  Purpose: The purpose of this study is to address the lack of uncertainty
quantification in numerical hemolysis models, which are critical for medical
device evaluations. Specifically, we aim to incorporate experimental
variability into these models using the Markov Chain Monte Carlo (MCMC) method
to enhance predictive accuracy and robustness.
  Methods: We applied the MCMC method to an experimental hemolysis dataset to
derive detailed stochastic distributions for the hemolysis Power Law model
parameters $C$, $\alpha$ and $\beta$. These distributions were then propagated
through a reduced order model of the FDA benchmark pump to quantify the
experimental uncertainty in hemolysis measurements with respect to the
predicted pump hemolysis.
  Results: The MCMC analysis revealed multiple local minima in the sum of
squared errors, highlighting the non-uniqueness of traditional Power Law model
fitting. The MCMC results showed a constant optimal $C=3.515x10-5$ and log
normal distributions of $\alpha$ and $\beta$ with means of 0.614 and 1.795,
respectively. The MCMC model closely matched the mean and variance of
experimental data. In comparison, conventional deterministic models are not
able to describe experimental variation.
  Conclusion: Incorporating Uncertainty quantification through MCMC enhances
the robustness and predictive accuracy of hemolysis models. This method allows
for better comparison of simulated hemolysis outcomes with in-vivo experiments
and can integrate additional datasets, potentially setting a new standard in
hemolysis modeling.
