Ray tracing, a simulation method to study the path of light through the eye, is increasingly used to evaluate factors that affect the quality of vision. In pseudophakia, for example, it provides a method to assess how light rays are refracted or reflected by an intraocular lens (IOL), which revealed the origin of glare symptoms in positive dysphotopsia.1 Another application of ray tracing is the evaluation of peripheral vision, as clinical techniques to quantitatively assess this part of vision are limited. In negative dysphotopsia (ND), for example, ray tracing was used to develop the hypothesis that the bothering shadow that patients experience in the temporal visual could be caused by light rays passing between the IOL and the iris.2,3 Later studies confirmed this hypothesis, and ray tracing subsequently contributed to the development of various treatments of this condition.4–8

As with any simulation technique, special care needs to be taken to assure that the outcomes of the calculations resemble the real-life quantity one is interested in. Therefore, different methods have been proposed to relate ray-tracing outcomes to clinical metrics, such as wavefront aberrations, modulation transfer functions, and retinal illumination intensities.2,9,10 Furthermore, different geometrical eye models have been developed to reproduce the optical characteristics of the general population while others have incorporated distinct anatomical features of eyes with specific conditions, such as ND.6,7,9,11 In ray-tracing simulations related to peripheral vision, however, one also needs to consider which segment of the retinal surface is used to see a specific part of the visual field. For this purpose, Simpson et al. determined the relation between the position of a light source, relative to the optical axis of their eye model, and the part of the retina which was illuminated.5 However, as in vivo optical elements of the eye are not aligned along one axis, van Vught et al. extended this approach by using the visual axis as a reference, thereby aiming to provide a more direct link to clinical measurements.6,12 Although these approaches aid in correlating ray-training analyses with measurements that use a fixation target as reference, such as peripheral aberrometry and perimetry, it does not necessarily reflect the spatial perception of a patient.9,13–16

To closer match this spatial perception in ray-tracing simulations, it is important to consider how the visual field is projected on the retina. For a phakic eye, it is known that the relation between the position of an object in the visual field and the retinal image of that object is approximately linear for the central visual field and nonlinear for the peripheral visual field.17,18 Since an IOL refracts light rays differently than the approximately 4 times thicker crystalline lens, this relation might change when the crystalline lens is exchanged for an IOL.19 In turn, this change can potentially induce a shift in the peripheral visual field, which could affect how peripheral visual phenomena, such as ND, are experienced by patients. Therefore, this study aims to evaluate whether IOL implantation induces shifts in the peripheral visual field.

METHODS

The effect of IOL implantation on the peripheral visual field was assessed using ray-tracing simulations with phakic and pseudophakic versions of the Escudero-Sanz eye model.11 All simulations were performed in OpticStudio (v. 20.3.2, Zemax, LCC) through the ZOSPy package (v. 0.6.1).6,20 A wavelength of 543 nm and corresponding refractive indices were used.11

Two different IOL designs were used for the pseudophakic eye model. These IOL designs included a simple biconvex IOL and a biconvex IOL with a conical flange on the anterior surface that approximately matches the geometry of the ZCB00 IOL (Johnson & Johnson Vision), hereafter named the biconvex IOL and the clinical IOL, respectively. The IOLs were positioned 4.51 mm posteriorly from the corneal endothelium (internal anterior chamber depth [ACD]) to create a distance of 1.46 mm between the anterior iris surface and the anterior IOL, as reported in the literature.21 The position of the iris was not adjusted between the phakic and pseudophakic eye models. Both IOLs had a refractive index of 1.47.6,22 The shape of the posterior surface of both IOLs was optimized to achieve an equal defocus in the pseudophakic and phakic eye models with a 3.0-mm pupil diameter. After this optimization, both IOLs had a power of 20 diopters (D).

Two additional sets of pseudophakic eye models were created to evaluate the potential effect of a different IOL location or power. In the first set, the ACD was adjusted by ±0.31 mm (±1 SD) and ±0.62 mm (±2 SD) while maintaining the same IOL geometry.21 In the second set, additional defocus of ±1 D, ±2 D, and ±3 D was induced in the eye model by altering the IOL power through modifications of the posterior IOL surface.

