Pulsatile MHD Flow in an Inclined Catheterized Stenosed Artery with Slip on the Wall

Affiliation(s)

Department of Mathematics, Guru Jambheshwar University of Science & Technology, Hisar, India.

Department of Mathematics, Guru Jambheshwar University of Science & Technology, Hisar, India.

ABSTRACT

Catheter is commonly used by the surgeons for various reasons in the treatment of a patient suffering with cardiovascular diseases. Catheterization increases the mean flow resistance in the arterial blood flow and many other complications are associated with the presence of catheter in the artery. Effects of catheter in stenosed artery can be estimated non-invasively by means of hemo-dynamic indicator-WSS, WSSG, volume flow rate and impedance. The effect of slip at the arterial wall, inclination of the artery and magnetic field on the hemodynamic indicators and flow profiles are computed, presented and discussed through graphs.

Catheter is commonly used by the surgeons for various reasons in the treatment of a patient suffering with cardiovascular diseases. Catheterization increases the mean flow resistance in the arterial blood flow and many other complications are associated with the presence of catheter in the artery. Effects of catheter in stenosed artery can be estimated non-invasively by means of hemo-dynamic indicator-WSS, WSSG, volume flow rate and impedance. The effect of slip at the arterial wall, inclination of the artery and magnetic field on the hemodynamic indicators and flow profiles are computed, presented and discussed through graphs.

Cite this paper

Sharma, M. , Singh, K. and Bansal, S. (2014) Pulsatile MHD Flow in an Inclined Catheterized Stenosed Artery with Slip on the Wall.*Journal of Biomedical Science and Engineering*, **7**, 194-207. doi: 10.4236/jbise.2014.74023.

Sharma, M. , Singh, K. and Bansal, S. (2014) Pulsatile MHD Flow in an Inclined Catheterized Stenosed Artery with Slip on the Wall.

References

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[2] McDonald, D.A. (1960) Blood Flow in Arteries. Arnold, London.

[3] Mazumdar, J.N. (1992) Bio-fluid Mechanics. Word Scientific Press.

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http://dx.doi.org/10.1115/1.3426241

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http://dx.doi.org/10.1016/0021-9290(96)00037-1

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[8] Liu, Z.-R., Xu, G., Chen, Y., Teng, Z.-Z. and Qin, K.-R. (2003) An Analysis Model of Pulsatile Blood Flow in Arteries. Applied Mathematics and Mechanics, 24, 230-240.

http://dx.doi.org/10.1007/BF02437630

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http://dx.doi.org/10.1007/s10483-006-0310-z

[10] Mekheimer, Kh.S. and El Kot, M.A. (2008) Influence of Magnetic Field and Hall Currents on Blood Flow through a Stenotic Artery. Applied Mathematics and Mechanics (English Edition), 29, 1093-1104.

[11] Kanai, H., Lizuka, M. and Sakamotos, K. (1996) One of the Problem in the Measurement of Blood Pressure by Catheterization: Wave Reflection at the Tip of Catheter. Medical & Biological Engineering, 28, 483-496.

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[13] Jones, A.L. (1966) On the Flow of Blood in a Tube. Biorheology, 3, 183-188.

[14] Nubar, Y. (1967) Effects of Slip on the Rheology of a Composite Fluid: Application to Blood Flow. Rheology, 4, 133-150.

[15] Brunn, P. (1975) The Velocity Slip of Polar Fluids. Rheologica Acta, 14, 1039-1054.

http://dx.doi.org/10.1007/BF01515899

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http://dx.doi.org/10.1126/science.155.3769.1554

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http://dx.doi.org/10.1142/S0219519407002303

[19] Ponalgusamy, R. (2007) Blood Flow through an Artery with Mild Stenosis: A Two-Layered Model, Different Shapes of Stenoses and Slip Velocity at the Wall. Journal of Applied Sciences, 7, 1071-1077.

http://dx.doi.org/10.3923/jas.2007.1071.1077

[20] Moreau, R. (1990) Magneto-Hydrodynamics. Kluwer Academic Publishers, Dordrecht.

[21] Kolin, A. (1936) An Electromagnetic Flowmeter: Principle of Method and Its Application to Blood Flow Acceleration , Experimental Biology and Medicine, 35, 53-56.

http://dx.doi.org/10.3181/00379727-35-8854P

[22] Barnothy, M.F. (1964) Biological Effects of Magnetic Fields. Plenum Press, New York.

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[24] Halder, K. and Ghosh, S.N. (1994) Effects of a Magnetic Field on Blood Flow through an Intended Tube in the Presence of Erythrocytes. Indian Journal of Pure and Applied Mathematics, 25, 345-352.

