Growing multiblock structures: a semi-automated approach to block placement for multiblock hexahedral meshing

Finite element (FE) analysis is a cornerstone of orthopaedic biomechanics research. Three-dimensional medical imaging provides sufficient resolution for the subject-specific FE models to be generated from these data-sets. FE model development requires discretisation of a three-dimensional domain, which can be the most time-consuming component of a FE study. Hexahedral meshing tools based on the multiblock method currently rely on the manual placement of building blocks for mesh generation. We hypothesise that angular analysis of the geometric centreline for a three-dimensional surface could be used to automatically generate building block structures for the multiblock hexahedral mesh generation. Our algorithm uses a set of user-defined points and parameters to automatically generate a multiblock structure based on a surface's geometric centreline. This significantly reduces the time required for model development. We have applied this algorithm to 47 bones of varying geometries and successfully generated a FE mesh in all cases. This work represents significant advancement in automatically generating multiblock structures for a wide range of geometries.     

Protocol for constructing subject-specific biomechanical models of knee joint

A robust protocol for building subject-specific biomechanical models of the human knee joint is proposed which uses magnetic resonance imaging, motion analysis and force platform data in conjunction with detailed 3D finite element models. The proposed protocol can be used for determining stress and strain distributions and contact kinetics in different knee elements at different body postures during various physical activities. Several examples are provided to highlight the capabilities and potential applications of the proposed protocol. This includes preliminary results on the role of body weight on the stresses and strains induced in the knee articular cartilages and meniscus during single-leg stance and calculations of the induced stresses and ligament forces during the gait cycle.     

Patient-specific modelling of the foot: automated hexahedral meshing of the bones

Subject-specific finite element modelling is a powerful tool for carrying out controlled investigations of the effects of geometric and material property differences on performance and injury risk. Unfortunately, the creation of suitable meshes for these models is a challenging and time-intensive task. This paper presents an automated method of generating fully hexahedral meshes of the bones of the feet which requires only surface representations as inputs. The method is outlined and example meshes, using two human feet and the foot of a Japanese macaque, are given to demonstrate its flexibility. Mesh quality is also evaluated for the calcaneus, first metatarsal, navicular and talus. Streamlining the generation of finite element meshes of the foot will ease investigations into the patient-specific biomechanics of injury.     

Gaussian curvature analysis allows for automatic block placement in multi-block hexahedral meshing

Musculoskeletal finite element analysis (FEA) has been essential to research in orthopaedic biomechanics. The generation of a volumetric mesh is often the most challenging step in a FEA. Hexahedral meshing tools that are based on a multi-block approach rely on the manual placement of building blocks for their mesh generation scheme. We hypothesise that Gaussian curvature analysis could be used to automatically develop a building block structure for multi-block hexahedral mesh generation. The Automated Building Block Algorithm incorporates principles from differential geometry, combinatorics, statistical analysis and computer science to automatically generate a building block structure to represent a given surface without prior information. We have applied this algorithm to 29 bones of varying geometries and successfully generated a usable mesh in all cases. This work represents a significant advancement in automating the definition of building blocks.     

Factors affecting subject-specific finite element models of implant-fitted rat bone specimens: critical analysis of a technical protocol

The authors propose a protocol to derive finite element (FE) models from micro computer tomography scans of implanted rat bone. A semi-automatic procedure allows segmenting the images using specimen-specific bone mineral density (BMD) thresholds. An open-source FE model generator processes the segmented images to a quality tetrahedral mesh. The material properties assigned to each element are integrated from the BMD field. Piecewise, threshold-dependent density–elasticity relationships are implemented to limit the effects of metal artefacts. A detailed sensitivity study highlights the coherence of the generated models and quantifies the influence of the modelling parameters on the results. Two applications of the protocol are proposed. The stiffness of bare and implanted rat tibiae specimens is predicted by simulating three-point bending and inter-implant displacement, respectively. Results are compared with experimental tests. The mean value and the variability between the specimens are well captured in both tests.     

