Acta Ophthalmologica 2015
The importance of angle kappa evaluation for implantation of diffractive multifocal intra-ocular lenses using pseudophakic eye model ın1 and Kla´ra Marta Karhanova´,1 Frantisˇ ek Pluha´cˇek,2 Petr Mlcˇa´k,1 Ondrej Vla´cˇil,1 Martin S Maresova´1 1 Department of Ophthalmology, Olomouc University Hospital and Faculty of Medicine and Dentistry, Palacky University, Olomouc, Czech Republic 2 Department of Optics, Faculty of Science, Palacky University, Olomouc, Czech Republic
ABSTRACT. Purpose: To determine the critical value of the angle kappa in connection with a higher risk of photic phenomena for the AcrySof ReSTOR and Tecnis multifocal intra-ocular lens (MIOL) on a standardized pseudophakic eye model. To analyse the impact of biometric value changes on the critical angle kappa. Methods: Geometrical optic rules applied to a suitable optical model of the pseudophakic eye were used to calculate the critical value of the angle kappa for the Tecnis and three types of the AcrySof ReSTOR MIOLs. The angle kappa was defined as critical if the incident ray passed through the first ring’s edge area. The influence of different positive optical corneal power (K), effective lens position (ELP) and axial length (AL) on the critical angle kappa (jc) was investigated. The dependence of jc on one of the parameters was studied for standardized values of the remaining parameters. Results: The highest value of the critical angle kappa was evaluated for the Tecnis MIOL. The increase in ELP and K caused an increase in jc under the given conditions. On the contrary, an increase in AL led to lower values of jc. Conclusion: We demonstrated the dependence of the critical angle kappa on the central part of the MIOL and on biometric parameters of the eye, especially on the effective lens position. According to these results, we conclude that shallow anterior chamber depth in connection with a higher angle kappa is an important risk factor for pronounced photic phenomena after implantation of a diffractive MIOL. Key words: angle kappa – anterior chamber depth – effective lens position – multifocal intraocular lens – photic phenomena
Acta Ophthalmol. 2015: 93: e123–e128 ª 2014 Acta Ophthalmologica Scandinavica Foundation. Published by John Wiley & Sons Ltd
doi: 10.1111/aos.12521
Introduction In recent years, multifocal intra-ocular lens (MIOL) implantation has become an increasingly common solution for cataract and presbyopic patients who want to find a spectacle-free option after surgery. However, patient expectations
and demands regarding refractive outcomes are still increasing. Although excellent results are reported in many recent studies after MIOL implantation, there are also some limitations. The weaknesses of MIOLs are, in particular, unsatisfactory visual acuity at specific
working distances (Blaylock et al. 2006; Hu¨tz et al. 2008), increased dysphotopsia compared to monofocal intra-ocular lenses (IOL) (Souza et al. 2006; Chiam et al. 2006; Hofmann et al. 2009), decreased contrast sensitivity (MontesMico´ & Ali o 2003; Zhao et al. 2010) and increased intra-ocular straylight (De Vries et al. 2008). Unfortunately, in some cases, even an IOL exchange is required (Woodward et al. 2009). However, the bag-in-the-lens could only be implanted in 70% of the eyes (Tassignon et al. 2014). A lot of studies have focused directly on the analysis of the governing factors for patient satisfaction or dissatisfaction after MIOL implantation and attempted to find criteria for patient selection (Walkow & Klemen 2001; Blaylock et al. 2008; Kohnen et al. 2008; Pepose 2008; Woodward et al. 2009; De Vries et al. 2011). It has been confirmed that the main complaints in dissatisfied patients are blurred vision and photic phenomena (Woodward et al. 2009; De Vries et al. 2011). The causes associated with disturbing photic phenomena have included MIOL decentration, posterior capsular opacification, retained lens fragment, dry eye syndrome, uncorrected visual acuity, use of spectacles for distance purposes, postoperative astigmatism and postoperative spherical equivalent (Walkow & Klemen 2001; Woodward et al. 2009). In the last years, the angle kappa has also attracted interest in connection with a possible higher risk of disturbing photic phe-
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nomena after MIOL implantation. It is assumed that, in patients with a higher angle kappa, a MIOL may induce more aberrations, glare and halo. To date, only few studies in larger cohorts of patients have been published concerning this problem (De Vries et al. 2011; Prakash et al. 2011; Karhanov a et al. 2013). Although Prakash et al. (2011) found a statistically significant association between the angle kappa and photic phenomena, they also noted that many patients with a high angle kappa were asymptomatic. Up to now, there has been no clear explanation of this fact. None of the published papers addressed the question regarding which value of the angle kappa is already a risk when implanting a MIOL. Only recommendations based on experience from the practice have been published. The aim of this study was to determine the critical value of the angle kappa in connection with a higher risk of developing photic phenomena for four diffractive MIOLs, the Tecnis (Abbot, Illinois, USA) and three types of AcrySof ReSTOR (Alcon, TX, USA), on a standardized pseudophakic eye model. The second aim was to analyse the impact of biometric value changes in the pseudophakic eye on the critical angle kappa and to find out whether angle kappa evaluation is necessary for every patient before planned implantation of a diffractive-type MIOL.
