The Physics of Pulsatile Flow

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Februar 2000



The goal of this book is to provide in a single source, and at the level of textbook, a complete treatment of the fluid dynamics of steady and pulsatile flow in tubes with the required mathematics and emphasis on basic mechanics. The style and level of the book will be accessible to students and researchers in biophysics, biology, medicine, bioengineering and applied mathematics, in theoretical or clinical work on the cardiovascular system, as well as in the design of new instrumentation, medical imaging systems and artificial organs. The book includes problems and exercises, with chapters on basic equations, flow in rigid and elastic tubes, vascular trees, and wave reflections.


1 Preliminary Concepts.- 1.1 Flow in a Tube.- 1.2 What Is a Fluid?.- 1.3 Microscopic and Macroscopic Scales.- 1.4 What Is Flow?.- 1.5 Eulerian and Lagrangian Velocities.- 1.6 Acceleration in a Flow Field.- 1.7 Is Blood a Newtonian Fluid?.- 1.8 No-Slip Boundary Condition.- 1.9 Laminar and Turbulent Flow.- 1.10 Problems.- 1.11 References and Further Reading.- 2 Equations of Fluid Flow.- 2.1 Introduction.- 2.2 Equations at a Point.- 2.3 Equations and Unknowns.- 2.4 Conservation of Mass: Equation of Continuity.- 2.5 Momentum Equations.- 2.6 Forces on a Fluid Element.- 2.7 Constitutive Equations.- 2.8 Navier-Stokes Equations.- 2.9 Problems.- 2.10 References and Further Reading.- 3 Steady Flow in Tubes.- 3.1 Introduction.- 3.2 Simplified Equations.- 3.3 Steady-State Solution: Poiseuille Flow.- 3.4 Properties of Poiseuille Flow.- 3.5 Balance of Energy Expenditure.- 3.6 Cube Law.- 3.7 Arterial Bifurcation.- 3.8 Arterial Tree.- 3.9 Entry Length.- 3.10 Noncircular Cross Section.- 3.11 Problems.- 3.12 References and Further Reading.- 4 Pulsatile Flow in a Rigid Tube.- 4.1 Introduction.- 4.2 Oscillatory Flow Equations.- 4.3 Fourier Analysis.- 4.4 Bessel Equation.- 4.5 Solution of Bessel Equation.- 4.6 Oscillatory Velocity Profiles.- 4.7 Oscillatory Flow Rate.- 4.8 Oscillatory Shear Stress.- 4.9 Pumping Power.- 4.10 Oscillatory Flow at Low Frequency.- 4.11 Oscillatory Flow at High Frequency.- 4.12 Tubes of Elliptic Cross Sections.- 4.13 Problems.- 4.14 References and Further Reading.- 5 Pulsatile Flow in an Elastic Tube.- 5.1 Introduction.- 5.2 Bessel Equations and Solutions.- 5.3 Balance of Forces.- 5.4 Equations of Wall Motion.- 5.5 Coupling with Fluid Motion.- 5.6 Matching at the Tube Wall.- 5.7 Wave Speed.- 5.8 Arbitrary Constants.- 5.9 Flow Properties.- 5.10 Problems.- 5.11 References and Further Reading.- 6 Wave Reflections.- 6.1 Introduction.- 6.2 One-Dimensional Wave Equations.- 6.3 Basic Solution of Wave Equation.- 6.4 Primary Wave Reflections in a Tube.- 6.5 Secondary Wave Reflections in a Tube.- 6.6 Pressure-Flow Relations.- 6.7 Effective Admittance.- 6.8 Vascular Tree Structure.- 6.9 Problems.- 6.10 References and Further Reading.- Appendix B. Solutions to Problems.


The author, originally trained in fluid dynamics, has been teaching and working on the dynamics of blood flow in general and coronary blood flow in particular for the past thirty years.
EAN: 9780387989259
ISBN: 0387989250
Untertitel: 'Biological and Medical Physics, Biomedical Engineering'. 2000. Auflage. Book. Sprache: Englisch.
Verlag: Springer
Erscheinungsdatum: Februar 2000
Seitenanzahl: 244 Seiten
Format: gebunden
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