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Towards efficient uncertainty quantification in complex and large-scale biomechanical problems based on a Bayesian

Jonas Biehler1, Michael W Gee, Wolfgang A Wall

  • 1Institute for Computational Mechanics, Technische Universität München, Boltzmannstr. 15, 85747, Garching b. München, Germany.

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Summary

This study introduces a new computational framework for uncertainty quantification in patient-specific biomechanical models. It accurately assesses variations in parameters, making complex simulations practical and revealing errors from using average values.

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Area of Science:

  • Computational Biomechanics
  • Uncertainty Quantification
  • Medical Simulation

Background:

  • Patient-specific biomechanical models are crucial for simulating cardiovascular diseases.
  • Obtaining accurate patient-specific parameters (e.g., constitutive properties) is challenging.
  • Traditional uncertainty quantification methods struggle with complex, large-scale biomechanical models due to computational costs and limitations.

Purpose of the Study:

  • To develop and present an uncertainty quantification (UQ) framework for patient-specific nonlinear biomechanical models.
  • To enable accurate UQ by effectively incorporating information from low-fidelity models.
  • To analyze the impact of parameter uncertainty on biomechanical quantities relevant to abdominal aortic aneurysm (AAA) rupture.

Main Methods:

  • Developed a UQ framework utilizing multi-fidelity sampling and Bayesian formulations.
  • Incorporated information from approximate, low-fidelity models to improve accuracy and reduce computational cost.
  • Modeled a constitutive parameter of the arterial wall as a 3D, non-Gaussian random field to capture inter- and intra-patient variations.
  • Validated the framework using patient-specific finite element models of abdominal aortic aneurysms (AAAs).

Main Results:

  • The proposed framework accurately computes response statistics of high-fidelity models, even with poor low-fidelity approximations.
  • Demonstrated significant reduction in computational costs, making UQ for complex patient-specific models feasible.
  • Quantified the impact of constitutive parameter uncertainty on AAA rupture-related metrics (von Mises stress, strain, strain energy).
  • Showcased the potential errors introduced by using population-averaged parameters in patient-specific simulations.

Conclusions:

  • The developed multi-fidelity UQ framework offers a computationally efficient and accurate approach for complex biomechanical simulations.
  • This method provides crucial insights into the variability of mechanical responses in patient-specific AAA models.
  • Highlights the importance of considering parameter uncertainties rather than relying on population-averaged values for accurate patient-specific predictions.