A Differential Approach to Calculating the Optical Power of IOLs for Ametropia: from Classical Formulas to Artificial Intelligence

One of the important criteria for visual quality and satisfaction after uncomplicated cataract surgery is achieving the “target refraction” without residual ametropia. Despite the availability of highly accurate preoperative assessment and advanced formulas for calculating the optical power of intraocular lenses (IOLs), failure to achieve a postoperative refraction within ±0,5 diopters of the target still occurs in approximately one quarter of cases. The problem is further complicated by the absence of a generally accepted consensus regarding the optimal IOL power calculation formulas for hyperopia or myopia. In addition to various options for postoperative refractive correction, promising approaches include the use of IOLs with adjustable optical power after implantation and new-generation artificial intelligence-based IOL power calculation formulas.

1. GBD 2019 Blindness and Vision Impairment Collaborators. Causes of blindness and vision impairment in 2020 and trends over 30 years, and prevalence of avoidable blindness in relation to VISION 2020: the Right to Sight: an analysis for the Global Burden of Disease Study. Lancet Glob Health 2021;9(2):e144–e160. doi: 10.1016/S2214-109X(20)30489-7.

2. Fang R, Yu YF, Li EJ, Lv NX, Liu ZC, Zhou HG, Song W. Global, regional, national burden and gender disparity of cataract: findings from the global burden of disease study 2019. BMC Public Health. 2022;22(1):2068. doi: 10.1186/s12889-022-14491-0.

3. Neroev VV, Malyugin BE, Trubilin VN, Zhudenkov KV, Orlova OM. Clinical and social burden of cataract treatment in Russia. Cataract and refraction surgery. 2016;16(1):4–14 (In Russ.).

4. Bro T, Behndig A, Viberg A, Zetterberg M, Kugelberg M, Nilsson I, Montan P, Lundström M. Two point four million cataract surgeries: 30 years with the Swedish National Cataract Register, 1992-2021. J Cataract Refract Surg. 2023;49(8):879–884. doi: 10.1097/j.jcrs.0000000000001209.

5. Bro T, Lundstrom M, Kugelberg M, Nilsson I, Zetterberg M, Viberg A, Montan P, Behndig A. [2.6 million cataract surgeries: 31 years with the Swedish National Cataract Register 1992–2022]. Lakartidningen 2024;121.

6. Informal consultation on analysis of blindness prevention outcomes. Geneva: World Health Organization; 1998.

7. Lundström M, Dickman M, Henry Y, Manning S, Rosen P, Tassignon MJ, Young D., Stenevi U. Risk factors for refractive error after cataract surgery: Analysis of 282 811 cataract extractions reported to the European Registry of Quality Outcomes for cataract and refractive surgery. J Cataract Refract Surg. 2018;44(4):447– 452. doi: 10.1016/j.jcrs.2018.01.031.

8. Behndig A, Montan P, Stenevi U, Kugelberg M, Zetterstrom C, Lundstrom M. Aiming for emmetropia after cataractsurgery: Swedish National Cataract Registerstudy. J Cataract Refract Surg. 2012; 38(7):1181–1186. doi: 10.1016/j.jcrs.2012.02.035.

9. Brogan K, Diaper CJM, Rotchford AP. Cataract surgery refractive outcomes: representative standards in a National Health Service setting. Br J Ophthalmol. 2019;103(4):539–543. doi: 10.1136/bjophthalmol-2018-312209.

10. Bikbov MM, Israfilova GZ. Results of a population-based study of the prevalence of cataract surgery and the causes of low postoperative visual function. Viewpoint East-West. 2022;1:16–22 (In Russ.). doi: 10.25276/2410-1257-2022-1-16-22.

11. Khoramnia R, Auffarth G, Labuz G, Pettit G, Suryakumar R. Refractive Outcomes after Cataract Surgery. Diagnostics (Basel). 2022;12(2):243. doi: 10.3390/diagnostics12020243.

12. Lundström M, Dickman M, Henry Y, Manning S Rosen P, Tassignon MJ, Young D., Stenevi U. Changing practice patterns in European cataract surgery as reflected in the European Registry of Quality Outcomes for Cataract and Refractive Surgery 2008 to 2017. J Cataract Refract Surg. 2021;47(3):373–378. doi: 10.1097/j.jcrs.0000000000000457.

13. Kugelberg M, Lundström M. Factors related to the degree of success in achieving target refraction in cataract surgery: Swedish National Cataract Register study. J Cataract Refract Surg. 2008;34(11):1935–1939. doi: 10.1016/j.jcrs.2008.06.036.

