Optimal design and uncertainty quantification in blood flow simulations for congenital heart disease

Recent work has demonstrated substantial progress in capabilities for patient-specific cardiovascular flow simulations. Recent advances include increasingly complex geometries, physiological flow conditions, and fluid structure interaction. There is now potential for these tools to make a significant clinical impact in optimizing the design of surgeries for cardiovascular disease. This is particularly true in pediatric cardiology because of the wide range of anatomies the occur among patients. Blood flow simulation tools can now be efficiently coupled to shape optimization algorithms for surgery design applications, and these tools should incorporate uncertainty information to allow for inevitable "fudge-factors" in the operating room. In this work, we present a unified and automated framework for derivative-free optimization of cardiovascular surgical geometries, and extend our previous methods to the case of optimization under uncertainty. Uncertainty arises in cardiovascular simulations through a number of simulation inputs, including noise in medical image data, catheter-derived pressures, and material properties. For simulations to predict clinically useful and reliable output information, it is necessary to quantify the effects of input uncertainties on outputs of interest. We systematically account for uncertainties in simulations using adaptive stochastic collocation. This framework for simulation, optimization and robust design is demonstrated on several cardiovascular flow problems including Fontan surgery design, Kawasaki disease, and bypass graft optimization.