A Computational Technique for Uncertainty Quantification and Robust Design in Cardiovascular Systems

Numerical simulations of blood flow in the human cardiovascular system are usually performed using custom Finite element methods and specialized boundary conditions. These simulations are performed to (a) understand the physics of blood flow in the human cardiovascular system and (b) a priori testing of proposed treatments/interventions whether surgical or endovascular. To perform these simulations, we require prior knowledge of parameters such as cardiovascular geometry, boundary conditions (inflow/outflow/pressure), etc. In the past, researchers have assumed exact values for these parameters. However, in reality, each of these parameters is uncertain. For example, inflow conditions into the model are dictated by the heart rate and cardiac output of the patient. Even during rest, there are variations in cardiac output and hence the corresponding blood inflow velocities need to be modeled as a random variable. Additionally, the cardiovascular geometry is built based on MRI-images. These are subject to uncertainties due to noise in the data and variability between users during model construction. We develop a computational toolbox that can account for uncertainties in such parameters in hemodynamic simulations. The uncertainties examined in this work include i) variation and accuracy of image-based model geometry ii) variability in inflow condition of the patient and iii) variability in the implementation of the final surgical design. The last source of uncertainty stems from the fact that optimally designed surgical parameters may not be exactly implemented in the operating room. We show numerical examples of (a) blood flow in stenotic vessels (b) effect of uncertainty in carotid sinus size on blood flow and (iii) develop a stochastic optimization technique to compute optimal parameters of an idealized Y-graft model for the Fontan surgery accounting for sources of uncertainties listed above.