Alberto de Castro

Tilt and decentration of intraocular lenses in vivo from Purkinje and Scheimpflug imaging. Validation study.

PURPOSE: To measure tilt and decentration of intraocular lenses (IOLs) with Scheimpflug and Purkinje imaging systems in physical model eyes with known amounts of tilt and decentration and patients. SETTING: Instituto de Óptica Daza de Valdés, Consejo Superior de Investigaciones Científicas, Madrid, Spain. METHODS: Measurements of IOL tilt and decentration were obtained using a commercial Scheimpflug system (Pentacam, Oculus), custom algorithms, and a custom‐built Purkinje imaging apparatus. Twenty‐five Scheimpflug images of the anterior segment of the eye were obtained at different meridians. Custom algorithms were used to process the images (correction of geometrical distortion, edge detection, and curve fittings). Intraocular lens tilt and decentration were estimated by fitting sinusoidal functions to the projections of the pupillary axis and IOL axis in each image. The Purkinje imaging system captures pupil images showing reflections of light from the anterior corneal surface and anterior and posterior lens surfaces. Custom algorithms were used to detect the Purkinje image locations and estimate IOL tilt and decentration based on a linear system equation and computer eye models with individual biometry. Both methods were validated with a physical model eye in which IOL tilt and decentration can be set nominally. Twenty‐one eyes of 12 patients with IOLs were measured with both systems. RESULTS: Measurements of the physical model eye showed an absolute discrepancy between nominal and measured values of 0.279 degree (Purkinje) and 0.243 degree (Scheimpflug) for tilt and 0.094 mm (Purkinje) and 0.228 mm (Scheimpflug) for decentration. In patients, the mean tilt was less than 2.6 degrees and the mean decentration less than 0.4 mm. Both techniques showed mirror symmetry between right eyes and left eyes for tilt around the vertical axis and for decentration in the horizontal axis. CONCLUSIONS: Both systems showed high reproducibility. Validation experiments on physical model eyes showed slightly higher accuracy with the Purkinje method than the Scheimpflug imaging method. Horizontal measurements of patients with both techniques were highly correlated. The IOLs tended to be tilted and decentered nasally in most patients.

Three-dimensional reconstruction of the crystalline lens gradient index distribution from OCT imaging

We present an optimization method to retrieve the gradient index (GRIN) distribution of the in-vitro crystalline lens from optical path difference data extracted from OCT images. Three-dimensional OCT images of the crystalline lens are obtained in two orientations (with the anterior surface up and posterior surface up), allowing to obtain the lens geometry. The GRIN reconstruction method is based on a genetic algorithm that searches for the parameters of a 4-variable GRIN model that best fits the distorted posterior surface of the lens. Computer simulations showed that, for noise of 5 μm in the surface elevations, the GRIN is recovered with an accuracy of 0.003 and 0.010 in the refractive indices of the nucleus and surface of the lens, respectively. The method was applied to retrieve three-dimensionally the GRIN of a porcine crystalline lens in vitro. We found a refractive index ranging from 1.362 in the surface to 1.443 in the nucleus of the lens, an axial exponential decay of the GRIN profile of 2.62 and a meridional exponential decay ranging from 3.56 to 5.18. The effect of GRIN on the aberrations of the lens also studied. The estimated spherical aberration of the measured porcine lens was 2.87 μm assuming a homogenous equivalent refractive index, and the presence of GRIN shifted the spherical aberration toward negative values (-0.97 μm), for a 6-mm pupil.

Corneal topography from spectral optical coherence tomography (sOCT)

We present a method to obtain accurate corneal topography from a spectral optical coherence tomography (sOCT) system. The method includes calibration of the device, compensation of the fan (or field) distortion introduced by the scanning architecture, and image processing analysis for volumetric data extraction, segmentation and fitting. We present examples of three-dimensional (3-D) surface topography measurements on spherical and aspheric lenses, as well as on 10 human corneas in vivo. Results of sOCT surface topography (with and without fan-distortion correction) were compared with non-contact profilometry (taken as reference) on a spherical lens, and with non-contact profilometry and state-of-the art commercial corneal topography instruments on aspheric lenses and on subjects. Corneal elevation maps from all instruments were fitted by quadric surfaces (as well as by tenth-order Zernike polynomials) using custom routines. We found that the discrepancy in the estimated radius of curvature from nominal values in artificial corneas decreased from 4.6% (without fan distortion correction) to 1.6% (after fan distortion correction), and the difference in the asphericity decreased from 130% to 5%. In human corneas, the estimated corneal radius of curvature was not statistically significantly different across instruments. However, a Bland-Altman analysis showed consistent differences in the estimated asphericity and corneal shape between sOCT topographies without fan distortion correction and the rest of the measurements.

