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Bulletin of Mathematical Biology

, Volume 77, Issue 7, pp 1377–1400 | Cite as

Oscillations and Multiple Equilibria in Microvascular Blood Flow

  • Nathaniel J. Karst
  • Brian D. Storey
  • John B. Geddes
Original Article

Abstract

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.

Keywords

Microvascular blood flow Fluid dynamics Nonlinear dynamics Discontinuity-induced bifurcations 

Notes

Acknowledgments

This work was supported by the Babson Faculty Research Fund (N. J. K.) and the National Science Foundation under contract DMS-1211640 (B. D. S. and J. B. G.). We thank the two reviewers of our original submission for their careful attention and helpful suggestions.

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Copyright information

© Society for Mathematical Biology 2015

Authors and Affiliations

  1. 1.Babson CollegeBabson ParkUSA
  2. 2.Olin CollegeNeedhamUSA

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