A.R. Sabinina – Master Degree Student, Department “Biomedical Techniques Systems”, 

Bauman Moscow State Technical University 

E-mail: anastasiya-sabinina@mail.ru 

L.P. Safonova – Ph.D. (Eng.), Associate Professor, Department “Biomedical Technical Systems”,  Bauman Moscow State Technical University

E-mail: larisa.safonova@gmail.com 

L.V. Zhezheleva – Ph.D. (Med.), Ophthalmologist, Botkin Hospital, Branch № 1 (Moscow)

E-mail: l_zhezheleva@mail.ru 

In the treatment of cataracts, the operation of phacoemulsification of a nontransparent lens and the implantation of an artificial intraocular lens (IOL) instead is recommended. Before the operation, the optical power of the IOL is calculated in order to provide the patient with the desired refraction. Since the standard of calculation has not been established, many methods are used in modern ophthalmic surgical practice. Achievement of the planned postoperative refractive outcome depends on many factors, including IOL parameters. In existing calculation methods, these parameters are reflected indirectly in the form of an A-constant, declared by the IOL manufacturer for a specific lens model, and uniform for all power ratings of this model. However, when using the declared constant in the calculations, refraction of the target is not always achieved, and therefore a personalized calculation of the constant is recommended. Thus, the use of the A-constant in calculations, which integrally indirectly reflects the geometric and optical parameters of the lens, is a source of additional error, difficult to predict and control, in calculating the optical power of the IOL. The aim of this work is to verify the need to take into account the direct geometric and optical parameters of the IOL when calculating its optical power in order to achieve the planned refractive result after cataract phacoemulsification with IOL implantation.

The study is based on a mathematical model of a two-component optical system of the eye, where the parameters of the eye correspond to the parameters of the schematic eye of Gullstrand. Based on the data on the possible values of the curvature of the front and back surfaces of the IOL, the thickness in the central optical zone and the refractive index of the lens material, the parameters of the diopter series of IOLs of various manufacturers are modeled. For each combination of the parameters, the absolute error of the indirect estimation of the optical power of the IOL is calculated. For use in the calculation of a two-component optical system of the eye, combinations with a minimum error are selected. The values of the second main focal length calculated in two ways are compared, and a conclusion about the influence of the IOL parameters on the error of the final refraction is made based on the magnitude of their difference.

The results of the study substantiate the need to use the direct geometric and optical parameters of the lens when calculating the optical power of the IOL in order to minimize deviations from the planned refraction. Neglecting the refractive index and the radii of curvature of the front and back surfaces results in an error of 0.5-1.0 diopters (D) in the final refraction. If the required accuracy of the manufacturing of the lens surfaces is not implemented, the error in the indirect estimation of the optical power of the IOL increases. The error value, in terms of the final refraction, is 0.1-1.0 diopters. Thus, the choice of the optimal combination of IOL parameters corresponding to the minimal influence of manufacturing errors and taking into account the peculiarities of the IOL shape in computational algorithms will improve the accuracy of correction of the optical system of the eye during cataract phacoemulsification with IOL implantation.

