The BESSt Formula
The BESSt (Borasio Edmondo Smith and Stevens) formula allows pseudophakic IOL power calculation in postrefractive eyes without any prerefractive surgery data. This new formula appears to be significantly more accurate than a variety of techniques that calculate pseudophakic IOL power.
Based on an improved Gaussian optics formula for paraxial imagery, the BESSt formula estimates corneal power with anterior and posterior corneal radii measurements and corneal thickness. These measurements are obtained by scanning the cornea with a rotating scheimpflug camera anterior segment imaging system (Pentacam; Oculus Optikgeräte GmbH, Wetzlar, Germany). Edmondo Borasio, MedCBQ Ophth, FEBO, developed the BESSt formula in collaboration with Julian D. Stevens, MRCP, FRCS, FRCOphth, and colleagues. We used a dataset of approximately 150 myopic and hyperopic eyes that underwent wavefront-guided LASIK or LASEK for refractive errors ranging from -10.00 D to 4.50 D. We derived the BESSt formula by adjusting Gaussian optics formula variables—for closest fit with K-values calculated from the clinical history method—using regression analysis and other adjustments.
REFRACTIVE SURPRISES
Standard keratometry and raw data taken from corneal topography often provide inaccurate determinations of true refractive corneal power in postrefractive surgery eyes. When data from these techniques for pseudophakic IOL power calculation are used, refractive surprises may result.
Several methods have been described to improve the estimated keratometric power in postkeratorefractive surgery eyes. We believe, however, that the ideal method should be based on direct corneal measurements, without any need for preoperative information. More accurate measurement of the cornea's posterior radius of curvature is now possible using the Pentacam, theoretically allowing direct calculation of corneal power with the Gaussian optics formula. It should be mentioned that the sole use of this formula results in significant underestimation of corneal power (approximately 0.90 D). We took this into account when developing the BESSt formula.
We studied 13 eyes with a prior history of refractive surgery (ie, LASIK, PRK, Epi-LASIK, conductive keratoplasty) for myopia (SE, -2.89 D to -8.62 D) or hyperopia (SE, 1.15 D to 8.55 D) that subsequently underwent phacoemulsification. Target refractions calculated using the BESSt formula corneal power were compared with the actual postoperative manifest refractions. Results were compared with those calculated using the (1) clinical history method alone, (2) clinical history method with double-K adjustment, (3) Holladay 2 formula with K-values derived from either hard contact lens over-refraction or from modern corneal topography (Atlas; Carl Zeiss Meditec AG, Jena, Germany).
The mean difference between the target and achieved refraction was 0.08 ±0.62 D with the BESSt formula. Using the history technique, the mean difference from the actual postoperative refraction was -0.07 D, but the standard deviation was 1.92 D. For the other methods, the standard deviations were significantly greater (ie, range, ±1.36 D to ±2.39 D).
SIMILAR STANDARD DEVIATIONS
When K-values from the Atlas topographer were used, standard deviation of the mean prediction error was similar between the BESSt and Holladay 2 formulas (±0.62 D vs ±0.61 D, respectively). The mean difference from the target refraction, however, was statistically significantly larger using the Holladay 2 compared with the BESSt formula (-0.55 D vs 0.08 D, respectively). Overall, the standard deviation of the mean absolute difference from the target refraction was two- to fourfold smaller using the BESSt formula versus other methods. It was also half of the standard deviation of the Holladay 2 formula using the Atlas K-values (±0.26 D vs ±0.49 D, respectively). The Holladay 2 formula also requires refractive data as well as phakic anterior chamber depth, lens thickness, and white-to-white distance measurements, which are not always available.
Using the BESSt formula, 46% of eyes were within 0.50 D of intended postoperative refraction, 77% were within 0.75 D of target, and 100% were ±1.00 D. Using the Holladay 2 with the Atlas K-value, 54% of eyes were ±0.50 D of intended refraction, but only 62% were ±0.75 D, and only 69% were ±1.00 D. Between 31% and 62% of eyes would have been within 1.00 D of the target using the other methods.
POWER CALCULATION SOFTWARE
The BESSt formula is implemented in an advanced IOL power calculation software program (BESSt Corneal Power Calculator; EB Eye Ltd., London) (Figures 1 through 3). A trial version is available for download at www.besstformula.com. The program also has an algorithm to automatically detect when IOL power calculation is inaccurate due to the zero argument or cusp phenomena that may occur in certain situations using the SRK/T formula. These phenomena arise when the argument of the square root in the estimated anterior chamber depth equation of the SRK/T formula becomes negative due to particular combinations of axial length and K-values (Figure 4). These phenomena may occur in virgin corneas, but are more frequently seen in eyes with steep corneas (eg, after a penetrating corneal graft or hyperopic refractive surgery). The program will automatically identify those situations and advise to use alternative formulae to further minimize the risk of a refractive surprise.
The BESSt formula determines corneal power in postrefractive surgery eyes using anterior and posterior corneal radii obtained with the Pentacam and with no need for prerefractive surgery information. This formula appears to be an advance for significantly improving IOL power calculation accuracy in postrefractive surgery eyes.
Edmondo Borasio, MedCBQ Ophth, FEBO, is a Refractive Surgery Fellow at Moorfields Eye Hospital, in London. Dr. Borasio states that he is an owner or shareholder in EB Eye, Ltd. He may be reached at tel: +44 0 78 3030 2863; fax: +44 0 78 3009 4422; or edmondoborasio@gmail.com. Giovanni Racciu is Dr. Borasio's software engineer, and is located in Torino, Italy.
Guy T. Smith, FRCOphth, is Honorary Consultant Ophthalmic Surgeon, at Moorfields Eye Hospital, in London. Dr. Smith states that he does not have any financial interest in the products or companies mentioned.
Julian D. Stevens, MRCP, FRCS, FRCOphth, is Consultant Ophthalmic Surgeon, Director of Refractive Surgery, at Moorfields Eye Hospital, in London. Dr. Stevens is a member of the CRST Europe Editorial Board. He states that he has no financial interest in the products or companies mentioned. Dr. Stevens may be reached at JulianStevens@compuserve.com.
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