Introduction

Sir Harold Ridley implanted the first intraocular lens (IOL) in 1949.[1] Postoperatively the patient had a refractive error of -18 dioptre sphere and -6.00 dioptre cylinder at 120 degrees. Later Binkhorst introduced an 18.0 D pre-pupillary lens. It left the patient with the same refractive error he had before the cataract surgery. Thus it was realized that merely an implant is insufficient, and accurate IOL power calculation is necessary. It is one of the most critical factors for the refractive outcome of cataract surgery.[2] 

In most patients, emmetropia is the targeted post-operative refraction, while some patients are targeted for residual myopia.[3] To reach the targeted refraction, the selection of the IOL formula must be performed according to the anatomical and optical parameters of the eye. Axial length is an essential parameter in IOL power calculation. 1 mm of change in axial length can alter the IOL power by 2.5-3.0D. Corneal power is another important factor. The cornea accounts for two-thirds of the total optical power. A change in corneal power by 1 Dioptre alters the IOL power by 1D.[4]

Apart from the axial length and keratometry, other parameters may also be required, such as anterior chamber depth and the corneal white-to-white distance.[5]

Function

All patients need near-perfect visual outcomes. This necessitates a highly accurate calculation of IOL power. IOL formula calculation was first started in 1960. Fyodorov first devised a formula to predict the IOL power that would allow the refracted ray of light to fall on the retina.[6] 

The formula was based on three parameters: axial length (AL), corneal refractive power (K), and anterior chamber depth (ACD). This formula was used for anterior chamber IOLs. This formula stressed knowing where the IOL will rest after surgery. This position is known as the effective lens position (ELP). This is the only parameter that cannot be measured preoperatively. ELP is defined as the effective distance between the anterior surface of the cornea and the lens plane, assuming that the lens is infinitely thin.[7] 

This ELP is the main limiting factor for postoperative refractive predictability, as the axial length and corneal power are accurately measured.[8] Over these 30 years, improvements in IOL power calculations resulted from improved predictability of the ELP. The future generation formulae aim at accurate prediction of this ELP.[9][10][11] Over time, many formulae have evolved. These IOL formulae fall into two major categories: Empirically determined regression formulae and vergence formulae.

Regression formulae: They are based on a mathematical and statistical analysis of many adult postoperative results. These formulae do not take into account the optics of the eye.

Vergence formulae: They are based on Gaussian optics. There are six variables in this theoretic formula which are

• Net corneal power (K)
• Axial length (AL)
• IOL power (IOLP)
• Effective lens position (ELP)
• Desired refraction (D Post Rx)
• Vertex distance (V)

Issues of Concern

ELP cannot be measured, but it can be predicted. The IOL manufacturer predicts the form of the A-constant.[12] The A-constant is an empirical value and is specific to the design of the IOL. The A constants vary with the IOL model. It depends upon the lens shape, size, composition, and behavior in the previously implanted eye. The surgeons can also optimize the lens constant for minor differences in biometry machines, surgical techniques, and patient factors.[12] 

All these factors, when taken into account, can predict the accurate IOL power for the desired refraction for a specific eye. As these various vergence formulae use up to 6 biometry parameters, the accuracy of these formulae depends on accurate biometry. All the biometry measurements can now be obtained in a single biometry machine which simplifies the IOL calculation and selection. Furthermore, newer imaging modalities, such as swept-source optical coherence tomography, have improved the repeatability of biometry measurements.[13][14][15] 

Over time, regression-based derivations have been incorporated into each new generation of formulae to predict the refractive behavior and outcomes of IOLs in eyes with different anatomical dimensions.

