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HomeDefect and Diffusion ForumDefect and Diffusion Forum Vol. 384Analytical Modeling of a Descending Aorta...

Analytical Modeling of a Descending Aorta Containing Human Blood Flow

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Abstract:

In the recent years, blood flow through an aorta has been the main focus of many investigators. It shows particular interest in analyzing human aortic stiffness and blood flow behavior. Mainly, an unsteady state is applied for incompressible fluid, which is assumed to be newtonian. Artery is considered an elastic tube and the wall boundaries are isotropic. The analytical modeling of blood involves adopting an asymptotic approach according to a small aspect radio, which is inversely proportional to Reynolds number. The wall has been assumed a thin shell, which generates a small axisymmetric vibration. The mathematical model of the wall is developed using the thin shell theory based on geodesic curvature parameter. In the end, the analytical results simulation is applied to have better understanding of the effects of blood flow behavior over the elasticity aortic wall properties.

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Transfer Phenomena in Fluid and Heat Flows V

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Defect and Diffusion Forum (Volume 384)

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117-129

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https://doi.org/10.4028/www.scientific.net/DDF.384.117

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Online since:

May 2018

Authors:

Mehdari Abdessamad*, Mohamed Hasnaoui, Mohamed Agouzoul

Keywords:

Analytical, Blood, Descending Aorta, Human, Modeling

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© 2018 Trans Tech Publications Ltd. All Rights Reserved

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[1] O. D. Makinde, Z. H. Khan, W. A. Khan, M. S. Tshehla, Magneto hemodynamics of nanofluid with heat and mass transfer in a slowly varying symmetrical channel, Inter J. of Eng Rese in Africa. 28 (2017) 118-141.

DOI: 10.4028/www.scientific.net/jera.28.118

[2] J. Prakash, O. D. Makinde, Radiative heat transfer to blood flow through a stenotic artery in the presence of erythrocytes and magnetic field, Lat Ameri Appli Resea. 41 (2011) 273-277.

[3] D. Derong, G. Peiqi, B. Wenboa. Numerical investigation of heat transfer characteristic of fixed planar elastic tube bundles, J of Energy Conversion and Management. 103 (2015) 859-870.

DOI: 10.1016/j.enconman.2015.06.082

[4] T.M. Squires, S.R. Quake. Micro-fluidics: fluid physics at the nanoliter scale , Reviews of modern physics. 77 (2005) 977–1026.

DOI: 10.1103/revmodphys.77.977

[5] L. Zhang, W. Xu, J. Long, Z. Lei. Surface roughening analysis of cold drawn tube based on macro–micro coupling finite element method, J of Materials Processing Technology. 224 (2015) 189-199.

DOI: 10.1016/j.jmatprotec.2015.05.009

[6] A. Matin. Main Gas pipelines: Fracture Resistance Assessment of Pipe, J of Mechanics Engineering and Automation. 3 (2013) 127-140.

[7] A. Milani, A. Abbas. Multiscale modeling and performance analysis of evacuated tube collectors for solar water heaters using diffuse flat reflector , Journal of renewable energy. 86 (2016) 360-374.

DOI: 10.1016/j.renene.2015.08.013

[8] M. Alimohammadi, J.M. Sherwood, M. Karimpour, O.Agu, S. Balabani, V. Diaz-Zuccarini. Aortic dissection simulation models for clinical support: fluid-structure interaction vs rigid wall model, J of BioMedical Engineering. (2015).

DOI: 10.1186/s12938-015-0032-6

[9] R.W. Ogden, C.A.J Schulze-Bauer. Phenomenological and structural aspects of the mechanical response of arteries, J of Mechanics in Medecine and Biology. 46 (2000) 125–140.

DOI: 10.1115/imece2000-1926

[10] A. Ghasemi, N.K.R. Kevlahan. The role of Reynolds number in the fluid-elastic instability of tube arrays, J of Fluids and Structures. 73 (2017) 16-36.

DOI: 10.1016/j.jfluidstructs.2017.05.004

[11] A. Mallios, B. Bouraak, K. Zannis, N. Borenstein, M. Combesa. A New Experimental Animal Protocol for the Direct Viewing of Endovascular Interventions Involving the Ascending Aorta and Aortic Arch, EJVES Extra. 25 (2013) e11-e13.

DOI: 10.1016/j.ejvsextra.2012.11.003

[12] L. Xiao T. Fan, F.A. Sun, X. Deng. Numerical simulation of nucleotide transport in the human thoracic aorta, J of Biomechanics. 46 (2013) 819-827.