For each eye model, the relation between the position of a source object in the visual field and the corresponding retinal location was assessed using nonsequential ray tracing and a 6.0-mm pupil diameter. The position of the object in the visual field, hereafter called the visual field angle, was defined as the angle between the object, the center of the pupil, and the optical axis through that center, omitting the influence of refraction induced by the cornea (Figure 1). The objects were positioned from central vision (visual field angle of 0 degree) to peripheral vision (maximum visual field angle of 100 degrees) with steps of 1 degree. Each object emitted 1 ray of light aimed at the center of the actual pupil. As these rays were refracted by the cornea, these rays did not always pass exactly through the actual pupil center (Figure 1, B). For each ray, the location where it illuminated the retina was determined, which was expressed as the angle with respect to the center of the retina (Figure 1).6

Figure 1.:

Definition of the visual field angle, retinal location, and visual field shift. A: Definition the visual field angle: the angle between the input ray, the optical axis, and the corresponding retinal location. B: For the patients with pseudophakia, the visual field shift is defined as the shift in the visual field that is required to illuminate the same retinal location in the phakic eye. This example shows both a positive and negative shift. A positive shift indicates that the pseudophakic visual field is shifted toward peripheral vision and negative shift that it is shifted toward central vision. Note that the peripheral rays do not exactly pass through the center of the pupil as the rays are aimed at the physical center of the pupil, and thus, the corneal refraction is not included in the determination of their initial direction. All shifts are exaggerated for illustration purposes.

The relation between the visual field angle and the illuminated retinal location in the phakic eye model was used as a reference to determine whether exchanging the crystalline lens for an IOL would induce a shift in the visual field. To that end, the illuminated retinal locations of the pseudophakic eye were mapped onto the illuminated retinal locations of the phakic eye. Using that mapping, the illuminated retinal locations of the pseudophakic eye models were projected back into the phakic visual field. Subsequently, the difference between that projection and the actual source objects was calculated, providing the visual field shift (Figure 1, B). In this article, a negative visual field shift indicates a shift toward central vision in pseudophakic eyes.

RESULTS

The relation between visual field angle and illuminated retinal location was similar in the phakic and pseudophakic eye models for the central visual field, with absolute differences below 1.0 degree for visual field angles up to 28 degrees (Figure 2). Over this range, the relationship between the visual field angle and the retinal location was nearly linear (all R2 ≈ 1.00), in which a 1.0-degree increase in visual field angle corresponded to a change in retinal location of 1.4 degrees.

Figure 2.:

Visual field shift in pseudophakic eyes. A: Overlay of nonsequential ray tracing in phakic and pseudophakic eye models, showing that rays originating from large visual field angles are refracted relatively more toward the center of the retina by the clinical IOL (cyan rays) than by the crystalline lens (red rays). B: Simulation results for the phakic eye and the pseudophakic eyes with the IOL positioned such that it reflected to the average position in the population. Top: The retinal location of illumination as a function of visual field angle for the crystalline lens, biconvex IOL, and clinical IOL. Bottom: The resulting visual field shift for both IOLs. A negative shift indicates a shift toward central vision.

Further into the peripheral visual field, larger differences in retinal location were apparent between the phakic and pseudophakic eye models. However, the results in the far periphery of certain eye models were affected by 2 distinct effects—light being refracted by the edge of the IOL and light missing the IOL. These effects only occurred in pseudophakic eye models in which the IOL was positioned further away from the iris than in the average eye, thereby creating a larger physical gap between the iris and the IOL. In the eye model with the biconvex IOL positioned with an internal ACD of 5.12 mm (+2 SD), for example, light rays originating from visual field angles between 74 degrees and 79 degrees pass through the biconvex IOL edge or even completely miss the IOL (Figure 3). This resulted in abrupt changes in illuminated retinal location from 92 to 81 degrees and subsequently to 102 degrees.

Figure 3.:

Refraction of peripheral rays of light by the crystalline lens and the IOLs. The displayed IOLs are axially positioned with an internal ACD of 5.12 mm (+2 SD). For the crystalline lens, all peripheral rays of light are refracted by the posterior lens surface. For the biconvex IOL, light originating from far peripheral visual field angles is refracted by the IOL edge rather than by the posterior IOL surface (orange arrow). The IOL edge refracts the light to a relatively more central retinal location. Light originating from even higher angles is not refracted by the IOL (red arrow). For the clinical IOL, the convex-concave anterior IOL surface generally results in a more continuous illumination of the peripheral retina, but some light rays are not refracted as expected (green arrow). ACD = anterior chamber depth

