The Individual Virtual Eye: a Computer Model for Advanced Intraocular Lens Calculation

Comparative clinical accuracy analysis of the newly developed ZZ IOL and four existing IOL formulas for post-corneal refractive surgery eyes

BACKGROUND

Intraocular lens (IOL) calculation using traditional formulas for post-corneal refractive surgery eyes can yield inaccurate results. This study aimed to compare the clinical accuracy of the newly developed Zhang & Zheng (ZZ) formula with previously reported IOL formulas.

STUDY DESIGN

Retrospective study.

METHODS

Post-corneal refractive surgery eyes were assessed for IOL power using the ZZ, Haigis-L, Shammas, Barrett True-K (no history), and ray tracing (C.S.O Sirius) IOL formulas, and their accuracy was compared. No pre-refractive surgery information was used in the calculations.

RESULTS

This study included 38 eyes in 26 patients. ZZ IOL yielded a lower arithmetic IOL prediction error (PE) compared with ray tracing (P = 0.04), whereas the other formulas had values like that of ZZ IOL (P > 0.05). The arithmetic IOL PE for the ZZ IOL formula was not significantly different from zero (P = 0.96). ZZ IOL yielded a lower absolute IOL PE compared with Shammas (P < 0.01), Haigis-L (P = 0.02), Barrett true K (P = 0.03), and ray tracing (P < 0.01). The variance of the mean arithmetic IOL PE for ZZ IOL was significantly smaller than those of Shammas (P < 0.01), Haigis-L (P = 0.03), Barrett True K (P = 0.02), and ray tracing (P < 0.01). The percentages of eyes within ± 0.5 D of the target refraction with the ZZ IOL, Shammas, Haigis-L, Barrett True-K, and ray-tracing formulas were 86.8 %, 45.5 %, 66.7 %, 73.7 %, and 50.0 %, respectively (P < 0.05 for Shammas and ray tracing vs. ZZ IOL).

CONCLUSIONS

The ZZ IOL formula might offer superior outcomes for IOL power calculation for post-corneal refractive surgery eyes without prior refractive data.

Comparison of spherical and aspherical intraocular lenses with decentration and tilt error using a physical model of human contrast vision and an image quality metric

PURPOSE

In this study, two intraocular lenses (spherical IOL SA60AT and aspherical IOL SN60WF) are examined in an eye model under conditions of misalignment (defocus, decentration and tilt). The lenses are rated using the contrast sensitivity function (CSF) based on Barten's physical model. The square root integral (SQRI) method is used as a quality criterion comparable to the subjective image quality assessment of the human eye.

METHODS

The IOLs to be tested are decentered from 0 to 1mm and tilted from -5 to +5 degrees in the Navarro eye model (optimized for far-point 6m and pupil aperture 3mm). The defocus of the IOLs is ±0.1mm at the anterior chamber depth (ACD). The optical modulation transfer function (MTF) is simulated with a ray tracing program. The SQRI is calculated using this MTF and the Barten CSF model (for in-focus at aperture 3 and 4.5mm and for defocus at 3mm).

RESULTS

With increasing decentration, the spherical IOL shows a significantly smaller loss of quality for both apertures compared to the aspherical lens. With an aperture of 4.5mm, the image quality of the aspherical IOL is better for small decentration and tilt. The loss of quality of the spherical IOL increases with increasing tilt in both directions. In contrast, the image quality of the aspherical IOL is reduced under decentration for certain tilt values. For ACD-0.1mm, both IOLs behave similarly to the in-focus situation. For ACD+0.1mm, the influence of tilt without decentration is small for both IOLs. With increasing decentration, the quality loss of the aspherical IOL is similar to that in-focus and greater than that of the spherical lens.

CONCLUSION

In general, under the same conditions the spherical SA60AT displays a lower tolerance in loss of quality of subjective vision with lens alignment errors, in comparison to the aspherical SN60WF, limited by certain combinations of decentration and tilt according to this study. This study shows a way to evaluate IOLs based on the subjective visual performance of the eye.

Evaluation of a New IOL Power Calculator in Cataract Patients with Normal and Long Axial Lengths

Purposes: To evaluate the accuracy of Ophtha Top and consistency between Ophtha Top and IOLMaster 500 in intraocular lens refractive power calculation among cataract patients with normal and long axial lengths. Methods: This study included cataract patients scheduled for phacoemulsification and IOL implantation surgery. The IOL power was calculated using Ophtha Top and IOLMaster 500 (integrated with SRK/T, Hoffer Q, Holladay 1 formula). The accuracy of IOL power calculation between Ophtha Top and IOLMaster 500 was compared. Bland-Altman plots were also used to assess agreement between Ophtha Top and IOLMaster 500. Results: Ninety-four patients (94 eyes) were included. The mean values of the arithmetic and absolute prediction errors of Ophtha Top were -0.22 ± 0.62 D and 0.52 ± 0.40 D for whole sample. Absolute refractive error showed no significant difference between Ophtha Top and IOLMaster 500 using 3 traditional formulas in eyes with normal and long axial lengths. In normal eyes, mean and medium absolute error of Ophtha Top was 0.49D and 0.48D, which were comparable to that of IOLMaster 500 (Hoffer Q:0.47D; 0.40D & Holladay 1: 0.48D; 0.37D). Similar trend was found in long eyes (Ophtha Top:0.58 D & IOLMaster using SRK/T:0.53D). Conclusions: Ophtha Top based on real ray-tracing method could provide predictable outcomes in all eyes, which was comparable to outcomes from IOLMaster 500 using SRK/T, Hoffer Q, Hollday 1 formula. Ophtha Top would be a promising alternative choice for IOL power calculation.

