$$ \newcommand{\partd}[2]{\frac{\partial #1}{\partial #2}} \newcommand{\partdd}[2]{\frac{\partial^{2} #1}{\partial {#2}^{2}}} \newcommand{\ddt}{\frac{d}{dt}} \newcommand{\Int}{\int\limits} \newcommand{\D}{\displaystyle} \newcommand{\dA}{\; \mbox{dA}} \newcommand{\dz}{\; \mbox{dz}} $$
Blood flow in compliant vessels

 

 

 

Blood flow in compliant vessels

Leif Rune Hellevik

Jun 25, 2015

Table of contents

      Nomenclature
Poiseuille flow in a compliant vessel
Infinitesimal derivation of the 1D governing equations for a compliant vessel
      Conservation of mass
      The momentum equation
Integral derivation of the 1D governing equations for a compliant vessel
      1D transport equation
      Mass conservation
      Momentum equation
      Example 1: Momentum equations for invicid flow
      Example 2: Momentum equations for polynomial velocity profiles
      Linearized and inviscid wave equations
      Characteristic impedance
      Progressive waves superimposed on steady flow
Input impedance
Wave reflections
General equations with reflection and friction
Wave propagation in blood vessels
Wave separation
Wave travel and reflection
Networks 1D compliant vessels
      Lumped heart model: varying elastance model
      Nonlinear wave separation
Fluid structure interaction for small deformations in Hookean vessel
      The governing equations for the Hookean vessel
      The governing equations for the fluid
Change of primary variables. The pQ, Au and other variations
      Example: From the pQ-system to the Au-system
Bibliography

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