Skip to content
Register Sign in Wishlist

Mathematical Modelling of the Human Cardiovascular System
Data, Numerical Approximation, Clinical Applications

Part of Cambridge Monographs on Applied and Computational Mathematics

  • Date Published: July 2019
  • availability: In stock
  • format: Hardback
  • isbn: 9781108480390


Add to wishlist

Other available formats:

Looking for an inspection copy?

This title is not currently available for inspection. However, if you are interested in the title for your course we can consider offering an inspection copy. To register your interest please contact providing details of the course you are teaching.

Product filter button
About the Authors
  • Mathematical and numerical modelling of the human cardiovascular system has attracted remarkable research interest due to its intrinsic mathematical difficulty and the increasing impact of cardiovascular diseases worldwide. This book addresses the two principal components of the cardiovascular system: arterial circulation and heart function. It systematically describes all aspects of the problem, stating the basic physical principles, analysing the associated mathematical models that comprise PDE and ODE systems, reviewing sound and efficient numerical methods for their approximation, and simulating both benchmark problems and clinically inspired problems. Mathematical modelling itself imposes tremendous challenges, due to the amazing complexity of the cardiovascular system and the need for computational methods that are stable, reliable and efficient. The final part is devoted to control and inverse problems, including parameter estimation, uncertainty quantification and the development of reduced-order models that are important when solving problems with high complexity, which would otherwise be out of reach.

    • A solid foundation for applied mathematicians, bioengineers and computational scientists interested in modelling the cardiovascular system
    • Describes the most recent and efficient numerical methods for mathematical models
    • Examples of possible applications illustrate the relevance of the methods
    Read more

    Reviews & endorsements

    'Overall, there is a nice interplay between the basic biology and physiology needed to understand the model, the pros and cons of different techniques of obtaining clinical data, and the implementation of the numerical methods. Each section includes beautifully colored schematic representations of the cardiovascular system …' Sarah Patterson, Mathematical Association of America

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity


    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?


    Product details

    • Date Published: July 2019
    • format: Hardback
    • isbn: 9781108480390
    • length: 290 pages
    • dimensions: 255 x 181 x 17 mm
    • weight: 0.78kg
    • contains: 46 b/w illus.
    • availability: In stock
  • Table of Contents

    Part I. Arterial Circulation:
    1. Basic facts about quantitative physiology
    2. An insight into vascular data
    3. Modelling blood flow
    Part II. Heart Function:
    4. Basic facts on quantitative cardiac physiology
    5. An insight into cardiac data
    6. Modelling the heart
    Part III. Optimization, Control, Uncertainty and Complexity Reduction:
    7. Beyond direct simulation
    8. Control and optimization
    9. Parameter estimation from clinical data
    10. Accounting for uncertainty
    11. Reduced-order modelling

  • Authors

    Alfio Quarteroni, Politecnico di Milano
    Alfio Quarteroni is Professor of Numerical Analysis at Politecnico di Milano. He has authored twenty-five books and over 350 papers in international scientific journals and conference proceedings. He received many awards and honours in recognition of his work, and is a member of the Italian Academy of Science, the European Academy of Science and the Academia Europaea. His research interests include mathematical modelling and its applications.

    Luca Dede', Politecnico di Milano
    Luca Dedè is Assistant Professor in Numerical Analysis at Politecnico di Milano. His research involves the development of efficient and accurate numerical methods for the approximation of partial differential equations, multiphysics and multiscale problems, and computational fluid dynamics.

    Andrea Manzoni, Politecnico di Milano
    Andrea Manzoni is Assistant Professor in Numerical Analysis at Politecnico di Milano. His 2012 Ph.D. thesis won one of two ECCOMAS Awards for the best Ph.D. theses in Europe about Computational Methods in Applied Sciences and Engineering. His research interests include the development of reduced order modelling techniques for partial differential equations, uncertainty quantification, PDE-constrained optimization, and computational and statistical inverse problems.

    Christian Vergara, Politecnico di Milano
    Christian Vergara is Associate Professor in Numerical Analysis at Politecnico di Milano. He works on the development of numerical methods for the cardiovascular system, in particular for the fluid-structure interaction problems and the electro-physiology of the ventricles. He has collaborated with hospitals and clinicians to use numerical and computational methods to address several problems of clinical interest.

Sign In

Please sign in to access your account


Not already registered? Create an account now. ×

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner Please see the permission section of the catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.


Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

Please fill in the required fields in your feedback submission.