DOI: 10.1016/j.jbiomech.2012.11.009

[13] A.C. Benim, A. Nahavandi, A. Assmann, D. Schubert, P. Feindt, S.H. Suh. Simulation of blood flow in human aorta with emphasis on outlet boundary conditions, J of Applied Mathematical Modelling. 35 (2011) 3175–3188.

DOI: 10.1016/j.apm.2010.12.022

[14] O. Prakash, O. D. Makinde, S. P. Singh, N. Jain, D. Kumar, Effects of stenosis on non-Newtonian flow of blood in blood vessels, Inter J. of Biomath. 8 (2015) No. 1, 1550010 (13pages).

DOI: 10.1142/s1793524515500102

[15] R. Patne, D. Gitibabu, V. Shankar. Consistent formulations for stability of fluid flow through deformable channels and tubes, J. of fluid Mechanics. 87(2017) 31-66.

DOI: 10.1017/jfm.2017.485

[16] O. Eugenio, Structural Analysis with The Finite Element Method. Linear Statics. Vol 1. Basic and Solids, First ed., CIMNE, Spain, (2009).

[17] L. John, JR. Giuliani. A general formulation of the thin shell approximation for axisymmetric, hypersonic, hydromagnetic flows, The astrophysical journal. 256 (1982) 624-636.

DOI: 10.1086/159939

[18] V.V. Novozhilov, J.M.R. Radok, Thin Shell Theory, Second ed., Springer, Netherlands, (2014).

[19] L. Serge, Mécanique Des Structures Tome 1: Solides Elastiques, Plaques et Coque, Second ed., Cépaduès, France, (2005).

[20] S. Taha. The flow of Newtonian and power law fluids in elastic tubes, International Journal of Non-Linear Mechanics. 67 (2014) 245–250.

DOI: 10.1016/j.ijnonlinmec.2014.09.013

[21] J. Leibinger, M. Dumbser, U. Iben, I. Wayand. A path-conservative Osher-type scheme for axially symmetric compressible flows in flexible visco-elastic tubes, Journal Applied Numerical Mathematics. 105 (2016) 47-63.

DOI: 10.1016/j.apnum.2016.02.001

[22] H. Demiray. Solitary waves in prestressed elastic tubes, Bulletin of Mathematical Biology. 58 (1996) 939-955.

DOI: 10.1007/bf02459491

[23] M. Alimohammadi, J. M. Sherwood, M. Karimpour, O. Agu, S. Balabani, V. Diaz- Zuccarini. Aortic dissection simulation models for clinical support: fluid-structure interaction vs. rigid wall models, Biomedical Engineering Online. (2015).

DOI: 10.1186/s12938-015-0032-6

[24] R. Fattori, P. Cao , P. De Rango, M. Czerny, A. Evangelista, C. Nienaber, H. Rousseau, M. Shepens. Interdisciplinary expert consensus document on management of type B aortic dissection, J. of the American College of Cardiology. 61(2013).

DOI: 10.1016/j.jacc.2012.11.072

[25] I.M Nordon, R.J. Hinchliffe , I.M Loftus, R.A Morgan, M.M Thompson. Management of acute aortic syndrome and chronic aortic dissection, J. of CardioVascular and Interventional Radiology. 34(2011)890-902.

DOI: 10.1007/s00270-010-0028-3

[26] A.K. Thukkani, S. Kinlay. Endovascular Intervention for Peripheral Artery Disease, Circulation Research. 116 (2015) 1599-1613.

DOI: 10.1161/circresaha.116.303503

[27] P. Luchini, M. Lupo and A. Pozzi. Unsteady stokes flow in a distensible pipe, J. of Applied Mathematics and Mechanics (ZAMM). 71 (1991) 367-378.

DOI: 10.1002/zamm.19910711002

[28] O. D. Makinde, Effect of variable viscosity on arterial blood flow, Far East J. Appl. Maths. 4 (2000) 43-58.

[29] O. D. Makinde, Chebyshev collocation approach to stability of blood flows in a large artery, Afric J. of Biotech. 11 (2012) 9881-9887.

[30] A. Redheuil, W. C. Yu , E. Mousseaux, A. A. Harouni, N. Kachenoura, C. O. Wu, D. Bluemke, J. A.C. lima, Age-related changes in aortic arch geometry: relationship with proximal aortic function and left ventricular mass and remodeling, J Am Coll Cardiol. 58 (2011).