14. Tekcan H, Mangan MS, Imamoglu S, Alpogan O. Refractive Outcomes of Uneventful Cataract Surgery in Pseudoexfoliation Syndrome and Pseudoexfoliation Glaucoma. Korean J Ophthalmol. 2022;36(3):226–235. doi: 10.3341/kjo.2021.0183.

15. Behndig A, Montan P, Lundstrom M, Zetterstrom C, Kugelberg M. Gender differences in biometry prediction error and intra-ocular lens power calculation formula. Acta Ophthalmol. 2014;92(8):759–763. doi: 10.1111/aos.12475.

16. Lee NS, Ong K. Factors contributing to long-term refractive error after cataract surgery. Int Ophthalmol. 2023;43(7):2335–2340. doi: 10.1007/s10792-022-02630-w.

17. Mehdizadeh M, Nowroozzadeh MH. Diurnal fluctuation of IOL power calculation in glaucomatous eyes. J Cataract Refract Surg. 2009;35(8):1481–1482; author reply 1482. doi: 10.1016/j.jcrs.2009.03.042.

18. Avetisov SE, Mamikonyan VR, Ivanov MN, Yusef YuN, Shevelev AYu, Voroshilova NA. Calculation of the focal power of an intraocular lens in the anterior segment sizes dis-proportional to the length of the anteroposterior axis of the eye. Russian Annals of Ophthalmology. 2008;124(6):10–13 (In Russ.).

19. Lee NS, Ong K. Changes in refraction after cataract phacoemulsification surgery. Int Ophthalmol. 2023;43(5):1545–1551. doi: 10.1007/s10792-022-02550-9.

20. Schuster AK, Schlichtenbrede FC, Harder BC, Beutelspacher SC, Jonas JB. Target refraction for best uncorrected distance and near vision in cataract surgery. Eur J Ophthalmol. 2014;24(4):509–515. doi: 10.5301/ejo.5000414.

21. Rönbeck M, Lundström M, Kugelberg M. Study of possible predictors associated with self-assessed visual function after cataract surgery. Ophthalmology. 2011;118(9):1732–1738. doi: 10.1016/j.ophtha.2011.04.013.

22. Coleman DJ, Carlin B. A new system for visual axis measurements in the human eye using ultrasound. Arch Ophthalmol. 1967;77(1):124–127. doi: 10.1001/archopht.1967.00980020126027.

23. Jansson F. Determination of the Axis Length of the Eye Roentgenologically and by Ultrasound. Acta Ophthalmol (Copenh). 1963;41:236–246. doi: 10.1111/j.17553768.1963.tb02432.x.

24. Ademola-Popoola DS, Nzeh DA, Saka SE, Olokoba LB, Obajolowo TS. Comparison of ocular biometry measurements by applanation and immersion A-scan techniques. J Curr Ophthalmol. 2015;27(3–4):110–114. doi: 10.1016/j.joco.2015.12.002.

25. Hoffmann PC, Hütz WW, Eckhardt HB, Heuring AH. Intraocular lens calculation and ultrasound biometry: immersion and contact procedures. Klin Monbl Augenheilkd. 1998;213(3):161–165. doi: 10.1055/s-2008-1034967.

26. Landers J, Goggin M. Comparison of refractive outcomes using immersion ultrasound biometry and IOLMaster biometry. Clin Exp Ophthalmol. 2009;37(6):566– 569. doi: 10.1111/j.1442-9071.2009.02091.x.

27. Pershin KB, Pashinova NF, Tsygankov Ayu, Legkikh SL, Likh IA. Biometry in IOL optical power calculating as a factor of succesful cataract surgery. Catarat and refraction surgery. 2016;16(2):15–22 (In Russ.).

28. Manning CA, Kloess PM. Comparison of portable automated keratometry and manual keratometry for IOL calculation. J Cataract Refract Surg. 1997;23(8):1213– 1216. doi: 10.1016/s0886-3350(97)80318-5.

29. Kanclerz P, Khoramnia R, Wang X. Current Developments in Corneal Topography and Tomography. Diagnostics (Basel). 2021;11(8):1466. doi: 10.3390/diagnostics11081466.

30. Epitropoulos AT, Matossian C, Berdy GJ, Malhotra RP, Potvin R. Effect of tear osmolarity on repeatability of keratometry for cataract surgery planning. Journal of Refractive Surgery. 2015;41(8):1672–1677. doi: 10.1016/j.jcrs.2015.01.016.

