Relation between the mesopic pupil size and diffractive zone of multifocal IOL

What should be the maximum size of the diffractive zone of a multifocal IOL that provide patients with good distance vision in mesopic conditions and yet help patients be comfortable to read? How could I arrive at a cut off value of the pupil size, based on the particular diffractive IOL I use?

These questions have often been raised especially in the context of diffractive multifocal IOL. But there is no easy answer to these questions. In this article, I will try to provide insights that may help to arrive towards some logical conclusion. In my view, both the questions above are interrelated. The size of the diffractive zone is constant on the IOL, but the pupil size of patients differs from one to the other as well as for varying light conditions in an individual. Thus finding the cut off value for mesopic pupil size may be important for clinicians to ensure that patients have a good distance vision even in low light. The cut off value may however differ from practice to practice, based on the device used to measure the pupil size, the light conditions in the clinic, etc. For example, Gedik and co-authors saw a large difference in measured mesopic pupil size value between the Nidek OPD Scan II and the Lenstar LS 900 II. Nevertheless, a broad idea may help in patient selection process.

Entrance Pupil: The pupil that you measure with optical biometry, is not its actual size, as the measurement is affected by the corneal magnification, whose overall effect is like that of a convex lens. Thus, we do not measure the physical or real pupil size at the iris plane, but the image of the pupil on the object side, thus measuring larger than the real pupil due to the corneal magnification. This is the entrance pupil, which is the image of the pupil at a point that is anterior to the iris. The entrance pupil is located approximately 3.0 mm away from the corneal vertex (1). On an average eye, with a corneal power of 44 diopter, ACD of 4.0 mm, the entrance pupil measured is almost 14% bigger than the actual pupil size (2). Jean-Philippe Colliac in his chapter on Gaussian Optics(3) provides a mathematical relation between the entrance pupil and actual pupil size. The values of actual pupil measured should be multiplied by a factor of 1.13 to arrive at the entrance pupil size. For a real pupil with a 2 mm diameter during photopic vision, the entrance pupil diameter is therefore 2* 1.13 = 2.26 mm. However, since the pupil measured in a clinic is the entrance pupil, therefore a measured value of 2.26 mm must be divided by a factor of 1.13 to arrive at the actual pupil size.

Exit Pupil: Like the entrance pupil, the exit pupil is the size of the aperture (pupil) as seen from the image side. It is the beam of light that will pass through the actual pupil and fall on the image side and on the IOL plane. Therefore, the size of the aperture or pupil that is seen from the image plane is the exit pupil. In the Gullstrand eye the position of the exit pupil from the corneal vertex is 3.664 mm, while the position of the entrance pupil from the corneal vertex is 3.045 mm.

To arrive at the size of the exit pupil, the diameter of the entrance pupil is to be multiplied by a factor of 0.92. Thus, if the entrance pupil size is 3.4 mm, the exit pupil is 3.4* 0.92= 3.1 mm. For the same entrance pupil, the actual pupil size will be 3.40/1.13 = 3.0 mm (as said before).

The exit pupil is important because, ultimately, the size of the aperture here will determine what portion of light will pass through the diffractive multifocal IOL to form the image on the retina. Thus, with the above example, a patient with 3.40 mm of mesopic pupil size at the entrance pupil position, will have only 3.12 mm of the IOL exposed that will contribute to vision.

If this relationship is well understood, let us now focus on the average pupil diameter for cataract patients in mesopic condition. The average bilateral pupil dilation in Indian patients was 3.92 in mesopic conditions (4). The median mesopic pupil size in a large cohort of 18335 eyes in Germany was found to be 4.1 mm (5). Wang and co-authors in a study on 716 patients of mainly Caucasian patients in USA found the average mesopic pupil size as 5.68 mm between all age groups. However they reported a reduced mean mesopic pupil size of 4.67 mm for patients above 65 years of age (8). It is widely acknowledged that pupil size reduces after cataract surgery. Camelin and coauthors reported a 10-13% average miosis after cataract surgery (6).

Considering all the above, if we assume a preoperative entrance mesopic pupil size of 4.0 mm, with a 10 percent miosis of pupil size post cataract surgery, thus bringing the size of actual pupil to 3.60 mm, the post operative mesopic exit pupil will amount to a size of 3.31 mm (3.60*.92). This is the effective size of all light passing through the physical pupil after surgery and being refracted or diffracted by the IOL and contributing to form the image on the retina. Thus, any light that falls outside the 4.0 mm of preoperative mesopic entrance pupil will be blocked by the iris postoperatively, and will not reach to form an image on the retina. Therefore, for patients to read even in a mesopic and low light situation, the minimum diffractive zone of any IOL will have to be 3.31 mm considering an entrance pupil of 4.0 mm.

