Edgar Janunts

Tomography-based customized IOL calculation model.

Purpose: To provide a mathematical calculation scheme for customized intraocular lens (IOL) design based on high resolution anterior segment optical coherence tomography (AS-OCT) of anterior eye segment and axial length data. Material and Methods: We use the corneal and anterior segment data from the high resolution AS-OCT and the axial length data from the IOLMaster to create a pseudophakic eye model. An inverse calculation algorithm for the IOL back surface optimization is introduced. We employ free form surface representation (bi-cubic spline) for the corneal and IOL surface. The merit of this strategy is demonstrated by comparing with a standard spherical model and quadratic function. Four models are calculated: (1) quadratic cornea + quadratic IOL; (2) spline cornea + quadratic IOL; (3) spline cornea + spline IOL; and (4) spherical cornea + spherical IOL. The IOL optimization process for the pseudophakic eye is performed by numerical ray-tracing method within a 6-mm zone. The spot diagram on the fovea (forward ray-tracing) and wavefront at the spectacle plane (backward ray-tracing) are compared for different models respectively. Results: The models with quadratic (1) or spline (3) surface representation showed superior image performance than the spherical model 4. The residual wavefront errors (peak to valley) of models 1, 2, and 3 are below one micron scale. Model 4 showed max wavefront error of about 15 µm peak to valley. However, the combination of quadratic best fit IOL with the free form cornea (model 2) showed one magnitude smaller wavefront error than the spherical representation of both surfaces (model 3). This results from higher order terms in cornea height profile. Conclusions: A four-surface eye model using a numerical ray-tracing method is proposed for customized IOL calculation. High resolution OCT data can be used as a sufficient base for a customized IOL characterization.

Customized aspheric IOL design by raytracing through the eye containing quadric surfaces.

Purpose: The purpose of the present study was to demonstrate a method of how to calculate intraocular lenses with a customized asphericity and how to apply this strategy to clinical examples in cases where biometric data of the cornea (front and back surface topography) as well as distances in the eye are known. Methods: (1) we demonstrated an algebraic method for tracing a bundle of rays through a schematic eye containing surfaces which can be represented by 2nd order surfaces (quadric surfaces), and (2) we introduced a strategy for customization of the lens’ back surface for compensating the optical path length differences of the rays from object to image in terms of a wave front correction while predefining the lens front surface. Results: The presented method was applied to three working examples: example 1 referred to a centered optical system with a spherical cornea (front and back surfaces) and a predefined spherical lens front surface, example 2 referred to a centered optical system with aspherical surfaces for the corneal front and back surfaces and a predefined spherical lens front surface, and example 3 referrred to a non-centered system with a decentered aspherical cornea (front and back surface), and a predefined spherical lens front surface. The parameterized ray intersection points with the lens back surface were optimized in terms of equalizing the ray path lengths and a quadric surface was fitted to these ray intersection points to characterize the customized lens. The fitting error, ray spot diagram, and the optical path length of the rays are provided. Conclusion: This simple calculation strategy may be the first step in developing individual aspherical lenses, which have the potential to fully compensate spherical aberrations based on individual measures of the eye.

Iteratively re-weighted bi-cubic spline representation of corneal topography and its comparison to the standard methods.

PURPOSE The aim of this study is to represent the corneal anterior surface by utilizing radius and height data extracted from a TMS-2N topographic system with three different mathematical approaches and to simulate the visual performance. METHODS An iteratively re-weighted bi-cubic spline method is introduced for the local representation of the corneal surface. For comparison, two standard mathematical global representation approaches are used: the general quadratic function and the higher order Taylor polynomial approach. First, these methods were applied in simulations using three corneal models. Then, two real eye examples were investigated: one eye with regular astigmatism, and one eye which had undergone refractive surgery. A ray-tracing program was developed to evaluate the imaging performance of these examples with each surface representation strategy at the best focus plane. A 6 mm pupil size was chosen for the simulation. RESULTS The fitting error (deviation) of the presented methods was compared. It was found that the accuracy of the topography representation was worst using the quadratic function and best with bicubic spline. The quadratic function cannot precisely describe the irregular corneal shape. In order to achieve a sub-micron fitting precision, the Taylor polynomials order selection behaves adaptive to the corneal shape. The bi-cubic spline shows more stable performance. Considering the visual performance, the more precise the cornea representation is, the worse the visual performance is. CONCLUSIONS The re-weighted bi-cubic spline method is a reasonable and stable method for representing the anterior corneal surface in measurements using a Placido-ring-pattern-based corneal topographer.