Prediction of the structural response of the femoral shaft under dynamic loading using subject-specific finite element models

The goal of this study was to predict the structural response of the femoral shaft under dynamic loading conditions using subject-specific finite element (SS-FE) models and to evaluate the prediction accuracy of the models in relation to the model complexity. In total, SS-FE models of 31 femur specimens were developed. Using those models, dynamic three-point bending and combined loading tests (bending with four different levels of axial compression) of bare femurs were simulated, and the prediction capabilities of five different levels of model complexity were evaluated based on the impact force time histories: baseline, mass-based scaled, structure-based scaled, geometric SS-FE, and heterogenized SS-FE models. Among the five levels of model complexity, the geometric SS-FE and the heterogenized SS-FE models showed statistically significant improvement on response prediction capability compared to the other model formulations whereas the difference between two SS-FE models was negligible. This result indicated the geometric SS-FE models, containing detailed geometric information from CT images with homogeneous linear isotropic elastic material properties, would be an optimal model complexity for prediction of structural response of the femoral shafts under the dynamic loading conditions. The average and the standard deviation of the RMS errors of the geometric SS-FE models for all the 31 cases was 0.46 kN and 0.66 kN, respectively. This study highlights the contribution of geometric variability on the structural response variation of the femoral shafts subjected to dynamic loading condition and the potential of geometric SS-FE models to capture the structural response variation of the femoral shafts.     

Sensitivity of corneal biomechanical and optical behavior to material parameters using design of experiments method

The optical performance of the human cornea under intraocular pressure (IOP) is the result of complex material properties and their interactions. The measurement of the numerous material parameters that define this material behavior may be key in the refinement of patient-specific models. The goal of this study was to investigate the relative contribution of these parameters to the biomechanical and optical responses of human cornea predicted by a widely accepted anisotropic hyperelastic finite element model, with regional variations in the alignment of fibers. Design of experiments methods were used to quantify the relative importance of material properties including matrix stiffness, fiber stiffness, fiber nonlinearity and fiber dispersion under physiological IOP. Our sensitivity results showed that corneal apical displacement was influenced nearly evenly by matrix stiffness, fiber stiffness and nonlinearity. However, the variations in corneal optical aberrations (refractive power and spherical aberration) were primarily dependent on the value of the matrix stiffness. The optical aberrations predicted by variations in this material parameter were sufficiently large to predict clinically important changes in retinal image quality. Therefore, well-characterized individual variations in matrix stiffness could be critical in cornea modeling in order to reliably predict optical behavior under different IOPs or after corneal surgery.     

Finite elements/Taguchi method based procedure for the identification of the geometrical parameters significantly affecting the biomechanical behavior of a lumbar disc

The aim of this work is to show a quick and simple procedure able to identify the geometrical parameters of the intervertebral disc that strongly affect the behavior of the FEM model. First, we allocated a selection criterion for the minimum number of geometrical parameters that describe, with a good degree of approximation, a healthy human vertebra. Next, we carried out a sensitivity analysis using the ‘Taguchi orthogonal array’ to arrive at a quick identification of the parameters that strongly affect the behavior of the Fem model.     

Mechanical significance of femoral head trabecular bone structure in Loris and Galago evaluated using micromechanical finite element models

Work on the interspecific and intraspecific variation of trabecular bone in the proximal femur of primates demonstrates important architectural variation between animals with different locomotor behaviors. This variation is thought to be related to the processes of bone adaptation whereby bone structure is optimized to the mechanical environment. Micromechanical finite element models were created for the proximal femur of the leaping Galago senegalensis and the climbing and quadrupedal Loris tardigradus by converting bone voxels from high-resolution X-ray computed tomography scans of the femoral head to eight-noded brick elements. The resulting models had approximately 1.8 million elements each. Loading conditions representing takeoff phase of a leap and more generalized load orientations were applied to the models, and the models were solved using the iterative "row-by-row" matrix-vector multiplication algorithm. The principal strain and Von Mises stress results for the leaping model were similar for both species at each load orientation. Similar hip joint reaction forces in the range of 4.9 x to 12 x body weight were calculated for both species under each loading condition, but the hip reaction values estimated for Loris were higher than predicted based on locomotor behavior. These results suggest that functional adaptation to hip joint loading may not fully explain the differences in femoral head trabecular bone structure in Galago and Loris. The finite element method represents a unique and useful tool for analyzing the functional adaptation of trabecular bone in a diversity of animals and for reconstructing locomotor behavior in extinct taxa.     

