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A Multi-Scale Model for the Mechanics of the Human Lens Capsule Harvey Burd Civil Engineering Research Group Department of Engineering Science, Oxford University, UK Finite element model Schematic eye capsule

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Scope Background Accommodation mechanism Finite element analysis of the human lens Mechanics of the lens capsule Uniaxial and biaxial test data. Structural constitutive model (Micronet) 1 Multi-scale finite element analysis Implementation of the Micronet model in an axisymmetric hyperelastic finite element program Example analyses 1. Burd (2009) Biomech Model Mechanobiol 8(3) 217-231

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Anatomy of the human eye Aqueous Vitreous Ciliary body Zonules

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Accommodation (Helmholtz 1909) Zonule Ciliary body Iris Cornea AccommodatedUnaccommodated

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Lens : geometric model ref. Wolffs Anatomy Axis of symmetry Lens outline MRI data on 29 and 45 year lenses. Hermans et al. 2008 Zonule geometry: Age-related model for the geometry of the intersection of zonules with capsule. Canals et al. 1996; Farnsworth and Shyne 1979 Ciliary body radius: MRI data. Strenk et al. 1999 Nucleus outline Brown, 1973; Dubbelman et al., 2003; Hermans et al., 2007; Kasthurirangan et al., 2008; Sweeney and Truscott, 1998; Ayaki et al., 1993; Gullapalli et al., 1995

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Lens capsule: geometric model http://www.kumc.edu/instruction/medicine/anatomy/h istoweb/eye_ear/eye_ear.htm 250 Microns Capsule Lens Data from: Barraquer et al. (2006). Human lens capsule thickness as a function of age and location along the sagittal lens perimeter. IOVS Capsule thickness Anterior pole Posterior pole

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(a) Uniaxial Test (Krag et al. 2003) Sample cut from lens capsule Stress MPa Strain % Mechanics of the lens capsule

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(b) Biaxial tests (i) Isolated capsule inflation test (Fisher 1969) Initial capsule geometry P

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(ii) In-situ capsule inflation (Pedrigi et al. 2007)

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uniaxial test biaxial test Linear elastic model; data on Youngs modulus

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A structural model for the lens capsule (a) Structure of the lens capsule Barnard et al. 1992 50 nm Filaments of collagen type IV Barnard et al. 1992 J. Struct. Biol.

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(b) Components of a structural model Non-linear pin-jointed bars ( 2 parameters) Neo-Hookean matrix ( 1 parameter) after Barnard et al. 1992

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(b) Components of a structural model (i) Strain energy density ( ii) Neo-Hookean model for matrix networkmatrix a1a1 a2a2

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(b) Components of a structural model (iii) Strain energy density for bars where

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Implementation in multi-scale finite element model a1a1 a2a2 internal bars edge bars Specify stretch ratios 1 and 2 Apply periodic boundary conditions Constrain one joint to be fixed Compute updated joint coordinates ( W=0) Compute derivatives Initial configuration

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Generating the internal mesh

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Calibration tests Membrane traction = (a) Uniaxial test (b) Biaxial test Membrane traction =

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Simulation of isolated capsule inflation test Fisher (1969)

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Simulation of in-situ capsule inflation test Pedrigi et al. (2007)

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Simulation of in-situ capsule inflation test Pedrigi et al. (2007)

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Simulation of in-situ capsule inflation test circumferential meridional Point D Point X

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Simulation of in-situ capsule inflation test Point D Point F

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Conclusions 3-parameter structural model for the lens capsule Implementation in axisymmetric finite element analysis Comparison with previous capsule inflation data