Parametric fitting of corneal height data to a biconic surface

As the average corneal shape can effectively be approximated by a conic section, a determination of the corneal shape by biconic parameters is desired. The purpose of the paper is to introduce a straightforward mathematical approach for extracting clinically relevant parameters of corneal surface, such as radii of curvature and conic constants for principle meridians and astigmatism. A general description for modeling the ocular surfaces in a biconic form is given, based on which an implicit parametric surface fitting algorithm is introduced. The solution of the biconic fitting is obtained by a two sequential least squares optimization approach with constrains. The data input can be raw information from any corneal topographer with not necessarily a uniform data distribution. Various simulated and clinical data are studied including surfaces with rotationally symmetric and non-symmetric geometries. The clinical data was obtained from the Pentacam (Oculus) for the patient having undergone a refractive surgery. A sub-micrometer fitting accuracy was obtained for all simulated surfaces: 0,08 μm RMS fitting error at max for rotationally symmetric and 0,125 μm for non-symmetric surfaces. The astigmatism was recovered in a sub-minutes resolution. The equality in rotational symmetric and the superiority in non-symmetric surfaces of the presented model over the widely used quadric fitting model is shown. The introduced biconic surface fitting algorithm is able to recover the apical radii of curvature and conic constants in principle meridians. This methodology could be a platform for advanced IOL calculations and enhanced contact lens fitting.

In Vitro Corneal Tomography of Donor Cornea Using Anterior Segment OCT.

Purpose: The aim of this study was to establish a tomographic screening method for revealing potential pathologies in corneal donors before keratoplasty so they may be excluded as candidates for corneal transplantation. Methods: Donor corneal tomographies were measured in a viewing chamber filled with preservation medium and with the use of a clinical optical coherence tomography (OCT) device. Custom-written software was developed to extract corneal surfaces from the raw data, which were analyzed in the central and peripheral regions. An adaptive nonlinear edge-enhancement algorithm was used to observe scars within the corneal volume. The thickness distribution map was analyzed to detect keratoconus and corneas with extreme topographic irregularities. Measurements were repeated 5 times to assess reproducibility. Results: Eight corneas were investigated: 6 randomly selected intact donors, unsuitable for implantation because of low endothelial cell densities, and 2 keratoconus corneas, excised from patients during corneal transplantation. A major thickness abnormality was detected in one of the intact donor corneas, so it was excluded from further analysis. The keratoconus corneas were clearly evident in optical coherence tomography cross-sectional images, and similarly, they could easily be identified by analyzing the thickness map. Overall, the measurements were reliable and had a Cronbachs alpha coefficient greater than 0.8. Conclusions: Donor corneal examination using sterile viewing chambers was found to be suitable as a pre-keratoplasty advanced screening routine. A proof of concept was demonstrated, which could identify both irregular corneas and those affected by keratoconus.

