Mathematical substantiation of retinal laser coagulation pattern using hexagonal pattern form in the treatment of active stages of retinopathy of prematurity

Purpose. To substantiate mathematically the tissue-preserving effect on  the  retinal  hexagonal  pattern  during  the  laser  treatment  of  active retinopathy of prematurity. Material and methods. At the first stage of the study, a mathematical rationale of  the application of a hexagonal pattern was carried out  to provide a tissue-sparing effect on the retina compared to the traditional laser coagulation pattern with matrix (rectangular) patterns.The second stage was performed as clinical studies in two groups of patients with an unfavorable course type II and III stages of active ROP. The main  group  consisted  of  44  infants, which  underwent  hexagonal Fyodorov Journal of Ophthalmic Surgery. 2020;1: 40–46.laser  coagulation  (7  applications  in  one  «honeycomb»  pattern).  The control group involved 41 infants who had a matrix laser coagulation (9 applications in one «rectangular» pattern). Results. At the first stage, it was proved  that  the hexagonal shape of  the  pattern is mathematically  substantiated  and  ensures  a  uniform distribution of laser applicates on the spherical surface of the retina due to  the equidistant  location of  the spots  inside one pattern and optimal matching of neighboring patterns.As a result of the second stage of research in both groups, a regression after laser treatment was obtained in more than 97% of cases at the ROP stage 2 and in 94% of cases at the ROP stage 3. The total energy load in the main group was less than in the control group. The increase in the inter-spot  distance  in  the  hexagonal  pattern  by 0.25  of  the  coagulum diameter  in  comparison  with the matrix pattern  made  it possible to maintain a high clinical efficacy and to ensure tissue-preserving effects on the retina. Conclusion. Optimization of  the pattern  laser coagulation method using a hexagonal-shaped pattern allows to shorten the duration of the intervention maintaining a high clinical efficacy in the treatment of active ROP.