Modeling of Physiological Flows [electronic resource] /
Ambrosi, Davide.editor.
Quarteroni, Alfio.editor.
Rozza, Gianluigi.editor.
This book offers a mathematical update of the state of the art of the research in the field of mathematical and numerical models of the circulatory system. It is structured into different chapters, written by outstanding experts in the field. Many fundamental issues are considered, such as: the mathematical representation of vascular geometries extracted from medical images, modelling blood rheology and the complex multilayer structure of the vascular tissue, and its possible pathologies, the mechanical and chemical interaction between blood and vascular walls, and the different scales coupling local and systemic dynamics. All of these topics introduce challenging mathematical and numerical problems, demanding for advanced analysis and efficient simulation techniques, and pay constant attention to applications of relevant clinical interest. This book is addressed to graduate students and researchers in the field of bioengineering, applied mathematics and medicine, wishing to engage themselves in the fascinating task of modeling the cardiovascular system or, more broadly, physiological flows.
Description based upon print version of record.
Title Page; Copyright Page; Preface; Table of Contents; 1 Assumptions in modelling of large artery hemodynamics; 1.1 Overview; 1.2 Rigid vs. compliant walls; 1.3 Compliance and flow boundary conditions; 1.4 Newtonian vs. non-Newtonian rheology; 1.5 Rheology and turbulence; 1.6 Conclusions; References; 2 Simplified blood flow model with discontinuous vessel properties: analysis and exact solutions; 2.1 Introduction; 2.2 Mathematical models; 2.2.1 Review of the basic equations; 2.2.2 Tube law; 2.3 Model for discontinuous properties; 2.3.1 Equations
2.3.2 Eigenstructure and characteristic fields2.3.3 Generalized Riemann invariants; 2.4 The Riemann problem; 2.4.1 Jump across shocks: Rankine-Hugoniot conditions; 2.4.2 Jump conditions across rarefactions; 2.4.3 Jump conditions across the stationary contact; 2.4.4 Solution of Riemann problem; 2.5 Sample solutions; 2.6 Collapse of vessels; 2.7 Conclusions; References; 3 Blood coagulation: a puzzle for biologists, a maze for mathematicians; 3.1 Introduction; 3.2 The modern view of blood coagulation; 3.2.1 The protagonists of hemostasis; Platelets (thrombocytes); The numbered Factor pairs
von Willebrand Factor (vWF)Tissue Factor (TF); Complexes in the blood coagulation process; Inhibitors of blood coagulation; 3.2.2 Primary hemostasis; 3.2.3 The cell-based model for the blood clot formation (secondary hemostasis); Initiation; Amplification; Propagation; Termination; 3.2.4 Fibrinolysis; 3.3 Congenital bleeding disorders and the inadequacy of the 3-pathway Cascade model; 3.3.1 Congenital bleeding disorders; 3.4 Mathematical models and numerical simulations; 3.4.1 Early models of blood coagulation; 3.4.2 Biochemical models; The role of activated platelets
Protein deficiencies and diseasesA model for Disseminated Intravascular Coagulation (DIC); 3.4.3 Models incorporating mechanical and biochemical actions; Fluid-platelets interaction models; Models incorporating the mechanical activation of platelets; A model with a platelets activation front and a clotting front; 3.5 Conclusions; References; 4 Numerical simulation of electrocardiograms; 4.1 Introduction; 4.2 Mathematical modelling; 4.2.1 Isolated heart modelling; 4.2.2 Coupling with the torso: ECG modelling; 4.3 Mathematical analysis; 4.4 ECG simulations; 4.4.1 Numerical approximation
4.4.2 Simulated ECG signals4.4.3 Impact of some modelling assumptions; Cell heterogeneity; Heart-torso uncoupling; Monodomain approximation; Conclusion; 4.5 Fully decoupled time-marching schemes; 4.5.1 Isolated bidomain model; Stability analysis; 4.5.2 Coupled heart-torso system; 4.6 Reduced-order modelling by proper orthogonal decomposition; 4.6.1 POD in a nutshell; 4.6.2 Examples of POD simulations with different sets of parameters; 4.6.3 Examples of POD simulations for several heart beats; 4.7 Conclusions; References
5 Mathematical and numerical methods for reaction-diffusion models in electrocardiology
Includes bibliographical references.
This book offers a mathematical update of the state of the art of the research in the field of mathematical and numerical models of the circulatory system. It is structured into different chapters, written by outstanding experts in the field. Many fundamental issues are considered, such as: the mathematical representation of vascular geometries extracted from medical images, modelling blood rheology and the complex multilayer structure of the vascular tissue, and its possible pathologies, the mechanical and chemical interaction between blood and vascular walls, and the different scales coupling local and systemic dynamics. All of these topics introduce challenging mathematical and numerical problems, demanding for advanced analysis and efficient simulation techniques, and pay constant attention to applications of relevant clinical interest. This book is addressed to graduate students and researchers in the field of bioengineering, applied mathematics and medicine, wishing to engage themselves in the fascinating task of modeling the cardiovascular system or, more broadly, physiological flows.
Computer mathematics.
Human physiology.
Mathematical models.
Bioinformatics .
Computational biology .
Partial differential equations.
Biomedical engineering.
Computational Mathematics and Numerical Analysis.
Human Physiology.
Mathematical Modeling and Industrial Mathematics.
Computer Appl. in Life Sciences.
Partial Differential Equations.
Biomedical Engineering and Bioengineering.