Age-related rarefaction in retinal vasculature is not linear

The fractal dimension is a global measure of complexity and is useful for quantifying anatomical structures, including the retinal vascular network. A previous study found a linear declining trend with aging on the retinal vascular fractal dimension (D_F); however, it was limited to the older population (49 years and older). This study aimed to investigate the possible models of the fractal dimension changes from young to old subjects (10-73 years). A total of 215 right-eye retinal samples, including those of 119 (55%) women and 96 (45%) men, were selected. The retinal vessels were segmented using computer-assisted software, and non-vessel fragments were deleted. The fractal dimension was measured based on the log-log plot of the number of grids versus the size. The retinal vascular D_F was analyzed to determine changes with increasing age. Finally, the data were fitted to three polynomial models. All three models are statistically significant (Linear: R² = 0.1270, 213 d.f., p < 0.001, Quadratic: R² = 0.1536, 212 d.f., p < 0.001, Cubic: R² = 0.1529, 211 d.f., p < 0.001). The quadratic regression is significantly better than the linear regression (p < 0.001); however, the increase in R² from the quadratic model to the cubic model is not significant (p = 0.97). These results suggest that the decreasing trend of the fractal dimension associated with aging is better explained by the quadratic model than by the linear and cubic models in a sample with a broader age spectrum.