

REVIEW ARTICLE 

Year : 2017  Volume
: 65
 Issue : 12  Page : 12891293 

Intraocular lens calculations in atypical eyes
Aazim A Siddiqui^{1}, Uday Devgan^{2}
^{1} Wilmer Eye Institute, Johns Hopkins Medical Institutions, Baltimore, Maryland, USA ^{2} UCLA School of Medicine, Jules Stein Eye Institute, Los Angeles, CA, USA
Date of Submission  18Sep2017 
Date of Acceptance  09Nov2017 
Date of Web Publication  5Dec2017 
Correspondence Address: Dr. Uday Devgan 11600 Wilshire Blvd, Suite 200, Los Angeles, CA 90025 USA
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/ijo.IJO_834_17
Cataract surgery is the most performed surgical procedure in the field of ophthalmology. The process of intraocular lens (IOL) calculations is a critical step to achieving successful outcomes. Many IOL formulae exist to guide surgeons through the difficult process of picking the most appropriate lens to achieve a certain target refraction. However, these formulae reach within 0.50 diopters of the target refraction only 75% of the time, leaving 25% of the eyes with a significant refractive surprise. A literature review was performed to investigate all the relevant published material on the history, progress, and recent advancements of IOL calculations. Based on this review, the appropriate history, evolution, progress, limitations, and recent advancements are analyzed and explained. Although the modern IOL formulae and biometric devices perform well for average eyes, they are suboptimal for eyes with atypical biometric parameters and also those that are postrefractive and keratoconic. There has not been a single, perfect formula that can resolve the complexities of this process. Various methods of formula optimization and newer generation of IOL formulae and devices may hold the key to improving outcomes in both typical and atypical eyes. These solutions minimize refractive error by introducing new input parameters and complex mathematical techniques to better estimate postoperative lens position. Keywords: Cataract surgery, cataract, ectasia intraocular lens calculations, intraocular lens calculations, intraocular lens formula, intraocular lens, keratoconus intraocular lens calculations, postrefractive intraocular lens calculations
How to cite this article: Siddiqui AA, Devgan U. Intraocular lens calculations in atypical eyes. Indian J Ophthalmol 2017;65:128993 
Cataract is the leading cause of worldwide blindness. It is responsible for 51% of blindness and a cause for bilateral loss of sight in >20 million individuals.^{[1]} As a result, cataract surgery with intraocular lens (IOL) implantation is the most commonly performed surgical procedure in the field of ophthalmology. The World Health Organization predicts an increase in the number of cataract surgeries performed yearly to 32 million by the year 2020.^{[2]} There are many factors that are involved in the presurgical preparation that can have an impact on patient outcome. One of the most critical of those is the process of IOL power calculations and the decisionmaking involved in picking the most appropriate IOL for a given patient.^{[3]}
The IOL is usually chosen to achieve a desired postoperative refractive target of emmetropia or slight myopia and to meet each patient's specific postoperative visual needs and desire.^{[4]} This is where IOL calculation formulae hold an important place in the process to guide the surgeons in calculating the most accurate IOL power which corresponds to the desired target refraction. Even though the modern IOL calculation formulae and methodologies have come a long way since the early days, there is still a sizable portion of eyes that do not achieve the targeted postoperative refraction. Approximately 60% of eyes are >0.25 diopters and 25% of eyes are >0.50 diopters off from their intended target when calculated using the thirdgeneration IOL formulae.^{[5]} Despite the improved simplicity and accuracy of these formulae, these statistics highlight the inaccuracies that remain in this process.
Modern IOL formulae are sophisticated and relatively accurate in calculating IOL power values for average eyes. However, given the complex nature of the optical and anatomical variations that exist in certain eyes that fall on the extremes of keratometry and axial length, better outcomes are difficult to achieve. The reason for this difficulty is the limited ability of formulae to account for the various types of eyes that exist.
Further challenges are encountered in the process of IOL calculations when cataract surgery is to be performed on eyes with a history of refractive surgery. The standard IOL formulae and biometric devices are unable to account for the nuances of the altered postrefractive eyes and are thus limited in their ability to perform accurately. Finally, eyes with corneal ectasia, such as keratoconus, also prove difficult for the surgeon in attempting to calculate accurate IOL power values using traditional methods.
