Physical model of human eye with implantable intraocular lenses Agnieszka Barcik MSc*, Jerzy Nowak Prof., Damian Siedlecki PhD, Marek Zając Prof., Józef Zarówny PhD Institute of Physics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, PL 50-370 Wrocław, Poland ABSTRACT An optomechanical model of human eye containing artificial cornea and a cuvette with immersion liquid is developed. An artificial implantable intraoculer lens (IOL) inserted into the cuvette stands for the eye crystalline lens. A special mechanical handle holding the IOL enables to move and rotate it thus simulationg possible errors during lens implantation procedure. The “retinal” image is recorded with the high resolution CCD camera. The image of Siemens star serves as qualitative measure of “retinal” image, while more quantitatively data come from Modulation Transfer Function obtained by the analysis of the images of sinusoidal tests generated on the computer screen. The whole eye model can be used for investigation of the impact of type and location of the IOL on the optical performance. Keywords: Intraocular lens, artificial eye model, imaging quality
1. INTRODUCTION In spite of vast development of medicine a cataract is still one of the most frequent causes of blindness [1, 2]. The only one method of its treatment is based on removing the opaque crystalline lens (this surgery being known since ancient times [3, 4, 5, 6]) and replacing it with artificial implant – intraocular lens (IOL). Since the first artificial intraocular lens developed by Harold Ridley in 1940 [7, 8] this technique has developed rapidly. The technique of cataract extraction and subsequent IOL implantation has evolved over the years and now is relatively low invasive procedure [9]. Also the IOLs itself has been changed with modern materials minimizing a risk of complications, and sophisticated design enabling easy and unfailing implanatation procedure (foldable lens) [10]. A lot of efforts and energy is now put into designing such IOL shape which ensures as good optical performance as possible. Recent developments in the field of multifocal IOL and pseudoaccommodating IOL are worth to note. [11, 12, 13]. In such situation it is necessary for the ophthalmic surgeon to have access to precise, quantitative information on IOL properties, and in particualr on the quality of retinal image in the aphakic eye with implanted IOL. There exists a number of papers describing visual outcome of patients after crystalline lens extraction and IOL implantation [14, 15, 16, 17, 18]. The clinical studies which evaluate and compare the visual outcomes in large patient populations have however serious drawback since it is difficult to separate the effect of IOL and the possible influence of other, possibly existing, eye abnormalities. It is impossible to compare retinal images before and after IOL implantation in the same person. One of possible approach to this problem is numerical modelling of imaging through a model eye with IOL included. Retinal images of object in form of Landold “C” calculated numerically were presented by Korynta et al [19]. Gullstrand eye model was a base for MTF calculation performed with WinSigma software by Norrby [20]. Franchini et al. [21] considered LeGrand eye model and typical ray-tracing programme to calculate spot diagram on the retinal surface. Teruwhenua [22] has calculated Point Spread Function (PSF) and Mutual Transfer Function (MTF) using Nawarro eye model and Zemax software. The MTF function for different IOL types and pupil diameters have been calculated using CodeV programme by Hunter et al. [23] using modified Dubbelman eye model. Siedlecki et al. [24] considered numerically classic (refractive) and hybrid (refractive-diffractive) IOLs. *
[email protected] 16th Polish-Slovak-Czech Optical Conference on Wave and Quantum Aspects of Contemporary Optics, edited by Agnieszka Popiolek-Masajada, Elzbieta Jankowska, Waclaw Urbanczyk, Proc. of SPIE Vol. 7141, 71411A · © 2008 SPIE · CCC code: 0277-786X/08/$18 · doi: 10.1117/12.822391 Proc. of SPIE Vol. 7141 71411A-1
The other approach includes analysis of image formed by IOL itself. The need for standardization and control was a stimulus to develop standards [25, 26] describing both: methods of IOL image evaluation and requirements to be met by IOL performance. Namely an MTF value should be greater than 0.43 at 100 c/mm or 70% of the calculated maximum attainable for the design, whichever is the smaller, but always greater than 0.25. In order to measure the MTF of single IOL numerous laboratory experiments were performed. Tognetto et al. [27] used specially designed optical bench. Testing of the IOL in air causes, however, some differences in their performance with respect to those obtained in real conditions. It is indicated that such measurements should be performed with great care to assure the same conditions as while IOL is implanted ito the living eye [28]. In order to correct these differences the IOL under investigation has to be located in the wet cell filled with immesive liquid miming the aqueous humour. [29, 30]. Peli and Lang [31] have determined experimentally MTF basing on the measured spread function given by multifocal IOL’s located in a wet cell. The best method to determine the optical performance of IOL in the conditions close to those in nature is to construct a model eye substituting the real one. As Gobbi et al. [32, 33] have pointed out such opto-mechanical eye model should immitate as close as possible the real human eye with its mechanical and optical parameters. In particular it should consist of a chamber filled with a liquid resembling the aqueous humour with its refractive index and Abbe number. Front window of this chamber should simulate cornea being a meniscus lens of the same focusing power as real cornea. The IOL should be placed in this chamber in the manner which allows to adjust the location (distance from the front window) as well as decentration and tilt. An iris corresponding to the eye pupil should be located in the anterior part of the artificial eye chamber. The overall length should correspond to the length of emmetropic eye, however in order to simulate refraction errors it is convenient if this length can be adjusted. The retina has to be replaced by electronic detector – CCD camera being a good solution. The other version of artificial eye developed by Castro, Rosales and Marcos [34] consist of PMMA water-cell with PMMA rigid contact lens simulating the cornea. Kawamorita and Uozato [35] have used wet cell with achromatic lens as a mimic of cornea.