Methods For an explanation of the photic phenomena, a geometrical construction of the incident rays through the nodal points is used. The ray passes through the first nodal point, and the foveally observed distant object defines the nodal axis. The nodal axis is commonly denoted as the visual axis. The angle kappa (j) is the angle between the nodal (visual) axis and the pupillary axis. The pupillary axis is considered identical with the optical axis of the eye (Tunnacliffe 1993). It is assumed that the photic phenomena markedly increase if the intersection of the nodal axis and the MIOL moves from its central part to the first ring of the MIOL. The relevant border value of the angle kappa is referred to as critical angle kappa jc (Fig. 1). The critical value jc of the angle kappa can be calculated using the geometrical optical rules applied to a
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Fig. 1. The schema of the used optical model of the pseudophakic eye with an optical axial length AL and an effective position ELP of a thin MIOL with the centre C of the MIOL on the eye optical axis. R marks the border of the central part of the IOL of the diameter d. The points N and N’ represent the first and second nodal points of the pseudophakic optical system, F’ is the second focal point of this system. The critical angle kappa kc is marked.
suitable optical model of the pseudophakic eye. The optical model applied in this text is based on the standardized pseudophakic schematic eye (Holladay 1997, 1998, 2007) with a thin IOL (Fig. 1). The distances used are oriented according to Fig. 1 with the positive values in the incident light direction (i.e. from left to right) and negative values in the opposite direction. The MIOL is perfectly centred to the pupil centre. The model is represented by a positive optical corneal power K, an optical axial length AL, a thin MIOL effective optical power P for distance correction, an effective position ELP of the thin MIOL and by a refractive index n of the aqueous and vitreous. The ELP means a distance of the MIOL optical centre from the anterior corneal vertex. A zero postoperative refraction of the pseudophakic eye is considered. Under these conditions, the P is a dependent variable. It can be shown that the relation n n P¼ n ð1Þ AL ELP K ELP holds for this eye optical model (Holladay 1997, 1998). The central part of the MIOL with the constant power has the diameter d.
The nodal visual axis corresponds to the ray passing from the observed object to the fovea through the nodal points. Moreover, it intersects the thin MIOL in the border R of its central part and the first ring for the critical angle kappa (see Fig. 1). According to the geometrical construction in Fig. 1 and to the rectangular triangle RCN’, the size |jc| of the jc can be computed by the relation jjc j ¼ arctan
d=2 AL ELP þ F0 N0
ð2Þ
F0 and N 0 are the second focal point and the second nodal point of the pseudophakic eye optical model, and C is the centre of the MIOL. It can be shown (Tunnacliffe 1993) that F0 N0 ¼ f ¼
1 F
ð3Þ
The quantity f is the equivalent first focal length of this optical system, and F is its equivalent optical power. The F can be obtained using a common equation for the equivalent lens power in the form F¼KþP
ELP KP n
ð4Þ
Acta Ophthalmologica 2015
The formula (2) can be rewritten using (3) and (4) to the form jjc j ¼ arctan
d=2 AL ELP
1 KþPELP n KP
ð5Þ The term (5) along with (1) describe the influence of the pseudophakic eye model parameters K, ELP, AL and n on the critical value jc for the given diameter d of the central MIOL part. For the calculation of the concrete value of critical angle kappa (jc), the standard parameters of the considered pseudophakic eye model (Holladay 1997, 1998, 2007) K = 43.27 D, ELP = 5.25 mm, AL = 23.65 mm and n = 1.336 were applied to the relation (5). The MIOL was modelled according to the Tecnis ZMB00 (addition +4.0 D) and AcrySof ReSTOR SV2STO (addition + 2.5 D), SB6AD1 (addition + 3.0 D) and SN6AD3 (addition + 4.0 D) MIOLs of the parameters d = 1.0 mm, d = 0.938 mm, d = 0.86 mm and d = 0.74 mm, respectively. All the data relating to these MIOLs were obtained from the manufacturers. Next, the influence of quantities K, ELP and AL on the jc was analysed in the case of the abovementioned MIOL parameters by the relation (5). In particular, the dependence of the jc on one of the parameters was studied for standardized values of the remaining parameters.
Results The values of the critical angle kappa were jc 15.48° for the Tecnis ZMB00 (d = 1.0 mm), jc 14.56° for the AcrySof ReSTOR SV2STO (d = 0.938 mm), jc 13.39° for the AcrySof ReSTOR SB6AD1 (d = 0.86) and jc 11.58° for the AcrySof ReSTOR SB6AD3 (d = 0.74). The results of the influence of quantities K, ELP and AL on the jc in the cases of these four multifocal lenses are presented in Figs 2–4 in the graphical form. The increase in ELP and K caused an increase in jc under the given conditions (Figs 2 and 3). On the contrary, the increase in AL led to lower values of jc (Fig. 4). The impact of the MIOL characteristics is evident, too – the higher d, the higher jc.
Fig. 2. Dependence of the critical angle kappa |kc| on the effective lens position ELP in the pseudophakic eye model for the standardized values K = 43.27 D and AL = 23.65 mm and for four values of d. The standardized value ELP = 5.25 mm is represented by the vertical dashed line.
Fig. 3. Dependence of the critical angle kappa |kc| on the optical corneal power K in the pseudophakic eye model for the standardized values ELP = 5.25 mm and AL = 23.65 mm and for four values of d. The standardized value K = 43.27 D is represented by the vertical dashed line.
Fig. 4. Dependence of the critical angle kappa |kc| on the optical axial length AL in the pseudophakic eye model for the standardized values K = 43.27 D and ELP = 5.25 mm and for four values of d. The standardized value of AL = 23.65 mm is represented by the vertical dashed line.
