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AVM modelling by multi-branching tube flow: large flow rates and dual solutions

AVM modelling by multi-branching tube flow: large flow rates and dual solutions
AVM modelling by multi-branching tube flow: large flow rates and dual solutions
Cerebral arteriovenous malformations (AVMs) present a common yet complex clinical challenge, through ÔstealÕ phenomena, haemorrhage risks and epilepsy effects, aspects which are little understood even for individual lesions. The main difficulty lies in understanding the detailed haemodynamics of AVMs and especially the enhanced through-flow associated with steal. Mathematically, as a basic step, the paper investigates a nonlinear inviscid model for the planar incompressible flow of fluid through a branched geometry consisting of a single feeding mother tube which splits into two or more non- aligned daughter tubes. Recurrence relations between the unknown flow profiles in the daughter tubes and the incoming rotational flow profile in the mother tube are derived, analysed, and solved in detail in order to find the total flow rate. The results show greatly enhanced through-flow arising, for a fixed value of the total downstream flow area, either from non-unique solutions to the problem or more particularly from an increase in the number of daughter tubes, or from both, depending on the distribution of pressure differences applied across the branching region and the total downstream flow area. Extensions of the basic flow model are noted, along with comparisons with recent direct numerical simulations and discussion of possible repercussions in the context of treatment and clinical observations of enhanced through-flows in AVMs.
arteriovenous malformations, branching, haemodynamics, modelling
1477-8599
183-204
Smith, F.T.
4da4a291-677c-402c-8e5f-387b3985071b
Jones, M.A.
6cfb0dde-3630-4df4-8f66-5335dec3b5fa
Smith, F.T.
4da4a291-677c-402c-8e5f-387b3985071b
Jones, M.A.
6cfb0dde-3630-4df4-8f66-5335dec3b5fa

Smith, F.T. and Jones, M.A. (2003) AVM modelling by multi-branching tube flow: large flow rates and dual solutions. Mathematical Medicine and Biology, 20 (2), 183-204. (doi:10.1093/imammb/20.2.183).

Record type: Article

Abstract

Cerebral arteriovenous malformations (AVMs) present a common yet complex clinical challenge, through ÔstealÕ phenomena, haemorrhage risks and epilepsy effects, aspects which are little understood even for individual lesions. The main difficulty lies in understanding the detailed haemodynamics of AVMs and especially the enhanced through-flow associated with steal. Mathematically, as a basic step, the paper investigates a nonlinear inviscid model for the planar incompressible flow of fluid through a branched geometry consisting of a single feeding mother tube which splits into two or more non- aligned daughter tubes. Recurrence relations between the unknown flow profiles in the daughter tubes and the incoming rotational flow profile in the mother tube are derived, analysed, and solved in detail in order to find the total flow rate. The results show greatly enhanced through-flow arising, for a fixed value of the total downstream flow area, either from non-unique solutions to the problem or more particularly from an increase in the number of daughter tubes, or from both, depending on the distribution of pressure differences applied across the branching region and the total downstream flow area. Extensions of the basic flow model are noted, along with comparisons with recent direct numerical simulations and discussion of possible repercussions in the context of treatment and clinical observations of enhanced through-flows in AVMs.

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Published date: 2003
Keywords: arteriovenous malformations, branching, haemodynamics, modelling

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Local EPrints ID: 29403
URI: http://eprints.soton.ac.uk/id/eprint/29403
ISSN: 1477-8599
PURE UUID: c7198a35-620c-4f4d-a2c1-0f89c0c2037b

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Date deposited: 12 May 2006
Last modified: 08 Jan 2022 09:56

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Author: F.T. Smith
Author: M.A. Jones

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