## IOL power calculation formulas

### IOL calculation formulas explained

When planning cataract surgery, one of the most crucial stages for treatment success is choosing the correct intraocular lens (IOL) power.^{1} To reach the targeted refraction, the selection must be performed according to the anatomical and optical parameters of the eye.^{2} In most cases, the target refraction is emmetropia but in some cases, depending on the specific needs and demands of the individual patient, other targets might be required, such as leaving some level of residual myopia in one eye (monovision).^{3} One of the most important parameters in IOL calculation, particularly in non-syndromic myopia, is axial length (AL). AL is a combination of anterior chamber depth (ACD), lens thickness and vitreous chamber depth and can change the IOL power by up to 2.5 to 3 times. [Meng 2011, Eyewiki] Corneal power is another important component of IOL power determination and keratometry (K) is the measurement of the corneal radius of curvature. The cornea is the transparent part of the eye that covers the iris, pupil and anterior chamber and it accounts for around two thirds of the eye's total optical power. Changes in corneal power can alter the IOL power in a ratio of nearly 1:1. As well as AL and K, other parameters that may be also required, depending on the type of formula used, are the preoperative ACD^{5} and the corneal white-to-white distance (WTW; also called the horizontal corneal diameter).^{6} The anterior chamber is the fluid-filled space between the iris and the innermost surface of the cornea and the WTW distance is the horizontal distance between the borders of the corneal limbus.

### What is the effective lens position?

The only parameter that cannot be measured preoperatively is the position where the IOL "settles down" after surgery, which is also known as the effective lens position (ELP). Prediction of this parameter is initially performed by the IOL manufacturer in form of the A-constant. The A-constant is an empirical value and is specific to the design of the IOL. This constant is later refined by statistical optimizations that reflect the variance of the patient's particular preoperative biometry, and the surgeon's personal surgical technique is also taken into account. ELP is defined as the effective distance between the anterior surface of the cornea and the lens plane if the lens was infinitely thin.^{4,5} The ELP is considered to be the main limiting factor for refractive predictability after cataract surgery, as the accuracy of AL and corneal power measurements has been widely demonstrated.^{7} Improvements in IOL power calculations over the past 30 years are the result of improved predictability of the ELP variable.

Mathematical formulas have been developed for best estimation of the ELP, most of which are based on paraxial optics (Figure 1).^{2,4} In these formulas, some ocular parameters are required and the surgeon should know the intended target refraction.^{2,4}

### What are the differences between the IOL formulas?

Many published and unpublished IOL formulas are available. The most frequently used formulas are based on two measurements, AL and K, as well as a single IOL constant^{8} (Holladay 1^{,9} SRK/T^{10} and Hoffer Q^{11}). Predictions of ACD, which increases relative to the increase of AL, are based on initial and generally large datasets from which the formulas have been derived; however individual ACD measurements were not included in the prediction model. The Haigis formula therefore uses three measurements, AL, K and pre-operative ACD with the three IOL constants a0, a1 and a2.^{12} Olsen's formula is based on two additional measurements - pre-operative refraction and lens thickness - and delivers one IOL constant whereas the Holladay 2 formula is based on seven measurements, including the patient's age and the horizontal WTW measurement.^{1,5} Finally, the Barrett formula uses a theoretical model eye whereby ACD is related to AL and K, and is also determined by the relationship between the A-constant and a ‘lens factor'. The position of the principle plane of the IOL is kept as a relevant variable.^{13}

SRKI/II, SRK/T, | Holladay 1 | Hoffer Q | Haigis |

A-constant | sf (surgeon factor) | pACD | a0, a1, a2 |

### Which formula to use for which eye (length)?

For normal ALs of 22.5 to 24.5 mm most formulas work well with minimal discrepancies. In 1993^{11} and again in 2000,^{14} Hoffer performed studies to analyse which formula was the most accurate for ALs of a shorter or longer length than normal. These studies concluded that the Hoffer Q formula provided the most reliable results in short eyes (AL < 22.0 mm) while the SRK/T formula was best in long eyes (AL > 26.0 mm).^{11,14} Recently, in a database study of 8,108 eyes undergoing cataract surgery, the Hoffer Q formula was found to provide the best refractive outcomes in eyes shorter than 21.00 mm and the Holladay 1 and Hoffer Q formulas were equally reliable for eyes with an AL between 21.00 mm and 21.49 mm.^{15} This same study also concluded that the Holladay 1 formula may perform marginally better for eyes between 23.50 mm and 25.99 mm, although the Hoffer Q, Holladay I and SRK-T formulas gave comparable refractive outcomes.^{14} Finally, these authors found that the SRK/T formula performed significantly better for eyes with an AL of 27.00 mm or longer.^{15} For highly myopic eyes the Barrett II formula may be a suitable choice and other studies have demonstrated the high level of accuracy of the Haigis formula in extreme hyperopia.^{16 ,17} See Figure 1.

In conclusion, calculation of the IOL power can be performed using a great variety of formulas. According to clinical studies, the SRK-T formula is recommended for rather long eyes whereas the Hoffer Q formula is recommended for rather short eyes. The Holladay 1 and Hoffer Q formulas are equally good for eyes with an AL between 21.00 mm and 21.49 mm and the Holladay 1 formula seems to perform better than the Hoffer Q formula for eyes between 23.50 mm and 25.99 mm. Fourth generation formulas, like the Barrett, Haigis or Holladay 2 formula, have the advantage of including the non-proportional relationship between the ACD and AL and therefore should provide the highest accuracy over the full range of ALs.

### Formulas for IOL Power Calculation

Which modern intraocular lens (IOL) calculation formula gives the best results for prediction of the effective lens position (ELP) is a widely debated topic. In this section you'll find an overview of the latest generation of formulas for rotationally symmetrical IOL designs (post-laser vision correction eyes are excluded) with their philosophy explained in a nutshell. Furthermore the parameters of each formula used for the ELP prediction are listed as well as recommendations of formulas for different eye types according to various sources.

**Barrett**

The Barrett Universal 2 formula uses a theoretical model eye in which anterior chamber depth (ACD) is elated to axial length (AL) and keratometry. A relationship between the A-constant and a "lens factor" is also used to determine ACD.^{19} The important difference between the Barrett formula and other formulas is that the location of the principle plane of refraction of the IOL is retained as a relevant variable in the formula.

**Parameters used for ELP prediction**

AL, corneal power, ACD (optional), lens thickness (optional), white-to-white corneal diameter (optional).

**Recommended eye type**

The Barrett formula is recommended for short – long eyes.^{20}

visit the website

**Haigis**

The Haigis formula recommends an IOL power based on a three-variable (a_{0}, a_{1} and a_{2}) function. The a_{1} constant is tied to the measured ACD, while the a_{2} constant is tied to the measured AL. This allows all three constants to be optimized for a wide range of ALs and ACDs using double-regression analysis.

**Parameters used for ELP prediction**

These are AL and ACD.

**Recommended eye type**

Haigis (a_{0} optimized only): normal eyes^{20}

Haigis (a_{0}, a_{1}, a_{2} optimized): short – long eyes^{20},*

**Hoffer Q**

The Hoffer Q formula relies on a personalized ACD, AL and corneal curvature. The personalized ACD (pACD) is developed from any given series of a particular IOL style. It includes (1) a factor that increases the ACD with increasing AL, (2) a factor that increases the ACD with increasing corneal curvature, (3) a factor that moderates the change in ACD for extremely long and short eyes, and (4) a constant added to the ACD.^{21}

**Parameters used for ELP prediction**

These are AL and corneal power.