Reproducibility and normal values of static pupil diameters

Purpose: To provide additional information on normal values of static pupil diameter measurements for binocular infrared pupillometry with PupilX, a commercial pupillometer, and assess the reproducibility of this device’s measurements. Methods: The pupil diameters from 91 study participants with normal eyes with an average age of 39.7 years (SD 16.4 years) were measured with PupilX under scotopic (0 lx), mesopic (1 lx), and photopic (16 lx) illumination. To assess the repeatability of the device, each measurement was repeated 5 times. Results: The mean pupil diameters were 6.5 mm (SD 1.3 mm), 5.5 mm (SD 1.2 mm), and 4.03 mm (SD 0.9 mm) under scotopic, mesopic, and photopic illumination. Left and right eyes showed no difference in mean pupil diameters. The mean unsigned anisocoria was 0.26 mm (SD 0.32 mm) under scotopic, 0.26 mm (SD 0.27 mm) under mesopic, and 0.19 mm (SD 0.19 mm) under photopic illumination. The decrease in pupil diameter with age was largest for scotopic (≈0.057 mm/y) and smallest for photopic illumination (≈0.025 mm/y). The repeatability of the pupillometer was better than 0.2 mm. Conclusions: This study provides reference values for age- and light-related pupil diameters measured with the PupilX digital pupillometer in normal subjects.

Penetrating Keratoplasty for Keratoconus – Excimer Versus Femtosecond Laser Trephination

Background: In case of keratoconus, rigid gas-permeable contact lenses as the correction method of first choice allow for a good visual acuity for quite some time. In a severe stage of the disease with major cone-shaped protrusion of the cornea, even specially designed keratoconus contact lenses are no more tolerated. In case of existing contraindications for intrastromal ring segments, corneal transplantation typically has a very good prognosis. Methods: In case of advanced keratoconus – especially after corneal hydrops due to rupture of Descemet’s membrane – penetrating keratoplasty (PKP) still is the surgical method of first choice. Noncontact excimer laser trephination seems to be especially beneficial for eyes with iatrogenic keratectasia after LASIK and those with repeat grafts in case of “keratoconus recurrences” due to small grafts with thin host cornea. For donor trephination from the epithelial side, an artificial chamber is used. Wound closure is achieved with a double running cross-stitch suture according to Hoffmann. Graft size is adapted individually depending on corneal size („as large as possible – as small as necessary“). Limbal centration will be preferred intraoperatively due to optical displacement of the pupil. During the last 10 years femtosecond laser trephination has been introduced from the USA as a potentially advantageous approach. Results: Prospective clinical studies have shown that the technique of non-contact excimer laser PKP improves donor and recipient centration, reduces “vertical tilt” and “horizontal torsion” of the graft in the recipient bed, thus resulting in significantly less “all-sutures-out” keratometric astigmatism (2.8 vs. 5.7 D), higher regularity of the topography (SRI 0.80 vs. 0.98) and better visual acuity (0.80 vs. 0.63) in contrast to the motor trephine. The stage of the disease does not influence functional outcome after excimer laser PKP. Refractive outcomes of femtosecond laser keratoplasty, however, resemble that of the motor trephine. Conclusions: In contrast to the undisputed clinical advantages of excimer laser keratoplasty with orientation teeth/notches in keratoconus, the major disadvantage of femtosecond laser application is still the necessity of suction and applanation of the cone during trephination with intraoperative pitfalls and high postoperative astigmatism.

Reliability of a Single Light Source Purkinjemeter in Pseudophakic Eyes.

