Improving the validation of finite element models with quantitative full-field strain comparisons.

The techniques used to validate finite element (FE) models against experimental results have changed little during the last decades, even though the traditional approach of using single point measurements from strain gauges has major limitations: the strain distribution across the surface is not captured and the accurate determination of strain gauge positions on the model surface is difficult if the 3D surface topography of the bone surface is not measured. The full-field strain measurement technique of digital speckle pattern interferometry (DSPI) can overcome these problems, but the potential of this technique has not yet been fully exploited in validation studies. Here we explore new ways of quantifying and visualising the variation in strain magnitudes and orientations within and between repeated DSPI measurements as well as between the DSPI measurements and FEA results. We show that our approach provides a much more comprehensive and accurate validation than traditional methods. The measurement repeatability and the correspondence between measured and predicted strains vary to a great degree within and between measurement areas. The two models used in this study predict the measured strain directions and magnitudes surprisingly well considering that homogeneous and isotropic mechanical properties were assigned to the models. However, the full-field comparisons also reveal some discrepancies between measured and predicted strains that are most probably caused by inaccuracies in the models' geometries and the degree of simplification of the modelled material properties.

The effects of the periodontal ligament on mandibular stiffness: a study combining finite element analysis and geometric morphometrics.

It is generally accepted that the periodontal ligament (PDL) plays a crucial role in transferring occlusal forces from the teeth to the alveolar bone. Studies using finite element analysis (FEA) have helped to better understand this role and show that the stresses and strains in the alveolar bone are influenced by whether and how PDL is included in FE models. However, when the overall distribution of stresses and strains in crania and mandibles are of interest, PDL is often not included in FE models, although little is known about how this affects the results. Here we study the effect of representing PDL as a layer of solid material with isotropic homogeneous properties in an FE model of a human mandible using a novel application of geometric morphometrics. The results show that the modelling of the PDL affects the deformation and thus strain magnitudes not only of the alveolar bone around the biting tooth, but that the whole mandible deforms differently under load. As a result, the strain in the mandibular corpus is significantly increased when PDL is included, while the strain in the bone beneath the biting tooth is reduced. These results indicate the importance of the PDL in FE studies. Thus we recommend that the PDL should be included in FE models of the masticatory apparatus, with tests to assess the sensitivity of the results to changes in the Young's modulus of the PDL material.

Validating a voxel-based finite element model of a human mandible using digital speckle pattern interferometry.

Finite element analysis is a powerful tool for predicting the mechanical behaviour of complex biological structures like bones, but to be confident in the results of an analysis, the model should be validated against experimental data. In such validation experiments, the strains in the loaded bones are usually measured with strain gauges glued to the bone surface, but the use of strain gauges on bone can be difficult and provides only very limited data regarding surface strain distributions. This study applies the full-field strain measurement technique of digital speckle pattern interferometry to measure strains in a loaded human mandible and compares the results with the predictions of voxel-based finite element models of the same specimen. It is found that this novel strain measurement technique yields consistent, reliable measurements. Further, strains predicted by the finite element analysis correspond well with the experimental data. These results not only confirm the usefulness of this technique for future validation studies in the field of bone mechanics, but also show that the modelling approach used in this study is able to predict the experimental results very accurately.