0
Research Papers

Microscale Fiber Network Alignment Affects Macroscale Failure Behavior in Simulated Collagen Tissue Analogs

[+] Author and Article Information
Mohammad F. Hadi

e-mail: hadix004@umn.edu

Victor H. Barocas

e-mail: baroc001@umn.edu
Department of Biomedical Engineering,
University of Minnesota,
7-105 Hasselmo Hall,
312 Church Street SE,
Minneapolis MN 55455

1Corresponding author.

Contributed by the Bioengineering Division of ASME for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received October 22, 2012; final manuscript received January 7, 2013; accepted manuscript posted January 18, 2013; published online February 7, 2013. Editor: Beth Winkelstein.

J Biomech Eng 135(2), 021026 (Feb 07, 2013) (8 pages) Paper No: BIO-12-1502; doi: 10.1115/1.4023411 History: Received October 22, 2012; Revised January 07, 2013; Accepted January 18, 2013

A tissue's microstructure determines its failure properties at larger length scales, however, the specific relationship between microstructure and macroscopic failure in native and engineered soft tissues (such as capsular ligaments, aortic aneurysms, or vascular grafts) has proven elusive. In this study, variations in the microscale fiber alignment in collagen gel tissue analogs were modeled in order to understand their effects on macroscale damage and failure outcomes. The study employed a multiscale finite-element (FE) model for damage and failure in collagen-based materials. The model relied on microstructural representative volume elements (RVEs) that consisted of stochastically-generated networks of discrete type-I collagen fibers. Fiber alignment was varied within RVEs and between layers of RVEs in a macroscopic FE model of a notched dogbone geometry. The macroscale stretch and the microscale response of fibers for each of the differently aligned cases were compared as the dogbone was uniaxially extended to failure. Networks with greater fiber alignment parallel to the direction of extension failed at smaller strains (with a 6–22% reduction in the Green strain at failure), however, at greater grip forces (a 28–60% increase) than networks with fibers aligned perpendicular to the extension. Alternating layers of crisscrossed network alignments (aligned ±45 deg to the direction of extension) failed at smaller strains but at greater grip forces than those created using one fiber alignment type. In summary, variations in microscale structure via fiber alignment produced different macroscale failure trends. To conclude, these findings may be significant in the realm of tissue engineering and in soft tissue biomechanics.

