Biomechanics and Modeling in Mechanobiology

, Volume 18, Issue 3, pp 617–630 | Cite as

GAG content, fiber stiffness, and fiber angle affect swelling-based residual stress in the intact annulus fibrosus

  • Bo Yang
  • Grace D. O’ConnellEmail author
Original Paper


Biological tissues with a high glycosaminoglycan (GAG) content have an excellent ability to swell by absorbing water molecules from the surrounding environment. Our recent work showed that anisotropy in tissue swelling depends on the fiber-network architecture, including fiber angle, fiber stiffness, and lamellae structure. However, that work did not evaluate the effect of in situ boundary conditions, such as the kidney-bean shape of the annulus fibrosus (AF), on swelling behavior. The biochemical composition of intact AF is inhomogeneous with respect to GAG composition, collagen fiber angle, and fiber stiffness. Moreover, the GAG content in the inner AF decreases significantly with degeneration. In this study, we investigated the role of GAG content, fiber angle, and fiber stiffness in AF swelling and residual strain development using a finite element model based on a human lumbar disk. Our results showed that the annular ring structure had a great impact on swelling by developing region-dependent compressive stress/stretch in the inner layers and tensile stress/stretch in the outer AF. Swelling-based residual stretch was comparable to experimentally measured values, suggesting an important role of tissue swelling in maintaining residual stresses. Moreover, GAG loss in the inner AF, as observed with degeneration, decreased circumferential-direction stress by over 65%. Homogeneous distributions of fiber angle and stiffness overestimated or underestimated AF swelling behavior, such as swelling ratio, circumferential/axial stretch, and fiber stretch/reorientation. These findings demonstrate the need to include native fiber architecture in finite element models, to accurately predict tissue failure, as well as to cultivate engineered disks.


Swelling Residual stress Residual strain Annulus fibrosus Intervertebral disk Fiber angle Degeneration 


Authors’ contribution

Bo Yang and Grace D. O’Connell participated in study design, data analysis, data interpretation, and manuscript writing. Bo Yang did all the simulations. Both authors provided final approval for publication.