31. Kawahara A. Nishi Y, Nagaoka N, Nakano K, Yoshida A, Ueno S, Hayashi T, Kondo M. Management of Dry Eye Disease for Intraocular Lens Power Calculation in Cataract Surgery: A Systematic Review. Bioengineering (Basel). 2024;11(6):597. doi: 10.3390/bioengineering11060597

32. Stopyra W, Langenbucher A, Grzybowski A. Intraocular Lens Power Calculation Formulas-A Systematic Review. Ophthalmol Ther. 2023;12(6):2881–2902. doi: 10.1007/s40123-023-00799-6.

33. Fedorov SN, Kolinko AI. Methodology for calculating the optical power of an intraocular lens. Annals of Ophthalmology. 1967;80(4):27–31.

34. Retzlaff J. Posterior chamber implant power calculation: regression formulas. J Am Intraocul Implant Soc. 1980;6(3):268–270. doi: 10.1016/s0146-2776(80)80076-0.

35. Sanders DR, Kraff MC. Improvement of intraocular lens power calculation using empirical data. J Am Intraocul Implant Soc. 1980;6(3):263–267. doi: 10.1016/s0146-2776(80)80075-9.

36. Olsen T. Calculation of intraocular lens power: a review. Acta Ophthalmol Scand 2007; 85(5):472–485. doi: 10.1111/j.1600-0420.2007.00879.x.

37. Holladay JT, Prager TC, Chandler TY, Musgrove KH, Lewis JW, Ruiz RS. A threepart system for refining intraocular lens power calculations. J Cataract Refract Surg. 1988;14(1):17–24. doi: 10.1016/s0886-3350(88)80059-2.

38. Sanders DR, Retzlaff J, Kraff MC. Comparison of the SRK II formula and other second generation formulas. J Cataract Refract Surg. 1988;14(2):136–141. doi: 10.1016/s0886-3350(88)80087-7.

39. Ivanov MN, Shevelyov AYu. Formula for IOL optic power calculation. Russian Annals of Ophthalmology. 2003;119(2):10–14 (In Russ.).

40. Retzlaff JA, Sanders DR, Kraff MC. Development of the SRK/T intraocular lens implant power calculation formula. J Cataract Refract Surg. 1990;16(3):333–340. doi: 10.1016/s0886-3350(13)80705-5.

41. Kasyanov AA. Analysis of methods for calculating the optical power of IOL. Refractive surgery and ophthalmology. 2004;4(1):61–65 (In Russ.).

42. Carmona Gonzalez D, Palomino Bautista C. Accuracy of a new intraocular lens power calculation method based on artificial intelligence. Eye (Lond). 2021;35(2):517–522. doi: 10.1038/s41433-020-0883-3.

43. Kane JX, Van Heerden A, Atik A, Petsoglou C. Accuracy of 3 new methods for intraocular lens power selection. J Cataract Refract Surg. 2017;43(3):333–339. doi: 10.1016/j.jcrs.2016.12.021.

44. Hoffer KJ, Savini G. Update on Intraocular Lens Power Calculation Study Protocols: The Better Way to Design and Report Clinical Trials. Ophthalmology. 2021;128(11):e115–e120. doi: 10.1016/j.ophtha.2020.07.005.

45. Ma S, Li C, Sun J, Yang J, Wen K, Chen X, Lin H, Liu Y, Chen W. Comparative Analysis of Eighteen IOL Power Calculation Formulas Using a Modified Formula Performance Index Across Diverse Biometric Parameters. Am J Ophthalmol. 2025;273:221–230. doi: 10.1016/j.ajo.2025.02.035.

46. Voytsekhivskyy OV, Hoffer KJ, Cooke DL, Savini G. IOL Power Calculation Project: Accuracy of 36 Formulas. Am J Ophthalmol. 2025;277:45–56. doi: 10.1016/j.ajo.2025.05.004.

47. Voytsekhivskyy OV, Hoffer KJ, Tutchenko L, Cooke DL, Savini G. Accuracy of 24 IOL Power Calculation Methods. J Refract Surg. 2023;39(4):249–256. doi: 10.3928/1081597X-20230131-01.

48. Stopyra W, Cooke DL, Grzybowski A. A Review of Intraocular Lens Power Calculation Formulas Based onArtificialIntelligence. JClin Med. 2024;13(2):498. doi: 10.3390/jcm13020498.

49. Cheng H, Kane JX, Liu L, Li J, Cheng B, Wu M. Refractive Predictability Using the IOLMaster 700 and Artificial Intelligence-Based IOL Power Formulas Compared to Standard Formulas. J Refract Surg. 2020;36(7):466–472. doi: 10.3928/1081597X20200514-02.

