Early stage cerebral aneurysms are characterized by the disruption of the internal elastic lamina. The cause of this breakdown is still not understood, but it has been conjectured to be due to fatigue failure and/or by a breakdown in homeostatic mechanisms in the wall arising from some aspect of the local hemodynamics and wall tension. We propose to model this disruption using a structural damage model. It is built on a previously introduced nonlinear, inelastic multi-mechanism model for cerebral arteries (2005, “An Inelastic Multi-Mechanism Constitutive Equation for Cerebral Arterial Tissue,” Biomech. Model. Mechanobiol., 4(4), pp. 235–248), as well as a recent generalization to include the wall anisotropy (2009, “A Structural Multi-Mechanism Constitutive Equation for Cerebral Arterial Tissue,” Int. J. Solids Struct., 46(14–15), pp. 2920–2928). The current model includes subfailure damage of the elastin, represented by changes in the tissue mechanical properties and unloaded reference length. A structural model is used to characterize the gradual degradation, failure of elastin, and recruitment of anisotropic collagen fibers. The collagen fibers are arranged in two helically oriented families with dispersion in their orientation. Available inelastic experimental data for cerebral arteries are used to evaluate the constitutive model. It is then implemented in a commercial finite element analysis package and validated using analytical solutions with representative values for cerebral arterial tissue.
Issue Section:
Research Papers
Keywords:
biomechanics,
blood vessels,
brain,
diseases,
failure analysis,
fatigue,
finite element analysis,
haemodynamics,
proteins,
cerebral arteries,
multi-mechanism,
aneurysms,
structural damage model
Topics:
Damage,
Biological tissues,
Fibers,
Stress,
Aneurysms,
Finite element analysis,
Hemodynamics
1.
Atkinson
, J. L. D.
, Sundt
, T. M.
, Houser
, O. W.
, and Whisnant
, J. P.
, 1989, “Angiographic Frequency of Anterior Circulation Intracranial Aneurysms
,” J. Neurosurg.
0022-3085, 70
, pp. 551
–555
.2.
Inagawa
, T.
, and Hirano
, A.
, 1990, “Autopsy Study of Unruptured Incidental Intracranial Aneurysms
,” Surg. Neurol.
0090-3019, 34
, pp. 361
–365
.3.
Broderick
, J. P.
, Brott
, T. G.
, Duldner
, J. E.
, Tomsick
, T.
, and Leach
, A.
, 1994, “Initial and Recurrent Bleeding Are the Major Causes of Death Following Subarachnoid Hemorrhage
,” Stroke
0039-2499, 25
, pp. 1342
–1347
.4.
Ingall
, T. J.
, Whisnant
, J. P.
, Wiebers
, D. O.
, and O‘Fallon
, W. M.
, 1989, “Has There Been a Decline in Subarachnoid Hemorrhage Mortality?
,” Stroke
0039-2499, 20
, pp. 718
–724
.5.
Scanarini
, M.
, Mingrino
, S.
, Giordano
, R.
, and Baroni
, A.
, 1978, “Hisotological and Ultrastructural Study of Intracranial Saccular Aneurysmal Wall
,” Acta Neurochir. Suppl. (Wien)
0065-1419, 43
, pp. 171
–182
.6.
Stehbens
, W. E.
, 1963, “Histopathology of Cerebral Aneurysms
,” Arch. Neurol.
0003-9942, 8
, pp. 272
–285
.7.
Gao
, L.
, Hoi
, Y.
, Swartz
, D. D.
, Kolega
, J.
, Siddiqui
, A.
, and Meng
, H.
, 2008, “Nascent Aneurysm Formation at the Basilar Terminus Induced by Hemodynamics
,” Stroke
0039-2499, 39
, pp. 2085
–2090
.8.
Hashimoto
, N.
, Kim
, C.
, Kikuchi
, H.
, Kojima
, M.
, Kang
, Y.
, and Hazama
, F.
, 1987, “Experimental Induction of Cerebral Aneurysms in Monkeys
,” J. Neurosurg.
0022-3085, 67
(6
), pp. 903
–905
.9.
Kondo
, S.
, Hashimoto
, N.
, Kikuchi
, H.
, Hazama
, F.
, Nagata
, I.
, and Kataoka
, H.
