Recent advances in modulating collagen building blocks enable the design and control of the microstructure and functional properties of collagen matrices for tissue engineering and regenerative medicine. However, this is typically achieved by iterative experimentations and that process can be substantially shortened by computational predictions. Computational efforts to correlate the microstructure of fibrous and/or nonfibrous scaffolds to their functionality such as mechanical or transport properties have been reported, but the predictability is still significantly limited due to the intrinsic complexity of fibrous/nonfibrous networks. In this study, a new computational method is developed to predict two transport properties, permeability and diffusivity, based on a microstructural parameter, the specific number of interfibril branching points (or branching points). This method consists of the reconstruction of a three-dimensional (3D) fibrous matrix structure based on branching points and the computation of fluid velocity and solute displacement to predict permeability and diffusivity. The computational results are compared with experimental measurements of collagen gels. The computed permeability was slightly lower than the measured experimental values, but diffusivity agreed well. The results are further discussed by comparing them with empirical correlations in the literature for the implication for predictive engineering of collagen matrices for tissue engineering applications.
Issue Section:
Research Papers
References
1.
Crabb
, R. A. B.
, and Hubel
, A.
, 2008
, “Influence of Matrix Processing on the Optical and Biomechanical Properties of a Corneal Stroma Equivalent
,” Tissue Eng. Part A
, 14
(1
), pp. 173
–182
.10.1089/ten.a.2007.01392.
Roeder
, B. A.
, Kokini
, K.
, Sturgis
, J. E.
, Robinson
, J. P.
, and Voytik-Harbin
, S. L.
, 2002
, “Tensile Mechanical Properties of Three-Dimensional Type I Collagen Extracellular Matrices With Varied Microstructure
,” ASME J. Biomech. Eng.
, 124
(2
), pp. 214
–222
.10.1115/1.14499043.
Bailey
, J. L.
, Critser
, P. J.
, Whittington
, C.
, Kuske
, J. L.
, Yoder
, M. C.
, and Voytik-Harbin
, S. L.
, 2011
, “Collagen Oligomers Modulate Physical and Biological Properties of Three-Dimensional Self-Assembled Matrices
,” Biopolymers
, 95
(2
), pp. 77
–93
.10.1002/bip.215374.
Chen
, M. Y.
, Sun
, Y. L.
, Zhao
, C. F.
, Zobitz
, M. E.
, An
, K. N.
, Moran
, S. L.
, and Amadio
, P. C.
, 2007
, “Factors Related to Contraction and Mechanical Strength of Collagen Gels Seeded With Canine Endotenon Cells
,” J. Biomed. Mater. Res. Part B
, 82B
(2
), pp. 519
–525
.10.1002/jbm.b.307575.
Buehler
, M. J.
, 2006
, “Nature Designs Tough Collagen: Explaining the Nanostructure of Collagen Fibrils
,” Rep. Natl. Acad. Sci. U.S.A.
, 103
(33
), pp. 12285
–12290
.10.1073/pnas.06032161036.
Ramanujan
, S.
, Pluen
, A.
, McKee
, T. D.
, Brown
, E. B.
, Boucher
, Y.
, and Jain
, R. K.
, 2002
, “Diffusion and Convection in Collagen Gels: Implications for Transport in the Tumor Interstitium
,” Biophys. J.
, 83
(3
), pp. 1650
–1660
.10.1016/S0006-3495(02)73933-77.
Tierney
, C. M.
, Haugh
, M. G.
, Liedl
, J.
, Mulcahy
, F.
, Hayes
, B.
, and O′Brien
, F. J.
, 2009
, “The Effects of Collagen Concentration and Crosslink Density on the Biological, Structural and Mechanical Properties of Collagen-GAG Scaffolds for Bone Tissue Engineering
,” J. Mech. Behav. Biomed. Mater.
, 2
(2
), pp. 202
–209
.10.1016/j.jmbbm.2008.08.0078.
Johnson
, E. M.
, Berk
, D. A.
, Jain
, R. K.
, and Deen
, W. M.
, 1996
, “Hindered Diffusion in Agarose Gels: Test of Effective Medium Model
,” Biophys. J.
, 70
(2
), pp. 1017
–1023
.10.1016/S0006-3495(96)79645-59.
Kosto
, K. B.
, and Deen
, W. M.
, 2004
, “Diffusivities of Macromolecules in Composite Hydrogels
,” AIChE J.
, 50
(11
), pp. 2648
–2658
.10.1002/aic.1021610.
Erikson
, A.
, Andersen
, H. N.
, Naess
, S. N.
, Sikorski
, P.
, and Davies
, C. D.
, 2008
, “Physical and Chemical Modifications of Collagen Gels: Impact on Diffusion
,” Biopolymers
, 89
(2
), pp. 135
–143
.10.1002/bip.2087411.
