Effect of Slip Velocity on Blood Flow through a Catheterized Artery

ABSTRACT

A mathematical model for pulsatile flow of blood in a catheterized artery in presence of an axisymmetric stenosis with a velocity slip at the constricted wall is proposed. The expressions for the flow characteristics, velocity profiles, the flow resistance, the wall shear stress, the effective viscosity are obtained in the present analysis. The effects of slip velocity on the blood flow characteristics are shown graphically and discussed briefly.

A mathematical model for pulsatile flow of blood in a catheterized artery in presence of an axisymmetric stenosis with a velocity slip at the constricted wall is proposed. The expressions for the flow characteristics, velocity profiles, the flow resistance, the wall shear stress, the effective viscosity are obtained in the present analysis. The effects of slip velocity on the blood flow characteristics are shown graphically and discussed briefly.

Cite this paper

nullN. Verma, S. Mishra, S. Siddiqui and R. Gupta, "Effect of Slip Velocity on Blood Flow through a Catheterized Artery,"*Applied Mathematics*, Vol. 2 No. 6, 2011, pp. 764-770. doi: 10.4236/am.2011.26102.

nullN. Verma, S. Mishra, S. Siddiqui and R. Gupta, "Effect of Slip Velocity on Blood Flow through a Catheterized Artery,"

References

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[2] D. A. McDonald, “On Steady Flow through Modeled Vascular Stenosis,” Journal of Biomechanics, Vol. 12, No. 1, 1979, pp. 13-20.

[3] D. F. Young and F. Y. Tsai, “Flow Characteristics in Model of Arterial Stenosis—Steady Flow,” Journal of Biomechanics, Vol. 6, No. 4, 1973, pp. 395-410. doi:10.1016/0021-9290(73)90099-7

[4] D. F. Young, “Effects of a Time-Dependent Stenosis of Flow through a Tube,” Journal of Engineering for Industry, Vol. 90, No. 1, 1968, pp. 248-254.

[5] A. S. Ahmed and D. P. Giddens, “Velocity Measurements in Steady Flow through Axisymmetric Stenosis at Moderate Reynolds Number,” Journal of Biomechanics, Vol. 16, No. 7, 1983, pp. 505-516. doi:10.1016/0021-9290(83)90065-9

[6] M. Siouffi, V. Depleno and R. Pelissier, “Experimental Analysis of Unsteady Flow through Stenosis,” Journal of Biomechanics, Vol. 31, No. 1, 1998, pp. 11-19.

[7] H. Liu and T. Yamaguchi, “Waveform Dependence of Pulsatile Flow in a Stenosed Channel,” Journal of Biomechanical Engineering Transactions ASME, Vol. 123, No. 1, 2001, p. 88.

[8] S. Chakravarty, P. K. Mandal and A. Mandal, “Mathematical Model of Pulsatile Blood Flow in a Distensible Aortic Bifurcation Subject to Body Acceleration,” International Journal of Engineering Sciences, Vol. 38, No. 2, 2000, pp. 215-238. doi:10.1016/S0020-7225(99)00022-1

[9] J. M. Siegel and C. P. Markou, “A Scaling Law for Wall Shear Rate through an Arterial Stenosis,” Journal of Biomechanical Engineering Transactions ASME, Vol. 116, No. 1, 1996, pp. 446-451.

[10] S. U. Siddiqui, N. K. Verma and R. S. Gupta, “A Mathematical Model for Pulsatile Flow of Herschel Bulkley Fluid through Stenosed Arteries,” Journal of Science and Technology, Vol. 5, No. 4, 2010, pp. 49-66.

[11] S. U. Siddiqui, N. K. Verma, S. Mishra and R. S. Gupta, “Mathematical Modelling of Pulsatile Flow of Casson’s Fluid in Arterial Stenosis,” Applied Mathematics and Computation, Vol. 210, No. 1, 2009a, pp. 1-10. doi:10.1016/j.amc.2007.05.070

[12] S. U. Siddiqui, N. K. Verma, S. Mishra and R. S. Gupta, “Mathematical Modelling of Pulsatile Flow of Blood through a Time Dependent Stenotic Blood Vessel,” International Journal of Physical Sciences, Vol. 21, No.1, 2009b, pp. 241-248.

[13] I. Takuji and L. F. R. Guimaraes, “Effect of Non-Newtonian Property of Blood on Flow through a Stenosed Tube,” Fluid Dynamics Research, Vol. 22, No. 5, 1998, pp. 251-264. doi:10.1016/S0169-5983(97)00041-5

[14] R. Roos and P. S. Lykoudis, “The Fluid Mechanics of the Ureter with an Inserted Catheter,” Journal of Fluid Mechanics, Vol. 46, No. 4, 1971, pp. 625-630. doi:10.1017/S0022112071000752

[15] D. A. McDonald, “Pulsatile Flow in a Catheterized Artery,” Journal of Biomechanics, Vol. 19, No. 3, 1986, pp. 239-249. doi:10.1016/0021-9290(86)90156-9