, 1997, “Cerebral Aneurysms Arising at Nonbranching Sites. An Experimental Study
,” Stroke
0039-2499, 28
(2
), pp. 398
–404
.10.
Morimoto
, M.
, Miyamoto
, S.
, Mizoguchi
, A.
, Kume
, N.
, Kita
, T.
, and Hashimoto
, N.
, 2002, “Mouse Model of Cerebral Aneurysm: Experimental Induction by Renal Hypertension and Local Hemodynamic Changes
,” Stroke
0039-2499, 33
(7
), pp. 1911
–1915
.11.
Meng
, H.
, Swartz
, D. D.
, Wang
, Z.
, Hoi
, Y.
, Kolega
, J.
, Metaxa
, E. M.
, Szymanski
, M. P.
, Yamamoto
, J.
, Sauvageau
, E.
, and Levy
, E. I.
, 2006, “A Model System for Mapping Vascular Responses to Complex Hemodynamics at Arterial Bifurcations In Vivo
,” Neurosurgery
0148-396X, 59
(5
), pp. 1094
–1101
.12.
Meng
, H.
, Wang
, Z.
, Hoi
, Y.
, Gao
, L.
, Metaxa
, E.
, Swartz
, D. D.
, and Kolega
, J.
, 2007, “Complex Hemodynamics at the Apex of an Arterial Bifurcation Induces Vascular Remodeling Resembling Cerebral Aneurysm Initiation
,” Stroke
0039-2499, 38
, pp. 1924
–1931
.13.
Metaxa
, E.
, Tremmel
, M.
, Xiang
, J.
, Kolega
, J.
, Mandelbaum
, M.
, Siddiqui
, A.
, Mocco
, J.
, and Meng
, H.
, 2009, “High Wall Shear Stress and Positive Wall Shear Stress Gradient Trigger the Initiation of Intracranial Aneurysms
,” Proceedings of the ASME 2009 Summer Bioengineering Conference (SBC-2009)
, Lake Tahoe, CA.14.
Scott
, S.
, Ferguson
, G. G.
, and Roach
, M. R.
, 1972, “Comparison of the Elastic Properties of Human Intracranial Arteries and Aneurysms
,” Can. J. Physiol. Pharmacol.
0008-4212, 50
(4
), pp. 328
–332
.15.
Fonck
, E.
, Prod‘hom
, G.
, Roy
, S.
, Augsburger
, L.
, Rüfenacht
, D. A.
, and Stergiopulos
, N.
, 2007, “Effect of Elastin Degradation on Carotid Wall Mechanics as Assessed by a Constituent-Based Biomechanical Model
,” Am. J. Physiol. Heart Circ. Physiol.
0363-6135, 292
, pp. H2754
–H2763
.16.
Canham
, P. B.
, and Ferguson
, G. G.
, 1985, “A Mathematical Model for the Mechanics of Saccular Aneurysms
,” Neurosurgery
0148-396X, 17
(2
), pp. 291
–295
.17.
Hademenos
, G. J.
, Massoud
, T.
, Valentino
, D. J.
, Duckwiler
, G.
, and Viñuela
, F.
, 1994, “A Nonlinear Mathematical Model for the Development and Rupture of Intracranial Saccular Aneurysms
,” Neurol. Res.
0160-6412, 16
(5
), pp. 376
–384
.18.
Hung
, E. J.
, and Botwin
, M. R.
, 1975, “Mechanics of Rupture of Cerebral Saccular Aneurysms
,” J. Biomech.
0021-9290, 8
(6
), pp. 385
–392
.19.
Ryan
, J. M.
, and Humphrey
, J. D.
, 1999, “Finite Element Based Predictions of Preferred Material Symmetries in Saccular Aneurysms
,” Ann. Biomed. Eng.
0090-6964, 27
(5
), pp. 641
–647
.20.
Robertson
, A. M.
, Li
, D.
, and Wulandana
, R.
, 2007, “The Biomechanics of Cerebral Aneurysm Initiation and Development
,” Proceedings of the Seventh International Congress of Future Medical Engineering Based on Bio-Nanotechnology 21st Century Center of Excellence (COE) Program
, Sendai, Japan, pp. 18
–21
.21.
Wulandana
, R.
, and Robertson
, A. M.
