A Physics-Informed Machine Learning for Topological Optimisation of Patient-Specific Medical Plates
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Accurate structural modelling of biomedical systems remains challenging due to the complexity of anatomical geometries and physiologically realistic loading conditions [1]. Conventional finite element analysis (FEA) often requires simplifying assumptions to maintain numerical tractability, particularly when modelling nonlinear loading paths and heterogeneous material behaviour. Recent developments in physics-informed machine learning provide an alternative computational approach, leveraging energy conservation principles to solve governing equations in a mesh-free, differentiable framework that overcomes these limitations [2]. This work presents an energy-driven topology optimisation framework composed of two coupled neural networks for the design of patient-specific orthopaedic plates. The Displacement Enforcing Mechanics Network approximates the displacement field by minimising the residual between the internal energy and the external work, while enforcing Dirichlet and Neumann boundary conditions through penalty-based regularisation. In parallel, the Spatial Prediction and Interpolation Network predicts material density distributions by minimising structural compliance, satisfying a global volume constraint, and enforcing connectivity via geometric regularisation. The networks operate in a closed loop configuration, allowing mechanical response prediction and topology evolution to be jointly optimised. It has been seen that the neural network can develop mechanically viable designs for given patient parameters. The framework is demonstrated through the optimisation of a femoral plate, a clinically relevant case where full anatomical loading is rarely incorporated due to its computational complexity. Prior topology optimisation studies typically impose symmetry or reduce boundary conditions to stabilise the numerical problem [3]. In contrast, the proposed method accommodates asymmetric, physiologically realistic loading without requiring such simplifications, enabling the recreation of in vivo biomechanics. These findings highlight the potential of physics‑informed optimisation as a viable computational tool for the design of complex biomedical devices that match patients’ anatomical needs.
