Biomedical subjects

Jochen Wahl

Publications and source records attributed to Jochen Wahl.

6 recordsLinked to original sources

PubMed2005

Topography-based intraocular lens power selection.

PURPOSE: To provide mathematical tools for selecting intraocular lens (IOL) power for normal eyes and for "odd" eyes, particularly after corneal refractive surgery. SETTING: Universitats-Augenklinik, Mainz, Germany. METHODS: First, IOL power is selected based on the radii and numerical eccentricity of the cornea, extracted from corneal topography in a consistent numerical model of the cornea. To fine-tune the result, the visual impression is simulated by blurred Landolt rings superimposed on the retinal receptor grid. The calculation uses numerical ray tracing of the whole pseudophakic eye comprising all monochromatic errors. The error contributions of the influencing parameters, such as anterior and posterior corneal shape and corneal thickness, are quantified in detail. The method is verified in IOL power selection for normal eyes and for eyes after corneal refractive surgery. RESULTS: The main difference between normal corneas and corneas after refractive surgery results from different asphericities. Normal corneas are prolate, with typical numerical eccentricities of 0.5, whereas corneas after laser surgery for myopia are oblate. This causes the main difference (hyperopic shift up to 2.0 diopters) in IOL power selection. Shifts in the posterior corneal radius and corneal thickness are of minor importance. CONCLUSION: Intraocular power selection after corneal refractive surgery should be based on all the information corneal topography provides.

Cataract Extraction↗

PubMed2004

Predicting postoperative intraocular lens position and refraction.

PURPOSE: To predict the postoperative IOL position and refraction as accurately as possible independent of individualization of the parameters. SETTING: Universitats-Augenklinik, Mainz, Germany, and Vienna, Austria. METHODS: One patient cohort (189 eyes, Vienna) was used to calibrate the prediction method, which was then applied to a second cohort (65 eyes, Mainz). All calculations were based on consistent numerical ray tracing of the pseudophakic eye using the original manufacturer's intraocular lens (IOL) data (radii, thickness, refractive index). A new algorithm to predict IOL position was developed. Ultrasound (US) axial lengths were calibrated relative to partial coherence interferometry (PCI). Corneal radii extracted from topography were checked against radii measured with the IOLMaster (Zeiss) and by Littmann keratometry. RESULTS: Zero mean prediction errors for IOL position and refraction were obtained without adjusting the parameters and with PCI lengths or US lengths calibrated relative to the PCI values. There was no significant loss of accuracy of US data compared to PCI data. Corneal radii extracted from topography were slightly but statistically significantly different from the Littmann values, and they were more accurate than the latter with respect to prediction error. The measured mean central IOL position (distance from posterior corneal surface) for all IOL types was 4.580 mm, a value very close to the mean recalculated from A-constants (4.587 mm). The difference in the individual central IOL position relative to the mean value depended only linearly (ie, no higher orders such as square or cubic are needed) on axial length, with the mean central IOL position as a free parameter. This parameter should be 4.6 +/- 0.2 mm (the same value as independently measured or recalculated) to obtain zero steepness of the prediction error as a function of axial length, producing zero bias for long and short eyes. CONCLUSIONS: Calculation errors from formulas and confusing adjusting parameters can be avoided if calculations and measurements are performed on a clear and simple physical basis. Nevertheless, an individual prediction error, typically 0.5 to 1.0 diopter, seems to be unavoidable.

Adult↗

PubMed2003

Simplified mathematics for customized refractive surgery.

PURPOSE: To describe a simple mathematical approach to customized corneal refractive surgery or customized intraocular lens (IOL) design that allows "hypervision" and to investigate the accuracy limits. SETTING: University eye hospital, Mainz, Germany. METHODS: Corneal shape and at least 1 IOL surface are approximated by the well-known Cartesian conic section curves (ellipsoid, paraboloid, or hyperboloid). They are characterized by only 2 parameters, the vertex radius and the numerical eccentricity. Residual refraction errors for this approximation are calculated by numerical ray tracing. These errors can be displayed as a 2-dimensional refraction map across the pupil or by blurring the image of a Landolt ring superimposed on the retinal receptor grid, giving an overall impression of the visual outcome. RESULTS: If the eye is made emmetropic for paraxial rays and if the numerical eccentricities of the cornea and lens are appropriately fitted to each other, the residual refractive errors are small enough to allow hypervision. Visual acuity of at least 2.0 (20/10) appears to be possible, particularly for mesopic pupil diameters. However, customized optics may have limited application due to their sensitivity to misalignment errors such as decentrations or rotations. CONCLUSIONS: The mathematical approach described by Descartes 350 years ago is adequate to calculate hypervision optics for the human eye. The availability of suitable mathematical tools should, however, not be viewed with too much optimism as long as the accuracy of the implementation in surgical procedures is limited.

