Mechanical loading protocols in tissue engineering (TE) aim to improve the deposition of a properly organized collagen fiber network. In addition to collagen remodeling, these conditioning protocols can result in tissue compaction. Tissue compaction is beneficial to tissue collagen alignment, yet it may lead to a loss of functionality of the TE construct due to changes in geometry after culture. Here, a mathematical model is presented to relate the changes in collagen architecture to the local compaction within a TE small blood vessel, assuming that under static conditions, compaction is the main factor responsible for collagen fiber organization. An existing structurally based model is extended to incorporate volumetric tissue compaction. Subsequently, the model is applied to describe the collagen architecture of TE constructs under either strain based or stress based stimulus functions. Our computations indicate that stress based simulations result in a helical collagen fiber distribution along the vessel wall. The helix pitch angle increases from a circumferential direction in the inner wall, over about 45 deg in the middle vessel layer, to a longitudinal direction in the outer wall. These results are consistent with experimental data from TE small diameter blood vessels. In addition, our results suggest a stress dependent remodeling of the collagen, suggesting that cell traction is responsible for collagen orientation. These findings may be of value to design improved mechanical conditioning protocols to optimize the collagen architecture in engineered tissues.
Issue Section:
Research Papers
References
1.
Langer
, R.
, and Vacanti
, J. P.
, 1993, “Tissue Engineering
,” Science
, 260
(5110
), pp. 920
–926
.2.
Butler
, D. L.
, Goldstein
, S. A.
, and Guilak
, F.
, 2000, “Functional Tissue Engineering: The Role of Biomechanics
,” ASME J. Biomech. Eng.
, 122
(6
), pp. 570
–575
.3.
Niklason
, L. E.
, Gao
, J.
, Abbott
, W. M.
, Hirschi
, K. K.
, Houser
, S.
, Marini
, R.
, and Langer
, R.
, 1999, “Functional Arteries Grown in vitro
,” Science
, 284
(5413
), pp. 489
–493
.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. Elasticity
, 61
(1–3
), pp. 1
–48
.5.
Lanir
, Y.
, 1983, “Constitutive-Equations for Fibrous Connective Tissues
,” J. Biomech.
, 16
(1
), pp. 1
–12
.6.
Sacks
, M. S.
, 2003, “Incorporation of Experimentally-Derived Fiber Orientation into a Structural Constitutive Model for Planar-Collagenous Tissues
,” ASME J. Biomech. Eng.
, 125
(2
), pp. 280
–287
.7.
Driessen
, N. J. B.
, Cox
, M. A. J.
, Bouten
, C. V. C.
, and Baaijens
, F. P. T.
, 2008, “Remodelling of the Angular Collagen Fiber Distribution in Cardiovascular Tissues
,” Biomech. Model. Mechanobiol.
, 7
(2
), pp. 93
–103
.8.
Dahl
, S. L. M.
, Vaughn
, M. E.
, and Niklason
, L. E.
, 2007, “An Ultrastructural Analysis of Collagen in Tissue Engineered Arteries
,” Ann. Biomed. Eng.
, 35
(10
), pp. 1749
–1755
.9.
Mol
, A.
, Driessen
, N. J. B.
, Rutten
, M. C. M.
, Hoerstrup
, S. P.
, Bouten
, C. V. C.
, and Baaijens
, F. P. T.
, 2005, “Tissue Engineering of Human Heart Valve Leaflets: A Novel Bioreactor for a Strain-Based Conditioning Approach
,” Ann. Biomed. Eng.
, 33
(12
), pp. 1778
–1788
.10.
Stekelenburg
, M.
, Rutten
, M. C. M.
, Snoeckx
, L. H. E. H.
, and Baaijens
, F. P. T.
, 2009, “Dynamic Straining Combined With Fibrin Gel Cell Seeding Improves Strength of Tissue-Engineered Small-Diameter Vascular Grafts
,” Tissue Eng. Part A
, 15
(5
), pp. 1081
–1089
.11.
Rodriguez
, E. K.
, Hoger
, A.
, and Mcculloch
, A. D.
, 1994, “Stress-Dependent Finite Growth in Soft Elastic Tissues
,” J. Biomech.
, 27
(4
), pp. 455
–467
.12.
Taber
, L. A.
, and Eggers
, D. W.
, 1996, “Theoretical Sudy of Stress-Modulated Growth in the Aorta
,” J. Theor. Biol.
, 180
(4
), pp. 343
–357
.13.
Taber
, L. A.
, 1998, “A Model for Aortic Growth Based on Fluid Shear and Fiber Stresses
,” ASME J. Biomech. Eng.
, 120
(3
), pp. 348
–354
.14.
Ambrosi
, D.
, and Guana
, F.
, 2007, “Stress-Modulated Growth
,” Math. Mech. Solids
, 12
(3
), pp. 319
–342
.15.
Ambrosi
, D.
, and Guillou
, A.
, 2007, “Growth and Dissipation in Biological Tissues
,” Continuum Mech. Thermodyn.
, 19
(5
), pp. 245
–251
.16.
Alford
, P. W.
, Humphrey
, J. D.
, and Taber
, L. A.
, 2008, “Growth and Remodeling in a Thick-Walled Artery Model: Effects of Spatial Variations in Wall Constituents
,” Biomech. Model. Mechanobiol.
, 7
(4
), pp. 245
–262
.17.
Rubbens
, M. P.
, Mol
, A.
, van Marion
, M. H.
, Hanemaaijer
, R.
, Bank
, R. A.
