Xabier Larrea

Biomechanical model of human cornea based on stromal microstructure.

The optical characteristics of the human cornea depends on the mechanical balance between the intra-ocular pressure and intrinsic tissue stiffness. A wide range of ophthalmic surgical procedures alter corneal biomechanics to induce local or global curvature changes for the correction of visual acuity. Due to the large number of surgical interventions performed every day, a deeper understanding of corneal biomechanics is needed to improve the safety of these procedures and medical devices. The aim of this study is to propose a biomechanical model of the human cornea, based on stromal microstructure. The constitutive mechanical law includes collagen fiber distribution based on X-ray scattering analysis, collagen cross-linking, and fiber uncrimping. Our results showed that the proposed model reproduced inflation and extensiometry experimental data [Elsheikh et al., Curr. Eye Res., 2007; Elsheikh et al., Exp. Eye Res., 2008] successfully. The mechanical properties obtained for different age groups demonstrated an increase in collagen cross-linking for older specimens. In future work such a model could be used to simulate non-symmetric interventions, and provide better surgical planning.

Oxygen and glucose distribution after intracorneal lens implantation.

Purpose. Insertion of an implant in the cornea to achieve corneal multifocality has been suggested as a solution for presbyopia. However, unresolved issues related to nutrient transport need to be resolved. Our aim was to find the best lens position and influence lens transport properties in order to optimize nutrient supply to corneal cells. Method. An axisymmetric corneal model was built to simulate the nutrient transport in the cornea. Oxygen and glucose concentrations were calculated for normal cornea and intracorneal lens wearing conditions. The simulation considers the different tissue layers (epithelium, stroma, and endothelium) as well as layer and solute concentration dependent consumption. Results. The minimum oxygen tension in the cornea was found to be higher when the lens was placed at 3/4 of the corneal thickness. Moreover, in this position, the influence of the inlay diffusivity was smaller than at more anterior or posterior placements. The diffusivity of the inlay affects the way nutrients will be transported through the cornea. The threshold where glucose may diffuse through or around the implant was found to be 1/100th of the stromal diffusivity. Conclusions. Computational methods are especially attractive to study nutrient transport in the cornea due to the difficulties associated with in vivo or in vitro measurements. The exact parameters that dictate the corneal metabolism are not known. However, the combined analysis of oxygen and glucose distribution is valuable in order to predict the complex physiological changes that arise under intracorneal lens implantation.

A transient diffusion model of the cornea for the assessment of oxygen diffusivity and consumption.

PURPOSE Oxygen diffusivity and consumption in the human cornea have not been directly measured yet; current models rely on properties measured in vitro in rabbit corneas. The aim of this study was to present a mathematical model of time-dependent oxygen diffusion that permits the estimation of corneal consumption and diffusivity. METHODS The current oxygen diffusion model was extended to include the temporal domain and was used to simulate in vivo noninvasive measurements of tear oxygen tension in human corneas. RESULTS The new model reproduced experimental data successfully, provided values for corneal diffusivity and consumption, and described the relationship between oxygen consumption and oxygen tension in the cornea. Estimated values were three times higher than those reported previously in in vitro rabbit experiments. CONCLUSIONS This model allowed for the further investigation of oxygen transport in the cornea, including a better mathematical description and a determination of the transport properties of the cornea and the specific oxygen uptake rate of the tissue. The combination of this model and tear oxygen tension measurements can be useful in determining the individual oxygen uptake rate and exploring the relationship between oxygen transport and corneal abnormalities.

Influence of Smoothing on Voxel-Based Mesh Accuracy in Micro-Finite Element

The interest in automatic volume meshing for finite element analysis (FEA) has grown more since the appearance of microfocus CT (μCT), due to its high resolution, which allows for the assessment of mechanical behaviour at a high precision. Nevertheless, the basic meshing approach of generating one hexahedron per voxel produces jagged edges. To prevent this effect, smoothing algorithms have been introduced to enhance the topology of the mesh. However, whether smoothing also improves the accuracy of voxel-based meshes in clinical applications is still under question. There is a trade-off between smoothing and quality of elements in the mesh. Distorted elements may be produced by excessive smoothing and reduce accuracy of the mesh. In the present work, influence of smoothing on the accuracy of voxel-based meshes in micro-FE was assessed. An accurate 3D model of a trabecular structure with known apparent mechanical properties was used as a reference model. Virtual CT scans of this reference model (with resolutions of 16, 32 and 64 μm) were then created and used to build voxel-based meshes of the microarchitecture. Effects of smoothing on the apparent mechanical properties of the voxel-based meshes as compared to the reference model were evaluated. Apparent Young’s moduli of the smooth voxel-based mesh were significantly closer to those of the reference model for the 16 and 32 μm resolutions. Improvements were not significant for the 64 μm, due to loss of trabecular connectivity in the model. This study shows that smoothing offers a real benefit to voxel-based meshes used in micro-FE. It might also broaden voxel-based meshing to other biomechanical domains where it was not used previously due to lack of accuracy. As an example, this work will be used in the framework of the European project ContraCancrum, which aims at providing a patient-specific simulation of tumour development in brain and lungs for oncologists. For this type of clinical application, such a fast, automatic, and accurate generation of the mesh is of great benefit.

Automatic Mesh Smoothing For Finite Element Modeling From 3d Image Data

Automatic volumetric meshing algorithms on computerized tomography (CT) data have shown to be of great value for Finite Element (FE) modeling since they provide a fast and non-invasive way to study structural behavior. The interest on these methods has grown more since the apparition of microfocus CT ( CT) due to its high resolution, allowing assessment of mechanical behavior at a high precision. The basic meshing approach of generating hexahedra per voxel has the problem of producing jagged edges. Smoothing of the mesh can be then performed by using the Laplacian operator, but this method produces mesh shrinkage, which is unwanted in FE studies. In this paper an automatic meshing and smoothing algorithm for FE meshes from 3D image data is presented.