2012, 9(1): 199-214. doi: 10.3934/mbe.2012.9.199

Effect of branchings on blood flow in the system of human coronary arteries

1. 

Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand, Thailand

2. 

Department of Mathematics and Statistics, Curtin University of Technology, Perth, WA 6845, Australia

3. 

Department of Radiology, Faculty of Medicine Siriraj Hospital, Mahidol University, Bangkoknoi, Bangkok, 10700, Thailand

Received  October 2010 Revised  July 2011 Published  December 2011

In this work, we investigate the behavior of the pulsatile blood flow in the system of human coronary arteries. Blood is modeled as an incompressible non-Newtonian fluid. The transient phenomena of blood flow through the coronary system are simulated by solving the three dimensional unsteady state Navier-Stokes equations and continuity equation. Distributions of velocity, pressure and wall shear stresses are determined in the system under pulsatile conditions on the boundaries. Effect of branching vessel on the flow problem is investigated. The numerical results show that blood pressure in the system with branching vessels of coronary arteries is lower than the one in the system with no branch. The magnitude of wall shear stresses rises at the bifurcation.
Citation: Benchawan Wiwatanapataphee, Yong Hong Wu, Thanongchai Siriapisith, Buraskorn Nuntadilok. Effect of branchings on blood flow in the system of human coronary arteries. Mathematical Biosciences & Engineering, 2012, 9 (1) : 199-214. doi: 10.3934/mbe.2012.9.199
References:
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V. Fuster, R. W. Alexander and R. A. O'Rourke, "Hurst's the Heart," 10th edition,, McGraw-Hill, (2001).

[2]

L. Ai and K. Vafai, A coupling model for macromolecule transport in a stenosed arterial wall,, Int. J. Heat Mass Transfer, 49 (2006), 1568. doi: 10.1016/j.ijheatmasstransfer.2005.10.041.

[3]

G. Anastasi, G. Cutroneo, F. Tomasello, S. Lucerna, A. Vitetta, P. Bramanti, P. Di Bella, A. Parenti, A. Porzionato, V. Macchi and R. De Caro, In vivo basal ganglia volumetry through application of NURBS models to MR images,, Neuroradiology, 48 (2006), 338. doi: 10.1007/s00234-005-0041-4.

[4]

F. G. Basombrío, E. A. Dari, G. C. Buscaglia and R. A. Feijóo, Numerical experiments in complex hemodynamic flows. Non-Newtonian effects,, XI Congress on Numerical Methods and their Applications (San Carlos de Bariloche, 16 (2002), 231.

[5]

C. Bertolotti and V. Deplano, Three-dimensional numerical simulations of flow through a stenosed coronary bypass,, J. Biomech., 33 (2000), 1011. doi: 10.1016/S0021-9290(00)00012-9.

[6]

J.-J. Chiu and S. Chien, Effects of disturbed flow on vascular endothelium: Pathophysiological basis and clinical perspectives,, Physiological Review, 91 (2011), 327. doi: 10.1152/physrev.00047.2009.

[7]

C. R. Ethier, D. A. Steinman, X. Zhang, S. R. Karpik and M. Ojha, Flow waveform effects on end-to-side anastomotic patterns,, J. Biomech., 31 (1998), 609. doi: 10.1016/S0021-9290(98)00059-1.

[8]

D. Y. Fei, J. D. Thomas and S. E. Rittgers, The effect of angle and flow rate upon hemodynamics in distal vascular graft anastomoses: A numerical model study,, J. Biomech Eng., 116 (1994), 331. doi: 10.1115/1.2895739.

[9]

Z. J. Huang and J. M. Tarbell, Numerical simulation of mass transfer in porous media blood vessel walls,, Am. J. Physiol Heart Circ Physiol., (1997), 464.

[10]

J. Chen and X. Y. Lu, Numerical investigation of non-Newtonian blood flow in a bifurcation model with non-planar branch,, J. Biomech., 37 (2004), 1899. doi: 10.1016/j.jbiomech.2004.02.030.

[11]

B. M. Johnston, P. R. Johnstona, S. Corney and D. Kilpatrick, Non-Newtonian blood flow in human right coronary arteries: Steady state simulations,, J. Biomech., 34 (2004), 709. doi: 10.1016/j.jbiomech.2003.09.016.