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Discussion Angle kappa is defined as the angle between the visual axis (connects the point of fixation with the fovea) and the pupillary axis (a line through the centre of the pupil perpendicular to the cornea). A positive angle kappa is associated with an out-turning of the eye (the pupillary axis is temporal relative to the visual axis), while a negative angle kappa is an inward turning of the eye (the pupillary axis is nasal relative to the visual axis). Thus, when an eye fixates on a light source, the reflection on the cornea (Purkinje image) will not be centred but will be located nasal (positive angle kappa) or temporal (negative angle kappa) to the pupillary centre. According to the published literature, a positive kappa angle varies from 3.5 to 6° in emmetropic eyes and from 6.0 to 9.0° in hyperopic eyes. In myopic eyes, the angle kappa is smaller, averaging approximately 2.0°, and can even be negative (Von Noorden & Campos 2002). Basmak et al. (2007a,b) also reported the angle kappa to be higher in hyperopes than in emmetropes and myopes. Hashemi et al. (2010) found mean angle kappa values of 5.52 1.19° in hyperopic eyes, 5.72 1.10° in emmetropic eyes and 5.13 1.5° in myopic eyes. With the development of new types of intra-ocular lenses, angle kappa is coming to the forefront of interest of cataract surgeons. Kottler et al. (2004) reported a hyperopic patient with a large angle kappa in whom the residual refractive error after toric phakic intraocular lens implantation was improved by displacement of the lens according to the visual axis. De Vries et al. (2011) suggested that three major causes of discomfort after MIOL implantation (ReSTOR, Alcon Laboratories; Rezoom, Abbott Medical Optics; Tecnis, Abbott Medical, Optics) were residual refractive error, posterior capsule opacification and large pupil size. However, a large angle kappa and MIOL decentration from the visual axis should also be considered. Soda & Yaguchi (2012) evaluated the influence of horizontal decentration on optical performance in different MIOLs using an eye model. He found that clinically relevant effects are not to be expected up to a decentration of 0.75 mm. But a possible influence of angle kappa on these
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results was not taken into account. We confirmed in our previous study (Karhanova´ et al. 2013) that temporal decentration of the ReSTOR multifocal IOL (in cases of a positive angle kappa) was associated with the greatest risk of photic phenomena. By contrast, nasal decentration (in cases of a positive angle kappa) did not cause pronounced photic phenomena. Prakash et al. (2011) evaluated the role of angle kappa in the occurrence of photic phenomena after MIOL implantation (Rezoom). They reported that patient complaints about glare and halo showed positive correlation with the preoperative values of angle kappa. On the other hand, they found that many patients with a high angle kappa were asymptomatic. The assumed cause of pronounced photic phenomena after implantation of diffractive-design MIOLs in patients with a higher angle kappa is that the fovea centric ray would pass closer to the edge of the rings and not through the central area of the MIOL (Fig. 5A and B). To date, several MIOLs of this design have been available and commonly used in practice. For the purpose of our study, we evaluated the AcrySof ReSTOR (Alcon Laboratories, Inc., Fort Worth, Texas) and the Tecnis (Abbot Illinois, USA) MIOLs. The AcrySof ReSTOR is designed to provide quality near and distance vision by combining apodized diffractive and refractive technologies. The centre of the lens consists of apodized diffractive optic that focuses light for near through distance vision. Apodization is the gradual tapering of diffractive steps from the centre to the outside edge of the lens. It helps to create a smooth transition of the light between distant, intermediate and near focal points. The refractive zone surrounds the apodized diffractive region. To date, three types of the AcrySof ReSTOR IOL have been introduced in the market – AcrySof ReSTOR SN6AD3 (addition + 4.0 D), SB6AD1 (addition + 3.0 D) and SV2STO (addition + 2.5 D). They vary not only in add power, but also in central zone diameter and in the number of diffractive rings. The Tecnis MIOL is a full diffractive optic. The diffraction pattern of this lens is on the posterior surface of the lens (as compared to the AcrySof ReSTOR lens on the anterior surface of the lens), and the lens has the
aspheric prolate technology. We evaluated these four lenses in our study because of their different central diameters (d). The mentioned differences in MIOL design did not influence our analysis because the MIOL was replaced with a thin lens in our model and was represented only by its equivalent optical power P and central zone diameter d. By comparing these four MIOLs on the pseudophakic eye model, we confirmed that the higher the central zone diameter, the higher must be the angle kappa to reach the edge of the first ring of the IOL. In all four types of MIOLs, the critical angle kappa (reaching the edge of the ring) calculated was higher than that found in normal population. On this theoretical model, we also confirmed the influence of K, AL and ELP on the critical angle kappa. For better illustration, we calculated the border values of parameters K, AL and ELP corresponding to the critical angle kappa jc = 7° (which can be found in normal population) for all four types of the MIOL as a model case (Table 1). Two of the eye model parameters always have standard values and one of them was calculated. The values of K and AL for this particular model case are out of normal range, but the border values of ELP achieve a realistic size. According to these results, we suggest that the most important biometric value that can influence the possible occurrence of photic phenomena after MIOL implantation in connection with a higher angle kappa be ELP. When the interdependence of ELP and preoperative anterior chamber depth are taken into account (Olsen et al. 1990; Holladay 1993; Olsen 2006), it can be established that patients with preoperative shallow anterior chamber depth are at a higher risk. In our study, we presumed the MIOL to be perfectly centred to the pupil centre. In the case of a decentred MIOL, the considered border point R (see Fig. 1) shifts according to the direction and size of the decentration. Thus, the term d/2 in the equation (2) as well as (5) must be corrected – it must be increased for the decentration towards the visual axis or decreased for the opposite direction. In the simplest approximation, the term d/2 can be replaced by the term d/2 + D or d/2 – D, where D represents the decentration size (in length units). The resultant
Acta Ophthalmologica 2015
(A)
(B) Fig. 5. Schematic ray diagram showing that in eyes with a small angle kappa, a fovea centric ray may pass through the central area of the MIOL (A), while in those with a higher angle kappa, a fovea centric ray may pass close to the edge of the ring, thus causing photic phenomena (B).