[25] McKay, J.C., Prato, F.S. and Thomas, A.W. (2007) A Literature Review: The Effects of Magnetic Field Explore on Blood Flow and Blood Vessels in the Microvasculature. Bioelectromagnetics, 28, 81-98.

http://dx.doi.org/10.1002/bem.20284

[26] Tzirtzilakis, E.E. (2005) A Mathematical Model for Blood Flow in Magnetic Field. Physics of Fluids, 17, 1-15.

http://dx.doi.org/10.1063/1.1978807

[27] Layek, G.C. and Mukho-padhyay, S. (2008) Numerical Modeling of a Stenosed Artery Using Mathematical Model of Variable Shape. International Journal of Applications and Applied Mathematics, 3, 308-328.

[28] Kumar, S., Sharma, M.K., Singh, K. and Garg, N.R. (2011) MHD Two-Phase Blood Flow through an Artery with Axially Non-Symmetric Stenosis. International Journal of Mathematical Sciences & Engineering Applications (IJMSEA), 5, 63-74.

[29] Mekheimer, Kh.S. (2003) Non-Linear Peristaltic Transport of Magnetohydrodynamic Flow in an Inclined Planar Channel. The Arabian Journal for Science and Engineering, 28, 183-201.

[30] Tashtoush, B. and Magableh, A. (2008) Magnetic Field Effect on Heat Transfer and Fluid Flow Characteristics of Blood Flow in Multi-Stenotic Arteries. Heat and Mass Transfer, 44, 297-304.

http://dx.doi.org/10.1007/s00231-007-0251-x

[31] Cowling, T.G. (1957) Magnetohydrodynamics. Interscience Publishers, New York.

[32] Meng, H., Swartz, D.D., Wang, Z., Hoi, Y., Kolega, J., Metaxa, E.M., Szymanski, M.P., Yamamoto, J., Sauvageau, E. and Levy, E.I. (2006) A Model System for Mapping Vascular Responses to Complex Hemodynamics at Arterial Bifurcations in Vivo. Neurosurgery, 59, 1094-1101.

http://dx.doi.org/10.1227/01.NEU.0000245599.92322.53

[33] Chaichana, T., Sun, Z. and Jewkes, J. (2011) Computation of Hemodynamics in the Left Coronary Artery with Variable Angulations. Journal of Biomechanics, 44, 1869-1878.

http://dx.doi.org/10.1016/j.jbiomech.2011.04.033

[1] Fung, Y.C. (1984) Biodynamics Circulation. Springer-Verlag, New York.

[2] McDonald, D.A. (1960) Blood Flow in Arteries. Arnold, London.

[3] Mazumdar, J.N. (1992) Bio-fluid Mechanics. Word Scientific Press.

[4] Zamir, M. (2005) The Physics of Coronary Blood Flow. Springer, New York.

[5] Young, D.F. (1979) Fluid Mechanics of Arterial Stenoses. Journal of Biomechanical Engineering, 101, 157-175.

http://dx.doi.org/10.1115/1.3426241

[6] Srivastava, V.P. (1996) Two Phase Model of Blood Flow through Stenosed Tubes in the Presence of a Peripheral Layer: Applications, Journal of Biomechanics, 29, 1377-1382.

http://dx.doi.org/10.1016/0021-9290(96)00037-1

[7] Srivastava, V.P. (2002) Particulate Suspension Blood Flow through Stenotic Arteries: Effect of Hematocrit and Stenosis Shape. Indian Journal of Pure and Applied Mathematics, 33, 1353-1360.

[8] Liu, Z.-R., Xu, G., Chen, Y., Teng, Z.-Z. and Qin, K.-R. (2003) An Analysis Model of Pulsatile Blood Flow in Arteries. Applied Mathematics and Mechanics, 24, 230-240.

http://dx.doi.org/10.1007/BF02437630

[9] Yao, L. and Li, D.-Z. (2006) Pressure and Pressure Gradient in an Axisymmetric Rigid Vessel with Stenosis. Applied Mathematics and Mechanics (English Edition), 27, 347-351.

http://dx.doi.org/10.1007/s10483-006-0310-z

[10] Mekheimer, Kh.S. and El Kot, M.A. (2008) Influence of Magnetic Field and Hall Currents on Blood Flow through a Stenotic Artery. Applied Mathematics and Mechanics (English Edition), 29, 1093-1104.

[11] Kanai, H., Lizuka, M. and Sakamotos, K. (1996) One of the Problem in the Measurement of Blood Pressure by Catheterization: Wave Reflection at the Tip of Catheter. Medical & Biological Engineering, 28, 483-496.

[12] Back, L.H., Kwack, E.Y. and Back, M.R. (1996) Flow Rate-Pressure Drop Relation in Coronary Angioplasty: Catheter Obstruction Effect. Journal of Biomechanical Engineering, 118, 83-89.