**Recommended eye type**

The Hoffer Q formula should be used for eyes measuring < 22 mm, according to the Royal College of Ophthalmology guidelines.^{22}

**Holladay 1**

The Holladay 1 formula uses the postoperative stabilized refraction value, the dioptric power of the implanted IOL, and the preoperative corneal and AL measurements to calculate a personalized surgeon factor. Thus, the surgeon factor is defined as the distance from the post-operative anterior iris plane to the effective optical plane of the IOL. As with other constants the surgeon factor is not actually a measurement, but a number representing a particular surgeon's previous experience.^{23}

**Parameters used for ELP prediction**

These are AL and corneal power.

**Recommended eye type**

The Holladay 1 is recommended for eyes measuring between 24.6 mm – 26.0 mm.^{22}

**Holladay 2**

The Holladay 2 formula is conceptually based on the Holladay 1 formula; however it uses seven parameters for predicting the surgeon factor. These are the AL, corneal power, ACD, lens thickness, age, white-to-white corneal diameter and pre-operative refraction data. How the formula works in detail has not yet been revealed by Jack Holladay.

**Parameters used for ELP prediction**

These are AL, corneal power, ACD, lens thickness (optional), age (optional), white to-white corneal diameter (optional), pre-operative refraction data (optional).

**Recommended eye type**

The Holladay 2 formula is recommended for short – long* eyes.^{20}

*W-K adjustment has been shown to extend the usage from "short – normal eyes" to "short – long eyes" for meniscus IOLs designs in the low plus to minus power range.^{24}

**SRK/T**

The SRK/T formula is a theoretical (T) approach to IOL power calculation under the SRK umbrella of empirical formulas using existing A-constants and optimization methods. Empirical optimization methods of the SRK/T model primarily consist of (1) postoperative ACD prediction, (2), a retina thickness correction factor and (3) corneal refractive index.^{25}

**Parameters for ELP prediction**

These are AL and corneal power.

**Recommended eye type**

The SRK/T formula should be used for eyes > 26 mm. A combination of Hoffer Q, Holladay 1, and SRK/T should be used for eyes 22.0–24.5 mm.^{22}

**SRK I and SRK II**

The SRK I and SRK II formulas are obsolete and should no longer be used.^{26}

## Intraocular lens power calculation

The aim of an accurate **intraocular lens power calculation** is to provide an intraocular lens (IOL) that fits the specific needs and desires of the individual patient. The development of better instrumentation for measuring the eye's axial length (AL) and the use of more precise mathematical formulas to perform the appropriate calculations have significantly improved the accuracy with which the surgeon determines the IOL power.

In order to determine the power of intraocular lens several values need to be known:

- Eye's axial length (AL)
- Corneal power (K)
- Postoperative IOL position within the eye known as estimated lens position (ELP)
- The anterior chamber constant: A-constant or another lens related constant

Of these parameters the first two are measured before the implantation, the third parameter, the ELP, need to be estimated mathematically before the implantation and the last parameter is provided by the manufacturer of the intraocular lens.

### Axial Length[edit]

The axial length (AL) is the distance between the anterior surface of the cornea and the fovea and usually measured by A-scan ultrasonography or optical coherence biometry. The AL is the most important factor in IOL calculation: A 1-mm error in AL measurement results in a refractive error of approximately 2.88 D or about 3.0-3.5 D error of IOL power in an average eye. A mean shortening of 0.25–0.33mm can translate into an error of IOL power by approximately 1 D^{[1]}

### Ultrasonography[edit]

In A-scan ultrasound biometry, a crystal oscillates to generate a high-frequency sound wave that penetrates into the eye. When the sound wave encounters a media interface, part of the sound wave is reflected back toward the probe. These echoes allow us to calculate the distance between the probe and various structures in the eye. Ultrasonography does not measure the distance but rather the time required for a sound pulse to travel from the cornea to the retina. The speed of sound varies in different parts of the eye. The eye is divided ultrasonographically into four components:Cornea, Anterior chamber, Lens thickness and Vitreous cavity. The velocity of sound in these compartments are 1620, 1532, 1641, 1532 m/s respectively.^{[2]} Through normal eyes an average velocity of 1555 m/s is accepted for calculation. Modern instruments use separate sound velocities for the different eye components to obtain the total axial length. The measured transit time is converted to a distance using the formula d=t/v Where d is the distance, t is the time and v is the velocity.^{[1]}

Two types of A-scan ultrasound biometry are currently in use. The first is contact applanation biometry. This technique requires placing an ultrasound probe on the central cornea. While this is a convenient way to determine the axial length for most normal eyes, errors in measurement almost invariably result from the probe indenting the cornea and shallowing the anterior chamber. Since the compression error is variable, it cannot be compensated for by a constant. IOL power calculations using these measurements will lead to an overestimation of the IOL power. In shorter eyes, this effect is amplified. The second type is immersion A-scan biometry, which requires placing a saline filled scleral shell between the probe and the eye. Since the probe does not exert direct pressure on the cornea, compression of the anterior chamber is avoided. A mean shortening of 0.25–0.33mm has been reported between applanation and immersion axial length measurements, which can translate into an error of IOL power by approximately 1 D. In general, immersion biometry has been shown to be more accurate than contact applanation biometry in several studies. The main limitation with the A-scan ultrasound is the poor image resolution due to the use of a relatively long, low-resolution wavelength (10 MHz) to measure a relatively short distance. In addition, variations in retinal thickness surrounding the fovea contribute to inconsistency in the final measurement.^{[3]}

### Partial coherence interferometry[edit]

The technique of partial coherence interferometry measures the time required for infrared light to travel to the retina. Because light travels at too high a speed to be measured directly, light interference methodology is used to determine the transit time and thus the AL. This technique does not require contact with the globe, so corneal compression artifacts are eliminated. Compared with ultrasonography, the partial coherence interferometry provides more accurate, reproducible AL measurement. However, it is difficult to obtain a measurement in the presence of a dense cataract or other media opacities, which limits the use of this technique.

Another advantage of PCI over ultrasound biometry is that the axial length measurement is performed through the visual axis since the patient is asked to fixate into the laser spot. In highly myopic or staphylomatous eyes, this can be particularly advantageous since it can sometimes be difficult to measure the true axial length through the visual axis with an ultrasound probe. PCI is also superior to ultrasound in the measurement of pseudophakic and silicone oil-filled eyes. For optical biometry, it is not as critical how the media change because the correction factor that must be applied is much smaller than in ultrasound biometry.^{[3]} The axial length obtained from PCI may be slightly longer than that obtained from ultrasound. This is due to PCI measuring the distance from the corneal surface to the RPE while ultrasound measures to the anterior retinal surface. Therefore, many IOL measurement machines require refined IOL constants unique to their mechanism.

### Corneal Power[edit]

The central corneal power is the second important factor in the calculation formula. To simplify the calculation, the cornea is assumed to be a thin spherical lens with a fixed anterior to posterior corneal curvature ratio and an index of refraction of 1.3375. Central corneal power can be measured by keratometry or corneal topography. Corneal radius of curvature relates to corneal power with the equation: r = 337.5/K.^{[3]}

### IOL power calculation formulas[edit]

Intraocular lens power calculation formulas fall into two major categories: regression formulas and theoretical formulas. Regression formulas are now obsolete and modern theoretic formulas are used instead.^{[4]} The regression formulas are empiric formulas generated by averaging large numbers of postoperative clinical results (i.e. from retrospective computer analysis of data obtained from a great many patients who have undergone surgery). The most common regression formulas are the SRK and SRK II. In the 1980s SRK and SRK II were popular because they were simple to use. However, power error often resulted from the use of these formulas.

