Predicting the structural integrity of bone defects repaired using bone graft materials

Bone defects create stress concentrations which can cause fracture under impact or cyclic loading. Defects are often repaired by filling them with a bone graft material; this will reduce the stress concentration, but not completely, because these materials have lower stiffness than bone. The fracture risk decreases over time as the graft material is replaced by living bone. Many new bone graft materials are being developed, using tissue engineering and other techniques, but currently there is no rational way to compare these materials and predict their effectiveness in repairing a given defect. This paper describes, for the first time, a theoretical model which can be used to predict failure by brittle fracture or fatigue, initiating at the defect. Preliminary results are presented, concentrating on the prediction of stress fracture during the crucial post-operative period. It is shown that the likelihood of fracture is strongly influenced by the shape of the defect as well as its size, and also by the level of post-operative exercise. The most important finding is that bone graft materials can be successful in preventing fracture even when their mechanical properties are greatly inferior to those of bone. Future uses of this technique include pre-clinical assessment of bone replacement materials and pre-operative planning in orthopaedic surgery.     

3D strain map of axially loaded mouse tibia: a numerical analysis validated by experimental measurements

A combined experimental/numerical study was performed to calculate the 3D octahedral shear strain map in a mouse tibia loaded axially. This study is motivated by the fact that the bone remodelling analysis, in this in vivo mouse model should be performed at the zone of highest mechanical stimulus to maximise the measured effects. Accordingly, it is proposed that quantification of bone remodelling should be performed at the tibial crest and at the distal diaphysis. The numerical model could also be used to furnish a more subtle analysis as a precise correlation between local strain and local biological response can be obtained with the experimentally validated numerical model.     

A Comparative Analysis of Different Treatments for Distal Femur Fractures using the Finite Element Method

The main objective of this work is the evaluation, by means of the finite element method (FEM) of the mechanical stability and long-term microstructural modifications in bone induced to three different kinds of fractures of the distal femur by three types of implants: the Condyle Plate, the less invasive stabilization system plate (LISS) and the distal femur nail (DFN). The displacement and the stress distributions both in bone and implants and the internal bone remodelling process after fracture and fixation are obtained and analysed by computational simulation. The main conclusions of this work are that distal femoral fractures can be treated correctly with the Condyle Plate, the LISS plate and the DFN. The stresses both in LISS and DFN implant are high especially around the screws. When respect to remodelling, the LISS produces an important resorption in the fractured region, while the other two implants do not strongly modify bone tissue microstructure.     

Modelling the early phases of bone regeneration around an endosseous oral implant

The objective of this study was to see whether a mathematical model of fracture healing was able to mimic bone formation around an unloaded screw-shaped titanium implant as it is well-believed that both processes exhibit many biological similarities. This model describes the spatio-temporal evolution of cellular activities, ranging from mesenchymal stem cell migration, proliferation, differentiation to bone formation, which are initiated and regulated by the growth factors present at the peri-implant site. For the simulations, a finite volume code was used and adequate initial and boundary conditions were applied. Two sets of analyses have been performed, in which either initial and boundary condition or model parameter values were changed with respect to the fracture healing model parameter values. For a number of combinations, the spatio-temporal evolution of bone density was well-predicted. However reducing cell proliferation rate and increasing osteoblast differentiation and osteogenic growth factor synthesis rates, the simulation results were in agreement with the experimental data.     

Finite element analysis of peri-implant bone volume affected by stresses around Morse taper implants: effects of implant positioning to the bone crest

Abstract

Objectives: The purpose of the present study was to evaluate the distribution and magnitude of stresses through the bone tissue surrounding Morse taper dental implants at different positioning relative to the bone crest. Materials and Methods: A mandibular bone model was obtained from a computed tomography scan. A three-dimensional (3D) model of Morse taper implant-abutment systems placed at the bone crest (equicrestal) and 2?mm bellow the bone crest (subcrestal) were assessed by finite element analysis (FEA). FEA was carried out on axial and oblique (45°) loading at 150 N relatively to the central axis of the implant. The von Mises stresses were analysed considering magnitude and volume of affected peri-implant bone. Results: On vertical loading, maximum von Mises stresses were recorded at 6-7?MPa for trabecular bone while values ranging from 73 up to 118?MPa were recorded for cortical bone. On oblique loading at the equiquestral or subcrestal positioning, the maximum von Mises stresses ranged from 15 to 21?MPa for trabecular bone while values at 150?MPa were recorded for the cortical bone. On vertical loading, >99.9vol.% cortical bone volume was subjected to a maximum of 2?MPa while von Mises stress values at 15?MPa were recorded for trabecular bone. On oblique loading, >99.9vol.% trabecular bone volume was subjected to maximum stress values at 5?MPa, while von Mises stress values at 35?MPa were recorded for >99.4vol.% cortical bone. Conclusions: Bone volume-based stress analysis revealed that most of the bone volume (>99% by vol) was subjected to significantly lower stress values around Morse taper implants placed at equicrestal or subcrestal positioning. Such analysis is commentary to the ordinary biomechanical assessment of dental implants concerning the stress distribution through peri-implant sites.     

Prediction of shape and internal structure of the proximal femur using a modified level set method for structural topology optimisation

A computational framework was developed to simulate the bone remodelling process as a structural topology optimisation problem. The mathematical formulation of the Level Set technique was extended and then implemented into a coronal plane model of the proximal femur to simulate the remodelling of internal structure and external geometry of bone into the optimal state. Results indicated that the proposed approach could reasonably mimic the major geometrical and material features of the natural bone. Simulation of the internal bone remodelling on the typical gross shape of the proximal femur, resulted in a density distribution pattern with good consistency with that of the natural bone. When both external and internal bone remodelling were simulated simultaneously, the initial rectangular design domain with a regularly distributed mass reduced gradually to an optimal state with external shape and internal structure similar to those of the natural proximal femur.     

The use of preserved tissue in finite element modelling of fresh ovine vertebral behaviour

The aim of this study was to investigate whether the predicted finite element (FE) stiffness of vertebral bone is altered when using images of preserved rather than fresh tissue to generate specimen-specific FE models. Fresh ovine vertebrae were used to represent embalmed (n = 3) and macerated dry-bone (n = 3) specimens and treated accordingly. Specimens were scanned pre- and post-treatment using micro-computed tomography. A constant threshold level derived from these images was used to calculate the respective bone volume fraction (BV/TV) from which the conversion factor validated for fresh tissue was used to determine material properties that were assigned to corresponding FE models. Results showed a definite change in the BV/TV between the fresh and the preserved bone. However, the changes in the predicted FE stiffness were not generally greater than the variations expected from assignment of loading and boundary conditions. In conclusion, images of preserved tissue can be used to generate FE models that are representative of fresh tissue with a tolerable level of error.     

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.