The purpose of this review is to highlight the limitations of modern IOL formulae and to provide various solutions that have been suggested in the literature to address these limitations.
Methods   
A literature review was performed to investigate all the relevant published material on the history, progress, and recent advancements of IOL calculations using the United States National Library of Medicine database with the following search terms in all languages: IOL formula, IOL calculations, Hoffer, Holladay I, Holladay I with Koch adjustment, SandersRetzlaffKraff (SRK)/T, Haigis, postrefractive IOL calculations, and IOL calculations in keratoconus. Based on this review, the appropriate history, evolution, progress, limitations, and recent advancements are presented.
Evolution of Intraocular Lens Formulae   
The modernday IOL formulae had a humble beginning when in 1949, Sir Harold Ridley pioneered the very first IOL and the lens implant surgery.^{[6]} Initially, these implantations resulted in enormous myopia; but eventually, the innovation spawned the field of IOL calculations to help minimize the refractive surprise. The earliest of IOL formulae were rudimentary and could only aim for emmetropia by simply accounting for the power of the natural lens. Subsequent formulae, however, were based on theoretical and regressionbased approaches that helped improve accuracy.^{[7]}
The original SRK formula was developed in the 1980s and is an example of a firstgeneration IOL formula.^{[8]} This formula was derived by performing regressionanalysis on a dataset of actual postoperative outcomes. Conceptually, it seemed an appropriate methodology, and the formula performed reasonably well for eyes that were of average parameters resembling those from the dataset used to create the formula. However, the formula was fairly inaccurate for eyes that fell on the extremes of axial length.
The need to improve results for extremely short and long eyes eventually gave rise to the secondgeneration of IOL formulae. The SRK II formula was an example of such a formula which was given the ability to vary with axial lengths.^{[9]} This was done by adding an axial lengthdependent “fudge factor” to the Aconstant value.
The late 1980s and early 1990s gave rise to the thirdgeneration of IOL formulae which included the Holladay I,^{[10]} SRK/T,^{[11]} and Hoffer Q formulae.^{[12]} These formulae were built with more robust and improved theoretical principles which took into account the geometric and optical characteristics of the eye. The key improvement, however, involved a better method of calculating the postoperative estimated lens position (ELP) by considering the corneal power as well as the axial length of the eye.^{[7]} These formulae performed with reasonable accuracy and had the simplicity to become part of clinical practice. With time, advanced and more complex fourthgeneration of IOL formulae were developed by Holladay (i.e., Holladay II formula), Barrett,^{[13]} Olsen, and Haigis.^{[14]} These formulae set themselves apart with their ability to incorporate additional variables in the ELP calculation such as axial length, corneal power, whitetowhite measurement, measured anterior chamber depth (ACD), lens thickness, and patient age.
Eyes With Atypical Parameters   
Limitations of intraocular lens formulae
The evolution of the IOL formulae has inched closer to more accurate results with the ultimate goal of successfully reaching a given target refraction 100% of the time. However, this is a difficult outcome to achieve given the limitations of the IOL formulae to accommodate for the variety of eyes that exist. Dr. Jack Holladay provided a classification of the nine types of “eyes” based on the size of the anterior segment and the axial length.^{[15]} As can be seen in [Table 1], only 73.4% of eyes in general are considered to belong to the category of “normal” axial length and anterior segment. The remainder of eyes can then fall into the categories of axial myopia, axial hyperopia, nanophthalmos, microcornea with or without axial myopia, buphthalmos, and megalocornea with and without axial hyperopia. It should be less surprising, then, that only 75% of the eyes reach within 0.50 diopters of target refraction.^{[5]} Such diversity of eyes requires a dynamic calculation methodology which will consider the specific biometric parameters of each eye to enhance outcomes.