An innovative approach for determining the customized refractive index of ectatic corneas in cataractous patients

The aim of this study is to determine the customized refractive index of ectatic corneas and also propose a method for determining the corneal and IOL power in these eyes. Seven eyes with moderate and severe corneal ectatic disorders, which had been under cataract surgery, were included. At least three months after cataract surgery, axial length, cornea, IOL thickness and the distance between IOL from cornea, and aberrometry were measured. All the measured points of the posterior and anterior parts of the cornea converted to points cloud and surface by using the MATLAB and Solidworks software. The implanted IOLs were designed by Zemax software. The ray tracing analysis was performed on the customized eye models, and the corneal refractive index was determined by minimizing the difference between the measured aberrations from the device and resulted aberrations from the simulation. Then, by the use of preoperative corneal images, corneal power was calculated by considering the anterior and posterior parts of the cornea and refractive index of 1.376 and the customized corneal refractive index in different regions and finally it was entered into the IOL power calculation formulas. The corneal power in the 4 mm region and the Barrett formula resulted the prediction error of six eyes within ± 1 diopter. It seems that using the total corneal power along with the Barrett formula can prevent postoperative hyperopic shift, especially in eyes with advanced ectatic disorders.

Ray tracing 3D spectral scenes through human optics models

Scientists and engineers have created computations and made measurements that characterize the first steps of seeing. ISETBio software integrates such computations and data into an open-source software package. The initial ISETBio implementations modeled image formation (physiological optics) for planar or distant scenes. The ISET3d software described here extends that implementation, simulating image formation for three-dimensional scenes. The software system relies on a quantitative computer graphics program that ray traces the scene radiance through the physiological optics to the retinal irradiance. We describe and validate the implementation for several model eyes. Then, we use the software to quantify the impact of several physiological optics parameters on three-dimensional image formation. ISET3d is integrated with ISETBio, making it straightforward to convert the retinal irradiance into cone excitations. These methods help the user compute the predictions of optics models for a wide range of spatially rich three-dimensional scenes. They can also be used to evaluate the impact of nearby visual occlusion, the information available to binocular vision, or the retinal images expected from near-field and augmented reality displays.

Relationship between effective lens position and axial position of a thick intraocular lens

PURPOSE

To discuss the impact of intraocular lens-(IOL)-power, IOL-thickness, IOL-shape, corneal power and effective lens position (ELP) on the distance between the anterior IOL vertex (ALP) of a thick IOL and the ELP of its thin lens equivalent.

METHODS

We calculated the ALP of a thick IOL in a model eye, which results in the same focal plane as a thin IOL placed at the ELP using paraxial approximation. The model eye included IOL-power (P), ELP, IOL-thickness (Th), IOL-shape-factor (X), and corneal power (DC). The initial values were P = 10 D (diopter: 1 D = 1 m-1), 20 D, 30 D, Th = 0.9 mm, ELP = 5 mm, X = 0, DC = 43 D. The difference between ALP and the ELP was illustrated as a function of each of the model parameters.

RESULTS

The ALP of a thick lens has to be placed in front of the ELP for P>0 IOLs to achieve the same optical effect as the thin lens equivalent. The difference ALP-ELP for the initial values is -0.57 mm. Minus power IOLs (ALP-ELP = -0.07 mm, for IOL-power = -5 D) and convex-concave IOLs (ALP-ELP = -0.16 mm, for X = 1) have to be placed further posterior. The corneal power and ELP have less influence, but corneal power cannot be neglected.

CONCLUSION

The distance between ELP and ALP primarily depends on IOL-power, IOL-thickness, and shape-factor.

Comparison of Corneal Tomography: Repeatability, Precision, Misalignment, Mean Elevation, and Mean Pachymetry

PURPOSE

To compare corneal tomography and its statistical uncertainty for measurements obtained by three clinically used corneal tomographers: A Scheimpflug camera (Pentacam HR), a swept source optical coherence tomography system (CASIA SS-1000), and Placido ring imaging (TMS-5).