The SRK formula is calculated easily by hand as , where is the IOL power to be used for emmetropia, is the IOL specific A constant, is the average corneal refractive power (diopters), and is the length of the eye (mm). The SRK II formula adjusts the A constant utilized depending on the axial length: increasing the A constant for short eyes and decreasing the A constant for long eyes.

Theoretical formulas are based on geometrical optics. The eye is considered a two lens system (i.e. IOL and cornea) and the predicted distance between them which is called the estimated lens position (ELP) is used to calculate the power of the IOL. All formulas require an estimation of the position that the IOL will sit in the eye, a factor known as the ELP, which is defined as the distance between the cornea and the IOL. ELP correlates with the placement of the IOL inside the eye, whether it is in the anterior chamber in the sulcus or in the capsular bag. It also varies with the implant’s configuration and the location of its optical center. For example, the use of a meniscus lens calls for a smaller ELP value than a biconvex IOL.

IOL calculation formulas differ in the way they calculate ELP. In the original theoretical formula the ELP is considered a constant value of 4 mm for every lens in every patient.^{[4]} Better results are obtained by relating the expected ELP to the axial length and corneal curvature. Modern theoretical formulas predict ELP differently based on axial length and corneal power: ELP decreases in the shorter eyes and flat corneas and increases in the longer eyes and steeper corneas. The improvements in IOL power calculation are the result of improvements in the predictability of the ELP.^{[2]}

The best known modern formulas are SRK-T, Holladay 1, Holladay 2, Hoffer-Q and Haigis. These formulas are programmed into the IOLMaster, Lenstar and most modern ultrasonographic instruments, thus eliminating any need for regression formulas.^{[1]}

### A-constant[edit]

The A-constant was originally designed for the SRK equation and depends on multiple variables including IOL manufacturer, refraction index, style and placement within the eye. Because of its simplicity, the A-constant became the value used to characterize intraocular implants.

A-constants are used directly in SRK II and SRK/T formulas. The constant is a theoretical value that relates the lens power to AL and keratometry, it is not expressed in units and is specific to the design of the IOL and its intended location and orientation within the eye.

Using A-constants is practical when a decision on the implant power has to be made during surgery because the power of the lens varies in a 1:1 relationship with the A-constants: if A decreases by 1 diopter, IOL power decreases by 1 diopter also. This straight relationship adds to the simplicity and popularity of the A-constant. Other constants used in modern IOL formulas include the ACD value in Binkhorst and Hoffer-Q formulas, the a_{0}, a_{1}, and a_{2} constants of the Haigis formula, and the Surgeon factor (SF) in Holladay formulas. True anterior chamber depth (ACD) is measured between the posterior corneal surface and the anterior lens surface. This measure is not to be confused with the anterior chamber constant (ACD constant) used in IOL power calculation formulas.^{[2]}

All lens constants are estimates, to begin with. To obtain the best possible results, it is imperative that these constants be optimized. Optimization is a process that is user-specific and incorporates the various systematic errors attributable to measurement of ocular parameters. In order to optimize a lens-constant, the user must back calculate the formula so that the actual post-operative refractive error is included. This means that one must calculate the constant so that a recalculation of the formula would predict exactly the same refractive error as actually observed.

### Intraocular lens power calculation after refractive surgery[edit]

Cataract extraction following refractive surgery poses special problems for the patient and the surgeon because the corneal change as a result of refractive surgery complicates accurate keratometry, a key element of lens implant power calculation. After laser refractive surgery for myopia, this could result in overestimation of corneal power, underestimation of the IOL power required, and hyperopic outcomes after cataract surgery.

The difficulty arises from several factors:^{[1]}

- The instruments used by ophthalmologists to measure the corneal power (keratometers, corneal topographers) cannot obtain accurate measurements in eyes that have undergone corneal refractive surgery. Most manual keratometers measure at the 3-mm zone of the central cornea, which often misses the central flatter zone of effective corneal power.
- The assumed index of refraction of the normal cornea is based on the relationship between the anterior and posterior corneal curvatures. This relationship is changed in LASIK eyes.
- Most IOL power formulas use the axial length and keratometric reading (K) to predict the position of the IOL postoperatively (ELP). In post-LASIK eyes this causes an error in this prediction because the anterior chamber dimensions do not really change in these eyes commensurately with the much flatter K. In order to address this problem the double-K method was developed, which uses the pre-LASIK corneal power for the calculation of the ELP, and the post-LASIK corneal power for the calculation of the Vergence component of the formula.

### Auditing of Results[edit]

Auditing of results helps to compare formulae and optimisation strategies amongst each other. Due to considerable confusion in the past, a clear set of guidelines now exists to report IOL power related data. There are six key measures that are to be reported. In recognition of the fact that comparison of ideal IOL powers is likely to be error-prone, all comparisons are done for actual or predicted refractive errors.

1. Mean Error (ME) and standard deviation (SD) in prediction.

2. Mean Absolute Error (MAE) and standard deviation (SD) in prediction.

3. The percentage of eyes ± 0.5 D from the predicted target refraction.

4. The percentage of eyes ± 1.0 D from the predicted target refraction.

5. The percentage of eyes > 2.0 D from the predicted target refraction.

6. Range of errors from maximum plus error to maximum minus error.

Software tools can be used in order to perform an audit.

### See also[edit]

### References[edit]

- ^
^{a}^{b}^{c}^{d}*Basic and Clinical Science Course, Section 3: Clinical Optics*(2011-2012 ed.). American Academy of Ophthalmology. 2011. pp. 211–223. ISBN . - ^
^{a}^{b}^{c}Roger F. Steinert; David F. Chang (2010).*Cataract surgery*(3rd ed.). Saunders. ISBN . - ^
^{a}^{b}^{c}Lee, AC; Qazi, MA; Pepose, JS (January 2008). "Biometry and intraocular lens power calculation".*Current Opinion in Ophthalmology*.**19**(1): 13–7. doi:10.1097/ICU.0b013e3282f1c5ad. PMID 18090891. - ^
^{a}^{b}Myron Yanoff; Jay S. Duker (2009).*Ophthalmology*(3rd ed.). Mosby Elsevier. pp. 416–419. ISBN .

### External links[edit]

Toric Intraocular lens power calculator - http://aurolab.com/auroflextoric-hydrophilic-iol.asp Dr. Hill lens calculation materials - http://www.doctor-hill.com/iol-main/formulas.htm

Online calculation of intraocular lenses using different IOL formulas - http://www.augenklinik.uni-wuerzburg.de/uslab/iolfrme.htm

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**IOL Power Calculation Formulas.**

For axial lengths from 22.50 mm to 24.00 mm, and central corneal powers ranging from 42.00 D to 45.00 D and a normal anterior chamber depth, most modern IOL power calculation formulas will give good outcomes. However, for eyes outside this range, our results indicate that Haigis (with properly optimized a0, a1 and a2 constants) and the newer generation formulas, such as Holladay 2, Olsen and Barrett give better results.

For Holladay 1, SRK/T, Haigis and Holladay 2, an adjustment is required for the high to extreme axial myope and axial lengths above 25.00 mm. How to do this is outlined at:

http://www.doctor-hill.com/iol-main/extreme_axial_myopia.htm

The Journal of Cataract and Refractive Surgery paper that describes this approach can be found at:

Wang L, et al. Optimizing intraocular lens power calculations in eyes with axial lengths above 25.0 mm. JCRS 2011; 37:2018-2027.

