Cardiovascular Mathematics

1. Front Matter

   Pages I-XIII

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2. Physiology and pathology of the cardiovascular system: A physical perspective

   • Marc Thiriet, Kim H. Parker

   Pages 1-45

3. Basic mathematical models and motivations

   • Luca Formaggia, Karl Perktold, Alfio Quarteroni

   Pages 47-75

4. The derivation of the equations for fluids and structure

   • Miguel A. Fernández, Luca Formaggia, Jean-Frédéric Gerbeau, Alfio Quarteroni

   Pages 77-121

5. From image data to computational domains

   • Luca Antiga, Joaquim Peiró, David A. Steinman

   Pages 123-175

6. Geometry and flow

   • Denis Doorly, Spencer Sherwin

   Pages 177-209

7. Rheological models for blood

   • Anne M. Robertson, Adélia Sequeira, Robert G. Owens

   Pages 211-241

8. Mathematical models of mass transfer in the vascular walls

   • Karl Perktold, Martin Prosi, Paolo Zunino

   Pages 243-278

9. Analysis of coupled models for fluid-structure interaction of internal flows

   • Yvon Maday

   Pages 279-306

10. Algorithms for fluid-structure interaction problems

    • Miguel A. Fernández, Jean-Frédéric Gerbeau

    Pages 307-346

11. Reduced models of the cardiovascular system

    • Joaquim Peiró, Alessandro Veneziani

    Pages 347-394

12. Multiscale models of the vascular system

    • Luca Formaggia, Alfio Quarteroni, Alessandro Veneziani

    Pages 395-446

13. Applications and test cases

    • J. Alastruey Arimon, Denis Doorly, Sergio Giordana, Joaquim Peiró, Spencer Sherwin

    Pages 447-475

14. Back Matter

    Pages 477-522

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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.

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

• MOX, Department of Mathematics, Politecnico di Milano, Milan, Italy

  Luca Formaggia, Alfio Quarteroni, Alessandro Veneziani

• CMCS-IACS, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

  Alfio Quarteroni

• Department of Mathematics and Computer Science, Emory University, Atlanta, USA

  Alessandro Veneziani

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