Computational modeling of mechanical anisotropy in the cornea and sclera
ABSTRACT 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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ABSTRACT: It is thought that corneal surface topography may be stabilised by the angular orientation of out-of plane lamellae that insert into the anterior limiting membrane. In this study micro-focus x-ray scattering data were used to obtain quantitative information about lamellar inclination (with respect to the corneal surface) and the x-ray scatter intensity throughout the depth of the cornea from the centre to the temporal limbus. The average collagen inclination remained predominantly parallel to the tissue surface at all depths. However, in the central cornea, the spread of inclination angles was greatest in the anterior-most stroma (reflecting the increased lamellar interweaving in this region), and decreased with tissue depth; in the peripheral cornea inclination angles showed less variation throughout the tissue thickness. Inclination angles in the deeper stroma were generally higher in the peripheral cornea, suggesting the presence of more interweaving in the posterior stroma away from the central cornea. An increase in collagen x-ray scatter was identified in a region extending from the sclera anteriorly until about 2mm from the corneal centre. This could arise from the presence of larger diameter fibrils, probably of scleral origin, which are known to exist in this region. Incorporation of this quantitative information into finite element models will further improve the accuracy with which they can predict the biomechanical response of the cornea to pathology and refractive procedures.Journal of The Royal Society Interface 01/2015; 12(104). DOI:10.1098/rsif.2014.0717 · 3.86 Impact Factor
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ABSTRACT: To demonstrate a Scheimpflug-based imaging procedure for investigating the depth- and time-dependent strain response of the human cornea to inflation testing of whole eye globes.PLoS ONE 11/2014; 9(11):e112169. DOI:10.1371/journal.pone.0112169 · 3.53 Impact Factor
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ABSTRACT: A numerical model based in continuum mechanics theory has been developed which represents the 3D anisotropic behaviour of the corneal stroma. Experimental data has been gathered from a number of previous studies to provide the basis and calibration parameters for the numerical modelling. The resulting model introduces numerical representation of collagen fibril density and its related regional variation, interlamellar cohesion and age-related stiffening in an anisotropic model of the human cornea. Further, the model incorporates previous modelling developments including representation of lamellae anisotropy and stiffness of the underlying matrix. Wide angle X-ray scattering has provided measured data which quantifies relative fibril anisotropy in the 2D domain. Accurate numerical description of material response to deformation is essential to providing representative simulations of corneal behaviour. Representing experimentally obtained 2D anisotropy and regional density variation in the 3D domain is an essential component of this accuracy. The constitutive model was incorporated into finite element analysis. Combining with inverse analysis, the model was calibrated to an extensive experimental database of ex vivo corneal inflation tests and ex vivo corneal shear tests. This model represents stiffness of the underlying matrix which is 2-3 orders of magnitude than the mechanical response representing the collagen fibrils in the lamellae. The presented model, along with its age dependent material coefficients, allows finite element modelling for an individual patient with material stiffness approximated based on their age. This has great potential to be used in both daily clinical practice for the planning and optimization of corrective procedures and in pre-clinical optimization of diagnostic procedures.Journal of the Mechanical Behavior of Biomedical Materials 11/2014; 42. DOI:10.1016/j.jmbbm.2014.11.006 · 3.05 Impact Factor