The volume aims at creating a closer connection for the researchers devoted to the mathematical and numerical study of the vascular and cardiac systems in order to provide a scientific exchange of the recent developments on such topics, including modern emerging ones like scientific machine learning and high performance computing. The volume contains contributions from leading experts in computational physiology, numerical analysis, applied mathematics, and scientific computing, with the objective of reviewing recent advances in cardiovascular modeling and exploring new methodological frontiers. The chapters included here reflect the scientific quality and interdisciplinary breadth of the discussions that took place during the meeting. The works collected in this volume highlight the essential role of mathematical and numerical modeling in understanding cardiovascular dynamics, improving computational methods for physiological simulation, and supporting clinically relevant applications. The contributions range across reduced-order modelling, data assimilation, boundary conditions in haemodynamics, cardiac electrophysiology, heterogeneous tissue modelling, high-performance computing simulation, and patient-specific computational methodologies.

Gianluigi Rozza is professor in Numerical Analysis and Scientific computing at International School for Advanced Studies -SISSA, Trieste, Italy. 

Luca F. Pavarino is professor at Department of Mathematics of University of Pavia, Pavia, Italy. 

Simone Scacchi is professor at Dipartimento di Matematica of Università degli Studi di Milano, Milano, Italy.

Christian Vergara is professor at Dipartimento di Chimica, Materiali e Ingegneria Chimica “Giulio Natta”, Politecnico di Milano, Milano, Italy.