The Dynamics of Human Central Arterial System

• Autorzy: Paszyński M. , Kalita P. , Schaefer R.
• Języki publikacji: EN

Abstrakty

EN

The paper presents mathematical and numerical models of the blood flow in human arteries. We describe selected modelling techniques for the mechanical phenomena occurring in the arteries: blood flow, displacement of the wall and the fluid-structure interaction be-tween the blood and the wall. The paper concentrates on the theoretical results showing the conditions of applicability of presented models. We describe variational models for the Casson flow of blood as well as stochastic Fluid Particle Model (FPM) modified for the nonlinear flows. For the artery wali we describe the model which is the physically nonlinear Koiter shell and the Finite Element Method (FEM). We also present the simulations of the fluid-structure interaction that uses the weakly coupled approach of FPM for blood with FEM for the wall.

Słowa kluczowe

EN

biomechanics; blood flow; Fluid Particle Model (FPM); variational models

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Schedae Informaticae
• Rocznik: 2005
• Tom: Vol. 14
• Strony: 35--59
• Opis fizyczny: Bibliogr. 24 poz., rys.

Twórcy

autor

Paszyński M.

• The University of Texas at Austin, Institute for Computational Engineering and Sciences
• AGH University of Science and Technology,Department of Computer Methods in Metallurgy

autor

Kalita P.

• Jagiellonian University, Institute of Computer Science

autor

Schaefer R.

• Jagiellonian University, Institute of Computer Science

Bibliografia

• [1] Allen M.P., Tildesley D.J.; Computer Simulation of Liquids, Clarendon Press, Oxford 1987.
• [2] Bathe M., Kamm R.D.; Fluid-structure interaction analysis in biomechanics,in: Proceedings of the First MIT Conference on Computational Fluid and Solid Mechanics, Elsevier, Oxford 2001, pp. 1068–1072.
• [3] Berne R.M., Levy M.N., (eds.); Physiology, The C. V. Mosby Company, St. Louis, Toronto 1983.
• [4] Blouza A., Le Dret H.; Existence and uniqueness for the linear Koiter model for shells with little regularity, Quart. Appl. Math., 57, 1999, pp. 317–337.
• [5] Chapmann S., Cowling T.G.; The mathematical theory of non-uniform gases,Cambridge Mathematical Library, 1970.
• [6] Chung C.I., Kamm R.D., Younis H.F.; Challenges in developing an accuratemodel for cariotid bifurcation blood flow and wall mechanics, in: Proceedings of the First MIT Conference on Computational Fluid and Solid Mechanics, Elsevier, Oxford 2001, pp. 1434–1439.
• [7] Ciarlet P.G.; Finite Elements Method for Elliptic Problems, North-HollandPublishing Company, 1978.
• 8] Ciarlet P.G., Schultz M.H., Varga R.S.; Numerical Method of High Order Ac-curacy for Nonlinear Boundary Value Problems, Numer. Math., 13, 1969.
• [9] Espanol P.; Fluid Particle Model, Physical Review E, 57(3), 1998, pp. 2930–2948.
• [10] Espanol P., Revenga M., Zuniga I.; Boundary Conditions in Dissipative Particle Dynamics, Comput. Phys. Commun., 121–122, 1999, pp. 309–313.
• [11] Flugge S.; The non-linear field theories of mechanics, in: Encyclopedia of physics, Volume III/3, Springer-Verlag, 1965.
• [12] Fung Y.C.; Biomechanics, Springer-Verlag, New York 1984.
• [13] Hoogerbrugge P.J., Koelman J.M.; Simulating Microscopic Hydrodynamic Phenomena with Dissipative Particle Dynamics, Europhysics Letters, 19(3), 1992,pp. 155–160.
• [14] Kalita P., Paszyński M., Pelc A.; Simulation of the initiation of pulse wave inthe ascending aorta with the connected use of FPM and FEM, in: Proceedingsof VIII National Conference on Application of Mathematics in Biology andMedicine, Lajs, Poland, 2002, pp. 63–68.
• [15] Kalita P.; Koiter shell governed by strongly monotone constitutive equations,Preprint, http://www.ii.uj.edu.pl/preprint/kalita01/, Kraków 2002.
• [16] Kalita P.; Arterial wall modeled by physically nonlinear Koiter shell, in: Proceedings of 15th International Conference on Computer Methods in MechanicsCMM-2003, Gliwice/Wis la.
• [17] Paszyński M., Object Oriented Software System that Performs Fluid Particle Model Simulation in the Area with Moving Boundary and its Application to the Blood Flow Problem, Computer Assisted Mechanics and Engineering Science,3, 2003.
• [18] Paszyński M.; Algorithms of blood flow simulations in the cardiovascular sys-tem, PhD Thesis, Institute of Computer Science, Jagiellonian University, Cracow 2003.
• [19] Paszyński M., Schaefer R.; The modeling of non-linear fluid by the fluid particlemodel, with the application to the blood flow simulations, in: Proc. of the 8thNational Conference on Application of Mathematics in Biology and Medicine, Lajs, Poland, 2002, pp. 101–107.
• [20] Perktold K., Verdonck P., (eds.); Intra and Extracorporeal Cardiovascular Fluid Dynamics, Vol. 2: Fluid Structure Interactions, WIT Press, Southampton,Boston 2000.
• [21] Quarteroni A., Tuveri M., Veneziani A.; Computational vascular fluid dynamics: problems, models and methods, Comput. Visual Sci., 2, 2000, pp. 163–197.
• [22] Quarteroni A., Valli A.; Numerical Approximation for Partial Differential Equations, Springer-Verlag, New York 1994.
• [23] Temam R.; Navier-Stokes Equations Theory and Numerical Analysis, North-Holland, 1979.
• [24] Turek S., Kuzmin D.; Flux correction tools for finite elements, Int. J. Comput.Phys., 175, 2002, pp. 1–34.