Table 1. The results of values of optical corneal power K, effective position ELP of the thin IOL and optical axial length AL corresponding to the critical angle kappa jc = 7° for four different diameters d of the central part of the MIOL and for the refractive index n = 1.336. Two of the eye model parameters always have standard values, and one is changed in each combination. Only the values of ELP achieve a realistic size. d [mm]
K [D] (ELP = 5.25 mm, AL = 23.65 mm)
ELP [mm] (K = 43.27 D, AL = 23.65 mm)
AL [mm] (K = 43.27 D, ELP = 5.25 mm)
0.74 0.86 0.938 1.0
26.70 19.22 14.10 9.86
3.66 3.04 2.63 2.31
35.95 40.93 44.17 46.74
curves presented in Figs 2–4 shift upwards or downwards in this case. It means that the decentration towards the visual axis causes an increase in the jc and the risk of photic phenomena evoked by a large angle kappa should be reduced. In the practice, different methods for compensating for a large angle kappa (decentration of the MIOL towards the visual axis) have been described (Melki & HarissiDagher 2011). However, due to mem-
ory of the haptics, contraction of the capsule, and IOL rotation, it is uncertain whether the lens would stay in the decentred position (Prakash et al. 2011). Conversely, the opposite decentration causes a decrease of the jc and can heighten the risk of photic phenomena. These results are in accordance with the study by Karhanov a et al. (2013). Moreover, as mentioned above, a shallow preoperative anterior chamber leads to a lower ELP (Olsen
et al. 1990; Holladay 1993; Olsen 2006) and a lower jc (see Fig. 2). Thus, the effect of the opposite decentration on the risk of photic phenomena should be taken into account particularly for shallow preoperative anterior chambers. This study also has some limitations. The optical model of pseudophakic eye used simplifies the situation in a real eye. In a real eye, all three observed parameters (K, AL and ELP) vary. Also, the ELP is influenced by several factors, not only by preoperative axial length, anterior chamber depth and curvature of the cornea, but also by lens thickness and refraction (Olsen et al. 1990). The principal limitation is the simplifying presumption that photic phenomena are induced by the interaction of the central ray (corresponding to the nodal axis in our model) with the first MIOL ring. This approach, also considered in another study (Prakash et al. 2011), enables to derive a relation between the critical angle kappa and other parameters of the eye and MIOL based on geometrical optics and the thin MIOL approximation (see above), but does not take into account other optical effects caused by diffraction, etc. Thus, this approach does not allow a detailed analysis of the influence of the angle kappa on the photic phenomena, and the real values of the critical angle kappa can differ from our results based on simplified computations. Nevertheless, according to the aim of this study, the relationships obtained show which parameters should be considered for angle kappa evaluation with regard to the risk of photic phenomena and how their values can influence this risk. Despite these limitations, we think that the results of our study, especially the dependence on biometrical parameters of the eye, can help to find a possible explanation for the contradiction why some patients with a higher angle kappa are asymptomatic while others complain of disturbing photic phenomena. Further studies on real eyes will be required to confirm this hypothesis. In conclusion, the perception of photic phenomena is multifactorial. Our study suggests that angle kappa may also play a role. We confirmed the dependence of critical angle kappa on the central zone diameter of the multifocal IOL and on biometric parameters
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of the eye, especially on the effective lens position. According to these results, it can be concluded that especially shallow anterior chamber depth in connection with a higher angle kappa could be an important risk factor for pronounced photic phenomena after multifocal IOL implantation. We incorporated this conclusion in our daily practice. We recommend to evaluate the angle kappa in all patients with preoperative shallow anterior chamber depth before planned implantation of a diffractive-design MIOL. In cases when a larger angle kappa is confirmed, we prefer to implant another type of presbyopia-correcting IOLs. By contrast, in patients with normal or deeper anterior chamber, we do not require angle kappa evaluation before diffractive-design MIOL implantation.
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Hashemi H, KhabazKhoob M, Yazdani K, Mehravaran S, Jafarzadehpur E & Fotouhi A (2010): Distribution of angle kappa measurements with Orbscan II in a populationbased survey. J Cataract Refract Surg 26: 966–971. Hofmann T, Zuberbuhler B, Cervino A & Montes-Mic o R & Haefliger E (2009): Retinal straylight and complaint scores 18 months after implantation of the AcrySof monofocal and ReSTOR diffractive intraocular lenses. J Refract Surg 25: 485–492. Holladay JT (1993): Refractive power calculations for intraocular lenses in the phakic eye. Am J Ophthalmol 116: 63–66. Holladay JT (1997): Standardizing constants for ultrasonic biometry, keratometry, and intraocular lens power calculations. J Cataract Refract Surg 23: 1356–1370. Holladay JT (1998): Intraocular lens power calculations for the refractive surgeon. Oper Tech Cataract Refract Surg 1: 105–117. Holladay JT (2007): IOL power calculations for multifocal lenses. Cataract Refract Surg Today 7: 71–73. Hu¨tz WW, Eckhardt HB, Rohring B & Grolmus R (2008): Intermediate vision and reading speed with Array, Tecnis, and ReSTOR intraocular lenses. J Refract Surg 24: 251–256. Karhanova´ M, Maresova K, Pluhaček F, Mlčak P & Vlačil O & Sı´ n M (2013): The importance of angle kappa for centration of multifocal intraocular lenses. Cesk Slov Oftalmol 69: 64–68. Kohnen T, Kook D, Auffarth GU & Derhartunian V (2008): Use of multifocal intraocular lenses and criteria for patient selection. Ophthalmology 105: 527–532. Kottler UB, Tehrani M & Dick B (2004): Impact of the line of sight on toric phakic intraocular lenses for hyperopia. J Cataract Refract Surg 30: 1799–1801. Melki SA & Harissi-Dagher M (2011): Coaxially sighted intraocular lens light reflex for centration of the multifocal single piece intraocular lens. Can J Ophthalmol 46: 319–321. Monte´s-Mico´ R & Ali o JL (2003): Distance and near contrast sensitivity function after multifocal intraocular lens implantation. J Cataract Refract Surg 29: 703–711. Olsen T (2006): Prediction of the effective postoperative (intraocular lens) anterior chamber depth. J Cataract Refract Surg 32: 419–424. Olsen T, Olesen H, Thim K & Corydon L (1990): Prediction of postoperative intraocular lens chamber depth. J Cataract Refract Surg 16: 587–590. Pepose JS (2008): Maximizing satisfaction with presbyopia correcting intraocular lenses: the missing links. Am J Ophthalmol 146: 641– 648.
