Research Papers

Multiscale Mechanical Simulations of Cell Compacted Collagen Gels

[+] Author and Article Information
Maziar Aghvami

Department of Biomedical Engineering,
University of Iowa,
Iowa City, IA 52242

V. H. Barocas

Department of Biomedical Engineering,
University of Minnesota,
Minneapolis, MN 55455

E. A. Sander

Department of Biomedical Engineering,
University of Iowa,
Iowa City, IA 52242
e-mail: edward-sander@uiowa.edu

1Corresponding author.

Contributed by the Bioengineering Division of ASME for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received January 8, 2013; final manuscript received May 1, 2013; accepted manuscript posted May 8, 2013; published online June 11, 2013. Assoc. Editor: Keith Gooch.

J Biomech Eng 135(7), 071004 (Jun 11, 2013) (9 pages) Paper No: BIO-13-1010; doi: 10.1115/1.4024460 History: Received January 08, 2013; Revised May 01, 2013; Accepted May 08, 2013

Engineered tissues are commonly stretched or compressed (i.e., conditioned) during culture to stimulate extracellular matrix (ECM) production and to improve the mechanical properties of the growing construct. The relationships between mechanical stimulation and ECM remodeling, however, are complex, interdependent, and dynamic. Thus, theoretical models are required for understanding the underlying phenomena so that the conditioning process can be optimized to produce functional engineered tissues. Here, we continue our development of multiscale mechanical models by simulating the effect of cell tractions on developing isometric tension and redistributing forces in the surrounding fibers of a collagen gel embedded with explants. The model predicted patterns of fiber reorganization that were similar to those observed experimentally. Furthermore, the inclusion of cell compaction also changed the distribution of fiber strains in the gel compared to the acellular case, particularly in the regions around the cells where the highest strains were found.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.


