Optimization and Uncertainty
Overview
In our lab, we develop methods based on statistics to determine optimal medical device designs and estimate the effects of uncertain parameters on simulation results. The property that makes these problems challenging is the size of the space where the optimization takes place, and the fact that evaluating the cardiovascular model for each parameter choice is computationally expensive.
Derivative-free Optimization
We employ derivative-free optimization methods for systematic design of surgeries and devices. These methods, called the Surrogate Management Framework (SMF) are based on pattern search theory and incorporate surrogate functions (e.g. Kriging) for improved efficiency. We have demonstrated SMF methods on design of surgical methods for the Fontan Y-graft design, the Assisted Bidirectional Glenn, and other cardiovascular test problems. We have also used SMF methods to accelerate parameter estimation for vascular growth and remodeling.
Funding: NSF CAREER
Uncertainty Quantification
We have pioneered the development of uncertainty quantification (UQ) methods for cardiovascular simulation. We have used stochastic collocation and multi-resolution chaos approaches for propagation of uncertainties from model input paramters to output quantities of interest. UQ methods allow for placement of confidence intervals on simulation predictions.
Funding: NSF CDSE, NIH NIBIB
Parameter Estimation
Parameter estimation is necessary for automated tuning of model parameters to match clinical and physiologic data. We are developing a suite of automated parameter estimation tools for the assimilation of clinical data into multiscale models using a Bayesian approach. These methods are currently being applied to coronary artery and single ventricle models in ongoing projects.