This work was supported by the Signatures Innovation Fellowship from the University of California.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. Acaroglu ER, Iatridis JC, Setton LA, Foster RJ, Mow VC, Weidenbaum M (1995) Degeneration and aging affect the tensile behavior of human lumbar anulus fibrosus. Spine 20:2690–2701CrossRefGoogle Scholar
  2. Adams MA, Roughley PJ (2006) What is intervertebral disc degeneration, and what causes it? Spine 31:2151–2161CrossRefGoogle Scholar
  3. Amiel D, Frank C, Harwood F, Fronek J, Akeson W (1983) Tendons and ligaments: a morphological and biochemical comparison. J Orthop Res 1:257–265CrossRefGoogle Scholar
  4. Antoniou J et al (1996) The human lumbar intervertebral disc: evidence for changes in the biosynthesis and denaturation of the extracellular matrix with growth, maturation, ageing, and degeneration. J Clin Investig 98:996–1003CrossRefGoogle Scholar
  5. Ateshian GA, Chahine NO, Basalo IM, Hung CT (2004) The correspondence between equilibrium biphasic and triphasic material properties in mixture models of articular cartilage. J Biomech 37:391–400CrossRefGoogle Scholar
  6. Ateshian GA, Costa KD, Azeloglu EU, Morrison B, Hung CT (2009) Continuum modeling of biological tissue growth by cell division, and alteration of intracellular osmolytes and extracellular fixed charge density. J Biomech Eng 131:101001CrossRefGoogle Scholar
  7. Azeloglu EU, Albro MB, Thimmappa VA, Ateshian GA, Costa KD (2008) Heterogeneous transmural proteoglycan distribution provides a mechanism for regulating residual stresses in the aorta American Journal of Physiology-Heart and Circulatory. Physiology 294:H1197–H1205Google Scholar
  8. Bezci SE, O’connell GD (2018) Osmotic pressure alters time-dependent recovery behavior of the intervertebral disc. Spine 43:E334–E340Google Scholar
  9. Bezci SE, Nandy A, O’Connell GD (2015) Effect of hydration on healthy intervertebral disk mechanical stiffness. J Biomech Eng 137:101007CrossRefGoogle Scholar
  10. Botsford D, Esses S, Ogilvie-Harris D (1994) vivo diurnal variation in intervertebral disc volume and morphology. Spine 19:935–940CrossRefGoogle Scholar
  11. Bowles RD, Williams RM, Zipfel WR, Bonassar LJ (2010) Self-assembly of aligned tissue-engineered annulus fibrosus and intervertebral disc composite via collagen gel contraction. Tissue Eng Part A 16:1339–1348CrossRefGoogle Scholar
  12. Cassidy J, Hiltner A, Baer E (1989) Hierarchical structure of the intervertebral disc. Connect Tissue Res 23:75–88CrossRefGoogle Scholar
  13. Chuong C-J, Fung Y-C (1986) Residual stress in arteries. In: Schmid-Schönbein GW, Woo SLY, Zweifach BW (eds) Frontiers in biomechanics. Springer, New York, NY, pp 117–129CrossRefGoogle Scholar
  14. Cortes DH, Jacobs NT, DeLucca JF, Elliott DM (2014) Elastic, permeability and swelling properties of human intervertebral disc tissues: a benchmark for tissue engineering. J Biomech 47:2088–2094CrossRefGoogle Scholar
  15. Demirkoparan H, Pence TJ (2018) Swelling–twist interaction in fiber-reinforced hyperelastic materials: the example of azimuthal shear. J Eng Math 109:63–84MathSciNetCrossRefzbMATHGoogle Scholar
  16. 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
  17. Ebara S, Iatridis JC, Setton LA, Foster RJ, Mow VC, Weidenbaum M (1996) Tensile properties of nondegenerate human lumbar anulus fibrosus. Spine 21:452–461CrossRefGoogle Scholar
  18. Emanuel KS, van der Veen AJ, Rustenburg CM, Smit TH, Kingma I (2018) Osmosis and viscoelasticity both contribute to time-dependent behaviour of the intervertebral disc under compressive load: a caprine in vitro study. J Biomech 70:10–15CrossRefGoogle Scholar
  19. Eyre DR, Muir H (1976) Types I and II collagens in intervertebral disc. Interchanging radial distributions in annulus fibrosus. Biochem J 157:267–270CrossRefGoogle Scholar
  20. Fung Y (1991) What are the residual stresses doing in our blood vessels? Ann Biomed Eng 19:237–249CrossRefGoogle Scholar
  21. Guerin HAL, Elliott DM (2006) Degeneration affects the fiber reorientation of human annulus fibrosus under tensile load. J Biomech 39:1410–1418CrossRefGoogle Scholar
  22. Gullbrand SE et al (2018) Towards the scale up of tissue engineered intervertebral discs for clinical application. Acta Biomater 70:154–164CrossRefGoogle Scholar
  23. Holzapfel GA, Schulze-Bauer C, Feigl G, Regitnig P (2005) Single lamellar mechanics of the human lumbar anulus fibrosus. Biomech Model Mechanobiol 3:125–140CrossRefGoogle Scholar
  24. Jackson AR, Yuan T-Y, Huang C-Y, Gu WY (2009) A conductivity approach to measuring fixed charge density in intervertebral disc tissue. Ann Biomed Eng 37:2566–2573CrossRefGoogle Scholar
  25. 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 47:2540–2546CrossRefGoogle Scholar
  26. Lai WM, Hou J, Mow VC (1991) A triphasic theory for the swelling and deformation behaviors of articular cartilage. J Biomech Eng 113:245–258CrossRefGoogle Scholar
  27. Maas SA, Ellis BJ, Ateshian GA, Weiss JA (2012) FEBio: finite elements for biomechanics. J Biomech Eng 134:011005CrossRefGoogle Scholar
