A growth-based model for the prediction of fiber angle distribution in the intervertebral disc annulus fibrosus

  • Arthur J. MichalekEmail author
Original Paper


There is a growing interest in the development of patient-specific finite element models of the human lumbar spine for both the assessment of injury risk and the development of treatment strategies. A current challenge in implementing these models is that the outer annulus fibrosus of the disc is composed of concentric sheets of aligned collagen fibers, the helical angles of which vary spatially. In finite element models, fiber angle is typically assumed to be constant, based on average experimental measurements from a small number of locations. The present study hypothesized that the full spatial distribution of fiber angles in the annulus fibrosus may be predicted for any disc geometry by assuming growth from a thin cylinder with constant fiber angle. This hypothesis was tested by developing an analytical model of disc growth and calibrating it with fiber angle measurements of adult bovine caudal discs. The calibrated model was then run on a representative human lumbar disc geometry. The model was able to accurately predict fiber angle distributions in both the experimental bovine caudal disc measurements and literature-reported human lumbar disc measurements. Despite its theoretical basis in development, the model requires only mature state geometry, making it practical for implementation in patient-specific finite element analyses, in which disc geometry is obtained from clinical imaging.


Tissue microstructure Patient-specific modeling Bovine caudal Developmental 



Support for this work was provided by the Clarkson University Department of Mechanical & Aeronautical Engineering. Bovine IVD specimens were provided by Tri-Town Packing, Brasher Falls, NY, and were prepared with assistance from Sarah E Duclos.