Marinković, A., Mih, J. D., Park, J. A., Liu, F., and Tschumperlin, D. J., 2012, “Improved Throughput Traction Microscopy Reveals Pivotal Role for Matrix Stiffness in Fibroblast Contractility and TGF-β Responsiveness,” Am. J. Physiol. Lung Cell. Mol. Physiol., 303(3), pp. 169–180. [CrossRef]
Sieminski, A., Hebbel, R., and Gooch, K., 2004, “The Relative Magnitudes of Endothelial Force Generation and Matrix Stiffness Modulate Capillary Morphogenesis In Vitro,” Expt. Cell Res., 297(2), pp. 574–584. [CrossRef]
Engler, A. J., Sen, S., Sweeney, H. L., and Discher, D. E., 2006, “Matrix Elasticity Directs Stem Cell Lineage Specification,” Cell, 126(4), pp. 677–689. [CrossRef] [PubMed]
Discher, D. E., Janmey, P., Wang, Y., 2005, “Tissue Cells Feel and Respond to the Stiffness of Their Substrate,” Science, 310(5751), pp. 1139–1143. [CrossRef] [PubMed]
Wells, R. G., 2005, “The Role of Matrix Stiffness in Hepatic Stellate Cell Activation and Liver Fibrosis,” J. Clin. Gastroenterol., 39(4), pp. S158–S161. [CrossRef] [PubMed]
Schwartz, M. A., and DeSimone, D. W., 2008, “Cell Adhesion Receptors in Mechanotransduction,” Curr. Opin. Cell Biol., 20(5), pp. 551–556. [CrossRef] [PubMed]
Wozniak, M. A., Modzelewska, K., Kwong, L., and Keely, P. J., 2004, “Focal Adhesion Regulation of Cell Behavior,” Biochim. Biophys. Acta Mol. Cell Res., 1692(2), pp. 103–119. [CrossRef]
Genin, G. M., Abney, T. M., Wakatsuki, T., and Elson, E. L., 2011, “Cell-Cell Interactions and the Mechanics of Cells and Tissues Observed in Bioartificial Tissue Constructs,” Mechanobiology of Cell-Cell and Cell-Matrix Interactions, Springer, New York, pp. 75–103.
Peacock, M., Turner, C. H., Econs, M. J., and Foroud, T., 2002, “Genetics of Osteoporosis,” Endocrine Rev., 23(3), pp. 303–326. [CrossRef]
Rubin, C. T., and Lanyon, L. E., 2005, “Osteoregulatory Nature of Mechanical Stimuli: Function as a Determinant for Adaptive Remodeling in Bone,” J. Orthop. Res., 5(2), pp. 300–310. [CrossRef]
Burgoyne, C. F., Crawford Downs, J., Bellezza, A. J., Francis Suh, J. K., and Hart, R. T., 2005, “The Optic Nerve Head as a Biomechanical Structure: A New Paradigm for Understanding the Role of IOP-Related Stress and Strain in the Pathophysiology of Glaucomatous Optic Nerve Head Damage,” Prog. Retin Eye Res., 24(1), pp. 39–73. [CrossRef] [PubMed]
Sander, E., Downs, J., Hart, R., Burgoyne, C., and Nauman, E., 2006, “A Cellular Solid Model of the Lamina Cribrosa: Mechanical Dependence on Morphology,” ASME, J. Biomech. Eng., 128, p. 879. [CrossRef]
Moore, J. E., Xu, C., Glagov, S., Zarins, C. K., and Ku, D. N., 1994, “Fluid Wall Shear Stress Measurements in a Model of the Human Abdominal Aorta: Oscillatory Behavior and Relationship to Atherosclerosis,” Atherosclerosis, 110(2), pp. 225–240. [CrossRef] [PubMed]
Nerem, R., 1992, “Vascular Fluid Mechanics, The Arterial Wall, and Atherosclerosis,” ASME, J. Biomech. Eng., 114(3), p. 274. [CrossRef]
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, 39(7), pp. 2085–2090. [CrossRef] [PubMed]
Paszek, M. J., Zahir, N., Johnson, K. R., Lakins, J. N., Rozenberg, G. I., Gefen, A., Reinhart-King, C. A., Margulies, S. S., Dembo, M., Boettiger, D., Hammer, D. A., and Weaver, V. M., 2005, “Tensional Homeostasis and the Malignant Phenotype,” Cancer Cell, 8(3), pp. 241–254. [CrossRef] [PubMed]
Huang, S., and Ingber, D. E., 2005, “Cell Tension, Matrix Mechanics, and Cancer Development,” Cancer Cell, 8(3), pp. 175–176. [CrossRef] [PubMed]
Pathak, A., and Kumar, S., 2012, “Independent Regulation of Tumor Cell Migration by Matrix Stiffness and Confinement,” Proc. Natl. Acad. Sci., 109(26), pp. 10334–10339. [CrossRef]
