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Shock formation and non-linear dispersion in a microvascular capillary network

Shock formation and non-linear dispersion in a microvascular capillary network
Shock formation and non-linear dispersion in a microvascular capillary network
Temporal and spatial fluctuations are a common feature of blood flow in microvascular networks. Among many possible causes, previous authors have suggested that the non-linear rheological properties of capillary blood flow (notably the Fåhræus effect, the Fåhræus–Lindqvist effect and the phase-separation effect at bifurcations) may be sufficient to generate temporal fluctuations even in very simple networks. We have simulated blood flow driven by a fixed pressure drop through a simple arcade network using coupled hyperbolic partial differential equations (PDEs) that incorporate well-established empirical descriptions of these rheological effects, accounting in particular for spatially varying haematocrit distributions; we solved the PDE system using a characteristic-based method. Our computations indicate that, under physiologically realistic conditions, there is a unique steady flow in an arcade network which is linearly stable and that plasma skimming suppresses the oscillatory decay of perturbations. In addition, we find that non-linear perturbations to haematocrit distributions can develop shocks via the Fåhræus effect, providing a novel mechanism for non-linear dispersion in microvascular networks.

microcirculation, capillary network, haematocrit, blood rheology
1477-8599
379-400
Pop, S.R.
57375012-0f81-4c0e-bd28-dd7ca58f04d1
Richardson, Giles
3fd8e08f-e615-42bb-a1ff-3346c5847b91
Waters, S.L.
215b3849-eee9-4979-9702-bc8bd996436b
Jensen, O.E.
b72436bc-7fa6-4a5d-9373-b5bb648a762f
Pop, S.R.
57375012-0f81-4c0e-bd28-dd7ca58f04d1
Richardson, Giles
3fd8e08f-e615-42bb-a1ff-3346c5847b91
Waters, S.L.
215b3849-eee9-4979-9702-bc8bd996436b
Jensen, O.E.
b72436bc-7fa6-4a5d-9373-b5bb648a762f

Pop, S.R., Richardson, Giles, Waters, S.L. and Jensen, O.E. (2007) Shock formation and non-linear dispersion in a microvascular capillary network. Mathematical Medicine and Biology, 24 (4), 379-400. (doi:10.1093/imammb/dqm007).

Record type: Article

Abstract

Temporal and spatial fluctuations are a common feature of blood flow in microvascular networks. Among many possible causes, previous authors have suggested that the non-linear rheological properties of capillary blood flow (notably the Fåhræus effect, the Fåhræus–Lindqvist effect and the phase-separation effect at bifurcations) may be sufficient to generate temporal fluctuations even in very simple networks. We have simulated blood flow driven by a fixed pressure drop through a simple arcade network using coupled hyperbolic partial differential equations (PDEs) that incorporate well-established empirical descriptions of these rheological effects, accounting in particular for spatially varying haematocrit distributions; we solved the PDE system using a characteristic-based method. Our computations indicate that, under physiologically realistic conditions, there is a unique steady flow in an arcade network which is linearly stable and that plasma skimming suppresses the oscillatory decay of perturbations. In addition, we find that non-linear perturbations to haematocrit distributions can develop shocks via the Fåhræus effect, providing a novel mechanism for non-linear dispersion in microvascular networks.

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Published date: 2007
Keywords: microcirculation, capillary network, haematocrit, blood rheology

Identifiers

Local EPrints ID: 156343
URI: http://eprints.soton.ac.uk/id/eprint/156343
ISSN: 1477-8599
PURE UUID: 395ff941-6a22-4e17-a2fa-2a177d47ced6

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Date deposited: 03 Jun 2010 10:30
Last modified: 08 Jan 2022 08:39

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Contributors

Author: S.R. Pop
Author: S.L. Waters
Author: O.E. Jensen

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