Computational modeling of mechanical anisotropy in the cornea and sclera

Department of Mechanical Engineering, Stanford University, Stanford, California 94305-4040, USA.
Journal of Cataract and Refractive Surgery (Impact Factor: 2.72). 02/2005; 31(1):136-45. DOI: 10.1016/j.jcrs.2004.10.048
Source: PubMed


To determine the biomechanical deformation of the cornea resulting from tissue cutting and removal by use of a new computational model and to investigate the effect of mechanical anisotrophy resulting from the fibrillar architecture.
Department of Mechanical Engineering, Stanford University, Stanford, California, USA.
A mathematical model for a typical lamella that explicitly accounts for the strain energy of the collagen fibrils, extrafibrillar matrix, and proteoglycan cross-linking was developed. A stromal model was then obtained by generalized averaging of the lamella properties through the stromal thickness, taking into account the preferred orientations of the collagen fibrils, which were obtained from x-ray scattering data.
The model was used to predict astigmatism induced by a tunnel incision in the sclera, such as is used for cataract extraction and intraocular lens implantation. The amount of induced cylinder was in good agreement with published clinical data. Results show it is important for the model to incorporate preexisting corneal physiological stress caused by intraocular pressure.
The mathematical model described appears to provide a framework for further development, capturing the essential features of mechanical anisotropy of the cornea. The tunnel incision simulation indicated the importance of the anisotropy in this case.

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    • "Specifically, we described the mechanical behavior of the matrix phase using a nearly incompressible neo-Hookean model [14] [17] [55] "
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    ABSTRACT: The objective of this study was to measure the collagen fiber structure and estimate the material properties of 7 human donor scleras, from age 53 to 91. The specimens were subjected to inflation testing, and the full-field displacement maps were measured by digital image correlation (DIC). After testing, the collagen fiber structure was mapped using wide-angle x-ray scattering (WAXS). A specimen-specific inverse finite element method was applied to calculate the material properties of the collagen fibers and inter-fiber matrix by minimizing the difference between the experimental displacements and model predictions. Age effects on the fiber structure and material properties were estimated using multivariate models accounting for spatial autocorrelation. Older age was associated with a larger matrix stiffness (p=0.001), a lower degree of fiber alignment in the peripapillary sclera (p=0.01), and a lower mechanical anisotropy in the peripapillary sclera (p=0.03).
    Journal of Biomechanical Engineering 12/2014; 137(4). DOI:10.1115/1.4029430 · 1.78 Impact Factor
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    • "It has been shown (Cortes et al. 2010) that for somewhat dispersed orientations, the models can be inaccurate for large strains. Optimally, the distribution of fiber orientations should be integrated over a directional distribution function (Pinsky et al. 2005; Nguyen et al. 2008). In some cases, closed-form solutions exist for approximated distributions. "
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    ABSTRACT: During the maturation of some mammals such as mice and rats, corneal epithelial cells tend to develop into patterns such as spirals over time. A better understanding of these patterns can help to understand how the organ develops and may give insight into some of the diseases affecting corneal development. In this paper, a framework for explaining the development of the epithelial cells forming spiral patterns due to the effect of tensile and shear strains is proposed. Using chimeric animals, made by combining embryonic cells from genetically distinguishable strains, we can observe the development of patterns in the cornea. Aggregates of cell progeny from one strain or the other called patches form as organs and tissue develop. The boundaries of these patches are fitted with logarithmic spirals on confocal images of adult rat corneas. To compare with observed patterns, we develop a three-dimensional large strain finite element model for the rat cornea under intraocular pressure to examine the strain distribution on the cornea surface. The model includes the effects of oriented and dispersed fibrils families throughout the cornea and a nearly incompressible matrix. Tracing the directions of critical strain vectors on the cornea surface leads to spiral-like curves that are compared to the observed logarithmic spirals. Good agreement between the observed and numerical curves supports the proposed assumption that shear and tensile strains facilitate sliding of epithelial cells to develop spiral patterns.
    Biomechanics and Modeling in Mechanobiology 06/2014; 14(1). DOI:10.1007/s10237-014-0592-6 · 3.15 Impact Factor
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    • "Recently, the mathematical characterization of such tissues has seen important advances (Soldatos, 2009). Among others, we can mention the spatial distribution of the fiber orientation (Alastru√© et al., 2006; Federico and Gasser, 2010; Gasser et al., 2006; Kroon and Holzapfel, 2008; Pandolfi and Vasta, 2012; Pinsky et al., 2005; Raghupathy and Barocas, 2009; Roy et al., 2010; Vasta et al., 2013; Wang et al., 2012). "

    International Journal of Engineering Science 01/2014; 74:48. · 2.67 Impact Factor
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