[12]

G. Karner and K. Perktold, Effect of endothelial injury and increased blood flow pressure on albumin accumulation in the arterial wall: A numerical study,, J Biomech., 33 (2000), 709. doi: 10.1016/S0021-9290(99)00226-2.

[13]

D. K. Stangeby and E. R. Ethier, Computational analysis of coupled blood-wall arterial LDL transport,, J. Biomech Eng., 124 (2002), 1. doi: 10.1115/1.1427041.

[14]

N. Kowalczyk and J. D. Mace, "Radiographic Pathology for Technologists,", MOSBY Elsevier, (2009).

[15]

Y. Papaharilaou, D. J. Doorly and S. J. Sherwin, The influence of out-of-plane geometry on pulsatile flow within a distal end-to-side anatomosis,, J. Boimech., 35 (2002), 1225. doi: 10.1016/S0021-9290(02)00072-6.

[16]

A. Quarteroni and L. Formaggia, Mathematical modelling and numerical simulation of the cardiovascular system,, in, (2004), 3.

[17]

N. H. Staalsen, M. Ulrich, W. Y. Kim, E. M. Pedersen, T. V. How and J. M. Hasenkam, In vivo analysis and three-dimensional visualization of blood flow patterns at vascular end-to-side anastomoses,, Eur. J. Vasc Endovasc Surg., 10 (1995), 168. doi: 10.1016/S1078-5884(05)80108-X.

[18]

S. Tada and J. M. Tarbell, Interstital flow through the internal elastic lamina affects shear stress on arterial smooth muscle cells,, Am. J. Physiol Heart Circ. Physiol., 278 (2000), 1589.

[19]

D. Tang, C. Yang, S. Kobayashi and D. N. Ku, Steady flow and wall compression in stenotic arteries: A three-dimensional thick-wall model with fluid-wall interactions,, J. Biomech Eng., 123 (2001), 548. doi: 10.1115/1.1406036.

[20]

R. C. Ward, M. W. Yambert, R. J. Toedte, N. B. Munro, C. E. Easterly, E. P. Difilippo and D. C. Stallings, Creating a human phantom for the virtual human program,, Stud. Health Technol. Inform., 70 (2000), 368.

[21]

B. Wiwatanapataphee, D. Poltem, Y. H. Wu and Y. Lenbury, Simulation of pulsatile flow of blood in stenosed coronary artery bypass with graft,, Math Biosci Eng., 3 (2006), 371. doi: 10.3934/mbe.2006.3.371.

[22]

F. G. Basombrío, E. A. Dari, G. C. Buscaglia and R. A. Feijóo, Numerical experiments in complex hemodynamic flows. Non-Newtonian effects,, Int. J. of Computational Fluid Dynamics, 16 (2002), 231.

[23]

C. Bertolotti and V. Deplano, Three-dimensional numerical simulations of flow through a stenosed coronary bypass,, J. Biomech., 33 (2000), 1011. doi: 10.1016/S0021-9290(00)00012-9.

[24]

J.-J. Chiu and S. Chien, Effects of disturbed flow on vascular endothelium: Pathophysiological basis and clinical perspectives, Physiological Review, 91 (2011), 327. doi: 10.1152/physrev.00047.2009.

[25]

C. R. Ethier, D. A. Steinman, X. Zhang, S. R. Karpik and M. Ojha, Flow waveform effects on end-to-side anastomotic patterns,, J. Biomech., 31 (1998), 609. doi: 10.1016/S0021-9290(98)00059-1.

[26]

D. Y. Fei, J. D. Thomas and S. E. Rittgers, The effect of angle and flow rate upon hemodynamics in distal vascular graft anastomoses: A numerical model study,, J. Biomech Eng., 116 (1994), 331. doi: 10.1115/1.2895739.

[27]

Z. J. Huang and J. M. Tarbell, Numerical simulation of mass transfer in porous media blood vessel walls,, Am. J. Physiol Heart Circ. Physiol., (1997), 464.

[28]

J. Chen and X. Y. Lu, Numerical investigation of non-Newtonian blood flow in a bifurcation model with non-planar branch,, J. Biomech., 37 (2004), 1899. doi: 10.1016/j.jbiomech.2004.02.030.

