Preface; Contents; Acronyms; 1 Hemorheology and Hemodynamics; 1.1 Historical Remarks; 1.2 The Human Circulatory System; 1.2.1 Systemic Circulation; 1.2.2 Mathematical Models for Blood Flow Dynamics; 1.2.2.1 Modeling the Local Flow Dynamics in Compliant Vessels; 1.2.2.2 A 3D FSI Model; 1.2.2.3 Modeling the Global Flow Dynamics with Reduced Models; 1.2.2.4 1D Wave Propagation Models; 1.2.2.5 0D Lumped Parameter Models; 1.2.2.6 The Geometrical Multiscale Approach: Coupling 3D FSI with Reduced Models; 1.3 Blood Rheology

1.3.1 Blood Components1.3.2 Non-Newtonian Properties of Blood; 1.3.2.1 Viscosity of Blood; 1.3.2.2 Viscoelasticity and Thixotropy of Blood; 1.3.2.3 Yield Stress of Blood; 1.3.3 Constitutive Models for Blood; 1.3.3.1 Viscosity Models; 1.3.3.2 Viscoelastic Constitutive Models; 1.3.3.3 Yield Stress Models; 1.4 Hemodynamics and Microcirculation; 1.4.1 A New Approach to Modeling Microcirculation; 1.4.2 The Microcirculation Model; 1.5 Vasomotion; 1.5.1 The Elusive Phenomenon of Vessel Oscillations; 1.5.2 Arterioles; 1.5.3 Venules

1.6 Atherosclerosis1.6.1 The Pathogenesis of Atherosclerosis; 1.6.2 Mathematical Modeling; References; 2 Blood Coagulation; 2.1 Introduction; 2.2 Historical Remarks; 2.3 Cells and Proteins Intervening in the Formation and Dissolution of Clots; 2.3.1 Blood Cells and Coagulation; 2.3.2 Platelets Regulators; 2.3.3 The Coagulation Factors; 2.3.4 Fibrinolysis Factors; 2.3.5 Factors Inhibitors; 2.4 The Cell-Based Model for Secondary Hemostasis; 2.4.1 Secondary Hemostasis; 2.4.2 Fibrinolysis; 2.5 Bleeding Disorders

2.6 The 3-Pathway Cascade Model2.7 Anticoagulant Drugs, Thrombolytic Drugs,Hemophilia Therapies; 2.7.1 Anticoagulant Drugs; 2.7.2 Thrombolytic Drugs; 2.7.3 Hemophilia Therapies; 2.8 Mathematical Models for Blood Coagulation; 2.8.1 ODE's Models; 2.8.2 PDE's Models; References; 3 Blood Filtration in Kidneys; 3.1 Historical Remarks; 3.2 General Structure of Kidneys; 3.3 Calculating Glomerular Filtration Rate; 3.4 The Steady Flow and the Glomerular Filtration Rate; References; 4 Extracorporeal Blood Ultrafiltration

4.1 Historical Remarks4.2 The Hollow Fibers Dialyzer; 4.2.1 General Description of the Apparatus; 4.2.2 A Mathematical Model Based on the UpscalingTechnique; 4.2.3 Modeling the Device; 4.2.4 Modeling the Body Reaction; 4.2.5 Modeling the Evolution of Masses and Volumes; 4.3 Numerical Simulations; 4.4 Going Further; References; 5 Extracorporeal Blood Oxygenation; 5.1 About Extracorporeal Blood Treatments; 5.2 Gases in Blood; 5.3 Historical Remarks; 5.4 Mathematical Models; 5.4.1 Heart-Lung Machine; 5.4.2 ECMO; 5.4.3 IMO