O′Brien
, F. J.
, Harley
, B. A.
, Waller
, M. A.
, Yannas
, I. V.
, Gibson
, L. J.
, and Prendergast
, P. J.
, 2007
, “The Effect of Pore Size on Permeability and Cell Attachment in Collagen Scaffolds for Tissue Engineering
,” Technol. Health Care
, 15
(1
), pp. 3
–17
.12.
Karande
, T. S.
, Ong
, J. L.
, and Agrawal
, C. M.
, 2004
, “Diffusion in Musculoskeletal Tissue Engineering Scaffolds: Design Issues Related to Porosity, Permeability, Architecture, and Nutrient Mixing
,” Ann. Biomed. Eng.
, 32
(12
), pp. 1728
–1743
.10.1007/s10439-004-7825-213.
Al-Munajjed
, A. A.
, Hien
, M.
, Kujat
, R.
, Gleeson
, J. P.
, and Hammer
, J.
, 2008
, “Influence of Pore Size on Tensile Strength, Permeability and Porosity of Hyaluronan-Collagen Scaffolds
,” J. Mater. Sci.-Mater. Med.
, 19
(8
), pp. 2859
–2864
.10.1007/s10856-008-3422-514.
Hollister
, S. J.
, 2005
, “Porous Scaffold Design for Tissue Engineering
,” Nat. Mater.
, 4
(7
), pp. 518
–524
.10.1038/nmat142115.
Drummond
, J. E.
, and Tahir
, M. I.
, 1984
, “Laminar Viscous-Flow Through Regular Arrays of Parallel Solid Cylinders
,” Int. J. Multiphase Flow
, 10
(5
), pp. 515
–540
.10.1016/0301-9322(84)90079-X16.
Bechtold
, G.
, and Ye
, L.
, 2003
, “Influence of Fibre Distribution on the Transverse Flow Permeability in Fibre Bundles
,” Compos. Sci. Technol.
, 63
(14
), pp. 2069
–2079
.10.1016/S0266-3538(03)00112-X17.
Phillips
, R. J.
, 2000
, “A Hydrodynamic Model for Hindered Diffusion of Proteins and Micelles in Hydrogels
,” Biophys. J.
, 79
(6
), pp. 3350
–3353
.10.1016/S0006-3495(00)76566-018.
Tomadakis
, M. M.
, and Robertson
, T. J.
, 2005
, “Viscous Permeability of Random Fiber Structures: Comparison of Electrical and Diffusional Estimates With Experimental and Analytical Results
,” J. Compos. Mater.
, 39
(2
), pp. 163
–188
.10.1177/002199830504643819.
Masoud
, H.
, and Alexeev
, A.
, 2010
, “Permeability and Diffusion Through Mechanically Deformed Random Polymer Networks
,” Macromolecules
, 43
(23
), pp. 10117
–10122
.10.1021/ma102052m20.
Chandran
, P. L.
, Stylianopoulos
, T.
, and Barocas
, V. H.
, 2008
, “Microstructure-Based, Multiscale Modeling for the Mechanical Behavior of Hydrated Fiber Networks
,” Multiscale Model. Simul.
, 7
(1
), pp. 22
–43
.10.1137/07068950421.
Stylianopoulos
, T.
, and Barocas
, V. H.
, 2007
, “Volume-Averaging Theory for the Study of the Mechanics of Collagen Networks
,” Comput. Methods Appl. Mech. Eng.
, 196
(31–32
), pp. 2981
–2990
.10.1016/j.cma.2006.06.01922.
Stylianopoulos
, T.
, Yeckel
, A.
, Derby
, J. J.
, Luo
, X. J.
, Shephard
, M. S.
, Sander
, E. A.
, and Barocas
, V. H.
, 2008
, “Permeability Calculations in Three-Dimensional Isotropic and Oriented Fiber Networks
,” Phys. Fluids
, 20
(12
), p. 123601
.10.1063/1.302147723.
Stylianopoulos
, T.
, Diop-Frimpong
, B.
, Munn
, L. L.
, and Jain
, R. K.
, 2010
, “Diffusion Anisotropy in Collagen Gels and Tumors: The Effect of Fiber Network Orientation
,” Biophys. J.
, 99
(10
), pp. 3119
–3128
.10.1016/j.bpj.2010.08.06524.
Whittington
, C. F.
, Brandner
, E.
, Teo
, K. Y.
, Han
, B.
, Nauman
, E.
, and Voytik-Harbin
, S. L.
, 2013
, “Oligomers Modulate Interfibril Branching and Mass Transport Properties of Collagen Matrices
,” Microsc. Microanal.
, 19
(5
), pp. 1323
–1333
.10.1017/S143192761300193125.
