Journal article
Key structural features of microvascular networks leading to the formation of multiple equilibria
- Abstract:
- We analyse mathematical models of blood flow in two simple vascular networks in order to identify structural features that lead to the formation of multiple equilibria. Our models are based on existing rules for blood rheology and haematocrit splitting. By performing bifurcation analysis on these simple network flow models, we identify a link between the changing flow direction in key vessels and the existence of multiple equilibria. We refer to these key vessels as redundant vessels, and relate the maximum number of equilibria with the number of redundant vessels. We vary geometric parameters of the two networks, such as vessel length ratios and vessel diameters, to demonstrate that equilibria are uniquely defined by the flow in the redundant vessels. Equilibria typically emerge in sets of three, each having a different flow characteristic in one of the network’s redundant vessels. For one of the three equilibria, the flow within the relevant redundant vessel will be smaller in magnitude than the other two and the redundant vessel will contain few Red Blood Cells (RBCs), if any. For the other two equilibria, the redundant vessel contains RBCs and significant flow in the two available directions. These structural features of networks provide a useful geometric property when studying the equilibria of blood flow in microvascular networks.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 1.3MB, Terms of use)
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- Publisher copy:
- 10.1007/s11538-024-01404-y
Authors
- Publisher:
- Springer
- Journal:
- Bulletin of Mathematical Biology More from this journal
- Volume:
- 87
- Issue:
- 2
- Article number:
- 30
- Publication date:
- 2025-01-23
- Acceptance date:
- 2024-12-20
- DOI:
- EISSN:
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1522-9602
- ISSN:
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0092-8240
- Language:
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English
- Keywords:
- Pubs id:
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2074523
- Local pid:
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pubs:2074523
- Deposit date:
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2025-01-05
- ARK identifier:
Terms of use
- Copyright holder:
- Atkinson et al.
- Copyright date:
- 2025
- Rights statement:
- Copyright © 2025, The Author(s). This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
- Licence:
- CC Attribution (CC BY)
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