Analysis of non-linear pulsatile blood flow in artery through a generalized multiple stenosis

Arabian Journal of Mathematics - Tập 5 Số 1 - Trang 51-61 - 2016
Changdar, Satyasaran1, De, Soumen2
1Institute of Engineering & Management, Kolkata, India
2Department of Applied Mathematics, University of Calcutta, Kolkata, India

Tóm tắt

The non-linear blood flow under the influence of periodic body acceleration through a generalized multiple stenosed artery is investigated with the help of numerical simulation. The arterial segment is simulated by a cylindrical tube filled with a viscous incompressible Newtonian fluid described by the Navier–Stokes equation. The non-linear equation is solved numerically using finite difference with the proper boundary conditions and pressure gradient that arise from the heart. The effect of Reynolds number is also discussed. Results are shown in comparison with the existing models.

Tài liệu tham khảo

citation_journal_title=Annu. Rev. Biomed. Eng.; citation_title=Fluid mechanics of vascular systems, diseases and thrombosis; citation_author=D.M. Wooton, D.N. Ku; citation_volume=1; citation_publication_date=1999; citation_pages=299-329; citation_doi=10.1146/annurev.bioeng.1.1.299; citation_id=CR1 citation_journal_title=Annu. Rev. Fluid Mech.; citation_title=Experimental and computational methods in cardiovascular fluid mechanics; citation_author=C.A. Taylor, T. Draney Mary; citation_volume=36; citation_publication_date=2004; citation_pages=197-231; citation_doi=10.1146/annurev.fluid.36.050802.121944; citation_id=CR2 citation_journal_title=Comput. Biol. Med.; citation_title=Simulation of a pulsatile non-Newtonian flow past a stenosed 2D artery with atherosclerosis; citation_author=B. Fang, L. Zhu, P. Fok, X. Lu; citation_volume=43; citation_publication_date=2013; citation_pages=1098-1113; citation_doi=10.1016/j.compbiomed.2013.05.023; citation_id=CR3 citation_journal_title=Math. Comput. Model.; citation_title=Mathematical modelling of blood flow through an overlapping arterial stenosis; citation_author=S. Chakravarty, P.K. Mondal; citation_volume=19; citation_publication_date=1994; citation_pages=59-70; citation_doi=10.1016/0895-7177(94)90116-3; citation_id=CR4 citation_journal_title=Med. Eng. Phys.; citation_title=Modelling of Flowand wall behaviour in a mildly stenosed tube; citation_author=K.W. Lee, X.Y. Xu; citation_volume=24; citation_publication_date=2002; citation_pages=575-586; citation_doi=10.1016/S1350-4533(02)00048-6; citation_id=CR5 citation_journal_title=Math. Comput. Model.; citation_title=Mathematical modelling of three-dimensional flow through an asymmetric arterial stenosis; citation_author=K.C. Ang, J.N. Mazumdar; citation_volume=25; citation_publication_date=1997; citation_pages=19-29; citation_doi=10.1016/S0895-7177(96)00182-3; citation_id=CR6 citation_journal_title=J. Comput. Appl. Math.; citation_title=Unsteady response of non-Newtonian blood flow through a stenosed artery in magnetic field; citation_author=Md.A. Ikbal, S. Chakravarty, K.K.L. Wong, J. Majumdar, P.K. Mandal; citation_volume=230; citation_publication_date=2009; citation_pages=243-259; citation_doi=10.1016/j.cam.2008.11.010; citation_id=CR7 citation_journal_title=J. Magn. Reson. Imaging.; citation_title=MRI measurement of wall shear stress vectors in bifurcation models and comparis on with CFD predictions; citation_author=U. Kohler, I. Marshall, M.B. Robertson, Q. Long, X.Y. Xu; citation_volume=14; citation_publication_date=2001; citation_pages=563-573; citation_doi=10.1002/jmri.1220; citation_id=CR8 citation_journal_title=J. Biomech. Eng.; citation_title=Numerical analysis of flow through a severely stenotic carotid artery bifurcation; citation_author=J.S. Stroud, S.A. Berger, D. Saloner; citation_volume=124; citation_publication_date=2002; citation_pages=9-20; citation_doi=10.1115/1.1427042; citation_id=CR9 citation_journal_title=Comput. Meth. Appl. Mech. Eng.; citation_title=Simulation of high Reynolds number vascular flows; citation_author=P.F. Fischer, F. Loth, S.E. Lee, S.W. Lee, D. Smith, H. Bassiouny; citation_volume=196; citation_publication_date=2007; citation_pages=3049-3060; citation_doi=10.1016/j.cma.2006.10.015; citation_id=CR10 citation_journal_title=J. Fluid. Mech.; citation_title=Nonlinear flow phenomena in a symmetric sudden expansion; citation_author=R.M. Fearn, T. Mullin, K.A. Clile; citation_volume=211; citation_publication_date=1990; citation_pages=595-608; citation_doi=10.1017/S0022112090001707; citation_id=CR11 citation_journal_title=J. Fluid Mech.; citation_title=The plane symmetric sudden expansion; citation_author=F. Durst, J.C. Pereira, C. Tropea; citation_volume=248; citation_publication_date=1993; citation_pages=567-581; citation_doi=10.1017/S0022112093000916; citation_id=CR12 citation_journal_title=Int. J. Non-Linear Mech.; citation_title=Unsteady laminar separated flow through constricted channel; citation_author=T. Mahapatra, G.C. Layek, M.K. Maiti; citation_volume=37; citation_publication_date=2002; citation_pages=171-186; citation_doi=10.1016/S0020-7462(00)00104-9; citation_id=CR13 citation_journal_title=Math. Comput. Model.; citation_title=Effect of body acceleration on blood flow in an irregular stenosed artery; citation_author=S. Chakravarty, A.K. Sannigrahi; citation_volume=19; citation_publication_date=1994; citation_pages=93-103; citation_doi=10.1016/0895-7177(94)90092-2; citation_id=CR14 citation_journal_title=Phys. Med. Biol; citation_title=The influence of anomalous viscosity of blood upon its oscillatory flow; citation_author=M.G. Taylor; citation_volume=3; citation_publication_date=1959; citation_pages=273-290; citation_doi=10.1088/0031-9155/3/3/307; citation_id=CR15 citation_title=Physiology and Biophysics of the Circulation, Introductory Text; citation_publication_date=1966; citation_id=CR16; citation_author=A.C. Burton; citation_publisher=Year Book Medical Publisher citation_journal_title=J. Fluid. Mech.; citation_title=A nonlinear analysis of pulsatile flow in arteries; citation_author=S.C. Ling, H.B. Atabek; citation_volume=55; citation_publication_date=1972; citation_pages=493-511; citation_doi=10.1017/S0022112072001971; citation_id=CR17 citation_journal_title=J. Biomech.; citation_title=Finite element simulation of pulsatile flow through arterial stenosis; citation_author=C. Tu, M. Deville, L. Dheur, L. Vanderschuren; citation_volume=25; citation_publication_date=1992; citation_pages=1141-1152; citation_doi=10.1016/0021-9290(92)90070-H; citation_id=CR18