New Approach for the Quantitative Assessment of Scleral Staphyloma: Discrete Curvature Measure Analysis of the Sclera

Current methods for evaluating scleral staphyloma morphology fail to provide curvature data of global scleral deformation. This study aimed to develop a quantitative method based on discrete differential geometry for analyzing scleral deformation caused by staphyloma.

This study retrospectively analyzed 128 eyes of 73 patients with pathological myopia. All patients underwent orbital magnetic resonance imaging and three-dimensional (3D) reconstruction. The discrete Gaussian curvature measures (DGCMs) and discrete mean curvature measures (DMCMs) of all vertices on the ocular 3D model were calculated. We further established a computational method for the degree of scleral staphyloma expansion (E/U ratio).

The posterior scleral DGCM (pDGCM) and DMCM (pDMCM) standard deviations (SDs) were significantly greater in the staphyloma group than in the non-staphyloma group (0.069 ± 0.026 vs. 0.025 ± 0.005 and 0.335 ± 0.096 vs. 0.154 ± 0.027, respectively; both P < 0.0001). The E/U ratio was strongly linearly correlated with both the pDGCM and pDMCM SDs (both P < 0.01). For staphyloma diagnosis, the areas under the receiver operating characteristic (ROC) curves for pDGCM and pDMCM SDs were 0.994 (95% confidence interval [CI], 0.984-1.000) and 0.993 (95% CI, 0.982-1.000), respectively (both P < 0.001).

The variation in the curvature of the posterior sclera is significantly greater in eyes with staphyloma than in those without. This variation is highly specific and sensitive for staphyloma diagnosis.

This method, based on discrete differential geometry, enables the direct quantification of scleral deformation, potentially providing a quantitative basis for the diagnosis and evaluation of staphyloma.