Finite element implementation of a multiscale model of the human lens capsule
- 298 Downloads
An axisymmetric finite element implementation of a previously described structural constitutive model for the human lens capsule (Burd in Biomech Model Mechanobiol 8(3):217–231, 2009) is presented. This constitutive model is based on a hyperelastic approach in which the network of collagen IV within the capsule is represented by an irregular hexagonal planar network of hyperelastic bars, embedded in a hyperelastic matrix. The paper gives a detailed specification of the model and the periodic boundary conditions adopted for the network component. Momentum balance equations for the network are derived in variational form. These balance equations are used to develop a nonlinear solution scheme to enable the equilibrium configuration of the network to be computed. The constitutive model is implemented within a macroscopic finite element framework to give a multiscale model of the lens capsule. The possibility of capsule wrinkling is included in the formulation. To achieve this implementation, values of the first and second derivatives of the strain energy density with respect to the in-plane stretch ratios need to be computed at the local, constitutive model, level. Procedures to determine these strain energy derivatives at equilibrium configurations of the network are described. The multiscale model is calibrated against previously published experimental data on isolated inflation and uniaxial stretching of ex vivo human capsule samples. Two independent example lens capsule inflation analyses are presented.
KeywordsMultiscale Human lens capsule Accommodation Collagen
The mesh for the in situ capsule inflation analysis was generated by GS Wilde. The authors acknowledge the assistance provided by RI Barraquer, S Krag, H Martin and R Michael in providing numerical values of previously published experimental data. RAR gratefully acknowledges funding from the US Army Medical Research and Materiel Command (USAMRMC) grant W81XWH-10-1-1036, the US–UK Fulbright Commission, and the Royal Society International Exchanges Scheme.
- Bron AJ, Tripathi RC, Tripathi BJ (1997) Wolff’s anatomy of the eye and orbit. Chapman Hall, LondonGoogle Scholar
- D’Amore A, Amoroso N, Gottardi R, Hobson C, Carruthers C, Watkins S, Wagner WR and Sacks MS (2014) From single fiber to macro-level mechanics: a structural finite-element model for elastomeric fibrous biomaterials. J Mech Behav Biomed Mater 39:146–161Google Scholar
- Fisher RF, Pettet BE (1972) The postnatal growth of the capsule of the human crystalline lens. J Anat 112(2):207–214Google Scholar
- Holzapfel GA (2000) Nonlinear solid mechanics: a continuum approach for engineering. Wiley, LondonGoogle 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):357–363Google Scholar
- Martin H, Schmidt W, Schmitz KP, Schneider H, Guthoff R, Terwee T (2003) Material properties of the isolated human capsular bag. Curr Asp Hum Accommod II:127–133Google Scholar
- Oyster CW (1999) The human eye: structure and function. Sinauer, Sunderland, MAGoogle Scholar
- Schumacher S, Oberheide U, Fromm M, Ripken T, Ertmer W, Gerten G, Wegener A, Lubatschowski H (2009) Femtosecond laser induced flexibility change of human donor lenses. Vis Res 49(14):1853–1859Google 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):836–844CrossRefGoogle Scholar