Refractive changes after descemet stripping endothelial keratoplasty: a simplified mathematical model.

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PURPOSE: To develop a mathematical model that can predict refractive changes after Descemet stripping endothelial keratoplasty (DSEK). METHODS: A mathematical formula based on the Gullstrand eye model was generated to estimate the change in refractive power of the eye after DSEK. This model was applied to four DSEK cases retrospectively, to compare measured and predicted refractive changes after DSEK. RESULTS: The refractive change after DSEK is determined by calculating the difference in the power of the eye before and after DSEK surgery. The power of the eye post-DSEK surgery can be calculated with modified Gullstrand eye model equations that incorporate the change in the posterior radius of curvature and change in the distance between the principal planes of the cornea and lens after DSEK. Analysis of this model suggests that the ratio of central to peripheral graft thickness (CP ratio) and central thickness can have significant effect on refractive change where smaller CP ratios and larger graft thicknesses result in larger hyperopic shifts. This model was applied to four patients, and the average predicted hyperopic shift in the overall power of the eye was calculated to be 0.83 D. This change reflected in a mean of 93% (range, 75%-110%) of patients' measured refractive shifts. CONCLUSIONS: This simplified DSEK mathematical model can be used as a first step for estimating the hyperopic shift after DSEK. Further studies are necessary to refine the validity of this model.





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Hwang, Richard Y, Daniel J Gauthier, Dana Wallace and Natalie A Afshari (2011). Refractive changes after descemet stripping endothelial keratoplasty: a simplified mathematical model. Invest Ophthalmol Vis Sci, 52(2). pp. 1043–1054. 10.1167/iovs.10-5839 Retrieved from

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Daniel J. Gauthier

Research Professor of Physics

Prof. Gauthier is interested in a broad range of topics in the fields of nonlinear and quantum optics, and nonlinear dynamical systems.

In the area of optical physics, his group is studying the fundamental characteristics of highly nonlinear light-matter interactions at both the classical and quantum levels and is using this understanding to develop practical devices.

At the quantum level, his group has three major efforts in the area of quantum communication and networking. In one project, they are investigating hybrid quantum memories where one type of memory is connected to another through the optical field (so-called flying qubits). In particular, they are exploring nonlinear optical methods for frequency converting and impedance matching photons emitted from one type of quantum memory (e.g., trapped ions) to another (e.g., quantum dots).

In another project, they are exploring methods for efficiently transmitting a large number of bits of information per photon. They are encoding information on the various photon degrees of freedom, such as the transverse modes, one photon at a time, and using efficient mode sorters to direct the photons to single-photon detectors. The experiments make use of multi-mode spontaneous down conversion in a nonlinear crystal to produce quantum correlated or entangled photon pairs.

Another recent interest is the development of the world's most sensitive all-optical switch. Currently, they have observed switching with an energy density as low as a few hundred yoctoJoules per atomic cross-section, indicating that the switch should be able to operate at the single-photon level. The experiments use a quasi-one-dimensional ultra-cold gas of rubidium atoms as the nonlinear material. They take advantage of a one-dimensional optical lattice to greatly increase the nonlinear light-matter interaction strength.

In the area of nonlinear dynamics, his group is interested in the control and synchronization of chaotic devices, especially optical and radio-frequency electronic systems.  They are developing new methods for private communication of information using chaotic carriers, using chaotic elements for distance sensing (e.g., low-probability-of-detection radar), using networks of chaotic elements for remote sensing, and using chaotic elements for generating truly random numbers at high data rates. Recently, the have observed 'Boolean chaos,' where complex behavior is observed in a small network of commercially-available free-running logic gates.

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