[29]

B. M. Johnston, P. R. Johnstona, S. Corney and D. Kilpatrick, Non-Newtonian blood flow in human right coronary arteries: Steady state simulations,, J. Biomech., 34 (2004), 709. doi: 10.1016/j.jbiomech.2003.09.016.

[30]

G. Karner and K. Perktold, Effect of endothelial injury and increased blood flow pressure on albumin accumulation in the arterial wall: A numerical study,, J. Biomech., 33 (2000), 709. doi: 10.1016/S0021-9290(99)00226-2.

[31]

D. K. Stangeby and E. R. Ethier, Computational analysis of coupled blood-wall arterial LDL transport,, J. Biomech Eng., 124 (2002), 1. doi: 10.1115/1.1427041.

[32]

N. Kowalczyk and J. D. Mace, "Radiographic Pathology for Technologists,", MOSBY Elsevier, (2009).

[33]

Y. Papaharilaou, D. J. Doorly and S. J. Sherwin, The influence of out-of-plane geometry on pulsatile flow within a distal end-to-side anatomosis,, J. Boimech., 35 (2002), 1225. doi: 10.1016/S0021-9290(02)00072-6.

[34]

A. Quarteroni and L. Formaggia, Mathematical modelling and numerical simulation of the cardiovascular system,, in, (2004).

[35]

N. H. Staalsen, M. Ulrich, W. Y. Kim, E. M. Pedersen, T. V. How and J. M. Hasenkam, In vivo analysis and three-dimensional visualization of blood flow patterns at vascular end-to-side anastomoses,, Eur. J. Vasc. Endovasc. Surg., 10 (1995), 168. doi: 10.1016/S1078-5884(05)80108-X.

[36]

S. Tada and J. M. Tarbell, Interstital flow through the internal elastic lamina affects shear stress on arterial smooth muscle cells,, Am. J. Physiol Heart Circ. Physiol., 278 (2000), 1589.

[37]

D. Tang, C. Yang, S. Kobayashi and D. N. Ku, Steady flow and wall compression in stenotic arteries: A three-dimensional thick-wall model with fluid-wall interactions,, J. Biomech Eng., 123 (2001), 548. doi: 10.1115/1.1406036.

[38]

R. C. Ward, M. W. Yambert, R. J. Toedte, N. B. Munro, C. E. Easterly, E. P. Difilippo and D. C. Stallings, Creating a human phantom for the virtual human program,, Stud. Health Technol. Inform., 70 (2000), 368.

[39]

B. Wiwatanapataphee, D. Poltem, Y. H. Wu and Y. Lenbury, Simulation of pulsatile flow of blood in stenosed coronary artery bypass with graft,, Math Biosci Eng., 3 (2006), 371. doi: 10.3934/mbe.2006.3.371.

show all references

References:
[1]

V. Fuster, R. W. Alexander and R. A. O'Rourke, "Hurst's the Heart," 10th edition,, McGraw-Hill, (2001).

[2]

L. Ai and K. Vafai, A coupling model for macromolecule transport in a stenosed arterial wall,, Int. J. Heat Mass Transfer, 49 (2006), 1568. doi: 10.1016/j.ijheatmasstransfer.2005.10.041.

[3]

G. Anastasi, G. Cutroneo, F. Tomasello, S. Lucerna, A. Vitetta, P. Bramanti, P. Di Bella, A. Parenti, A. Porzionato, V. Macchi and R. De Caro, In vivo basal ganglia volumetry through application of NURBS models to MR images,, Neuroradiology, 48 (2006), 338. doi: 10.1007/s00234-005-0041-4.

[4]

F. G. Basombrío, E. A. Dari, G. C. Buscaglia and R. A. Feijóo, Numerical experiments in complex hemodynamic flows. Non-Newtonian effects,, XI Congress on Numerical Methods and their Applications (San Carlos de Bariloche, 16 (2002), 231.

[5]

C. Bertolotti and V. Deplano, Three-dimensional numerical simulations of flow through a stenosed coronary bypass,, J. Biomech., 33 (2000), 1011. doi: 10.1016/S0021-9290(00)00012-9.

