To achieve the maximum level of collagen strengthening within the shortest treatment time possible, we have developed a mathematical model which is used to optimize the process of corneal cross-linking. This model is able to predict the temporal and spatial distribution of generated cross-links within the corneal stroma and hence the increase in the elasticity modulus. Theory predicts corneal strengthening at low radiation intensities and the absence of the strengthening effect at radiation intensities above the threshold level, which agrees with the experimental results. The model takes account of the initial riboflavin concentration and bleaching, light intensity and time of illumination.
We studied in vitro the response of the topography of the cornea to its full-area laser ablation (the laser beam spot diameter is commensurable with the size of the interface) outside of the central zone with an excimer laser having a Gaussian fluence distribution across the beam. Subject to investigation were the topographically controlled surface changes of the anterior cornea in 60 porcine eyes with a 5 ± 1.25-diopter artificially induced astigmatism, the changes being caused by laser ablation of the stromal collagen in two 3.5-mm-dia. circular areas along the weaker astigmatism axis. Experimental relationships are presented between the actual astigmatism correction and the expected correction for the intact optical zones 1, 2, 3, and 4 mm in diameter. The data for each zone were approximated by the least-squares method with the function d = a + bx. The coefficient b is given with the root-mean-square error. The statistical processing of the data yielded the following results: d = (0.14 ± 0.037)x for the 1-mm-dia. optical zone, (1.10 ± 0.036)x for the 2-mm-dia. optical zone, (1.04 ± 0.020)x for the 3-mm-dia. optical zone, and (0.55 ± 0.04)x for the 4-mm-dia. optical zone. Full astigmatism correction was achieved with ablation effected outside of the 3-mm-dia. optical zone. The surface changes of the cornea are shown to be due not only to the removal of the corneal tissue, but also to the biomechanical topographic response of the cornea to its strain caused by the formation of a dense pseudomembrane in the ablation area.
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