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Methods of mathematical modeling of fundus laser exposure for therapeutic effect evaluation
A.S. Shirokanev 1,2, A.S. Kibitkina 1,2, N.Y. Ilyasova 1,2, A.A. Degtyarev 1

1 Samara National Research University, 443086, Samara, Russia, Moskovskoye Shosse 34,
2 IPSI RAS – Branch of the FSRC "Crystallography and Photonics" RAS,
443001, Samara, Russia, Molodogvardeyskaya 151

 PDF, 3117 kB

DOI: 10.18287/2412-6179-CO-760

Pages: 809-820.

Full text of article: Russian language.

Abstract:
When laser coagulation of eye retina is carried out, the laser beam is directed to target retinal areas selected by an ophthalmologist. The exposure to laser light produces a photocoagulate. When using laser coagulation, the main problem is selecting both the laser exposure areas that would cover all pathological zones and the laser exposure parameters to prevent retina damage. Any patient has an individual fundus structure. The individual structure of pathological and anatomical elements must be taken into account to achieve the desired therapeutic effect.
     The formation of coagulates in all hemorrhage-affected areas results in the desired therapeutic effect. The vascular layer must be heated to a sufficient temperature to form a coagulate. Such an effect can be predicted using mathematical modeling of laser exposure.
     In this paper, we consider methods of mathematical modeling of laser exposure based on the solution of a heat equation. The methods are compared in terms of their computational complexity and solution stability. An analysis of the possibility of predicting the therapeutic effect using methods of mathematical modeling of laser exposure is carried out.

Keywords:
diabetic retinopathy, laser coagulation, therapeutic effect, mathematical modeling, heat equation, initial and boundary conditions.

Citation:
Shirokanev AS, Kibitkina AS, Ilyasova NY, Degtyarev AA. Methods of mathematical modeling of fundus laser exposure for therapeutic effect evaluation. Computer Optics 2020; 44(5): 809-820. DOI: 10.18287/2412-6179-CO-760.

Acknowledgements:
This work was funded by the Russian Foundation for Basic Research under RFBR projects ##19-31-90160, 19-29-01135 and the Ministry of Science and Higher Education of the Russian Federation within a State assignment to Samara University and the FSRC “Crystallography and Photonics” RAS.

References:
  1. Polyakov MV, Hoperskov AV. Mathematical modeling of the spatial distribution of the radiation field in biological tissue: determination of brightness temperature for diagnosis [In Russian]. Bulletin of Volgograd State University 2016; 36(5): 73-84.
  2. Zamytskiy E, et al. Analysis of the coagulates intensity in laser treatment of diabetic macular edema in a Navilas robotic laser system. Saratov Journal of Medical Scientific Research 2017; 13(2): 375-378.
  3. Ilyasova N. Evaluation of geometric features of the spatial structure of blood vessels. Computer Оptics 2014; 38(3): 529-538.
  4. Khorin P, Ilyasova N, Paringer R. Informative feature selection based on the Zernike polynomial coefficients for various pathologies of the human eye cornea. Computer Optics 2018; 42(1): 159-166.
  5. Astakhov YS, Shadrichev FE, Krasavina MI, Grigoryeva NN. Modern approaches to the treatment of a diabetic macular edema [In Russian]. Ophthalmologic Sheet 2009; 4: 59-69.
  6. Kozak I, Luttrull J. Modern retinal laser therapy. Saudi Journal of Ophthalmology 2014; 29(2): 137-146.
  7. Polyakov MV. Numerical modeling of the dynamics of temperature distribution in biological tissue [In Russian]. Materials of the All-Russian School-Conference of Young Scientists 2015: 971-978.
  8. Ilyasova NYu. Diagnostic computer complex for vascular fundus image analysis [In Russian]. Biotehnosfera 2014; 3(33): 20-24.
  9. Ilyasova NYu. Methods for digital analysis of human vascular system. Literature review. Computer Optics 2013; 37(4): 511-535.
  10. Ilyasova NYu, Kupriyanov AV, Gavrilova NA, Shilkin GA, Lanevskaya NI. Biomechanical characteristics of blood vessels for digital image analysis fundus [In Russian]. Biomehanika Glaza 2002; 18-30.
  11. Soifer VA, Ilyasova NYu, Kupriyanov AV, Khramov AG, Ananin MA. Methods for computer diagnostics using eye’s fundus images [In Russian]. Technologies of the Living Systems 2008; 5(5-6): 61-71.
  12. Simchera VM. Methods of multivariate statistical analysis [In Russian]. Moscow: “Financy I Statistika” Publisher; 2008.
  13. Fukunaga K. Introduction to statistical pattern recognition. New York, London: Academic Press; 1972.
  14. Pushkaryova AE. Mathematical modeling methods in optics of biological tissue [In Russian]. Saint-Petersburg: "SPbGU ITMO" Publisher; 2008.
  15. Liu G. Digital focusing of OCT images based on scalar diffraction theory and information entropy. Biomed Opt Express 2012; 3(11): 2774-2783.
  16. Jiang H, Quanyong Y, Xiaoyan J, Guoxu X. Morphologic features of retina pigment epithelial around fluorescein leakage sites in acute central serous chorioretinopathy before and after laser coagulation. Chinese Journal of Ocular Fundus Diseases 2016; 32(3): 266-269.
  17. Kistenev Y, Buligin A, Sandykova E, Sim E, Vrazhnov D. Modeling of IR laser radiation propagation in bio-tissues. Proc SPIE 2019; 11208: 112081Q.
  18. Moës N, Béchet E, Tourbier M. Imposing Dirichlet boundary conditions in the extended finite element method. Int J Numer Methods Eng 2006; 67(12): 1641-1669.
  19. Wolfram S. The Mathematica book (3rd ed.). Assem Autom 1999; 19(1): 77-77.
  20. Samarskiy AA. High accuracy schemes for the multidimensional heat equation [In Russian]. Journal of Computational Mathematics and Mathematical Physics 1963; 3(5): 812-840.
  21. Rudoi EM. Mathematical analysis. Numerical and functional series. Novosibirsk: "Novosibirsk State Pedagogical University" Publisher; 2010.
  22. Khvatsev AA. Partial differential equations. Pskov: "Pskov State University" Publisher; 2016.

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