- Technische Universität München
- probability density function
- polynomial chaos
- material property
- personalized medicine
- Monte Carlo
- computed tomography
- femur
- femoral neck

To quantify the inuence we developed a probabilistic framework based on polynomial chaos that propagates stochastic input variables through any computational model

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- Computational models based on computed tomography are widely used to predict 3 the mechanical behavior of human femurs
- We demonstrate uncertainty quantication for the personalized analysis of one human proximal femur, with focus on the prediction of principal strain magnitudes and directions
- When Y is approximated with a polynomial chaos expansion of order p = 1, 2, 3, or 4 for instance, the computation of all 5, 15, 35, or 70 coecients with requires only 9, 41, 137, or 385 simulation runs with the model M, respectively
- The deterministic Finite Cell Method has a high predictive accuracy: computed strains matched well the ones measured in the experiment. Convergence in energy norm was achieved for pFCM = 4
- A probabilistic framework was developed to quantify the inuence of material and load26 ing uncertainties on the prediction of principal strains within a personalized analysis of a human proximal femur
- The coecient of variation was ≈ 40% for both 1 and 3 at all locations with suciently large 8 mean values. This relative variability within the principal strain predictions is larger than 9 the one reported in Taddei et al, which computed coecients of variation of less than 10 9% for max 1 and max 3. These dierences may be explained by the uncertainty in the E11 ρ relationship, which is larger in the current study
- The global sensitivity indices can be used 2 to identify input parameters that have a negligible inuence on the stochastic response and 3 can be safely considered as deterministic parameter

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