MATERIAL AND METHODS

Repeated measurements with all three devices on 34 normal eyes were used to estimate the repeatability, precision, and mean values of corneal elevation and pachymetry within 8 mm diameter. The repeatability (standard deviation) was calculated for each data point of the corneal elevation data-maps of anterior and posterior cornea as well as for the pachymetry data-maps. Uncertainty on the position of the eye at each measurement might contribute to the differences between elevation data-maps. To take this into account, we defined the precision as the standard deviation for the elevation data-maps of anterior and posterior cornea after correction of misalignment-effects (rotation, translation). The mean elevation and pachymetry data-maps were fitted with Zernike polynomials for interdevice-comparison.

RESULTS

Pentacam HR offered the best repeatability and precision for the anterior corneal elevation (<3 and <1.6 μm, respectively). CASIA SS-1000 offered good repeatability and precision with high resolution for posterior corneal elevation, and the best repeatability for pachymetry (<3 μm). TMS-5 measured anterior elevation with similar repeatability to CASIA SS-1000 (<6 μm). The data-maps of the three tomographers could not be used interchangeably. The largest differences were observed for pachymetry and posterior corneal elevation data-maps.

CONCLUSIONS

Misalignment limited the repeatability of TMS-5 and Pentacam HR, but had little influence on the repeatability of CASIA SS-1000.

Analysis of long-term visual quality with numerical 3D ray tracing after corneal crosslinking treatment

A numerical 3D ray tracing model was used to evaluate the long-term visual effects of two regimens of corneal crosslinking (CXL) treatment of 48 patients with the corneal degeneration keratoconus. The 3D ray tracing analyses were based on corneal elevation data measured by Scheimpflug photography. Twenty-two patients were treated with standard CXL applied uniformly across the corneal surface, whereas 26 patients underwent a customized, refined treatment only at local zones on the cornea (photorefractive intrastromal CXL; PiXL). Spot diagrams, spot root-mean-square (RMS) values, and Strehl ratios were evaluated for the patients prior to and 1, 3, 6, and 12 months after treatment. It was found that the group of patients treated with PiXL, on average, tended to attain a long-term improvement of the corneal optical performance, whereas only minor changes of the optical parameters were found for group treated with standard CXL. Our results confirmed that standard CXL treatment stabilizes the corneal optical quality over time, and thus halts the progression of the corneal degeneration. In addition to stabilization, the results showed that a significantly higher proportion of subjects treated with PiXL improved in RMS, 3, 6, and 12 months after treatment, compared to with CXL (p<0.05). This finding indicates that the PiXL treatment might improve optical quality over time.

Optimization of an intraocular lens for correction of advanced corneal refractive errors

Based on numerical 3D ray tracing, we propose a new procedure to optimize personalized intra-ocular lenses (IOLs). The 3D ray tracing was based on measured corneal elevation data from patients who suffered from advanced keratoconus. A mathematical shape description of the posterior IOL surface, by means of a tensor product cubic Hermite spline, was implemented. The optimized lenses provide significantly reduced aberrations. Our results include a trade-off study that suggests that it is possible to considerably reduce the aberrations with only minor perturbations of an ideal spherical lens. The proposed procedure can be applied for correction of aberrations of any optical system by modifying a single surface.

Three-dimensional ray-tracing model for the study of advanced refractive errors in keratoconus

We propose a numerical three-dimensional (3D) ray-tracing model for the analysis of advanced corneal refractive errors. The 3D modeling was based on measured corneal elevation data by means of Scheimpflug photography. A mathematical description of the measured corneal surfaces from a keratoconus (KC) patient was used for the 3D ray tracing, based on Snell's law of refraction. A model of a commercial intraocular lens (IOL) was included in the analysis. By modifying the posterior IOL surface, it was shown that the imaging quality could be significantly improved. The RMS values were reduced by approximately 50% close to the retina, both for on- and off-axis geometries. The 3D ray-tracing model can constitute a basis for simulation of customized IOLs that are able to correct the advanced, irregular refractive errors in KC.

Fast ray-tracing of human eye optics on Graphics Processing Units

We present a new technique for simulating retinal image formation by tracing a large number of rays from objects in three dimensions as they pass through the optic apparatus of the eye to objects. Simulating human optics is useful for understanding basic questions of vision science and for studying vision defects and their corrections. Because of the complexity of computing such simulations accurately, most previous efforts used simplified analytical models of the normal eye. This makes them less effective in modeling vision disorders associated with abnormal shapes of the ocular structures which are hard to be precisely represented by analytical surfaces. We have developed a computer simulator that can simulate ocular structures of arbitrary shapes, for instance represented by polygon meshes. Topographic and geometric measurements of the cornea, lens, and retina from keratometer or medical imaging data can be integrated for individualized examination. We utilize parallel processing using modern Graphics Processing Units (GPUs) to efficiently compute retinal images by tracing millions of rays. A stable retinal image can be generated within minutes. We simulated depth-of-field, accommodation, chromatic aberrations, as well as astigmatism and correction. We also show application of the technique in patient specific vision correction by incorporating geometric models of the orbit reconstructed from clinical medical images.