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

Addresses the mathematical and numerical modelling of the human cardiovascular system, from patient data to clinical applications.

Alfio Quarteroni (Author), Luca Dede' (Author), Andrea Manzoni (Author), Christian Vergara (Author)

9781108480390, Cambridge University Press

Hardback, published 9 May 2019

290 pages, 46 b/w illus.
25.5 x 18.1 x 1.7 cm, 0.78 kg

'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

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 quanti?cation and the development of reduced-order models that are important when solving problems with high complexity, which would otherwise be out of reach.

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.

Subject Areas: Mathematical theory of computation [UYA], Biology, life sciences [PS], Mathematical modelling [PBWH], Biomedical engineering [MQW], Cardiovascular medicine [MJD]