TOWARDS THE DEVELOPMENT OF A FULLY COUPLED ARTERIAL-VENOUS 1D MODEL: SUITABILITY OF USING A 1D FINITE VOLUME METHOD WITH STAGGERED SPATIAL DISCRETIZATION

TOWARDS THE DEVELOPMENT OF A FULLY COUPLED ARTERIAL-VENOUS 1D MODEL: SUITABILITY OF USING A 1D FINITE VOLUME METHOD WITH STAGGERED SPATIAL DISCRETIZATION

Bogaers, A.E.J.; Villiers, A.M. de; Kok, S.; Ubbink, O.; Franz, T.; Reddy, B.D.; Toit, C.G. du

Full Article:

In this paper we outline the development of a 1D finite volume model to solve for blood flow through the arterial system. The model is based on a staggered spatial discretization which leads to a stable solution scheme. This scheme can accurately capture the various pressure wave reflections at locations with distinct discontinuities (in both area and material properties) as well as naturally treat branching vessels. We investigate the behaviour and performance of the solver for both a stented and branching vessel and finally for a full arterial network consisting of 55 arteries within the human vascular network.

In this paper we outline the development of a 1D finite volume model to solve for blood flow through the arterial system. The model is based on a staggered spatial discretization which leads to a stable solution scheme. This scheme can accurately capture the various pressure wave reflections at locations with distinct discontinuities (in both area and material properties) as well as naturally treat branching vessels. We investigate the behaviour and performance of the solver for both a stented and branching vessel and finally for a full arterial network consisting of 55 arteries within the human vascular network.

Palavras-chave:

DOI: 10.5151/meceng-wccm2012-19026

Referências bibliográficas

• [1] B.S Brook and T.J. Pedley. A model for time-dependent flow in (giraffe jugular) veins: uniform tube properties. Journal of Biomechanics, 35:95–107, 2002.
• [2] R.L. Burden and J. D. Faires. Numerical Analysis. Brooks/Cole, ninth edition, 2011.
• [3] R. Collins and J.A. Maccario. Blood flow in the lung. Journal of Biomechanics, 12:373– 395, 1979.
• [4] J. P. Mynard and P. Nithiarasu. A 1d arterial blood flow model incorporating ventricular pressure, aortic valve and regional coronary flow using the locally conservative galerkin (lcg) method. Communications in Numerical Methods in Engineering, 24:367–417, 2008.
• [5] A. Quarteroni and L. Formaggia. Mathematical modelling and numerical simulation of the cardiovascular system. Handbook of numerical analysis, 12:3–127, 2004.
• [6] S.J. Sherwin, L. Formaggia, J. Peiró, and V. Franke. Computational modelling of 1d blood flow with variable mechanical properties and its application to the simulation of wave propogation in the human arterial system. International Journal for Numerical Methods in Fluids, 43:673–700, 2003.
• [7] S.J. Sherwin, V. Franke, J. Peiró, and K. Parker. One-dimensional modelling of a vascular network in space-time variables. Journal of Engineering Mathematics, 47:217–250, 2003.
• [8] J.J.Wang andW.H. Parker. Wave propogation in a model of the arterial circulation. Journal of Biomechanics, 37:457–470, 2003.

Como citar:

Bogaers, A.E.J.; Villiers, A.M. de; Kok, S.; Ubbink, O.; Franz, T.; Reddy, B.D.; Toit, C.G. du; "TOWARDS THE DEVELOPMENT OF A FULLY COUPLED ARTERIAL-VENOUS 1D MODEL: SUITABILITY OF USING A 1D FINITE VOLUME METHOD WITH STAGGERED SPATIAL DISCRETIZATION", p-2786-2801. In: In Proceedings of the 10th World Congress on Computational Mechanics [= Blucher Mechanical Engineering Proceedings, v. 1, n. 1]. São Paulo: Blucher, 2014.
ISSN 23580828, DOI 10.5151/meceng-wccm2012-19026