© 2009

Cardiovascular Mathematics

Modeling and simulation of the circulatory system

  • Luca Formaggia
  • Alfio Quarteroni
  • Alessandro Veneziani

Part of the MS&A book series (MS&A, volume 1)

Table of contents

  1. Front Matter
    Pages I-XIII
  2. Luca Formaggia, Karl Perktold, Alfio Quarteroni
    Pages 47-75
  3. Miguel A. Fernández, Luca Formaggia, Jean-Frédéric Gerbeau, Alfio Quarteroni
    Pages 77-121
  4. Luca Antiga, Joaquim Peiró, David A. Steinman
    Pages 123-175
  5. Denis Doorly, Spencer Sherwin
    Pages 177-209
  6. Anne M. Robertson, Adélia Sequeira, Robert G. Owens
    Pages 211-241
  7. Karl Perktold, Martin Prosi, Paolo Zunino
    Pages 243-278
  8. Miguel A. Fernández, Jean-Frédéric Gerbeau
    Pages 307-346
  9. Joaquim Peiró, Alessandro Veneziani
    Pages 347-394
  10. Luca Formaggia, Alfio Quarteroni, Alessandro Veneziani
    Pages 395-446
  11. J. Alastruey Arimon, Denis Doorly, Sergio Giordana, Joaquim Peiró, Spencer Sherwin
    Pages 447-475
  12. Back Matter
    Pages 477-522

About this book


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.


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

Editors and affiliations

  • Luca Formaggia
    • 1
  • Alfio Quarteroni
    • 1
    • 2
  • Alessandro Veneziani
    • 1
    • 3
  1. 1.MOX, Department of MathematicsPolitecnico di MilanoMilanItaly
  2. 2.CMCS-IACSÉcole Polytechnique Fédérale de LausanneLausanneSwitzerland
  3. 3.Department of Mathematics and Computer ScienceEmory UniversityAtlantaUSA

Bibliographic information