A non-intrusive surrogate model for hip implant positioning
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In clinical practice, physicians mainly rely on medical images and empirical knowledge for the planning of hip implant surgeries. To assist the physicians in their therapeutical decisions, sophisticated computational models are available to predict the short- and long-term stability of implants, considering patients' individual conditions. Long-term stability can be assessed by simulating the bone remodelling process, the adaption of the bone to altered loading conditions, which is reflected in changes to the bone mass density (BMD). However, these so-called high-fidelity models require a large computational effort due to their complexity and are not yet feasible for application in clinical practice. Further, these models need to be evaluated several times to determine an optimal implant position. In this work, a surrogate model with a reduced complexity is presented to enable fast evaluations of BMD changes in the femur after implantation. For the setup, isotopological Finite Element (FE) meshes with varying implant positions are generated using Laplace’s equation. This approach ensures that the mesh connectivity is maintained for all meshes, which eliminates the need for remeshing, and facilitates the application of model order reduction techniques. Subsequently, bone remodelling FE simulations are performed for the different implant positions and the resulting BMD distributions are stored. For the reduced model, the Proper Orthogonal Decomposition (POD) is combined with radial basis functions (RBF) interpolation [1, 2]. Thereby, the POD modes reflect the spatial variation in the BMD distribution and the RBFs incorporate the parameter dependency, in this case the change in implant position. The presented approach reduces the computation time for a new set of parameters from hours to milliseconds while maintaining a certain level of accuracy, which paves the way for application in the daily clinical practice. REFERENCES [1] Dang V. T., Labergere C. and Lafon P., “POD surrogate models using adaptive sampling space parameters for springback optimization in sheet metal forming”, Procedia Engineering, 207, 1588-1593 (2017) [2] Dutta S., Farthing M. W., Perracchione E., Savant G. and Putti M., “A greedy non-intrusive reduced order model for shallow water equations”, Journal of Computational Physics, 439, 110378 (2021)