Mechanics of the maxillary central incisor. Influence of the periodontal ligament represented by beam elements

This study aimed to evaluate the influence of loading on a maxillary central incisor with the periodontal ligament (PDL) represented by 2D elastic beam elements using a 2D finite element analysis. Two models (M) were built varying the PDL representation: Mh (homogeneous PDL) and Mht (heterogeneous PDL with beam3 elements). Stress and displacements were determined for three loading conditions (L): Ll, lingual face loading at 45° with the tooth long axis; Li, perpendicular to the incisal edge; and Lip, on the incisal edge, parallel to the tooth long axis. Evaluation was performed on ANSYS software. Lip provided lower stress variation on the tooth and support structures when compared to Ll and Li. PDL's influence on stress values was lower for Lip. Oblique loading showed stress and displacement not observed in parallel loading condition through PDL's heterogeneous representation and it is probably incompatible with the in vivo condition.     

Left ventricular wall stress compendium

Left ventricular (LV) wall stress has intrigued scientists and cardiologists since the time of Lame and Laplace in 1800s. The left ventricle is an intriguing organ structure, whose intrinsic design enables it to fill and contract. The development of wall stress is intriguing to cardiologists and biomedical engineers. The role of left ventricle wall stress in cardiac perfusion and pumping as well as in cardiac pathophysiology is a relatively unexplored phenomenon. But even for us to assess this role, we first need accurate determination of in vivo wall stress. However, at this point, 150 years after Lame estimated left ventricle wall stress using the elasticity theory, we are still in the exploratory stage of (i) developing left ventricle models that properly represent left ventricle anatomy and physiology and (ii) obtaining data on left ventricle dynamics. In this paper, we are responding to the need for a comprehensive survey of left ventricle wall stress models, their mechanics, stress computation and results. We have provided herein a compendium of major type of wall stress models: thin-wall models based on the Laplace law, thick-wall shell models, elasticity theory model, thick-wall large deformation models and finite element models. We have compared the mean stress values of these models as well as the variation of stress across the wall. All of the thin-wall and thick-wall shell models are based on idealised ellipsoidal and spherical geometries. However, the elasticity model's shape can vary through the cycle, to simulate the more ellipsoidal shape of the left ventricle in the systolic phase. The finite element models have more representative geometries, but are generally based on animal data, which limits their medical relevance. This paper can enable readers to obtain a comprehensive perspective of left ventricle wall stress models, of how to employ them to determine wall stresses, and be cognizant of the assumptions involved in the use of specific models.     

A semi-automated method for hexahedral mesh construction of human vertebrae from CT scans

Generation of finite element (FE) meshes of vertebrae from computed tomography (CT) scans is labour intensive due to their geometric complexity. As such, techniques that simplify creation of meshes of vertebrae are needed to make FE analysis feasible for large studies and clinical applications. Techniques to obtain a geometric representation of bone contours from CT scans of vertebrae and construct a hexahedral mesh from the contours were developed. An automated edge detection technique was developed to identify surface contours of the vertebrae, followed by atlas based B-spline curve fitting to construct curves from the edge points. The method was automatic and robust to missing data, with a controllable degree of smoothing and interpolation. Parametric mapping was then used to generate nodes for each CT slice, which were connected between slices to obtain a hexahedral mesh. This method could be adapted for modelling a variety of orthopaedic structures.     

Comparative analysis of bone remodelling models with respect to computerised tomography-based finite element models of bone

Subject-specific finite element models are an extensively used tool for the numerical analysis of the biomechanical behaviour of human bones. However, bone modelling is not an easy task due to the complex behaviour of bone tissue, involving non-homogeneous and anisotropic mechanical properties. Moreover, bone is a living tissue and therefore its microstructure and mechanical properties evolve with time in a known process called bone remodelling. This phenomenon has been widely studied, many being the numerical models that have been formulated to predict density distribution and its evolution in several bones. The aim of the present study is to assess the capability of a bone remodelling model to predict the bone density distribution of different types of human bone (femur, tibia and mandible) comparing the obtained results with the bone density estimated by means of computerised tomography. Good accuracy was observed for the bone remodelling predictions including the thickness of the cortical layer.     