  28. Marchand F, Ahmed AM (1990) Investigation of the laminate structure of lumbar disc anulus fibrosus. Spine 15:402–410CrossRefGoogle Scholar
  29. Martin J et al (2017) In vitro maturation and in vivo integration and function of an engineered cell-seeded disc-like angle ply structure (DAPS) for total disc arthroplasty. Sci Rep 7:15765CrossRefGoogle Scholar
  30. Mengoni M, Kayode O, Sikora SN, Zapata-Cornelio FY, Gregory DE, Wilcox RK (2017) Annulus fibrosus functional extrafibrillar and fibrous mechanical behaviour: experimental and computational characterisation. R Soc Open Sci 4:170807CrossRefGoogle Scholar
  31. Michalek A, Gardner-Morse M, Iatridis J (2012) Large residual strains are present in the intervertebral disc annulus fibrosus in the unloaded state. J Biomech 45:1227–1231CrossRefGoogle Scholar
  32. Nerurkar NL, Sen S, Huang AH, Elliott DM, Mauck RL (2010) Engineered disc-like angle-ply structures for intervertebral disc replacement. Spine 35:867CrossRefGoogle Scholar
  33. O’connell GD, Vresilovic EJ, Elliott DM (2007) Comparison of animals used in disc research to human lumbar disc geometry. Spine 32:328–333CrossRefGoogle Scholar
  34. O’Connell GD, Guerin HL, Elliott DM (2009) Theoretical and uniaxial experimental evaluation of human annulus fibrosus degeneration. J Biomech Eng 131:111007CrossRefGoogle Scholar
  35. Peloquin JM, Yoder JH, Jacobs NT, Moon SM, Wright AC, Vresilovic EJ, Elliott DM (2014) Human L3L4 intervertebral disc mean 3D shape, modes of variation, and their relationship to degeneration. J Biomech 47:2452–2459CrossRefGoogle Scholar
  36. Rachev A, Greenwald S (2003) Residual strains in conduit arteries. J Biomech 36:661–670CrossRefGoogle Scholar
  37. Rigozzi S, Müller R, Snedeker JG (2009) Local strain measurement reveals a varied regional dependence of tensile tendon mechanics on glycosaminoglycan content. J Biomech 42:1547–1552CrossRefGoogle Scholar
  38. Roccabianca S, Ateshian GA, Humphrey JD (2014) Biomechanical roles of medial pooling of glycosaminoglycans in thoracic aortic dissection. Biomech Model Mechanobiol 13:13–25CrossRefGoogle Scholar
  39. Rohlmann A, Zander T, Schmidt H, Wilke H-J, Bergmann G (2006) Analysis of the influence of disc degeneration on the mechanical behaviour of a lumbar motion segment using the finite element method. J Biomech 39:2484–2490CrossRefGoogle Scholar
  40. Roughley P, Hoemann C, DesRosiers E, Mwale F, Antoniou J, Alini M (2006) The potential of chitosan-based gels containing intervertebral disc cells for nucleus pulposus supplementation. Biomaterials 27:388–396CrossRefGoogle Scholar
  41. Schmidt H, Kettler A, Rohlmann A, Claes L, Wilke H-J (2007) The risk of disc prolapses with complex loading in different degrees of disc degeneration–a finite element analysis. Clin Biomech 22:988–998CrossRefGoogle Scholar
  42. Screen HR, Chhaya VH, Greenwald SE, Bader DL, Lee DA, Shelton JC (2006) The influence of swelling and matrix degradation on the microstructural integrity of tendon. Acta Biomater 2:505–513CrossRefGoogle Scholar
  43. Shirazi-Adl A, Ahmed AM, Shrivastava SC (1986) Mechanical response of a lumbar motion segment in axial torque alone and combined with compression. Spine 11:914–927CrossRefGoogle Scholar
  44. Skaggs D, Weidenbaum M, Iatridis JC, Ratcliffe A, Mow VC (1994) Regional variation in tensile properties and biochemical composition of the human lumbar anulus fibrosus. Spine 19:1310–1319CrossRefGoogle Scholar
  45. Stadie WC, Sunderman FW (1931) The osmotic coefficient of sodium in sodium hemoglobinate and of sodium chloride in hemoglobin solution. J Biol Chem 91:227–241Google Scholar
  46. Urban J, Maroudas A (1979) The measurement of fixed charged density in the intervertebral disc. Biochimica et Biophysica Acta (BBA)-Gen Subj 586:166–178CrossRefGoogle Scholar
  47. Vergroesen P-PA, van der Veen AJ, Emanuel KS, van Dieën JH, Smit TH (2016) The poro-elastic behaviour of the intervertebral disc: a new perspective on diurnal fluid flow. J Biomech 49:857–863CrossRefGoogle Scholar
  48. Yang B, O’Connell GD (2017) Effect of collagen fibre orientation on intervertebral disc torsion mechanics. Biomech Model Mechanobiol 16:2005–2015CrossRefGoogle Scholar
  49. Yang B, O’Connell GD (2018) Swelling of fiber-reinforced soft tissues is affected by fiber orientation, fiber stiffness, and lamella structure. J Mech Behav Biomed Mater 82:320–328CrossRefGoogle Scholar
  50. Yasuda H, Lamaze C, Ikenberry L (1968) Permeability of solutes through hydrated polymer membranes. Part I. Diffusion of sodium chloride. Macromol Chem Phys 118:19–35CrossRefGoogle Scholar
  51. Żak M, Pezowicz C (2016) Analysis of the impact of the course of hydration on the mechanical properties of the annulus fibrosus of the intervertebral disc. Eur Spine J 25:2681–2690CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of California, BerkeleyBerkeleyUSA
  2. 2.Department of Orthopaedic SurgeryUniversity of California, San FranciscoSan FranciscoUSA

Personalised recommendations