A Brief explanation of modern IOL power calculation formulas
- Subhabrata Bhattacharya
- Sep 4
- 10 min read
Updated: Sep 5
This article will give you an idea of the modern IOL calculation formulas like Barrett Universal, Holladay II, EVO, Kane, etc. to give you an understanding of how these formulas work, calculates the Effective Lens Position (ELP) of the Intra Ocular Lens (IOL) and brings in an improvement over older third generation formulas.
To begin with, if you ask that what is the difference between the older generation IOL calculation formulas like SRK T or Holladay I, and the current generation modern formulas, the first thing that comes to mind is the difference of IOL power calculation by thin and thick optics.
What is thin and thick optics formula? This is explained in detail in the article, Gaussian optics, Gullstrand eye, & Biometry ( https://www.quickguide.org/post/all-about-gaussian-optics-gullstrand-eye-theoretical-and-ray-tracing-formula ). Basically, a thin lens is such that its thickness is so negligible that all refraction is considered to happen only at one plane. However, no lens, be it IOL or any other, will have some finite thickness. A thick lens formula considers the lens optic to have separate pairs of refracting plane - one anterior and the other posterior refracting plane.
The first principal plane is where light rays appear to refract as they enter the lens or system from the object side.
The second principal plane is where rays appear to emerge after they have refracted through the system and exit towards the image side.
Older two variable formulas like the Holladay I, SRK T, or the Hoffer Q have calculated the IOL power and ELP of the IOL based on thin lens optics. The new generation formulas like the Barrett, EVO or Kane are however based on the thick optics approximation. In such formulas, both IOL power and ELP are based on the two refracting planes.
Here you can access a calculator that helps you understand IOL power based on thick lens formula. https://sheet.zoho.com/sheet/open/oxim98090819123a94bd99435f9a6bc62eed2?sheetid=0&range=F15
Let us know how these individual formulas are different from each other. Let us start with the modern thick lens IOL calculation formulas.
Barrett Universal II:
The Barrett is an unpublished formula. However, I have given a brief explanation of the formula in the below video:
https://www.youtube.com/watch?v=1JDDL1la0Gw ( click to link)
In brief, the Barrett Universal formula being based on thick lens formula, determines the principal planes of refraction through input variables like corneal power (K readings), axial length (AL), horizontal white to white (HWTW), anterior chamber depth (ACD). It uses Lens Factor (LF) to determine the final principal planes of refraction and thus the ELP of the IOL. The LF is the distance from the iris plane to the second principal plane of the IOL. The LF however is mostly influenced by the anatomical pre surgery ACD and the A constant of the IOL. For this a relationship between the A constant of IOL and the Lens Factor was derived.
Thus Barrett Universal formula is based on paraxial rays (rays that travel close to the optical axis of the lens) and is based on thick lens mathematical calculation.
The Barrett Universal formula is a theoretical formula that divides the entire eye globe into two spheres, the anterior and posterior spheres. The interaction of the two spheres is based on the patient data you input (AL, K, LT ,etc.) which would determine the position of the ciliary root, which in turn will determine the lens position through the Lens Factor or LF.
The Barrett Toric Calculator provides an option to enter measured posterior cornea values. If you have values of posterior cornea then you may select the appropriate biometry/topography device from the drop down menu and input only posterior corneal values (see image1). For IOL Master 700 TK, only PK1 and PK2 values to be input. If you are working for post lasik patients, then Barrett True K should be used for determining IOL power. In this case also, you may enter the measured posterior cornea power in the same way.
Emmetropia Verifying Optical (EVO) formula
The brain behind this formula is Dr Tun Kuan Yeo, a doctor based out of Singapore. When the formula was conceived in 2015, a lot of attention was being given to posterior corneal astigmatism (PCA), and Dr Douglas Koch and his team's work that showed that the risk of not considering the PCA was under correcting against-the-rule astigmatism or over correcting with-the-rule astigmatism. While Douglas Koch's findings published in 2011 came at a time when not many devices measured PCA, yet there was the promise that biometry and IOL power prediction would take a leapfrog with a IOL calculation formula that would take measured PCA into account once such measurement was available.
The EVO formula was launched in 2016 that took into account axial length, corneal power, anterior chamber depth, lens thickness, horizontal white to white. In 2019 the EVO next version was launched that provided post Lasik IOL power calculation. In the advanced options, notice you can input the measured posterior corneal values and choose from the drop down menu the device used to measure. Do not enter IOL Master TK values in place of measured posterior cornea but only the posterior corneal values from the IOL Master 700. In the 2019 version, you can enter the central corneal thickness (CCT) values to help determine the ELP of the IOL more precisely.
