Reduced order parameterized viscous optimal flow control problems and applications in coronary artery bypass grafts with patient-specific geometrical reconstruction and data assimilation

Coronary artery bypass graft surgery is an invasive procedure performed to circumvent partial or complete blood flow blockage in coronary artery disease (CAD). In this thesis, we will construct a numerical framework combining parametrized optimal flow control and reduced order methods and will apply to real-life clinical case of triple coronary artery bypass grafts surgery. In this mathematical framework, we will propose patient-specific physiological data assimilation in the optimal flow control part, with the aim to minimize the discrepancies between the patient-specific physiological data and the computational hemodynamics. The optimal flow control paradigm proves to be a handy tool for the purpose and is being commonly used in the scientific community. However, the discrepancies between clinical measurements and computational hemodynamics modeling are usually due to unrealistic quantification of hard-to-quantify outflow conditions and computational inefficiency. In this work, we will utilize the unknown control in the optimal flow control pipeline to automatically quantify the boundary flux, specifically the outflux, required to minimize the data misfit, subject to different parametrized scenarios. Furthermore, the challenge of attaining reliable solutions in a time-efficient manner for such many-query parameter dependent problems will be addressed by reduced order methods.