, Baaijens
, F. P. T.
, and Bouten
, C. V. C.
, 2009, “Straining Mode-Dependent Collagen Remodeling in Engineered Cardiovascular Tissue
,” Tissue Eng. Part A
, 15
(4
), pp. 841
–849
.18.
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.
, 127
(3
), pp. 494
–503
.19.
van Oijen
, C. H. G. A.
, 2003, “Mechanics and Design of Fiber-Reinforced Vascular Protheses
,” Ph.D. thesis, Technische Universiteit Eindhoven.20.
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
.21.
Fung
, Y. C.
, Fronek
, K.
, and Patitucci
, P.
, 1979, “Pseudoelasticity of Arteries and the Choice of its Mathematical Expression
,” Am. J. Physiol.
, 237
(5
), pp. H620
–H631
.22.
Chuong
, C. J.
, and Fung
, Y. C.
, 1983, “3-Dimensional Stress-Distribution in Arteries
,” ASME J. Biomech. Eng.
, 105
(3
), pp. 268
–274
.23.
Canham
, P. B.
, Talman
, E. A.
, Finlay
, H. M.
, and Dixon
, J. G.
, 1991, “Medial Collagen Organization in Human Arteries of the Heart and Brain by Polarized-Light Microscopy
,” Connect. Tissue Res.
, 26
(1–2
), pp. 121
–134
.24.
Canham
, P. B.
, Finlay
, H. M.
, and Boughner
, D. R.
, 1997, “Contrasting Structure of the Saphenous Vein and Internal Mammary Artery Used as Coronary Bypass Vessels
,” Cardiovasc. Res.
, 34
(3
), pp. 557
–567
.25.
Wicker
, B. K.
, Hutchens
, H. P.
, Wu
, Q.
, Yeh
, A. T.
, and Humphrey
, J. D.
, 2008, “Normal Basilar Artery Structure and Biaxial Mechanical Behaviour
,” Comput. Methods Biomech. Biomed. Eng.
, 11
(5
), pp. 539
–551
.26.
Bishop
, J. E.
, and Lindahl
, G.
, 1999, “Regulation of Cardiovascular Collagen Synthesis by Mechanical Load
,” Cardiovasc. Res.
, 42
(1
), pp. 27
–44
.27.
MacKenna
, D.
, Summerour
, S. R.
, and Villarreal
, F. J.
, 2000, “Role of Mechanical Factors in Modulating Cardiac Fibroblast Function and Extracellular Matrix Synthesis
,” Cardiovasc. Res.
, 46
(2
), pp. 257
–263
.28.
Stopak
, D.
, and Harris
, A. K.
, 1982, “Connective-Tissue Morphogenesis by Fibroblast Traction. 1. Tissue-Culture Observations
,” Dev. Biol.
, 90
(2
), pp. 383
–398
.29.
Sawhney
, R. K.
, and Howard
, J.
, 2002, “Slow Local Movements of Collagen Fibers by Fibroblasts Drive the Rapid Global Self-Organization of Collagen Gels
,” J. Cell Biol.
, 157
(6
), pp. 1083
–1091
.30.
hlmann Noor
, A. H.
, Martin-Martin
, B.
, Eastwood
, M.
, Khaw
, P. T.
, and Bailly
, M.
, 2007, “Dynamic Protrusive Cell Behaviour Generates Force and Drives Early Matrix Contraction by Fibroblasts
,” Exp. Cell Res.
, 313
(20
), pp. 4158
–4169
.31.
Lam
, M. T.
, Clem
, W. C.
, and Takayama
, S.
, 2008, “Reversible On-Demand Cell Alignment Using Reconfigurable Microtopography
,” Biomaterials
, 29
(11
), pp. 1705
–1712
.32.
Houtchens
, G. R.
, Foster
, M. D.
, Desai
, T. A.
, Morgan
, E. F.
, and Wong
, J. Y.
, 2008, “Combined Effects of Microtopography and Cyclic Strain on Vascular Smooth Muscle Cell Orientation
,” J. Biomech.
, 41
(4
), pp. 762
–769
.33.
Lin
, I. E.
, and Taber
, L. A.
, 1995, “A Model for Stress-Induced Growth in the Developing Hheart
,” ASME J. Biomech. Eng.
, 117
(3
), pp. 343
–349
.34.
Cowin
, S. C.
, 1996, “Strain or Deformation Rate Dependent Finite Growth in Soft Tissues
,” J. Biomech.
, 29
(5
), pp. 647
–649
.35.
Carver
, W.
, Nagpal
, M. L.
, Nachtigal
, M.
, Borg
, T. K.
, and Terracio
, L.
, 1991, “Collagen Expression in Mechanically Stimulated Cardiac Fibroblasts
,” Circ. Res.
, 69
(1
), pp. 116
–122
.36.
Balguid
, A.
, Driessen
, N. J.
, Mol
, A.
, Schmitz
, J. P. J.
, Verheyen
, F.
, Bouten
, C. V. C.
, and Baaijens
, F. P. T.
, 2008, “Stress Related Collagen Ultrastructure in Human Aortic Valves—Implications for Tissue Engineering
,” J. Biomech.
, 41
(12
), pp. 2612
–2617
.37.
Stekelenburg
, M.
, 2006, “Strain-Based Optimization of Hhuman Tissue Engineered Small Diameter Blood Vessels
,” Ph.D. thesis, Technische Universiteit Eindhoven.Copyright © 2011
by American Society of Mechanical Engineers
You do not currently have access to this content.