For light rays passing through the posterior IOL surface, light originating from far peripheral visual field angles was refracted to a relatively more central retinal location by the IOL than by the crystalline lens in almost all pseudophakic eye models. The maximal shift in retinal location between the phakic and pseudophakic eye models was −5.5 degrees, which related to a −5.1-degree shift of the visual field toward central vision. Some variation in the maximal visual field shift was present between the pseudophakic eye models (Figure 4). For the pseudophakic models with the IOL positioned such that it reflected the average position in the population, the maximum shift was −3 degrees with the clinical IOL and −1.5 degrees with the biconvex IOL (Figure 2, B). Changing the axial location of the IOL affected the magnitude of the visual field shift for both IOL designs, although to a different extent. Overall, a more anteriorly located IOL resulted in a more peripheral visual field shift, with a maximum observed shift of +4.7 degrees toward peripheral at a visual field angle of 79 degrees (Figure 4, A). Changing the axial location of the biconvex IOL toward posterior had little additional effect on the visual field shift, with an additional shift of less than 0.2 degrees. This change in axial location had a larger effect with the clinical IOL, with a maximal observed visual field shift of −5.4 degrees at a visual field angle of 76 degrees (Figure 4, A). Changing the IOL power had a relatively small additional effect on the shift of both the central and peripheral visual fields (Figure 4, B). Overall, changing the IOL power to induce a defocus of up to ±3 D shifted the visual field over a range of approximately 1.0 degrees with the biconvex IOL design and approximately 2.7 degrees with the clinical IOL design.

Figure 4.:

Effect of axial IOL position and IOL power on the visual field shift. A: Visual field shifts with the IOL positioned at various internal ACDs for the biconvex IOL (left) and the clinical IOL (right). B: Visual field shifts with varying IOL powers for the biconvex IOL (left) and the clinical IOL (right). Data re shown based on the additional defocus induced in the eye model by the new IOL power. A negative visual field shift corresponds to a shift toward central vision. ACD = anterior chamber depth

DISCUSSION

This study evaluated whether the implantation of an IOL induces a shift in the visual field. The induced shifts were small for central vision up to visual field angles of approximately 30 degrees, with visual field shifts of 1 degree or less regardless of the axial position or IOL power. Stronger effects were apparent for the more peripheral visual field, where IOLs in specific configurations can induce an over 5-degree shift in the visual field. The exact magnitude of the shift depended mainly on the design and axial position of the IOL (Figure 4).

These visual field shifts, especially the shifts toward central vision, can potentially affect how patients experience peripheral optical phenomena. For example, perimetry measurements showed that the shadow experienced by pseudophakic patients with ND might be measured between 70 degrees and 75 degrees in the visual field using a kinetic perimeter.23 The results of perimetry are quantified using the location of the light stimulus in the visual field, which corresponds to the visual field angle used in this study. The results of this study show that this object space-based annotation might not reflect the patient's experience as the light source could illuminate a more central or peripheral part of the retina than anticipated. For example, ND measured between 70 degrees and 75 degrees can be experienced by the patient between 65 degrees and 70 degrees, making it more noticeable and burdensome.23 In addition, at even higher visual field angles, a shift toward central vision could result in peripheral visual phenomena shifting onto the functional retina, and thereby becoming noticed by the patient. However, it is important to acknowledge that neuroadaptation might over time (partly) compensate for these visual field shifts.

Since the magnitude and direction visual field shift showed to be dependent on the design and axial position of the IOL, the shift will differ between patients. These differences might explain why only a subset of patients experience peripheral visual complaints and why treatments for these complaints, such as a piggyback IOL implantation or IOL exchange, are effective in some, but not all patients.15,24–26 This effectiveness will, however, likely depend on the interplay between ocular anatomy and IOL design, and therefore, the current results cannot directly be applied to an individual patient and a specific IOL design. Similarly, only 1 model of the crystalline lens was used, although both its shape and refractive index vary in the population.27,28 However, additional simulations with varying lens shapes showed minimal, less than 0.5 degrees, changes in the results (Supplemental Figure 1, available at https://links.lww.com/JRS/A991).

Nonetheless, it is noteworthy that the shift in retinal illumination in the pseudophakic eye will directly affect the image size on the peripheral retina. The change from a slightly positive to progressively more negative shift will result in a reduction of the image size. Such changes can directly affect clinical imaging of the peripheral retina, which can in turn affect treatments. For example, ultra-widefield funduscopic images are used as an input in ocular radiotherapy planning, and optical distortions could thus result in errors in tumor definition.29,30 Whether the current methodology can directly be used to correct clinical imaging or measurement devices will differ per case. Some optical properties are calculated with respect to the chief ray, the ray that travels from the light source to the retina through the center of the pupil. In these cases, a slightly different definition of the incoming light rays has to be taken using chief rays, which includes the apparent shift in pupil location because of corneal refraction (Figure 1, A).

