Proportional conservation of vectorial non-summation in corneal astigmatism: a thick-lens analysis in normal and keratoconic eyes

Purpose To test whether the residual between ray-traced total corneal astigmatism and the vector sum of the anterior and posterior second-order astigmatic components is an independent, disease-related signal or a proportionally conserved feature of corneal thick-lens optics. Methods Secondary analysis of a deidentified multicenter database of unoperated eyes examined with Pentacam HR and Corvis ST, restricted to clinically normal eyes and bilateral keratoconus, one eye per subject (1,680 normal; 1,181 keratoconic). Second-order Zernike astigmatic vectors were extracted over a 6.0 mm zone for the anterior (F) and posterior (B) surfaces and the ray-traced total cornea (T). The primary endpoint was the non-summation magnitude |T−F−B|. Pre-specified secondary analyses normalized the residual to total and anterior astigmatism, examined meridional-axis behavior, and tested associations with dynamic corneal response and composite indices. A sensitivity analysis added very asymmetric ectasia eyes. Results Absolute non-summation was greater in keratoconic than in normal eyes (median 0.223 vs 0.155 µm; P < 0.001; Cliff's δ = 0.225, a small effect), but every astigmatic magnitude was scaled by a similar factor (anterior ×1.48, posterior ×1.28, total ×1.52, non-summation ×1.43). Within each group the residual was near-collinear with anterior astigmatism (Spearman ρ = 0.99), and its normalized fraction was essentially identical in normal and keratoconic eyes (median 0.149 vs. 0.147; Cliff's δ = −0.06) and in both eyes of patients with very asymmetric ectasia (0.147–0.149). Front–back meridional misalignment did not differ (5.89° vs. 5.63°; P = 0.49). Partial correlations with dynamic corneal response and composite indices, adjusted for astigmatism magnitude, were uniformly weak (| ρ | < 0.11). Conclusions Corneal astigmatism is not fully described by vector summation of the two surfaces. The residual, compatible with thick-lens coupling and device-specific optical conventions, is larger in absolute terms in keratoconus but represents a constant proportion of each eye's astigmatism across the ectatic spectrum. We interpret it as a magnitude-coupled optical descriptor, not an independent diagnostic or biomechanical signal. Clinically, these findings caution against assuming direct additivity of the exported anterior and posterior astigmatic components; implications for toric and refractive planning require validation against clinically relevant optical outputs and postoperative outcomes. Future studies should model corneal and tear-film refractive-index effects explicitly.