The general principle behind every IOL formula is to calculate the vergence and predict the postoperative ELP. The greatest challenge for an IOL formula is the difficulty in predicting an accurate ELP given the wide spectrum of eyes that exist. The earlier generation of IOL formulae performed reasonably well for the vergence calculation, but the methods of ELP calculation were rudimentary. The first generation of IOL formulae considered the ELP to be a constant numeric value. Subsequent generations of more advanced theoretical and regression formulae began using more biometric data to calculate the ELP. The use of axial length, corneal power, measured ACD, and whitetowhite measurement further helped refine the accuracy of ELP prediction.^{[7]}
Potential solutions
The IOL calculation methodologies have steadily improved over the past few decades. The results of which significantly improved with the emergence of theoretical formulae such as Holladay I, SRK/T, and Hoffer Q.^{[10],[11],[12]} Despite the progress, there still exists substantial room for improvement in these formulae. There is no one single, perfect formula. Indeed, when you compare just two of the modern IOL formulae (Holladay I and SRK/T) over the entire range of axial length and corneal power, there are large areas of clinical disparity of >0.50 diopters between the two formulae notably in the atypical ranges of axial length and corneal power [Figure 1]. This emphasizes the disparate nature of modern IOL formulae and further explains the existence of a lack of a single solution.  Figure 1: The LadasSiddiqui Graph. A topographical comparison of two modern IOL formulae (Holladay I and SandersRetzlaffKraff/T). The green color highlights areas of clinical agreement where the two formulae differ from each other by ≤0.50 diopters. The red color highlights areas of clinical disparity where the two formulae differ from each other by >0.50 diopters.^{[18]}
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To best utilize the existing IOL formulae, certain modifications and “rules of thumb” have been devised. Based on peerreviewed literature, the ophthalmology community has come up with certain formulae that perform best for eyes that fall under a certain axial length range. In a study of >8000 eyes comparing the thirdgeneration Hoffer Q, Holladay I, and SRK/T formulae, the Hoffer Q formula was shown to have the lowest mean absolute error for eyes with axial length between 20.00 and 20.99 mm.^{[5]} Both Hoffer Q and Holladay I formulae shared the lowest mean absolute error value for axial length 21.00 to 21.49 mm. For axial length 27.00 mm and longer, the SRK/T formula was found to have the lowest mean absolute error. The Koch adjustment to the axial length in the Holladay I formula has also been shown to yield improved results.^{[16]}
Other methods of improving results of IOL formulae are based on the manufacturer's Aconstant modification and personalization as was seen with the SRK II formula. This methodology can be used to finetune modern IOL formulae based on postoperative outcomes. Indeed, a global group of experts – known as user group for laser interference biometry – have collaborated to create an optimized Aconstant library based on postoperative outcomes for many of the lenses available today.^{[17]}
The fourth generation of IOL formulae are theoretically an improvement over the thirdgeneration formulae and may perform better for all eyes. Holladay II, Haigis,^{[14]} Olsen, and Barrett are examples of such formulae.^{[13]} These require an increased number of variables in their calculation of IOL power. This helps improve not only the vergence calculation but also more importantly the ELP calculation. The Holladay II formula, for instance, calculates the ELP by leveraging the axial length, corneal power, whitetowhite measurement, measured ACD, lens thickness, and patient age. The Haigis formula requires the measured ACD value whereas the Barrett formula requires that in addition to lens thickness and whitetowhite measurement.
Studies have been published which compare the third and fourthgeneration IOL formulae. A study of >3000 eyes compared the Hoffer Q, Holladay I, Holladay II, SRK/T, Barrett, Haigis, and T2 (a variation of the SRK/T formula) formulae.^{[18]} It found that the Barrett formula was the bestperforming formula for axial lengths 22.00 mm and longer. All formulae tested performed similarly for eyes shorter than 22.00 mm.
A new wave of IOL formulae have recently emerged and are being recognized as the fifth generation of IOL formulae. One such example is the Hoffer H5 formula which is based on the fourthgeneration Holladay II and the thirdgeneration Hoffer Q formula. It offers a more personalized framework which can be closely customized to each patient with the addition of the gender and race variables. Like the fourthgeneration formulae, the Hoffer H5 formula may offer improved outcome for a wider spectrum of eyes as it takes into account the male gender's slightly longer eye with a flatter cornea and deeper ACD.