Balestrini, J. L., and Billiar, K. L., 2009, “Magnitude and Duration of Stretch Modulate Fibroblast Remodeling,” ASME, J. Biomech. Eng., 131, p. 051005. [CrossRef]
Rubbens, M. P., Driessen-Mol, A., Boerboom, R. A., Koppert, M. M. J., Van Assen, H. C., TerHaar Romeny, B. M., Baaijens, F. P. T., and Bouten, C. V. C., 2009, “Quantification of the Temporal Evolution of Collagen Orientation in Mechanically Conditioned Engineered Cardiovascular Tissues,” Ann. Biomed. Eng., 37(7), pp. 1263–1272. [CrossRef] [PubMed]
Seliktar, D., Black, R. A., Vito, R. P., and Nerem, R. M., 2000, “Dynamic Mechanical Conditioning of Collagen-Gel Blood Vessel Constructs Induces Remodeling In Vitro,” Ann. Biomed. Eng., 28(4), pp. 351–362. [CrossRef] [PubMed]
Juncosa-Melvin, N., Matlin, K. S., Holdcraft, R. W., Nirmalanandhan, V. S., Butler, D. L., 2007, “Mechanical Stimulation Increases Collagen Type I and Collagen Type III Gene Expression of Stem Cell-Collagen Sponge Constructs For Patellar Tendon Repair,” Tissue Eng., 13(6), pp. 1219–1226. [CrossRef] [PubMed]
Brown, R., Prajapati, R., McGrouther, D., Yannas, I., and Eastwood, M., 1998, “Tensional Homeostasis in Dermal Fibroblasts: Mechanical Responses to Mechanical Loading in Three-Dimensional Substrates,” J. Cell Physiol., 175(3), pp. 323–332. [CrossRef] [PubMed]
Syedain, Z. H., Weinberg, J. S., and Tranquillo, R. T., 2008, “Cyclic Distension of Fibrin-Based Tissue Constructs: Evidence of Adaptation During Growth of Engineered Connective Tissue,” Proc. Natl. Acad. Sci., 105(18), p. 6537. [CrossRef]
Breuls, R., Sengers, B. G., Oomens, C., Bouten, C., and Baaijens, F., 2002, “Predicting Local Cell Deformations in Engineered Tissue Constructs: A Multilevel Finite Element Approach,” ASME, J. Biomech. Eng., 124(2), p. 198. [CrossRef]
Guilak, F., and Mow, V. C., 2000, “The Mechanical Environment of the Chondrocyte: A Biphasic Finite Element Model of Cell–Matrix Interactions in Articular Cartilage,” J. Biomech., 33(12), pp. 1663–1673. [CrossRef] [PubMed]
Stops, A., McMahon, L., O'Mahoney, D., Prendergast, P., and McHugh, P., 2008, “A Finite Element Prediction of Strain on Cells in a Highly Porous Collagen-Glycosaminoglycan Scaffold,” ASME, J. Biomech. Eng., 130, p. 061001. [CrossRef]
Barocas, V. H., and Tranquillo, R. T., 1997, “An Anisotropic Biphasic Theory of Tissue-Equivalent Mechanics: The Interplay Among Cell Traction, Fibrillar Network Deformation, Fibril Alignment, and Cell Contact Guidance,” J. Biomech. Eng., 119, p. 137. [CrossRef] [PubMed]
Susilo, M. E., Bell, B. J., Roeder, B. A., Voytik-Harbin, S. L., Kokini, K., Nauman, E. A., 2012, “Prediction of Equibiaxial Loading Stress in Collagen-Based Extracellular Matrix Using a Three-Dimensional Unit Cell Model,” Acta Biomater., 9, pp. 5544–5553. [CrossRef] [PubMed]
Corin, K. A., and Gibson, L. J., 2010, “Cell Contraction Forces in Scaffolds With Varying Pore Size and Cell Density,” Biomaterials, 31(18), pp. 4835–4845. [CrossRef] [PubMed]
Wakatsuki, T., Kolodney, M. S., Zahalak, G. I., and Elson, E. L., 2000, “Cell Mechanics Studied by a Reconstituted Model Tissue,” Biophys. J., 79(5), pp. 2353–2368. [CrossRef] [PubMed]
Chandran, P. L., and Barocas, V. H., 2007, “Deterministic Material-Based Averaging Theory Model of Collagen Gel Micromechanics,” ASME, J. Biomech. Eng., 129, p. 137. [CrossRef]
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. [CrossRef]
Sander, E. A., Stylianopoulos, T., Tranquillo, R. T., and Barocas, V. H., 2009, “Image-Based Biomechanics of Collagen-Based Tissue Equivalents,” Eng. Med. Biol. Mag. IEEE, 28(3), pp. 10–18. [CrossRef]
