This book offers a mathematical update of the state of the art of the research in the field of mathematical and numerical models of the circulatory system. It is structured into different chapters, written by outstanding experts in the field. Many fundamental issues are considered, such as: the mathematical representation of vascular geometries extracted from medical images, modelling blood rheology and the complex multilayer structure of the vascular tissue, and its possible pathologies, the mechanical and chemical interaction between blood and vascular walls, and the different scales coupling local and systemic dynamics. All of these topics introduce challenging mathematical and numerical problems, demanding for advanced analysis and efficient simulation techniques, and pay constant attention to applications of relevant clinical interest. This book is addressed to graduate students and researchers in the field of bioengineering, applied mathematics and medicine, wishing to engage themselves in the fascinating task of modeling the cardiovascular system or, more broadly, physiological flows.
Assumptions in modelling of large artery hemodynamics by D.A. Steinman. - Simplified blood flow model with discontinous vessel properties by E.F. Toro and S. Siviglia. - Blood coagulation: a puzzle for biologists, a maze for mathematicians by A. Fasano et al. - Numerical simulation of electrocardiagrams by J.F. Gerbeau et al. - Mathematical and numerical methods for reaction-diffusion models in electrocardiology by P. Colli-Franzone et al. - Structurally motivated damage models for arterial walls by A.M. Robertson et al. - Arterial growth and remodelling is driven by hemodynamics by L. Cardamone and J.D. Humphrey. - The VPH-Physiome Project: standards, tools and database for multi-scale physiological modelling by P. Hunter et al. - Role of the variational formulation in the dimensionally-heterogeneous modelling of the human cardiovascular system by P. Blanco and R. Feijoo. - Multiscale modelling of hematologic disorders by G.E. Karniadakis et al. - Multiscale computational analysis of degradable polymers by P. Zunino et al. - Applications of variational data assimilitation in computational hemodynamics by A. Veneziani et al. - Quality open source mesh generation for cardiovascular flow simulations by E. Marchandise et al.