Mathematical modelling of the human cardiovascular system : data, numerical approximation, clinical applications

Contents
Introduction
PART ONE ARTERIAL CIRCULATION
1 Basic facts about quantitative physiology
2 An insight into vascular data
	2.1 Geometric vascular data
	2.2 Boundary vascular data
	2.3 Biological vascular data
3 Modelling blood flow
	3.1 The fluid problem
	3.2 Mechanical wall models
	3.3 The coupled fluid–structure interaction problem
	3.4 The boundary issue
	3.5 Geometric reduced models and the geometric multiscale approach
	3.6 Numerical strategies
PART TWO HEART FUNCTION
4 Basic facts on quantitative cardiac physiology
	4.1 Basic anatomy
	4.2 The cardiac cycle
	4.3 Electrical propagation
	4.4 Mechanisms of contraction and cardiac blood fluid dynamics
	4.5 A brief summary of heart diseases
5 An insight into cardiac data
	5.1 Cardiac geometric data
	5.2 Cardiac boundary data
	5.3 Cardiac biological data
6 Modelling the heart
	6.1 Cardiac electrical activity
	6.2 Cardiac mechanics and electromechanical coupling
	6.3 The ventricular fluid dynamics
	6.4 Modelling the valves
	6.5 Modelling the entire heart function
PART THREE OPTIMIZATION, CONTROL, UNCERTAINTY AND COMPLEXITY REDUCTION
7 Beyond direct simulation
8 Control and optimization
	8.1 Optimality conditions
	8.2 Numerical approximation
	8.3 Applications to cardiovascular modelling
9 Parameter estimation from clinical data
	9.1 Variational approach: PDE-constrained optimization
	9.2 Sequential approach: Kalman filter and extensions
	9.3 Applications to cardiovascular modelling
10 Accounting for uncertainty
	10.1 Forward uncertainty quantification
	10.2 Inverse uncertainty quantification
	10.3 Applications to cardiovascular modelling
11 Reduced-order modelling
References
Index