June 2015
Volume 56, Issue 7
ARVO Annual Meeting Abstract  |   June 2015
A computational model for collagen-swelling interaction in the in vivo human cornea
Author Affiliations & Notes
  • Xi Cheng
    Mechanical Engineering, Stanford University, Stanford, CA
  • Steven J Petsche
    Mechanical Engineering, Stanford University, Stanford, CA
  • Peter Michael Pinsky
    Mechanical Engineering, Stanford University, Stanford, CA
  • Footnotes
    Commercial Relationships Xi Cheng, None; Steven Petsche, None; Peter Pinsky, None
  • Footnotes
    Support None
Investigative Ophthalmology & Visual Science June 2015, Vol.56, 1109. doi:
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      Xi Cheng, Steven J Petsche, Peter Michael Pinsky; A computational model for collagen-swelling interaction in the in vivo human cornea. Invest. Ophthalmol. Vis. Sci. 2015;56(7 ):1109.

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      © ARVO (1962-2015); The Authors (2016-present)

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Purpose: The mechanical behavior and stability of the in vivo cornea depends on the 3-D organization of stromal lamellae, on the stromal hydration, and on the interaction between collagen and swelling forces. A computational biomechanical model for the in vivo cornea, based on the full 3-D lamella organization and osmotic pressure-based swelling, is used to investigate: (i) the role of the specific collagen architecture in corneal biomechanical behavior, including depth-dependent lamella inclination and interweaving, and (ii) collagen-swelling interaction in normal and diseased cornea.

Methods: A continuum mechanics-based 3-D model of corneal behavior has been developed with two principal modeling inputs: (i) the elasticity of the stroma, and (ii) the swelling behavior. The elasticity is based on averaging with lamella orientation distributions at every point in the cornea, and where the orientation distributions are derived from a synthesis of X-ray diffraction data and second harmonic-generated image processing. The swelling behavior is modeled using equilibrium thermodynamics for osmotic pressure and accounting for active endothelial ion transport which modifies stromal ionic concentrations. The coupled models are embedded in a general 3-D finite element framework and used to simulate corneal biomechanical performance in the normal and swollen state.

Results: Depth-dependence of lamella inclination was found to significantly affect mechanical and in vivo swelling behavior. Shear stiffness is predicted to be greater in the anterior cornea, which was confirmed by direct experimental measurement. Modeling of swollen corneas (Fuch’s dystrophy) predicts predominant swelling in the posterior stroma and the role of lamella inclination is clarified by synthetically varying inclination. Adapted to ex vivo conditions, the model accurately predicts swelling pressure experimental measurements.

Conclusions: The model quantifies both lamella-lamella and lamella-swelling structural interactions and predicts a relatively rigid anterior stromal region. In vivo swelling simulations reproduce observed primary swelling in the posterior stroma and little change in anterior surface curvature. The model can predict swelling due to reduction in active endothelial ion transport. The proposed model is a significant improvement over existing pure elasticity approaches which cannot address swelling.


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