Vector Analysis Comparison Of Barrett T K, Kane And Zcalc Toric Calculators In Toric Intraocular Lenses

To compare prediction accuracy and directional bias of Barrett TK, Kane Toric and Z CALC calculators using vector analysis in toric intraocular lenses.

This study was conducted at Vietnam-Russia International Eye Hospital at Hochiminh City, Vietnam. We investigated eyes of patients who had undergone cataract surgery with toric lenses from July 2025 to November 2025. We eliminated patients who had other ocular surgeries before, post-op visual acuity <20/30 or had no refractive data 3 weeks postoperatively.

This retrospective study included 56 eyes implanted with AT TORBI 709M or AT Lisa Tri toric 939M. Biometry was perfomed using the IOL Master 700. Predicted residual astigmatism was calculated using Barrett TK, Kane, and Z CALC calculators. Prediction error was analyzed using vector analysis. Accuracy was assessed using mean absolute error (MAE), centroid prediction error and the proportion of eyes within ±0.5D and  ±0.75D. Subgroup analyses were performed for astigmatism type and IOL model.

MAE differed significantly among forrmulas (Barrett TK  0.47±0.31 D, Kane 0.59±0.29, Z CALC 0.34±0.20; p<0.05), with ZCALC showing the lowest error.The proportion of eyes within ±0.5 D of prediction error was highest with Z CALC (85.7%), followed by Barrett TK (60.7%) and Kane (42.9%). Within ±0.75 D, Z CALC also showed the highest percentage (96.4%), compared with Kane (76.8%) and Barrett TK (67.9%). Overall centroid prediction errors was small for Barrett TK (0.09D @ 165^o) and Kane (0.09D @ 159^o), while Z CALC showed 0.14D @ 167^o  and was the only calculator with a statistically significant overall centroid deviation from zero (p<0.05), indicating systematic ATR-directed bias. Subgroup analysis also showed significant centroid deviation.

Z CALC demonstrated superior toric prediction accuracy compared with Barrett TK and Kane, with substantially more eyes within ±0.5D and ±0.75D. Despite this improved accuracy, systemic ATR-directed bias was identified, highlighting the importance of understanding calculator-specific tendencies to further optimize toric IOL selection and refractive precision.