The current study demonstrated that the TCRP and EKR could potentially reflect the cornea power change after hyperopic SMILE.
The study found that all cornea power underestimated the CHM. The good predictor with minimum error was PR 4.0 mm (− 0.14 ± 1.03 D), followed by PR 3.0 mm (− 0.21 ± 0.99 D), EKR 4.5 mm (− 0.21 ± 1.02 D) and Km (− 0.28 ± 0.81D). It was reasonable that Km showed the highest correlation and narrowest LOA. Because in current study CHM was calculated based on Km. Km was one traditional keratometry calculating by thin-lens formula. It is equivalent to the simulated K of traditional corneal topographers, which was proved to be an accurate method to predict cornea power . Our results demonstrated Km can be alternative of CHM after hyperopic SMILE.
Both EKR 4.0 mm and EKR 4.5 mm showed no difference with CHM, though the LOAs were relatively wide. The EKR was the same value measured by standard keratometry on the front surface, but considering the effect of the back surface power difference from normal. Holladay et al. found the optimal zone was EKR 4.5 mm in determining the IOL power. Compared with CHM, the average error was − 0.06 ± 0.56 D with range being − 1.63 to ±1.34 D . In myopic LASIK, Alex et al.  demonstrated EKR 4.0 mm was the closest agreement with CHM. In myopic SMILE, Pan et al.  found EKR 4.0 mm and 4.5 mm showed no difference with CHM. The present study added the evidence of EKR after hyperopic SMILE.
In TCRP calculation, center location had no effect on TCRP values. Though hyperopia usually owes a higher kappa angle, our results were in agreement with previous studies [7, 9]. One reason was probably small sample size which lacks representation. Another interfering factor is pupil center may change with pupil size. Further studies in a larger population are warranted to explore this topic.
Among four methods, we found values at diameter 3.0 to 4.0 mm showed relative higher agreement. Previous studies have compared different curvature calculation methods, such as sim K, true net power and TCRP. All of them have come to the conclusion that TCRP is more suitable for actual refractive changes than only analyzing the axial refractive power of corneal surface [12, 14]. In hyperopic LASIK [14, 15], the TCRP 4.0 mm/5.0 mm zone calculation was proved to best predicted the surgically induced change in manifest refraction. Though their comparison standard is sphere equivalent change, not CHM in present study. Besides, the ablation method of LASIK is different from SMILE. The LASIK uses excimer laser ablates the peripheral cornea while retaining the central cornea (3 mm generally) unchanged, while the SMILE uses femtosecond laser to create complete stromal lens inside the corneal stroma, so the changes of corneal curvature should be different. This study takes the lead in analyzing the curvature changes of hyperopic SMILE, which may be of guiding significance for its clinical application and exploration.
Correlation analysis showed that preoperative corneal thickness affected the accuracy of TCRP in evaluating cornea power. The thinner the corneal thickness, the more likely TCRP underestimated the cornea power. The relationship between corneal thickness and corneal curvature is controversial. Some scholars believe that there is no correlation between corneal thickness and refraction and corneal curvature , while others hold the opposite opinion . In addition, the accuracy of calculation may also be related to corrected refraction level, cornea aberration and other factors [25, 26]. Therefore, the inclusion of larger samples and more reference factors in the future is of great value to the accuracy of prediction.
One of the limitations is that the sample size is small and the influencing factors are not comprehensive enough, so the application of the results is limited, including the correlation with CHM may altered several years later. It should not be ignored that hyperopia SMILE has a relatively long recovery period, so longer-term postoperative corneal topography and curvature changes are still very valuable, and more factors should be considered, such as epithelial thickness, corneal aberration, etc. The above points can be continuations of present study in the future.