Cardiovascular Mathematics

by Formaggia, Luca; Quarteroni, Alfio; Veneziani, Alessandro

• ISBN13: 9788847011519
• ISBN10: 8847011515
• Format: Hardcover
• Copyright: 2009-06-03
• Publisher: Springer Nature

Summary

Cardiovascular diseases have a major impact in Western countries. Mathematical models and numerical simulations can aid 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, but 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 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.

Table of Contents

Preface	p. V
Physiology and pathology of the cardiovascular system: a physical perspective	p. 1
Basic mathematical models and motivations	p. 47
The derivation of the equations for fluids and structure	p. 77
From image data to computational domains	p. 123
Geometry and flow	p. 177
Rheological models for blood	p. 211
Mathematical models of mass transfer in the vascular walls	p. 243
Analysis of coupled models for fluid-structure interaction of internal flows	p. 279
Algorithms for fluid-structure interaction problems	p. 307
Reduced models of the cardiovascular system	p. 347
Multiscale models of the vascular system	p. 395
Applications and test cases	p. 447
Glossary of medical terms	p. 477
Symbol explanation	p. 481
References	p. 483
Index	p. 513
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