if the elements in those models are not the same size. The qualitative results of all three models were in agreement, however, indicating that qualitative comparisons of FE models may be made.

Automated three-dimensional finite element modelling of bone: a new method

Three-dimensional finite element stress analysis of bone is a key to understanding bone remodelling, assessing fracture risk, and designing prostheses; however, the cost and complexity of predicting the stress field in bone with accuracy has precluded the routine use of this method. A new, automated method of generating patient-specific three-dimensional finite element models of bone is presented — it uses digital computed tomographic (CT) scan data to derive the geometry of the bone and to estimate its inhomogeneous material properties. Cubic elements of a user-specified size are automatically defined and then individually assigned the CT scan-derived material properties. The method is demonstrated by predicting the stress, strain, and strain energy in a human proximal femur in vivo. Three-dimensional loading conditions corresponding to the stance phase of gait were taken from the literature and applied to the model. Maximum principal compressive stresses of 8–23 MPa were computed for the medial femoral neck. Automated generation of additional finite element models with larger numbers of elements was used to verify convergence in strain energy.

Automated three-dimensional finite element modeling of bone

Automated three-dimensional finite element modeling of bone

Subject index to volume 8

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 0.5 mm 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.