Oscillations and Multiple Equilibria in Microvascular Blood Flow

We investigate the existence of oscillatory dynamics and multiple steady-state flow rates in a network with a simple topology and in vivo microvascular blood flow constitutive laws. Unlike many previous analytic studies, we employ the most biologically relevant models of the physical properties of w...

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Bibliographic Details
Published in:Bulletin of mathematical biology 2015-07, Vol.77 (7), p.1377-1400
Main Authors: Karst, Nathaniel J., Storey, Brian D., Geddes, John B.
Format: Article
Language:English
Subjects:
Blood Flow Velocity
Blood Viscosity
Cell Biology
Computer Simulation
Hematocrit
Hemorheology
Humans
Life Sciences
Mathematical and Computational Biology
Mathematical Concepts
Mathematics
Mathematics and Statistics
Microvessels - physiology
Models, Cardiovascular
Nonlinear Dynamics
Original Article
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Summary:We investigate the existence of oscillatory dynamics and multiple steady-state flow rates in a network with a simple topology and in vivo microvascular blood flow constitutive laws. Unlike many previous analytic studies, we employ the most biologically relevant models of the physical properties of whole blood. Through a combination of analytic and numeric techniques, we predict in a series of two-parameter bifurcation diagrams a range of dynamical behaviors, including multiple equilibria flow configurations, simple oscillations in volumetric flow rate, and multiple coexistent limit cycles at physically realizable parameters. We show that complexity in network topology is not necessary for complex behaviors to arise and that nonlinear rheology, in particular the plasma skimming effect, is sufficient to support oscillatory dynamics similar to those observed in vivo.
ISSN:0092-8240
1522-9602
DOI:10.1007/s11538-015-0089-1