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  3. Mathematical Modelling of the Human Cardiovascular System
  • Cited by 51
Publisher:
Cambridge University Press
Online publication date:
April 2019
Print publication year:
2019
Online ISBN:
9781108616096
DOI:
https://doi.org/10.1017/9781108616096
Subjects:
Mathematics, Computational Science, Medicine, Mathematical Modeling and Methods, Cardiovascular Medicine
Series:
Cambridge Monographs on Applied and Computational Mathematics (33)
Information

Book 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.

Reviews

'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 Source: Mathematical Association of America

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