Prakash G, Prakash DR, Agarwal A, Kumar DA, Agarwal A & Jacob S (2011): Predictive factor and angle kappa analysis for visual satisfactions in patients with multifocal IOL implantation. Eye 25: 1187–1193. Soda M & Yaguchi S (2012): Effect of decentration on the optical performance in multifocal intraocular lenses. Ophthalmologica 227: 197–204. Souza CE, Muccioli C, Soriano ES et al. (2006): Visual Performance of AcrySof ReSTOR Apodized Diffractive IOL: a Prospective Comparative Trial. Am J Ophthalmol 141: 827–832. Tassignon MJ, Bartholomeeusen E, Rozema JJ, Jongenelen S & Mathysen DG (2014): Feasibility of multifocal intra-ocular lens exchange and conversion to the bag-in-thelens implantation. Acta Ophthalmol 92: 265–269. Tunnacliffe AH (1993): Introduction to visual optics. London: Gresham Press. Von Noorden G & Campos E (2002): Examination of the patient II. In: Von Noorden G & Campos E (eds). Binocular vision and ocular motility – theory and management of strabismus. 6th Edn. St. Louis: Mosby 168– 173. Walkow L & Klemen UM (2001): Patient satisfaction after implantation of diffractive designed multifocal intraocular lenses in dependence on objective parameters. Graefes Arch Clin Exp Ophthalmol 239: 683–687. Woodward MA, Randleman JB & Stulting RD (2009): Dissatisfaction after multifocal intraocular lens implantation. J Cataract Refract Surg 3: 992–997. Zhao G, Zhang J, Zhou Y, Hu L & Che CH & Jiang N (2010): Visual function after monocular implantation of apodized diffractive multifocal or single-piece monofocal intraocular lens: randomized prospective comparison. J Cataract Refract Surg 36: 282–285.
Received on February 14th, 2014. Accepted on July 3rd, 2014. Correspondence Martin Sˇı´ n, MD, PhD, FEBO Department of Ophthalmology University Hospital Olomouc I. P. Pavlova 6 77900 Olomouc, Czech Republic Tel: +420 588 444 202 Fax: +420 588 422 530 Email: [email protected] This research was supported by Grant No. PrF_2013_021 from the Faculty of Science of Palacky University, Olomouc, Czech Republic. The authors have no financial interest in any product mentioned in the text and no potential conflict of interest in this article.
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The importance of angle kappa evaluation for implantation of diffractive multifocal intra-ocular lenses using pseudophakic eye model ın1 and Kla´ra Marta Karhanova´,1 Frantisˇ ek Pluha´cˇek,2 Petr Mlcˇa´k,1 Ondrej Vla´cˇil,1 Martin S Maresova´1 1 Department of Ophthalmology, Olomouc University Hospital and Faculty of Medicine and Dentistry, Palacky University, Olomouc, Czech Republic 2 Department of Optics, Faculty of Science, Palacky University, Olomouc, Czech Republic
ABSTRACT. Purpose: To determine the critical value of the angle kappa in connection with a higher risk of photic phenomena for the AcrySof ReSTOR and Tecnis multifocal intra-ocular lens (MIOL) on a standardized pseudophakic eye model. To analyse the impact of biometric value changes on the critical angle kappa. Methods: Geometrical optic rules applied to a suitable optical model of the pseudophakic eye were used to calculate the critical value of the angle kappa for the Tecnis and three types of the AcrySof ReSTOR MIOLs. The angle kappa was defined as critical if the incident ray passed through the first ring’s edge area. The influence of different positive optical corneal power (K), effective lens position (ELP) and axial length (AL) on the critical angle kappa (jc) was investigated. The dependence of jc on one of the parameters was studied for standardized values of the remaining parameters. Results: The highest value of the critical angle kappa was evaluated for the Tecnis MIOL. The increase in ELP and K caused an increase in jc under the given conditions. On the contrary, an increase in AL led to lower values of jc. Conclusion: We demonstrated the dependence of the critical angle kappa on the central part of the MIOL and on biometric parameters of the eye, especially on the effective lens position. According to these results, we conclude that shallow anterior chamber depth in connection with a higher angle kappa is an important risk factor for pronounced photic phenomena after implantation of a diffractive MIOL. Key words: angle kappa – anterior chamber depth – effective lens position – multifocal intraocular lens – photic phenomena
Acta Ophthalmol. 2015: 93: e123–e128 ª 2014 Acta Ophthalmologica Scandinavica Foundation. Published by John Wiley & Sons Ltd
doi: 10.1111/aos.12521
Introduction In recent years, multifocal intra-ocular lens (MIOL) implantation has become an increasingly common solution for cataract and presbyopic patients who want to find a spectacle-free option after surgery. However, patient expectations
and demands regarding refractive outcomes are still increasing. Although excellent results are reported in many recent studies after MIOL implantation, there are also some limitations. The weaknesses of MIOLs are, in particular, unsatisfactory visual acuity at specific
working distances (Blaylock et al. 2006; Hu¨tz et al. 2008), increased dysphotopsia compared to monofocal intra-ocular lenses (IOL) (Souza et al. 2006; Chiam et al. 2006; Hofmann et al. 2009), decreased contrast sensitivity (MontesMico´ & Ali o 2003; Zhao et al. 2010) and increased intra-ocular straylight (De Vries et al. 2008). Unfortunately, in some cases, even an IOL exchange is required (Woodward et al. 2009). However, the bag-in-the-lens could only be implanted in 70% of the eyes (Tassignon et al. 2014). A lot of studies have focused directly on the analysis of the governing factors for patient satisfaction or dissatisfaction after MIOL implantation and attempted to find criteria for patient selection (Walkow & Klemen 2001; Blaylock et al. 2008; Kohnen et al. 2008; Pepose 2008; Woodward et al. 2009; De Vries et al. 2011). It has been confirmed that the main complaints in dissatisfied patients are blurred vision and photic phenomena (Woodward et al. 2009; De Vries et al. 2011). The causes associated with disturbing photic phenomena have included MIOL decentration, posterior capsular opacification, retained lens fragment, dry eye syndrome, uncorrected visual acuity, use of spectacles for distance purposes, postoperative astigmatism and postoperative spherical equivalent (Walkow & Klemen 2001; Woodward et al. 2009). In the last years, the angle kappa has also attracted interest in connection with a possible higher risk of disturbing photic phe-
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nomena after MIOL implantation. It is assumed that, in patients with a higher angle kappa, a MIOL may induce more aberrations, glare and halo. To date, only few studies in larger cohorts of patients have been published concerning this problem (De Vries et al. 2011; Prakash et al. 2011; Karhanov a et al. 2013). Although Prakash et al. (2011) found a statistically significant association between the angle kappa and photic phenomena, they also noted that many patients with a high angle kappa were asymptomatic. Up to now, there has been no clear explanation of this fact. None of the published papers addressed the question regarding which value of the angle kappa is already a risk when implanting a MIOL. Only recommendations based on experience from the practice have been published. The aim of this study was to determine the critical value of the angle kappa in connection with a higher risk of developing photic phenomena for four diffractive MIOLs, the Tecnis (Abbot, Illinois, USA) and three types of AcrySof ReSTOR (Alcon, TX, USA), on a standardized pseudophakic eye model. The second aim was to analyse the impact of biometric value changes in the pseudophakic eye on the critical angle kappa and to find out whether angle kappa evaluation is necessary for every patient before planned implantation of a diffractive-type MIOL.
