Modeling and optimization for pediatric cardiovascular surgeries
Keywords: Mechanical Engineering.

Historically, guidelines and practices in cardiovascular surgery have been developed through trial-and-error in human and animal studies. Improvements in these practices concerning overall hemodynamics in the patient require extensive experience, often gained through large clinical trials. The development of realistic patient-specific simulation capabilities offers a safe and inexpensive sand-box for rapidly testing new surgical techniques and medical devices. Recent developments in image acquisition, anatomical modeling, and predictive hemodynamics simulations have given rise to the paradigm of virtual surgical planning for cardiovascular surgeries, building on personalized treatments found in other areas of medicine. Despite these developments, clinical translation of virtual surgical planning tools have been limited by computational cost of patient-specific simulations, intractable run-times for parametric studies, and complexity of modeling cardiovascular surgery. In this thesis, I address the last two limitations, that is, reduction of run-time for design discovery, through a simulation-based optimization framework, and expansion of the current set of cardiovascular surgical modeling tools. We select the Surrogate Management Framework (SMF) is selected as the optimization framework of choice, owing to its' flexibility, ability to handle general constraints, non-smooth convergence theory, and popularity as a black-box optimizer. To reduce the SMF run-time in a high-performance computing environment, two fully concurrent variants of the SMF are developed. The trade-off between total computational expense and time-efficiency for these variants are shown for a set of analytical functions. Substantial savings in time is also obtained on a model simulation-based optimization problem. The concurrent methods also showed more robustness to choice of initialization set. The developed concurrent SMF is then applied to a problem of clinical interest: the design of a systemic-to-pulmonary shunt for the assisted bidirectional Glenn (ABG), a recently proposed alternative for stage-1 single ventricle palliation. With the goal of maximizing pulmonary flow subject to physiological Vena Caval pressure constraint, optimal pulmonary flow-SVC pressure behavior is found to depend strongly on pulmonary vascular resistance. Pulmonary vascular resistance values in neonates, assessed from literature and from a retrospective study, show theoretical viability of optimal ABG designs, as well as raise fundamental questions on existing notions of oxygen delivery in single ventricle neonates. These questions are discussed in detail with the help of lumped parameter models. Prior efforts to model complex vascular interventions in-silico have been limited to either placement of medical devices, such as stents, or to the addition or removal of whole vessels or grafts. A new direction for extending analysis-based virtual surgery modeling is presented through the example of an end-to-end resection surgery for aortic coarctation patients. A mesh generated from an anatomical model is altered directly using computational geometric operations, instead of analytical features of the model. This allows for a more physical parametrization of the surgical method used for coarctation repair. The developed pipeline is demonstrated on an animal model of aortic coarctation. Future directions for extending computational geometric tools for analysis-driven virtual surgery are also motivated