Whittington
, C. F.
, Yoder
, M. C.
, and Voytik-Harbin
, S. L.
, 2013
, “Collagen-Polymer Guidance of Vessel Network Formation and Stabilization by Endothelial Colony Forming Cells In Vitro
,” Macromol. Biosci.
, 13
(9
), pp. 1135
–1149
.10.1002/mabi.20130012826.
Pedersen
, J. A.
, Boschetti
, F.
, and Swartz
, M. A.
, 2007
, “Effects of Extracellular Fiber Architecture on Cell Membrane Shear Stress in a 3D Fibrous Matrix
,” J. Biomech.
, 40
(7
), pp. 1484
–1492
.10.1016/j.jbiomech.2006.06.02327.
Pedersen
, J. A.
, Lichter
, S.
, and Swartz
, M. A.
, 2010
, “Cells in 3D Matrices Under Interstitial Flow: Effects of Extracellular Matrix Alignment on Cell Shear Stress and Drag Forces
,” J. Biomech.
, 43
(5
), pp. 900
–905
.10.1016/j.jbiomech.2009.11.00728.
Swartz
, M. A.
, and Fleury
, M. E.
, 2007
, “Interstitial Flow and Its Effects in Soft Tissues
,” Annu. Rev. Biomed. Eng.
, 9
, pp. 229
–256
.10.1146/annurev.bioeng.9.060906.15185029.
Snyder
, M. A.
, and Vlachos
, D. G.
, 2007
, “Nano-Patterned Standards for Improving the Quantitative Capability of Laser Scanning Confocal Microscopy for Materials Characterization
,” Microporous Mesoporous Mater.
, 102
(1–3
), pp. 101
–110
.10.1016/j.micromeso.2006.12.02830.
Park
, S.
, Seawright
, A.
, Park
, S.
, Craig Dutton
, J.
, Grinnell
, F.
, and Han
, B.
, 2015
, “Preservation of Tissue Microstructure and Functionality During Freezing by Modulation of Cytoskeletal Structure
,” J. Mech. Behav. Biomed. Mater.
, 45C
, pp. 32
–44
.10.1016/j.jmbbm.2015.01.01431.
Johnson
, E. M.
, and Deen
, W. M.
, 1996
, “Hydraulic Permeability of Agarose Gels
,” AIChE J.
, 42
(5
), pp. 1220
–1224
.10.1002/aic.69042050432.
Valentine
, M. T.
, Perlman
, Z. E.
, Gardel
, M. L.
, Shin
, J. H.
, Matsudaira
, P.
, Mitchison
, T. J.
, and Weitz
, D. A.
, 2004
, “Colloid Surface Chemistry Critically Affects Multiple Particle Tracking Measurements of Biomaterials
,” Biophys. J.
, 86
(6
), pp. 4004
–4014
.10.1529/biophysj.103.03781233.
Abouali
, O.
, Nikbakht
, A.
, Ahmadi
, G.
, and Saadabadi
, S.
, 2009
, “Three-Dimensional Simulation of Brownian Motion of Nano-Particles in Aerodynamic Lenses
,” Aerosol Sci. Technol.
, 43
(3
), pp. 205
–215
.10.1080/0278682080258788834.
Roache
, P. J.
, 1997
, “Quantification of Uncertainty in Computational Fluid Dynamics
,” Annu. Rev. Fluid Mech.
, 29
, pp. 123
–160
.10.1146/annurev.fluid.29.1.12335.
Barth
, T. J.
, and Jesperson
, D. C.
, 1989
, “The Design and Application of Upwind Schemes on Unstructured Meshes
,” AIAA
Paper No. 89-0366.10.2514/6.1989-36636.
Kreger
, S. T.
, Bell
, B. J.
, Bailey
, J.
, Stites
, E.
, Kuske
, J.
, Waisner
, B.
, and Voytik-Harbin
, S. L.
, 2010
, “Polymerization and Matrix Physical Properties as Important Design Considerations for Soluble Collagen Formulations
,” Biopolymers
, 93
(8
), pp. 690
–707
.10.1002/bip.2143137.
Nicholson
, C.
, and Tao
, L.
, 1993
, “Hindered Diffusion of High-Molecular-Weight Compounds in Brain Extracellular Microenvironment Measured With Integrative Optical Imaging
,” Biophys. J.
, 65
(6
), pp. 2277
–2290
.10.1016/S0006-3495(93)81324-938.
Thorne
, R. G.
, and Nicholson
, C.
, 2006
, “In Vivo Diffusion Analysis With Quantum Dots and Dextrans Predicts the Width of Brain Extracellular Space
,” Proc. Natl. Acad. Sci. U. S. A.
, 103
(14
), pp. 5567
–5572
.10.1073/pnas.050942510339.