[13] Jones, A.L. (1966) On the Flow of Blood in a Tube. Biorheology, 3, 183-188.

[14] Nubar, Y. (1967) Effects of Slip on the Rheology of a Composite Fluid: Application to Blood Flow. Rheology, 4, 133-150.

[15] Brunn, P. (1975) The Velocity Slip of Polar Fluids. Rheologica Acta, 14, 1039-1054.

http://dx.doi.org/10.1007/BF01515899

[16] Bugliarello, G. and Sevilla, J. (1970) Velocity Distribution and Other Characteristics of Steady and Pulsatile Blood Flow in Fine Glass Tubes. Biorheology, 7, 85-107.

[17] Bennet, L. (1967) Red Cell Slip at a Wall in Vitro. Science, 155, 1554-1556.

http://dx.doi.org/10.1126/science.155.3769.1554

[18] Misra, J.C. and Shit, G.C. (2007) Role of Slip Velocity in Blood Flow through Stenosed Arteries: A Non-Newtonian Model. Journal of Mechanics in Medicine and Biology, 7, 337-353.

http://dx.doi.org/10.1142/S0219519407002303

[19] Ponalgusamy, R. (2007) Blood Flow through an Artery with Mild Stenosis: A Two-Layered Model, Different Shapes of Stenoses and Slip Velocity at the Wall. Journal of Applied Sciences, 7, 1071-1077.

http://dx.doi.org/10.3923/jas.2007.1071.1077

[20] Moreau, R. (1990) Magneto-Hydrodynamics. Kluwer Academic Publishers, Dordrecht.

[21] Kolin, A. (1936) An Electromagnetic Flowmeter: Principle of Method and Its Application to Blood Flow Acceleration , Experimental Biology and Medicine, 35, 53-56.

http://dx.doi.org/10.3181/00379727-35-8854P

[22] Barnothy, M.F. (1964) Biological Effects of Magnetic Fields. Plenum Press, New York.

[23] Korchevskii, E.M. and Marochnik, L.S. (1965) Magneto Hydrodynamic Version of Movement of Blood. Biophysics, 10, 411-413.

[24] Halder, K. and Ghosh, S.N. (1994) Effects of a Magnetic Field on Blood Flow through an Intended Tube in the Presence of Erythrocytes. Indian Journal of Pure and Applied Mathematics, 25, 345-352.

[25] McKay, J.C., Prato, F.S. and Thomas, A.W. (2007) A Literature Review: The Effects of Magnetic Field Explore on Blood Flow and Blood Vessels in the Microvasculature. Bioelectromagnetics, 28, 81-98.

http://dx.doi.org/10.1002/bem.20284

[26] Tzirtzilakis, E.E. (2005) A Mathematical Model for Blood Flow in Magnetic Field. Physics of Fluids, 17, 1-15.

http://dx.doi.org/10.1063/1.1978807

[27] Layek, G.C. and Mukho-padhyay, S. (2008) Numerical Modeling of a Stenosed Artery Using Mathematical Model of Variable Shape. International Journal of Applications and Applied Mathematics, 3, 308-328.

[28] Kumar, S., Sharma, M.K., Singh, K. and Garg, N.R. (2011) MHD Two-Phase Blood Flow through an Artery with Axially Non-Symmetric Stenosis. International Journal of Mathematical Sciences & Engineering Applications (IJMSEA), 5, 63-74.

[29] Mekheimer, Kh.S. (2003) Non-Linear Peristaltic Transport of Magnetohydrodynamic Flow in an Inclined Planar Channel. The Arabian Journal for Science and Engineering, 28, 183-201.

[30] Tashtoush, B. and Magableh, A. (2008) Magnetic Field Effect on Heat Transfer and Fluid Flow Characteristics of Blood Flow in Multi-Stenotic Arteries. Heat and Mass Transfer, 44, 297-304.

http://dx.doi.org/10.1007/s00231-007-0251-x

[31] Cowling, T.G. (1957) Magnetohydrodynamics. Interscience Publishers, New York.

[32] Meng, H., Swartz, D.D., Wang, Z., Hoi, Y., Kolega, J., Metaxa, E.M., Szymanski, M.P., Yamamoto, J., Sauvageau, E. and Levy, E.I. (2006) A Model System for Mapping Vascular Responses to Complex Hemodynamics at Arterial Bifurcations in Vivo. Neurosurgery, 59, 1094-1101.

http://dx.doi.org/10.1227/01.NEU.0000245599.92322.53

[33] Chaichana, T., Sun, Z. and Jewkes, J. (2011) Computation of Hemodynamics in the Left Coronary Artery with Variable Angulations. Journal of Biomechanics, 44, 1869-1878.

http://dx.doi.org/10.1016/j.jbiomech.2011.04.033