Based on these variables, the IOL formulae can also be categorized as the following:

1) First-generation formula. 2) Second generation formula 3) Third generation formula 4) Fourth generation formula

First-generation

In 1967, Fyodorov developed his theoretical formula based on keratometry and axial length. Soon many authors devised their theoretical formula. In 1980 multiple papers were published on large IOL series. All authors found that axial length and keratometry were the most important parameters. Thus the SRK formula was devised, which was P= A - 2.5L - 0.9K.[16] P is the IOL power. A is the lens-specific constant. L is the axial length, and K is the corneal curvature. For the first time, this formula introduced the concept of lens-specific constant, considering the design and position of the IOL. This was the first regression formula.

Second-generationThe first-generation formulae were quite accurate in regular eyes. But it did not work in extremely long or short eyes. Thus there was a need to adjust the formula for the axial length to be accurately factored. The second generation regression formula, the SRK II, was developed by adding a C-value to the original SRK formula: P= A - 2.5L - 0.9K + C.[17] 

If the axial length is 10 to 20 mm, the C value is 3. If the axial length is 20 to 21 mm, the C value is 2.0. IF 21 to 22 mm, the C value is 1. For 22 to 24.5 mm, it is 0. If the axial length is more than 24.5, the C value is -0.5. Other formulae, such as Hoffer's adjustment of ACD and the modified Binkhorst Formula, used the measured axial length.[18][19]  These formulae, theoretical or regression, were termed the Second Generation formula.

Third-generation

The first generation of IOL formulae had a fixed constant for all axial lengths, such as the A constant in the SRK formula.[20] These formulae led to postoperative refractive errors. The second-generation formula modified this constant according to the axial length of the eyeball.[21][22] But still, it was far from perfect as it had a residual refractive error. Meanwhile, researchers were also studying the relationship between IOL power, axial length, and corneal curvature. Thus with numerous mathematical and statistical calculations, the third-generation formulae were derived. The SRK/T equation was devised, which optimized the ACD.[23] 

Holladay 1 formula divided the ACD into corneal thickness, the distance between the endothelium and iris, plus the distance between the iris and the lens. The last measurement was known as the surgeon factor, which varied according to the lens type. This factor required optimization.[10][20] 

Hoffer Q formula recommended a personalized ACD.[20] Compared to their predecessors, these formulae were quite accurate in IOL power calculations. The SRK/T formula is recommended for long eyeballs > 26 mm.[24][25][26][27][28] Hoffer Q is suitable for short eyes.[27][21] In the middle range, all formulae were more or less comparable.[25] Thus the third-generation formulae tried to mathematically correlate AL and ACD. 

Fourth-generation

The third-generation formulae were fair in the IOL power calculations. But still, they needed refinement. More studies were going on that incorporated more patient parameters to further decrease postoperative refractive errors. The Haigis formula introduced three A constants such as a0, a1, and a2. All three constants can be personalized to refine the IOL power.[29] The Holladay2 formula introduced seven variables in IOL power calculation. They were AL, keratometry, ACD, white-to-white measurement, lens thickness (LT), preoperative refraction, and age.[30][31][10] 

The Barrett formula was introduced, which was based on a model eye. It incorporated the final plane of the position of the IOL, which increased its accuracy.[9][27] It was quite accurate in all ranges of axial lengths. The SRK/T formula was updated to the T2 formula by doing a regression analysis of its postoperative outcomes. This led to a significant decrease in errors.[32] 

Newer technologies are evolving to refine these formulae further. It is difficult to calculate the exact IOL power in high myopes. A Wang-Koch (WK) adjustment has been suggested to some third- and fourth-generation formulae to optimize the calculation for AL >25 mm.[33] 

Apart from the vergence and regression-based formulae, newer techniques have evolved in the last few years for IOL power calculation with increased accuracy.

Ray tracing method: The Olsen formula is based on studying axial and paraxial light through the eye with a particular IOL.[34][35][36] It has a C constant, which is dependent on the position of IOL and preoperative ACD, and lens thickness. Here the C constant does not depend upon the axial length and corneal curvature. It depends upon the nature of the crystalline lens and anterior chamber dimension. This formula has the advantage that it needs less number of surgical cases to optimize the C constant.[35][11] Thus the surgeons can have exact results with fewer patients.