Methods For an explanation of the photic phenomena, a geometrical construction of the incident rays through the nodal points is used. The ray passes through the first nodal point, and the foveally observed distant object defines the nodal axis. The nodal axis is commonly denoted as the visual axis. The angle kappa (j) is the angle between the nodal (visual) axis and the pupillary axis. The pupillary axis is considered identical with the optical axis of the eye (Tunnacliffe 1993). It is assumed that the photic phenomena markedly increase if the intersection of the nodal axis and the MIOL moves from its central part to the first ring of the MIOL. The relevant border value of the angle kappa is referred to as critical angle kappa jc (Fig. 1). The critical value jc of the angle kappa can be calculated using the geometrical optical rules applied to a
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Fig. 1. The schema of the used optical model of the pseudophakic eye with an optical axial length AL and an effective position ELP of a thin MIOL with the centre C of the MIOL on the eye optical axis. R marks the border of the central part of the IOL of the diameter d. The points N and N’ represent the first and second nodal points of the pseudophakic optical system, F’ is the second focal point of this system. The critical angle kappa kc is marked.
suitable optical model of the pseudophakic eye. The optical model applied in this text is based on the standardized pseudophakic schematic eye (Holladay 1997, 1998, 2007) with a thin IOL (Fig. 1). The distances used are oriented according to Fig. 1 with the positive values in the incident light direction (i.e. from left to right) and negative values in the opposite direction. The MIOL is perfectly centred to the pupil centre. The model is represented by a positive optical corneal power K, an optical axial length AL, a thin MIOL effective optical power P for distance correction, an effective position ELP of the thin MIOL and by a refractive index n of the aqueous and vitreous. The ELP means a distance of the MIOL optical centre from the anterior corneal vertex. A zero postoperative refraction of the pseudophakic eye is considered. Under these conditions, the P is a dependent variable. It can be shown that the relation n n P¼ n ð1Þ AL ELP K ELP holds for this eye optical model (Holladay 1997, 1998). The central part of the MIOL with the constant power has the diameter d.
The nodal visual axis corresponds to the ray passing from the observed object to the fovea through the nodal points. Moreover, it intersects the thin MIOL in the border R of its central part and the first ring for the critical angle kappa (see Fig. 1). According to the geometrical construction in Fig. 1 and to the rectangular triangle RCN’, the size |jc| of the jc can be computed by the relation jjc j ¼ arctan
d=2 AL ELP þ F0 N0
ð2Þ
F0 and N 0 are the second focal point and the second nodal point of the pseudophakic eye optical model, and C is the centre of the MIOL. It can be shown (Tunnacliffe 1993) that F0 N0 ¼ f ¼
1 F
ð3Þ
The quantity f is the equivalent first focal length of this optical system, and F is its equivalent optical power. The F can be obtained using a common equation for the equivalent lens power in the form F¼KþP
ELP KP n
ð4Þ
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The formula (2) can be rewritten using (3) and (4) to the form jjc j ¼ arctan
d=2 AL ELP
1 KþPELP n KP
ð5Þ The term (5) along with (1) describe the influence of the pseudophakic eye model parameters K, ELP, AL and n on the critical value jc for the given diameter d of the central MIOL part. For the calculation of the concrete value of critical angle kappa (jc), the standard parameters of the considered pseudophakic eye model (Holladay 1997, 1998, 2007) K = 43.27 D, ELP = 5.25 mm, AL = 23.65 mm and n = 1.336 were applied to the relation (5). The MIOL was modelled according to the Tecnis ZMB00 (addition +4.0 D) and AcrySof ReSTOR SV2STO (addition + 2.5 D), SB6AD1 (addition + 3.0 D) and SN6AD3 (addition + 4.0 D) MIOLs of the parameters d = 1.0 mm, d = 0.938 mm, d = 0.86 mm and d = 0.74 mm, respectively. All the data relating to these MIOLs were obtained from the manufacturers. Next, the influence of quantities K, ELP and AL on the jc was analysed in the case of the abovementioned MIOL parameters by the relation (5). In particular, the dependence of the jc on one of the parameters was studied for standardized values of the remaining parameters.
