[ Log In | Register]
! Skip Navigation Links
Skip Navigation Links
Image of Journal of Applied Nonlinear Dynamics
ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Unsteady Analysis on Intravenous Drug Delivery and its Uptake in Tissue

Journal of Applied Nonlinear Dynamics 10(3) (2021) 531--546 | DOI:10.5890/JAND.2021.09.012

Reima D. Alsemiry$^{1,2}$, Sarifuddin$^{3}$, Prashanta K. Mandal$^{4}$ , Hamed M. Sayed$^{1,5}$, Norsarahaida Amin$^{2}$

$^{1}$ Department of Mathematics, Faculty of Science, Taibah University, P.O.Box 89, Yanbu 41911, Saudi Arabia

$^{2}$ Department of Mathematical Sciences, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia

$^{3}$ Department of Mathematics, Berhampore College 742101, West Bengal, India

$^{4}$ Department of Mathematics, Visva-Bharati University, Santiniketan 731235, West Bengal, India

$^{5}$ Department of Mathematics, Faculty of Education, Ain Shams University, Roxy 11757, Cairo, Egypt

Download Full Text PDF

 

Abstract

An investigation of drug transport in the lumen as well as in the tissue, in the presence of absorbing interface is studied. The streaming blood is considered as a power-law fluid, whereas, the transport of luminal and tissue drug as a convection-diffusion process. Predicted results show the length of flow separation increases with increasing Re. Simulation predicts the diminishing tissue content with increasing wall absorption parameter. The luminal concentration reaches its quasi steady-state more rapidly than that in the tissue.

References

  1. [1]  Rana, J. and Murthy, P.V.S.N. (2016), Unsteady solute dispersion in Herschel-Bulkley fluid in a tube with wall absorption, Physics of Fluids, 28(11), 111903.
  2. [2]  Sankarasubramanian, R. and Gill, W.N. (1973), Unsteady convective diffusion with interphase mass transfer, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 333(1952), 115-132.
  3. [3]  Dash, R.K., Jayaraman, G., and Mehta, K.N. (2000), Shear augmented dispersion of a solute in a Casson fluid flowing in a conduit, Annals of Biomedical Engineering, 28(4), 373-385.
  4. [4]  Mazumder, B.S. and Mondal, K.K. (2005), On solute transport in oscillatory flow through an annular pipe with a reactive wall and its application to a catheterized artery, Quarterly Journal of Mechanics and Applied Mathematics, 58(3), 349--365.
  5. [5]  Ng, C.O. and Rudraiah, N. (2008), Convective diffusion in steady flow through a tube with a retentive and absorptive wall, Physics of Fluids, 20(7), 073604.
  6. [6]  Paul, S. (2011), Effect of wall oscillation on dispersion in axi-symmetric flows between two coaxial cylinders, ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik, 91 (1), 23-37.
  7. [7]  Rana, J. and Murthy, P.V.S.N. (2016), Unsteady solute dispersion in non-Newtonian fluid flow in a tube with wall absorption, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 472(2193), 20160294.
  8. [8]  Rana, J. and Murthy, P.V.S.N. (2016), Solute dispersion in pulsatile Casson fluid flow in a tube with wall absorption, Journal of Fluid Mechanics, 793, 877-914.
  9. [9]  Debnath, S., Saha, A.K., Mazumder, B., and Roy, A.K. (2017), Dispersion phenomena of reactive solute in a pulsatile flow of three-layer liquids, Physics of Fluids, 29(9), 097107.
  10. [10]  Calo, V.M., Brasher, N.F., Bazilevs, Y., and Hughes, T.J.R. (2008), Multiphysics model for blood flow and drug transport with application to patient-specific coronary artery flow, Computational Mechanics, 43(1), 161-177.
  11. [11]  Hossain, S.S., Hossainy, S.F.A., Bazilevs, Y., Calo, V.M., and Hughes, T.J.R. (2012), Mathematical modeling of coupled drug and drug-encapsulated nanoparticle transport in patient-specific coronary artery walls, Computational Mechanics, 49(2), 213-242.
  12. [12]  Griffiths, I.M., Howell, P.D., and Shipley, R.J. (2013), Control and optimization of solute transport in a thin porous tube, Physics of Fluids, 25(3), 033101.
  13. [13]  Dejam, M., Hassanzadeh, H., and Chen, Z. (2016), Shear dispersion in a capillary tube with a porous wall, Journal of Contaminant Hydrology, 185, 87-104.
  14. [14]  Saltzman, W.M. (2001), Drug delivery: engineering principles for drug therapy, Oxford University Press.
  15. [15]  Ku, D.N. (1997), Blood flow in arteries, Annual Review of Fluid Mechanics, 29(1), 399-434.
  16. [16]  Huckaba, C.E. and Hahn, A.W. (1968), A generalized approach to the modeling of arterial blood flow, Bulletin of Mathematical Biology, 30(4), 645-662.
  17. [17]  Johnston, B.M., Johnston, P.R., Corney, S., and Kilpatrick, D. (2004), Non-Newtonian blood flow in human right coronary arteries: steady state simulations, Journal of Biomechanics, 37(5), 709--720.
  18. [18]  Mandal, P.K. (2005), An unsteady analysis of non-Newtonian blood flow through tapered arteries with a stenosis, International Journal of Non-Linear Mechanics, 40(1), 151-164.
  19. [19]  Ikbal, Md. A., Chakravarty, S. and Mandal, P.K. (2008), An unsteady peristaltic transport phenomenon of non-Newtonian fluid - a generalised approach, Applied Mathematics and Computation, 201(1-2), 16-34.
  20. [20]  Ikbal, Md. A., Chakravarty, S., Wong, K.K.L., Mazumdar, J., and Mandal, P.K. (2009), Unsteady response of non-Newtonian blood flow through a stenosed artery in magnetic field, Journal of Computational and Applied Mathematics, 230(1), 243-259.
  21. [21]  Sarifuddin, Chakravarty, S., and Mandal, P.K. (2009), Effect of asymmetry and roughness of stenosis on non-Newtonian flow past an arterial segment, International Journal of Computational Methods, 6(3), 361-388.
  22. [22]  Bakheet, A., Alnussaiyri, E.A., Ismail, Z., and Amin, N. (2016), Blood flow through an inclined stenosed artery, Applied Mathematical Sciences, 10(5--8), 235-254.
  23. [23]  Bakheet, A., Alnussaiyri, E.A., Ismail, Z. and Amin, N. (2018), Generalized power-law model of magnetohydrodynamic blood flow with heat transfer, Indian Journal of Public Health Research {$\&$ Development}, 9(12), 794-800.
  24. [24]  Harlow, F.H. and Welch, J.E. (1965), Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface, The Physics of Fluids, 8(12), 2182-2189.
  25. [25]  Sarifuddin, Chakravarty, S., Mandal, P.K., and Layek, G.C. (2008), Numerical simulation of unsteady generalized Newtonian blood flow through differently-shaped distensible arterial stenoses, Journal of Medical Engineering {$\&$ Technology}, 32(5), 385-399.
  26. [26]  Mustapha, N., Mandal, P.K., Abdullah, I., Amin, N., and Hayat, T. (2010), Numerical simulation of generalized newtonian blood flow past a couple of irregular arterial, Numerical Methods for Partial Differential Equations, 27(4), 960-981.
  27. [27]  Amsden, A. and Harlow, F. (1970), The SMAC method: a numerical technique for calculating incompressible fluid flows, Los Alamos Scientific Laboratory of the University of California.

Copyright © 2011-2023 L & H Scientific Publishing. All rights reserved. Wildcard SSL Certificates