This study used the IOLMaster 700 to calculate ΔK and ΔTK for cataract patients with corneal astigmatism ≥ 0.75 D. The vector error between ΔK and ΔTK was analyzed using vector analysis, revealing a significant difference between ΔK and ΔTK. The difference was smaller in WTR astigmatism individuals, increased with higher ΔK magnitudes and age, and showed no correlation with gender, Km, or WTW. Multiple regression analysis confirmed that ΔK axis, ΔK magnitude, and age were independent influencing factors for the |ΔTK − ΔK|.

A study by Sharma et al. on 152 individuals and 213 eyes with cataracts showed that ΔTK was greater than ΔK after analysis with the IOLMaster 700 [13]. Similar to this study, the cataract population with corneal astigmatism ≥ 0.75 D showed ΔTK greater than ΔK when examined with the IOLMaster 700, with an arithmetic error absolute value of 0.19 D (0.12–0.27) and an absolute value of 0.24 D (0.18–0.32), indicating an axial difference. Another study by HO on a group with corneal astigmatism greater than 1.0 D using Pentacam showed an arithmetic error absolute value of 0.26 ± 0.17 D [14] for total corneal astigmatism compared with simulated corneal astigmatism considering only the anterior surface, similar to the results obtained with the IOLMaster 700 in the present study. However, Savini et al. [10] reported a negligible difference between the magnitude of keratometric astigmatism and that of total corneal astigmatism in the general population not undergoing corneal refractive surgery. One possible reason is that the inclusion standard was corneal astigmatism ≥ 0.50 D. As shown in this study, there was a significant difference between ΔK and ΔTK obtained by IOLMaster 700 in cataract cases with corneal astigmatism ≥ 0.75 D.

The results of this study indicated that the |ΔTK − ΔK| was smaller in the WTR astigmatism group than in the ATR astigmatism group. Similarly, findings by Shao et al. suggested that in ATR astigmatism eyes, the vector error between total corneal astigmatism and simulated corneal astigmatism considering only the anterior surface calculated with Pentacam was the highest (0.34 D), followed by oblique astigmatism eyes (0.28 D) and WTR eyes (0.19) [15]. In this study, the WTR astigmatism group showed ΔK greater than ΔTK, while the ATR astigmatism group showed ΔTK greater than ΔK, with no difference in the oblique astigmatism group, aligning with findings by Savini et al. [10]. K was derived from Simk = ((n − 1)/r), where n is the corneal refractive index, 1 is the air refractive index, and r is the anterior keratometry radius, by using the anterior keratometry. Therefore, the astigmatism axis obtained by K was consistent with that of anterior corneal astigmatism. When anterior corneal astigmatism is of the WTR type, there is a 91.75% probability that posterior corneal astigmatism is ATR astigmatism [14], and keratometric astigmatism would overestimate corneal astigmatism. When anterior corneal astigmatism is of the ATR type, there is a 57.65% probability that posterior corneal astigmatism is ATR astigmatism [16], and keratometric astigmatism would underestimate corneal astigmatism. A study by Jiang et al. verified this hypothesis [17]. This may explain why ΔK was larger than ΔTK in the WTR astigmatism group, while the opposite was found in the ATR astigmatism group.

In this study, as simulated corneal astigmatism increased, the |ΔTK − ΔK| showed an increasing trend. A study by Zheng et al. analyzing the differences between simulated corneal astigmatism and total corneal astigmatism using Pentacam also showed a positive correlation with the magnitude of corneal astigmatism [18]. Analysis of the basic characteristics of corneal astigmatism subgroups revealed no significant differences in age or axis distribution among the groups. Multiple regression analysis confirmed that the magnitude of astigmatism was an independent influencing factor for the |ΔTK − ΔK|. It was posited that with increasing corneal astigmatism, the characteristics of the posterior corneal astigmatism in terms of magnitude or axis distribution might change, affecting the accuracy of predicting real corneal astigmatism with simulated corneal astigmatism, thereby impacting the distribution of the vector error between simulated corneal astigmatism and total corneal astigmatism.

In the present study, the difference between ΔK and ΔTK increased with age. Findings by Shao et al. using Pentacam found that the vector error between total corneal astigmatism and simulated corneal astigmatism considering only the anterior surface increased with age [15], consistent with the results of this study. Unlike the distribution of the |ΔTK − ΔK|, the magnitude of ΔK and ΔTK showed no differences in younger age groups (≤ 49 years, 50–59 years, and 60–69 years), while in older age groups (70–79 years, and ≥ 80 years), ΔTK was greater than ΔK. The differences in ΔK and ΔTK across different age groups correlated with the axis distribution of astigmatism in the respective age groups. The proportion of WTR astigmatism was higher in younger age groups, decreasing with age, while the proportion of ATR astigmatism increased [19]. The results of this study confirmed that in the WTR astigmatism group, ΔK was greater than ΔTK, while in the non-with-the-rule astigmatism group, ΔTK was greater than ΔK, explaining why in the older age group ΔTK was greater than ΔK.

Compared to previous studies, this research focuses on the cataract population with corneal astigmatism ≥ 0.75D, which is the target group for the application of astigmatism IOL. The exploration of the difference between △K and △TK serves as the basis for determining which one, K or TK, is more precise in the calculation of astigmatism IOL. Previous investigations on △K and △TK merely compared their magnitudes, disregarding the distinctions caused by their varying directions. In this study, both the magnitudes and directions of △K and △TK are taken into consideration. The vector errors of the two are calculated, and the disparities between them are compared more comprehensively and accurately. Nevertheless, there are also limitations in this research: 1. this study only compared the simulated corneal astigmatism obtained by the IOLMaster 700 with total corneal astigmatism and did not compare the results with those from Pentacam examinations. 2. The simulated corneal astigmatism and total corneal astigmatism were not substituted into the formula for calculating artificial crystals, and the results were not compared, too. Further research and validation are needed to study the accuracy of simulated corneal astigmatism and total corneal astigmatism calculated by the IOLMaster 700 and their implications for planning the use of Toric intraocular lenses.