Here is something to consider. As surgeons, we are now mostly being judged by our patients and our peers by our refractive outcomes. It seems to a little odd to spend tens of thousand of dollars on the next most accurate measurement technology, but continue to rely on calculation methods that are not from this century. Optimal outcomes require the best possible measurement technology and the best possible calculation methods.

**The chart below** represents our experience with popular IOL power selection methods where the measurements have been made by optical biometry. We are now using only the Barrett Universal II formula and the Hill-RBF pattern recognition method for all of our calculations. For the high to extreme axial myope we will also look at the Wang-Koch axial length modification of the Holladay 1 formula. Eight years of experience has shown the best pre-operative measurements have been with the Haag-Streit Lenstar.

## Formulas iol calculation

## Introduction

Alpa S. Patel, M.D., Jordan Scott Masters, MD, Chris O’Brien, MD MBA, Hussain Syed Faraaz Shahzad, Koushik Tripathy, MD (AIIMS), FRCS (Glasgow), Derek W DelMonte, MD

Assigned status **Up to Date**

### Background

Biometry is the method of applying mathematics to biology. The term was originally used by Whewell in the 1800s for calculating life expectancy. The refractive power of the eye primarily depends upon the cornea, the lens, ocular media, and the axial length of the eye. When planning for cataract surgery, in order to achieve the desired post-operative refraction, the required power of the intraocular lens (IOL) implant can be calculated if the corneal refractive power, media type, and axial length are known. ^{[1]}

### History

In 1949, Harold Ridley implanted the first IOL but his patient had a refractive surprise of nearly 20 diopters. Fyodorov and co-workers ^{[2]} first estimated the optical power of an IOL using vergence formulas in 1967. In the 1970s, after availability of accurate “A” scans, several studies were conducted to establish and publish various theoretical vergence formulas. In the early 1980s, several IDEM (ideal emmetropia) lenses were also attempted, so named as the pre- and post – refraction from them were similar. On similar lines, Standard lenses were also attempted, after Gernet and Zorkendorfer in 1982 showed that the average refractive power of natural lens is +23.70D. Although these were neither strictly mathematical nor ethically sound, they should be mentioned for their due respect in a historical perspective. The theoretical formulas derived around the same time have been subjected to minor and major alterations in the variables since then in order to increase accuracy. ^{[3]}

### Definitions

### Outcome

Emmetropia or no refractive error is the ideal outcome sought, in accordance with which maximum biometry is carried out. However, in certain circumstances some may benefit from either a hypermetropic or myopic status postoperatively. In cases where the patient prefers a certain refractive state for either occupational or social needs, including low vision aids. Sometimes the other eye refractive state has to be considered, as in cases of monovision or anisometropia, which should be kept less than 3 diopters.

### Refractive State of the Cornea or keratometry (K)

The measurement of corneal power though not absolutely accurate is based upon the steepness of the cornea. The cornea is assumed to be a perfect spherical optical mirror with a fixed anterior to posterior corneal curvature ratio. The cornea then acts as a perfect convex mirror, leading to a virtual image of the target. The corneal curvature is predicted from this, which is then used to determine the corneal power. The basic error in most keratometers is that they do not provide enough information to calculate corneal curvature accurately. Moreover, the cornea must be assumed to be a perfect sphere with par-axial optics, and the power of the back of the cornea must also be estimated (if not calculated with newer posterior imaging techniques) . Computerized videokeratography is now gaining standardization for more accurate results. ^{[4]}^{[5]}

### Axial length (AL)

Axial length is defined as the distance from the anterior corneal surface to the retinal pigment epithelium. Can be performed using optical or ultrasound methods, which can further be done by direct contact or immersion. A combination of these measurements prevents errors in AL measurements. Optical methods like IOL master have benefits of non-contact procedures along with greater accuracy, but can be inaccurate or difficult to obtain in dense cataracts. Contact ultrasound measurements have been the gold standard earlier, but are likely to have more subjective errors due to corneal compression. Immersion avoids the corneal compression but has less control over alignment, hence can give rise to varied results. Hence a combination of techniques can give better results. ^{[4]}^{[5]}

### A-constant

A-constant, although called a constant is actually highly variable depending upon multiple factors – IOL dependent: type, material, position; surgeon dependent: technique of incision, placement of incision; K and AL measurement adjustments; or even adjustment for the manner of carrying out biometry. Once fixed for a particular surgeon, IOL and machine for the scan, it is applied as a constant to the appropriate formula. It approximately varies with a ratio of 1:1 with the IOL power. ^{[5]}^{[6]}

### Gain

Defined as the electronic amplification factor of the sound waves received by the transducer, it is measured in decibel (dB). Normal setting is around 70% -75%. But it may be increased where high echoes are inadequate (hard cataracts, dense ocular opacities, high myopia). It is decreased when artifacts are seen near the retinal spikes (silicone filled eyes & in pseudophakics)^{[7]}.

### IOL Formulae for calculation

Formula for calculation of IOL power have been evolving since their inception. These can be classified on the basis of their derivation (theoretical, regression analysis or combination) or according to their evolution as per generations. By derivation, theoretical formula are determined by application of geometrical optics to the schematic and reduced eyes using various constants. Later; regression analysis using the actual post-operative results of implant power as a function of the variables of corneal power and axial length were derived. Sanders, Retzlaff and Kraff developed the SRK formula which was widely used. Though now replaced with the newer generation formulas, it is still useful for understanding the relation of the variables and A-constant to the IOL Power (P).

P = A – 0.9 K – 2.5 ALWhere

P= Power of the IOL in diopters

A= A constant

K= Average keratometry value in diopters

AL= axial length in mm

This is rarely used to calculate IOL power manually where other tools are not available, but should be avoided whenever possible. The various generations of formula are discussed under the “Mathematics and Measurements” subheading^{[5]}^{[6]}^{[7]}.

### Underlying Principles & Parameters

Most of the modern day formulae are based upon the theoretical equation formulated by Fyodorov and its modifications. Here the IOL power is chosen as the variable, which is calculated on the basis of this equation and its derivatives…

P = (1336/[AL-ELP]) – (1336/[1336/{1000/([1000/DPostRx] - V) + K} - ELP])Where

- Net corneal power (K)
- Axial length (AL)
- IOL power (P)
- Effective lens position (ELP)
- Desired refraction (DPostRx)
- Vertex distance (V)

The only variable which cannot be measured pre-operatively is ELP and most of the later day formulae like Holladay, Hoffer Q, SRK/T or Haigis attempt to calculate ELP more accurately^{[8]}.

### Effective lens position (ELP)

ELP was the term used to denote the position of the lens in the eye- specifically the distance that the principal plane of the IOL will sit behind the cornea. As the older variable, anterior chamber depth (ACD); was found to be inaccurate anatomically for “in the bag” implanted IOL. In accordance with these variables the formulae can be divided as …

^{[9]}

The newer modifications have continued since, but the improved accuracy of post-operative refraction is also due to increased surgical proficiency and cataract techniques over the years. Example being the Holladay 2 which uses patient age and preoperative refraction as further variables to improve accuracy; while Haigis replaced K with preoperative ACD to improve accuracy. The Barrett formula additionally incorporates ACD into its calculations.