Marelli
, B.
, Ghezzi
, C. E.
, Barralet
, J. E.
, and Nazhat
, S. N.
, 2011
, “Collagen Gel Fibrillar Density Dictates the Extent of Mineralization In Vitro
,” Soft Matter
, 7
(21
), pp. 9898
–9907
.10.1039/c1sm06027a40.
Salami
, S.
, Rondeau-Mouro
, C.
, Barhoum
, M.
, van Duynhoven
, J.
, and Mariette
, F.
, 2014
, “Translational and Rotational Diffusion of Flexible PEG and Rigid Dendrimer Probes in Sodium Caseinate Dispersions and Acid Gels
,” Biopolymers
, 101
(9
), pp. 959
–965
.10.1002/bip.2249241.
Hosseini
, S. A.
, and Tafreshi
, H. V.
, 2010
, “Modeling Permeability of 3-D Nanofiber Media in Slip Flow Regime
,” Chem. Eng. Sci.
, 65
(6
), pp. 2249
–2254
.10.1016/j.ces.2009.12.00242.
Myllyharju
, J.
, and Kivirikko
, K. I.
, 2004
, “Collagens, Modifying Enzymes and Their Mutations in Humans, Flies and Worms
,” Trends Genet.
, 20
(1
), pp. 33
–43
.10.1016/j.tig.2003.11.00443.
Israelowitz
, M.
, Rizvi
, S. W. H.
, Kramer
, J.
, and von Schroeder
, H. P.
, 2005
, “Computational Modeling of Type I Collagen Fibers to Determine the Extracellular Matrix Structure of Connective Tissues
,” Protein Eng. Des. Sel.
, 18
(7
), pp. 329
–335
.10.1093/protein/gzi03744.
Sanjeevi
, R.
, Ramanthan
, N.
, and Viswanathan
, B.
, 1976
, “Pore-Size Distribution in Collagen Fiber Using Water-Vapor Adsorption Studies
,” J. Colloid Interface Sci.
, 57
(2
), pp. 207
–211
.10.1016/0021-9797(76)90194-645.
Boki
, K.
, Kawasaki
, N.
, Minami
, K.
, and Takahashi
, H.
, 1993
, “Structural-Analysis of Collagen-Fibers by Nitrogen Adsorption Method
,” J. Colloid Interface Sci.
, 157
(1
), pp. 55
–59
.10.1006/jcis.1993.115746.
Giesa
, T.
, and Buehler
, M. J.
, 2013
, “Nanoconfinement and the Strength of Biopolymers
,” Annu. Rev. Biophys.
, 42
, pp. 651
–673
.10.1146/annurev-biophys-083012-13034547.
Hambli
, R.
, and Barkaoui
, A.
, 2012
, “Physically Based 3D Finite Element Model of a Single Mineralized Collagen Microfibril
,” J. Theor. Biol
, 301
, pp. 28
–41
.10.1016/j.jtbi.2012.02.00748.
Barkaoui
, A.
, Chamekh
, A.
, Merzouki
, T.
, Hambli
, R.
, and Mkaddem
, A.
, 2014
, “Multiscale Approach Including Microfibril Scale to Assess Elastic Constants of Cortical Bone Based on Neural Network Computation and Homogenization Method
,” Int. J. Numer. Methods Biomed. Eng.
, 30
(3
), pp. 318
–338
.10.1002/cnm.260449.
Barkaoui
, A.
, and Hambli
, R.
, 2011
, “Finite Element 3D Modeling of Mechanical Behavior of Mineralized Collagen Microfibrils
,” J. Appl. Biomater. Biomech.
, 9
(3
), pp. 199
–206
.50.
Davies
, C. N.
, 1952
, “The Separation of Airborne Dust and Particles
,” Proc. Inst. Mech. Eng.
, 1
(4
), pp. 185
–213
.51.
Spielman
, L.
, and Goren
, S. L.
, 1968
, “Model for Predicting Pressure Drop and Filtration Efficiency in Fibrous Media
,” Environ. Sci. Technol.
, 2
(4
), pp. 279
–287
.10.1021/es60016a00352.
Jackson
, G. W.
, and James
, D. F.
, 1986
, “The Permeability of Fibrous Porous-Media
,” Can. J. Chem. Eng.
, 64
(3
), pp. 364
–374
.10.1002/cjce.545064030253.
Yazdchi
, K.
, Srivastava
, S.
, and Luding
, S.
, 2011
, “Microstructural Effects on the Permeability of Periodic Fibrous Porous Media
,” Int. J. Multiphase Flow
, 37
(8
), pp. 956
–966
.10.1016/j.ijmultiphaseflow.2011.05.003Copyright © 2015 by ASME
You do not currently have access to this content.