Comparison between mechanical stress and bone mineral density in the femur after total hip arthroplasty by using subject-specific finite element analyses

The mechanism underling bone mineral density (BMD) loss that occurs in the femur after total hip arthroplasty (THA) remains unknown. We compared the equivalent stress and strain energy density (SED) to BMD in the femur after THA using subject-specific finite element analyses. Twenty-four patients who had undergone primary cementless THA were analysed. BMD was measured using dual-energy X-ray absorptiometry (DEXA) at 1 week and 3, 6 and 12 months after THA. Seven regions of interest (ROIs) were defined in accordance with Gruen's system (ROIs 1–7). Computed tomography images of the femurs were acquired pre- and postoperatively, and the images were converted into three-dimensional finite element (FE) models. Equivalent stress and SED were analysed and compared with DEXA data. BMD was maintained 1 year after THA in ROIs 3, 4, 5 and 6, whereas BMD decreased in ROIs 1, 2 and 7. FE analysis revealed that equivalent stress in ROIs 3, 4, 5 and 6 was much higher than that in ROIs 1, 2 and 7. A significant correlation was observed between the rate of changes in BMD and equivalent stress. Reduction of equivalent stress may contribute to decrease in BMD in the femur after THA.     

Validation of plantar pressure simulations using finite and discrete element modelling in healthy and diabetic subjects

Plantar pressure simulation driven by integrated 3D motion capture data, using both a finite element and a discrete element model, is compared for ten healthy and ten diabetic neuropathic subjects. The simulated peak pressure deviated on average between 16.7 and 34.2% from the measured peak pressure. The error in the position of the peak pressure was on average smaller than 4.2 cm. No method was more accurate than the other although statistical differences were found between them. Both techniques are thus complementary and useful tools to better understand the alteration of diabetic foot biomechanics during gait.     

Quantification of soft tissue balance in total knee arthroplasty using finite element analysis

Unbalanced contact force on the tibial component has been considered a factor leading to loosening of the implant and increased wear of the bearing surface in total knee arthroplasty. Because it has been reported that good alignment cannot guarantee successful clinical outcomes, the soft tissue balance should be checked together with the alignment. Finite element models of patients' lower extremities were developed to analyse the medial and lateral contact force distribution on the tibial insert. The distributions for four out of five patients were not balanced equally, even though the alignment angles were within a clinically acceptable range. Moreover, the distribution was improved by changing soft tissue release and ligament tightening for the specific case. Integration of the biomechanical modelling, image matching and finite element analysis techniques with the patient-specific properties and various dynamic loading would suggest a clinically relevant pre-operative planning for soft tissue balancing.     

Computer simulation of orthodontic tooth movement using CT image-based voxel finite element models with the level set method

Orthodontic tooth movement (OTM) is an adaptive biomechanical response of dentoalveolar components to orthodontic forces, in which remodeling of the alveolar bone occurs in response to changes in the surrounding mechanical environment. In this study, we developed a framework for OTM simulation by combining an image-based voxel finite element method, with a surface-tracking level set method using three-dimensional computer models. For a case study to demonstrate its capability of expressing clinical tooth movement, we observed displacement and rotation of the tooth under three types of force conditions. The simulation results demonstrate that the proposed simulation method has the potential to predict clinical OTM.     

A poroviscohyperelastic model for numerical analysis of mechanical behavior of single chondrocyte

The aim of this paper is to use a poroviscohyperelastic (PVHE) model, which is developed based on the porohyperelastic (PHE) model to explore the mechanical deformation properties of single chondrocytes. Both creep and relaxation responses are investigated by using finite element analysis models of micropipette aspiration and atomic force microscopy experiments, respectively. The newly developed PVHE model is compared thoroughly with the standard neo-Hookean solid and PHE models. It has been found that the PVHE can accurately capture both creep and stress relaxation behaviors of chondrocytes better than other two models. Hence, the PVHE is a promising model to investigate mechanical properties of single chondrocytes.     

