Proton Bunch Self-Modulation in Plasma with Density Gradient.

We study experimentally the effect of linear plasma density gradients on the self-modulation of a 400 GeV proton bunch. Results show that a positive or negative gradient increases or decreases the number of microbunches and the relative charge per microbunch observed after 10 m of plasma. The measured modulation frequency also increases or decreases. With the largest positive gradient we observe two frequencies in the modulation power spectrum. Results are consistent with changes in wakefields' phase velocity due to plasma density gradients adding to the slow wakefields' phase velocity during self-modulation growth predicted by linear theory.

An extremely robust strong-field control of atomic coherence.

We propose and analyze a scheme for adiabatic creation of maximum coherence of 0.5 with a controllable phase between a ground state and the excited state in a model Λ-structured atom using two short laser pulses. One of the pulses has constant carrier frequency quasi-resonant with transition between an initially empty ground and the excite states. The frequency of the second pulse is swept through the resonance with the adjacent transition between the initially populated ground state and the common excited state of the atom. We demonstrate high degree of robustness of the scheme against variation of parameters of the laser radiation in relatively broad region of values. The proposed scheme may find practical applications in the field of multi-photon ionization, high-order harmonics and Raman sideband generation, as well as in nonlinear wave mixing in coherently prepared media.

Biomechanical model of corneal transplantation.

PURPOSE: Refractive consequences of corneal transplants are analyzed using corneal biomechanical models assuming homogeneous and inhomogeneous stiffness distributions across the cornea. Additionally, refractive effects of grafts combined with volume removal procedures are also evaluated to develop methods to reduce postoperative refractive management of patients. METHODS: Refinements of a two-dimensional finite element model are applied to simulate the biomechanical and refractive effects of different corneal transplant procedures: anterior lamellar keratoplasty, posterior lamellar keratoplasty, and penetrating keratoplasty. The models are based on a nonlinearly elastic, isotropic formulation. Predictions are compared with published clinical data. RESULTS: The model simulating the penetrating keratoplasty procedure predicts more change in the postoperative corneal curvature than models simulating anterior lamellar keratoplasty or posterior lamellar keratoplasty procedures. When a lenticle-shaped tissue with a central thickness of 50 microns and a diameter of 4 mm is removed from the anterior corneal surface along with the anterior lamellar keratoplasty or posterior lamellar keratoplasty, the models predict a refractive correction of -8.6 and -8.9 diopters, respectively. CONCLUSIONS: Simulations indicate that a posterior lamellar keratoplasty procedure is preferable for obtaining a better corneal curvature profile, eliminating the need for specific secondary treatments.

A finite element model for ultrafast laser-lamellar keratoplasty.

A biomechanical model of the human cornea is employed in a finite element formulation for simulating the effects of Ultrafast Laser-Lamellar Keratoplasty. Several computer simulations were conducted to study curvature changes of the central corneal zone under various physiological and surgical factors. These factors included the combined effect of corneal flap and residual stromal bed thickness on corneal curvature; the effect of the shape of the lenticle on the surgical procedure outcomes and the effect of flap thickness on stress distribution in the cornea. The results were validated by comparing computed refractive power changes with clinical results. The effect of flap thickness on the amount of central flattening indicates that for flap thickness values 28% over the corneal thickness, central corneal flattening decreases. Moreover, the change in corneal curvature induced by subtraction of a plano-convex lenticle under a uniform flap, naturally imply a smaller change in the structure of the anterior layers of the cornea, but a bigger deformation in the structure of the posterior layers that are left behind the resection of the lenticle. In addition, the model also verified that the corneal curvature increased peripherally with simultaneous thinning centrally after subtraction of corneal tissue. This result shows that not only the treated zone is affected by the surgery, indicating the important role of the biomechanical response of the corneal tissue to refractive surgery, which is unaccounted for in current ablation algorithms. The results illustrate the potentialities of finite element modeling as an aid to the surgeon in evaluating variables.

Finite element analysis applied to cornea reshaping.

A 2-D finite element model of the cornea is developed to simulate corneal reshaping and the resulting deformation induced by refractive surgery. In the numerical simulations, linear and nonlinear elastic models are applied when stiffness inhomogeneities varying with depth are considered. Multiple simulations are created that employ different geometric configurations for the removal of the corneal tissue. Side-by-side comparisons of the different constitutive laws are also performed. To facilitate the comparison, the material property constants are identified from the same experimental data, which are obtained from mechanical tests on corneal strips and membrane inflation experiments. We then validate the resulting models by comparing computed refractive power changes with clinical results. Tissue deformations created by simulated corneal tissue removal using finite elements are consistent with clinically observed postsurgical results. The model developed provides a much more predictable refractive outcome when the stiffness inhomogeneities of the cornea and nonlinearities of the deformations are included in the simulations. Finite element analysis is a useful tool for modeling surgical effects on the cornea and developing a better understanding of the biomechanics of the cornea. The creation of patient-specific simulations would allow surgical outcomes to be predicted based on individualized finite element models.

An analytically solvable model for biomechanical response of the cornea to refractive surgery.

An analttically solvable model that considers the elasticity of the cornea is developed for use in the current and novel corneal refractive surgery procedures. The model assumes that the cornea is a thin spheroid shell with an elastic response to intraocular pressure. The value of the Young's modulus of the post-operative cornea and its dependence on the geometric parameters of the ablation zone are estimated employing "best-fit" approach to nomograms currently used in corneal refractive surgery. These elasticity parameters are applied for quantitative modeling of different types of refractive surgery for myopia.