Abstract
The three-dimensional biomechanical behavior of the vascular wall is best described by means of strain energy functions. Significant effort has been devoted lately in the development of structure-based models of the vascular wall, which account for the individual contribution of each major structural component (elastin, collagen, and vascular smooth muscle). However, none of the currently proposed structural models succeeded in simultaneously and accurately describing both the pressure-radius and pressure-longitudinal force curves. We have hypothesized that shortcomings of the current models are, in part, due to unaccounted anisotropic properties of elastin. We extended our previously developed biomechanical model to account for elastin anisotropy. The experimental data were obtained from inflation-extension tests on facial veins of five young white New Zealand rabbits. Tests have been carried out under a fully relaxed state of smooth muscle cells for longitudinal stretch ratios ranging from 100% to 130% of the in vivo length. The experimental data (pressure-radius, pressure-force, and zero-stress-state geometries) provided a complete biaxial mechanical characterization of rabbit facial vein and served as the basis for validating the applicability and accuracy of the new biomechanical model of the venous wall. When only the pressure-radius curves were fitted, both the anisotropic and the isotropic models gave excellent results. However, when both pressure-radius and pressure-force curves are simultaneously fitted, the model with isotropic elastin shows an average weighted residual sum of squares of 8.94 and 23.9 in the outer radius and axial force, respectively, as compared to averages of 6.07 and 4.00, when anisotropic elastin is considered. Both the Alkaike information criterion and Schwartz criterion show that the model with the anisotropic elastin is more successful in predicting the data for a wide range of longitudinal stretch ratios. We conclude that anisotropic description of elastin is required for a full 3D characterization of the biomechanics of the venous wall.
Issue Section:
Research Papers
1.
Vito
, R. P.
, and Dixon
, S. A.
, 2003, “Blood Vessel Constitutive Models-1995-2002
,” Annu. Rev. Biomed. Eng.
1523-9829, 5
, pp. 413
–439
.2.
Fung
, Y. C.
, and Liu
, S. Q.
, 1995, “Determination of the Mechanical Properties of the Different Layers of Blood Vessels In Vivo
,” Proc. Natl. Acad. Sci. U.S.A.
0027-8424, 92
(6
), pp. 2169
–2173
.3.
Silver
, F. H.
, Snowhill
, P. B.
, and Foran
, D. J.
, 2003, “Mechanical Behavior of Vessel Wall: A Comparative Study of Aorta, Vena Cava, and Carotid Artery
,” Ann. Biomed. Eng.
0090-6964, 31
(7
), pp. 793
–803
.4.
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
(1–3
), pp. 1
–48
.5.
Holzapfel
, G. A.
, Gasser
, T. C.
, and Stadler
, M.
, 2002, “A Structural Model for the Viscoelastic Behavior of Arterial Walls: Continuum Formulation and Finite Element Analysis
,” Eur. J. Mech. A/Solids
0997-7538, 21
(3
), pp. 441
–463
.6.
Monos
, E.
, Berczi
, V.
, and Nadasy
, G.
, 1995, “Local Control of Veins: Biomechanical, Metabolic, and Humoral Aspects
,” Physiol. Rev.
0031-9333, 75
(3
), pp. 611
–666
.7.
Zulliger
, M. A.
, Kwak
, N. T. M. R.
, Tsapikouni
, T.
, and Stergiopulos
, N.
, 2002, “Effects of Longitudinal Stretch on VSM Tone and Distensibility of Muscular Conduit Arteries
,” Am. J. Physiol. Heart Circ. Physiol.
0363-6135, 283
(6
), pp. H2599
–H2605
.8.
Marieb
, E. N.
, 2007, Human Anatomy and Physiology
, Pearson Benjamin Cummings
, San Fransisco
.9.
Zulliger
, M. A.
, Fridez
, P.
, Stergiopulos
, N.
, and Hayashi
, K.
, 2004, “A Strain Energy Function for Arteries Accounting for Wall Composition and Structure
,” J. Biomech.
0021-9290, 37
(7
), pp. 989
–1000
.10.
Chuong
, C. J.
, and Fung
, Y. C.
, 1983, “3-Dimensional Stress-Distribution in Arteries
,” ASME J. Biomech. Eng.
0148-0731, 105
(3
), pp. 268
–274
.11.
Takamizawa
, K.
, and Hayashi
, K.
, 1987, “Strain-Energy Density-Function and Uniform Strain Hypothesis for Arterial Mechanics
,” J. Biomech.
0021-9290, 20
(1
), pp. 7
–17
.12.
Zulliger
, M. A.
, Stergiopulos
, N.
, and Rachev
, A.
, 2004, “A Constitutive Formulation of Arterial Mechanics Including Vascular Smooth Muscle Tone
,” Am. J. Physiol. Heart Circ. Physiol.