Hadi, M., Sander, E., Ruberti, J., and Barocas, V., 2011, “Simulated Remodeling of Loaded Collagen Networks Via Strain-Dependent Enzymatic Degradation and Constant-Rate Fiber Growth,” Mech. Mater., 44, pp. 72–82. [CrossRef]
Chandran, P. L., and Barocas, V. H., 2006, “Affine Versus Non-Affine Fibril Kinematics in Collagen Networks: Theoretical Studies of Network Behavior,” J. Biomech. Eng., 128, p. 259. [CrossRef] [PubMed]
Stylianopoulos, T., Bashur, C. A., Goldstein, A. S., Guelcher, S. A., and Barocas, V. H., 2008, “Computational Predictions of the Tensile Properties of Electrospun Fibre Meshes: Effect of Fibre Diameter and Fibre Orientation,” J. Mech. Beh. Biomed. Mater., 1(4), pp. 326–335. [CrossRef]
Stylianopoulos, T., and Barocas, V. H., 2007, “Multiscale, Structure-Based Modeling for the Elastic Mechanical Behavior of Arterial Walls,” ASME, J. Biomech. Eng., 129, p. 611. [CrossRef]
Nemat-Nasser, S., and Hori, M., 1999, Micromechanics: Overall Properties of Heterogeneous Materials, Elsevier, Amsterdam.
Drew, D. A., 1971, “Averaged Field Equations For Two-Phase Media,” StudApplMath, 50(2), pp. 133–166.
Sander, E., and Barocas, V., 2009, “Comparison of 2D Fiber Network Orientation Measurement Methods,” J. Biomed. Mater. Res., Part A, 88(2), pp. 322–331. [CrossRef]
Sander, E., Barocas, V., and Fratzl, P., 2008, Biomimetic Collagen Tissues: Collagenous Tissue Engineering and Other Applications, Springer, New York.
Stopak, D., and Harris, A. K., 1982, “Connective Tissue Morphogenesis by Fibroblast Traction: I. Tissue Culture Observations,” Dev. Biol., 90(2), pp. 383–398. [CrossRef] [PubMed]
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. 1083–1092. [CrossRef] [PubMed]
Provenzano, P. P., Inman, D. R., Eliceiri, K. W., Trier, S. M., and Keely, P. J., 2008, “Contact Guidance Mediated Three-Dimensional Cell Migration is Regulated by Rho/ROCK-Dependent Matrix Reorganization,” Biophys. J., 95(11), pp. 5374. [CrossRef] [PubMed]
Chang Yan, K., Nair, K., and Sun, W., 2010, “Three Dimensional Multi-Scale Modelling and Analysis of Cell Damage in Cell-Encapsulated Alginate Constructs,” J. Biomech., 43(6), pp. 1031–1038. [CrossRef] [PubMed]
Sander, E., Stein, A., Swickrath, M., and Barocas, V., 2010, “Out of Many, One: Modeling Schemes for Biopolymer and Biofibril Networks,” Trends in Computational Nanomechanics, 9, pp. 557–602. [CrossRef]
Janmey, P. A., Euteneuer, U., Traub, P., and Schliwa, M., 1991, “Viscoelastic Properties of Vimentin Compared With Other Filamentous Biopolymer Networks,” J. Cell Biol., 113(1), pp. 155–160. [CrossRef] [PubMed]
Reinhardt, J. W., Krakauer, D. A., and Gooch, K. J., 2013, “Complex Matrix Remodeling and Durotaxis Can Emerge From Simple Rules for Cell-Matrix Interaction in Agent-Based Models,” ASME, J. Biomech. Eng., 135(7), p. 071003. [CrossRef]
Zielinski, R., Mihai, C., Kniss, D., and Ghadiali, S. N., 2013, “Finite Element Analysis of Traction Force Microscopy: Influence of Cell Mechanics, Adhesion and Morphology,” ASME, J. Biomech. Eng., 135(7), p. 071009. [CrossRef]
Dallon, J. C., Scott, M., and Smith, W. V., 2013, “A Force Based Model of Individual Cell Migration With Discrete Attachment Sites and Random Switching Terms,” ASME, J. Biomech. Eng., 135(7), p. 071008. [CrossRef]
Sander, L. M., 2013, “Alignment Localization in Non-Linear Biological Media,” ASME, J. Biomech. Eng., 135(7), p. 071006. [CrossRef]
Freyman, T., Yannas, I., Yokoo, R., and Gibson, L., 2002, “Fibroblast Contractile Force is Independent of the Stiffness Which Resists the Contraction,” Exp. Cell Res., 272(2), pp. 153–162. [CrossRef] [PubMed]