2. MODEL EYE Optomechanical model of the human eye designed for testing the optical performance of different intraocular lenses is presented in the Figure 1.
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Fig. 1. Optomechanical model of human eye a) draft, b) outer appearance
The model consists of a) Chamber (wet cell) to be filled with immersion liquid. It can be filled in and emptied with help of a syringe in such a way that no air bubbles originate. As the immersion liquid simulating aqueous humour and vitreous we used destilled water.
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b) Cornea made of PMMA of refractive index n = 1.491 in form of convex-concave meniscus of outer radius r1 = 7.77 mm and inner radius r2 = 6.40 mm and central thickness d =0.50 mm. In the future we plan to exchange this “cornea” with the the aspherical one of the shape more adequate to the real one. c) Rear window made of glass BK51664 of refractive index n = 1.516. Outer radius equals to r1 = 16.50 mm and inner radius r2 = 18.90 mm and central thickness d =2.40 mm. d) Exchangeable diaphragm modelling eye pupil. In order to avoid deformations and polluting of the image formed by the optical system of model eye the length of its chamber is a little longer than equivalent emmetropic eye. Thus the “retinal image” is formed in the air behind the rear window. This aerial image is imaged with a microscope objective with linear magnification p = 6.6 times on the CCD detector being a part of typical CANON photographic camera. The detector consist of 10M pixels of dimensions 6.6 µm. Spectral sensitivity of the CCD detector is similar to the spectral sensitivity of human eye, It is possible, however, to record the image in monochromatic light. The image is recorder in the RAW formate. The spherical rear window has its centre in the point which corresponds to the centre of rotation of the simulated eye ball. The image recording part (microscope objective and camera) is mounted on the movable arm with the axis of rotation in the same point. Intraocular lens under investigation is fixed in a special holder with a possibility of its shift and tilt (moving along the model eye axis, decentration and rotation around 3 perpendicular axes).
3. MEASUREMENTS AND RESULTS For tests used monofocal intraocular lens Alcon MA60BM. Power of lens amounted 25.5 D For qualitative analysis we used Siemens star test. The test was printed on a white paper and has 72 black & white sectors. Its outer radius was equal to 140 mm so tha lowest spatial frequency was equal to 16 c/mm. The highest frequency – in the middle of the test - was about 320 c/mm. The distance from test to the model eye was equal to 3.27 m, so we could treat this experiment as simulation of typical distant vision. Since the goal of the first experiment was to analyse the image quality in the case of emmetropic eye we looked for the correct image plane experimentally. Consecutive images of Siemens star were recorded with detecting system (camera with microscope objective) moved along the optical axis with steps of 0.01/0.05 mm. The position in which the image was estimated as the best one was treated as the position of best focus and the detecting system was fixed in it. An exemplary image of the Siements star is presented in the Figure 2. Satisfactiory good symmetry is seen which testifies to correct adjusting of the IOL in the model eye. A cut-off frequency can be estimated on the base of this picture. We estimated it to 40 c/deg.
Fig. 2. Exemplary image of Siemens star test
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More “quantitative” imformation of the imaging qualite can be obtained from the image of an edge. Such object was simulated either physically (real edge of a metal foil illuminated from its back with diffused light) or on a computer screen. We did not notice any important difference in the obtained images. An exemplary image of an edge-like object together with the light intensity distribution in its one-dimensional cross-section is presented in the Figure 3.
