Vein maladaptation, leading to poor long-term patency, is a serious clinical problem in patients receiving coronary artery bypass grafts (CABGs) or undergoing related clinical procedures that subject veins to elevated blood flow and pressure. We propose a computational model of venous adaptation to altered pressure based on a constrained mixture theory of growth and remodeling (G&R). We identify constitutive parameters that optimally match biaxial data from a mouse vena cava, then numerically subject the vein to altered pressure conditions and quantify the extent of adaptation for a biologically reasonable set of bounds for G&R parameters. We identify conditions under which a vein graft can adapt optimally and explore physiological constraints that lead to maladaptation. Finally, we test the hypothesis that a gradual, rather than a step, change in pressure will reduce maladaptation. Optimization is used to accelerate parameter identification and numerically evaluate hypotheses of vein remodeling.
Issue Section:
Research Papers
References
1.
Sankaran
, S.
, Esmaily Moghadam
, M.
, Kahn
, A. M.
, Guccione
, J.
, Tseng
, E.
, and Marsden
, A. L.
, 2012
, “Patient-Specific Multiscale Modeling of Blood Flow for Coronary Artery Bypass Graft Surgery
,” Ann. Biomed. Eng.
, 40
(10
), pp. 2228
–2242
.10.1007/s10439-012-0579-32.
Humphrey
, J. D.
, 2002
, Cardiovascular Solid Mechanics: Cells, Tissues, and Organs
, Springer
, NY
.3.
Lüscher
, T. F.
, Turina
, M.
, and Braunwald
, E.
, 1994
, Coronary Artery Graft Disease: Mechanisms and Prevention
, Springer-Verlag, Berlin
, Germany
.4.
Kanterman
, R. Y.
, Vesely
, T. M.
, Pilgram
, T. K.
, Guy
, B. W.
, Windus
, D. W.
, and Picus
, D.
, 1995
, “Dialysis Access Grafts: Anatomic Location of Venous Stenosis and Results of Angioplasty
,” Radiology
, 195
(1
), pp. 135
–139
.10.1148/radiology.195.1.78924545.
Cox
, J. L.
, Chiasson
, D. A.
, and Gotlieb
, A. I.
, 1991
, “Stranger in a Strange Land: The Pathogenesis of Saphenous Vein Graft Stenosis With Emphasis on Structural and Functional Differences Between Veins and Arteries
,” Prog. Cardiovasc. Dis.
, 34
(1
), pp. 45
–68
.10.1016/0033-0620(91)90019-I6.
Sokolis
, D. P.
, 2008
, “Passive Mechanical Properties and Constitutive Modeling of Blood Vessels in Relation to Microstructure
,” Med. Biol. Eng. Comput.
, 46
(12
), pp. 1187
–1199
.10.1007/s11517-008-0362-77.
Shelton
, M. E.
, Forman
, M. E.
, Virmani
, R.
, Bajaj
, A.
, Stoney
, W. S.
, and Atkinson
, J. B.
, 1988
, “A Comparison of Morphologic and Angiographic Findings in Long-Term Internal Mammary Artery and Saphenous Vein Bypass Grafts
,” J.Am. Coll. Cardiol.
, 11
(2
), pp. 297
–307
.10.1016/0735-1097(88)90094-08.
Liu
, S. Q.
, and Fung
, Y. C.
, 1998
, “Changes in the Organization of the Smooth Muscle Cells in Rat Vein Grafts
,” Ann. Biomed. Eng.
, 26
(1
), pp. 86
–95
.10.1114/1.529.
Liu
, S. Q.
, 1998
, “Influence of Tensile Strain on Smooth Muscle Cell Orientation in Rat Blood Vessels
,” ASME J. Biomech. Eng.
, 120
(3
), pp. 313
–320
.10.1115/1.279799610.
Galt
, S. W.
, Zwolak
, R. W.
, Wagner
, R. J.
, and Gilbertson
, J. J.
, 1993
, “Differential Response of Arteries and Vein Grafts to Blood Flow Reduction
,” J. Vasc. Surg.
, 17
(3
), pp. 563
–570
.10.1016/0741-5214(93)90156-G11.
Fillinger
, M.
, Cronenwett
, J. L.
, Besso
, S.
, Walsh
, D. B.
, and Zwolak
, R. M.
, 1994
, “Vein Adaptation to the Hemodynamic Environment of Infrainguinal Grafts
,” J. Vasc. Surg.
, 19
(6
), pp. 970
–979
.10.1016/S0741-5214(94)70208-X12.
Baek
, S.
, Rajagopal
, K. R.
, and Humphrey
, J. D.
, 2006
, “A Theoretical Model of Enlarging Intracranial Fusiform Aneurysms
,” ASME J. Biomech. Eng.
, 128
(1
), pp. 142
–149
.10.1115/1.213237413.