Using Gaussian reduction equations, the formula for calculating IOL power can also be expressed in accordance with the refractive index…

P = [nv/(AL - C)] - [K/(l- Kx C/nA )]where^{[10]} P = power of the target IOL (in diopters [D]) K = average dioptric power of the central cornea (in D) AL = visual axial length (in millimeters) C = ELP (in millimeters), the distance from the anterior corneal surface to the principal plane of the IOL nv = index of refraction of the vitreous nA = index of refraction of the aqueous

Figure 1 Diagrammatic representation with Reduced Optics correlation and A-scan (Redrawn by Dr F. Hussain, not to scale)

See figure 1, for diagrammatic correlation.

The ELP in the original formulae was a constant, as the lenses used were mostly in the anterior chamber. Hence this was incorporated into the “A” constant in the later regression analysis like SRK. Today, the newer formulae generally use only one constant incorporated as A-constant or Surgeon Factor (SF). The original A-constant developed in the 1980s was so widely used that every lens was designed with a specific A-constant by the manufacturer. Even though regression analysis is not recommended today; the A-constant still remains due to its benefits in emergency usage and manual derivation for confirmation^{[11]}.

### Corneal Power (K)

It is considered the second most important factor for IOL power determination. Changes in K reading; alters the IOL power in a ratio of nearly 1:1. It can be measured either by keratometry or topography but neither measures the actual corneal power directly. The mathematical principle behind the keratometry method is that the central cornea is assumed to be a perfect sphere and acts as a spherical convex mirror. Further the posterior corneal curvature is assumed to be 1.2mm steeper than the anterior; this is especially altered after refractive surgeries due to which increased errors are observed. From the size of the reflected image from the cornea acting as a convex mirror, the radius of curvature is determined, which is then converted to power in diopter or mm.

Radius(r) of curvature (mm) = 2u (mm) multiplied by Size of Image/ Size of Objectu = distance of object from principle plane And

D = (n2 – n1) / rn = Refractive index of medium 1 & 2 respectively.

Topographical methods use the Scheimpflug principle via the Pentacam or the Galilei (double Scheimpflug) to measure the anterior and posterior radii of corneal curvature along with the corneal thickness which is then used to measure corneal power in diopters. In a normal phakic eye the average anterior corneal radius of curvature is 7.5mm, which corresponds to 44.44D using keratometric refractive index of 1.3333(4/3) which was found to be more accurate than the older one used 1.3375. The posterior corneal radius of curvature averages 1.2mm less than the anterior surface radius^{[12]}.

### Axial Length (AL)

It is perhaps the most important parameter in most modern day formulae. It changes the IOL power by nearly 2.5 to 3 times, more so in short eyes than in longer ones. Can be measured using Ultrasonography (contact or immersion) or Optical methods (IOL Master & Lenstar). Ultrasonography uses mechanical waves to calculate the time needed for a pulse to travel from the cornea to the retina. Sound travels with different speeds as per the media, more in lens and cornea (1641m/s) and less in aqueous and vitreous (1532m/s). This is then converted to distance by

Distance (m) = time (s) X velocity (m/s)Average velocity of a normal phakic eye is 1555 m/s. Ultrasonography methods can be applanation or immersion, the former is more inaccurate due to indentation, but the latter has less control. The A –scan (Amplitude modification) is a one dimensional display in which echoes are represented as vertical spikes from a baseline. Optical Methods use partial coherence laser for AL measurement. Similar to ultrasonography, optical methods also measure time needed for infrared light to travel from cornea to retina, but uses interferometry principle in order to avoid the problem of very high light speed measurements. As it is a non-contact procedure, no indentation errors occur. Two main instruments are available for optical methods IOL Master from Zeiss and the Lenstar from Haag-Streit. It has been reported that there are no statistically significant difference in the measurement of AL by IOL Master, Lesntar and immersion ultrasonography by Montes- Mico^{[13]}. Average AL in a normal phakic eye is about 24mm in adults^{[14]}.

### Measurements (IOL Master & Lenstar)

Optical methods of measuring AL need more elaboration as compared to immersion ultrasonography.

^{[15]}^{[16]}

Because of these about 8-17 % of eyes cannot be measured using the Optical methods, hence immersion continues to have a role. ^{[16]} A comparison between the newer devices for optical methods of measurements is also useful as one must be aware of the available options and their benefits…

From the work of Sahin – Hamrah et al. ^{[4]}

### In Aphakia

The parameter altered is the speed of travel of sound, which now averages 1532m/s, and the two lens spikes in A-scan are absent, being replaced by a single spike of the anterior vitreous face and posterior capsule. Immersion method is preferred rather than contact, newer devices have specially programmed modes for aphakia^{[7]}. Most of the values remain similar in the theoretical equations already discussed, except the manufacturer’s ACD and the measured K reading. As the manufacturer’s ACD is for in the bag placement, unless special lenses are utilized, the value should be reduced by 0.25 mm for sulcus placement. For posterior iris fixation a further reduction of ACD by 0.25mm is needed^{[17]}. Similarly the measured K reading must be converted to the net K reading with RI 4/3 or 1.3333. ^{[18]}

### In Pseudophakia

This can be important for IOL exchange or for comparison while doing biometry for the other eye. Eyes with IOL have an extremely high spike at the lens followed by an artificial chain of reduplication echoes which can be confused with retinal spikes. This is avoided by reducing gain to decrease the artificial spikes and make retinal ones more prominent. The speed of sound travel now depends upon the type of IOL and its parameters. In newer devices prefilled data is available in accordance with the type of implant. ^{[7]} Optical Biometry is preferred which offers more accurate correction of the AL by correction factor (CF) which varies as per the lens type and thickness. ^{[19]} Common examples: PMMA, the conversion factor is +0.45; for silicone it is either -0.56 or -0.41 (depending on the style and manufacturer); and for acrylic it is +0.30. These must be applied to the formulas

Lens thickness (t) must be obtained from the manufacturer. ^{[20]}

### In Pediatric age group

The problems in pediatric age, especially the very young; includes the increased errors in AL measurement, which compounds the final IOL power errors due to shorter AL. AL and K value must be measured under general anesthesia. The IOL power chosen should allow good vision in growing age to prevent amblyopia and ideally also give emmetropia in adult age.

Currently all infants above two years are advised IOL implantation; while some controversy exists in younger ages. The greatest concern at such an early age is to prevent amblyopia. The development of the eye necessitates initial under-correction to avoid later myopic shift. The growth of the anterior segment is usually completed at around two years hence the IOL aimed for is about 80% of the calculated amount of power.

Note: These corrections are to be made on the newer generation formulas like SRK/T. ^{[21]}^{[22]}^{[23]}

Piggy back IOLs with one implant being permanent in the bag and the other temporary in the ciliary sulcus has been suggested by Dr. M. Edward, where in the temporary one is removed at adult age. ^{[24]}

### After Posterior segment Surgery

The major issue is with silicone filled eyes after vitrectomy in which IOL implantation is being considered. The velocity of sound in silicone is slower than in vitreous which must be corrected for measurement of the AL accurately. The two most common types of silicone have different tissue velocities, 1050 or 980 m/s; hence one must know which velocity to select to avoid a small mistake in axial length.This is usually achieved after alteration of settings in the newer machines.

Moreover silicone in the eye itself acts as a negative lens when a biconvex IOL is implanted hence the IOL power must be adjusted by 3-5 D. Measurement adjustment to improve accuracy can also be achieved by calculating each segments ratio and then obtaining the IOL value by appropriate alteration^{[25]}. Measurement of AL by optical method has been found to much more accurate for silicone filled eyes^{[26]}.