Grahic Jump Location
Fig. 1

“Strap” formation between explants and the multiscale modeling strategy. (A) A triangular explant configuration develops strong fiber alignment between fibroblast explants after 60 h. Images are montages of sixty 20 × DIC images (images from Dr. Sander's lab). (B) Multiscale models consist of cellular networks (blue) that are configured in an analogous manner to the experiments and that contract to 40% of their original length to produce tension and reorganization in the surrounding ECM networks.

Grahic Jump Location
Fig. 2

Top-view of fiber network realignment after 40% compaction for case 1. ECM networks develop varying patterns of fiber alignment between explants in a configuration dependent manner. The color map indicates the change in the degree of fiber alignment (Δα) between the initial traction free configuration and 40% compaction. Also depicted are the principal directions of fiber alignment (white crosses). For clarity, directions are only shown for those elements with Δα > 0.08.

Grahic Jump Location
Fig. 3

Strain developed during 20% and 40% compaction for three explants. (A), (D) Top, bottom, left, and right boundaries are fixed, (B), (E) top and bottom are fixed, and (C), (F) symmetry boundary conditions are applied to the left, bottom, and back faces. Maximum principal strain patterns change in accord with the applied boundary conditions. White arrows show principal direction.

Grahic Jump Location
Fig. 4

Comparison of mechanical response. (A) The force on the boundary during uniaxial extension for the case of 40% compaction for three explants (circles) is higher than the case where all of the networks are ECM networks (i.e., no explants). The inset plot shows the increase in force that develops on the boundary during the compaction process prior to uniaxial extension. (B), (C) Regional differences in strain, particularly around the explants, are apparent at full stretch (λ = 1.5).

Grahic Jump Location
Fig. 5

Histograms of fiber strain in all ECM networks for uniaxial stretch of the three explant model. (A), (B) During the compaction phase of the simulations a small fraction of fibers developed small tensile and compressive strains. (C) 25% uniaxial stretch, (D) 50% uniaxial stretch. With uniaxial stretch a wide range of fiber strains were observed, most of which were below the amount of stretch applied macroscopically (red line). The distribution of fiber strains in the no-explant model (data not shown) were similar in shape to those in (C) and (D).

Grahic Jump Location
Fig. 7

Behavior of selected networks. (A), (B) Average fiber strains in each element are depicted at select instances for the (A) Three-explant model and the no-explant model (B). The red circles highlight the locations of two networks depicted below. (C) Top-view of network 1, which is associated with an area of high fiber strain. The individual fibers reorganize to satisfy force equilibrium and are color coded to indicate the level of fiber strain. (D) Network 2 is associated with an area low average fiber strain. Prior to uniaxial stretch the network volume shrinks and some fibers are under compression. The fiber strain and kinematics in these networks are compared with those developed in the no-explant model (E), (F).

Grahic Jump Location
Fig. 6

Differences in average fiber-level strain at 50% uniaxial stretch. (A) Regional variations in the average fiber-level strain in each element were apparent when the strains in the no-explant model were subtracted from those in the three-explant model. The largest differences were found in the elements around the explants (white). Differences in fiber strain that exceeded ± 4% are highlighted with a star. Histograms of the strains for all 88,728 fibers in the starred elements for the (B) three-explant model and (C) no-explant model.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In