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Mathematics - Applications | Cardiovascular Mathematics

Cardiovascular Mathematics

Modeling and simulation of the circulatory system

Series: MS&A, Vol. 1

Formaggia, Luca, Quarteroni, Alfio, Veneziani, Alessandro (Eds.)

2009, XIII, 522p.

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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.

Content Level » Research

Keywords » Human physiology - Radiologieinformationssystem - biomedical engineering - cardiology - cardiovascular - computer applications in life sciences - diagnosis - partial differential equation - partial differential equations - simulation and modeling - tissue - vascular

Related subjects » Applications - Cardiology & Angiology - Dynamical Systems & Differential Equations - Mathematics

Table of contents 

Chapter 1 introduces the most important terms and concepts of cardiovascular physiopathology ,while Chapter 2 illustrates the basic mathematical models for blood flow and biochemical transfer. The derivation of the equations that governs blood flow is covered in Chapter 3, while Chapter 4 is devoted to the treatment of medical images to obtain geometries suitable for numerical computations. Chapter 5 illustrates the important relationship between geometry and type of flow, focusing on the main characteristics of the different flow regimes encountered in the cardiovascular system. Mathematical models for blood rheology are discussed in Chapter 6. In Chapter 7 mathematical and numerical models of biochemical transport are explained in detail, with practical examples. The mathematical analysis of coupled models for fluid-structure interaction is addressed in Chapter 8, while Chapter 9 focuses on numerical methods for the mechanical coupling between blood flow and the vessel structure. Reduced models play an important role in cardiovascular modelling to enable the simulating of large parts of (or even th whole) vascular system. Their derivation is presented in Chapter 10. The intertwining of such models with more complex three dimensional ones is the foundation of the so called geometric multiscale approach, illustrated in detail in Chapter 11. Finally, Chapter 12 provides a set of well described and reproducible test cases and applications.

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