Supplementary material

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  1. Alini M, Eisenstein SM, Ito K, Little C, Kettler AA, Masuda K, Melrose J, Ralphs J, Stokes I, Wilke HJ (2008) Are animal models useful for studying human disc disorders/degeneration? Eur Spine J 17(1):2–19CrossRefGoogle Scholar
  2. Berg-Johansen B, Fields AJ, Liebenberg EC, Li A, Lotz JC (2018) Structure-function relationships at the human spinal disc-vertebra interface. J Orthop Res 36(1):192–201Google Scholar
  3. Brown S, Rodrigues S, Sharp C, Wade K, Broom N, McCall IW, Roberts S (2017) Staying connected: structural integration at the intervertebral disc-vertebra interface of human lumbar spines. Eur Spine J 26(1):248–258CrossRefGoogle Scholar
  4. Cassidy JJ, Hiltner A, Baer E (1989) Hierarchical structure of the intervertebral disc. Connect Tissue Res 23(1):75–88CrossRefGoogle Scholar
  5. Chetoui MA, Boiron O, Dogui A, Deplano V (2017) Prediction of intervertebral disc mechanical response to axial load using isotropic and fiber reinforced FE models. Comput Methods Biomech Biomed Eng 20(sup1):39–40CrossRefGoogle Scholar
  6. Duclos SE, Michalek AJ (2017) Residual strains in the intervertebral disc annulus fibrosus suggest complex tissue remodeling in response to in vivo loading. J Mech Behav Biomed Mater 68:232–238CrossRefGoogle Scholar
  7. Francois RJ, Dhem A (1974) Microradiographic study of the normal human vertebral body. Acta Anat (Basel) 89(2):251–265CrossRefGoogle Scholar
  8. Holzapfel GA, Schulze-Bauer CA, Feigl G, Regitnig P (2005) Single lamellar mechanics of the human lumbar anulus fibrosus. Biomech Model Mechanobiol 3(3):125–140CrossRefGoogle Scholar
  9. Horton WG (1958) Further observations on the elastic mechanism of the intervertebral disc. J Bone Jt Surg Br 40-B(3):552–557CrossRefGoogle Scholar
  10. Inoue H (1973) Three-dimensional observation of collagen framework of intervertebral discs in rats, dogs and humans. Arch Histol Jpn 36(1):39–56CrossRefGoogle Scholar
  11. Jacobs NT, Cortes DH, Peloquin JM, Vresilovic EJ, Elliott DM (2014) Validation and application of an intervertebral disc finite element model utilizing independently constructed tissue-level constitutive formulations that are nonlinear, anisotropic, and time-dependent. J Biomech 47(11):2540–2546CrossRefGoogle Scholar
  12. Marchand F, Ahmed AM (1990) Investigation of the laminate structure of lumbar disc anulus fibrosus. Spine (Phila Pa 1976) 15(5):402–410CrossRefGoogle Scholar
  13. Matcher SJ, Winlove CP, Gangnus SV (2004) The collagen structure of bovine intervertebral disc studied using polarization-sensitive optical coherence tomography. Phys Med Biol 49(7):1295–1306CrossRefGoogle Scholar
  14. Michalek AJ, Iatridis JC (2012) Height and torsional stiffness are most sensitive to annular injury in large animal intervertebral discs. Spine J 12(5):425–432CrossRefGoogle Scholar
  15. Michalek AJ, Buckley MR, Bonassar LJ, Cohen I, Iatridis JC (2009) Measurement of local strains in intervertebral disc anulus fibrosus tissue under dynamic shear: contributions of matrix fiber orientation and elastin content. J Biomech 42(14):2279–2285CrossRefGoogle Scholar
  16. Momeni Shahraki N, Fatemi A, Goel VK, Agarwal A (2015) On the use of biaxial properties in modeling annulus as a Holzapfel–Gasser–Ogden material. Front Bioeng Biotechnol 3:69CrossRefGoogle Scholar
  17. Noailly J, Planell JA, Lacroix D (2011) On the collagen criss-cross angles in the annuli fibrosi of lumbar spine finite element models. Biomech Model Mechanobiol 10(2):203–219CrossRefGoogle Scholar
  18. O’Connell GD, Vresilovic EJ, Elliott DM (2007) Comparison of animals used in disc research to human lumbar disc geometry. Spine (Phila Pa 1976) 32(3):328–333CrossRefGoogle Scholar
  19. Rodrigues SA, Wade KR, Thambyah A, Broom ND (2012) Micromechanics of annulus-end plate integration in the intervertebral disc. Spine J 12(2):143–150CrossRefGoogle Scholar
  20. Rodrigues SA, Thambyah A, Broom ND (2017) How maturity influences annulus-endplate integration in the ovine intervertebral disc: a micro- and ultra-structural study. J Anat 230(1):152–164CrossRefGoogle Scholar
  21. Schmidt H, Galbusera F, Rohlmann A, Shirazi-Adl A (2013) What have we learned from finite element model studies of lumbar intervertebral discs in the past four decades? J Biomech 46(14):2342–2355CrossRefGoogle Scholar
  22. Schollum ML, Robertson PA, Broom ND (2008) ISSLS prize winner: microstructure and mechanical disruption of the lumbar disc annulus: part I: a microscopic investigation of the translamellar bridging network. Spine (Phila Pa 1976) 33(25):2702–2710CrossRefGoogle Scholar
  23. Schollum ML, Robertson PA, Broom ND (2009) A microstructural investigation of intervertebral disc lamellar connectivity: detailed analysis of the translamellar bridges. J Anat 214(6):805–816CrossRefGoogle Scholar
  24. Smith LJ, Elliott DM (2011) Formation of lamellar cross bridges in the annulus fibrosus of the intervertebral disc is a consequence of vascular regression. Matrix Biol 30(4):267–274CrossRefGoogle Scholar
  25. Stadelmann MA, Maquer G, Voumard B, Grant A, Hackney DB, Vermathen P, Alkalay RN, Zysset PK (2018) Integrating MRI-based geometry, composition and fiber architecture in a finite element model of the human intervertebral disc. J Mech Behav Biomed Mater 85:37–42CrossRefGoogle Scholar
  26. Tavakoli J, Elliott DM, Costi JJ (2016) Structure and mechanical function of the inter-lamellar matrix of the annulus fibrosus in the disc. J Orthop Res 34(8):1307–1315CrossRefGoogle Scholar
  27. Yang B, O’Connell GD (2018) GAG content, fiber stiffness, and fiber angle affect swelling-based residual stress in the intact annulus fibrosus. Biomech Model Mechanobiol. Google Scholar
  28. Zhu D, Gu G, Wu W, Gong H, Zhu W, Jiang T, Cao Z (2008) Micro-structure and mechanical properties of annulus fibrous of the L4-5 and L5-S1 intervertebral discs. Clin Biomech (Bristol, Avon) 23(Suppl 1):S74–S82CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mechanical and Aeronautical EngineeringClarkson UniversityPotsdamUSA

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