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Transmission conditions in a one-dimensional model of bifurcating blood vessel with an elastic wall
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
St. Petersburg State University, St. Petersburg State Polytechnical University, Russian Academy of Sciences, Russia.
2015 (Russian)In: Zapiski Nauchnykh Seminarov POMI, ISSN 0132-6678 (print), Vol. 438, 138-177 p.Article in journal (Other academic) Published
Abstract [en]

We derive transmission conditions at a bifurcation point in a one-dimensional model of blood vessels by using a three-dimensional model. Both classical Kirchhoff conditions ensuring the continuity of pressure and zero flux flow in the node has to be modified in order to reflect properly the elastic properties of blood vessels and the nodes themselves. A simple approximate calculation scheme for the new physical parameters in the transmission conditions is proposed. We develop a simplified model of straight fragments of arteries with localized defects such as lateral micro-aneurysms and cholesterol plaques – these models also require setting transmission conditions.

Place, publisher, year, edition, pages
St. Petersburg Department of V. A. Steklov Mathematical Institute, Russian Academy of Sciences , 2015. Vol. 438, 138-177 p.
Keyword [en]
artery bifurcation, branching of blood vessels, modified Kirchhoff conditions, elastic walls, thin flow, matrix of pressure jumps.
National Category
Other Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-132109OAI: oai:DiVA.org:liu-132109DiVA: diva2:1037612
Available from: 2016-10-17 Created: 2016-10-17 Last updated: 2016-12-09Bibliographically approved

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