Uncertainty quantification for soft tissue biomechanics

Uncertainty quantification for soft tissue biomechanics

GENERAL AIM OF THE WORK

– Assessing the effects of uncertainty in material parameters in soft tissue models.
– The sensitivity derivative Monte Carlo method provides one to two orders of magnitude better convergence than the standard Monte Carlo method.
– Complex models with only few lines of Python code (DOLFIN/FEniCS).

SUMMARY

– Stochastic FE analysis.
– Uncertainty quantification (material properties, loading, geometry, etc.).
– Random variables/fields.

image_RF

Two realisations (log-normal distribution)

– Global and local sensitivity analysis.
– Biomechanical modeling, simulation and analysis with random parameters.

fig_brain   ci

METHODS

– Monte Carlo and quasi Monte Carlo methods (Caflisch, 1998).
– Accelerating Monte Carlo estimation with sensitivity derivatives (Hauseux, Hale, and Bordas, 2016).
– Non-intrusive multi-level polynomial chaos expansion method.
– Multi Level Monte Carlo methods (Giles, 2015).

NUMERICAL IMPLEMENTATION

– DOLFIN/FEniCS:
– UFL (Unified Form Language) (Logg, Mardal, and Wells, 2012).
– Automatically deriving tangent linear models with FEniCS !
– Parallel computing (Ipyparallel and mpi4py).
– Python package for uncertainty quantification (Chaospy, SALib).

PUBLICATIONS

Accelerating Monte Carlo estimation with derivatives of high-level finite element models: Hauseux P., Hale J. and Bordas S.
Image to analysis pipeline: single and double balloons kyphoplasty: Baroli D., Hauseux P., Hale J. and Bordas S.
Bayesian statistical inference on the material parameters of a hyperelastic body: Hale J., Farrel P. and Bordas, S.

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