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Efficient sampling for polynomial chaos-based uncertainty quantification and sensitivity analysis using weighted

Kyle M Burk1,2, Akil Narayan3,4, Joseph A Orr1,2

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This study introduces weighted approximate Fekete points (WAFP) for efficient uncertainty quantification (UQ) and sensitivity analysis (SA) in physiological models. WAFP-based polynomial chaos expansion significantly improves computational efficiency for cardiovascular models.

Keywords:
approximate Fekete pointscardiovascular modelingoxyhemoglobin dissociationpolynomial chaos expansionsensitivity analysisuncertainty quantification

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Area of Science:

  • Computational physiology
  • Mathematical modeling
  • Biomedical engineering

Background:

  • Uncertainty quantification (UQ) and sensitivity analysis (SA) are crucial for patient-specific physiological models.
  • UQ and SA assess model fidelity and parameter influence, but require computational efficiency.
  • Optimization of UQ and SA methods is an active research area.

Purpose of the Study:

  • To investigate a novel, efficient sampling method for least-squares polynomial approximation: weighted approximate Fekete points (WAFP).
  • To demonstrate the utility of WAFP in stochastic analysis of a cardiovascular model.
  • To evaluate the performance of WAFP-based polynomial chaos (PC) expansion for UQ and SA.

Main Methods:

  • Developed and applied weighted approximate Fekete points (WAFP) for polynomial approximation.
  • Utilized WAFP for polynomial chaos (PC) expansion in a cardiovascular model.
  • Performed stochastic analysis to quantify uncertainty and identify influential parameters.

Main Results:

  • WAFP-based PC expansion achieved comparable results to Monte Carlo for uncertainty quantification and sensitivity analysis.
  • WAFP-based PC expansion demonstrated significantly higher computational efficiency.
  • Identified key influential input parameters and their interactions in the oxyhemoglobin saturation model.

Conclusions:

  • WAFP-based PC expansion is a computationally efficient and effective method for UQ and SA in physiological models.
  • This technique is valuable for analyzing oxyhemoglobin dissociation response models.
  • The approach can enhance the fidelity assessment of models for clinical applications.