Like the Barrett, EVO is a thick lens formula based on Gaussian optics (refer to my article Gaussian optics, Gullstrand eye, & Biometry ( https://www.quickguide.org/post/all-about-gaussian-optics-gullstrand-eye-theoretical-and-ray-tracing-formula ) for more details on Gaussian optics. As indicated in the article, Gaussian optics is based on paraxial rays only, and it does not take into account the spherical aberration associated with marginal rays. Unlike Olsen formula, both EVO and Barrett are theoretical paraxial ray formula.
In Cooke Modified Axial Length or CMAL ( available at https://www.quickguide.org/post/cooke-modified-axial-length-cmal ) I had provided an idea how CMAL uses sum of segments to convert axial length with group refractive index to an axial length based on actual refractive index of each of the mediums of eye. The CMAL axial length is the distance from the cornea to the retinal pigment epithelium (RPE). The concept of sum of segment based axial length (example Argos) as opposed to group refractive index based axial length ( IOL Master or Lenstar) is explained in the article Optical Biometry- Myth & Science ( https://www.quickguide.org/post/optical-biometry-myth-science ).
The EVO formula utilizes the CMAL approach in converting the axial length from group refractive index to an axial length based on sum of segments(1). Therefore, the EVO formula considers axial length from the cornea to the RPE based on the sum of segments approach.
The anterior corneal power together with the central corneal thickness and the Gullstrand anterior posterior cornea ratio of 0.883 helps the EVO formula to derive the posterior corneal power. Where a central corneal thickness value is not available, a default value of 540 micron is taken into account.
The EVO formula being a thick lens formula uses the IOL optic configuration to locate the first and second principal plane of refraction. These principal planes of refraction are important to understand the location of the IOL or ELP post surgery. Therefore, you should select the IOL from the drop down menu. If you cannot find the IOL that you are implanting from the drop down menu, like the HOYA IOL, Vivinex, you may use the standard option that uses a biconvex optic configuration with an anterior to posterior ratio of the IOL as 1:1. In reality however, most IOLs are not a perfect biconvex IOL. Therefore, each lens manufacturer should work with such authors of the formula, to study the optic configuration of their IOL and include in the formula. To understand more of this subject, you should visit my article https://www.quickguide.org/post/constant-thick-lens ( Why present day IOL box A constant based on thin optics concept needs to be reworked to improve IOL power prediction with thick lens formulae )
Where does the word emmetropization come from in the formula Emmetropia Verifying Optical (EVO) formula ? Emmetropization is the natural developmental process where the eye adjusts its growth to align the focal plane with the retina, achieving clear vision over time.
The cornea may be the main instrument for the process of emmetropization. Notice, the shape of cornea is relatively constant since birth, whereas the axial length grows over more than first decade of birth. The EVO formula is based on a set of algorithm that determines what should be the axial length and lens position based on corneal power for the person to have the rays of light fall on the fovea. Patients are however often myopic or hyperopic, and the EVO formula compensates if the axial length differs from the emmetropic or ideal axial length for a given corneal power.
Kane Formula:
The Kane formula is not based on the thick lens formula. While the Kane formula utilizes theoretical optics, it also incorporates regression and artificial intelligence (AI) with large datasets to optimize its predictions, incorporating elements of both theoretical optics and big data. It is a hybrid method that combines thin lens formula features with advanced statistical and AI components, making it a new generation formula.
it is a hybrid formula that incorporates a combination of principles:
Theoretical optics: The formula uses optical principles to model the eye.
Regression analysis: This technique uses a large dataset of patient outcomes to find patterns and refine predictions.
Artificial intelligence (AI): The formula uses AI components to further optimize its accuracy.
It has also introduced IOL calculation for Keratoconus patients. In Keratoconus patients, the anterior to posterior ratio of cornea (A/P ratio) is not the same. The normal A/P ratio is around 82%, which is much lower in case of keratoconus patients. Thus the common K index (corneal refractive index or keratometry index) of 1.3375 used in most keratometry may not be perfect. The use of a standard K index in keratoconus patients can lead to an overestimation of corneal power, and an underestimation of IOL power, thus leading to hyperopic outcomes.
The Kane keratoconus formula aims to reduce the influence of corneal power on effective lens position prediction. This formula is available at www.iolformula.com and was developed by theoretically modifying the original Kane formula. The Kane keratoconus formula aims to provide a more appropriate corneal power measurement and reduce the influence of corneal power on ELP prediction.
