Numerical investigation of bone adaptation to exercise and fracture in Thoroughbred racehorses

Third metacarpal bone (MC3) fracture has a massive welfare and economic impact on horse racing, representing 45% of all fatal lower limb fractures, which in themselves represent more than 80% of reasons for death or euthanasia on the UK racecourses. Most of these fractures occur due to the accumulation of tissue fatigue as a result of repetitive loading rather than a specific traumatic event. Despite considerable research in the field, including applying various diagnostic methods, it still remains a challenge to accurately predict the fracture risk and prevent this type of injury. The objective of this thesis is to develop computational tools to quantify bone adaptation and resistance to fracture, thereby providing the basis for a viable and robust solution. Recent advances in subject-specific finite element model generation, for example computed tomography imaging and efficient segmentation algorithms, have significantly improved the accuracy of finite element modelling. Numerical analysis techniques are widely used to enhance understanding of fracture in bones and provide better insight into relationships between load transfer and bone morphology. This thesis proposes a finite element based framework allowing for integrated simulation of bone remodelling under specific loading conditions, followed by the evaluation of its fracture resistance. Accurate representation of bone geometry and heterogeneous material properties are obtained from calibrated computed tomography scans.The material mapping between CT-scan data and discretised geometries for the finite element method is carried out by using Moving Least Squares approximation and L2-projection. Thus is then used for numerical investigations and assessment of density gradients at the common site of fracture. Bone is able to adapt its density to changes in external conditions. This property is one of the most important mechanisms for the development of resistance to fracture. Therefore, a finite element approach for simulating adaptive bone changes (also called bone remodelling) is proposed. The implemented method is based on a phenomenological model of the macroscopic behaviour of bone based on the thermodynamics of open systems. Numerical results showed that the proposed technique has the potential to accurately simulate the long-term bone response to specified training conditions and also improve possible treatment options for bone implants. Assessment of the fracture risk was conducted with crack propagation analysis. The potential of two different approaches was investigated: smeared phase-field and discrete configurational mechanics approach. The popular phase-field method represents a crack by a smooth damage variable leading to a phase-field approximation of the variational formulation for brittle fracture. A robust solution scheme was implemented using a monolithic solution scheme with arc-length control. In the configurational mechanics approach, the driving forces, and fracture energy release rate, are expressed in terms of nodal quantities, enabling a fully implicit formulation for modelling the evolving crack front. The approach was extended for the first time to capture the influence of heterogeneous density distribution. The outcomes of this study showed that discrete and smeared crack approximations are capable of predicting crack paths in three-dimensional heterogeneous bodies with comparable results. However, due to the necessity of using significantly finer meshes, phase-field was found to be less numerically efficient. Finally, the current state of the framework's development was assessed using numerical simulations for bone adaptation and subsequent fracture propagation, including analysis of an equine metacarpal bone. Numerical convergence was demonstrated for all examples, and the use of singularity elements proved to further improve the rate of convergence. It was shown that bone adaptation history and bone density distribution influence both fracture resistance and the resulting crack path. The promising results of this study offer a~novel framework to simulate changes in the bone structure in response to exercise and quantify the likelihood of a fracture