[6]

J.-J. Chiu and S. Chien, Effects of disturbed flow on vascular endothelium: Pathophysiological basis and clinical perspectives,, Physiological Review, 91 (2011), 327. doi: 10.1152/physrev.00047.2009.

[7]

C. R. Ethier, D. A. Steinman, X. Zhang, S. R. Karpik and M. Ojha, Flow waveform effects on end-to-side anastomotic patterns,, J. Biomech., 31 (1998), 609. doi: 10.1016/S0021-9290(98)00059-1.

[8]

D. Y. Fei, J. D. Thomas and S. E. Rittgers, The effect of angle and flow rate upon hemodynamics in distal vascular graft anastomoses: A numerical model study,, J. Biomech Eng., 116 (1994), 331. doi: 10.1115/1.2895739.

[9]

Z. J. Huang and J. M. Tarbell, Numerical simulation of mass transfer in porous media blood vessel walls,, Am. J. Physiol Heart Circ Physiol., (1997), 464.

[10]

J. Chen and X. Y. Lu, Numerical investigation of non-Newtonian blood flow in a bifurcation model with non-planar branch,, J. Biomech., 37 (2004), 1899. doi: 10.1016/j.jbiomech.2004.02.030.

[11]

B. M. Johnston, P. R. Johnstona, S. Corney and D. Kilpatrick, Non-Newtonian blood flow in human right coronary arteries: Steady state simulations,, J. Biomech., 34 (2004), 709. doi: 10.1016/j.jbiomech.2003.09.016.

[12]

G. Karner and K. Perktold, Effect of endothelial injury and increased blood flow pressure on albumin accumulation in the arterial wall: A numerical study,, J Biomech., 33 (2000), 709. doi: 10.1016/S0021-9290(99)00226-2.

[13]

D. K. Stangeby and E. R. Ethier, Computational analysis of coupled blood-wall arterial LDL transport,, J. Biomech Eng., 124 (2002), 1. doi: 10.1115/1.1427041.

[14]

N. Kowalczyk and J. D. Mace, "Radiographic Pathology for Technologists,", MOSBY Elsevier, (2009).

[15]

Y. Papaharilaou, D. J. Doorly and S. J. Sherwin, The influence of out-of-plane geometry on pulsatile flow within a distal end-to-side anatomosis,, J. Boimech., 35 (2002), 1225. doi: 10.1016/S0021-9290(02)00072-6.

[16]

A. Quarteroni and L. Formaggia, Mathematical modelling and numerical simulation of the cardiovascular system,, in, (2004), 3.

[17]

N. H. Staalsen, M. Ulrich, W. Y. Kim, E. M. Pedersen, T. V. How and J. M. Hasenkam, In vivo analysis and three-dimensional visualization of blood flow patterns at vascular end-to-side anastomoses,, Eur. J. Vasc Endovasc Surg., 10 (1995), 168. doi: 10.1016/S1078-5884(05)80108-X.

[18]

S. Tada and J. M. Tarbell, Interstital flow through the internal elastic lamina affects shear stress on arterial smooth muscle cells,, Am. J. Physiol Heart Circ. Physiol., 278 (2000), 1589.

[19]

D. Tang, C. Yang, S. Kobayashi and D. N. Ku, Steady flow and wall compression in stenotic arteries: A three-dimensional thick-wall model with fluid-wall interactions,, J. Biomech Eng., 123 (2001), 548. doi: 10.1115/1.1406036.

[20]

R. C. Ward, M. W. Yambert, R. J. Toedte, N. B. Munro, C. E. Easterly, E. P. Difilippo and D. C. Stallings, Creating a human phantom for the virtual human program,, Stud. Health Technol. Inform., 70 (2000), 368.

[21]

B. Wiwatanapataphee, D. Poltem, Y. H. Wu and Y. Lenbury, Simulation of pulsatile flow of blood in stenosed coronary artery bypass with graft,, Math Biosci Eng., 3 (2006), 371. doi: 10.3934/mbe.2006.3.371.

[22]

F. G. Basombrío, E. A. Dari, G. C. Buscaglia and R. A. Feijóo, Numerical experiments in complex hemodynamic flows. Non-Newtonian effects,, Int. J. of Computational Fluid Dynamics, 16 (2002), 231.

