Physics of Pulsatile Flow

Abstract

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.