Study of dispersion of drug in blood flow with the impact of chemical reaction through stenosed artery

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Research Paper 13/09/2022
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Study of dispersion of drug in blood flow with the impact of chemical reaction through stenosed artery

Sapna Ratan Shah
Int. J. Biosci. 21(3), 199-208, September 2022.
Copyright Statement: Copyright 2022; The Author(s).
License: CC BY-NC 4.0

Abstract

The present study mathematically examines the dispersion of drugs in blood flow through cosine and sine-shaped stenosed arteries with the impact of chemical reaction where blood has been considered as Herschel-Bulkley blood fluid model. The deposition of cholesterols, fats and lipids plaques on the artery wall causes stenosis and leads to the narrowing of the artery. The stenosis shape and chemical reaction have an imperative impact on the effectiveness of the drug dispersion. The nonlinear differential equations are solved to achieve blood velocity. The dispersion function is gained in this model to generalized dispersion expression. Results show a good agreement with the results without the chemical reaction or stenosis.

Ali N Zaman A, Sajid M, Nieto J, Torres A. 2015. Unsteady non-Newtonian blood flow through a tapered overlapping stenosed catheterized vessel, Mathematical Sciences 269, 94-103. http://dx.doi.org/10.1016/j.mbs.2015.08.018.

Bazrov BM. 2010. Classification of Joints, Russian Engineering Research 30, 399–403. https://doi.org/10.3103/S1068798X10040192.

Biswas D, Laskar RB. 2011. Steady Flow of Blood through a Stenosed Artery: A Non-Newtonian Fluid Model, Assam University Journal of Science and Technology 7(11), 144-153. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.895.8706&rep=rep1&type=pdf

Chakravarty S, Datta A. 1992. Dynamic Response Of Stenotic Blood Flow In Vivo, Mathematical and Computer Modelling 16(2), 3-20. https://www.sciencedirect.com/science/article/pii/0895717792900023

Chakravarty S, Datta A. 1989. Effects Of Stenosis On Arterial Rheology Through A Mathematical Model, Mathematical and Computer Modelling 12, 1601-1612. https://www.sciencedirect.com/science/article/pii/0895717789903361

Chakravarty S. 1987. Effect Of Stenosis On The Flow Behaviour Of Blood In An Artery, International Journal of Engeneering Science 25, 1003-1018. https://doi.org/10.1016/0020-7225(87)90093-0

Damiano J, Bardin T. 2004. Synovial Fluid, Emc-Rhumatologie-Orthopedie 1, 2–16. https://www.sciencedirect.com/science/article/abs/pii/S1762420703000036

Dash RK, Jayaraman G, Mehta KN. 2000. Shear augmented dispersion of a solute in a Casson fluid flowing in a conduit, Annals of Biomedical Engineering 28, 373-385. https://link.springer.com/article/10.1114/1.287

Deheri GH, Patel R, Patel T. 2011. Load Carrying Capacity And Time Height Relation For Squeeze Film Between Rough Porous Rectangular Plates Annals of Faculty Engineering Hunedoara, International Journal of Engineering 9, 33-38. http://annals.fih.upt.ro/pdf-full/2011/ANNALS-2011-1-03.pdf

Echarm S, Kurland G. 1965. Viscometry Of Human Blood For Shear Rates 0-100,00sec-1 Nature 206, 617-618. http://dx.doi.org/10.1038/206617A0

Ellahi R, Rahman SU, Mudassar M, Nadeem Vafai K. 2014. Mathematical Study Of Non Newtonian Micropolar Fluid In Arterial Blood Flow Through Composite Stenosis, Aplied Mathematics And Information Science 8(4), 1567-1573. http://dx.doi.org/10.12785/amis/080410

Forrester JH, Young DF. 1970. Flow Through A Converging Diverging Tube And Its Implications In Occlusive Vascular Disease, Journal of Biomechanics 3, 297-316. http://dx.doi.org/10.1016/0021-9290(70)90031-x.

Fry DL. 1968. Acute Vascular Endothelial Changes Associated With Increased Blood Velocity Gradient, Circulation Research 22, 165-197. http://dx.doi.org/10.1161/01.res.22.2.165.

Gill W, Sankarasubramanian R. 1970. Exact analysis of unsteady convective diffusion Proceedings of the Royal Society A Mathematical, Physical and Engineering Sciences 316(1526), 341-350. https://doi.org/10.1098/rspa.1970.0083

Jaafar NA. 2017. Mathematical Analysis of Herschel-Bulkley Fluid Model for Solute Dispersion in Blood Flow through Narrow Conduits, Phd thesis Universiti Sains Malaysia. http://eprints.usm.my/45470/1/NURUL%20AINI%20JAAFAR.pdf

Jaafar  NA, Yatim YM, Sankar D.  2016. Influence of Chemical Reaction on the Steady Dispersion of Solute in Blood Flow-A Mathematical Model, Far East Journal of Mathematical Sciences, 100(4), 617-642. http://dx.doi.org/10.17654/MS100040617

Jaafar NA, Yatim YM, Sankar DS. 2016. Mathematical analysis for unsteady dispersion of solute with chemical reaction in blood flow AIP. Conference Proceedings 1750(1), 030-033.  https://doi.org/10.1063/1.4954569