, 1999, “Use of a Multi-Mechanism Constitutive Model for Inflation of Cerebral Arteries
,” Proceedings of the First Joint BMES/EMBS Conference Serving Humanity, Advancing Technology
, Atlanta, GA, p. 235
.22.
Wulandana
, R.
, and Robertson
, A. M.
, 2005, “An Inelastic Multi-Mechanism Constitutive Equation for Cerebral Arterial Tissue
,” Biomech. Model. Mechanobiol.
1617-7959, 4
(4
), pp. 235
–248
.23.
Lanir
, Y.
, 1983, “Constitutive Equations for Fibrous Connective Tissues
,” J. Biomech.
0021-9290, 16
(1
), pp. 1
–12
.24.
Holzapfel
, G. A.
, Gasser
, T. C.
, and Ogden
, R. W.
, 2000, “A New Constitutive Framework for Arterial Wall Mechanics and a Comparative Study of Material Models
,” J. Elast.
0374-3535, 61
, pp. 1
–48
.25.
Canham
, P. B.
, Finlay
, H. M.
, Dixon
, J. G.
, Boughner
, D. R.
, and Chen
, A.
, 1989, “Measurements From Light and Polarised Light Microscopy of Human Coronary Arteries Fixed at Distending Pressure
,” Cardiovasc. Res.
0008-6363, 23
(11
), pp. 973
–982
.26.
Finlay
, H. M.
, McCullough
, L.
, and Canham
, P. B.
, 1995, “Three-Dimensional Collagen Organization of Human Brain Arteries at Different Transmural Pressures
,” J. Vasc. Res.
1018-1172, 32
(5
), pp. 301
–312
.27.
Gasser
, T. C.
, Ogden
, R. W.
, and Holzapfel
, G. A.
, 2006, “Hyperelastic Modelling of Arterial Layers With Distributed Collagen Fibre Orientations
,” J. R. Soc. Interface
, 3
(6
), pp. 15
–35
. 1742-568928.
Slaughter
, W. S.
, and Sacks
, M. S.
, 2001, “Modeling Fatigue Damage in Chemically Treated Soft Tissues
,” Key Eng. Mater.
1013-9826, 198–199
, pp. 255
–260
.29.
Avolio
, A.
, Jones
, D.
, and Tafazzoli-Shadpour
, M.
, 1988, “Quantification of Alterations in Structure and Function of Elastin in the Arterial Media
,” Hypertension
0194-911X, 32
, pp. 170
–175
.30.
Li
, D.
, and Robertson
, A. M.
, 2009, “A Structural Multi-Mechanism Constitutive Equation for Cerebral Arterial Tissue
,” Int. J. Solids Struct.
0020-7683, 46
(14–15
), pp. 2920
–2928
.31.
Li
, D.
, and Robertson
, A. M.
, 2008, “A Structural Multi-Mechanism Damage Model for Cerebral Arterial Tissue and Its Finite Element Implementation
,” Proceedings of the ASME 2008 Summer Bioengineering Conference (SBC-2008)
, Marco Island, FL.32.
Simo
, J. C.
, and Ju
, J. W.
, 1987, “Strain- and Stress-Based Continuum Damage Models I. Formulation
,” Int. J. Solids Struct.
0020-7683, 23
, pp. 821
–840
.33.
Inci
, S.
, and Spetzler
, R. F.
, 2000, “Intracranial Aneurysms and Arterial Hypertension: A Review and Hypothesis
,” Surg. Neurol.
0090-3019, 53
, pp. 530
–542
.34.
Stehbens
, W. E.
, 1989, “Etiology of Intracranial Berry Aneurysms
,” J. Neurosurg.
0022-3085, 70
, pp. 823
–831
.35.
Hashimoto
, T.
, Meng
, H.
, and Young
, W. L.
, 2006, “Intracranial Aneurysms: Links Among Inflammation, Hemodynamics and Vascular Remodeling
,” Neurol. Res.
0160-6412, 28
, pp. 372
–380
.36.
Sho
, E.
, Sho
, M.
, Singh
, T. M.
, Nanjo
, H.
, Komatsu
, M.
, Xu
, C.
, Masuda
, H.
, and Zarins
, C. K.
, 2002, “Arterial Enlargement in Response to High Flow Requires Early Expression of Matrix Metalloproteinases to Degrade Extracellular Matrix
,” Exp. Mol. Pathol.
