Anil Kumar, C. L. Varshney, G. C. Sharma. Computational Technique for Flow in Blood Vessels With Porous Effects[J]. Applied Mathematics and Mechanics, 2005, 26(1): 58-66.
Citation: Anil Kumar, C. L. Varshney, G. C. Sharma. Computational Technique for Flow in Blood Vessels With Porous Effects[J]. Applied Mathematics and Mechanics, 2005, 26(1): 58-66.

Computational Technique for Flow in Blood Vessels With Porous Effects

  • Received Date: 2002-10-17
  • Publish Date: 2005-01-15
  • A finite element solution for the Navier-Stokes equations for steady flow under the porosity effects through a double branched two dimensional section of a three dimensional model of a canine aorta was obtained.The numerical solution involves transforming a physical coordinates to a curvilinear boundary fitted coordinate system.The steady flow,branch flow and shear stress under the porous effects were discussed in detail.The shear stress at the wall was calculated for Reynold's number of 1000 with branch to main aortic flow rate ratio as a parameter.The results are compared with earlier works involving experimental data and it has observed that our results are very close to the exact solutions.This work in fact is an improvement of the work of Sharma et al.(2001) in the sense that computations technique is economic and Reynolds number is large.
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  • [1]
    Anderson J L,Malone D M.Mechanism of osmotic flow in porous membranes[J].Biophysical Journal,1974,14:957—982. doi: 10.1016/S0006-3495(74)85962-X
    [2]
    Thompson J F,Thomes F C,Martin C W.Automatic numerical generations of body fitted curvilinear coordinates system for field containing any of arbitrary two dimensional bodies[J].J Computational Physics,1974,15:299—319. doi: 10.1016/0021-9991(74)90114-4
    [3]
    Hellsten S, Pettersson H.Hydro and hemodynamics effects of catheterization of vessels Ⅳ,catherterization in the dog[J].Acta Radiologia Diagonosis,1977,18:17—24.
    [4]
    Gokhale V V,Tanner R I,Bischoff K B.Finite element solution of Navier-Stokes equations for two-dimensional steady flow through a section of canine aorta model[J].J Biomechanics,1978,11:241—249. doi: 10.1016/0021-9290(78)90050-7
    [5]
    Greshno R M,Lee R L,Sani K L.Lawrence Livemore Laboratory Rept[R]. UCRL 83282 Sept,1979.
    [6]
    Pedley T J.The Fluid Mechanics of Large Blood Vessels[M].N Y:Cambridge University Press,1980.
    [7]
    Mishra J C,Singh S T.A large deformation analysis for aortic walls under a physiological loading[J].J Engg Sciences,1983,21:1193—1202. doi: 10.1016/0020-7225(83)90083-6
    [8]
    Zarins C K,Giddens D P,Bharadvaj B K,et al.Carotid bifurcation atherosclerosis, quantitative correlation of plaque localization with flow velocity profiles and wall shear stress[J].Circulation Research,1983,53:502—514. doi: 10.1161/01.RES.53.4.502
    [9]
    Angonafer D,Watkins C B,Cannon J N.Computation of steady flow in a two dimensional arterial model[J].J Biomechanics,1985,18(8):693—701.
    [10]
    Bramely J S,Sloan J S.Numerical solution for two-dimensional flow in abranching channel using boundary fitted coordinates[J].Comput Fluids,1987,15:297—311. doi: 10.1016/0045-7930(87)90012-0
    [11]
    Rieu R,Pelissier R,Farahifor D.An experimental investigation of flow characterstics in bifurcation models[J].Eur J Mech,1989,8(1):73—101.
    [12]
    Rodkiewicz C M,Sinha P,Kennedy J S.On the application of constitutive equation for whole human blood[J].J Bio Mechanical Engg,1990,112:198—210.
    [13]
    Johonston P R,Kilpatrick D.Mathematical modelling of flow through irregular arterial stenosis[J].J Biomechanics,1991,24:1069—1077. doi: 10.1016/0021-9290(91)90023-G
    [14]
    Friedman M H,Fry D L.Arterili permeability dynamics and vascular disease[J].Atherosclerosis,1993,104:189—194. doi: 10.1016/0021-9150(93)90190-6
    [15]
    Tamamidis P,Assamis D N.Prediction of three-dimensional steady incompressible flows using body-fitted coordinate[J].Trans ASME J Fluids Engg,1993,115:475—462.
    [16]
    Henderson J M,Fry D L,Friedman M H.Analysis of models of arterial permeability dynamics[A].In:Liepsch D Ed.Bio Fluid Mechanics[C]. For tschritt-Berichte,Reihe,17,Nr;107,VDI-Verlag-Dusseldorf,1994,717—725.
    [17]
    Shipley R E,Gregg D E.The effect of external constriction of a blood vessel on blood flow[J].American J Physiology,1994,141:289—294.
    [18]
    Katz I,Shaughnessy F,Gress B.A technical problem in the calculation of laminar flow near irregular surface described by sampled geometric data[J].J Biomechanics,1995,28(4):461—464. doi: 10.1016/0021-9290(94)00086-J
    [19]
    Lever M J,Coleman P J.Fractionation of plasma proteins during their passage through blood vessels walls[A].In:Bioengg Conf B Ed[C].29,A SME,New York,1995,133—134.
    [20]
    Perktold K,Rappitsch G.Computer simulation of arterial blood flow vessel diseases under the aspect of local hemodynamics[A].In:Jaffrin M Y,Caro C G Eds.Biological Flows[C].New York:Plenum Press, 1995,83—144.
    [21]
    Huang Z J,Tarbell J M.Numerical simulation of mass transfer in porous media of blood vessel walls[J].American J Physiology,1997,273:H464—H477.
    [22]
    Korenga R,Ando J,Kamiya A.The effect of laminar flow on the gene expression of the adhesion molecule in endothelial cells[J].Japanese J Medical Electronics and Biological Engg,1998,36:266—272.
    [23]
    Dash R K,Jayaraman G,Mehta K M.Flow cathertized curved artery with stenosis[J].J Biomechanics,1999,32:46—61.
    [24]
    Karner G,Perktold K.Effect of endothelial injury and increased blood pressure on albumin accumulation in the arterial wall: a numerical study[J].J Biomechanics,2000,33:709—715. doi: 10.1016/S0021-9290(99)00226-2
    [25]
    Stroud J S,Berger S A,Saloner D.Influence of stenosis morphology on flow through severely stenotic vessels; implications for plaque rupture[J].J Biomechanics,2000,33:443—455. doi: 10.1016/S0021-9290(99)00207-9
    [26]
    Sharma G C.Madhu Jain,Anil Kumar.MHD flow in stenosed artery[A].In:Proceedings in Int Conf on Mathematical Modelling[C].Jan,29-31,Rookee,2001,683—687,
    [27]
    Shivkumar P N.Mathematical modelling of some problems in industry and biology[A].In:Proceedings in Int Conf on Mathematical Modelling[C].Jan 29-31,Rookee,2001,601—604.
    [28]
    夏玛 G C,马德胡 J,克乌玛 A.动脉血管流动计算的伽辽金有限元法研究[J].应用数学和力学,2001,22(9):911—917.
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