In vivo human crystalline lens topography

Custom high-resolution high-speed anterior segment spectral domain optical coherence tomography (OCT) was used to characterize three-dimensionally (3-D) the human crystalline lens in vivo. The system was provided with custom algorithms for denoising and segmentation of the images, as well as for fan (scanning) and optical (refraction) distortion correction, to provide fully quantitative images of the anterior and posterior crystalline lens surfaces. The method was tested on an artificial eye with known surfaces geometry and on a human lens in vitro, and demonstrated on three human lenses in vivo. Not correcting for distortion overestimated the anterior lens radius by 25% and the posterior lens radius by more than 65%. In vivo lens surfaces were fitted by biconicoids and Zernike polynomials after distortion correction. The anterior lens radii of curvature ranged from 10.27 to 14.14 mm, and the posterior lens radii of curvature ranged from 6.12 to 7.54 mm. Surface asphericities ranged from −0.04 to −1.96. The lens surfaces were well fitted by quadrics (with variation smaller than 2%, for 5-mm pupils), with low amounts of high order terms. Surface lens astigmatism was significant, with the anterior lens typically showing horizontal astigmatism (Z22 ranging from −11 to −1 µm) and the posterior lens showing vertical astigmatism (Z22 ranging from 6 to 10 µm).

Full OCT anterior segment biometry: an application in cataract surgery.

In vivo three-dimensional (3-D) anterior segment biometry before and after cataract surgery was analyzed by using custom high-resolution high-speed anterior segment spectral domain Optical Coherence Tomography (OCT). The system was provided with custom algorithms for denoising, segmentation, full distortion correction (fan and optical) and merging of the anterior segment volumes (cornea, iris, and crystalline lens or IOL), to provide fully quantitative data of the anterior segment of the eye. The method was tested on an in vitro artificial eye with known surfaces geometry at different orientations and demonstrated on an aging cataract patient in vivo. Biometric parameters CCT, ACD/ILP, CLT/ILT Tilt and decentration are retrieved with a very high degree of accuracy. IOL was placed 400 μm behind the natural crystalline lens, The IOL was aligned with a similar orientation of the natural lens (2.47 deg superiorly), but slightly lower amounts (0.77 deg superiorly). The IOL was decentered superiorly (0.39 mm) and nasally (0.26 mm).

Intraocular lens alignment from Purkinje and Scheimpflug imaging

The improved designs of intraocular lenses (IOLs) implanted during cataract surgery demand understanding of the possible effects of lens misalignment on optical performance. In this review, we describe the implementation, set‐up and validation of two methods to measure in vivo tilt and decentration of IOLs, one based on Purkinje imaging and the other on Scheimpflug imaging. The Purkinje system images the reflections of an oblique collimated light source on the anterior cornea and anterior and posterior IOL surfaces and relies on the well supported assumption of the linearity of the Purkinje images with respect to IOL tilt and decentration. Scheimpflug imaging requires geometrical distortion correction and image processing techniques to retrieve the pupillary axis, IOL axis and pupil centre from the three‐dimensional anterior segment image of the eye. Validation of the techniques using a physical eye model indicates that IOL tilt is estimated within an accuracy of 0.261 degree and decentration within 0.161 mm. Measurements on patients implanted with aspheric IOLs indicate that IOL tilt and decentration tend to be mirror symmetric between left and right eyes. The average tilt was 1.54 degrees and the average decentration was 0.21 mm. Simulated aberration patterns using custom models of the patients eyes, built using anatomical data of the anterior cornea and foveal position, the IOL geometry and the measured IOL tilt and decentration predict the experimental wave aberrations measured using laser ray tracing aberrometry on the same eyes. This reveals a relatively minor contribution of IOL tilt and decentration on the higher‐order aberrations of the normal pseudophakic eye.

Distortions of the posterior surface in optical coherence tomography images of the isolated crystalline lens: effect of the lens index gradient

We quantify the posterior surface distortions in optical coherence tomography (OCT) images of isolated crystalline lenses. The posterior radius of curvature and asphericity obtained from OCT images acquired with the beam incident first on the anterior, and then the posterior, surface were compared. The results were compared with predictions of a ray-tracing model which includes the index gradient. The results show that the error in the radius of curvature is within the measurement reproducibility and that it can be corrected by assuming a uniform refractive index. However, accurate asphericity values require a correction algorithm that takes into account the gradient.

Age-dependent variation of the Gradient Index profile in human crystalline lenses.