As with any simulation study, some limitations should be considered when interpreting the results. First, only 1 specific eye model and 2 types of IOLs were evaluated. It is, however, likely that the observed relation between visual field angle and location of retinal illumination will depend on the patient's biometry and corneal shape (Figure 2, B).31 While there are intersubject variations in those anatomical properties, these variations likely have a relatively minor effect on the observed visual field shifts, as these shifts are determined relative to the phakic state of the same eye.32 Furthermore, this study evaluated a small subset of the possible variations in IOL designs and properties. Although some design parameters, such as the posterior IOL shape, seemed to have little effect on the observed shifts, increasing the diameter of the optic is expected to have a more significant effect on far peripheral vision.8,33 Similarly, a more different IOL geometry, such as the recently introduced meniscus-shaped optic, will likely have larger effects.34 Frosting the IOL edge, another common IOL property, would induce a random scatter of rays that pass through the IOL edge resulting in a loss of relation to a specific retinal location.35

Second, a rotationally symmetric model of the eye was used in these evaluations while it is known that the eye has a certain amount of asymmetry.13 The use of a population mean shift of 5 degrees, related to the angle alpha, has been proposed, but care has to be taken when applying such a generic correction as the relevant ocular asymmetries can differ between groups of patients.4,13 Furthermore, this correction would be based on the assumption that angle alpha is unaffected by the cataract surgery. While such a correction would change the visual field angle at which a certain visual field shift is experienced, the magnitude of this shift will also be unaffected.

In conclusion, ray tracing showed that IOL implantation tends to induce little changes in the central visual field but could induce a peripheral visual field shift of over 5 degrees in the perceived peripheral eccentricities. These shifts should be taken into account when evaluating the peripheral vision of patients with pseudophakia through ray-tracing simulations, as they can have a direct effect on the patient's perception.WHAT WAS KNOWN IOLs refract light rays differently than the approximately 4 times thicker crystalline lens. The relation between visual field angle and location of retinal illumination depends on biometry and retinal shape.

