Modeling the cross-sectional shape of the human crystalline lens using age-related parameters instead of the conic...

Traditional conic-based models rely on conic constants, which exhibit high interindividual variability and limited age correlation, hindering population-level modeling. This study introduces a modified Poisson-Gauss (moPG) model, an enhancement of the Poisson-Gauss (PG) framework, to describe the human crystalline lens cross-sectional shape using solely age-related geometric parameters. The moPG extends the Poisson parameter m to real values via the Gamma function for continuous accommodation simulation and incorporates an equatorial curvature parameter k, inspired by Köller's egg equation, for independent equatorial control. Analyzing pupil-limited conditions in OCT and MRI datasets, a non-zero k was suggested for biological plausibility. Evaluations on in vitro lens profiles (n=10) showed better fitting than the PG model, with reduced dependence on the lens shape factor. moPG-derived surface areas, estimated from eigenlenses-model-derived geometric parameters, correlated strongly (Pearson correlation r=0.999,p<0.001) with eigenlenses surface area estimates from 83 in vivo measurements. Age-dependent simulations using two regression datasets yielded similar anterior-posterior thickness ratios but differing conic constants, further supporting the geometric consistency of the moPG formulation. Moreover, age-related equatorial changes arise from complementary effects: decreasing k>0 drives equatorial radius increase, while increasing m promotes progressive equatorial rounding.