An investigation was carried out with the aim of reconstructing the gradient index (GRIN) profile of human crystalline lenses ex-vivo using optical coherence tomography (OCT) imaging with an optimization technique and to study the dependence of the GRIN profile with age. Cross-sectional images of nine isolated human crystalline lenses with ages ranging from 6 to 72 (post-mortem time 1 to 4 days) were obtained using a custom-made OCT system. Lenses were extracted from whole cadaver globes and placed in a measurement chamber filled with preservation medium (DMEM). Lenses were imaged with the anterior surface up and then flipped over and imaged again, to obtain posterior lens surface profiles both undistorted and distorted by the refraction through the anterior crystalline lens and GRIN. The GRIN distribution of the lens was described with three variables by means of power function, with variables being the nucleus and surface index, and a power coefficient that describes the decay of the refractive index from the nucleus to the surface. An optimization method was used to search for the parameters that produced the best match of the distorted posterior surface. The distorted surface was simulated with accuracy around the resolution of the OCT system (under 15 µm). The reconstructed refractive index values ranged from 1.356 to 1.388 for the surface, and from 1.396 to 1.434 for the nucleus. The power coefficient ranged between 3 and 18. The power coefficient increased significantly with age, at a rate of 0.24 per year. Optical coherence tomography allowed optical, non-invasive measurement of the 2D gradient index profile of the isolated human crystalline lens ex vivo. The age-dependent variation of the changes is consistent with previous data using magnetic resonance imaging, and the progressive formation of a refractive index plateau.

Influence of shape and gradient refractive index in the accommodative changes of spherical aberration in nonhuman primate crystalline lenses.

PURPOSE To estimate changes in surface shape and gradient refractive index (GRIN) profile in primate lenses as a function of accommodation. To quantify the contribution of surface shape and GRIN to spherical aberration changes with accommodation. METHODS Crystalline lenses from 15 cynomolgus monkeys were studied in vitro under different levels of accommodation produced by a stretching system. Lens shape was obtained from optical coherence tomography (OCT) cross-sectional images. The GRIN was reconstructed with a search algorithm using the optical path measured from OCT images and the measured back focal length. The spherical aberration of the lens was estimated as a function of accommodation using the reconstructed GRIN and a homogeneous refractive index. RESULTS The lens anterior and posterior radii of curvature decreased with increasing lens power. Both surfaces exhibited negative asphericities in the unaccommodated state. The anterior surface conic constant shifted toward less negative values with accommodation, while the value of the posterior remained constant. GRIN parameters remained constant with accommodation. The lens spherical aberration with GRIN distribution was negative and higher in magnitude than that with a homogeneous equivalent refractive index (by 29% and 53% in the unaccommodated and fully accommodated states, respectively). Spherical aberration with the equivalent refractive index shifted with accommodation toward negative values (-0.070 μm/diopter [D]), but the reconstructed GRIN shifted it farther (-0.124 μm/D). CONCLUSIONS When compared with the lens with the homogeneous equivalent refractive index, the reconstructed GRIN lens has more negative spherical aberration and a larger shift toward more negative values with accommodation.

Distortion Correction of OCT Images of the Crystalline Lens: Gradient Index Approach

Purpose. To propose a method to correct optical coherence tomography (OCT) images of posterior surface of the crystalline lens incorporating its gradient index (GRIN) distribution and explore its possibilities for posterior surface shape reconstruction in comparison to existing methods of correction. Methods. Two-dimensional images of nine human lenses were obtained with a time-domain OCT system. The shape of the posterior lens surface was corrected using the proposed iterative correction method. The parameters defining the GRIN distribution used for the correction were taken from a previous publication. The results of correction were evaluated relative to the nominal surface shape (accessible in vitro) and compared with the performance of two other existing methods (simple division, refraction correction: assuming a homogeneous index). Comparisons were made in terms of posterior surface radius, conic constant, root mean square, peak to valley, and lens thickness shifts from the nominal data. Results. Differences in the retrieved radius and conic constant were not statistically significant across methods. However, GRIN distortion correction with optimal shape GRIN parameters provided more accurate estimates of the posterior lens surface in terms of root mean square and peak values, with errors <6 and 13 &mgr;m, respectively, on average. Thickness was also more accurately estimated with the new method, with a mean discrepancy of 8 &mgr;m. Conclusions. The posterior surface of the crystalline lens and lens thickness can be accurately reconstructed from OCT images, with the accuracy improving with an accurate model of the GRIN distribution. The algorithm can be used to improve quantitative knowledge of the crystalline lens from OCT imaging in vivo. Although the improvements over other methods are modest in two dimension, it is expected that three-dimensional imaging will fully exploit the potential of the technique. The method will also benefit from increasing experimental data of GRIN distribution in the lens of larger populations.