0363-6135, 287
(3
), pp. H1335
–H1343
.13.
Driessen
, N. J. B.
, Bouten
, C. V. C.
, and Baaijens
, F. P. T.
, 2005, “A Structural Constitutive Model for Collagenous Cardiovascular Tissues Incorporating the Angular Fiber Distribution
,” ASME J. Biomech. Eng.
0148-0731, 127
(3
), pp. 494
–503
.14.
Pasquali Ronchetti
, I.
, Alessandrini
, A.
, Baccarani Contri
, M.
, Fornieri
, C.
, Mori
, G.
, Quaglino
, Jr., D.
, and Valdre
, U.
, 1998, “Study of Elastic Fiber Organization by Scanning Force Microscopy
,” Matrix Biol.
0945-053X, 17
(1
), pp. 75
–83
.15.
Sherebrin
, M. H.
, Song
, S. H.
, and Roach
, M. R.
, 1983, “Mechanical Anisotropy of Purified Elastin From the Thoracic Aorta of Dog and Sheep
,” Can. J. Physiol. Pharmacol.
0008-4212, 61
(6
), pp. 539
–545
.16.
Lillie
, M. A.
, David
, G. J.
, and Gosline
, J. M.
, 1998, “Mechanical Role of Elastin-Associated Microfibrils in Pig Aortic Elastic Tissue
,” Connect. Tissue Res.
0300-8207, 37
(1–2
), pp. 121
–141
.17.
Snowhill
, P.
, and Silver
, F.
, 2005, “A Mechanical Model of Porcine Vascular Tissues-Part II: Stress-Strain and Mechanical Properties of Juvenile Porcine Blood Vessels
,” Cardiovascular Engineering
, 5
(4
), pp. 157
–169
.18.
Clark
, J. M.
, and Glagov
, S.
, 1985, “Transmural Organization of the Arterial Media—The Lamellar Unit Revisited
,” Arteriosclerosis (Dallas)
0276-5047, 5
(1
), pp. 19
–34
.19.
Fung
, Y. C.
, 1990, Biomechanics: Motion, Flow, Stress and Growth
, Springer-Verlag
, New York
.20.
Holzapfel
, G. A.
, and Ogden
, R. W.
, 2003, Biomechanics of Soft Tissue in Cardiovascular Systems
, Springer
, Wien
.21.
Gundiah
, N.
, Ratcliffe
, M. B.
, and Pruitt
, L. A.
, 2007, “Determination of Strain Energy Function for Arterial Elastin: Experiments Using Histology and Mechanical Tests
,” J. Biomech.
0021-9290, 40
(3
), pp. 586
–594
.22.
Lillie
, M. A.
, and Gosline
, J. M.
, 2002, “Unusual Swelling of Elastin
,” Biopolymers
0006-3525, 64
(3
), pp. 115
–126
.23.
Pioletti
, D. P.
, and Rakotomanana
, L. R.
, 2000, “Non-Linear Viscoelastic Laws for Soft Biological Tissues
,” Eur. J. Mech. A/Solids
0997-7538, 19
(5
), pp. 749
–759
.24.
Rockafellar
, R. T.
, 1997, Convex Analysis
, Princeton University Press
, Princeton, NJ
.25.
Landaw
, E. M.
, and DiStefano
, III, J. J.
, 1984, “Multiexponential, Multicompartmental, and Noncompartmental Modeling. II. Data Analysis and Statistical Considerations
,” Am. J. Physiol. Regulatory Integrative Comp. Physiol.
0363-6119, 246
(5
), pp. R665
–R677
.26.
Schulze-Bauer
, C. A. J.
, Mörth
, C.
, and Holzapfel
, G. A.
, 2003, “Passive Biaxial Mechanical Response of Aged Human Iliac Arteries
,” ASME J. Biomech. Eng.
0148-0731, 125
(3
), pp. 395
–406
.27.
Gaballa
, M. A.
, Jacob
, C. T.
, Raya
, T. E.
, Liu
, J.
, Simon
, B.
, and Goldman
, S.
, 1998, “Large Artery Remodeling During Aging: Biaxial Passive and Active Stiffness
,” Hypertension
0194-911X, 32
(3
), pp. 437
–443
.28.
Lichtenstein
, O.
, Safar
, M. E.
, Poitevin
, P.
, and Levy
, B. I.
, 1995, “Biaxial Mechanical Properties of Carotid Arteries From Normotensive and Hypertensive Rats
,” Hypertension
0194-911X, 26
(1
), pp. 15
–19
.29.
Doriot
, P. A.
, and Dorsaz
, P. A.
, 2005, “Estimation of the Axial Wall Strains Induced by an Arterial Stenosis at Peak Flow
,” Med. Phys.