Results The values of the critical angle kappa were jc 15.48° for the Tecnis ZMB00 (d = 1.0 mm), jc 14.56° for the AcrySof ReSTOR SV2STO (d = 0.938 mm), jc 13.39° for the AcrySof ReSTOR SB6AD1 (d = 0.86) and jc 11.58° for the AcrySof ReSTOR SB6AD3 (d = 0.74). The results of the influence of quantities K, ELP and AL on the jc in the cases of these four multifocal lenses are presented in Figs 2–4 in the graphical form. The increase in ELP and K caused an increase in jc under the given conditions (Figs 2 and 3). On the contrary, the increase in AL led to lower values of jc (Fig. 4). The impact of the MIOL characteristics is evident, too – the higher d, the higher jc.
Fig. 2. Dependence of the critical angle kappa |kc| on the effective lens position ELP in the pseudophakic eye model for the standardized values K = 43.27 D and AL = 23.65 mm and for four values of d. The standardized value ELP = 5.25 mm is represented by the vertical dashed line.
Fig. 3. Dependence of the critical angle kappa |kc| on the optical corneal power K in the pseudophakic eye model for the standardized values ELP = 5.25 mm and AL = 23.65 mm and for four values of d. The standardized value K = 43.27 D is represented by the vertical dashed line.
Fig. 4. Dependence of the critical angle kappa |kc| on the optical axial length AL in the pseudophakic eye model for the standardized values K = 43.27 D and ELP = 5.25 mm and for four values of d. The standardized value of AL = 23.65 mm is represented by the vertical dashed line.
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Discussion Angle kappa is defined as the angle between the visual axis (connects the point of fixation with the fovea) and the pupillary axis (a line through the centre of the pupil perpendicular to the cornea). A positive angle kappa is associated with an out-turning of the eye (the pupillary axis is temporal relative to the visual axis), while a negative angle kappa is an inward turning of the eye (the pupillary axis is nasal relative to the visual axis). Thus, when an eye fixates on a light source, the reflection on the cornea (Purkinje image) will not be centred but will be located nasal (positive angle kappa) or temporal (negative angle kappa) to the pupillary centre. According to the published literature, a positive kappa angle varies from 3.5 to 6° in emmetropic eyes and from 6.0 to 9.0° in hyperopic eyes. In myopic eyes, the angle kappa is smaller, averaging approximately 2.0°, and can even be negative (Von Noorden & Campos 2002). Basmak et al. (2007a,b) also reported the angle kappa to be higher in hyperopes than in emmetropes and myopes. Hashemi et al. (2010) found mean angle kappa values of 5.52 1.19° in hyperopic eyes, 5.72 1.10° in emmetropic eyes and 5.13 1.5° in myopic eyes. With the development of new types of intra-ocular lenses, angle kappa is coming to the forefront of interest of cataract surgeons. Kottler et al. (2004) reported a hyperopic patient with a large angle kappa in whom the residual refractive error after toric phakic intraocular lens implantation was improved by displacement of the lens according to the visual axis. De Vries et al. (2011) suggested that three major causes of discomfort after MIOL implantation (ReSTOR, Alcon Laboratories; Rezoom, Abbott Medical Optics; Tecnis, Abbott Medical, Optics) were residual refractive error, posterior capsule opacification and large pupil size. However, a large angle kappa and MIOL decentration from the visual axis should also be considered. Soda & Yaguchi (2012) evaluated the influence of horizontal decentration on optical performance in different MIOLs using an eye model. He found that clinically relevant effects are not to be expected up to a decentration of 0.75 mm. But a possible influence of angle kappa on these
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results was not taken into account. We confirmed in our previous study (Karhanova´ et al. 2013) that temporal decentration of the ReSTOR multifocal IOL (in cases of a positive angle kappa) was associated with the greatest risk of photic phenomena. By contrast, nasal decentration (in cases of a positive angle kappa) did not cause pronounced photic phenomena. Prakash et al. (2011) evaluated the role of angle kappa in the occurrence of photic phenomena after MIOL implantation (Rezoom). They reported that patient complaints about glare and halo showed positive correlation with the preoperative values of angle kappa. On the other hand, they found that many patients with a high angle kappa were asymptomatic. The assumed cause of pronounced photic phenomena after implantation of diffractive-design MIOLs in patients with a higher angle kappa is that the fovea centric ray would pass closer to the edge of the rings and not through the central area of the MIOL (Fig. 5A and B). To date, several MIOLs of this design have been available and commonly used in practice. For the purpose of our study, we evaluated the AcrySof ReSTOR (Alcon Laboratories, Inc., Fort Worth, Texas) and the Tecnis (Abbot Illinois, USA) MIOLs. The AcrySof ReSTOR is designed to provide quality near and distance vision by combining apodized diffractive and refractive technologies. The centre of the lens consists of apodized diffractive optic that focuses light for near through distance vision. Apodization is the gradual tapering of diffractive steps from the centre to the outside edge of the lens. It helps to create a smooth transition of the light between distant, intermediate and near focal points. The refractive zone surrounds the apodized diffractive region. To date, three types of the AcrySof ReSTOR IOL have been introduced in the market – AcrySof ReSTOR SN6AD3 (addition + 4.0 D), SB6AD1 (addition + 3.0 D) and SV2STO (addition + 2.5 D). They vary not only in add power, but also in central zone diameter and in the number of diffractive rings. The Tecnis MIOL is a full diffractive optic. The diffraction pattern of this lens is on the posterior surface of the lens (as compared to the AcrySof ReSTOR lens on the anterior surface of the lens), and the lens has the
aspheric prolate technology. We evaluated these four lenses in our study because of their different central diameters (d). The mentioned differences in MIOL design did not influence our analysis because the MIOL was replaced with a thin lens in our model and was represented only by its equivalent optical power P and central zone diameter d. By comparing these four MIOLs on the pseudophakic eye model, we confirmed that the higher the central zone diameter, the higher must be the angle kappa to reach the edge of the first ring of the IOL. In all four types of MIOLs, the critical angle kappa (reaching the edge of the ring) calculated was higher than that found in normal population. On this theoretical model, we also confirmed the influence of K, AL and ELP on the critical angle kappa. For better illustration, we calculated the border values of parameters K, AL and ELP corresponding to the critical angle kappa jc = 7° (which can be found in normal population) for all four types of the MIOL as a model case (Table 1). Two of the eye model parameters always have standard values and one of them was calculated. The values of K and AL for this particular model case are out of normal range, but the border values of ELP achieve a realistic size. According to these results, we suggest that the most important biometric value that can influence the possible occurrence of photic phenomena after MIOL implantation in connection with a higher angle kappa be ELP. When the interdependence of ELP and preoperative anterior chamber depth are taken into account (Olsen et al. 1990; Holladay 1993; Olsen 2006), it can be established that patients with preoperative shallow anterior chamber depth are at a higher risk. In our study, we presumed the MIOL to be perfectly centred to the pupil centre. In the case of a decentred MIOL, the considered border point R (see Fig. 1) shifts according to the direction and size of the decentration. Thus, the term d/2 in the equation (2) as well as (5) must be corrected – it must be increased for the decentration towards the visual axis or decreased for the opposite direction. In the simplest approximation, the term d/2 can be replaced by the term d/2 + D or d/2 – D, where D represents the decentration size (in length units). The resultant
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(A)
(B) Fig. 5. Schematic ray diagram showing that in eyes with a small angle kappa, a fovea centric ray may pass through the central area of the MIOL (A), while in those with a higher angle kappa, a fovea centric ray may pass close to the edge of the ring, thus causing photic phenomena (B).