Eberth
, J. F.
, Cardamone
, L.
, and Humphrey
, J. D.
, 1995
, “Evolving Biaxial Mechanical Properties of Mouse Carotid Arteries in Hypertension
,” J. Biomech.
, 21
, pp. 460
–471
.14.
Humphrey
, J. D.
, Baek
, S.
, and Niklason
, L. E.
, 2007
, “Biochemomechanics of Cerebral Vasospasm and Its Resolution: I. A New Hypothesis and Theoretical Framework
,” Ann. Biomed. Eng.
, 35
(9
), pp. 1485
–1497
.10.1007/s10439-007-9321-y15.
Baek
, S.
, Valentin
, A.
, and Humphrey
, J. D.
, 2007
, “Biochemomechanics of Cerebral Vasospasm and Its Resolution: II. Constitutive Relations and Model Simulations
,” Ann. Biomed. Eng.
, 35
(9
), pp. 1498
–1509
.10.1007/s10439-007-9322-x16.
Dobrin
, P.
, Littooy
, F. N.
, and Endean
, E. D.
, 1989
, “Mechanical Factors Predisposing to Intimal Hyperplasia and Medial Thickening in Autogenous Vein Grafts
,” Surgery
, 105
, pp. 393
–400
.17.
Tran-Son-Tay
, R.
, Hwang
, M.
, Garbey
, M.
, Jiang
, Z.
, Ozaki
, C. K.
, and Berceli
, S.
, 2008
, “An Experiment-Based Model of Vein Graft Remodeling Induced by Shear Stress
,” Ann. Biomed. Eng.
, 36
(7
), pp. 1083
–1091
.10.1007/s10439-008-9495-y18.
Lee
, Y. U.
, Naito
, Y.
, Kurobe
, H.
, Breuer
, C. K.
, and Humphrey
, J. D.
, 2013
, “Biaxial Mechanical Properties of the Inferior Vena Cava in C57BL/6 and CB-17 SCID/bg Mice
,” J. Biomech.
, 46
(13
), pp. 2277
–2282
.10.1016/j.jbiomech.2013.06.01319.
Valentin
, A.
, Cardamone
, L.
, Baek
, S.
, and Humphrey
, J. D.
, 2009
, “Complementary Vasoactivity and Matrix Remodelling in Arterial Adaptations to Altered Flow and Pressure
,” J. R. Soc. Interface
, 6
(32
), pp. 293
–306
.10.1098/rsif.2008.025420.
Humphrey
, J. D.
, and Rajagopal
, K. R.
, 2002
, “A Constrained Mixture Model for Growth and Remodeling of Soft Tissues
,” Math. Models Methods Appl. Sci.
, 12
(3
), pp. 407
–430
.10.1142/S021820250200171421.
Gleason
, R. L.
, and Humphrey
, J. D.
, 2004
, “A Mixture Model of Arterial Growth and Remodeling in Hypertension: Altered Muscle Tone and Tissue Turnover
,” J. Vasc. Res.
, 41
(4
), pp. 352
–363
.10.1159/00008069922.
Karšaj
, I.
, and Humphrey
, J. D.
, 2012
, “A Multilayered Wall Model of Arterial Growth and Remodeling
,” Mech. Mater.
, 44
, pp. 110
–119
.10.1016/j.mechmat.2011.05.00623.
Humphrey
, J. D.
, and Taylor
, C. A.
, 2008
, “Intracranial and Abdominal Aortic Aneurysms: Similarities, Differences, and Need for a New Class of Computational Models
,” Ann. Rev. Biomed. Eng.
, 10
, pp. 221
–246
.10.1146/annurev.bioeng.10.061807.16043924.
Sokolis
, D. P.
, 2013
, “Experimental Investigation and Constitutive Modeling of the 3D Histomechanical Properties of Vein Tissue
,” Biomech. Modell. Mechanobiol.
, 12
(3
), pp. 431
–451
.10.1007/s10237-012-0410-y25.
Fung
, Y. C.
, 1993
, Biomechanics: Mechanical Properties of Living Tissues
, Springer-Verlag
, NY
.26.
Rachev
, A.
, and Hayashi
, K.
, 1999
, “Theoretical Study of the Effects of Vascular Smooth Muscle Contraction on Strain and Stress Distributions in Arteries
,” Ann. Biomed. Eng.
, 27
(4
), pp. 459
–468
.10.1114/1.19127.
Zhang
, R.
, Gashev
, A. A.
, Zawieja
, D. C.
, and Davis
, M. J.
, 2007
, “Length–Tension Relationships of Small Arteries, Veins, and Lymphatics From the Rat Mesenteric Microcirculation
,” Am. J. Physiol. Heart Circ. Physiol.
, 292
, pp. H1943
–H1952
.10.1152/ajpheart.01000.200528.
Langille
, B. L.
