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Today's Practice | May 2012

The BESSt and BMR-BHR Formulas

These formulas are useful for eyes that have previously undergone myopic or hyperopic laser treatments.

Using standard keratometry and raw data taken from corneal topography to calculate refractive corneal power in postrefractive surgery eyes can result in an inaccurate representation of the true corneal power. In these cases, instead of using a pseudophakic IOL power calculation that incorporates preoperative data, which can result in refractive surprises, I prefer to use direct corneal measurements.

I use two approaches to calculate IOL power following laser refractive surgery, the first of which, the Borasio Edmondo Smith and Stevens formulas (BESSt and BESSt 2), is based on direct anterior and posterior corneal surface measurements and requires the Pentacam (Oculus Optikgeräte GmbH).1 The second approach, the more recently developed Borasio Myopic Regression and Borasio Hyperopic Regression (BMR-BHR) formula, requires direct measurements from the IOLMaster (Carl Zeiss Meditec). These formulas can be used for eyes that have previously undergone myopic or hyperopic excimer laser treatments, even if there is a lack of prerefractive surgery information.


Based on direct anterior and posterior corneal curvature and corneal thickness measurements using the Pentacam and a modified Gaussian optics formula, the BESSt algorithm estimates corneal power in eyes after laser refractive surgery for myopia or hyperopia. It is not possible to use values obtained from the Gaussian optics formula in most current IOL power formulas because they are calibrated using a standard keratometric index of 1.3375, which does not take true posterior corneal curvature into account. This can therefore yield inaccurate results, especially in postrefractive surgery eyes where the relationship between the anterior and posterior corneal radii is no longer constant. BESSt starts from the true net corneal power as calculated with the Gaussian optics formula, but then it makes crucial adjustments based on the actual measured postoperative corneal radii and the altered anterior/posterior radius relationship.

We have found that the BESSt 2, a second iteration of the formula, results in greater prediction accuracy and less risk of refractive surprise after hyperopic treatments (unpublished data). BESSt 2 incorporates the following improvements compared with its predecessor: (1) automatic prediction of the preoperative anterior corneal radius from postoperative posterior corneal radius measurement, thus allowing automatic application of Aramberri’s double-K adjustment for a more accurate prediction of the estimated IOL position, (2) two separate algorithms based on the results of regression analyses, one for myopic and one for hyperopic treatments, (3) automatic application of the BESSt 2-derived corneal power to a modified third-generation formula for the purpose of IOL power calculation, and (4) an error-limitation algorithm to prevent serious errors in eyes with extreme axial lengths.


The latest formulas I have developed for postrefractive surgery eyes, the BMR and BHR, require the use of the IOLMaster to measure K values and axial length.2-4 From the measured postrefractive surgery K value, a new corneal power value is obtained by using one of these regression formulas. The resulting corneal power values are then automatically entered into the SRK/T formula, yielding a suggested IOL power.

The BMR-BHR formulas are based on linear, logarithmic, and polynomial regression analyses and give similar results in most cases, with no greater than 0.25 D difference between the analyses with the exception of eyes with very steep or very flat corneas, where differences can be more substantial. Further studies are needed to determine which formula is the most accurate, but I tend to use linear regression. Polynomial regression has a smaller error in the majority of cases, but it can also have more serious outliers than linear regression; logarithmic regression lies in between the other two. It is best to use polynomial regression only when the suggested IOL power value is neither too low nor too high. BMR-BHR is currently available only as part of Eye Pro 2012 for the iPhone/iPad. A desktop version will soon be available as an upgrade to the BESSt 2 IOL Power Calculator.


The same considerations apply to the BESSt, BESSt 2, and BMR-BHR formulas; they should not be used in the presence of significant corneal haze or scarring or after incisional refractive surgery such as radial keratotomy. Additionally, these formulas should be used with caution in eyes that have undergone astigmatic keratotomy; in eyes that have previously undergone myopic or hyperopic treatments for severe refractive errors; or in eyes that were operated on a long time ago using small optical zones. Other considerations include the following:

• The BMR-BHR requires K values specifically measured by the IOLMaster;
• I recommended comparing BESSt 2 with BMRBHR. If the BESSt 2 formula suggests a very low (or very high) IOL power, I either use the BMR-BHR formula instead or the average of the two. It is always advisable to compare with other methods before proceeding with surgery. Whenever in the doubt, opt for a stronger IOL to target myopia;
• Be suspicious of very low or very high IOL powers resulting from BMR-BHR or BESSt in eyes with very steep or very flat corneas. These cases are at the extreme edges of any regression analysis, and the risk of a refractive surprise is high; and
• The BESSt 2 and the Eye Pro have not been approved by the US Food and Drug Administration (FDA) or received the Conformiteé Europeénne (CE) Mark.

