Abstract
We show that large microvascular networks with realistic topologies, geometries, boundary conditions, and constitutive laws can exhibit many steady-state flow configurations. This is in direct contrast to most previous studies which have assumed, implicitly or explicitly, that a given network can only possess one equilibrium state. While our techniques are general and can be applied to any network, we focus on two distinct network types that model human tissues: perturbed honeycomb networks and random networks generated from Voronoi diagrams. We demonstrate that the disparity between observed and predicted flow directions reported in previous studies might be attributable to the presence of multiple equilibria. We show that the pathway effect, in which hematocrit is steadily increased along a series of diverging junctions, has important implications for equilibrium discovery, and that our estimates of the number of equilibria supported by these networks are conservative. If a more complete description of the plasma skimming effect that captures red blood cell allocation at junctions with high feed hematocrit were to be obtained empirically, then the number of equilibria found by our approach would at worst remain the same and would in all likelihood increase significantly.
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Acknowledgements
The authors would like to thank Brian Storey for helpful discussions throughout the early parts of this work, and an anonymous reviewer for his/her helpful comments on the initial submission of this manuscript.
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Karst, N.J., Geddes, J.B. & Carr, R.T. Model Microvascular Networks Can Have Many Equilibria. Bull Math Biol 79, 662–681 (2017). https://doi.org/10.1007/s11538-017-0251-z
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DOI: https://doi.org/10.1007/s11538-017-0251-z