The latest development in IOL formulae revolves around harnessing more complex mathematical algorithms to help predict IOL power. An example of such an approach is the HillRadial basis function (RBF) formula which is purely a machinelearned formula based on a dataset of eyes. However, similar to the SRK I formula, the HillRBF formula is based on and thus limited to a certain dataset, lens type, and a single biometer. Another formula is the FullMonte method based on mathematical neural networks which rely on the Monte Carlo Markov Chain algorithm. The formula that may hold the promise of being a singular solution which may work for all eyes is the Ladas Super Formula.^{[19]} This formula is an amalgamation of multiple third and fourthgeneration IOL formulae. It combines the bestperforming portions of each of the modern IOL formulae. Future iterations of this formulae will rely on artificial intelligence to further hone its accuracy. A study of >3000 eyes compared these three new IOL formula methodologies (HillRBF, FullMonte method, and Ladas Super Formula) with Holladay I and Barrett formula.^{[20]} Although the study showed slightly better results for Holladay I and the Barrett formula, it concluded that of the three latest methods, the Ladas Super Formula resulted in the lowest mean absolute error and was the best overall performing formula for short axial lengths.
Intraocular Lens Calculations In Postrefractive Eyes   
Since the development of refractive surgery in the late 1980s and early 1990s, a significant portion of patients has had some form of a refractive procedure to improve their vision. Ironically, changes that occur to the cornea due to refractive surgery make the process of achieving similarly excellent outcomes with subsequent cataract surgery more difficult.
As most modern IOL formulae and biometric devices were developed before the advent of refractive surgery, they are appropriate for physiologic corneas but not for those that have undergone refractive surgery. Corneal flattening or steepening effects of myopic or hyperopic refractive surgery, respectively, result in inaccurate measurement and calculation of two main variables needed for modern IOL formulae calculation: corneal power and ELP.^{[21]}
Specifically, the changes to the anterior corneal surface by refractive surgery affect the refractive relationship between the anterior and posterior surface of the cornea.^{[21]} Thus, standard keratometers and topographers are unable to accurately estimate posterior corneal power and thus measure the true corneal power values for postrefractive eyes. Furthermore, changes to the anterior cornea also limit the ability of ELP calculation by traditional IOL formulae. With myopic surgery, as the cornea is flattened, a more forward lens position is predicted, which leads to calculation of an underpowered lens which results in more hyperopic refractive outcomes. With hyperopic surgery, as the cornea is steepened, a more backward lens position is predicted, which leads to calculation of an overpowered lens which results in more myopic refractive outcomes.^{[21],[22]}
Several solutions and devices [Table 2] have been developed to address the challenges of IOL calculations in postrefractive eyes. These can be categorized as those that require prerefractive “historical data” or not and further by those which require topographic measurements or not.
The current “gold standard” for IOL calculations in postrefractive eyes is the “clinical history” method which relies on the biometric and refractive data prior to the refractive surgery. Prerefractive corneal power, manifest refraction, and surgically induced refractive change in manifest refraction are used to estimate the postrefractive corneal power. However, extra precautions need to be taken to ensure that these data are accurate and acquired using calibrated instruments. Several methods have been described which use historical data with and without the use of topographic measurements to calculate IOL power. Approaches to IOL calculations in postrefractive eyes have also been described when biometric and refractive data before the refractive surgery are unavailable. These methods rely on algorithms which modify the postrefractive corneal power values to estimate the prerefractive corneal power values.
In addition, newer devices have also been introduced which attempt to measure the posterior corneal power directly in postrefractive eyes. These include the scanning slit topographers, Orbscan II (Bausch and Lomb, NY, USA) topographer, Oculus Pentacam Scheimpflug device (Oculus Inc., Wetzlar, Germany), and Galilei Dual Scheimpflug Analyzer (Ziemer Ophthalmic Systems, Port, Switzerland).