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Fig. 3. Image of an edge-like object generated on a computer screen (a) and the light intensty distribution in one of its cross-section (b)
Though necessary information on the imaging quality can be deduced from the image of an edge the modulation transfer function (MTF) seems to be more convenient for analysis. Estimation of the MTF gives very important information on the quality of retinal image. The function can be defined as the ratio of Michelson contrast in the image of sinusoidal luminance distribution to the contrast in the said distribution itself [36];. From this definition a simple method of its measurement follows. We have generated sinusoidal test patterns on a computer screen and recorded their images. Exemplary picture of such record is presented in the Figure 4. In the test pattern we added three regions: of minimum luminance (“black”), of maximum luminance (“white”) and of linearly increasing luminance (“wedge”) denoted “b”, “w” and “wedge” on the picture, respectively. Images of regions “black” and “white” were used for calibrating the detector, and image of “wedge” was used for checking the recording linearity.
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Fig. 4. Image of a sinusoidal test pattern generated on a computer screen (a) and the light intensty distribution in one of its crosssection (b)
In order to evaluate the MTF of model eye with the IOL implanted we used severakl sinusoidal tests of spatial frequeny varying within the range of 0.1 – 7 cykli/cm presented from the distance equal to 3.27 m, which means that angular spatial frequency varied from 0.5 to 40 c/deg. Contrast of the test was set on 100% or 50%. The MTF estimated in such way is presented in Figures 5a and 5b. Both curves were obtained for different initial contrast (100% and 50%) but they do not differ noticeably.
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Fig. 5a. Modulation Transfer Function measured with 100% contrast of initial test pattern 1 0,9 0,8 0,7
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Fig. 5b. Modulation Transfer Function measured with 50% contrast of initial test pattern
It is worth noting that the shape of obtained curves corresponds well to the MTF curves obtained by other Authors, either numerical [37], in model [38] or experimentally. For comparison we racall the simplified numerical model of the wyw MTF developed by Artal and Navarro, who, basing on their own measurements, suggested an analytical form for MTF curve of healthy eye in dependency on the pupil diameter [39]
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MTF (u, p ) = (1 − C1 + C2 p )exp{− A1 exp( A2 p )u} + (C1 − C2 p )exp{− B1 exp(B2 p )u}
(1)
where A1 = 3.52, A2 = 0.43, B1 = 1.69, B2 = 0.28, C1 = 0.48, C2 = 0.037 p is a pupil diameter in milimeters, u is normalized spatial frequency with cutoff depending on pupil size. Assuming pupil diameter equal to 2.5 mm, 4 mm and 6 mm from equation (1) and Artal & Navarro data we receive “theoretical” MTF for emmetropic eye which can be taken as reference to our measurements as (Figure 6)
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Fig. 6. Modulation Transfer Function of healthy eye with 2.5 mm, 4 mm and 6 mm pupil diametr according to Artal & Nawarro model.
SUMMARY The most important problem according to visual acuity is to obtain information with regard to commercial, clinical and technical issues. It is important to take into consideration expected visual modifications arising from used materials and IOLs’ optics (except factors like safety, biocompatibility, simplicity of implementation). Optomechanical model of eye enables objective assessment of IOLs construction using contrast transfer function and qualitative representation, potentially useful to characterize and distinguish different types of IOLs.
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33. Pier Giorgio Gobbi, Francesco Fasce, Stefano Bozza, Giliola Calori, Rosario Brancato: “Far and near visual acuity with multifocal intraocular lenses in an optomechanical eye model with imaging capability”, J Cataract Refract Surg 33, 1082–1094 (2007). 34. Alberto de Castro, Patricia Rosales, Susana Marcos: “Tilt and decentration of intraocular lenses in vivo from Purkinje and Scheimpflug imaging”, J Cataract Refract Surg 3, 418–429 (2007). 35. Takushi Kawamorita, CO, Hiroshi Uozato: „Modulation transfer function and pupil size in multifocal and monofocal intraocular lenses in vitro”, J Cataract Refract Surg 31, 2379–2385 (2005). 36. „How to measure MTF nad other Properties of Lenses”, Optikos Corporation, Cambridge, USA (1999). 37. Jennifer J. Hunter, Melanie C.W. Campbell, Edward Geraghty: „Optical analysis of an accommodating intraocular lens”, J Cataract Refract Surg 32, 269–278 (2006). 38. Sverker Norrby, Patricia Piers, Charles Campbell, Marie vad der Mooren: „Model eyes for evaluation of intraocular lenses”, Appl. Optics 46, 6595-6605 (2007). 39. Pablo Artal, Rafael Navarro: “Monochromatic modulation transfer function of the human eye for different pupil diameters: an analyticsl expreccion”, J. Opt. Soc. Am. A 11, 246-249 (1994).
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