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

$72.00 USD

Part of Cambridge Monographs on Applied and Computational Mathematics

  • Date Published: April 2019
  • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • format: Adobe eBook Reader
  • isbn: 9781108572293

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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
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    Product details

    • Date Published: April 2019
    • format: Adobe eBook Reader
    • isbn: 9781108572293
    • contains: 46 b/w illus.
    • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • Table of Contents

    Introduction
    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
    References
    Index.

  • 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.

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