Vibration Analysis of Carotid Arteries Conveying Non-Newtonian Blood Flow Surrounding by Tissues

Document Type: Research Paper

Authors

1 Faculty of Mechanical Engineering, University of Tehran, Tehran, Iran

2 Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran --- Institute of Nanoscience & Nanotechnology, University of Kashan, Kashan, Iran

3 Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran

Abstract

The high blood rate that often occurs in arteries may play a role in artery failure and tortuosity which leads to blackouts, transitory ischemic attacks and other diseases. However, vibration and instability analysis of carotid arteries are lacking. The objective of this study is to investigate the vibration and instability of the carotid arteries conveying blood under axial tension with surrounding tissue support. Arteries are modeled as elastic cylindrical vessels based on first order shear deformation theory (FSDT) within an elastic substrate. The elastic medium is simulated with visco-Pasternak foundation. The blood flow in carotid artery is modeled with non-Newtonian fluid based on Carreau, power law and Casson models. Applying energy method, Hamilton principle and differential quadrature method (DQM), the frequency, critical blood velocity and transverse displacement of the carotid arteries are obtained. It can be seen that increasing the tissue stiffness would delay critical blood velocity. The current model provides a powerful tool for further experimental investigation arteries tortuosity. In addition, the dimensionless transverse displacement predicted by Newtonian model is lower than that of non-Newtonian models.
 

Keywords

[1] Pancera P., Ribul M., Presciuttini B., Lechi A., 2000, Prevalence of carotid artery kinking in 590 consecutive subjects evaluated by Echocolordoppler. Is there a correlation with arterial hypertension, Journal of Internal Medicine 248:7-12.
[2] Brown W.R., Moody D.M., Challa V.R., Thore C.R., Anstrom J.A., 2002, Venous collagenosis and arteriolar tortuosity in leukoaraiosis, Journal of the Neurological Sciences 203:159-163.
[3] Hiroki M., Miyashita K., Oda M., 2002, Tortuosity of the white matter medullary arterioles is related to the severity of hypertension, Cerebrovascular Disease 13:242-250.
[4] Aleksic M., Schutz G., Gerth S., Mulch J., 2004, Surgical approach to kinking and coiling of the internal carotid artery, The Journal of Cardiovascular Surgery 45:43-48.
[5] Helisch A., Schaper W., 2003, Arteriogenesis: the development and growth of collateral arteries, Microcirculation 10:83-97.
[6] Weibel J., Fields W.S., 1965, Tortuosity, coiling, and kinking of the internal carotid artery. Ii. relationship of morphological variation to cerebrovascular insufficiency, Neurology 15:462-468.
[7] Jackson Z.S., Dajnowiec D., Gotlieb A.I., Langille B.L., 2005, Partial off-loading of longitudinal tension induces arterial tortuosity, Arteriosclerosis, Thrombosis, and Vascular Biology 25:957-962.
[8] Han H.Ch., 2007, A biomechanical model of artery buckling, Journal of Biomechanics 40:3672-3678.
[9] Han H.Ch., 2008, Nonlinear buckling of blood vessels: A theoretical study, Journal of Biomechanics 41:2708-2713.
[10] Han H.Ch., 2009, Blood vessel buckling within soft surrounding tissue generates tortuosity, Journal of Biomechanics 42:2797-2801.
[11] Han H.Ch., 2012, Mechanical buckling of artery under pulsatile pressure, Journal of Biomechanics 45:1192-1198.
[12] Han H.Ch., 2013, Mechanical buckling of arterioles in collateral development, Journal of Theoretical Biology 316:42-48.
[13] Pedley T.J., 1980, The Fluid Mechanics of Large Blood Vessels, Cambridge University Press, Cambridge.
[14] Cho Y.I., Kensey R., 1991, Effects of the non-newtonian viscosity of blood flows in a diseased arterial vessel. Part 1: steady flows, Biorheology 28:241-262.
[15] Dash R.K., Jayaraman G., Metha K.N., 1999, Flow in a catheterized curved artery with stenosis, Journal of Biomechanics 32:49-61.
[16] Chen J., Lu X.Y., 2004, Numerical investigation of the non-Newtonian blood flow in a bifurcation model with a non-planar branch, Journal of Biomechanics 37:1899-1911.
[17] Barbara Johnston M., Johnston P.R., Corney S., Kilpatrick D., 2004, Non-Newtonian blood flow in human right coronary arteries: steady state simulations, Journal of Biomechanics 37:709-720.
[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 40:151-164.
[19] Sankar D.S., Hemalatha K., 2007, A non-Newtonian fluid flow model for blood flow through a catheterized artery—Steady flow, Applied Mathematical Modeling 31:1847-1864.
[20] Boyd J., Buick J.M., Green S., 2007, Analysis of the Casson and Carreau-Yasuda non-Newtonian blood models in steady and oscillatory flows using the lattice Boltzmann method, Physics of Fluids 19:093103.
[21] Abdollahian M., Ghorbanpour Arani A., Mosallaie Barzoki A.A., Kolahchi R., Loghman A., 2013, Non-local wave propagation in embedded armchair TWBNNTs conveying viscous fluid using DQM, Physica B 418:1-15.
[22] Ghorbanpour Arani A., Abdollahian M., Kolahchi R., Rahmati A.H., 2013, Electro-thermo-torsional buckling of an embedded armchair DWBNNT using nonlocal shear deformable shell model, Composite Part B: Engineering 51:291-299.
[23] Taj M., Zhang J.Q., 2012, Analysis of vibrational behaviors of microtubules embedded within elastic medium by Pasternak model, Biochemical and Biophysical Research Communications 424:89-93.
[24] Ghorbanpour Arani A., Shiravand A., Rahi M., Kolahchi R., 2012, Nonlocal vibration of coupled DLGS systems embedded on Visco-Pasternak foundation, Physica B 407:4123-4131.
[25] Wang L., Ni Q., 2009, A reappraisal of the computational modelling of carbon nanotubes conveying viscous fluid, Mechanics Research Communication 36:833-837.
[26] Ghorbanpour Arani A., Kolahchi R., Khoddami Maraghi Z., 2013, Nonlinear vibration and instability of embedded double-walled boron nitride nanotubes based on nonlocal cylindrical shell theory, Applied Mathematical Modeling 37:7685-7707.
[27] Ghorbanpour Arani A., Kolahchi R., Mosallaie Barzoki A.A., Mozdianfard M.R., Noudeh Farahani S.M., 2012, Elastic foundation effect on nonlinear thermo-vibration of embedded double-layered orthotropic graphene sheets using differential quadrature method, Journal of Mechanical Engineering Science 227:862-879.
[28] Jozwik K., Obidowski D., 2010, Numerical simulations of the blood flow through vertebral arteries, Journal of Biomechanics 43:177-185.
[29] Cho Y.I., Kensey K.R., 1991, Effects of the non-Newtonian viscosity of blood on flows in a diseased arterial vessel. Part 1: steady flows, Biorheology 28:241-262.
[30] Han H.C., Zhao L., Huang M., Hou L.S., Huang Y.T., Kuang Z.B., 1998, Postsurgical changes of the opening angle of canine autogenous vein graft, Journal of Biomechanical Engineering 120:211-216.