Development a Method for Estimating a Safe Distance between Coagulates to Automatically Plan Retinal Laser Coagulation in Diabetic Retinopathy Treatment

Abstract

Introduction. Diabetes mellitus is a common endocrine disease that can lead to retinal vascular damage caused by the spread of macular edema and the development of diabetic retinopathy. Currently, diabetic retinopathy is treated using retinal laser coagulation. However, since even modern systems do not demonstrate sufficient treatment efficacy, methods for providing laser coagulation support on the basis of patient data analysis are required.Aim. This paper aims to develop and study a method for estimating a safe distance between coagulates via the mathematical modeling of coagulation in order to provide laser coagulation support.Materials and methods. The problem of thermal conductivity is numerically modeled for laser action in a multilayer medium.Results. A method for estimating a safe distance between coagulates has been developed via the mathematical modeling of the thermal conductivity problem. An algorithm was established for reconstructing a three-dimensional fundus structure from OCT images. It was demonstrated that the convergence rate of the integro-interpolation method is higher than that of the finite difference method. The study revealed that the retina heats up to 45 ºС due to heat redistribution from the epithelial layer, as well as laser exposure. According to the study results, the developed method yields a safe distance of 180 µm. By increasing the delay between laser pulses by more than 10 ms, this distance can be reduced to 160 μm.Conclusion. The developed method can calculate distance corresponding to that used in medical practice. Besides safe distance, the use of this method will allow other laser coagulation parameters to be determined non-invasively: laser power and pulse duration recommended to achieve a therapeutic effect. These estimates can be used to automatically produce a preliminary laser coagulation plan to support diabetic retinopathy treatment.

Keywords

• fundus
• diabetic retinopathy
• laser coagulation
• mathematical modeling
• thermal conductivity equation
• finite difference method
• integro-interpolation method
• splitting method