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A fluid mechanical view on abdominal aortic aneurysms



Abdominal aortic aneurysms are a dilatation of the aorta, localized preferentially above the bifurcation of the iliac arteries, which increases in time. Understanding their localization and growth rate remain two open questions that can have either a biological or a physical origin. In order to identify the respective role of biological and physical processes, we address in this article these questions of the localization and growth using a simplified physical experiment in which water (blood) is pumped periodically (amplitude a, pulsation ω) in an elastic membrane (aorta) (length L, cross-section A0 and elastic wave speed c0) and study the deformation of this membrane while decharging in a rigid tube (iliac artery; hydraulic loss K). We first show that this pulsed flow either leads to a homogenous deformation or inhomogenous deformation depending on the value of the non-dimensional parameter c02/(aLω2K). These different regimes can be related to the aneurysm locations. In the second part, we study the growth of aneurysms and show that they only develop above a critical flow rate which scales as A0c0/ .


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Alexander, J. J. 2004 The pathobiology of aortic aneurysms. J. Surg. Res. 117, 163175.
Carpenter, P. W. & Pedley, T. J. 2003 Flow in Collapsible Tubes and Past Other Highly Complaint Boundaries. Kluwer.
Chandran, K. B. & Yearwood, T. L. 1981 Experimental study of physiological pulsatile flow in a curved tube. J. Fluid Mech. 111, 5985.
Chater, E. & Hutchinson, J. W. 1984 a On the propagation of bulges and buckles. J. Appl. Mech. 51, 269277.
Chater, E. & Hutchinson, J. W. 1984 b Mechanical analogs of coexistent phases. In Phase Transformations and Material Instabilities in Solids, pp. 2136. Academic Press Inc. ISBN 0-12-309770-3.
de Chauliac, G. 1373 La grande chirurgie (ed. Michel, C.). Imprimeur de l'Université de Montpellier.
Cheng, C. P., Herfkens, R. J. & Taylor, C. A. 2003 Abdominal aortic hemodynamic conditions in healthy subjects aged 50–70 at rest and during lower limb exercise: in vivo quantification using MRI. Atherosclerosis 168, 323331.
Frank, O. 1905 Der Puls in den Arterien. Z. Biol. 45, 441553.
Fung, Y. C. 1990 Biomechanics: Motion, Flow, Stress and Growth. Springer.
Fung, Y. C. 1997 Biomechanics: Circulation. Springer.
Gray, H. 1918 Anatomy of the Human Body. Lea and Febiger.
Glagov, S., Rowley, D. A. & Kohut, R. 1961 Atherosclerosis of human aorta and its coronary and renal arteries. Arch. Pathol. Lab. Med. 72, 558568.
Groenink, M., Langevaka, S. E., Vanbavel, Ed., van der Wall, E. E., Mulder, B. J. M., van der Wal, A. C. & Spaan, J. A. E. 1999 The influence of aging and aortic stiffness on permanent dilation and breaking stress of the thoracic descending aorta. Cardiovasc. Res. 43, 471480.
Guirguis, E. M. & Barber, G. G. 1991 The natural history of abdominal aortic aneurysms. Am. J. Surg. 162, 481483.
Hirsch, C. 1989 Numerical Computation of Internal and External Flows. Wiley.
Humphrey, J. D. & Delange, S. L. 2004 An Introduction to Biomechanics (Solids and Fluids, Analysis and Design). Springer.
Ku, D. N. 1997 Blood flow in arteries. Annu. Rev. Fluid Mech. 29, 399434.
Ku, D. N., Zeigler, M. N. & Downing, J. M. 1990 One-dimensional steady inviscid flow through a stenotic collapsible tube. J. Biomech. Engng 112, 444450.
Laennec, R. T. H. 1819 De l'auscultation Médiate ou Traité du Diagnostic des Maladies des Poumons et du Coeur, Fondé Principalement Sur ce Nouveau Moyen d'exploitation. J. A. Brosson & J. S. Chaud.
Lasheras, J. C. 2007 The biomechanics of arterial aneurysms. Annu. Rev. Fluid Mech. 39, 293319.
Li, J. K., Malbin, J., Riffle, R. A. & Noodergraaf, A. 1981 Pulse wave propagation. Circ. Res. 49, 442452.
Lighthill, J. 1975 Mathematical Biofluiddynamics. SIAM.
McAuley, L. M., Fisher, A., Hill, A. B. & Joyce, J. 2002 Les Implants Endovasculaires Comparativement à la Chirurgie Sanglante Dans la Réparation de L'anévrisme de L'aorte Abdominale: Pratique au Canada et Examen Systématique. Rapport Technologique no. 33. Office canadien de coordination de l'évaluation des technologies de la santé.
McDonald, D. A. 1960 Blood Flow in Arteries. Edward Arnold.
McDonald, D. A. 1968 Regional pulse-wave velocity in the arterial tree. J. Appl. Physiol. 24, 7378.
Medynsky, A. O., Holdsworth, D. W., Sherebrin, M. H., Rankin, R. N. & Roach, M. R. 1998 Elastic response of human iliac arteries in-vitro to balloon angioplasty using high-resolution CT1. J. Biomech. 31, 747751.
Olsen, J. H. & Shapiro, A. H. 1967 Large amplitude unsteady flow in liquid-filled elastic tubes. J. Fluid Mech. 29, 513538.
Païdoussis, M. P. 2006 Wave propagation in physiological collapsible tubes and a proposal for a Shapiro number. J. Fluids Struct. 22, 721725.
Paquerot, J. F. & Lambrakos, S. G. 1994 Monovariable representation of blood flow in a large elastic artery. Phys. Rev. E 49, 34323439.
Pedley, T. J. 1980 The Fluid Mechanics of Large Blood Vessels. Cambridge University Press.
Plateau, J. A. F. 1849 Statique expérimentale et théorique des liquides soumis aux seules forces moléculaires. Acad. Sci. Brux. Mem. 23, 5.
Prandtl, L. & Tietjens, O. G. 1957 Applied Hydro and Aeromechanics. Dover.
Rayleigh, Lord. 1879 On the instability of jets. Proc. Lond. Math. Soc. 10, 413.
Reinke, W., Johnson, P. C. & Gaehtgens, P. 1986 Effect of shear rate variation on apparent viscosity of human blood in tubes of 29 to 94 microns diameter. Circ. Res. 59, 124132.
Roberts, J. C., Moses, C. & Wilkins, R. H. 1847 Autopsy studies in atherosclerosis: distribution and severity of atherosclerosis in patients dying without any morphologic evidence of atherosclerotic catastrophe. Circulation 20, 511519.
Savart, F. 1833 Mémoire sur la constitution des veines liquides lancées par des orifices circulaires en mince paroi. Ann. de Chim. 53, 337386.
Shapiro, A. H. 1977 Steady flow in collapsible tubes. ASME J. Biomech. Engng 99, 126147.
Womersley, J. R. 1957 Oscillatory flow in arteries: the constrained elastic tube as a model of arterial flow and pulse transmission. Phys. Med. Biol. 2, 178187.
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A fluid mechanical view on abdominal aortic aneurysms



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