*Article* **Modeling of Fundus Laser Exposure for Estimating Safe Laser Coagulation Parameters in the Treatment of Diabetic Retinopathy**

**Aleksandr Shirokanev 1,2, Nataly Ilyasova 12, Nikita Andriyanov 3, Evgeniy Zamytskiy 4, Andrey Zolotarev <sup>5</sup> and Dmitriy Kirsh 1,2,\***


**Abstract:** A personalized medical approach can make diabetic retinopathy treatment more effective. To select effective methods of treatment, deep analysis and diagnostic data of a patient's fundus are required. For this purpose, flat optical coherence tomography images are used to restore the three-dimensional structure of the fundus. Heat propagation through this structure is simulated via numerical methods. The article proposes algorithms for smooth segmentation of the retina for 3D model reconstruction and mathematical modeling of laser exposure while considering various parameters. The experiment was based on a two-fold improvement in the number of intervals and the calculation of the root mean square deviation between the modeled temperature values and the corresponding coordinates shown for the convergence of the integro-interpolation method (balance method). By doubling the number of intervals for a specific spatial or temporal coordinate, a decrease in the root mean square deviation takes place between the simulated temperature values by a factor of 1.7–5.9. This modeling allows us to estimate the basic parameters required for the actual practice of diabetic retinopathy treatment while optimizing for efficiency and safety. Mathematical modeling is used to estimate retina heating caused by the spread of heat from the vascular layer, where the temperature rose to 45 ◦C in 0.2 ms. It was identified that the formation of two coagulates is possible when they are located at least 180 μm from each other. Moreover, the distance can be reduced to 160 μm with a 15 ms delay between imaging.

**Keywords:** mathematical modeling; numerical methods; integro-interpolation method; splitting method; convergence of models; standard deviation of the error; diabetic retinopathy; ocular fundus; laser coagulation; optical coherence tomography; image processing; segmentation; safe treatment
