Paper Info

Title | ||
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The Onset of Oscillations in Microvascular Blood Flow |

Abstract | ||
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We explore the stability of equilibrium solution(s) of a simple model of microvascular blood flow in a two-node network. The model takes the form of convection equations for red blood cell concentration, and contains two important rheological effects-the F (a) over circle hrus-Lindqvist effect, which governs viscosity of blood flow in a single vessel, and the plasma skimming effect, which describes the separation of red blood cells at diverging nodes. We show that stability is governed by a linear system of integral equations, and we study the roots of the associated characteristic equation in detail. We demonstrate using a combination of analytical and numerical techniques that it is the relative strength of the F (a) over circle hrus-Lindqvist effect and the plasma skimming effect which determines the existence of a set of network parameter values which lead to a Hopf bifurcation of the equilibrium solution. We confirm these predictions with direct numerical simulation and suggest several areas for future research and application. |

Year | DOI | Venue |
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2007 | 10.1137/060670699 | SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS |

Keywords | Field | DocType |

blood flow,microvascular network,instability,bifurcation | Direct numerical simulation,Hemorheology,Characteristic equation,Blood flow,Mathematical analysis,Control theory,Flow (psychology),Instability,Integral equation,Hopf bifurcation,Mathematics | Journal |

Volume | Issue | ISSN |

6 | 4 | 1536-0040 |

Citations | PageRank | References |

0 | 0.34 | 1 |

Authors | ||

4 |

Authors (4 rows)

Cited by (0 rows)

References (1 rows)

Name | Order | Citations | PageRank |
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John B. Geddes | 1 | 8 | 3.39 |

Russell T. Carr | 2 | 0 | 0.34 |

Nathaniel Karst | 3 | 19 | 3.83 |

F Wu | 4 | 2 | 0.79 |