Surgical design for the Fontan procedure using computational fluid dynamics and derivative-free optimization

Single ventricle heart defects are among the most serious forms of congenital heart disease. For hypoplastic left heart syndrome (HLHS), a three-staged surgical course, consisting of the Norwood, Glenn, and Fontan surgeries is performed. In the extracardiac Fontan procedure, the inferior vena cava (IVC) is connected to the PAs either via a Gore-Tex tube. Serious clinical challenges remain despite post-operative survival rates upwards of 90\%. A novel Y-shaped graft has been proposed to replace current tube-shaped grafts showing promising preliminary results. To refine the Y-graft design and further study the hemodynamic performance of the Y-graft, a 3D time- dependent finite element flow solver was coupled to a derivative free optimization algorithm using surrogate management framework (SMF) and mesh adaptive direct search (MADS). In the first part of this dissertation, an idealized Y-graft model was parameterized and optimized for energy efficiency. Constrained optimization with a wall shear stress (WSS) constraint was performed in order to study the risk of thrombosis. In the second part of this dissertation, patient specific Glenn models were virtually converted into Fontan models by implanting Y- and tube-shaped grafts for comparison. Particular attention was paid to the hepatic flow distribution (HFD), a clinical parameter that plays an important role in the formation of pulmonary arteriovenous malformations (PAVMs). In a third study, we coupled Lagrangian particle tracking to an optimal design framework to study the effects of boundary conditions and geometry on HFD. Two patient-specific examples showed that optimization-derived Y-grafts effectively improved HFD, compared to initial non -optimized designs. Based on our preliminary simulation results, the Y-graft has been translated into use in a clinical pilot study. Post-operative flow simulations showed good agreement with the lung perfusion data measured in the clinic. The development of thrombosis in one patient's Y-graft was investigated from a hydrodynamic point of view. Results suggested that low WSS area and flow stasis should be taken into account in the surgical design for improved HFD. To our knowledge, this is the first study to apply formal optimization to the Fontan surgical design. Findings in this dissertation may provide guidelines for the future Y-graft surgerie