FIGURES IN THIS ARTICLE
<>
Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Anssari-Benam, A., Gupta, H. S., and Screen, H. R., 2012, “Strain Transfer Through the Aortic Valve,” ASME J. Biomech. Eng., 134(6), p. 061003. [CrossRef]
Quinn, K. P., and Winkelstein, B. A., 2011, “Detection of Altered Collagen Fiber Alignment in the Cervical Facet Capsule After Whiplash-Like Joint Retraction,” Ann. Biomed. Eng., 39(8), pp. 2163–2173. [CrossRef] [PubMed]
Keyes, J. T., Haskett, D. G., Utzinger, U., Azhar, M., and Van de Geest, J. P., 2011, “Adaptation of a Planar Microbiaxial Optomechanical Device for the Tubular Biaxial Microstructural and Macroscopic Characterization of Small Vascular Tissues,” ASME J. Biomech. Eng., 133(7), p. 075001. [CrossRef]
Ritter, M. C., Jesudason, R., Majumdar, A., Stamenović, D., Buczek-Thomas, J. A., Stone, P. J., Nugent, M. A., and Suki, B., 2009, “A Zipper Network Model of the Failure Mechanics of Extracellular Matrices,” Proc. Natl. Acad. Sci., 106(4), pp. 1081–1086. [CrossRef]
Ayturk, U. M., Gadomski, B., Schuldt, D., Patel, V., and Puttlitz, C. M., 2012, “Modeling Degenerative Disk Disease in the Lumbar Spine: A Combined Experimental, Constitutive, and Computational Approach,” ASME J. Biomech. Eng., 134(10), p. 101003. [CrossRef]
Kao, P. H., Lammers, S., Tian, L., Hunter, K., Stenmark, K. R., Shandas, R., and Qi, H. J., 2011, “A Microstructurally-Driven Model for Pulmonary Artery Tissue,” ASME J. Biomech. Eng., 133(5), p. 051002. [CrossRef]
Hamed, E., Jasiuk, I., Yoo, A., Lee, Y., and Liszka, T., 2012, “Multi-Scale Modelling of Elastic Moduli of Trabecular Bone,” J. R. Soc., Interface, 9(72), pp. 1654–1673. [CrossRef]
Hadi, M. F., Sander, E. A., Ruberti, J. W., and Barocas, V. H., 2012, “Simulated Remodeling of Loaded Collagen Networks via Strain-Dependent Enzymatic Degradation and Constant-Rate Fiber Growth,” Mech. Mater., 44, pp. 72–82. [CrossRef] [PubMed]
Wang, C. W., and Sastry, A. M., 2000, “Structure, Mechanics and Failure of Stochastic Fibrous Networks—Part II: Network Simulations and Application,” ASME J. Eng. Mater. Technol., 122, pp. 460–469. [CrossRef]
Zhang, B., Yang, Z., Wu, Y., and Sun., H., 2010, “Hierarchical Multiscale Modeling of Failure in Unidirectional Fiber-Reinforced Plastic Matrix Composite,” Mater. Des., 31(5), pp. 2312–2318. [CrossRef]
Lee, D. J., and Winkelstein, B. A., 2012, “The Failure Response of the Human Cervical Facet Capsular Ligament During Facet Joint Retraction,” J. Biomech., 45(14), pp. 2325–2329. [CrossRef] [PubMed]
Raghavan, M. L., Hanaoka, M. M., Kratzberg, J. A., Higuchi, M. D. L., and Da Silva, E. S., 2011, “Biomechanical Failure Properties and Microstructural Content of Ruptured and Unruptured Abdominal Aortic Aneurysms,” J. Biomech., 44(13), pp. 2501–2507. [CrossRef] [PubMed]
Volokh, K., and Vorp, D., 2008, “A Model of Growth and Rupture of Abdominal Aortic Aneurysm,” J. Biomech., 41(5), pp. 1015–1021. [CrossRef] [PubMed]
Drilling, S., Gaumer, J., and Lannutti, J., 2009, “Fabrication of Burst Pressure Competent Vascular Grafts via Electrospinning: Effects of Microstructure,” J. Biomed. Mater. Res. Part A, 88(4), pp. 923–934. [CrossRef]
Hang, F., and Barber, A. H., 2011, “Nano-Mechanical Properties of Individual Mineralized Collagen Fibrils From Bone Tissue,” J. R. Soc., Interface, 8(57), pp. 500–505. [CrossRef]
Ito, S., Ingenito, E. P., Brewer, K. K., Black, L. D., Parameswaran, H., Lutchen, K. R., and Suki, B., 2005, “Mechanics, Nonlinearity, and Failure Strength of Lung Tissue in a Mouse Model of Emphysema: Possible Role of Collagen Remodeling,” J. Appl. Physiol., 98(2), pp. 503–511. [CrossRef] [PubMed]
