CEE Seminar - Data Assimilation, Optimization and Reduced Order Modeling in Cardiovascular Mathematics

Reduced-order models (ROM) provide practical solutions to problems that were once considered too computationally expensive. In Cardiovascular Mathematics, surgical optimization takes Personalized Medicine to an unprecedented level. Meanwhile, Data Assimilation (DA) may play a pivotal role in bridging theory with clinical practice. DA involves a set of techniques that integrate mathematical models with measurements to improve our understanding of specific problems. In clinical settings, efficient methods that combine physics-informed models with available data-i.e., background and foreground knowledge-can offer a deeper and more precise understanding of a patient's condition. Although the mathematical formulations of these problems are well-established, high computational costs have historically prevented their translation into clinical practice. In fact, these problems require the timely solution of constrained optimization, fluid and/or structural mechanics; this is not feasible without methods that reduce computational costs. ROM presents a viable workaround, with the potential for significant impact in medicine. In this talk, we will explore applications in pediatric surgery (specifically Total Cavopulmonary Connection), as well as coronary diseases (including stent optimization and wall shear stress data assimilation). We will also discuss the use of Proper Orthogonal Decomposition and the potential role of Physics-Informed Neural Networks in these contexts.