### After Refractive Surgery

Corneal Refractive surgeries alter the basic assumptions on which the biometry for IOL calculations is based – namely the perfectly spherical nature of cornea. The refractive surgeries mainly affect the central cornea, as well as alter the posterior corneal curvature, which is not routinely measured. The errors occur due to instruments, index of refraction and formulas used.

Instrument errors occur due to the inability of keratometers to measure the central zone of effective corneal power. While they measure a 3.2mm zone diameter, this misses the central effective zone. Flatter the cornea, greater the measurement zone hence greater the error.

Refractive index (RI) is based upon the ratio between the anterior and posterior corneal curvatures. As may be recalled most instruments only measure the anterior curvature while making assumptions about the posterior curvature to derive at the RI, hence K. The relationship between the curvatures is altered in PRK, LASIK & LASEK, but avoided in RK which causes alteration of curvatures such that the relation is maintained. This overestimates the corneal power by 1D for every 7D of correction of refractive error.

Formulas error occurs in nearly all modern ones like Holladay, SRK/T (but not in Haigis), all of which use the AL & K to predict ELP post-operatively. As the other dimensions of the anterior chamber are not altered proportional to the central cornea after the refractive surgeries, this prediction leads to erroneous results^{[27]}. Methods to measure IOL post-Refractive surgery can be divided as “Indirect” or “Direct” based on the measurement of the corneal power after surgery (direct involves actual measurement, while indirect makes assumptions based on historical data or theoretical analysis.)

^{[26]}

### Indirect

So named because they utilize measurement apart from post-refractive surgery corneal power reading.

#### Clinical History or Calculation method

Needs 3 parameters:

- Pre-op K
- Pre-op Refraction
- Stabilized refraction after keratorefractive procedure.

The stabilized refraction must be measured before changes in refraction occur due to cataractous alterations.

Here,

K postReSx = K preReSx – difference in Spherical Equivalent{ReSx = Refractive surgery}

It is most accurate as the pre-op values are precise up to +/-0.25mm ^{[28]}.

#### Contact Lens over-refraction

Needs 4 parameters:

- Base curve of contact lens in Diopters (BC)
- Power of contact lens (P)
- Manifest refraction (MRx) before ORx

This formula is:

K postReSx = BC + P + (ORx - MRx)The limitation is the reliability of refraction in the patient with cataract ^{[29]}.

#### Vertexed IOL method

Based on theoretical studies by Feiz, Latkany and their colleagues, various nomograms were developed after calculating IOL power post LASIK with SRK/T and three other formulas. The change in the spherical equivalent after LASIK was used to modify the IOL power. Its main limitation is the theoretical nature of the study and the lack of large published data with regards to its accuracy.

#### Intraoperative auto-refraction measurement

It directly uses intraoperative refraction data to calculate the IOL power, without need of knowing AL and K. A special “A-constant” is formulated for the same. Main limitation is the lack of support by large data studies ^{[29]}.

#### DBR Method

Like the calculation method, needs data from both before and after surgery…

##### Pre-operative:

- Refraction
- Keratometry
- AL
- IOL Power for emmetropia

##### Post-operative:

- Refraction plane
- Residual refractive error after stabilization of refraction

This co-relation is then used to obtain the IOL power post refractive surgery ^{[7]}.

### Direct methods

So named as one actually measure the corneal power post-operatively to calculate the effective keratometric dioptres. Although most modern devices do not directly measure the posterior corneal curvature, they use alternative algorithms to approximately assume the RI change induced or simply use different variables to predict ELP ^{[30]}.

#### Gaussian optics and linear regression

##### The Gaussian formula uses:

- Anterior & Posterior radius of curvature
- RI of air (1.0); of Anterior K (1.376) & of Aqueous humour (1.336)
- Corneal thickness

To calculate the Effective Refractive Power (EffRP), the posterior corneal curvature is not directly measured but predicted from the data of Oslen et al. ^{[31]}. EffRP was then used to predict ELP, along with the application of linear regression analysis ^{[32]}. Errors of nearly 0.5 D are still noted.

#### Topography method

It uses the keratometric reading and the flattest corneal power in the central 3mm zone to calculate the simulated K (SimK). This is then used to predict ELP. Errors occur due to central zone giving steeper K values ^{[33]}.

Maloney topographic method uses SimK from topography and applies it to the formula

K = 376/ (337.5/SimK) – 5.5This K reading then predicts the IOL power^{[34]}.

#### Aramberri “double K” method

Aramberri reported in 2002 that the flatter K should not be used in modern formulae. The pre-operative K is used to predict ELP while the post-operative K is incorporated in the formula for actual IOL power prediction. This was later incorporated in the Holladay 2 vergence calculation formula ^{[35]}^{[36]}.

#### Camellin and Calossi

They reported a formula which uses induced refractive change as well as anterior and posterior curvature of cornea to predict IOL power^{[37]}.

#### Rosa method

This uses a correction factor (R factor) for corneal radius which was derived from a regression formula and then compared with the calculation method and double K method. In their study of 19 eyes R factor was found to be superior when applied to the SRK/T and Holladay 1. The actual formula for IOL power is derived from manual measurements of corneal power (K) and axial length (AL).

K = (0.0276 x AL + 0.3635) manual K^{[38]}^{[39]}

#### Direct measurements of Anterior & Posterior corneal power

With the invention of these newer instruments direct measurement of the posterior corneal power is also possible, which then gives more accurate results for IOL calculation after refractive surgery. The Orbscan and the Pentacam both have been used to measure posterior corneal power, with the Pentacam having slight advantage. But these need more study and data^{[40]}^{[41]}^{[42]}.

Despite the various methods described, the science of IOL power calculation after refractive surgery is still in its nascent stages and needs more research. Generally calculation method is considered most accurate, followed by corneal topography and automated K^{[5]}.

### In Corneal Transplants

It is extremely difficult to accurately predict corneal power in transplant patients. If a triple procedure is planned it is suggested that K readings of other eye be used. An alternative option is to use the average k readings from a series of previous transplants. If there is a corneal scar, but no graft is planned, other eye readings can be used or even the power calculated using AL and refractive error of affected eye ^{[43]}^{[44]}.

### For Piggy-back IOLs

In patients with post IOL refractive surprise or in those with large dioptric requirement, a piggy back IOL in sulcus can be placed along with the primary implant. This method does not require knowledge of the power of the primary implant or of the axial length. Minor adjustments are needed, which can be achieved using these formulae:

- Myopic correction: P = 1.0 x Error
- Hyperopic correction: P = 1.5 x Error
- where
- P = the needed power in the piggyback lens
- Error = the residual refractive error that needs to be corrected
^{[45]}^{[46]}

### Common pitfalls

### Limits of Biometry

It has to be acknowledged that calculation of IOL power is not absolute due to the large number of individual variations in human eyes. Major sources of error have been documented in a study by Norrby et al…

^{[47]}

Sources of error can also be due to acts of omission and commission

^{[48]}^{[1]}

### Improving outcomes

Albeit not perfect, biometry for IOL power calculation can be made very precise, if one follows simple guidelines.

### Patient counselling and requirements

All patients may not want emmetropia and some it may not be possible to ensure the same pre-operatively, as in very dense cataracts where macular lesions can be missed. Counselling the patient well is a must; who should be informed and then offered the options as per his/her needs.

