Mathematical modelling of the human cardiovascular system : data, numerical approximation, clinical applications
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Bibliographic Information
Mathematical modelling of the human cardiovascular system : data, numerical approximation, clinical applications
（Cambridge monographs on applied and computational mathematics, 33）
Cambridge University Press, 2019
- : hardback
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Note
Includes bibliographical references (p. [235]-275) and index
Description and Table of Contents
Description
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.
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.
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