Title
The Onset of Oscillations in Microvascular Blood Flow
Abstract
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
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
Name
Order
Citations
PageRank
John B. Geddes183.39
Russell T. Carr200.34
Nathaniel Karst3193.83
F Wu420.79