, 1996
, “Arterial Remodeling: Relation to Hemodynamics
,” Can. J. Physiol. Pharmacol.
, 74
(7
), pp. 834
–841
.10.1139/y96-08229.
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. Phys. Sci. Solids
, 61
, pp. 1
–48
.10.1016/S0022-3697(99)00252-830.
Marsden
, A. L.
, Wang
, M.
, Dennis
, J. E.
, and Moin
, P.
, 2007
, “Trailing-Edge Noise Reduction Using Derivative-Free Optimization and Large-Eddy Simulation
,” J. Fluid Mech.
, 572
, pp. 13
–36
.10.1017/S002211200600323531.
Marsden
, A. L.
, Wang
, M.
, Dennis
, J. E.
, Jr., and Moin
, P.
, 2004
, “Suppression of Vortex-Shedding Noise via Derivative-Free Shape Optimization
,” Phys. Fluids
, 16
(10
), pp. L83
–L86
.10.1063/1.178655132.
Yang
, W.
, Feinstein
, J. A.
, and Marsden
, A. L.
, 2010
, “Constrained Optimization of an Idealized Y-Shaped Baffle for the Fontan Surgery at Rest and Exercise
,” Comput. Methods Appl. Mech. Eng.
, 199
(33–36
), pp. 2135
–2149
.10.1016/j.cma.2010.03.01233.
Booker
, A. J.
, Dennis
, J. E.
, Jr., Frank
, P. D.
, Serafini
, D. B.
, Torczon
, V.
, and Trosset
, M. W.
, 1999
, “A Rigorous Framework for Optimization of Expensive Functions by Surrogates
,” Struct. Optim.
, 17
(1
), pp. 1
–13
.10.1007/BF0119770834.
Marsden
, A. L.
, Wang
, M.
, Dennis
, J. E.
, Jr., and Moin
, P.
, 2004
, “Optimal Aeroacoustic Shape Design Using the Surrogate Management Framework
,” Optim. Eng.
, 5
(2
), pp. 235
–262
.10.1023/B:OPTE.0000033376.89159.6535.
Sankaran
, S.
, and Marsden
, A. L.
, 2010
, “The Impact of Uncertainty on Shape Optimization of Idealized Bypass Graft Models in Unsteady Flow
,” Phys. Fluids
, 22
(12
), p. 121902
.10.1063/1.352944436.
Sankaran
, S.
, Humphrey
, J. D.
, and Marsden
, A. L.
, 2013
, “An Efficient Framework for optimization and Parameter Sensitivity Analysis in Arterial Growth and Remodeling Computations
,” Comput. Methods Appl. Mech. Eng.
, 256
, pp. 200
–210
.10.1016/j.cma.2012.12.01337.
Audet
, C.
, and Dennis
, J. E.
, Jr., 2006
, “Mesh Adaptive Direct Search Algorithms for Constrained Optimization
,” SIAM J. Optim.
, 17
(1
), pp. 188
–217
.10.1137/04060337138.
Nissen
, R.
, Cardinale
, G. J.
, and Udenfriend
, S.
, 1978
, “Increased Turnover of Arterial Collagen in Hypertensive Rats
,” Proc. Natl. Acad. Sci. U.S.A.
, 75
(1
), pp. 451
–453
.10.1073/pnas.75.1.45139.
Xu
, C.
, Lee
, S.
, Singh
, T. M.
, Sho
, E.
, Li
, X.
, Sho
, M.
, Masuda
, H.
, and Zarins
, C. K.
, 2001
, “Molecular Mechanisms of Aortic Wall Remodeling in Response to Hypertension
,” J. Vasc. Surg.
, 33
(3
), pp. 570
–578
.10.1067/mva.2001.11223140.
Sassani
, S. G.
, Theofani
, A.
, Sokrates
, T.
, and Sokolis
, D. P.
, 2013
, “Time-Course of Venous Wall Biomechanical Adaptation in Pressure and Flow-Overload: Assessment by a Microstructure-Based Material Model
,” J. Biomech.
, 46
(14
), pp. 2451
–2462
.10.1016/j.jbiomech.2013.07.01141.
Dajnowiec
, D.
, and Langille
, B.
, 2007
, “Arterial Adaptations to Chronic Changes in Haemodynamic Function: Coupling Vasomotor Tone to Structural Remodelling
,” Clin. Sci.
, 113
, pp. 15
–23
.10.1042/CS2006033742.
Humphrey
, J. D.
, 2008
, “Mechanisms of Arterial Remodeling in Hypertension Coupled Roles of Wall Shear and Intramural Stress
,” Hypertension
, 52
, pp. 195
–200
.10.1161/HYPERTENSIONAHA.107.10344043.
Hwang
, M.
, Berceli
, S. A.
, Garbey
, M.
, Kim
, N. H.