[16] G. T. Karahalios, “Some Possible Effects of a Catheter on the Arterial Wall,” Medical Physiology, Vol. 17, No. 5, 1990, pp. 922-925. doi:10.1118/1.596448

[17] R. K. Dash, G. Jayaraman and K. N. Mehta, “Estimation of Increased Flow Resistance in a Narrow Catheterized Artery—A Theoretical Model,” Journal of Biomechanics, Vol. 29, No. 7, 1996, pp. 917-930. doi:10.1016/0021-9290(95)00153-0

[1] J. H. Forestor and D. F. Young, “Flow through a Converging Diverging Tube and Its Implications in Occlusive Vascular Disease,” Journal of Biomechanics, Vol. 3, No. 2, 1970, pp. 297-316. doi:10.1016/0021-9290(70)90031-X

[2] D. A. McDonald, “On Steady Flow through Modeled Vascular Stenosis,” Journal of Biomechanics, Vol. 12, No. 1, 1979, pp. 13-20.

[3] D. F. Young and F. Y. Tsai, “Flow Characteristics in Model of Arterial Stenosis—Steady Flow,” Journal of Biomechanics, Vol. 6, No. 4, 1973, pp. 395-410. doi:10.1016/0021-9290(73)90099-7

[4] D. F. Young, “Effects of a Time-Dependent Stenosis of Flow through a Tube,” Journal of Engineering for Industry, Vol. 90, No. 1, 1968, pp. 248-254.

[5] A. S. Ahmed and D. P. Giddens, “Velocity Measurements in Steady Flow through Axisymmetric Stenosis at Moderate Reynolds Number,” Journal of Biomechanics, Vol. 16, No. 7, 1983, pp. 505-516. doi:10.1016/0021-9290(83)90065-9

[6] M. Siouffi, V. Depleno and R. Pelissier, “Experimental Analysis of Unsteady Flow through Stenosis,” Journal of Biomechanics, Vol. 31, No. 1, 1998, pp. 11-19.

[7] H. Liu and T. Yamaguchi, “Waveform Dependence of Pulsatile Flow in a Stenosed Channel,” Journal of Biomechanical Engineering Transactions ASME, Vol. 123, No. 1, 2001, p. 88.

[8] S. Chakravarty, P. K. Mandal and A. Mandal, “Mathematical Model of Pulsatile Blood Flow in a Distensible Aortic Bifurcation Subject to Body Acceleration,” International Journal of Engineering Sciences, Vol. 38, No. 2, 2000, pp. 215-238. doi:10.1016/S0020-7225(99)00022-1

[9] J. M. Siegel and C. P. Markou, “A Scaling Law for Wall Shear Rate through an Arterial Stenosis,” Journal of Biomechanical Engineering Transactions ASME, Vol. 116, No. 1, 1996, pp. 446-451.

[10] S. U. Siddiqui, N. K. Verma and R. S. Gupta, “A Mathematical Model for Pulsatile Flow of Herschel Bulkley Fluid through Stenosed Arteries,” Journal of Science and Technology, Vol. 5, No. 4, 2010, pp. 49-66.

[11] S. U. Siddiqui, N. K. Verma, S. Mishra and R. S. Gupta, “Mathematical Modelling of Pulsatile Flow of Casson’s Fluid in Arterial Stenosis,” Applied Mathematics and Computation, Vol. 210, No. 1, 2009a, pp. 1-10. doi:10.1016/j.amc.2007.05.070

[12] S. U. Siddiqui, N. K. Verma, S. Mishra and R. S. Gupta, “Mathematical Modelling of Pulsatile Flow of Blood through a Time Dependent Stenotic Blood Vessel,” International Journal of Physical Sciences, Vol. 21, No.1, 2009b, pp. 241-248.

[13] I. Takuji and L. F. R. Guimaraes, “Effect of Non-Newtonian Property of Blood on Flow through a Stenosed Tube,” Fluid Dynamics Research, Vol. 22, No. 5, 1998, pp. 251-264. doi:10.1016/S0169-5983(97)00041-5

[14] R. Roos and P. S. Lykoudis, “The Fluid Mechanics of the Ureter with an Inserted Catheter,” Journal of Fluid Mechanics, Vol. 46, No. 4, 1971, pp. 625-630. doi:10.1017/S0022112071000752

[15] D. A. McDonald, “Pulsatile Flow in a Catheterized Artery,” Journal of Biomechanics, Vol. 19, No. 3, 1986, pp. 239-249. doi:10.1016/0021-9290(86)90156-9

[16] G. T. Karahalios, “Some Possible Effects of a Catheter on the Arterial Wall,” Medical Physiology, Vol. 17, No. 5, 1990, pp. 922-925. doi:10.1118/1.596448

[17] R. K. Dash, G. Jayaraman and K. N. Mehta, “Estimation of Increased Flow Resistance in a Narrow Catheterized Artery—A Theoretical Model,” Journal of Biomechanics, Vol. 29, No. 7, 1996, pp. 917-930. doi:10.1016/0021-9290(95)00153-0