DOI: 10.1016/j.jacc.2011.06.012

[31] P. Reymonda, P. Crosettob, S. Deparisb, A. Quarteronib, N. Stergiopulosa. Physiological simulation of blood flow in the aorta: Comparison of hemodynamic indices as predicted by 3-D FSI, 3-D rigid wall and 1-D models, J. of Medical Engineering & Physics. 35 (2013).

DOI: 10.1016/j.medengphy.2012.08.009

[32] M. Pilarczyk, A. Rygula, A. Kaczor, L. Mateuszuk, E. Maslak, S. Chlopicki, M. Baranska. A novel approach to investigate vascular wall in 3D: Combined Raman spectroscopy and atomic force microscopy for aorta en face imaging. J. of Vibrational Spectroscopy. 75 (2014).

DOI: 10.1016/j.vibspec.2014.09.004

[33] S. Jerez, M. Uh. A flux-limiter method for modeling blood flow in the aorta artery. J. of Mathematical and Computer Modelling. 52 (2010) 962-968.

DOI: 10.1016/j.mcm.2010.01.010

[34] J. Bramwell, A. Hill. The Velocity of the Pulse Wave in Man, Proceedings of the Royal Society of London. 93 (1922) 298-306.

[35] A. Redheuil, W.C. Yu, O.W. Colin, E. Mousseaux, A. Cesar, R. Yan, N. Kachenoura, D. Bluemke, J.A.C. Lima, Reduced Ascending Aortic Strain and Distensibility Earliest Manifestations Of vascular Aging in Humans, American Heart Association Hypertension. (2010).

DOI: 10.1161/hypertensionaha.109.141275

[36] P.C. Tang, P.D. DiMusto, N.C. De oliveira, B.L. Rademacher, J.L. Philip, S.A. Akhter, C.W. Acher, Natural history of the proximal aorta in patients with descending thoracic aortic disease, J. Vascular Surgery. (2017).

DOI: 10.1016/j.jvs.2017.10.062

[37] C.M Garcia-Herrera, D.J. Celentano, M. Cruchaga , F.J. Rojo, J.M. Atienza, G.V. Guinea, Mechanical characterisation of the human thoracic descending aorta: experiments and modelling. J of Comput Methods Biomech Biomed Engin. 15 (2012).

DOI: 10.1080/10255842.2010.520704

[38] C.L. Lake, P.D. Booker, Pediatric cardiac anesthesia, Fourth ed, Lippincott Williams and Wilkins, New York, (2005).

[39] J. Ferruzzi, M.R. Bersi, S. Uman, H. Yanagisawa, J.D. Humphrey. Decreased Elastic Energy Storage, Not Increased Material Stiffness, Characterizes Central Artery Dysfunction in Fibulin-5 Deficiency Independentof Sex, J Biomech Eng. 137(2015).

DOI: 10.1115/1.4029431

[40] F. Cuomo, S. Roccabianca, D. Dillon-Murphy, N. Xiao, J. D. Humphrey, C. A. Figueroa. Effects of age-associated regional changes in aortic stiffness on human hemodynamics revealed by computational modeling, J. of Plos One. 12 (2017).

DOI: 10.1371/journal.pone.0173177

[41] I. Voges, M. Jerosch-Herold, J. Hedderich, E. Pardun, C. Hart, D. D. Gabbert, J. H. Hansen, C. Petko, H. H. Kramer, C. Rickers. Normal values of aortic dimensions, distensibility, and pulse wave velocity in children and young adults: a cross-sectional study, J. of Cardiovascular Magnetic Resonance. 14 (2012).

DOI: 10.1186/1532-429x-14-77

[42] A. Hemmasizadeh, A. Tsamis , R. Cheheltani, S. Assari, A. D'Amore, M. Autieri, M. F. Kiania, N. Pleshko, W. R. Wagner, S. C. Watkins, D. Vorpd, K. Darvisha. Correlations between transmural mechanical and morphological properties in porcine thoracic descending aorta, J. of The Mechanical Behavior of biomedical Materials. 47 (2015).

DOI: 10.1016/j.jmbbm.2015.03.004

[43] A. Benbrahim, J. Gilbert,B. B. Milinazzo, D. F. Warnock, S. Dhara, J. P. Gertler, R. W. Orkin, W. M. Abbott. A compliant tubular device to study the influences of wall strain and fluid shear stress on cells of the vascular wall, J. of Vasc Surg. 20 (1994).

DOI: 10.1016/0741-5214(94)90005-1