Artificial intelligence: The Hill-radial basis function (RBF) calculator combines artificial intelligence with regression analysis of a large postsurgical patient to calculate the IOL power.[37] The Kane formula combines artificial intelligence with the theoretical optics of the eye for IOL power calculation. The variables required are gender, AL, corneal power, ACD, and an A-constant.[38] 

Then there is Ladas formula, also known as the super formula.[39] It automatically chooses the most appropriate formula according to the axial length and corneal power of the patient. The formulae incorporated are SRK/T, Hoffer Q, Holladay 1, Holladay with WK adjustment, and the Haigis. Generally, if the AL is <21.49 mm, it applies the Hoffer Q formula; if the AL is >25 mm, Holladay 1 formula with Wang Koch adjustment is applied, and for other axial lengths, Holladay 1 is used. 

Optimization

In the SRK formula, P=A-(2.5xAL)-(0.9xK). A is the lens constant. Its value depends upon the lens design, its make, haptic angulation, surgeon, and surgery method. The A constant can vary between individual surgeons for a particular cataract surgery technique. The A constant can vary for different IOL and surgical methods for a particular surgeon. The manufacturer provides the value of A constant, but every surgeon should optimize this value according to his surgical technique and IOL used. This is known as the optimization of the lens constant. Optimization is the process of finding the specific value of a lens constant, which, when used for that particular IOL type, will result in exact IOL power calculations.

The SRK formula can also be expressed as A= P+(2.5xAL)+(0.9xK). To know the A constant, one must know the ideal IOL power of that patient. That will depend upon the stable postoperative refractive error. This value will tell us how much deviation there is from the actual IOL power. Suppose a patient has a postoperative refractive error of +2.0D, and the IOL power implanted was 20.0D. It would be incorrect to assume that the ideal IOL power would be 22.0D because the refractive error at the spectacle plane is not the same as that at the IOL plane. To calculate the ideal IOL power using spectacle plane refraction, a Refractive Factor (RF) is needed. The RF is a value that needs to be multiplied by the refractive error to give us an estimate of the error at the IOL plane. Modern estimates of this RF value are in the range of 1.3 to 1.8.[40] 

If one takes RF as 1.5, in this example, the ideal power, Power (ideal)= Power (implanted)+ Refractive error X RF. Power (ideal)= 20.0+ (2x1.5)=23.0D. For myopic errors, the minus sign of the error would result in a lower actual IOL power. This process of back-calculation of the A-constant has to be repeated for several cases involving the same IOL model and surgery type. In each case, the A-constant is likely to be different, all these values are then averaged, and the resultant value is the optimized A-constant. This can be used for prospective calculations in place of the A-constant provided by the manufacturer.   

There are two components to accurate IOL power calculation – precise biometry and accurate IOL power calculation formulae.

Biometry

Biometry is the process of determining the ideal intraocular lens power by measuring the corneal power and the axial length of the eye. Earlier ultrasound was used to measure the axial length. It required contact with the ocular surface. This applanation A-scan caused variable corneal compression and was prone to error.[41] 

In 1998 optical biometry was introduced, which used infrared light. It was a non-contact instrument, and the measurement did not alter the axial length; thus, it was quite accurate.[42] Therefore optical biometry has largely replaced ultrasound biometry. It is based on one of the following principles. 1. Partial coherence interferometry (PCI) 2. Optical low coherence reflectometry (OLCR) 3. Swept-source optical coherence tomography (SS-OCT).

