Probabilistic finite element (FE) analysis allows researchers to explore biomechanical continuum behavior in the face of modeling uncertainty and/or in the context of in vivo variability. Since probabilistic model variation results in probabilistic outputs, these results must be assessed statistically. Most current approaches achieve this through reduction, ultimately by focusing on specific field regions. The main purpose of this study was to demonstrate how topological statistics can be used to assess probabilistic FE results in a global field–wide manner. Two models, a 3D femoral strain model and an axisymmetric heel pad indentation model, were adapted from the literature and were subjected to probabilistic simulation. A simple rigid pin placement scheme in the femur model, under simulated in vivo loading variation, revealed that topological statistics conform to mechanical expectation by identifying significant clusters at expected locations in the strain continuum. Probabilistic variation of hyperelastic material parameters in the heel pad model revealed that topological statistics can detect biomechanically relevant changes with greater degrees of sensitivity and spatial detail than discrete analysis of either model parameters or regional data. These results suggest that topological statistics may serve as a useful compliment to existing probabilistic FE approaches. The main advantages of topological statistics are that they produce easy–to–understand statistical results directly inside the modeled continuum and that they afford global field–wide analyses with no need for anatomical assumptions.
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- Topological Statistics for Probabilistic Finite Element Simulations
T. C. Pataky
- Springer Berlin Heidelberg