The Response of Cranial Biomechanical Finite Element Models to Variations in Mesh Density (original) (raw)
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Finite element analysis of the cranium: Validity, sensitivity and future directions
Comptes Rendus Palevol, 2017
Finite Element Analysis (FEA) is increasingly applied in skeletal biomechanical research in general, and in fossil studies in particular. Underlying such studies is the principle that FEA provides results that approximate reality. This paper provides further understanding of the reliability of FEA by presenting a validation study in which the deformations experienced by a real cadaveric human cranium are compared to those of an FE model of that cranium under equivalent simulated loading. Furthermore, model sensitivity to simplifications in segmentation and material properties is also assessed. Our results show that absolute deformations are not accurately predicted, but the distribution of the regions of relatively high and low strains, and so the modes of global deformation, are reasonably approximated. Résumé La méthode des éléments finis (FEA) est de plus en plus appliquée dans la recherche biomécanique du squelette en général, et dans les études de fossiles en particulier. Ces études sont fondées sur le principe selon lequel les FEA fournissent des résultats qui se rapprochent de la réalité. Ce article fournit une meilleure compréhension de la fiabilité de la méthode des FEA en présentant une étude de validité dans laquelle les déformations subies par un vrai crâne de cadavre humain sont comparées à celles d'un modèle par éléments finis de ce crâne sous un chargement simulé équivalent. En outre, la sensibilité du modèle vis-à-vis de simplifications dans la segmentation et des propriétés des matériaux est également évaluée. Nos résultats montrent que les déformations absolues ne sont pas prédites avec précision, mais la répartition des régions de relativement hautes et basses contraintes, et par conséquent les modes de déformation globale, sont raisonnablement estimés.
Sensitivity and ex vivo validation of finite element models of the domestic pig cranium.
A finite element (FE) validation and sensitivity study was undertaken on a modern domestic pig cranium. Bone strain data were collected ex vivo from strain gauges, and compared with results from specimen-specific FE models. An isotropic, homogeneous model was created, then input parameters were altered to investigate model sensitivity. Heterogeneous, isotropic models investigated the effects of a constant-thickness, stiffer outer layer (representing cortical bone) atop a more compliant interior (representing cancellous bone). Loading direction and placement of strain gauges were also varied, and the use of 2D membrane elements at strain gauge locations as a method of projecting 3D model strains into the plane of the gauge was investigated. The models correctly estimate the loading conditions of the experiment, yet at some locations fail to reproduce correct principal strain magnitudes, and hence strain ratios. Principal strain orientations are predicted well. The initial model was too stiff by approximately an order of magnitude. Introducing a compliant interior reported strain magnitudes more similar to the ex vivo results without notably affecting strain orientations, ratios or contour patterns, suggesting that this simple heterogeneity was the equivalent of reducing the overall stiffness of the model. Models were generally insensitive to moderate changes in loading direction or strain gauge placement, except in the squamosal portion of the zygomatic arch. The use of membrane elements made negligible differences to the reported strains. The models therefore seem most sensitive to changes in material properties, and suggest that failure to model local heterogeneity in material properties and structure of the bone may be responsible for discrepancies between the experimental and model results. This is partially attributable to a lack of resolution in the CT scans from which the model was built, and partially due to an absence of detailed material properties data for pig cranial bone. Thus, caution is advised when using FE models to estimate absolute numerical values of breaking stress and bite force unless detailed input parameters are available. However, if the objective is to compare relative differences between models, the fact that the strain environment is replicated well means that such investigations can be robust.
Rodents are defined by a uniquely specialized dentition and a highly complex arrangement of jaw-closing muscles. Finite element analysis (FEA) is an ideal technique to investigate the biomechanical implications of these specializations, but it is essential to understand fully the degree of influence of the different input parameters of the FE model to have confidence in the model's predictions. This study evaluates the sensitivity of FE models of rodent crania to elastic properties of the materials, loading direction, and the location and orientation of the models' constraints. Three FE models were constructed of squirrel, guinea pig and rat skulls. Each was loaded to simulate biting on the incisors, and the first and the third molars, with the angle of the incisal bite varied over a range of 45 degrees. The Young's moduli of the bone and teeth components were varied between limits defined by findings from our own and previously published tests of material properties. Geometric morphometrics (GMM) was used to analyse the resulting skull deformations. Bone stiffness was found to have the strongest influence on the results in all three rodents, followed by bite position, and then bite angle and muscle orientation. Tooth material properties were shown to have little effect on the deformation of the skull. The effect of bite position varied between species, with the mesiodistal position of the biting tooth being most important in squirrels and guinea pigs, whereas bilateral vs. unilateral biting had the greatest influence in rats. A GMM analysis of isolated incisor deformations showed that, for all rodents, bite angle is the most important parameter, followed by elastic properties of the tooth. The results here elucidate which input parameters are most important when defining the FE models, but also provide interesting glimpses of the biomechanical differences between the three skulls, which will be fully explored in future publications.