D'Amore, A., Stella, J. A., Wagner, W. R., and Sacks, M. S., 2010, “Characterization of the Complete Fiber Network Topology of Planar Fibrous Tissues and Scaffolds,” Biomaterials, 31(20), pp. 5345–5354. [CrossRef] [PubMed]
Christian Gasser, T., 2011, “An Irreversible Constitutive Model for Fibrous Soft Biological Tissue: A 3-D Microfiber Approach With Demonstrative Application to Abdominal Aortic Aneurysms,” Acta Biomater., 7(6), pp. 2457–2466. [CrossRef] [PubMed]
Nerurkar, N. L., Elliott, D. M., and Mauck, R. L., 2010, “Mechanical Design Criteria for Intervertebral Disc Tissue Engineering,” J. Biomech., 43(6), pp. 1017–1030. [CrossRef] [PubMed]
Hadi, M. F., Sander, E. A., and Barocas, V. H., 2012, “Multiscale Model Predicts Tissue-Level Failure From Collagen Fiber-Level Damage,” ASME J. Biomech. Eng., 134(9), p. 091005. [CrossRef]
Chandran, P. L., and Barocas, V. H., 2007, “Deterministic Material-Based Averaging Theory Model of Collagen Gel Micromechanics,” ASME J. Biomech. Eng., 129(2), pp. 137–147. [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]
Barber, C. B., Dobkin, D. P., and Huhdanpaa, H., 1996, “The Quickhull Algorithm for Convex Hulls,” ACM Trans. Math. Softw., 22(4), pp. 469–483. [CrossRef]
Billiar, K. L., and Sacks, M. S., 2000, “Biaxial Mechanical Properties of the Native and Glutaraldehyde-Treated Aortic Valve Cusp—Part II: A Structural Constitutive Model,” ASME J. Biomech. Eng., 122(4), p. 327. [CrossRef]
Sander, E. A., Stylianopoulos, T., Tranquillo, R. T., and Barocas, V. H., 2009, “Image-Based Multiscale Modeling Predicts Tissue-Level and Network-Level Fiber Reorganization in Stretched Cell-Compacted Collagen Gels,” Proc. Natl. Acad. Sci., 106(42), pp. 17675–17680. [CrossRef]
Lai, V. K., Lake, S. P., Frey, C. R., Tranquillo, R. T., and Barocas, V. H., 2012, “Mechanical Behavior of Collagen-Fibrin Co-Gels Reflects Transition From Series to Parallel Interactions With Increasing Collagen Content,” ASME J. Biomech. Eng., 134(1), p. 011004. [CrossRef]
Lake, S. P., Hadi, M. F., Lai, V. K., and Barocas, V. H., 2012, “Mechanics of a Fiber Network Within a Non-Fibrillar Matrix: Model and Comparison With Collagen-Agarose Co-Gels,” Ann. Biomed. Eng., 40(10), pp. 2111–2121. [CrossRef] [PubMed]
Sander, E. A., and Barocas, V. H., 2009, “Comparison of 2D Fiber Network Orientation Measurement Methods,” J. Biomed. Mater. Res. Part A, 88(2), pp. 322–331. [CrossRef]
Sander, E. A., Stylianopoulos, T., Tranquillo, R. T., and Barocas, V. H., 2009, “Image-Based Biomechanics of Collagen-Based Tissue Equivalents: Multiscale Models Compared to Fiber Alignment Predicted by Polarimetric Imaging,” IEEE Eng. Med. Biol. Mag., 28(3), pp. 10–18. [CrossRef] [PubMed]
Nerurkar, N. L., Baker, B. M., Sen, S., Wible, E. E., Elliott, D. M., and Mauck, R. L., 2009, “Nanofibrous Biologic Laminates Replicate the Form and Function of the Annulus Fibrosus,” Nature Mater., 8(12), pp. 986–992. [CrossRef]
Nerurkar, N. L., Elliott, D. M., and Mauck, R. L., 2007, “Mechanics of Oriented Electrospun Nanofibrous Scaffolds for Annulus Fibrosus Tissue Engineering,” J. Orthop. Res., 25(8), pp. 1018–1028. [CrossRef] [PubMed]
Lake, S. P., Miller, K. S., Elliott, D. M., and Soslowsky, L. J., 2009, “Effect of Fiber Distribution and Realignment on the Nonlinear and Inhomogeneous Mechanical Properties of Human Supraspinatus Tendon Under Longitudinal Tensile Loading,” J. Orthop. Res., 27(12), pp. 1596–1602. [CrossRef] [PubMed]
Cummings, C. L., Gawlitta, D., Nerem, R. M., and Stegemann, J. P., 2004, “Properties of Engineered Vascular Constructs Made From Collagen, Fibrin, and Collagen–Fibrin Mixtures,” Biomaterials, 25(17), pp. 3699–3706. [CrossRef] [PubMed]

