Skip to main content
SpringerLink
Log in

A structural constitutive model for the human lens capsule

  • Original Paper
  • Published:
Biomechanics and Modeling in Mechanobiology Aims and scope Submit manuscript

Abstract

Published data on the mechanical performance of the human lens capsule when tested under uniaxial and biaxial conditions are reviewed. It is concluded that two simple phenomenological constitutive models (namely a linear elastic model and a Fung-type hyperelastic model) are unable to provide satisfactory representations of the mechanical behaviour of the capsule for both of these loading conditions. The possibility of resolving these difficulties using a structural constitutive model for the capsule, of a form that is inspired by the network of collagen IV filaments that exist within the lens capsule, is explored. The model is implemented within a rectangular periodic cell. Prescribed stretches are imposed on the periodic cell and the network is allowed to deform in a non-affine manner. The performance of the constitutive model correlates well with previously published test data. One possible application of the model is in the development of a multi-scale analysis of the mechanics of the human lens capsule.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Barnard K, Burgess SA, Carter DA, Woolley DM (1992) Three-dimensional structure of type IV collagen in the mammalian lens capsule. J Struct Biol 108(1): 6–13

    Article  Google Scholar 

  • Belaidi A, Pierscionek BK (2007) Modeling internal stress distributions in the human lens: can opponent theories coexist?. J Vis 7(11): 1–12

    Article  Google Scholar 

  • Bonet J, Wood RD (1997) Nonlinear continuum mechanics for finite element analysis. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Burd HJ, Judge SJ, Cross JA (2002) Numerical modelling of the accommodating lens. Vis Res 42(18): 2235–2251

    Article  Google Scholar 

  • Cavalcante FSA, Ito S, Brewer K, Sakai H, Alencar AM, Almeida MP, Andrade JS Jr, Majumdar A, Ingenito EP, Suki B (2005) Mechanical interactions between collagen and proteoglycans: implications for the stability of lung tissue. J Appl Physiol 98(2): 672–679

    Article  Google Scholar 

  • Chandran PL, Barocas VH (2006) Affine versus non-affine fibril kinematics in collagen networks: theoretical studies of network behavior. J Biomech Eng 128(2): 259–270

    Article  Google Scholar 

  • Chandran PL, Barocas VH (2007) Deterministic material-based averaging theory model of collagen gel micromechanics. J Biomech Eng 129(2): 137–147

    Article  Google Scholar 

  • Crisfield MA (1996) Non-linear finite element analysis of solids and structures: essentials, vol 1. Wiley, London

    Google Scholar 

  • Danielsen CC (2004) Tensile mechanical and creep properties of Descemet’s membrane and lens capsule. Exp Eye Res 79(3): 343–350

    Article  Google Scholar 

  • David G, Humphrey JD (2007) Finite element model of stresses in the anterior lens capsule of the eye. Comput Methods Biomech Biomed Eng 10(3): 237–243

    Article  Google Scholar 

  • David G, Pedrigi RM, Heistand MR, Humphrey JD (2007) Regional multiaxial mechanical properties of the porcine anterior lens capsule. J Biomech Eng 129(1): 97–104

    Article  Google Scholar 

  • Deshpande VS, Ashby MF, Fleck NA (2001) Foam topology: bending versus stretching dominated architectures. Acta Mater 49(6): 1035–1040

    Article  Google Scholar 

  • Dubbelman M, Van der Heijde GL, Weeber HA (2005) Change in shape of the aging human crystalline lens with accommodation. Vis Res 45(1): 117–132

    Article  Google Scholar 

  • Fisher RF (1969) Elastic constants of the human lens capsule. J Physiol 201(1): 1–19

    Google Scholar 

  • Gathercole LJ, Barnard K, Atkins EDT (1989) Molecular organization of type IV collagen: polymer liquid crystal-like aspects. Int J Biol Macromol 11(6): 335–338

    Article  Google Scholar 

  • Hermans EA, Dubbelman M, van der Heijde GL, Heethaar RM (2006) Estimating the external force acting on the human eye lens during accommodation by finite element modelling. Vis Res 46(21): 3642–3650

    Article  Google Scholar 

  • Holzapfel GA (2000) Nonlinear solid mechanics: a continuum approach for engineering. Wiley, Chichester

    MATH  Google Scholar 

  • Holzapfel GA, Gasser TC, Ogden RW (2000) A new constitutive framework for arterial wall mechanics and a comparative study of material models. J Elast 61(1–3): 1–48

    Article  MATH  MathSciNet  Google Scholar 

  • Hutchinson RG, Fleck NA (2006) The structural performance of the periodic truss. J Mech Phys Solids 54(4): 756–782

    Article  MATH  MathSciNet  Google Scholar 

  • Inoue S (1994) Basic structure of basement membranes is a fine network of ‘cords,’ irregular anastomosing strands. Micros Res Tech 28(1): 29–47