Influence of bicortical techniques in internal connection placed in premaxillary area by 3D finite element analysis

The aim of study was to evaluate the stress distribution in implant-supported prostheses and peri-implant bone using internal hexagon (IH) implants in the premaxillary area, varying surgical techniques (conventional, bicortical and bicortical in association with nasal floor elevation), and loading directions (0°, 30° and 60°) by three-dimensional (3D) finite element analysis. Three models were designed with Invesalius, Rhinoceros 3D and Solidworks software. Each model contained a bone block of the premaxillary area including an implant (IH, Ø4 × 10 mm) supporting a metal-ceramic crown. 178 N was applied in different inclinations (0°, 30°, 60°). The results were analyzed by von Mises, maximum principal stress, microstrain and displacement maps including ANOVA statistical test for some situations. Von Mises maps of implant, screws and abutment showed increase of stress concentration as increased loading inclination. Bicortical techniques showed reduction in implant apical area and in the head of fixation screws. Bicortical techniques showed slight increase stress in cortical bone in the maximum principal stress and microstrain maps under 60° loading. No differences in bone tissue regarding surgical techniques were observed. As conclusion, non-axial loads increased stress concentration in all maps. Bicortical techniques showed lower stress for implant and screw; however, there was slightly higher stress on cortical bone only under loads of higher inclinations (60°).     

The mechanical significance of morphological variation in the macaque mandibular symphysis during mastication

Catarrhine symphyseal morphology displays considerable variation. Although this has been related to dentition, phylogeny, sexual dimorphism, and facial orientation, most emphasis has been given to the functional significance of the symphysis to mechanical loading during mastication. The current state of knowledge regarding the mechanical significance of the symphysis is based on a combination of in vivo experimental and comparative studies on Macaca fascicularis. These approaches have provided considerable insight into the stereotypical patterns of loading in the symphyseal region during chewing and hypotheses related to the associated symphyseal morphologies. Finite element analysis (FEA) was used to assess how in silico manipulation translates into the mechanical loading hypotheses previously proposed experimentally. In particular, this study tests the form-function relationship of the symphysis of an adult M. fascicularis mandible during lateral transverse bending and dorsoventral shear of the mandibular symphysis, and a series of modified hypothetical morphologies including absence/presence of tori and variation in the inclination and depth of the symphysis. FEA results of this study support previous findings that stresses associated with lateral transverse bending and dorsoventral shear of the mandibular symphysis can be minimized via an increased labio-lingual thickness in the superior transverse torus, an oblique symphyseal inclination, and/or an increased symphyseal depth. The finding that reduction of strains related to lateral transverse bending and dorsoventral shear can be achieved through a number of different morphologies contributes to our understanding of the influence of morphological and/or developmental constraints, such as dental development, on symphyseal form.     

Finite element analysis of a hemi-pelvis: the effect of inclusion of cartilage layer on acetabular stresses and strain

An appropriate method of application of the hip-joint force and stress analysis of the pelvic bone, in particular the acetabulum, is necessary to investigate the changes in load transfer due to implantation and to calculate the reference stimulus for bone remodelling simulations. The purpose of the study is to develop a realistic 3D finite element (FE) model of the hemi-pelvis and to assess stress and strain distribution during a gait cycle. The FE modelling approach of the pelvic bone was based on CT scan data and image segmentation of cortical and cancellous bone boundaries. Application of hip-joint force through an anatomical femoral head having a cartilage layer was found to be more appropriate than a perfectly spherical head, thereby leading to more accurate stress–strain distribution in the acetabulum. Within the acetabulum, equivalent strains varied between 0.1% and 0.7% strain in the cancellous bone. High compressive (15–30 MPa) and low tensile (0–5 MPa) stresses were generated within the acetabulum. The hip-joint force is predominantly transferred from the acetabulum through the lateral cortex to the sacroiliac joint and the pubic symphysis. The study is useful to understand the load transfer within the acetabulum and for further investigations on acetabular prosthesis.     

Structural parameters determining the strength of the porcine vertebral body affected by tumours

Spinal metastatic disease could lead to catastrophic consequences for the patient. However, the structural parameters that explain the weakening of vertebrae affected by tumours are not fully understood. In this study, we developed a specimen-specific finite element model to predict the strength of the porcine vertebra with simulated tumours and used it to find the structural parameters determining the strength. We validated our model with mechanical testing and then we analysed the compressive strength of intact vertebrae and seven defects with different size and shape. The results showed that the minimum bone mineral mass of the cross section and areal defect fraction were the best predictors of the normalized strength. We also found that areal parameters appeared to be better predictors than the volumetric ones. In conclusion, reduction in bone strength for vertebrae weakened by metastatic tumours is mostly associated with decrease in the mechanical properties of the cross section.