Figures

Grahic Jump Location
Fig. 1

(a) Multiscale damage model consisted of a millimeter-scale finite element continuum (in a notched dogbone geometry) with representative volume elements of micrometer-scale collagen fiber networks of varying alignment at each Gauss point. Fibers were allowed to fail when stretched beyond a critical value. The model contained 624 finite elements, with 8 Gauss points per element and with over 500 fibers in each network. The dogbone was fixed at one grip and extended under displacement control from the opposite grip along axis 1 to a final stretch ratio of 1.5. Microscale network fiber alignments were characterized using the orientation tensor Ω and were subsequently rotated relative to the axis of extension. (b) Isotropic networks had initial orientation tensor values of Ω11 = Ω22 = Ω33 = 0.33. (c) Transverse biaxially aligned networks had orientation values of Ω11 = 0.43, Ω22 = 0.13, and Ω33 = 0.43. (d) Uniaxially aligned networks had orientation values of Ω11 = 0.53, Ω22 = 0.23, and Ω33 = 0.23.

Grahic Jump Location
Fig. 2

(a) Macroscopic grip force varied based on model microscale fiber alignments as dogbone samples were uniaxially stretched to failure. (b) The corresponding mechanical work for these deformations also varied by the alignment case. (c)–(e) At the same grip displacement of 7.0 mm, differences in the stress and deformation for each case were apparent.

Grahic Jump Location
Fig. 3

(a) The mean fiber stretch, (b) the mean percentage of failed fibers, and (c) the mean fiber orientation parameter Ω11 varied over the macroscale sample stretch for each fiber alignment case. (d) Fibers were analyzed from a region of notch-adjacent elements. The same region was used to generate the plots in Figs. 7 and 8.

Grahic Jump Location
Fig. 4

A single microscale network in the model experienced distinct fiber stretches and failure at varying grip displacements for each alignment case. The network was selected from a notch-adjacent element.

Grahic Jump Location
Fig. 5

Contour plots of the macroscale (a) peak grip force, (b) displacement at peak grip force, and (c) work were interpolated as functions of the initial network fiber orientation parameter Ω11 and the network rotation. The largest forces occurred when fibers were aligned parallel to extension and the largest prefailure strains when fibers were aligned perpendicular to extension.

Grahic Jump Location
Fig. 6

(a) Macroscopic grip force varied based on differing microscale composite or uniform fiber alignments as dogbone samples were uniaxially stretched to failure. (b) The corresponding mechanical work for these deformations also varied based on the composite or uniform fiber alignment type. (c)–(e) At the same grip displacement of 7.0 mm, differences in the macroscopic Green strain were apparent between the (c) all +45 deg rotated aligned networks, (d) layered ±45 deg networks, and (e) all −45 deg network cases. To illustrate the propagation of failure along the direction of fiber alignment for the (f) all +45 deg and (g) all −45 deg cases, elements with the greatest fiber losses (approximately the top 10%) were removed from plots of notch strains at a grip displacement of 10.8 mm.

Grahic Jump Location
Fig. 7

(a) The mean fiber stretch, (b) the mean percentage of failed fibers, and (c) the mean fiber orientation parameter Ω11 varied over the macroscale sample stretch for each composite or uniform fiber alignment case. Fibers were analyzed from the notch-adjacent elements depicted in Fig. 3.

Grahic Jump Location
Fig. 8

Fiber stretch distributions varied for the (a)–(c) merged, and (d)–(f) rotated aligned network cases at equivalent grip displacements, but were similar at equal grip forces. Fibers were analyzed from the notch-adjacent elements depicted in Fig. 3.

Tables

Errata

Discussions

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