A number of various solutions exist for postrefractive IOL calculations for each given scenario and availability of data. There is a lack of large clinical studies which provide appropriate conclusions regarding the ideal solution in a particular postrefractive eye. One may use either the clinical history method or one of the “nonhistorical data” regression methods such as Shammas and HaigisL formulae based on the availability of a patient's stable and reliable prior refractive and biometric information. One may also choose methods which rely on adjusting postrefractive corneal power measured using standard keratometers and topographers in the absence of prerefractive data. A surgeon could also choose to use multiple methods and select the flattest or steepest keratometric values in the case of a postmyopic or posthyperopic eye, respectively. Patients must also be informed of the more challenging nature of their case and the possibility of a secondary procedure due to the higher likelihood of ametropia. Surgeons should also favor targeting myopia in most cases as the resulting unaided near vision would be useful to the patient and further corneal flattening for residual myopia is typically easier to perform than steepening of the already altered corneal tissue for residual hyperopia.
Intraocular Lens Calculations in Corneal Ectasia   
The progressive thinning and steepening of the cornea in corneal ectasia also pose a challenge for accurate IOL power calculations. Although the most common form of corneal ectasia is keratoconus, it can also occur secondary to certain refractive procedures. Specifically, the corneal power values vary significantly in a small area of the cornea due to corneal irregularities. Further, changes to the ACD due to corneal irregularities also affect the calculation of the ELP by IOL formulae.
The suboptimal measurements of axial length and corneal power values and calculation of ELP are the basis of IOL calculation inaccuracies in ectatic corneas. Traditional keratometers and topographers are unable to accurately measure corneal power values due to the highly irregular and steeper nature of an ectatic cornea with its offcentered apex. These eyes also have longer axial lengths and deeper anterior chambers. Inaccurate measurements of these values make it harder to estimate an accurate ELP.
Standard biometers, keratometers, and topographers are unable to accurately measure the true corneal power values of ectatic corneas. In nonectatic corneas, these devices measure the true corneal power by directly measuring the anterior corneal curvature and estimating the posterior corneal curvature. To best measure the true corneal power values in ectatic eyes, direct measurement of the anterior and posterior corneal powers is needed. Corneal topographers are the gold standard and should be used for acquiring true corneal power values in ectatic corneas. These devices are capable of directly measuring the corneal curvature of both the anterior and posterior cornea. This method avoids the need to make assumptions for posterior corneal power when calculating true corneal power. The most commonly used devices are the Pentacam and Galilei.
There is a paucity of large studies that have considered which IOL formulae perform best in eyes with keratoconus. Traditional IOL formulae and keratometers are unable to account for corneal irregularities that are found in an eye with corneal ectasia. Therefore, it is recommended to use modern topographers which directly measure the anterior and posterior corneal power in combination modern IOL formulae. Newer generation formulae such as the Barrett Universal II, Ladas Super Formula, and the HillRBF are promising, but larger studies in ectatic corneas are needed.
The surgeon should generally use the lowest corneal power values in the central pupil zone as measured by topographers to err on the side of postoperative residual myopia. In addition, surgeons should always inform their patients about the minimal risk of corneal decompensation and worsening of corneal health in the aftermath of cataract surgery. These patients also often require a more frequent postoperative followup than nonkeratoconic patients.
Conclusion   
An ophthalmologist's preoperative workflow is extensive when it comes to performing IOL calculations and picking the most appropriate lens for each patient. The process is generally a timeconsuming one which may involve a surgeon struggling through a thought process or many IOL formulae and picking the most appropriate formula to use. With so many formulae to pick from, the surgeon may easily become confused, overwhelmed, and make mistakes. Given this is an already difficult process, expectations these days are to reach a refraction that is within 0.50 diopters of the target. Although the modern IOL calculation solutions do well under certain circumstances, they are weak in others. This is largely due to the gaps in the modern IOL formulae and biometric devices to more accurately calculate eyes that are atypical, postrefractive, and ectatic. There has not been a single, perfect formula that can simplify this complex process. The potential solutions offered in this review work to minimize the complexity of this process by introducing new input parameters and rely on artificial intelligence to further hone in on a more accurate ELP estimation. Future studies will need to be conducted to compare some of the modern methodologies to provide a definitive answer as to which approach is the most ideal.
Financial support and sponsorship
Nil.
Conflicts of interest
There are no conflicts of interest.
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[Figure 1]
[Table 1], [Table 2]
