Background
Delicate-tuned refractive outcome is essential to all patients with pre-existing corneal astigmatism for toric intraocular lens (IOL) implantation. Several factors can contribute to residual refractive astigmatism error, including surgical induced corneal astigmatism (SICA), errors in toric IOL alignment, and methodologic error in predicting the toricity of IOL power [
1]. Notably, most calculations for corneal astigmatism are based on anterior keratometry which can cause predictable error in both with-the-rule (WTR) and against-the-rule (ATR) astigmatism presumably due to the neglect of posterior astigmatism. A previous study has demostrated that posterior corneal astigmatism must not be neglected in predicting residual refractive astigmatism in toric intraocular lens implantation, because posterior corneal surface has significant influence on total corneal astigmatism [
2,
3].
Unfortunately, current keratometry or corneal topography does not appear to reflect the true corneal astigmatism perfectly. To overcome this disadvantage, several solutions have been proposed. The Baylor nomogram and Barret toric calculation considering predicting values of posterior corneal astigmatism have been suggested [
4,
5]. The new Schiempflug imaging devices including Pentacam and Galilei can allow us to obtain the keratometry (K) value of posterior corneal surface and calculate the true power of corneal astigmatism by combining the anterior corneal surface power using the net summation or ray tracing assay. With the Galilei system, Koch et al. have demonstrated that its ATR was successfully corrected, while there are still rooms for improvements for WTR [
4]. Nevertheless, these vigorous attempts to predict accurate corneal astigmatism do not always guarantee a fine refractive outcome for toric IOL implantation. Therefore, the objective of this study was to evaluate and compare the astigmatism prediction errors taken with the Pentacam measurements, Baylor nomogram, and Barrett formula for toric IOL implantation.
Discussion
It is well known that the utilization of conventional keratometric device regarding only anterior corneal surface can result in a significant residual astigmatism error for the determination of toric IOL cylinder. Overcorrection can occur in WTR astigmatism, while undercorrection can occur in ATR astigmatism [
4,
13,
14]. In this study, negative value (WTR eyes; overcorrection, ATR eyes; undercorrection) of WTR/ATR prediction error was also found in conventional keratometry, IOLMaster. This error could be mainly attributed to a concealed posterior astigmatism mostly aligning along the vertical steep axis which cannot be measured in conventional keratometry [
4,
13]. To overcome this pitfalls, the Baylor nomogram and Barrett toric calculator were introduced to adjust toric IOL power to account for posterior corneal astigmatism by regression analysis and theoretical model, respectively [
4,
5]. To measure the actual corneal astigmatism, Pentacam and Galilei are the alternative devices using Schiempflug imaging that takes posterior corneal surface into account [
8,
15]. However, a measurement of true corneal astigmatism for toric IOL selection is still controversial since the Baylor nomogram and Barrett toric calculator do not reflect the actual posterior astigmatism, and the usefulness of Schiempflug imaging devices is not universally validated for toric IOL implantation. To solve the current issues for toric IOL implantation, we investigated and compared the accuracy of astigmatism measurements derived from diverse modalties, including anterior surface-based modality (IOLMaster and SimK), adjusted modality (Baylor-IOLMaster, Baylor-SimK, Barrett-IOLMaster, and Barrett-SimK), and both surface-based modality (wavefront, TNP, TCP, and vector).
Similar to previous clinical outcomes in Pentacam measurements for toric IOL implantation [
5,
16], wavefront, TNP, TCP, and vector were superior to IOLMaster and SimK in terms of prediction error or ICC. Among them, vector was the best way to predict corneal astigmatism for toric IOL selection by showing minimum prediction error with substantial agreement with the estimated preoperative corneal astigmatism values for both WTR and ATR eyes.
With a careful subgroup analysis in prediction error, significant WTR/ATR prediction errors were found in the IOLMaster, SimK, Baylor-IOLMaster, Barrett-IOLMaster of WTR eyes and Baylor-SimK of ATR eyes at two time periods (postoperative 1- and 3-month) but no significant error in the majority of both surface-based modalities (except wavefront in WTR eyes). Notably, a rare prediction error of vector was observed in both WTR and ATR eyes. In contrast, Koch et al. [
4] have reported significant negative values of WTR/ATR prediction errors (overcorrection in WTR eyes and undercorrection in ATR eyes) in all keratometries or topographic devices except an adequate correction in ATR astigmatism (but not in WTR astigmatism) using the Galilei Placido-dual Schiempflug analyzer [
4]. The following two possible reasons might explain such difference in astigmatism correction between the two studies. First, the adjustment of SICA for the estimation of preoperative corneal astigmatism used in the current study might have influenced the non-significant difference to the zero diopter of the WTR/ATR prediction error. This was not performed in the other study [
4]. Second, the disparity of correction in WTR astigmatism between Pentacam and Galilei might have attributed to the measurement difference between the two devices. In the study of Koch’s et al. [
4], the prediction errors of WTR eyes between anterior keratometry (−0.47 to −0.60 D) and Galillei (−0.57 D) were similar to each other. Therefore, underestimation of posterior K value in Gailei cannot be rejected. However, in the current study, different ranges of the mean WTR/ATR prediction errors between IOLMaster (−0.33 to −0.42 D), SimK (−0.46 to −0.56 D), and vector (−0.03 to 0.06 D) were found, probably reflecting the influence of mean posterior corneal astigmatism (0.56 D) on vector of WTR eyes.