Cornea↗

PubMed2003

Corneal model.

PURPOSE: To describe the optical region of the cornea with as few parameters as possible and to compare this approach to commonly used mathematical models for the cornea. SETTING: University eye hospital, Mainz, Germany. METHODS: Corneal surface is approximated by a simple model (SM) that is defined by 2 perpendicular vertex radii, their angle to the horizontal, and a unique numerical eccentricity. These parameters, together with a parameter quantifying the decentration of the recording, are obtained in a consistent fit of corneal topographic data. The SM is compared to Zernike polynomial approximations of the 4th (Z4 model) and 8th (Z8 model) radial orders. Residual refraction errors for these approximations are calculated by numerical ray tracing, allowing a comparison of the different approaches. The statistical evaluation was carried out in 100 healthy eyes. RESULTS: The model approximation accuracy for the SM was at least as high as the reproducibility of the topographic measurements. For small optical zones up to 4.0 mm in diameter, the SM was on average more accurate than the Z4 model. CONCLUSIONS: The parameters of the SM, which are closely related to conventional parameters of the cornea, provided a highly accurate basis for following refractive interventions (customized corneal or cataract surgery). Zernike polynomials tend to improve peripheral optical quality at the expense of the central quality. Except in cases of technical optics, this is an unwanted effect in the human eye.

Adolescent↗

PubMed2003

Determining postoperative anterior chamber depth.

PURPOSE: To compare measured and calculated postoperative anterior chamber depths (ACDs). SETTING: Department of Ophthalmology and Institute of Medical Physics, University of Vienna, Vienna, Austria, and Department of Ophthalmology, University of Mainz, Mainz, Germany. METHODS: The postoperative ACD was measured in 189 pseudophakic eyes using a laboratory prototype of partial coherence interferometry (PCI). In 6 intraocular lens (IOL) groups, the mean ACD was calculated by ray tracing based on the best-known A-constants of the SRK formulas. In addition, for each IOL type, each measured ACD was compared with a value calculated using the individual spherical equivalent of the postoperative refraction. RESULTS: The measured and the calculated ACD values were close and did not show systematic differences. The ACD values obtained in the study, however, differed significantly from the values published by the IOL manufacturers. A comparison of the PCI-assessed ACDs and the calculated values using the postoperative refraction showed more scattered results for the refraction-based data, which was probably the result of higher measurement errors with the autorefractometer than with PCI. CONCLUSIONS: High-precision interferometry measurements and ray-tracing calculations confirmed each other. The resulting mean ACD values should be used instead of the manufacturers' values. The refractive outcome of cataract surgery can be improved by combining preoperative high-precision PCI biometry and numerical ray tracing for IOL power calculations.

Anterior Chamber↗

PubMed2002

Ray tracing for intraocular lens calculation.

PURPOSE: To improve accuracy in intraocular lens (IOL) calculations and clarify the effect of various errors. SETTING: University eye hospitals, Mainz, Germany, and Vienna, Austria. METHODS: A numerical ray-tracing calculation has been developed for the pseudophakic eye. Individual rays are calculated and then undergo refractions on all surfaces of the IOL and cornea. The calculations do not use approximations; ie, the refractions are calculated exactly using Snell's law. Rays can be calculated for any distance from the optical axis and for other parameter variations. The effects of aspheric surfaces can also be investigated. Instead of IOL powers, manufacturers' IOL data (radii, refractive index, thickness) are used in the calculations for different IOL types. The resulting optical quality is visualized by using Landolt rings superimposed on the grid of retinal receptors. RESULTS: Intraocular lens design, corneal asphericity, and specific spherical aberration influence the visual quality of the pseudophakic eye significantly. The IOL refractive power is an ambiguous parameter that cannot characterize the visual outcome sufficiently accurately for an IOL implanted at a given position. The effects can be calculated only in numerical ray tracing, not in Gaussian optics. The accuracy of numerical ray tracing is independent of axial length. Therefore, very long or very short eyes gain the most from the higher accuracy of this approach. For average-size eyes, however, the results are the same as with SRK calculations. CONCLUSION: Calculations in Gaussian optics should be replaced by state-of-the-art numerical methods, which can be run on any standard personal computer.

Humans↗