The stability of blood vessels under the lumen blood pressure is essential to the maintenance of normal arterial function. Buckling equations have been established recently for linear and nonlinear elastic artery models with assumed sinusoidal mode shapes. However, the theoretical base for the assumption is not clear. This study established differential equations of artery buckling and then proved that straight arteries bifurcated into sinusoidal mode shapes when buckling occurs. These results set the buckling equation on a solid theoretical foundation.
Issue Section:
Technical Briefs
1.
Han
, H. C.
, 2007, “A Biomechanical Model of Artery Buckling
,” J. Biomech.
0021-9290, 40
(16
), pp. 3672
–3678
.2.
Han
, H. C.
, 2008, “Nonlinear Buckling of Blood Vessels: A Theoretical Study
,” J. Biomech.
0021-9290, 41
(12
), pp. 2708
–2713
.3.
Martinez
, R.
, Fierro
, C. A.
, and Han
, H. C.
, 2008, “Critical Buckling Pressure of Veins
,” ASME 2008 Summer Bioengineering Conference
, Marco Island, FL.4.
Gere
, J. M.
, 2004, “Mechanics of Materials
,” Sixth Ed., Belmont, Ca, Thomson (Brooks/Cole).5.
Aoki
, T.
, and Ku
, D. N.
, 1993, “Collapse of Diseased Arteries With Eccentric Cross Section
,” J. Biomech.
0021-9290, 26
(2
), pp. 133
–142
.6.
Fung
, Y. C.
, 1997, Biomechanics: Circulation
, Springer
, New York
, Chap. 4.7.
Drzewiecki
, G.
, Field
, S.
, Moubarak
, I.
, and Li
, J. K.
, 1997, “Vessel Growth and Collapsible Pressure-Area Relationship
,” Am. J. Physiol.
0002-9513, 273
(4
), pp. H2030
–H2043
.8.
Pedley
, T. J.
, and Luo
, X. Y.
, 1998, “Modelling Flow and Oscillations in Collapsible Tubes
,” Theor. Comput. Fluid Dyn.
0935-4964, 10
, pp. 277
–294
.9.
Fierro
, C. A.
, Johnson
, K.
, and Han
, H. C.
, 2007, “The Critical Buckling Pressure of Arteries
“ ASME 2007 Summer Bioengineering Conference (SBC2007)
, Keystone, CO.10.
Thore
, C. R.
, Anstrom
, J. A.
, Moody
, D. M.
, Challa
, V. R.
, Marion
, M. C.
, and Brown
, W. R.
, 2007, “Morphometric Analysis of Arteriolar Tortuosity in Human Cerebral White Matter of Preterm, Young, and Aged Subjects
,” J. Neuropathol. Exp. Neurol.
0022-3069, 66
(5
), pp. 337
–345
.11.
Metz
, H.
, Murray-Leslie
, R. M.
, Bannister
, R. G.
, Bull
, J. W.
, and Marshall
, J.
, 1961, “Kinking of the Internal Carotid Artery
,” Lancet
0140-6736, 1
, pp. 424
–426
.12.
Weibel
, J.
, and Fields
, W. S.
, 1965, “Tortuosity, Coiling, and Kinking of the Internal Carotid Artery. II. Relationship of Morphological Variation to Cerebrovascular Insufficiency
,” Neurology
0028-3878, 15
, pp. 462
–468
.13.
Cheung
, A. T.
, Ramanujam
, S.
, Greer
, D. A.
, Kumagai
, L. F.
, and Aoki
, T. T.
, 2001, “Microvascular Abnormalities in the Bulbar Conjunctiva of Patients With Type 2 Diabetes Mellitus
,” Endocr. Pract.
, 7
(5
), pp. 358
–363
. 1530-891X14.
Jakob
, M.
, Spasojevic
, D.
, Krogmann
, O. N.
, Wiher
, H.
, Hug
, R.
, and Hess
, O. M.
, 1996, “Tortuosity of Coronary Arteries in Chronic Pressure and Volume Overload
,” Cathet. Cardiovasc. Diagn.
, 38
(1
), pp. 25
–31
. 0098-656915.
Zegers
, E. S.
, Meursing
, B. T.
, Zegers
, E. B.
, and Oude Ophuis
, A. J.
, 2007, “Coronary Tortuosity: A Long and Winding Road
,” Neth. Heart J.
, 15
(5
), pp. 191
–195
. 1568-588816.
Nichols
, W. W.
, and O’Rourke
, M. F.
, 1998, McDonald's Blood Flow in Arteries: Theoretical, Experimental, and Clinical Principles
, 4th ed., Arnold Publisher
, London
, Chap. 16.17.
Moody
, D. M.
, Brown
, W. R.
, Challa
, V. R.
, Ghazi-Birry
, H. S.
, and Reboussin
, D. M.
, 1997, “Cerebral Microvascular Alterations in Aging, Leukoaraiosis, and Alzheimer's Disease
,” Ann. N.Y. Acad. Sci.
0077-8923, 826
, pp. 103
–116
.18.
Hiroki
, M.
, Miyashita
, K.
, and Oda
, M.
, 2002, “Tortuosity of the White Matter Medullary Arterioles Is Related to the Severity of Hypertension
,” Cerebrovasc Dis.
1015-9770, 13
(4
), pp. 242
–250
.19.
Pancera
, P.
, Ribul
, M.
, Presciuttini
, B.
, and Lechi
, A.
, 2000, “Prevalence of Carotid Artery Kinking in 590 Consecutive Subjects Evaluated by Echocolordoppler. Is There a Correlation With Arterial Hypertension?
,” J. Intern Med.
0954-6820, 248
(1
), pp. 7
–12
.20.
Del Corso
, L.
, Moruzzo
, D.
, Conte
, B.
, Agelli
, M.
, Romanelli
, A. M.
, Pastine
, F.
, Protti
, M.
, Pentimone
, F.
, and Baggiani
, G.
, 1998, “Tortuosity, Kinking, and Coiling of the Carotid Artery: Expression of Atherosclerosis or Aging?
,” Angiology
0003-3197, 49
(5
), pp. 361
–371
.Copyright © 2009
by American Society of Mechanical Engineers
You do not currently have access to this content.
