Mathematical Modelling of the Human Cardiovascular System
Data, Numerical Approximation, Clinical Applications
Published on 9. May 2019
Book
Hardback
290 pages
978-1-108-48039-0 (ISBN)
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 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.
Reviews / Votes
'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 AmericaMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Product notice
sewn/stitched
Cloth over boards
Illustrations
Worked examples or Exercises; 4 Halftones, black and white; 39 Line drawings, unspecified; 3 Line drawings, black and white
Dimensions
Height: 254 mm
Width: 213 mm
Thickness: 18 mm
Weight
771 gr
ISBN-13
978-1-108-48039-0 (9781108480390)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Alfio Quarteroni
Mathematical Modelling of the Human Cardiovascular System
Data, Numerical Approximation, Clinical Applications
E-Book
05/2019
Cambridge University Press
€68.99
Available for download
Alfio Quarteroni | Luca Dede' | Andrea Manzoni
Mathematical Modelling of the Human Cardiovascular System
Data, Numerical Approximation, Clinical Applications
E-Book
04/2019
Cambridge University Press
€76.49
Available for download
Persons
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.
Content
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.