0094-2405, 32
(2
), pp. 360
–368
.30.
Doriot
, P. A.
, 2003, “Estimation of the Supplementary Axial Wall Stress Generated at Peak Flow by an Arterial Stenosis
,” Phys. Med. Biol.
0031-9155, 48
(1
), pp. 127
–138
.31.
Zulliger
, M. A.
, and Stergiopulos
, N.
, 2007, “Structural Strain Energy Function Applied to the Ageing of the Human Aorta
,” J. Biomech.
0021-9290, 40
(14
), pp. 3061
–3069
.32.
Roy
, S.
, Silacci
, P.
, and Stergiopulos
, N.
, 2005, “Biomechanical Proprieties of Decellularized Porcine Common Carotid Arteries
,” Am. J. Physiol. Heart Circ. Physiol.
0363-6135, 289
(4
), pp. H1567
–H1576
.33.
Fonck
, E.
, Prod’hom
, G.
, Roy
, S.
, Augsburger
, L.
, Rufenacht
, D.
, and Stergiopulos
, N.
, 2007, “Effect of Elastin Degredation on Carotid Wall Mechanics as Assessed by a Constituent-Based Biomechanical Model
,” Am. J. Physiol. Heart Circ. Physiol.
0363-6135, 292
(6
), pp. H2754
–H2763
.34.
Milnor
, W. R.
, 1989, Hemodynamics
, Williams and Wilkins
, Baltimore
.35.
Bank
, A. J.
, Wang
, H.
, Holte
, J. E.
, Mullen
, K.
, Shammas
, R.
, and Kubo
, S. H.
, 1996, “Contribution of Collagen, Elastin, and Smooth Muscle to In Vivo Human Brachial Artery Wall Stress and Elastic Modulus
,” Circulation
0009-7322, 94
(12
), pp. 3263
–3270
.36.
Sokolis
, D. P.
, Zarbis
, N.
, Dosios
, T.
, Papalouka
, V.
, Papadimitriou
, L.
, Boudoulas
, H.
, and Karayannacos
, P. E.
, 2005, “Post-Vagotomy Mechanical Characteristics and Structure of the Thoracic Aortic Wall
,” Ann. Biomed. Eng.
0090-6964, 33
(11
), pp. 1504
–1516
.37.
Grut
, W.
, Edwards
, J.
, and Evans
, E. J.
, 1977, “Scanning Electron Microscopy of Freeze-Dried Aortic Elastin
,” J. Microsc.
0022-2720, 110
(3
), pp. 271
–275
.38.
Hoeve
, C. A.
, and Flory
, P. J.
, 1974, “The Elastic Properties of Elastin
,” Biopolymers
0006-3525, 13
(4
), pp. 677
–686
.39.
Dorrington
, K.
, Grut
, W.
, and McCrum
, N. G.
, 1975, “Mechanical State of Elastin
,” Nature (London)
0028-0836, 255
(5508
), pp. 476
–478
.40.
Gosline
, J. M.
, 1980, The Elastic Properties of Rubber-Like Proteins and Highly Extensible Tissues
, Cambridge University Press
, Cambridge
.41.
Pasquali-Ronchetti
, I.
, Fornieri
, C.
, Baccarani-Contri
, M.
, and Quaglino
, D.
, 1995, “Ultrastructure of Elastin
,” Ciba Found Symp.
0300-5208, 192
, pp. 31
–42
.42.
Lu
, Q.
, Ganesan
, K.
, Simionescu
, D. T.
, and Vyavahare
, N. R.
, 2004, “Novel Porous Aortic Elastin and Collagen Scaffolds for Tissue Engineering
,” Biomaterials
0142-9612, 25
(22
), pp. 5227
–5237
.43.
Silver
, F. H.
, Horvath
, I.
, and Foran
, D. J.
, 2001, “Viscoelasticity of the Vessel Wall: The Role of Collagen and Elastic Fibers
,” Crit. Rev. Biomed. Eng.
0278-940X, 29
(3
), pp. 279
–302
.44.
Monson
, K. L.
, Goldsmith
, W.
, Barbaro
, N. M.
, and Manley
, G. T.
, 2005, “Significance of Source and Size in the Mechanical Response of Human Cerebral Blood Vessels
,” J. Biomech.
0021-9290, 38
(4
), pp. 737
–744
.45.
VanDijk
, A. M.
, Wieringa
, P. A.
, van der Meer
, M.
, and Laird
, J. D.
, 1984, “Mechanics of Resting Isolated Single Vascular Smooth Muscle Cells From Bovine Coronary Artery
,” Am. J. Physiol.
0002-9513, 246
(3
), pp. C277
–C287
.Copyright © 2008
by American Society of Mechanical Engineers
You do not currently have access to this content.