, and Tran-Son-Tay
, R.
, 2012
, “The Dynamics of Vein Graft Remodeling Induced by Hemodynamic Forces: A Mathematical Model
,” Biomech. Modell. Mechanobiol.
, 11
(3–4
), pp. 411
–423
.10.1007/s10237-011-0321-344.
Wagenseil
, J. E.
, and Mecham
, R. P.
, 2009
, “Vascular Extracellular Matrix and Arterial Mechanics
,” Physiol. Rev.
, 89
, pp. 957
–989
.10.1152/physrev.00041.200845.
Kritharis
, E. P.
, Kakisis
, J. D.
, Giagini
, A. T.
, Manos
, T.
, Stergiopulos
, N.
, Tsangaris
, S.
, and Sokolis
, D. P.
, 2010
, “Biomechanical, Morphological and Zero-Stress State Characterization of Jugular Vein Remodeling in Arteriovenous Fistulas for Hemodialysis
,” Biorheology
, 47
, pp. 297
–319
.46.
El-Kurdi
, M. S.
, Hong
, Y. I.
, Stankus
, J. J.
, Soletti
, L.
, Wagner
, W. R.
, and Vorp
, D. A.
, 2008
, “Transient Elastic Support for Vein Grafts Using a Constricting Microfibrillar Polymer Wrap
,” Biomaterials
, 29
(22
), pp. 3213
–3220
.10.1016/j.biomaterials.2008.04.00947.
Liu
, S. Q.
, Moore
, M. M.
, and Yap
, C.
, 2000
, “Prevention of Mechanical Stretch-Induced Endothelial and Smooth Muscle Cell Injury in Experimental Vein Grafts
,” ASME J. Biomech. Eng.
, 122
(1
), pp. 31
–38
.10.1115/1.42962548.
Rhodin
, J. A. G.
, 2011
, “Architecture of the Vessel Wall
,” Compr. Physiol.
, pp. 1
–31
.10.1002/cphy.cp02020149.
Kamiya
, A.
, Bukhari
, R.
, and Togawa
, T.
, 1984
, “Adaptive Regulation of Wall Shear Stress Optimizing Vascular Tree Function
,” Bull. Math. Biol.
, 46
(1
), pp. 127
–137
.10.1007/BF0246372650.
Kudo
, F. A.
, Muto
, A.
, Maloney
, S.
, Pimiento
, J. M.
, Bergaya
, S.
, Fitzgerald
, T. N.
, Westvik
, T. S.
, Frattini
, J.
, Breuer
, C.
, Cha
, C.
, Nishibe
, T.
, Tellides
, G.
, Sessa
, W. C.
, and Dardik
, A.
, 2007
, “Venous Identity Is Lost but Arterial Identity Is Not Gained During Vein Graft Adaptation
,” Arteriosclerosis
, 27
, pp. 1562
–1571
.10.1161/ATVBAHA.107.14303251.
Lüscher
, T. F.
, 1991
, “Vascular Biology of Coronary Bypass Grafts
,” Curr. Opin. Cardiol.
, 6
, pp. 868
–876
.10.1097/00001573-199112000-0000352.
Manos
, T. A.
, Sokolis
, D. P.
, Giagini
, A. T.
, Davos
, C. H.
, Kakisis
, J. D.
, Kritharis
, E. P.
, Stergiopulos
, N.
, Karayannacos
, P. E.
, and Tsangaris
, S.
, 2010
, “Local Hemodynamics and Intimal Hyperplasia at the Venous Side of a Porcine Arteriovenous Shunt
,” IEEE Trans. Inf. Tech. Biomed.
, 14
(3
), pp. 681
–690
.10.1109/TITB.2010.204028853.
Ku
, D. N.
, Giddens
, D. P.
, Zarins
, C. K.
, and Glagov
, S.
, 1985
, “Pulsatile Flow and Atherosclerosis in the Human Carotid Bifurcation. Positive Correlation Between Plaque Location and Low Oscillating Shear Stress
,” Arterioscler., Thromb., Vasc. Biol.
, 5
, pp. 293
–302
.10.1161/01.ATV.5.3.29354.
Karšaj
, I.
, Sorić
, J.
, and Humphrey
, J. D.
, 2010
, “A 3-D Framework for Arterial Growth and Remodeling in Response to Altered Hemodynamics
,” Int. J. Eng. Sci.
, 48
(11
), pp. 1357
–1372
.10.1016/j.ijengsci.2010.06.03355.
Švejcar
, J.
, Přerovsk `y
, I.
, Linhart
, J.
, and Kruml
, J.
, 1962
, “Content of Collagen, Elastin, and Water in Walls of the Internal Saphenous Vein in Man
,” Circ. Res.
, 2
, pp. 296
–300
.10.1161/01.RES.11.2.296Copyright © 2015 by ASME
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