To further analyze the accuracy of Pentacam measurements for toric IOL implantation, we accessed their ICC with estimated corneal astigmatism. ICC is a useful tool in assessing both consistency and agreement in evaluation of measurement error [
17]. In this study, we found excellent agreement (WTR/ATR ICC > 0.8) for SimK, Baylor-SimK, Barrett-SimK, wavefront, and vector on WTR eyes and substantial agreement (WTR/ATR ICC > 0.6) for wavefront and vector on ATR eyes. Among the ten modalities, only vector showed lesser mean prediction error than the minimum allowed astigmatism value (0.3 D) [
12] simultaneously with substantial agreement index (both WTR/ATR and oblique ICC > 0.6) on both WTR and ATR eyes. Although the mean WTR/ATR prediction errors in both TNP and TCP were close to zero diopter, the WTR/ATR ICCs of them (0.61 ~ 0.70 in WTR eyes, 0.47 ~ 0.67 in ATR eyes) were significantly lower than those of vector (0.90 ~ 0.94 in WTR eyes, 0.74 in ATR eyes), implying the superiority of vector for predicting preoperative corneal astigmatism.
Intriguingly, rather lower values of vector in both WTR/ATR and oblique ICC for ATR eyes than that for WTR eyes was found, indicating the lesser reliability of vector for toric selection of ATR eyes. This complicated result is supported by a previous study showing that ATR eyes have larger estimation errors in astigmatism magnitude than WTR eyes [
18]. The greater amount of SICA in ATR eyes than that in WTR eyes and the potential measurement error of posterior K from Pentacam, especially in ATR eyes, might have contributed to the lower ICC of vector in ATR eyes. It has been acknowledged that the greater SICA is associated with older age [
19], and lower corneal hysteresis and resistance factor [
20]. The discrepancy between the assumed and substantial SICA appears to be inevitable. Larger samples are needed to prove these possibilities.
It has been suggested that the centroid errors in prediction error when using Pentacam measurements are lower for toric IOL selection compared to conventional keratometry measurements [
5,
16]. Similarly, this study revealed that there was minimal WTR/ATR prediction error when using TNP, TCP, and vector derived from Pentacam. On the other hand, the WTR/ATR ICCs for both TNP (0.56 ~ 0.70) and TCP (0.47 ~ 0.69) were significantly lower than that of vector (0.74 ~ 0.94). TNP is calculated by adding sagittal curvature values of the anterior and posterior corneal planes while TCP reflects both the exact light path and the corneal surface curvature [
16]. Both TNP and TCP do not appear to be appropriate for the determination of true corneal astigmatism. The reason why TNP and TCP were unpredictable for toric IOL selection in this study remains unclear. However, a previous study has reported the concern about the accuracy of TNP for predicting postoperative astigmatism after cataract surgery [
21]. The usefulness of TNP and TCP for toric IOL implantation should be further validated.
Interestingly, the application of Baylor nomogram and Barrett formula in our study yielded WTR residual refractive astigmatism (undercorrection in WTR eyes and overcorrection in ATR eyes), which is opposite to the outcome of ATR residual refractive astigmatism when using the anterior surface-based modalities. A similar result was revealed in a previous study comparing anterior keratometry (OLCR device) and Baylor nomogram [
16]. The Baylor nomogram and Barrett toric calculation provide an adjusted corneal reflecting a predicted posterior astigmatism based on anterior keratometry, ACD, or axial length [
4,
7]. Although leaving WTR refractive astigmatism would be helpful due to the anticipated ATR shift in most eyes [
4], the adjustment of posterior corneal astigmatism based on regression analysis (Baylor nomogram) or theoretical formula (Barrett toric calculation) appears to be overcompensated caused by a methodologic error itself.
Despite our vigorous effort to decrease the error in estimating preoperative corneal astigmatism, there are some pitfalls to predict the estimated preoperative corneal astigmatism. IOL tilt might have contributed to rest prediction error [
22]. Although the significant IOL tilt was not found from this study, the possibility of subtle IOL tilt could be associated with the remnant prediction error [
23].
ACD and effective lens position (ELP) were not considered when selecting the IOL toricity in our study. Precise preoperative ACD measurement ACD or ELP estimation is needed to to predict IOL corneal plane cylinder power [
24]. Eom has announced the influence of ELP with adjustment of AcrySof toric cylinder power up to 0.2 D [
25]. Further study is required to involve the effect of ACD or ELP.