### General guidelines

Each surgeon must review their own results and appropriately make alterations to biometry if needed. Regular checks and audits are a good habit. Training and monitoring the staff is equally important. While selecting the patient, ensure the eye and the papers are in order and correspond to each other. Cross checking with refraction is also a good adjunct if accurate retinoscopy is available. While performing the actual scan, ensure asepsis, especially in contact procedures. Patient comfort and appropriate anaesthesia should be monitored.

### AL measurement

Optical ultrasound is the gold standard for AL measurement due to ease of use, accuracy and reproducibility as well the non-contact nature of the procedure. As it cannot be accurate in certain conditions already seen, it can be supplemented with ultrasonography methods to improve outcomes. Immersion is preferred as it approaches the accuracy of optical methods, but is cumbersome to use. In cases where it is not available contact ultrasonography is still utilized. Appropriate machine calibration is necessary before the scan itself.

#### Good A-Scan graph: (see figure 1)

- Corneal echo is seen as a tall single spike
- No echoes from Aqueous humour
- Anterior and Posterior lens capsule produce tall echoes
- No echoes from Vitreous cavity
- Retina produces tall sharply rising spike with no staircase at origin
- Orbital fat produces medium to low echoes
- Check A-scan graphs: If the spike from retina is not followed by multiple small spikes it means one is hitting optic nerve, so discard that reading.
- If there is a reading where the anterior chamber depth and actual length reduces, it indicates that in that particular reading one is compressing the cornea. It should be discarded.
- Gain should be the minimum possible which gives good spikes.
- Average of 8-10 measurements increases accuracy

#### Some useful tips for contact procedures:

- Probe should be perpendicular, centred and pointing towards macula.
- No fluid between probe and cornea
- No depression of cornea

### K measurement

Can be calculated by either using automated or manual method. Performing a double check by both methods helps in improving accuracy.

#### Useful tips:

- No other contact procedure before keratometry
- Use topical anaesthetic before scan
- Calibrate keratometer before scan
- Take an average of 3 readings
- If discrepancy, ask a second person to cross check
- Compare the refraction, especially the axis with the K values
- Repeat if difference is more than 1.0D between the two eyes.

### Choice of formulas

Albeit controversial, some guidelines have been developed for which formulae to use under specific circumstances. Although earlier widely used, the SRK 2 and older ones now obsolete. Appropriate calibration of settings and adjustments of constants is a must before IOL power prediction. No single formulae has been found to be useful in all circumstances.

The newer formulae like T2 modification of SRK/T; Oslen’s formula, Hollady 2 and Haigis are still not widely available in the biometry software. Due to the absence of compelling comparative evidence of the superiority of these formulas over each other, it is justifiable to continue using an appropriate combination (according to axial length) of the two variable - single constant formulas. ^{[1]}^{[47]}^{[48]}^{[49]}

As technology and patient expectation increases, one must continue to look to improve our own precision.

### Formulas

Holladay IOL consultant (HIC) program uses Holladay 2 formula and performs complex power calculation for the surgeon. It has various other new features, but it still not widely available. Oslens’s formula uses pre-operative refraction and lens thickness for increasing accuracy^{[49]}. The newer vergence-based formula, the Barrett II universal, utilized 5 variables and has greatly increased post cataract surgery refractive outcomes over older formulas. Additionally, the artificial intelligence powered formal Hill-RBF, shows great promise in optimizing refractive outcomes in the future.^{[50]}

### Software based: Okulix

A new biometric computer program to stimulate whole pseudophakic eye aims to reduce calculation error and ensure a more reliable estimation of IOL strength. This approach separates the errors due to measurement and those due to calculation, helping us in correcting them better^{[48]}. The Olsen and Okulix formulae utilize ray-tracing, which adds the benefit of accounting for aberrations throughout the visual system.

### Newer Machines:

The Pentacam and Orbscan have already been used widely for corneal ectasia, but are now beginning to be utilized for precise corneal power measurements^{[26]}.

Intraoperative aberrometry is now being used as a way to confirm and improve accuracy of IOL calculations. The Optiwave Refractive Analysis device (ORA by Alcon) is one example of this. It has been shown to be at least equal to more the more advanced Barrett and Hill-RBF formulas, but may have special use in complex cases such as post-refractive and toric IOLs.^{[51]}

### IOL with tolerance

It has been suggested that manufacturers reduce the internal – tolerance levels of IOLs to +/- 0.25D, thereby increasing accuracy. However, these parameters are not routinely provided by manufacturers to clinicians^{[49]}.

Many options are now available for references as well as direct IOL calculations. Some of these are listed below.

