Finite element analysis of the cranium: Validity, sensitivity and future directions (original) (raw)
Related papers
The Anatomical Record, 2015
In recent years finite element analysis (FEA) has emerged as a useful tool for the analysis of skeletal form-function relationships. While this approach has obvious appeal for the study of fossil specimens, such material is often fragmentary with disrupted internal architecture and can contain matrix that leads to errors in accurate segmentation. Here we examine the effects of varying the detail of segmentation and material properties of teeth on the performance of a finite element model of a Macaca fascicularis cranium within a comparative functional framework. Cranial deformations were compared using strain maps to assess differences in strain contours and Procrustes size and shape analyses, from geometric morphometrics, were employed to compare large scale deformations. We show that a macaque model subjected to biting can be made solid, and teeth altered in material properties, with minimal impact on large scale modes of deformation. The models clustered tightly by bite point rather than by modeling simplification approach, and fell out as being distinct from another species. However localized fluctuations in predicted strain magnitudes were recorded with different modeling approaches, particularly over the alveolar region. This study indicates that, while any model simplification should be undertaken with care and attention to its effects, future applications of FEA to fossils with unknown internal architecture may produce reliable results with regard to general modes of deformation, even when detail of internal bone architecture cannot be reliably modeled.
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.
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.
Validation experiments on finite element models of an ostrich ( Struthio camelus ) cranium
PeerJ, 2015
The first finite element (FE) validation of a complete avian cranium was performed on an extant palaeognath, the ostrich (Struthio camelus).Ex-vivostrains were collected from the cranial bone and rhamphotheca. These experimental strains were then compared to convergence tested, specimen-specific finite element (FE) models. The FE models contained segmented cortical and trabecular bone, sutures and the keratinous rhamphotheca as identified from micro-CT scan data. Each of these individual materials was assigned isotropic material properties either from the literature or from nanoindentation, and the FE models compared to theex-vivoresults. The FE models generally replicate the location of peak strains and reflect the correct mode of deformation in the rostral region. The models are too stiff in regions of experimentally recorded high strain and too elastic in regions of low experimentally recorded low strain. The mode of deformation in the low strain neurocranial region is not replic...
The Response of Cranial Biomechanical Finite Element Models to Variations in Mesh Density
Finite element (FE) models provide discrete solutions to continuous problems. Therefore, to arrive at the correct solution, it is vital to ensure that FE models contain a sufficient number of elements to fully resolve all the detail encountered in a continuum structure. Mesh convergence testing is the process of comparing successively finer meshes to identify the point of diminishing returns; where increasing resolution has marginal effects on results and further detail would become costly and unnecessary. Historically, convergence has not been considered in most CT-based biomechanical reconstructions involving complex geometries like the skull, as generating such models has been prohibitively time-consuming. To assess how mesh convergence influences results, 18 increasingly refined CT-based models of a domestic pig skull were compared to identify the point of convergence for strain and displacement, using both linear and quadratic tetrahedral elements. Not all regions of the skull converged at the same rate, and unexpectedly, areas of high strain converged faster than low-strain regions. Linear models were slightly stiffer than their quadratic counterparts, but did not converge less rapidly. As expected, insufficiently dense models underestimated strain and displacement, and failed to resolve strain ‘‘hot-spots’’ notable in contour plots. In addition to quantitative differences, visual assessments of such plots often inform conclusions drawn in many comparative studies, highlighting that mesh convergence should be performed on all finite element models before further analysis takes place.
Several finite element models of a primate cranium were used to investigate the biomechanical effects of the tooth sockets and the material behavior of the periodontal ligament (PDL) on stress and strain patterns associated with feeding. For examining the effect of tooth sockets, the unloaded sockets were modeled as devoid of teeth and PDL, filled with teeth and PDLs, or simply filled with cortical bone. The third premolar on the left side of the cranium was loaded and the PDL was treated as an isotropic, linear elastic material using published values for Young's modulus and Poisson's ratio. The remaining models, along with one of the socket models, were used to determine the effect of the PDL's material behavior on stress and strain distributions under static premolar biting and dynamic tooth loading conditions. Two models (one static and the other dynamic) treated the PDL as cortical bone. The other two models treated it as a ligament with isotropic, linear elastic material properties. Two models treated the PDL as a ligament with hyperelastic properties, and the other two as a ligament with viscoelastic properties. Both behaviors were defined using published stress-strain data obtained from in vitro experiments on porcine ligament specimens. Von Mises stress and strain contour plots indicate that the effects of the sockets and PDL material behavior are local. Results from this study suggest that modeling the sockets and the PDL in finite element analyses of skulls is project dependent and can be ignored if values of stress and strain within the alveolar region are not required.
Comparison between two finlte-element modelling methods for measuring change in craniofacial form
The Anatomical Record, 1990
Finite-element modelling of form change is a useful morphometric technique for measuring differences between anatomical patterns. Two different finite-element algorithms currently are used. One method requires normalized coordinates as input data, while the second method uses globalized coordinates as input data. This study determines whether the two finite-element methods provide equivalent measures of three-dimensional form change when applied to the nasal septa of embryonic mice. Computer models of the nasal septa from mice of 15 and 17 days gestation were generated. Homologous landmarks were identified so that each nasal septum was represented by a tetrahedral finite-element. These elements were subjected to both finite-element modelling methods. Results show that the two algorithms use different interpolation functions and yield dissimilar intermediate results, but generate identical strain matrices as well as equivalent principal extensions, directions of form change, variables of form change, and graphical displays. Therefore, results are directly comparable from studies using either finite-element modelling method.
Computación y Sistemas, 2013
In this paper, we present a cranial deformation simulation by applying a stress model using the Finite Element Method (FEM). We determine the geometry of cranium by processing 134 Computed Tomography (CT) images. We implement an image segmentation algorithm to build a three-dimensional cranium structure. We simulate stress and propose the boundary conditions according to the final position of forces applied by a stereotactic frame fixed on the human head. We used probabilistic and adaptive methods to select points in the structure with the purpose of reducing the computational cost and computational error due to discretization problem. We implement the algorithms using parallel programming (PosixThread and MPI).
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.