    Article  Google Scholar 

  • Inoue S, Leblond CP (1988) Three-dimensional network of cords: the main component of basement membranes. Am J Anat 181(4): 341–358

    Article  Google Scholar 

  • Knupp C, Squire JM (2005) Molecular packing in network-forming collagens. Adv Protein Chem 70: 375–403

    Article  Google Scholar 

  • Krag S, Andreassen TT (2003) Mechanical properties of the human lens capsule. Prog Retin Eye Res 22(6): 749–767

    Article  Google Scholar 

  • Krag S, Thim K, Corydon L, Kyster B (1994) Biomechanical aspects of the anterior capsulotomy. J Cataract Refract Surg 20(4): 410–416

    Google Scholar 

  • Krag S, Olsen T, Andreassen TT (1997) Biomechanical characteristics of the human anterior lens capsule in relation to age. Invest Ophthalmol Vis Sci 38(2): 357–363

    Google Scholar 

  • Kuhn K (1995) Basement membrane (type IV) collagen. Matrix Biol 14(6): 439–445

    Article  Google Scholar 

  • Lanir Y (1983) Constitutive equations for fibrous connective tissues. J Biomech 16(1): 1–12

    Article  Google Scholar 

  • Menapace R, Findl O, Kriechbaum K, Leydolt-Koeppl C (2007) Accommodating intraocular lenses: a critical review of present and future concepts. Graefe’s Arch Clin Exp Ophthalmol 245(4): 473–489

    Article  Google Scholar 

  • Onck PR, Koeman T, van Dillen T, van der Giessen E (2005) Alternative explanation of stiffening in cross-linked semiflexible networks. Phys Rev Lett 95(17): 178102

    Article  Google Scholar 

  • Ostoja-Starzewski M (2002) Lattice models in micromechanics. Appl Mech Rev 55(1): 35–59

    Article  MathSciNet  Google Scholar 

  • Oyster CW (1999) The human eye: structure and function. Sinauer, Sunderland

    Google Scholar 

  • Pedrigi RM, David G, Dziezyc J, Humphrey JD (2007) Regional mechanical properties and stress analysis of the human anterior lens capsule. Vis Res 47(13): 1781–1789

    Article  Google Scholar 

  • Pinsky PM, van der Heide D, Chernyak D (2005) Computational modeling of mechanical anisotropy in the cornea and sclera. J Cataract Refract Surg 31(1): 136–145

    Article  Google Scholar 

  • Rosen AM, Denham DB, Fernandez V, Borja D, Ho A, Manns F, Parel J-M, Augusteyn RC (2006) In vitro dimensions and curvatures of human lenses. Vis Res 46(6–7): 1002–1009

    Article  Google Scholar 

  • Sacks MS (2003) Incorporation of experimentally-derived fiber orientation into a structural constitutive model for planar collagenous tissues. J Biomech Eng 125(2): 280–287

    Article  Google Scholar 

  • Stachs O, Martin H, Behrend D, Schmitz KP, Guthoff R (2006) Three-dimensional ultrasound biomicroscopy, environmental and conventional scanning electron microscopy investigations of the human zonula ciliaris for numerical modelling of accommodation. Graefe’s Arch Clin Exp Ophthalmol 244(7): 836–844

    Article  Google Scholar 

  • Timpl R, Brown JC (1996) Supramolecular assembly of basement membranes. BioEssays 18(2): 123–132

    Article  Google Scholar 

  • Weeber HA, van der Heijde RGL (2007) On the relationship between lens stiffness and accommodative amplitude. Exp Eye Res 85(5): 602–607

    Article  Google Scholar 

  • Yurchenco PD (1994) Assembly of laminin and type IV collagen into basement membrane networks. Extracellular matrix assembly and structure. Academic Press, San Diego, pp 351–388

  • Yurchenco PD, Ruben GC (1987) Basement membrane structure in situ: evidence for lateral associations in the type IV collagen network. J Cell Biol 105(6): 2559–2568

    Article  Google Scholar 

  • Yurchenco PD, Schittny JC (1990) Molecular architecture of basement membranes. FASEB J 4(6): 1577–1590

    Google Scholar 

  • Yurchenco PD, Tsilibary EC, Charonis AS, Furthmayr H (1986) Models for the self-assembly of basement membrane. J Histochem Cytochem 34(1): 93–102

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Engineering Science, Oxford University, Oxford, OX1 3PJ, UK

    Harvey John Burd

Authors
  1. Harvey John Burd
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Harvey John Burd.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Burd, H.J. A structural constitutive model for the human lens capsule. Biomech Model Mechanobiol 8, 217–231 (2009). https://doi.org/10.1007/s10237-008-0130-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10237-008-0130-5

Keywords

Search

Navigation