50. Aristodemou P, Knox Cartwright NE, Sparrow JM, Johnston RL. Formula choice: Hoffer Q, Holladay 1, or SRK/T and refractive outcomes in 8108 eyes after cataract surgery with biometry by partial coherence interferometry. J Cataract Refract Surg. 2011;37(1):63–71. doi: 10.1016/j.jcrs.2010.07.032.

51. Hoffer KJ. Clinical results using the Holladay 2 intraocular lens power formula. J Cataract Refract Surg. 2000;26(8):1233–1237. doi: 10.1016/s0886-3350(00)00376-x.

52. Eom Y, Kang SY, Song JS, Kim YY, Kim HM. Comparison of Hoffer Q and Haigis formulae forintraocularlens power calculation according to the anterior chamber depth in short eyes. Am J Ophthalmol. 2014;157(4):818–824. doi: 10.1016/j.ajo.2013.12.017.

53. Kane JX, Van Heerden A, Atik A, Petsoglou C. Intraocular lens power formula accuracy: Comparison of 7 formulas. J Cataract Refract Surg. 2016;42(10):1490–1500. doi: 10.1016/j.jcrs.2016.07.021.

54. Ma Y, Xiong R, Liu Z, Young CA, Wu Y, Zheng D, Yang Y, Zhao YE, Wang X, Li Z, Jin G, Liu Y, Chen W. Network Meta-analysis of Intraocular Lens Power Calculation Formula Accuracy in 1016 Eyes With Long Axial Length. Am J Ophthalmol. 2024;257:178–186. doi: 10.1016/j.ajo.2023.09.009.

55. Stopyra W, Voytsekhivskyy O, Grzybowski A. Prediction of Seven Artificial Intelligence-Based Intraocular Lens Power Calculation Formulas in Medium-Long Caucasian Eyes. Life (Basel). 2025;15(1):45. doi: 10.3390/life15010045.

56. Xu J, Zhang L, Mo E, Zhu K, Zhu Y, Feng K, Li Z., Chen W. The effect of corneal power on the accuracy of 14 IOL power formulas. BMC Ophthalmol. 2024;24(1):126. doi: 10.1186/s12886-024-03395-9.

57. Avetisov SE, Mamikonyan VR, Kasyanov AA. Features of IOL optical power calculation in patients with radial keratotomy. Ophthalmology in Russia. 2004;1(4):15– 24 (In Russ.).

58. Tsyrenzhapova EK, Rozanova OI, Senchenko NYa. Comparative analysis of methods for calculating the optical power of iols in patients after anterior radial keratotomy. Modern technologies in ophthalmology. 2019;5:152–156 (In Russ.). doi: 10.25276/2312-4911-2019-5-152-156.

59. Iusef YuN, Kas’ianov AA, Ivanov MN, Iusef SN, Vvedensky AS, Ryzhkova EG, Shevelev AYu. Calculation of intraocular lens power in non-standard clinical situations. Russian Annals of Ophthalmology. 2013;129(5):62–66 (In Russ.).

60. Karasiova SA, Krasilnikova VL. Cataract extraction after corneal surgery (literature review). Ophthalmology Eastern Europe. 2017;7(3):371–379 (In Russ.).

61. Kim J, Park J, Jo Y. Comparison of the formula accuracy for calculating multifocal intraocular lens power: a single center retrospective study in Korean patients. Sci Rep. 2024;14(1):4462. doi: 10.1038/s41598-024-54889-x.

62. Pershin KB, Pashinova NF, Tsygankov AI, Gurmizov EP, Batalina LV. Management of Residual Refractive Error after Cataract Phacoemulsification. Part 1. Keratorefractive Approaches. Ophthalmology in Russia. 2017;14(1):18–26 (In Russ.). doi: 10.18008/1816-5095-2017-1-18-26.

63. Pershin KB, Pashinova NF, Tsygankov AI, Gurmizov EP, Batalina LV. Management of residual refractive error after cataract phacoemulsification. Part 2. Intraocular approaches. Ophthalmology in Russia. 2017;14(2):106–112 (In Russ.). doi: 10.18008/1816-5095-2017-2-106-112.

64. Yusef YuN, Voronin GV, Volzhanin AV, Zelimkhanov SR, Budnikova EA, Hamdi A. Modern Directions of Intraocular Lenses Improvement. Literature Review. Ophthalmology in Russia. 2025;22(1):16–23 (In Russ.). doi: 10.18008/1816-5095-2025-1-16-23.