### Online options

### Offline Options

- ↑
^{1.0}^{1.1}^{1.2}Astbury N. and Ramamurthy B., How to avoid mistakes in biometry, Community Eye Health. 2006 Dec; 19(60): 70–71. - ↑ Fedorov SN, Kolinko AI, Kolinko AI. Estimation of optical power of the intraocular lens. Vestn Oftalmol 1967;80:27–31
- ↑ Hoffer KJ. The Hoffer Q formula: a comparison of theoretic and regression formulas. J Cataract Refract Surg 1993;19:700–12.
- ↑
^{4.0}^{4.1}^{4.2}Sahin A, Hamrah P. Clinically relevant biometry. Curr Opin Ophthalmol. 2012;23:47–53. doi: 10.1097/ICU.0b013e32834cd63e. - ↑
^{5.0}^{5.1}^{5.2}^{5.3}^{5.4}Frank W. Howes, Patient Workup for Cataract Surgery: Chapter 5.3, Ophthalmology, 4th Edition | Myron Yanoff, Jay Duker - ↑
^{6.0}^{6.1}Holladay JT. Standardizing constants for ultrasonic biometry, keratometry, and intraocular lens power calculations. J Cataract Refract Surg. 1997;23(9):1356-1370 - ↑
^{7.0}^{7.1}^{7.2}^{7.3}^{7.4}A. K. Khurana, Intraocular Lenses: Optical aspects and Power calculation: Chapter 9, Theory and Practice of Optics and Refraction, 2nd edition A. K. Khurana - ↑ Hoffer KJ. The Hoffer Q formula: a comparison of theoretic and regression formulas. J Cataract Refract Surg 1993;19:700–12.
- ↑ Olsen T, Corydon L, Gimbel H. Intraocular lens power calculation with an improved anterior chamber depth prediction algorithm. J Cataract Refract Surg 1995;21:313–9.
- ↑ Hoffer KJ. Modern TOL power calculations: Avoiding error and planning for special circumstances. Focal Points: Clinical Modules for Ophthalmologists. San Francisco: American AcademyofOphthalmology; 1999, module 12
- ↑ Haigis 'vv. The Haigis formula. Intraocular Lens Power Calculations. Shammas H], ed. Thorofare, NJ: Slack Inc; 2003:chap 5, pp 41-57
- ↑ Lowe RF, Clark BA. Posterior corneal curvature. Br J Ophthalmol 1973;57:464–70.
- ↑ Montés-Micó R, Carones F, Buttacchio A, et al. Comparison of Immersion Ultrasound, Partial Coherence Interferometry, and Low Coherence Reflectometry for Ocular Biometry in Cataract Patients. Journal of Refractive Surgery. 2011:1–7.
- ↑ Bhardwaj V, Rajeshbhai GP. Axial Length, Anterior Chamber Depth-A Study in Different Age Groups and Refractive Errors. Journal of Clinical And Diagnostic Research. 2013;7(10):2211–12.
- ↑ Haigis W, Lege B, Miller N, et al. Comparison of immersion ultrasound biometry and partial coherence interferometry for intraocular lens calculation according to Haigis. Graefes Arch Clin Exp Ophthalmol 2000;238:765–73.
- ↑
^{16.0}^{16.1}Rajan MS, Keilhorn I, Bell JA. Partial coherence laser interferometry vs conventional ultrasound biometry in intraocular lens power calculations. Eye 2002; 16:552–6. - ↑ Posterior Iris Fixation of the Iris-Claw intra-ocular lens implantation through a scleral tunnel incision. Am J Ophthalmol 2007;144(4):586–91
- ↑ Fedorov SN, Galin MA, Linksz A. A calculation of the optical power of intraocular lenses. Invest Ophthalmol 1975;14:625–8.
- ↑ Haigis W. Pseudophakic correction factors for optical biometry. Graefes Arch Clin Exp Ophthalmol. 2001 Aug;239(8):589-98.
- ↑ Holladay JT, Praeger TC: Accurate ultrasonic biometry in pseudophakia. (letter) Am J Ophthalmol 1993; 115(4): 536 – 537
- ↑ van Balen AT, Koole FD. Lens implantation in children. Ophthalmic Pediatr Genet 1988;9:121–125.
- ↑ Dahan E, Drusedau MUH. Choice of lens and dioptric power in pediatric pseudophakia. J Cataract Refract Surg 1997;23(Suppl.):S618–S623.
- ↑ Dahan E, Drusedau MUH. Choice of lens and dioptric power in pediatric pseudophakia. J Cataract Refract Surg 1997; 23 :618–23.
- ↑ Wilson ME, Peterseim MW, Englert JA, et al. Pseudophakia and polypseudophakia in the first year of life. J AAPOS 2001;5:238–245.
- ↑ Byrne SF. A-scan axial eye length measurements. Mars Hill (NC): Grove Park Publishers; 1995.
- ↑
^{26.0}^{26.1}^{26.2}Thomas C. Prager, PhD, MPHa,*, David R. Hardten, MDb,c, Benjamin J. Fogal, OD : Enhancing Intraocular Lens Outcome Precision: An Evaluation of Axial Length Determinations, Keratometry, and IOL Formulas, Ophthalmol Clin N Am 19 (2006) 435–448 - ↑ Neal H. Atebara, MD; Penny A. Asbell, MD; Dimitri T. Azar, MD; Forrest j. Ellis, Intraocular Lenses, Chapter 6. Clinical Optics, BCSC AAO 2011-2012
- ↑ Holladay JT. IOL calculations following RK. J Refract Corneal Surg 1989;5:203.
- ↑
^{29.0}^{29.1}Haigis W. Corneal power after refractive surgery for myopia: contact lens method. J Cataract Refract Surg 2003;29:1397–411. - ↑ Hamilton DR, Hardten DR. Cataract surgery in patients with prior refractive surgery. Curr Opin Ophthalmol 2003;14:44–53.
- ↑ Olsen T. On the calculation of power from curvature of the cornea. Br J Ophthalmol 1986;70:152–4.
- ↑ Hamed AM, Wang L, Misra M, et al. A comparative analysis of five methods of determining corneal refractive power in eyes that have undergone myopic laser in situ keratomileusis. Ophthalmology 2002; 109:651–8.
- ↑ Latkany RA, Chokshi AR, Speaker MG, et al. Intraocular lens calculations after refractive surgery. J Cataract Refract Surg 2005;31:562–70.
- ↑ Wang L, Booth MA, Koch DD. Comparison of intraocular lens power calculation methods in eyes that have undergone laser-assisted in-situ keratomileusis. Trans Am Ophthalmol Soc 2004;102:189–96 [discussion: 196–7]
- ↑ Hoffer KJ. Clinical results using the Holladay 2 intraocular lens power formula. J Cataract Refract Surg 2000;26:1233–7.
- ↑ Aramberri J. Intraocular lens power calculation after corneal refractive surgery: double-K method. J Cataract Refract Surg 2003;29:2063–8.
- ↑ Camellin M, Calossi A. A new formula for intraocular lens power calculaton after refractive corneal surgery. J Refract Surg 2006;22:187–99.
- ↑ Rosa N, Iura A, Romano M, et al. Correlation between automated and subjective refraction before and after photorefractive keratectomy. J Refract Surg 2002;18:449–53
- ↑ Rosa N, Capasso L, Lanza M, et al. Reliability of a new correcting factor in calculating intraocular lens power after refractive corneal surgery. J Cataract Refract Surg 2005;31:1020–4.
- ↑ Boscia F, La Tegola MG, Alessio G, et al. Accurac of Orbscan optical pachymetry in corneas with haze. J Cataract Refract Surg 2002;28:253–8.
- ↑ Prisant O, Calderon N, Chastang P, et al. Reliability of pachymetric measurements using Orbscan after excimer refractive surgery. Ophthalmology 2003; 110:511–5.
- ↑ Srivannaboon S, Reinstein DZ, Sutton HF, et al. Accuracy of Orbscan total optical power maps in detecting refractive change after myopic laser in situ keratomileusis. J Cataract Refract Surg 1999; 25:1596–9.
- ↑ Geggel HS.lntraocular lens implantation after penetrating keratoplasty. Improved unaided visual acuity, astigmatism, and safety in patients with combined corneal disease and cataract. Ophthalmology. t990;97(11): t460- 1467.
- ↑ Hoffer KJ. Triple procedure for intraocular lens exchange. Arch Ophtha/rnol. 1987; 105(5): 609- 610.
- ↑ Findl O , Menapace R. Piggyback intraocular lenses [letter].JCataract Refract SLlrg. 2000;26(3): 308~30 9.
- ↑ Findl O , Menapace R, Rainer G, Georgopoulos M. Contact zone of piggyback acryliCintraocular lenses. , Cataract Refract Surg. 1999;25(6):860- 862.
- ↑
^{47.0}^{47.1}Norrby S. Sources of error in intraocular lens power calculation. J Cataract Refract Surg 2008; 34: 368–376. - ↑
^{48.0}^{48.1}^{48.2}Dr. Rajesh Kapoor, Dr. Ajay Dudani, Dr.Vinod Goyel, HIGH PRECISION BIOMETRY: Avoiding surprises in Cataract surgery ; Journal of the Bombay Ophthalmologists’ Association : Jan - Mar 2002 Vol. 12 No. 1. - ↑
^{49.0}^{49.1}^{49.2}R Sheard, Optimising biometry for cataract surgery, Cambridge Ophthalmological Symposium, Eye (2014) 28, 118–125 - ↑Hill WE, Abuladia A, Wang L, Koch DD. Pursuing perfection in IOL calculations. II. Measurement foibles: Measurment errors, validation criteria, IOL constants, and lane length. K Cataract Refractive Surgery 2017:43;7;869-70.
- ↑Raufi N, Charlene J, Anthony K, Vann R. Intraoperative aberrometry vs modern preoperative formulas in predicting intraocular lens power. JCRS. PAP (Accepted March 11.2020).

- 9 Binkhorst RD. Intraocular lens power calculation manual. A guide to the author’s TI 58/59 IOL power module. 2nd ed. New York: Richard D Binkhorst; 1981.
- 10 Ram J, Pandav SS, Ram B, et al. Systemic disorders in age related cataract patients. Int Ophthalmol 1994;18:121–5.
- 32 Ianchulev T, Salz J, Hoffer K, et al. Intraoperative optical refractive biometry for intraocular lens power estimation without axial length and keratometry measurements. J Cataract Refract Surg 2005;31: 1530–6.

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