Cardiovascular mathematics: Modeling and simulation of the circulatory system

✍ Scribed by Luca Formaggia, Alfio Quarteroni, Allesandro Veneziani

• Publisher: Springer
• Year: 2009
• Tongue: English
• Leaves: 528
• Series: MS&A
• Category: Library

✦ Synopsis

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

Cover Page
......Page 1
Cardiovascular Mathematics......Page 2
Copyright Page
......Page 5
Preface
......Page 6
Contents
......Page 10
List of Contributors......Page 12
1
Physiology and pathology of the cardiovascular
system: a physical perspective......Page 15
2
Basic mathematical models and motivations......Page 60
3
The derivation of the equations for fluids and
structure......Page 89
4
From image data to computational domains......Page 134
5
Geometry and flow......Page 187
6
Rheological models for blood......Page 220
7
Mathematical models of mass transfer in the
vascular walls......Page 251
8
Analysis of coupled models for fluid-structure
interaction of internal flows......Page 287
9
Algorithms for fluid-structure interaction
problems......Page 315
10
Reduced models of the cardiovascular system......Page 355
11
Multiscale models of the vascular system......Page 403
12
Applications and test cases......Page 455
Glossary of medical terms......Page 484
Symbol explanation......Page 488
References......Page 489
Index
......Page 519