WHAT THIS PAPER ADDS IOL implantation can induce an over 5-degree shift in the peripheral visual field of the eye. REFERENCES 1. Erie JC, Bandhauer MH. Intraocular lens surfaces and their relationship to postoperative glare. J Cataract Refract Surg 2003;29:336–341 2. Simpson MJ. Double image in far peripheral vision of pseudophakic eye as source of negative dysphotopsia. J Opt Soc Am A Opt Image Sci Vis 2014;31:2642–2649 3. Holladay JT, Simpson MJ. Negative dysphotopsia: causes and rationale for prevention and treatment. J Cataract Refract Surg 2017;43:263–275 4. Simpson MJ. Simulated images of intraocular lens negative dysphotopsia and visual phenomena. J Opt Soc Am A Opt Image Sci Vis 2019;36:B44–B51 5. Simpson MJ. Intraocular lens far peripheral vision: image detail and negative dysphotopsia. J Cataract Refract Surg 2020;46:451–458 6. van Vught L, Que I, Luyten GPM, Beenakker JM. Effect of anatomical differences and intraocular lens design on negative dysphotopsia. J Cataract Refract Surg 2022;48:1446–1452 7. Erie JC, Simpson MJ, Bandhauer MH. Effect of a sulcus-fixated piggyback intraocular lens on negative dysphotopsia: ray-tracing analysis. J Cataract Refract Surg 2019;45:443–450 8. Erie JC, Simpson MJ, Mahr MA. Effect of a 7.0 mm intraocular lens optic on peripheral retinal illumination with implications for negative dysphotopsia. J Cataract Refract Surg 2022;48:95–99 9. Polans J, Jaeken B, McNabb RP, Artal P, Izatt JA. Wide-field optical model of the human eye with asymmetrically tilted and decentered lens that reproduces measured ocular aberrations. Optica 2015;2:124–134 10. Canovas C, Artal P. Customized eye models for determining optimized intraocular lenses power. Biomed Opt Express 2011;2:1649–1662 11. Escudero-Sanz I, Navarro R. Off-axis aberrations of a wide-angle schematic eye model. J Opt Soc Am A Opt Image Sci Vis 1999;16:1881–1891 12. Tabernero J, Benito A, Nourrit V, Artal P. Instrument for measuring the misalignments of ocular surfaces. Opt Express 2006;14:10945–10956 13. van Vught L, Luyten GPM, Beenakker JM. Distinct differences in anterior chamber configuration and peripheral aberrations in negative dysphotopsia. J Cataract Refract Surg 2020;46:1007–1015 14. Jaeken B, Lundström L, Artal P. Fast scanning peripheral wave-front sensor for the human eye. Opt Express 2011;19:7903–7913 15. Makhotkina NY, Dugrain V, Purchase D, Berendschot T, Nuijts R. Effect of supplementary implantation of a sulcus-fixated intraocular lens in patients with negative dysphotopsia. J Cataract Refract Surg 2018;44:209–218 16. Rozendal LRW, van Vught L, Luyten GPM, Beenakker JM. The value of static perimetry in the diagnosis and follow-up of negative dysphotopsia. Optom Vis Sci 2022;99:645–651 17. Drasdo N, Fowler CW. Non-linear projection of the retinal image in a wide-angle schematic eye. Br J Ophthalmol 1974;58:709–714 18. Suheimat M, Zhu HF, Lambert A, Atchison DA. Relationship between retinal distance and object field angles for finite schematic eyes. Ophthalmic Physiol Opt 2016;36:404–410 19. Jaeken B, Mirabet S, Marin JM, Artal P. Comparison of the optical image quality in the periphery of phakic and pseudophakic eyes. Invest Ophthalmol Vis Sci 2013;54:3594–3599 20. van Vught L, Beenakker JM. ZOSPy [Computer software]. Version v0.5.1. 2021. Available at: https://github.com/MREYE-LUMC/ZOSPy 21. Plat J, Hoa D, Mura F, Busetto T, Schneider C, Payerols A, Villain M, Daien V. Clinical and biometric determinants of actual lens position after cataract surgery. J Cataract Refract Surg 2017;43:195–200 22. Johnson & Johnson Vision. TECNIS Monofocal 1-Piece IOL. Available at: https://www.jnjvisionpro.com/products/tecnis%C2%AE-1-piece-iol. Accessed March 8, 2022 23. Makhotkina NY, Berendschot TT, Nuijts RM. Objective evaluation of negative dysphotopsia with Goldmann kinetic perimetry. J Cataract Refract Surg 2016;42:1626–1633 24. Davison JA. Positive and negative dysphotopsia in patients with acrylic intraocular lenses. J Cataract Refract Surg 2000;26:1346–1355 25. Vamosi P, Csakany B, Nemeth J. Intraocular lens exchange in patients with negative dysphotopsia symptoms. J Cataract Refract Surg 2010;36:418–424 26. Taubenslag KJ, Groos EB, Parker MG, Ewald MD, Pilkinton RD. Successful treatment of negative dysphotopsia with in-the-bag intraocular lens exchange using a wide ovoid IOL. J Cataract Refract Surg 2016;42:336–337 27. Meng J, Wei L, He W, Qi J, Lu Y, Zhu X. Lens thickness and associated ocular biometric factors among cataract patients in Shanghai. Eye Vis (Lond) 2021;8:22 28. Uhlhorn SR, Borja D, Manns F, Parel JM. Refractive index measurement of the isolated crystalline lens using optical coherence tomography. Vis Res 2008;48:2732–2738 29. Fantaguzzi F, Servillo A, Sacconi R, Tombolini B, Bandello F, Querques G. Comparison of peripheral extension, acquisition time, and image chromaticity of Optos, Clarus, and EIDON systems. Graefes Arch Clin Exp Ophthalmol 2023;261:1289–1297 30. Wulff J, Koska B, Heufelder J, Janson M, Bäcker CM, Siregar H, Behrends C, Bäumer C, Foerster A, Bechrakis NE, Timmermann B. Commissioning and validation of a novel commercial TPS for ocular proton therapy. Med Phys 2023;50:365–379 31. Hastings GD, Banks MS, Roorda A. Radial and tangential retinal magnifications as functions of visual field angle across spherical, oblate, and prolate retinal profiles. Transl Vis Sci Technol 2022;11:10 32. van Vught L, Shamonin DP, Luyten GPM, Stoel BC, Beenakker JM. MRI-based 3D retinal shape determination. BMJ Open Ophthalmol 2021;6:e000855 33. Bonsemeyer MK, Becker E, Liekfeld A. Dysphotopsia and functional quality of vision after implantation of an intraocular lens with a 7.0 mm optic and plate haptic design. J Cataract Refract Surg 2022;48:75–82 34. Villegas EA, Marin JM, Ginis H, Robles C, Alcón E, Hervella L, Prieto PM, Taña-Rivero P, Artal P. Peripheral refraction and contrast detection sensitivity in pseudophakic patients implanted with a new meniscus intraocular lens. J Refract Surg 2022;38:229–234 35. Meacock WR, Spalton DJ, Khan S. The effect of texturing the intraocular lens edge on postoperative glare symptoms: a randomized, prospective, double-masked study. Arch Ophthalmol 2002;120:1294–1298