Abstract: Objective To establish a mathematical model for retinal irradiance of 650 nm red laser, validate model accuracy, and explore effects of different laser powers, pupil diameters, and axial lengths on retinal irradiance. Design Animal experimental study. Participants Four two-month-old Tupaia and six four-month-old tricolor guinea pigs. Methods After enucleation of eyeballs (n=20), posterior sclera and corresponding retinal area were dissected. Retinal irradiance was measured at laser emission powers of 2 mW, 5 mW, 10 mW, and 18 mW. Ocular biological parameters were measured and combined with optical parameters to establish a light transmission model. The radiative transfer equation (RTE) mathematical model was constructed using the Henyey-Greenstein phase function, and theoretical values were compared with actual measurements. Main Outcome Measures Retinal irradiance under different conditions and theoretical model accuracy. Results For guinea pigs [pupil diameter (5.0±0.3)mm, axial length (7.52±0.11)mm], actual retinal irradiance at 2 mW, 5 mW, 10 mW, and 18 mW was 121.62 W/cm2, 396.67 W/cm2, 690.95 W/cm2 and 1335.24 W/cm2, respectively. Theoretical irradiance was 153.16 W/cm2, 381.84 W/cm2, 763.19 W/cm2 and 1373.75 W/cm2, with average relative differences of 0.259, 0.037, 0.105, 0.029. For tree shrews [pupil diameter (4.5±0.2)mm, axial length (6.78±0.17)mm], actual retinal irradiance was 163.21 W/cm2, 385.71 W/cm2, 751.19 W/cm2 and 1471.43 W/cm2, respectively, while theoretical values were 149.12 W/cm2, 372.80 W/cm2, 745.60 W/cm2 and 1339.66 W/cm2, with average relative differences of 0.086, 0.033, 0.007, 0.090. Based on the model's prediction for human eyes (axial length of 24 mm), at a laser power of 2 mW, as the pupil diameter increases from 2 mm to 7 mm, the retinal irradiance increases from 16.85 W/cm2 to 206.96 W/cm2. According to national laser safety standards, the safe exposure parameters for human eyes are determined as follows: for an exposure time of 180 s, the pupil diameter should not exceed 4.26 mm, and the emission laser power should not exceed 2 mW. Conclusion The RTE mathematical model accurately predicts retinal irradiance for 650 nm red laser. Retinal irradiance increases as laser power increases, axial length decreases, and pupil size increases, showing an incompletely linear relationship.

Key words: Myopia, Guinea pigs, Tree shrew, Low-intensity red light therapy, Mathematical model