  Performing uncertainty quantification (UQ) and sensitivity analysis (SA) is
vital when developing a patient-specific physiological model because it can
quantify model output uncertainty and estimate the effect of each of the
model's input parameters on the mathematical model. By providing this
information, UQ and SA act as diagnostic tools to evaluate model fidelity and
compare model characteristics with expert knowledge and real world observation.
Computational efficiency is an important part of UQ and SA methods and thus
optimization is an active area of research. In this work, we investigate a new
efficient sampling method for least-squares polynomial approximation, weighted
approximate Fekete points (WAFP). We analyze the performance of this method by
demonstrating its utility in stochastic analysis of a cardiovascular model that
estimates changes in oxyhemoglobin saturation response. Polynomial chaos (PC)
expansion using WAFP produced results similar to the more standard Monte Carlo
in quantifying uncertainty and identifying the most influential model inputs
(including input interactions) when modeling oxyhemoglobin saturation, PC
expansion using WAFP was far more efficient. These findings show the usefulness
of using WAFP based PC expansion to quantify uncertainty and analyze
sensitivity of a oxyhemoglobin dissociation response model. Applying these
techniques could help analyze the fidelity of other relevant models in
preparation for clinical application.