0014-4800, 73
, pp. 142
–153
.37.
Miehe
, C.
, 1995, “Discontinuous and Continuous Damage Evolution in Ogden-Type Large-Strain Elastic Materials
,” Eur. J. Mech. A/Solid.
, 14
, pp. 697
–720
.38.
Zeng
, Z.
, Chung
, B. -J.
, Durka
, M.
, and Robertson
, A. M.
, 2009, “An In Vitro Device for Evaluation of Cellular Response to Flows Found at the Apex of Arterial Bifurcations
,” Advances in Mathematical Fluid Mechanics
, A.
Sequeira
and R.
Rannacher
, eds., Springer-Verlag
, Vienna
, in press; http://www.springer.com/math/applications/book/978-3-642-04067-2http://www.springer.com/math/applications/book/978-3-642-04067-2.39.
De Vita
, R.
, and Slaughter
, W. S.
, 2006, “A Structural Constitutive Model for the Strain Rate-Dependent Behavior of Anterior Cruciate Ligaments
,” Int. J. Solids Struct.
0020-7683, 43
(6
), pp. 1561
–1570
.40.
Herrmann
, L. R.
, 1965, “Elasticity Equations for Incompressible and Nearly Incompressible Materials by a Variational Theorem
,” AIAA J.
0001-1452, 3
, pp. 1896
–1900
.41.
Oden
, J. T.
, and Key
, J. E.
, 1970, “Numerical Analysis of Finite Axisymmetric Deformations of Incompressible Elastic Solids of Revolution
,” Int. J. Solids Struct.
0020-7683, 6
, pp. 497
–518
.42.
Holzapfel
, G. A.
, 2000, Nonlinear Solid Mechanics
, Wiley
, New York
.43.
Ogden
, R. W.
, 1978, Non-Linear Elastic Deformations
, Dover
, New York
.44.
Spencer
, A. J. M.
, 1984, “Constitutive Theory for Strongly Anisotropic Solids
,” Continuum Theory of the Mechanics of Fibre-Reinforced Composites
(CISM Courses and Lectures
Vol. 282
), A. J. M.
Spencer
, ed., Springer-Verlag
, Vienna
, pp. 1
–32
.45.
Li
, D.
, and Robertson
, A. M.
, 2009, “Finite Element Modeling of Cerebral Angioplasty Using a Multi-Mechanism Structural Damage Model
,” Proceedings of the ASME 2009 Summer Bioengineering Conference (SBC-2009)
, Lake Tahoe, CA.46.
Chung
, B. -J.
, and Robertson
, A. M.
, 2003, “A Novel Flow Chamber to Evaluate Endothelial Cell Response to Flow at Arterial Bifurcations
,” Proceedings of the Biomedical Engineering Society (BMES)
, Nashville, TN, Paper No. 6P5.113.47.
Chung
, B. -J.
, 2004, “Studies of Blood Flow in Arterial Bifurcations: From Influence of Hemodynamics on Endothelial Cell Response to Vessel Wall Mechanics
,” Ph.D. thesis, University of Pittsburgh, Pittsburgh, PA.48.
Larkin
, J.
, Barrow
, J.
, Durka
, M.
, Remic
, D.
, Zeng
, Z.
, and Robertson
, A. M.
, 2007, “Design of a Flow Chamber to Explore the Initiation and Development of Cerebral Aneurysms
,” Proceedings of the 2007 Biomedical Engineering Society (BMES) Annual Fall Meeting
, Los Angeles, CA.49.
Sakamoto
, N.
, Ohashi
, T.
, and Sato
, M.
, 2008, “High Shear Stress Induces Production of Matrix Metalloproteinase in Endothelial Cells
,” Proceedings of the ASME 2008 Summer Bioengineering Conference (SBC2008)
, Marco Island, FL.50.
Szymanski
, M. P.
, Metaxa
, E.
, Meng
, H.
, and Kolega
, J.
, 2008, “Endothelial Cell Layer Subjected to Impinging Flow Mimicking the Apex of an Arterial Bifurcation
,” Ann. Biomed. Eng.
0090-6964, 36
(10
), pp. 1681
–1689
.Copyright © 2009
by American Society of Mechanical Engineers
You do not currently have access to this content.