On the level of computational model of a human skull: A comparative study
Applied and Computational Mechanics
In this study, different patient-specific computational models of the skull, which are often used in literature, were investigated, analysed and compared. The purpose of this study was to demonstrate the differences in computational model creation and results in case different computational models based on same computed tomography (CT) dataset are used. The selection of computational model directly influences the values of investigated parameters. The effort is to demonstrate, how the selection of the computational model influences the results of biomechanically relevant parameters. The comparison was based on total displacement of the skull and von Mises strain investigated around predefined paths around the skull. The strain values were evaluated according to criterion from literature. The results were obtained using finite element method. The values of the displacement of the skull were higher in case of considering cancellous bone tissue due to its poor material properties or heterogeneous material properties. The same situation occurred during the evaluation of strain. The values were higher in models which include cancellous bone tissue in the structure.
Finite-Element Modeling of Bones From CT Data: Sensitivity to Geometry and Material Uncertainties
Biomedical …, 2006
The aim of this paper is to analyze how the uncertainties in modelling the geometry and the material properties of a human bone affect the predictions of a finite-element model derived from computed tomography (CT) data. A sensitivity analysis, based on a Monte Carlo method, was performed using three femur models generated from in vivo CT datasets, each subjected to two different loading conditions. The geometry, the density and the mechanical properties of the bone tissue were considered as random input variables. Finite-element results typically used in biomechanics research were considered as statistical output variables, and their sensitivity to the inputs variability assessed. The results showed that it is not possible to define a priori the influence of the errors related to the geometry definition process and to the material assignment process on the finite-element analysis results. The errors in the geometric representation of the bone are always the dominant variables for the stresses, as was expected. However, for all the variables, the results seemed to be dependent on the loading condition and to vary from subject to subject. The most interesting result is, however, that using the proposed method to build a finite-element model of a femur from a CT dataset of the quality typically achievable in the clinical practice, the coefficients of variation of the output variables never exceed the 9%. The presented method is hence robust enough to be used for investigating the mechanical behavior of bones with subject-specific finite-element models derived from CT data taken in vivo.
High-Resolution Three-Dimensional Computer Simulation of Hominid Cranial Mechanics
In vivo data demonstrates that strain is not distributed uniformly on the surface of the primate skull during feeding. However, in vivo studies are unable to identify or track changes in stress and strain throughout the whole structure. Finite element (FE) analysis, a powerful engineering tool long used to predict the performance of man-made devices, has the capacity to track stress/strain in three dimensions (3-D) and, despite the time-consuming nature of model generation, FE has become an increasingly popular analytical device among biomechanists. Here, we apply the finite element method using sophisticated computer models to examine whether 3-D stress and strain distributions are nonuniform throughout the primate skull, as has been strongly suggested by 2-D in vivo strain analyses. Our simulations document steep internal stress/strain gradients , using models comprising up to three million tetrahedral finite elements and 3-D reconstructions of jaw adducting musculature with both cranium and mandible in correct anatomical position. Results are in broad concurrence with the suggestion that few regions of the hominid cranium are clearly optimized for routine feeding and also show that external stress/strain does not necessarily reflect internal distributions. Findings further suggest that the complex heterogeneity of bone in the skull may act to dissipate stress, but that consequently higher strain must be offset by additional strain energy. We hypothesize that, despite energetic costs, this system may lend adaptive advantage through enhancing the organism's ability to modify its behavior before reaching catastrophic failure in bony or dental structures.
Medical Engineering & Physics, 2007
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.
Finite element method modeling of craniofacial growth
American Journal of Orthodontics, 1985
The application of the concepts of continuum mechanics and of the numerical techniques of the finite element method permits the development of a new and potentially clinically useful method of describing craniofacial skeletal growth. This new method differs from those associated with customary roentgenographic cephalometry in that its descriptions and analyses are invariant; that is, they are independent of any method of registration and superimposition. Such invariance avoids the principal geometric constraint explicit in all analytical methods associated with conventional roentgenographic cephalometry. The conceptual and mathematical bases of the finite element method (FEM) are presented and illustrated by the numerical and graphic descriptions of the twodimensional growth of the rat skull, for which two sets of longitudinal growth data are used. In practice, the FEM permits analysis of the skull at a scale significantly finer than previously possible, by considering cranial structure as consisting of a relatively large number of contiguous finite elements. For each such element, independently, it is then possible to describe and depict both the magnitude and the direction of temporal size and shape changes occurring in that element relative to itself at some initial time. It is emphasized that such descriptions are completely independent of any local reference frame.