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Michael C. Mrochen, Silvia Schumacher, Bartha C. Verbiest, Daniel Simon, Theo Seiler; Beam Profile Calculations To Increase The Volume Of Cross-linked Of Corneal Tissue. Invest. Ophthalmol. Vis. Sci. 2012;53(14):6811.
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Corneal cross-linking volume and final stiffness depends on the concentration distribution of riboflavin and the light intensity distribution throughout the corneal stroma. The purpose of this work was to calculate an intensity distribution of the illumination system beam profile that allows a maximum in the overall cross-linked volume by considering the geometrical shape of the cornea, the concentration distribution and a safety margin of 100 microns in cross-linking depth, to protect the corneal endothelium.
A theoretical model for calculating the increase in corneal cross-linking by considering Fick’s second law of diffusion, Lambert-Beer’s law of light absorption and a photopolymerization rate equation. This model was used to calculate the UV-light intensity required at the corneal surface to achieve a specific cross-linking depth within the stroma. A variety of corneal shape factors such as radius of curvature, corneal asphericity and corneal thickness profile were taken from literature to derive the corneal surface intensity needed to achieve a specific cross-linking depth. The optimal cross-linking depth was determined by using the corneal thickness profile and a required safety margin of 50 microns distance between the maximum cross linking depth to the corneal endothelium. Reflection off the corneal surface and projection losses at the corneal surface were calculated to quantify their impact on the cross-linking depth. In addition, the relevance of optical penetration depth along the optical axis in the stroma was considered.
The key factor for calculating an increased cross-linking volume is the thickness profile of the cornea. An increase in thickness of about 8% (normal eyes) 22% (keratoconus eyes) from the center to the periphery (4mm) requires an increase intensity of 28% (normal eyes), 75% (keratoconus eyes) to achieve a maximum cross-linked volume. The reflection losses of UV-light at the corneal surface only have a minor impact on the cross-linking depth. Peripherally, at 4mm from the center of the cornea, the reflection losses are 3%, compared to 2.5% centrally. The projection losses were found to be insignificant, but the optical penetration depth along the optical axis needs to be taken into consideration. The shape of the anterior corneal surface only has a small relevance with respect to the cross-linking depth.
Our results show that, to achieve a maximum cross-linked volume for the treatment of keratoconus, the irradiation intensity should be increased peripherally, compared to the central part of the cornea. This can be realized by adjusting the illumination device beam profile accordingly.
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