[23]

C. Bertolotti and V. Deplano, Three-dimensional numerical simulations of flow through a stenosed coronary bypass,, J. Biomech., 33 (2000), 1011. doi: 10.1016/S0021-9290(00)00012-9.

[24]

J.-J. Chiu and S. Chien, Effects of disturbed flow on vascular endothelium: Pathophysiological basis and clinical perspectives, Physiological Review, 91 (2011), 327. doi: 10.1152/physrev.00047.2009.

[25]

C. R. Ethier, D. A. Steinman, X. Zhang, S. R. Karpik and M. Ojha, Flow waveform effects on end-to-side anastomotic patterns,, J. Biomech., 31 (1998), 609. doi: 10.1016/S0021-9290(98)00059-1.

[26]

D. Y. Fei, J. D. Thomas and S. E. Rittgers, The effect of angle and flow rate upon hemodynamics in distal vascular graft anastomoses: A numerical model study,, J. Biomech Eng., 116 (1994), 331. doi: 10.1115/1.2895739.

[27]

Z. J. Huang and J. M. Tarbell, Numerical simulation of mass transfer in porous media blood vessel walls,, Am. J. Physiol Heart Circ. Physiol., (1997), 464.

[28]

J. Chen and X. Y. Lu, Numerical investigation of non-Newtonian blood flow in a bifurcation model with non-planar branch,, J. Biomech., 37 (2004), 1899. doi: 10.1016/j.jbiomech.2004.02.030.

[29]

B. M. Johnston, P. R. Johnstona, S. Corney and D. Kilpatrick, Non-Newtonian blood flow in human right coronary arteries: Steady state simulations,, J. Biomech., 34 (2004), 709. doi: 10.1016/j.jbiomech.2003.09.016.

[30]

G. Karner and K. Perktold, Effect of endothelial injury and increased blood flow pressure on albumin accumulation in the arterial wall: A numerical study,, J. Biomech., 33 (2000), 709. doi: 10.1016/S0021-9290(99)00226-2.

[31]

D. K. Stangeby and E. R. Ethier, Computational analysis of coupled blood-wall arterial LDL transport,, J. Biomech Eng., 124 (2002), 1. doi: 10.1115/1.1427041.

[32]

N. Kowalczyk and J. D. Mace, "Radiographic Pathology for Technologists,", MOSBY Elsevier, (2009).

[33]

Y. Papaharilaou, D. J. Doorly and S. J. Sherwin, The influence of out-of-plane geometry on pulsatile flow within a distal end-to-side anatomosis,, J. Boimech., 35 (2002), 1225. doi: 10.1016/S0021-9290(02)00072-6.

[34]

A. Quarteroni and L. Formaggia, Mathematical modelling and numerical simulation of the cardiovascular system,, in, (2004).

[35]

N. H. Staalsen, M. Ulrich, W. Y. Kim, E. M. Pedersen, T. V. How and J. M. Hasenkam, In vivo analysis and three-dimensional visualization of blood flow patterns at vascular end-to-side anastomoses,, Eur. J. Vasc. Endovasc. Surg., 10 (1995), 168. doi: 10.1016/S1078-5884(05)80108-X.

[36]

S. Tada and J. M. Tarbell, Interstital flow through the internal elastic lamina affects shear stress on arterial smooth muscle cells,, Am. J. Physiol Heart Circ. Physiol., 278 (2000), 1589.

[37]

D. Tang, C. Yang, S. Kobayashi and D. N. Ku, Steady flow and wall compression in stenotic arteries: A three-dimensional thick-wall model with fluid-wall interactions,, J. Biomech Eng., 123 (2001), 548. doi: 10.1115/1.1406036.

[38]

R. C. Ward, M. W. Yambert, R. J. Toedte, N. B. Munro, C. E. Easterly, E. P. Difilippo and D. C. Stallings, Creating a human phantom for the virtual human program,, Stud. Health Technol. Inform., 70 (2000), 368.

[39]

B. Wiwatanapataphee, D. Poltem, Y. H. Wu and Y. Lenbury, Simulation of pulsatile flow of blood in stenosed coronary artery bypass with graft,, Math Biosci Eng., 3 (2006), 371. doi: 10.3934/mbe.2006.3.371.

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