PCI: This technology was developed in 1986 by Fercher and Roth. It utilizes infrared light, which is directed inside the eye. The different tissue planes reflect this light. Interferometric techniques are then applied to measure the axial length.[43] Pentacam AXL from Oculus, AL-Scan from Nidek, and IOL Master 500 from Carl Zeiss are based on this principle. OLCR:  It uses the principle of a Michealson interferometer. A superluminescent diode produces a low-coherence infrared light which is then split into double beams by a coupler. One beam is directed into the eye, and the other is projected to a scanning reference mirror. The various tissue planes then reflect this light. The emitted and reflected lights form an interference pattern detected by a detector and analyzed.[44] Lenstar (Haag-Streit), Aladdin (Topcon), and Galilei G6 (Zeimer) use this technology in their machines.

SSOCT: This technology uses a swift, sweeping laser as the light source. The interference pattern captured undergoes Fourier transformation.[45][46] The IOL Master 700 (Carl Zeiss) and Argos (Movu), and the Eyestar 900 (Haag-Streit) make use of this principle. The following will briefly discuss some common biometry machines.

Optical Biometers

IOL Master 500: This machine from Carl Zeiss uses an infrared laser of 780nm wavelength and is based on PCI technology. It is highly accurate, up to 0.02 mm.[47] It can measure axial length, keratometry, anterior chamber depth (ACD), and horizontal white-to-white (WTW) distance. It has incorporated the following formulae: SRK II, SRK-T, Haigis, Hoffer Q, Holladay-1, Haigis–L, and Holladay 2. The data can be exported to a computer-assisted surgery system, Callisto Eye, which can display an overlay in the microscope eyepiece during cataract surgery. However, it cannot accurately measure the axial length in dense cataracts and opaque corneas.[48]Nidek's AL-Scan: It uses PCI technology to measure axial length, ACD, WTW, pupil size, central corneal thickness (CCT), keratometry, and corneal topography. It also comes with an ultrasound pachymeter and A-scan.[49] All popular IOL calculation formulae are incorporated into the machine. 

Lenstar LS-900: This machine uses OLCR technology. A superluminescent diode produces an 820 nm low-coherent beam of light. It can measure lens thickness, axial length, ACD, keratometry, anterior corneal topography, WTW, and pupil diameter. The corneal topography is useful in planning toric IOL cases. All IOL calculation formulae are incorporated, including Barrett Suite, Hill-radial basis function (RBF), Masket, Modified Masket, and Shammas. It was one of the first devices to measure lens thickness (LT). 

IOL Master 700: This device is based on SS-OCT technology. It has a scan speed of 2000 scans per second. The inbuilt OCT scans the different ocular structures. The OCT image of the fovea allows the clinician to determine whether the fixation is central or not. It can measure both the anterior and posterior corneal curvature. It can take measurements in dense cataracts and opaque media. All the modern IOL power calculation formulae, including the Barret suite consisting of the Barret Universal 2, the Barrett True K, and the Barrett Toric, are available. It can also link with the Callisto eye system for toric IOL implantation.   

Tomey's OA 2000: This instrument uses a Placido disc-based topographer with an SS-OCT-based biometer. It measures keratometry, CCT, ACD, AL, LT, WTW, pupillometry, and corneal topography. All modern IOL power calculation formulae, including ones based on ray tracing, are available on board.

Eyestar 900 (Haag-Streit): It is an SS-OCT-based device. It can do elevation-based corneal topography, intraoperative aberrometry, and wavefront aberrometry during cataract surgery. This can make aphakic and pseudophakic refractive measurements. Real-time information on the toric IOL axis placement and position of limbal relaxing incisions can be taken by attaching it to the surgical microscope. Intraoperative aberrometry is useful in toric IOL, multifocal IOL, accommodative IOL, and post-refractive surgery cataract patients.

Pentacam-AXL: The Oculus Pentacam-AXL combines an elevation-based tomographer and a PCI-based optical biometer. A rotating Scheimpflug camera maps the corneal tomography, and PCI technology is used to determine the axial length. It also measures CCT and WTW. The advantage of Pentacam AXL is the ability to measure posterior corneal astigmatism, which is useful in toric IOL planning. It is also helpful in calculating IOL power in eyes with post-refractive surgery. This device can also perform wavefront analysis. It has all the popular IOL power calculation formulae in it.

