Numerical and Analytical Solution of Low-Density Lipoprotein Deposition in A Curved Arterial Wall Using Multilayer Model
الموضوعات :
1 - Islamic Azad University, Arak Branch
الکلمات المفتاحية: LDL Mass deposition, Atherosclerosis, Curved artery, Multilayer model,
ملخص المقالة :
The transport of macromolecules, such as low-density lipoproteins (LDLs), and their abnormal accumulation within the arterial wall plays an important role in formation and development of atherosclerosis. In this study, the numerical-analytical solution of the LDL mass transfer in lumen-wall of a 3D curved artery is investigated. The governing equations consist of, continuity, momentum conservation and the LDLs mass transfer equations are solved based on appropriate boundary conditions and the results are obtained in the form of main and secondary flow velocity field contours, shear stress profiles, concentration and penetration rate of the LDLs into the wall. In this investigation, a new model of the arterial wall, named multilayer model, was used. According to the results, because of centrifugal forces and formation of secondary flows, an increase in surface concentration and penetration rate at the inner part was seen compared with outer part. Also, the reduction of Reynolds number and curvature ratio will augment the LDLs accumulation at the arterial wall.
[1] Iasiello M, Vafai K, Andreozzi A, Bianco N (2016) Analysis of Non-Newtonian effects on low-density lipoprotein accumulation in an artery. J Biomech 49: 203–209.
[2] Stangeby DK, Ethier CR, (2002) Computational analysis of coupled blood-wall arterial LDL transport. J Biomech Eng 124: 1–8.
[3] Yang N, Vafai K, (2006) Modeling of low-density lipoprotein (LDL) transport in the artery-Effects of hypertension. Int J of Heat and Mass Trans 49: 850–867.
[4] Wang S, Vafai K, (2015) Analysis of low density lipoprotein (LDL) transport within a curved artery. Annal Biomed Eng 43: 1571–1584.
[5] Santra S, Mandal DK, Chakrabarti S, (2018) Effect of pulsatile blood flow on LDL transport in arterial layers. Prog Comput Fluid Dynamics 18: 177–187.
[6] Liu X, Fan Y, Deng X, Zhan F (2011) Effect of non-Newtonian pulsatile blood flow on mass transport in the human aorta. J Biomech 44: 1123–1131.
[7] Wang S, Vafai K (2013) Analysis of the effect of stent emplacement on LDL transport within an artery. Int J of Heat and Mass Trans 64: 1031–1040.
[8] Nematollahi A, Shirani E, Mirzaee I, Sadeghi MR (2012) Numerical simulation of LDL particle mass transport in human carotid artery under steady state condition. Sci Iranica 19: 519–524.
[9] Fazli S, Shirani E, Sadeghi MR (2011) Numerical simulation of LDL mass transfer in a common carotid artery under pulsatile flows. J Biomech 44: 68–76.
[10] Khakpour M, Vafai K (2008) Effects of gender-related geometrical characteristics of aorta-iliac bifurcation on hemodynamics and macromolecule concentration distribution. Int J Heat and Mass Trans 51: 5542–5551.
[11] Prosi M, Zunino P, Perktold K, Quarteroni A (2005) Mathematical and numerical models for transfer of low-density lipoprotein through the arterial walls: a new methodology for the model set up with applications to the study of disturbed luminal flow. J Biomech 38: 903–917.
[12] Fatouraee N, Deng X, De Champlain R, Guidoin R (1998) Concentration polarization of low density lipoprotein (LDL) in the arterial system. Annal New York Academy of Sci 858: 137–146.
[13] Karami F, Hossainpour S, Ghalichi F (2018) Numerical simulation of low-density lipoprotein mass transport in human srterial stenosis-calculation of the filtration velocity. Bio-Med Mat Eng 29: 95–108.
[14] Jesionek K, Kostur M (2015) Effects of shear stress on low-density lipoprotein (LDL) transport in the multi-layered arteries. Int J Heat and Mass Trans 81: 122–129.
[15] Tedqui A, Mallat Z (1999) Atherosclerotic plaque formation. Rev Prat 49: 2081–2086.
[16] Andre P, Baldit SC, Bonneau M, Pigaud G, Hainaud P, Azzam K, Douet L (1996) Which experimental model to choose to study arterial thrombosis and evaluate useful therapeutics?. Haemostasis 26: 55–69.