For a patient with a larger than 4.0 mm of postoperative entrance pupil        (the pupil size you measure post-surgery) and considering a IOL diffractive zone of 3.2 mm, the outer refractive zone will be exposed for the patient that would contribute to distance vision. On the other hand, patients who want to read with a  postoperative mesopic entrance pupil of 4.0 mm may benefit from a diffractive IOL that has a larger diffractive zone beyond 3.68 mm. The below table compares the preoperative entrance pupil with the physical or real pupil and exit pupil.

Relationship between Preoperative measured entrance pupil, real pupil, and exit pupil and the exposure of a imaginary IOL with a diffractive zone of 3.5 mm. quickgude.org

Umberto Camellin and co-authors(6) report a 10 to 14 percent reduction in pupil size post surgery. Therefore, for a preoperative mesopic entrance pupil size, consider the following:

Relationship between entrance and exit pupil considering a 10% miosis post cataract surgery with the size of the diffractive zone being 3.2 mm. quickguide.org

Thus, the minimum postoperative entrance pupil size for a patient to benefit from the outer refractive area of a diffractive IOL with a diffractive zone of 3.2 mm and with a pupil miosis of 10 percent post cataract surgery would be 3.60 mm, corresponding to a preoperative mesopic pupil size of 4.0 mm.

The objective of this article is to throw some light on the relationship between the real pupil, the commonly measured preoperative entrance pupil and the exit pupil, and how this is related to good quality of vision in mesopic condition with a limited diffractive zone of an IOL. More than the numbers discussed, what is important is to understand the concept and identify patients who may not be candidates for a diffractive IOL considering their preoperative entrance pupil size. Further inference may be made, based on the type of diffractive IOL being used in the clinic, the size of the diffractive ring, and the diameter of the entrance pupil being measured.

Reference:

1.        Zaher Atta Naeem, Human Eye Response to Pupil Size Variation Programmatically, Page No.: 3350-3353 Volume: 15, Issue 18, 2020 ISSN: 1816-949x Journal of Engineering and Applied Sciences

2.        Kenn A. Freedman, MD, PhD, Sandra M. Brown, MD, Steven M. Mathews, OD, PhD, Rockefeller S.L. Young, PhD, Pupil size and the ablation zone in laser refractive surgery: Considerations based on geometric optics, J Cataract Refract Surg 2003; 29:1924–1931

3.        Gaussian Optics, Basic Optics, Chapter 3, Page 83 to 101, Essentials in Ophthalmology

4.        Paryani, Mukesh J; Kharbanda, Varun; Kummelil, Mathew Kurian; Wadia, Kareeshma; Darak, Ambarish B, Pupillodynamics and corneal spherical aberrations in a set of Indian cataract patients and its implications for aberrometric customisation of intraocular lenses  Indian Journal of Ophthalmology 68(12):p 3012-3015, December 2020. | DOI: 10.4103/ijo.IJO_218_20

5.        J Ophthalmol. 2022 Sep 9;2022:9520512. doi: 10.1155/2022/9520512 Distribution of Pupil Size and Associated Factors: Results from the Population-Based Gutenberg Health Study

6.        Umberto Camellin, Massimo Camellin, Marcello Prantera, Roberta Di Pietro, Francesca Ponzetto, Pasquale Aragona Estimation of pupil size at iris plane and its magnification after cataract surgery, Indian J Ophthalmol. 2024 Aug 14;72(Suppl 5):S831–S837. doi: 10.4103/IJO.IJO_544_24

7. Sansal Gedik, MD, Bengu E. Koktekir, MD, Berker Bakbak, MD, Saban Gonul, MD. Comparison of pupil Brief Communication diameter measurement with Lenstar LS 900 and OPD Scan II. Not interchangeable devices, ww.smj.org.sa Saudi Med J 2012; Vol. 33 (11) 1239

8. Qiancheng Wang, Isabella M Stoakes, Majid Moshirfar, Devon H Harvey, Phillip C Hoopes, Assessment of Pupil Size and Angle Kappa in Refractive Surgery: A Population-Based Epidemiological Study in Predominantly American Caucasians, Cureus. 2023 Aug 23;15(8):e43998. doi: 10.7759/cureus.43998