Clinical Significance

Though much advancement has been made in IOL power calculations, there are certain situations where the power calculation becomes difficult. It is because of changing axial length, irregular corneal surface, or previous corneal surgeries. This article will discuss each scenario one by one.  

Aphakia

In aphakia, the double lens spikes of A-scan are replaced by a single spike of the anterior vitreous face and posterior capsule. The immersion method is preferred over contact biometry. Optical biometers have inbuilt modes for aphakia and are the most accurate method.

Pediatric Population

The long-term refractive outcomes among the pediatric pseudophakic population are hard to predict, and it is one of the biggest challenges in managing pediatric cataracts. Elongation of the eyeball and changing corneal curvature produce a tendency for the myopic shift.[50][51] Hence, during surgery, an under-correction is planned, and contact lenses or glasses do the residual refractive correction. The patients are uncooperative. Thus axial length measurement and keratometry should be done under general anesthesia. Minor measurement errors can cause a big shift in calculated IOL power.

The target IOL power should prevent amblyopia in the growing age and achieve emmetropia in adulthood.[52] Currently, all children above two years are advised for IOL implantation. IOL implantation in less than two years is controversial. The most significant concern at such an early age is to prevent amblyopia. The development of the eye necessitates initial under-correction to avoid myopic shifts in the future. The growth of the anterior segment is complete in two years hence the target IOL power aimed for is around 80% of the calculated power. Dahan proposed implantation of IOL, which is 20% less than the emmetropic IOL power for children <2 years of age and 10% less for children >2 years of age, to allow for myopic shift occurring during the emmetropization process.[53]

Enyedi proposed "the rule of 7". In this rule, the sum of the postoperative refractive goal and the child's age is 7. The target refraction is decided accordingly. Thus for a 1-year-old child, the postoperative refractive target should be +6, for a 2-year-old +5, for a 3-year-old +4, +3 for a 4-year-old, +2 for a 5-year-old, for a 6-year-old +1, 0 for a 7-year-old, and −1 to −2 for patients >8 years of age.[51] Up to 3 months of age, IOL implantation is controversial. The Pediatric IOL calculator is a computer program that uses the Holladay 1 algorithm. It has the pediatric normative data for AL and keratometry readings. These readings were established by Gordon and Donzis.[54][55] This calculator calculates the postoperative pseudophakic refraction during the immediate postoperative period and later predicts the refractive change as the child grows.

Corneal Ectasia

Certain conditions like keratoconus and pellucid marginal degeneration have irregular cornea. In them, reproducible estimation of corneal power is difficult because of disease progression and unstable corneal surface.[56] Optical biometers in keratoconus often overestimate the keratometry and underestimate the final IOL power resulting in postoperative hyperopia.[57] Pentacam is the most appropriate device in such conditions because it also measures the posterior corneal surface.[58] 

It also measures the flatter keratometry and thus avoids hyperopia. There are few studies on IOL power in corneal ectasia. In one study, Thebpatiphat et al. showed that in keratoconus patients, SRK II had the least postoperative error than the SRK and SRK/T formulae.[59] In other studies, SRK/T was found to have the least error compared to SRK II, Haigis, Hoffer Q, and Barrett Universal II formula.[60][61][62] 

Wang et al. analyzed Holladay I and II, Haigis, Barrett, SRK/T, and Hoffer Q formulae in 73 eyes of keratoconus patients. He concluded that  Barrett Universal II had the least mild and moderate keratoconus error.[63] For severe keratoconus, all formulae had similar error rates.[63] Literature suggests the role of corneal collagen cross-linking and intracorneal ring segments before cataract surgery to stabilize keratometry.[64] 

Previous studies have suggested good outcomes with measured K in cases with mild to moderate keratoconus (K<55D) provided slight myopia was aimed. In advanced cases (K >55D), standard keratometry with aimed slight myopia does well.[57] As far as the choice of IOL is concerned toric lenses are preferred only for milder keratoconus with relatively milder irregular astigmatism and good spectacle-corrected visual acuity.[65][66]

