Conference Agenda

In the early 20th century, imaging technologies—particularly X-rays—revolutionized medicine and, subsequently, clinical practice. Similarly, while the importance of mathematical models in cardiovascular science has been recognized for over three decades, their clinical impact remains limited. This gap stems largely from the intrinsic challenges of integrating mathematical abstractions with the uniqueness of each patient.

Personalized medicine, when framed mathematically, almost always involves solving inverse problems—such as those encountered in data assimilation or (shape) optimization. In this talk, we will explore how both classical and emerging methodologies are driving a new revolution in the clinical management of cardiovascular diseases, enabling more accurate diagnostics and automated, patient-specific therapies and devices.

Computational models that fuse physics-informed models (background knowledge) and real-time data (foreground knowledge) offer a precise and comprehensive understanding of individual patient conditions. Although the mathematical formulations underlying these approaches are well-established, their clinical translation has historically been hindered by prohibitive computational costs. These applications, in fact, demand the rapid solution of constrained optimization problems as well as fluid and structural mechanics simulations—tasks that are infeasible without significant model simplification. We will discuss how model order reduction and scientific machine learning, within the framework of Digital Twins, are poised to overcome these barriers and complete the mathematical revolution in cardiovascular clinics (and beyond).