Citation: Savini G, Naeser K. An analysis of the factors influencing the residual refractive astigmatism after cataract surgery with toric intraocular lenses. Invest Ophthalmol Vis Sci. 2015;56:827-835. DOI:10.1167/ iovs.14-15903 PURPOSE. To investigate the influence of posterior corneal astigmatism, surgically-induced corneal astigmatism (SICA), intraocular lens (IOL) orientation, and effective lens position on the refractive outcome of toric IOLs.METHODS. Five models were prospectively investigated. Keratometric astigmatism and an intended SICA of 0.2 diopters (D) were entered into model 1. Total corneal astigmatism, measured by a rotating Scheimpflug camera, was used instead of keratometric astigmatism in model 2. The mean postoperative SICA, the actual postoperative IOL orientation, and the influence of the effective lens position were added, respectively, into models 3, 4, and 5. Astigmatic data were vectorially described by meridional and torsional powers. A set of equations was developed to describe the error in refractive astigmatism (ERA) as the difference between the postoperative refractive astigmatism and the target refractive astigmatism.RESULTS. We enrolled 40 consecutive eyes. In model 1, ERA calculations revealed significant cylinder overcorrection in with-the-rule (WTR) eyes (meridional power ¼ À0.59 6 0.34 D, P < 0.0001) and undercorrection in against-the-rule (ATR) eyes (0.32 6 0.42 D, P ¼ 0.01). When total corneal astigmatism was used instead of keratometric astigmatism (model 2), the ERA meridional power decreased in WTR (À0.13 6 0.42 D) and ATR (0.07 6 0.59 D) eyes, both values being not statistically significant. Models 3 to 5 did not lead to significant improvement.CONCLUSIONS. Posterior corneal astigmatism exerts the highest influence on the ERA after toric IOL implantation. Basing calculations on total corneal astigmatism rather than keratometric astigmatism improves the prediction of the residual refractive astigmatism.Keywords: astigmatism, toric IOL, mathematics, polar values T oric intraocular lenses (IOLs) are a common choice to correct corneal astigmatism at the time of cataract surgery. Several articles have shown good results, but the refractive outcome is not yet perfect.1-3 Over-or undercorrection of the cylinder may be related to the influence of several factors, including posterior corneal astigmatism. [3][4][5][6] To evaluate the optical results of surgery and the influence of each factor, we developed a set of equations describing the astigmatism along the steeper corneal meridian of each eye. For this purpose, we first performed a standard analysis based on keratometric astigmatism and a mean estimated surgicallyinduced corneal astigmatism (SICA). The influence of the remaining factors was assessed by progressively adding information related to posterior corneal astigmatism, actual SICA, IOL orientation, and the effective lens position (ELP) of the individual case. METHODSA sample of consecutive patients undergoing phacoemulsification and toric IOL implantation was p...

The aim of the thesis was to develop methods for assessment of surgically induced astigmatism (SIA) in individual eyes, and in groups of eyes. The thesis is based on 12 peer-reviewed publications, published over a period of 16 years. In these publications older and contemporary literature was reviewed(1). A new method (the polar system) for analysis of SIA was developed. Multivariate statistical analysis of refractive data was described(2-4). Clinical validation studies were performed. The description of a cylinder surface with polar values and differential geometry was compared. The main results were: refractive data in the form of sphere, cylinder and axis may define an individual patient or data set, but are unsuited for mathematical and statistical analyses(1). The polar value system converts net astigmatisms to orthonormal components in dioptric space. A polar value is the difference in meridional power between two orthogonal meridians(5,6). Any pair of polar values, separated by an arch of 45 degrees, characterizes a net astigmatism completely(7). The two polar values represent the net curvital and net torsional power over the chosen meridian(8). The spherical component is described by the spherical equivalent power. Several clinical studies demonstrated the efficiency of multivariate statistical analysis of refractive data(4,9-11). Polar values and formal differential geometry describe astigmatic surfaces with similar concepts and mathematical functions(8). Other contemporary methods, such as Long's power matrix, Holladay's and Alpins' methods, Zernike(12) and Fourier analyses(8), are correlated to the polar value system. In conclusion, analysis of SIA should be performed with polar values or other contemporary component systems. The study was supported by Statens Sundhedsvidenskabeligt Forskningsråd, Cykelhandler P. Th. Rasmussen og Hustrus Mindelegat, Hotelejer Carl Larsen og Hustru Nicoline Larsens Mindelegat, Landsforeningen til Vaern om Synet, Forskningsinitiativet for Arhus Amt, Alcon Denmark, and Desirée and Niels Ydes Fond.

Background/aimsTo compare the accuracy of 13 formulas for intraocular lens (IOL) power calculation in cataract surgery.MethodsIn this retrospective interventional case series, optical biometry measurements were entered into these formulas: Barrett Universal II (BUII) with and without anterior chamber depth (ACD) as a predictor, EVO 2.0 with and without ACD as a predictor, Haigis, Hoffer Q, Holladay 1, Holladay 2AL, Kane, Næser 2, Pearl-DGS, RBF 2.0, SRK/T, T2 and VRF. The mean prediction error (PE), median absolute error (MedAE), mean absolute error and percentage of eyes with a PE within ±0.25, ±0.50, ±0.75 and ±1.00 diopters (D) were calculated.ResultsTwo hundred consecutive eyes were enrolled. With all formulas, the mean PE was zero. The BUII with no ACD had the lowest standard deviation (±0.343 D), followed by the T2 (0.347 D), Kane (0.348 D), EVO 2.0 with no ACD (0.348 D) and BUII with ACD (0.353 D) formulas. The difference among the MedAEs of all formulas was statistically significant (p<0.0001); the lowest values were achieved with the Kane (0.214 D), RBF 2.0 (0.215 D), BUII with and without ACD (0.218 D) and SRK/T (0.223 D). A percentage ranging from 80% to 88.5% of eyes showed a PE within ±0.50 D and all formulas achieved more than 50% of eyes with a PE within ±0.25 D.ConclusionAll investigated formulas achieved good results; there was a tendency towards better outcomes with newer formulas. Traditional formulas can still be considered an accurate option.

Univariate and bivariate polar value analyses, together with the surgically induced change in spherical equivalent power, yield an exact description of surgically induced change following refractive procedures.