Post-refractive Surgery

In refractive surgery, the anterior corneal surface is ablated. This results in an altered ratio of anterior to posterior corneal surface power. This causes inaccurate estimation of ELP.[67][68] Many formulae have been devised to overcome these problems. For laser-assisted in-situ keratomileusis (LASIK) or photorefractive keratectomy (PRK) cases Masket formula uses SRK/T for myopic and Hoffer Q for hyperopic eyes.[69] 

The Maloney formula uses preoperative anterior and posterior corneal power, and then post-LASIK anterior corneal power is added to calculate the post-refractive corneal power.[70] The Shammas formula calculates IOL power based on the post-refractive corneal power.[71][72][73] 

The Haigis-L formula uses ACD for IOL power calculation; thus, it does not require preoperative keratometry values. The Barrett True K similarly does not require preoperative data.[72] The American Society of Cataract and Refractive Surgery (ASCRS) calculator is another useful tool for suggesting IOL powers based on numerous post-refractive calculations (i.e., adjusted Atlas, Masket, modified- Masket, Wang-Koch-Maloney, Shammas, Haigis-L, Galilei) for all post-refractive surgery patients. Meanwhile, as more patients are being analyzed, newer methods such as ray tracing and artificial intelligence are being incorporated into formulae to predict accurate IOL power.

IOL power calculation in post-radial keratotomy (RK) eyes is a challenge. Certain inherent risks are associated with the procedure that makes accurate IOL power calculation challenging. Progressive hyperopia is one of the most common challenges. In conventional RK, the central zone is as small as 3 mm and falls beyond the usual range of the biometer's measurement (4 mm). This results in an overestimation of keratometry and subsequent hyperopia.[74] Keratometry values from the central 3 mm zone are helpful. A myopic target IOL power (0.5-1.5D) is aimed to tackle progressive hyperopia over the years.[75] Barrett True K and Haigis formulae perform better in eyes with RK.[68]

After Posterior Segment Surgery 

Pars plans vitrectomy with silicone oil tamponade have resulted in improved complicated retinal detachment surgery outcomes. But silicone oil can induce cataracts in phakic eyes. Thus phacoemulsification with lens implantation and silicone oil removal in cataractous patients. Sound velocity in aqueous and silicone oil is 1532 m/ s and  987 m/s, respectively.[76]

The A-scan uses ultrasound to measure the axial length. Thus, the sound waves take longer to reach the transducer from the back of the eye in a silicone oil-filled globe. So the measured axial length is greater in the presence of silicone oil.[77][78] 

The mean ratio of true axial length to measured axial length in the presence of silicone oil is 0.71.[79] This conversion factor should be used while calculating the axial length on A scan in a silicone oil-filled globe. Suppose A scan measures 30 mm axial length in a silicone oil-filled globe; then the true axial length will be (30x0.7) 21 mm. The optical method of biometry is more accurate than A scan for measuring AL in the silicone-filled eye.[80]

Enhancing Healthcare Team Outcomes

A patient with decreased vision due to cataracts presents to an ophthalmologist. If the patient requires cataract surgery, then the calculation of IOL power is a necessary procedure. The optometrist and the ophthalmologist should know all the generations of  IOL power formulae. They should know their indications and where to use them. The know-how of the A-scan, keratometer, and optical biometer is a must. The nursing staff, optometrist, and ophthalmologist should be conversant with the upkeep and usage of these instruments. Thus interdepartmental communication will ensure better patient management.

The primary physicians can follow up with the postoperative patients. The nursing will be the first medical staff to contact the follow-up patients. They can assess the postoperative refractive error and report any issues to the primary care clinician or the ophthalmologist. This collaborative, interdisciplinary approach to care can ensure better patient outcomes.