Ku DN. 1997 Blood Flow In Arteries, Annual Review Of Fluid Mechanics 29, 399434. https://doi.org/10.1146/annurev.fluid.29.1.399

Kudenatti RB, Murulidhara N, Patil HP. 2013. Numerical Study of Squeeze Film Lubrication Between Porous And Rough Rectangular Plates, Journal of Porous Media 16(3), 183–192. https://doi.org/10.5402/2013/724307

Kumar JV, Raghavendra R. 2015. Effects of Surface Roughness In Squeeze Film Lubrication Of Spherical Bearings, Procedia Engineering 127, 955–962. http://dx.doi.org/10.1016/j.proeng.2015.11.442

Kumar R, Shah SR. 2020 Mathematical Modeling of Blood Flow with the Suspension of Nanoparticles through a Tapered Artery with a Blood Clot. Frontiers in Nanotechnology 2, 596475 1-5. https://doi.org/10.3389/fnano.2020.596475

Kumar V, Shah SR. 2022 A Mathematical study for heat transfer phenomenological processes in human skin International Journal of Mechanical Engineering 7(6), 683-692. https://kalaharijournals.com/resources/JUNE-76.pdf

Kumar P, Shah SR. 2021 A Hydromechanical Perspective to Study the Effect of Body Acceleration through Stenosed Artery International journal of mathematical engineering and management sciences, 6(5), 1381-1390. http://dx.doi.org/10.33889/ijmems.2021.6.5.083

Lee JS, Fung YC. 1970 Flow In Locally Constricted Tubes At Low Reynolds Numbers Joornal of Applied Mechanics 37, 9-16. https://doi.org/10.1115/1.3408496

Miah MAK, Hossain S, Salehin S. 2020. Effects of Severity and Dominance of Viscous Force on Stenosis and Aneurysm during Pulsatile Blood Flow using Computational Modelling CFD Letters 12(8), 35-54. https://doi.org/10.37934/cfdl.12.8.3554

Misra JC, Shit GC. 2006. Blood Flow Through Arteries In A Pathological State: A Theoretical Study, International Journal Of Engineering Science 44(10), 662-671. https://doi.org/10.1016/j.ijengsci.2005.12.011

Misra JC, Shit GC. 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. https://doi.org/10.1142/S0219519407002303

Naduvinamani NB, Fathima ST, Hiremath PS. 2004. On The Squeeze Effect Of Lubricants With Additives Between Rough Porous Rectangular Plates, Journal of Applied Mathematics and Mechanics 84, 825–834.  https://doi.org/10.1002/zamm.200310138

Naduvinamani NB, Savitramma GK. 2013. Squeeze Film Lubrication Between Rough Poroelastic Rectangular Plates With Micropolar Fluid: A Special Reference To The Study Of Synovial Joint Lubrication, Isrn Tribology  2, 1–9. http://dx.doi.org/10.5402/2013/431508

Oka S. 1981. Cardiovascular Hemorheology, Cambridge University Press, London 28.

Petrila T, Tarif D. 2005. Basic Of Fluid Mechanics And Introduction To Computational Fluid Dynamics, Numerical Methods and Algorithms 3, Springer Science U.S.A. http://dl.icdst.org/pdfs/files1/f1687be72537c15e46a5b93cc612696a.pdf

Pustěovská P, Hron J, Málek J, Rajagopal KR. 2010. On The Modeling Of The Synovial Fluid, Advances in Tribology 104957, 1-12. https://doi.org/10.1155/2010/104957

Rana J, Murthy PVSN. 2017. Unsteady solute dispersion in small blood vessels using a two-phase Casson model Proceedings of the Royal Society A Mathematical, Physical and Engineering Sciences 473, 20170427. https://doi.org/10.1098/rspa.2017.0427

Ratchagar NP, Vijaya KR. 2019. Dispersion of solute with chemical reaction in blood flow Bulletin of Pure and Applied Sciences 38(1), 385-395. http://dx.doi.org/10.5958/2320-3226.2019.00042.0

Rana J, Murthy PVSN. 2016. Unsteady solute dispersion in Herschel-Bulkley fluid in a tube with wall absorption. Physics of fluids 28, 111903. https://doi.org/10.1063/1.4967210

Sadique MO, Shah SR. 2022 A Mathematical model to study the effect of PRG4, hyaluronic acid and lubricin on squeeze film characteristics of diseased synovial joint International Journal of Mechanical Engineering 7(6), 832-848. https://kalaharijournals.com/resources/JUNE94.pdf

Shah SR. 2021 Clinical influence of hydroxychloroquine with azithromycin on blood flow through blood vessels for the prevention and Treatment of covid-19 International journal of biology, pharmacy and allied science 10(7), 2195-2204. https://ijbpas.com/pdf/2021/July/MS_IJBPAS_2021_5530.pdf

Thurston GB. 1976. Effects Of Viscoelasticity Of Blood On Wave Propagation In the circulation. Journal of Biomechanics 9, 13-20. https://doi.org/10.1016/0021-9290(76)90134-2

Whitemore RL. 1968. Rheology Of The Circulation, Pergamon Press, Oxford. https://worldcat.org/en/title/598050314

Young DF, Tsai FY. 1973. Flow Characteristics In Models Of Arterial Stenosis- I Steady Flow Journal of Biomechanics 6, 395-411. https://doi.org/10.1016/0021-9290(73)90099-7

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