Kane Keratoconus Formula - Key points to remember
Do not input the total cornea values in Kane Keratoconus formula. Only input the anterior corneal values as the Kane formula theoretically derives the net corneal power from the anterior corneal values for a keratoconus patient.
The formula minimizes the effect of corneal power on ELP prediction to enable more accurate IOL power calculation.
The recommendations by Kane are to keep the target refraction unchanged for corneas with the keratometry up to 48.00 D, to aim for mild myopic refraction of −0.50 to −1.00 D in eyes with average corneal power between 48.00 D and 59.00 D and to aim for −1.50 to −2.50 D in eyes with keratometry greater than 59.00 D(2).
Olsen formula:
Gaussian optics is limited by the fact that it takes in account only the paraxial rays of light and does not take into account marginal rays of light. However, we know in the eye, spherical aberration plays an important role and therefore paraxial ray- based lens calculation has a room for improvement. Thus, the retinal image cannot be well described by rays close to the optical axis alone.
The Olsen (PhacoOptics®) as well as OKULIX Ray-Tracing-Calculation for the Pseudophakic Eye (Panopsis GmbH, Mainz, Germany) are ray tracing formula that takes in account both paraxial rays of light as well as marginal rays of light entering the eye. The advantage of ray tracing is that spherical aberration of cornea is taken in account. This may be especially useful in Lasik patients. In the post-LASIK case the front surface of the cornea is abnormal and it is not possible to apply standard models for the corneal optics. If you have more detailed information on the corneal asphericity (corneal asphericity is described in the article https://www.quickguide.org/post/spherical-aberration-cause-effect-of-undesired-higher-order-aberration) as well as front and back curvature of the cornea, ray tracing formula like PhacoOptics (Olsen) or OKULIX® can use these values directly in the calculations for better refractive outcome.
Thus ray tracing is based on Snell’s law of refraction :
n1 sin(i) = n2 sin(u)
where i is the angle of incident ray on the surface of the lens, u is the refracted angle, n1 is the refractive index of the first medium and n2 is the refractive index of the second medium. To get the full advantage of ray tracing formula it would be important to enter the full details of the eye and the lens. These are the radius of curvature as well as asphericity of the anterior and posterior corneal surfaces, IOL thickness, refractive index of the IOL, etc.
Because of the ray tracing, the physical data of the IOL need to be stated in more detail than in most formulas. The IOL constants are:
1. Refractive index of IOL
2. Anterior and posterior radius of curvature of an average-powered IOL
3. Thickness of an average-powered IOL
4. Wavefront Z(4,0) correction for spherical aberration
5. ACD constant (average value in representative population)
The advantage of ray tracing formulas is that it accounts for not only paraxial rays of light per Gaussian optics but also accounts for each marginal ray of light. Preussner (JCRS 2002) et al states that in the pseudophakic eye, difference between paraxial rays calculated with Gaussian thick lens formula and off-axis rays of light can be as much as 3.0 diopter in a worst case scenario. Using ray tracing, Olsen found that standard keratometry using Keratometry index of 1.3375 measures the corneal power as one diopter higher than when one measures with true indices of cornea with ray tracing methods. However, the exact refractive indices of cornea can not be used in any traditional IOL calculation formula, as most traditional IOL calculation formula are based on an assumed K index of 1.3375.
The ray tracing is not the only feature of the Olsen formula. It brings in an unique concept of C-constant to predict the Effective Lens Position ( ELP) of the IOL. The C constant can be thought of as a ratio by which the empty capsular bag will encapsulate and fixate an IOL following in-the-bag implantation. It is based on the observation that after standardized lens surgery and in-the-bag implantation, the IOL tends to locate itself in a defined manner that is predictable according to the formula
IOLc = ACDpre + C x LTpre
where IOLc is the center of the IOL, ACDpre is the preoperative anterior chamber depth (ACD) (including corneal thickness), LTpre is the preoperative thickness of the crystalline lens, and C is a constant related to the IOL type.
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References:
Essentials in Ophthalmology Essentials in Ophthalmology
ISBN 978-3-031-50665-9 ISBN 978-3-031-50666-6 (eBook)
Kane JX, Connell B, Yip H, McAlister JC, Beckingsale P, Snibson GR, Chan E. Accuracy of intraocular lens power formulas modified for patients with keratoconus. Ophthalmology 2020;127:1037–1042