I recently conducted a study in 62 eyes, of which 38 received a myopic treatment and 24 a hyperopic, to compare the accuracy of the BESSt, BESSt 2, and BMRBHR formulas. In the myopic group, BESSt and BESSt 2 performed similarly (mean error, -0.21 ±0.78 D and -0.02 ±0.81 D, respectively; P>.05), but in the hyperopic group BESSt 2 performed statistically significantly better (-1.10 ±0.90 D and 0.02 ±1.00 D, respectively; P<.05). The proportion of eyes within ±0.50 D of the intended target changed negligibly (from 37% to 38%) in the myopic group but improved significantly (from 13% to 38%) in the hyperopic group. The proportion of eyes within ±1.00 D of the target changed from 73% to 76% in the myopic group and from 38% to 75% in the hyperopic group.

Comparing the results with BESSt 2 to those with BMR and BHR, in the myopic group, the mean error was -0.02 ±0.81 D with BESSt 2 and 0.00 ±0.75 D with BMR (P>.05). In the hyperopic group, the mean error was 0.02 ±1.00 D for BESSt 2 and 0.01 ±0.75 D for BHR (P>.05). Although these differences were not statistically significant, 31% more eyes were ±0.50 D or less from the target refraction with BMR compared with BESSt 1 and 30% more compared with BESSt 2. Similarly, with BHR 50% more eyes were ±0.50 D or less from the target compared with BESSt 1 and 13% more compared with BESSt 2. We believe this represents an improvement.


The BESSt 2 IOL Power Calculator (EB Eye Ltd, UK; besstformula.com) is available as an optional software add-on for the Pentacam. The main advantage of this calculator is that it can be installed on the same computer as the Pentacam. Therefore, calculations can be done directly from the Pentacam program by clicking on the BESSt 2 button, which will export all the required data (anterior and posterior corneal curvature and central pachymetry) to the program for the calculations. The program also keeps a database of calculations for future reference and for recalculation. A standalone version for research purposes is also available and can be used on a laptop not physically connected to the Pentacam hardware.

Another feature of the BESSt 2 IOL Power Calculator for PC is real-time IOL power plotting to show the behavior of different biometry formulas when parameters are modified for any given axial length. This allows immediate identification of potential biometry artifacts that affect any given formula. Examples include the SRK/T negative square root and cusp phenomena that occur for certain combinations of axial length and K values (most frequently for steep corneas). When not identified, these artifacts can lead to inaccurate IOL power calculations.

The BESSt IOL Power Calculator also allows the practitioner to compare the results with the historical method— with or without the double-K adjustment, and using refractions at the spectacle or at the corneal plane—for eyes for which prerefractive surgery information is available.

A video presentation on BESSt and BMR-BHR is available at eyetube.net/?v=fireb.


A mobile version of the program, Eye Pro 2012 (Figure 1), is more suited for quick calculations. It includes not only BESSt 2 and BMR-BHR algorithms but also many other functions such as standard biometry and surgically induced astigmatism calculations. Our smartphone application (app) is a suite of ophthalmic calculators that includes the following advanced functions:

• Standard biometry (SRK/T, Hoffer Q formulas);
• BESSt 1 combined with third-generation formulas with double-K adjustment for biometry after refractive surgery;
• Toric IOL calculator that also accounts for surgically induced astigmatism (SIA);
• SIA calculator for K values or refractions;
• SIA plotter for group analysis showing both the vector and the arithmetic means;
• Visual acuity converter between Snellen/decimal/ logMAR notation;
• Refraction converter between corneal/spectacle plane;
• Astigmatism converter between cartesian/polar notation; and
Optical formulas including thin lens equation, Gaussian optics formula, and calculations using customized keratometric refractive indexes.

Eye Pro 2012 is available for the iPhone and iOScompatible devices and can be downloaded directly from the Apple store. A free trial version, Eye Pro Lite, is available at the Apple store and shows all the functions available in the 2012 version.

Edmondo Borasio, MD, MedCBQ Ophth, FEBO, is a Corneal Specialist and Consultant Ophthalmic Surgeon at Moorfields Eye Hospital Dubai. Dr. Borasio states that he is owner of and shareholder in EB Eye, Ltd. He may be reached at e-mail: dr@edmondoborasio.com.

  1. Borasio E, Stevens J, Smith GT. Estimation of true corneal power after keratorefractive surgery in eyes requiring cataract surgery: BESSt formula. J Cataract Refract Surg. 2006;32(12):2004-2014.
  2. Borasio E. BESSt and beyond: The Borasio regression. Paper presented at the: 6th IOL Power Club Meeting; September 2010; Venice, Italy.
  3. Borasio E. IOL power calculation accuracy in post-myopic and hyperopic ablations using the Borasio Regression formula. Paper presented at: the American Society of Cataract and Refractive Surgery Annual Meeting; March 2011; San Diego.
  4. Borasio E. Post-LASIK IOL power calculation with Pentacam without pre-refractive surgery information. Paper presented at: the World Ophthalmology Congress; June 2010; Berlin.