[17] Xie X, Tan J, Wei D, Lei D, Yin T, Huang J, Qiu J, Tang C, Wang G (2013) In Vitro investigations on the effects of low-density lipoprotein concentration polarization and hemodynamics on atherosclerosis localization in rabbit and zebrafish. J Roy Sci Int DOI: 10.1098/rsif/2012.1053.
[18] Yang N, Vafai K (2008) Low-density lipoprotein (LDL) transport in an artery-A simplified analytical solution. Int J Heat and Mass Trans 51: 497–505.
[19] Nisco GD, Kok AM, Chiastra C, Gallo D, Hoogendoorn A, Migliavacca F, Wentzel JJ, Morbiducci U (2019) The atheroprotective nature of helical flow in coronary arteries. Annal Biomed Eng 47: 519–524.
[20] Roustaei M, Nikmaneshi MR, Firoozabadi B (2018) Simulation of low density lipoprotein (LDL) permeation into multilayer coronary arterial wall: interactive effects of wall shear stress and fluid-structure interaction in hypertension. J Biomech 23: 114–122.
[21] Bukač M, Čanić S, Tambača J, Wang Y (2019) Fluid-structure interaction between pulsatile blood flow and a curved coronary artery on a beating heart: A four stent computational study. Comp Meth Appl Mech Eng 350: 679–700.
[22] Torri R, Oshima M, Kobayashi T, Tagaki K, Tezduyar TE (2009) Fluid-structure interaction modeling of blood flow and cerebral aneurysm: Significance of artery and aneurysm shapes. Comp Meth Appl Mech Eng 198: 3613–3621.
[23] Liu X, Fan Y, Deng X, Zhan F (2011) Effect of non-Newtonian and pulsatile blood flow on mass transport in human aorta. J Biomech 44: 1123–1131.
[24] Deyranlou A, Niazmand H, Sadeghi MR (2015) Low-density lipoprotein accumulation within a carotid artery with multilayer elastic porous wall: Fluid-structure interaction and non-Newtonian considerations. J Biomech 18: 2948–2959.
[25] Iasiello M, Vafai K, Andreozzi A, Bianco N (2017) Analysis of non-Newtonian effects within an aorta-iliac bifurcation region. J Biomech 64: 153–163.
[26] Rabby MG, Razzak A, Molla MM (2013) Pulsatile non-Newtonian blood flow through a model of arterial stenosis. Proc Eng 56: 225–231.
[27] Wada S, Karino T (2002) Theoretical prediction of low-density lipoproteins concentration at the luminal surface of an artery with a multiple bend. Annal Biomed Eng 30: 778–791.
[28] Tamim H, Abbassi A, Fatouraee N (2019) On the effects of straight extremities on low-density lipoprotein transport in the concentration boundary layer of curved arteries. Int J Num Meth Heat Fluid Flow Article in press.
[29] Jesionek K, Kostur M (2015) Effects of shear stress on low-density lipoprotein (LDL) transport in the multi-layered arteries. Int J Heat Mass Trans 81: 122–129.
[30] Nisco GD, Zhang P, Calo K, Liu X, Ponzini R, Bignardi C, Rizzo G, Deng X, Gallo D, Morbiducci U (2018) What is needed to make low-density lipoprotein transport in human aorta computational models suitable to explore links to atherosclerosis? Impact of initial and inflow boundary conditions. J Biomech 8: 33–42.
[31] Akbar NC (2016) Non-Newtonian model study for blood flow through a tapered artery with a stenosis. Alex Eng 55: 321–329.
[32] Chung S, Vafai K (2012) Effect of the fluid-structure interactions on low-density lipoprotein transport within a multi-layered arterial wall. J Biomech 45: 371–381.
[33] Chung S, Vafai K (2014) Mechanobiology of low-density lipoprotein transport within an arterial wall-Impact of hyperthermia and coupling effect. J Biomech 47: 137–147.
[34] Tamim H, Abbassi A, Fatouraee N (2020) Effects of pulsatile flow and straight length on low-density lipoprotein transport in a curved arterial wall. Math Meth Appl Sci Article in press.
[35] Chorin JA (1968) Numerical solution of the Navier-Stokes equations. Math Comp 22: 745–129.