Table 1. The results of values of optical corneal power K, effective position ELP of the thin IOL and optical axial length AL corresponding to the critical angle kappa jc = 7° for four different diameters d of the central part of the MIOL and for the refractive index n = 1.336. Two of the eye model parameters always have standard values, and one is changed in each combination. Only the values of ELP achieve a realistic size. d [mm]
K [D] (ELP = 5.25 mm, AL = 23.65 mm)
ELP [mm] (K = 43.27 D, AL = 23.65 mm)
AL [mm] (K = 43.27 D, ELP = 5.25 mm)
0.74 0.86 0.938 1.0
26.70 19.22 14.10 9.86
3.66 3.04 2.63 2.31
35.95 40.93 44.17 46.74
curves presented in Figs 2–4 shift upwards or downwards in this case. It means that the decentration towards the visual axis causes an increase in the jc and the risk of photic phenomena evoked by a large angle kappa should be reduced. In the practice, different methods for compensating for a large angle kappa (decentration of the MIOL towards the visual axis) have been described (Melki & HarissiDagher 2011). However, due to mem-
ory of the haptics, contraction of the capsule, and IOL rotation, it is uncertain whether the lens would stay in the decentred position (Prakash et al. 2011). Conversely, the opposite decentration causes a decrease of the jc and can heighten the risk of photic phenomena. These results are in accordance with the study by Karhanov a et al. (2013). Moreover, as mentioned above, a shallow preoperative anterior chamber leads to a lower ELP (Olsen
et al. 1990; Holladay 1993; Olsen 2006) and a lower jc (see Fig. 2). Thus, the effect of the opposite decentration on the risk of photic phenomena should be taken into account particularly for shallow preoperative anterior chambers. This study also has some limitations. The optical model of pseudophakic eye used simplifies the situation in a real eye. In a real eye, all three observed parameters (K, AL and ELP) vary. Also, the ELP is influenced by several factors, not only by preoperative axial length, anterior chamber depth and curvature of the cornea, but also by lens thickness and refraction (Olsen et al. 1990). The principal limitation is the simplifying presumption that photic phenomena are induced by the interaction of the central ray (corresponding to the nodal axis in our model) with the first MIOL ring. This approach, also considered in another study (Prakash et al. 2011), enables to derive a relation between the critical angle kappa and other parameters of the eye and MIOL based on geometrical optics and the thin MIOL approximation (see above), but does not take into account other optical effects caused by diffraction, etc. Thus, this approach does not allow a detailed analysis of the influence of the angle kappa on the photic phenomena, and the real values of the critical angle kappa can differ from our results based on simplified computations. Nevertheless, according to the aim of this study, the relationships obtained show which parameters should be considered for angle kappa evaluation with regard to the risk of photic phenomena and how their values can influence this risk. Despite these limitations, we think that the results of our study, especially the dependence on biometrical parameters of the eye, can help to find a possible explanation for the contradiction why some patients with a higher angle kappa are asymptomatic while others complain of disturbing photic phenomena. Further studies on real eyes will be required to confirm this hypothesis. In conclusion, the perception of photic phenomena is multifactorial. Our study suggests that angle kappa may also play a role. We confirmed the dependence of critical angle kappa on the central zone diameter of the multifocal IOL and on biometric parameters
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of the eye, especially on the effective lens position. According to these results, it can be concluded that especially shallow anterior chamber depth in connection with a higher angle kappa could be an important risk factor for pronounced photic phenomena after multifocal IOL implantation. We incorporated this conclusion in our daily practice. We recommend to evaluate the angle kappa in all patients with preoperative shallow anterior chamber depth before planned implantation of a diffractive-design MIOL. In cases when a larger angle kappa is confirmed, we prefer to implant another type of presbyopia-correcting IOLs. By contrast, in patients with normal or deeper anterior chamber, we do not require angle kappa evaluation before diffractive-design MIOL implantation.
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Received on February 14th, 2014. Accepted on July 3rd, 2014. Correspondence Martin Sˇı´ n, MD, PhD, FEBO Department of Ophthalmology University Hospital Olomouc I. P. Pavlova 6 77900 Olomouc, Czech Republic Tel: +420 588 444 202 Fax: +420 588 422 530 Email: [email protected] This research was supported by Grant No. PrF_2013_021 from the Faculty of Science of Palacky University, Olomouc, Czech Republic. The authors have no financial interest in any product mentioned in the text and no potential conflict of interest in this article.
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