Cardiovascular Mathematics

Cardiovascular diseases have a major impact in Western countries. Mathematical models and numerical simulations can help the understanding of physiological and pathological processes, complementing the information provided to medical doctors by medical imaging and other non-invasive means, and opening the possibility of a better diagnosis and more in-depth surgical planning.This book offers a mathematically sound and up-to-date foundation to the training of researchers, and serves as a useful reference for the development of mathematical models and numerical simulation codes. It is structured into different chapters, written by recognized experts in the field, and however it features a common thread, with consistency of notation and expressions and systematic cross-referencing. Many fundamental issues are faced, 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; the different scales coupling local and systemic dynamics. All of these topics introduce challenging mathematical and numerical problems, demanding for advanced analysis and simulation techniques. 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 how the cardiovascular system works.

Contenu

Physiology and pathology of the cardiovascular system: A physical perspective.- Basic mathematical models and motivations.- The derivation of the equations for fluids and structure.- From image data to computational domains.- Geometry and flow.- Rheological models for blood.- Mathematical models of mass transfer in the vascular walls.- Analysis of coupled models for fluid-structure interaction of internal flows.- Algorithms for fluid-structure interaction problems.- Reduced models of the cardiovascular system.- Multiscale models of the vascular system.- Applications and test cases.