PurposeTo study the reliability of Purkinje image analysis for assessment of intraocular lens tilt and decentration in pseudophakic eyes. MethodsThe study comprised 64 eyes of 39 patients. All eyes underwent phacoemulsification with intraocular lens implanted in the capsular bag. Lens decentration and tilt were measured multiple times by an infrared Purkinjemeter. A total of 396 measurements were performed 1 week and 1 month postoperatively. Lens tilt (Tx, Ty) and decentration (Dx, Dy) in horizontal and vertical directions, respectively, were calculated by dedicated software based on regression analysis for each measurement using only four images, and afterward, the data were averaged (mean values, MV) for repeated sequence of measurements. New software was designed by us for recalculating lens misalignment parameters offline, using a complete set of Purkinje images obtained through the repeated measurements (9 to 15 Purkinje images) (recalculated values, MV′). MV and MV′ were compared using SPSS statistical software package. ResultsMV and MV′ were found to be highly correlated for the Tx and Ty parameters (R2 > 0.9; p < 0.001), moderately correlated for the Dx parameter (R2 > 0.7; p < 0.001), and weakly correlated for the Dy parameter (R2 = 0.23; p < 0.05). Reliability was high (Cronbach &agr; > 0.9) for all measured parameters. Standard deviation values were 0.86 ± 0.69 degrees, 0.72 ± 0.65 degrees, 0.04 ± 0.05 mm, and 0.23 ± 0.34 mm for Tx, Ty, Dx, and Dy, respectively. ConclusionsThe Purkinjemeter demonstrated high reliability and reproducibility for lens misalignment parameters. To further improve reliability, we recommend capturing at least six Purkinje images instead of three.

Excimer versus Femtosecond Laser Assisted Penetrating Keratoplasty in Keratoconus and Fuchs Dystrophy: Intraoperative Pitfalls

Purpose. To assess the intraoperative results comparing two non-mechanical laser assisted penetrating keratoplasty approaches in keratoconus and Fuchs dystrophy. Patients and Methods. 68 patients (age 18 to 87 years) with keratoconus or Fuchs dystrophy were randomly distributed to 4 groups. 35 eyes with keratoconus and 33 eyes with Fuchs dystrophy were treated with either excimer laser ([Exc] groups I and II) or femtosecond laser-assisted ([FLAK] groups III and IV) penetrating keratoplasty. Main intraoperative outcome measures included intraoperative decentration, need for additional interrupted sutures, alignment of orientation markers, and intraocular positive pressure (vis a tergo). Results. Intraoperative recipient decentration occurred in 4 eyes of groups III/IV but in none of groups I/II. Additional interrupted sutures were not necessary in groups I/II but in 5 eyes of groups III/IV. Orientation markers were all aligned in groups I/II but were partly misaligned in 8 eyes of groups III/IV. Intraocular positive pressure grade was recognized in 12 eyes of groups I/II and in 19 eyes of groups III/IV. In particular, in group III, severe vis a tergo occurred in 8 eyes. Conclusions. Intraoperative decentration, misalignment of the donor in the recipient bed, and need for additional interrupted sutures as well as high percentage of severe intraocular positive pressure were predominantly present in the femtosecond laser in keratoconus eyes.

Eye-tracker-guided non-mechanical excimer laser assisted penetrating keratoplasty.

Purpose: The purpose of the study was to implement a new eye tracking mask which could be used to guide the laser beam in automated non-mechanical excimer laser assisted penetrating keratoplasty. Materials and methods: A new trephination mask design with an elevated surface geometry has been proposed with a step formation between conical and flat interfaces. Two recipient masks of 7.5/8.0 mm have been manufactured and tested. The masks have outer diameter of 12.5 mm, step formation at 10.5 mm, and slope of conical surfaces 15°. Its functionality has been tested in different lateral positions and tilts on a planar surface, and pig eye experiments. After successful validation on porcine eyes, new masks have been produced and tested on two patients. Results: The build-in eye tracking software of the MEL 70 was always able to capture the masks. It has been shown that the unwanted pigmentation/pattern induced by the laser pulses on the mask surface does not influence the eye-tracking efficiency. The masks could be tracked within the 18 × 14 mm lateral displacement and up to 12° tilt. Two patient cases are demonstrated. No complications were observed during the surgery, although it needs some attention for aligning the mask horizontally before trephination. Stability of eye tracking masks is emphasized by inducing on purpose movements of the patient head. Conclusion: Eye-tracking-guided penetrating keratoplasty was successfully applied in clinical practice, which enables robust tracking criteria within an extended range. It facilitates the automated trephination procedure of excimer laser-assisted penetrating keratoplasty.