1. Hoffer K.J., Savini G. IOL power calculation in short and long eyes. The Asia-Pacific Journal of Ophthalmology. 2017. V. 6. № 4. P. 330–331. 
2. Abulafia A., Barrett G.D., Rotenberg M., Kleinmann G., Levy A., Reitblat Intraocular lens power calculation for eyes with an axial length greater than 26.0 mm: comparison of formulas and methods. Journal of Cataract & Refractive Surgery. 2015. V. 41. №. 3. P. 548–556. 
3. Roberts T.V., Hodge C., Sutton G., Lawless M. Comparison of Hill radial basis function, Barrett Universal and current third generation formulas for the calculation of intraocular lens power during cataract surgery. Clinical & experimental ophthalmology. 2018. V. 46. №. 3. P. 240–246. 
4. Rong X., He W., Zhu Q., Qian D., Lu Y., Zhu X. Intraocular lens power calculation in eyes with extreme myopia: Comparison of Barrett Universal II, Haigis, and Olsen formulas. Journal of Cataract & Refractive Surgery. 2019. V. 45. № 6. P. 732–737.
5. Jeong J., Song H., Lee J.K., Chuck R.S., Kwon J.W. The effect of ocular biometric factors on the accuracy of various IOL power calculation formulas. BMC ophthalmology. 2017. V. 17. №. 1. P. 62. 
6. Hoffer K.J., Aramberri J., Haigis W., Olsen T., Savini G., Shammas H.J. Protocols for studies of intraocular lens formula accuracy. American journal of ophthalmology. 2015. V. 160. №. 3. P. 403–405.
7. Olsen T. Calculation of intraocular lens power: a review. Acta Ophthalmologica Scandinavica. 2007. V. 85. № 5. P. 472–485.
8. German I. Fizika organizma cheloveka. Dolgoprudnyj: Izdatel'skij dom «Intellekt». 2011. 992 s. (In Russian).
9. Zakaznov N.P., Kiryushin S.I., Kuzichev V.I. Teoriya opticheskih sistem. M.: Mashinostroenie. 1992. 448 s. (In Russian).
10. Patent № 2644694 (RF). Sposob opredeleniya opticheskoj sily intraokulyarnoj linzy posle radial'noj keratotomii / L.V.ZHezheleva, YU.A.Gusev, L.P.Safonova. 2018. (In Russian).
11. Tahchidi H.P., Iskakov I.A., Pichikova N.A. Sravnitel'naya ocenka rezul'tatov implantacii bifokal'nyh difrakcionno-refrakcionnyh i monofokal'nyh intraokulyarnyh linz. Oftal'mohirurgiya. 2009. T. 1. S. 18–20. (In Russian).
12. Tereshchenko A.V., Belyj YU.A., Dem'yanchenko S.K., Malyugin B.E. Sovremennye standarty hirurgii katarakty s implantaciej intraokulyarnoj linzy. Obzor literatury. Refrakcionnaya hirurgiya i oftal'mologiya. 2010. T. 10. № 3. S. 4–10 (In Russian).
13. Kulikov A.N., Kokareva E.V., Dzilihov A.A. Effektivnaya poziciya linzy. Obzor. Oftal'mohirurgiya. 2018. № 1. S. 92–97. (In Russian).
14. Kane J.X., Van Heerden A., Atik A., Petsoglou C. Intraocular lens power formula accuracy: comparison of 7 formulas. Journal of Cataract & Refractive Surgery. 2016. V. 42. № 10. P. 1490–1500.
15. User Group for Laser Interference Biometry (ULIB): [sajt]. – URL: http://ocusoft.de/ulib/ (data obrashcheniya 11.03.2020)
16. Veshchikova V.N. Elastichnaya «reversnaya» IOL v hirurgii katarakty pri miopii vysokoj stepeni: Avtoref. dis. … kand. med. nauk. M. 2014. 27 s. (In Russian).
17. Malyugin B.E., Panteleev E.N., Bessarabov A.N., Pokrovskij D.F., Semakina A.S., Abdullaeva S.A. Sravnitel'nyj analiz predskazuemosti refrakcionnogo rezul'tata pri irido-kapsul'noj i irido-vitreal'noj fiksacii dvuhploskostnoj modeli IOL. Oftal'mologiya. 2018. T. 15. № 2. S. 139–145. (In Russian).
18. Cooke D.L., Cooke T.L. Comparison of 9 intraocular lens power calculation formulas. Journal of Cataract & Refractive Surgery. 2016. V. 42. № 8.  P. 1157–1164. 
19. GOST R 31580.2-2012. Implantaty oftal'mologicheskie. Intraokulyarnye linzy. CH. 2. Opticheskie svojstva i metody ispytanij. M.: Standartinform, 2013. 37 s. (In Russian).
20. Patent № 2339341 (RF). Intraokulyarnaya linza / S.Hun , Cz. Se, St. Dzh. N. Van, D. Stenli, M. Karakelle, M. Dzh. Simpson, S. CHzhan. 2008.
21. GOST R 51580–2000. Linzy kontaktnye myagkie. Obshchie tekhnicheskie usloviya. M.: Standartinform, 2006. 8 s. (In Russian).
22. Goncharov A.S. Izuchenie opticheskih harakteristik intraokulyarnyh linz [Elektronnyj resurs]. Kafedra medicinskoj fiziki. Fizicheskij fakul'tet MGU im. M.V. Lomonosova: [sajt]. – URL: http://medphys.phys.msu.ru/n_iol.html (data obrashcheniya 26.03.2020). (In Russian).