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Modeling Elastic Vessels with the LBGK Method in Three Dimensions

  • Daniel Leitner
  • Siegfried Wassertheurer
  • Michael Hessinger
  • Andreas Holzinger
  • Felix Breitenecker
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4799)

Abstract

The Lattice Bhatnagar Gross and Krook (LBGK) method is widely used to solve fluid mechanical problems in engineering applications. In this work a brief introduction of the LBGK method is given and a new boundary condition is proposed for the cardiovascular domain. This enables the method to support elastic walls in two and three spatial dimensions for simulating blood flow in elastic vessels. The method is designed to be used on geometric data obtained from magnetic resonance angiography without the need of generating parameterized surfaces. The flow field is calculated in an arbitrary geometry revealing characteristic flow patterns and geometrical changes of the arterial walls for different time dependent input contours of pressure and flow. For steady flow the results are compared to the predictions of the model proposed by Y. C. Fung which is an extension of Poiseuille’s theory. The results are very promising for relevant Reynolds and Womersley numbers, consequently very useful in medical simulation applications.

Keywords

Simulation Lattice Boltzmann Model Haemodynamics Elasticity Computer Fluid Dynamics 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Daniel Leitner
    • 1
    • 2
  • Siegfried Wassertheurer
    • 1
  • Michael Hessinger
    • 3
  • Andreas Holzinger
    • 4
  • Felix Breitenecker
    • 2
  1. 1.Austrian Research Centers GmbH - ARC, Donau-City-Straße 1, A-1220 ViennaAustria
  2. 2.Vienna University of Technology, Institute for Analysis and Scientific Computing, Wiedner Hauptstraße 8-10, A-1040 ViennaAustria
  3. 3.Medical University of Graz, Clinical Department for vascular surgery, Auenbruggerplatz 29, 8036 Graz 
  4. 4.Medical University of Graz, Institute for Medical Informatics, Statistics and, Documentation, Auenbruggerplatz 2/V, A-8036 GrazAustria

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