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Self-sustained oscillations in blood flow through a honeycomb capillary network
1Department of Chemical Engineering, University of Massachusetts, Amherst, MA , 01003, USA, jmdavis@ecs.umass.edu.
Bulletin of Mathematical Biology
|August 22, 2014
Summary
Unsteady blood flow in honeycomb networks can exhibit self-sustained oscillations due to bifurcations. Blockages may cause flow reversal or unsteady flow, unlike tree networks.
Area of Science:
- Fluid Dynamics
- Biomedical Engineering
- Computational Biology
Background:
- Blood flow in complex networks is crucial for physiological function.
- Previous studies focused on tree-like networks, neglecting converging bifurcations.
- Honeycomb networks offer a more realistic model for certain biological systems.
Purpose of the Study:
- To simulate unsteady blood flow in honeycomb networks.
- To investigate the role of diverging and converging bifurcations.
- To analyze the conditions leading to flow instability and reversal.
Main Methods:
- Numerical simulations using a finite difference method.
- Modeling blood as a continuum with variable constitution.
- Analysis of flow dynamics at diverging and converging bifurcations.
Main Results:
- Steady flow can develop self-sustained oscillations via Hopf bifurcation.
- Instability parameters in honeycomb networks are weakly dependent on system size.
- Flow reversal or transition to unsteady flow can occur due to segment blockage or constriction.
Conclusions:
- Honeycomb network topology significantly influences blood flow dynamics.
- The cell partitioning law at bifurcations is critical for flow stability.
- Simulations provide insights into pathological flow conditions like blockages.
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