Which factors influence the ability of a computational model to predict the in vivo deformation behaviour of skeletal muscle?

Deep tissue injury (DTI) is a severe form of pressure ulcer where tissue damage starts in deep tissues underneath intact skin. Tissue deformation may play an important role in the aetiology, which can be investigated using an experimental–numerical approach. Recently, an animal-specific finite element model has been developed to simulate experiments in which muscle tissue was compressed with an indenter. In this study, the material behaviour and boundary conditions were adapted to improve the agreement between model and experiment and to investigate the influence of these adaptations on the predicted strain distribution. The use of a highly nonlinear material law and including friction between the indenter and the muscle both improved the quality of the model and considerably influenced the estimated strain distribution. With the improved model, the required sample size to detect significant differences between loading conditions can be diminished, which is clearly relevant in experiments involving animals.     

How does muscle stiffness affect the internal deformations within the soft tissue layers of the buttocks under constant loading?

Mechanical loading of soft tissues covering bony prominences can cause skeletal muscle damage, ultimately resulting in a severe pressure ulcer termed deep tissue injury (DTI). Deformation plays an important role in the aetiology of DTI. Therefore, it is essential to minimise internal muscle deformations in subjects at risk of DTI. As an example, spinal cord-injured (SCI) individuals exhibit structural changes leading to a decrease in muscle thickness and stiffness, which subsequently increase the tissue deformations. In the present study, an animal-specific finite element model, where the geometry and boundary conditions were derived from magnetic resonance images, was developed. It was used to investigate the internal deformations in the muscle, fat and skin layers of the porcine buttocks during loading. The model indicated the presence of large deformations in both the muscle and the fat layers, with maximum shear strains up to 0.65 in muscle tissue and 0.63 in fat. Furthermore, a sensitivity analysis showed that the tissue deformations depend considerably on the relative stiffness values of the different tissues. For example, a change in muscle stiffness had a large effect on the muscle deformations. A 50% decrease in stiffness caused an increase in maximum shear strain from 0.65 to 0.99, whereas a 50% increase in stiffness resulted in a decrease in maximum shear strain from 0.65 to 0.49. These results indicate the importance of restoring tissue properties after SCI, with the use of, for example, electrical stimulation, to prevent the development of DTI.     

Detailed finite element modelling of deep needle insertions into a soft tissue phantom using a cohesive approach

Detailed finite element modelling of needle insertions into soft tissue phantoms encounters difficulties of large deformations, high friction, contact loading and material failure. This paper demonstrates the use of cohesive elements in high-resolution finite element models to overcome some of the issues associated with these factors. Experiments are presented enabling extraction of the strain energy release rate during crack formation. Using data from these experiments, cohesive elements are calibrated and then implemented in models for validation of the needle insertion process. Successful modelling enables direct comparison of finite element and experimental force–displacement plots and energy distributions. Regions of crack creation, relaxation, cutting and full penetration are identified. By closing the loop between experiments and detailed finite element modelling, a methodology is established which will enable design modifications of a soft tissue probe that steers through complex mechanical interactions with the surrounding material.     

Validation of the Boussinesq equation for use in traction field determination

Cell traction force plays an important role in many biological processes. Several traction force microscopy methods have been developed to determine cell traction forces based on the Boussinesq solution. This approach, however, is rooted in a half-space assumption. The purpose of this study was to determine the error induced in the half-space assumption using a finite element method (FEM). It demonstrates that displacement error between the FEM and the Boussinesq equation can be used to measure the accuracy of the Boussinesq equation, although singularity exists in the loading point. For one concentrated force, significant difference between the FEM and the Boussinesq equation occurs in the whole field; this difference decreases with an increase in the plate thickness. However, in the case of the balanced forces, the offset of the balanced forces decreases the errors in the middle area. Overall, this study demonstrates that increasing the thickness of the polyacrylamide gel is important for reducing the error of the Boussinesq equation when determining the displacement field of the gel under loads.