A sloped piecemeal Gaussian model for characterising foveal pit shape

High-quality optical coherence tomography (OCT) macular scans make it possible to distinguish a range of normal and diseased states by characterising foveal pit shape. Existing mathematical models lack the flexibility to capture all known pit variations and thus characterise the pit with limited accuracy. This study aimed to develop a new model that provides a more robust characterisation of individual foveal pit variations.

A Sloped Piecemeal Gaussian (SPG) model, consisting of a linear combination of a tilted line and a piecemeal Gaussian function (two halves of a Gaussian connected by a separate straight line), was developed to fit retinal thickness data with the flexibility to characterise different degrees of pit asymmetry and pit bottom flatness. It fitted the raw pit data between the two rims of the fovea to improve accuracy. The model was tested on 3488 macular scans from both eyes of 581 young adults (376 myopes and 206 non-myopes, mean (S.D.) age 21.9 (1.4) years). Estimates for retinal thickness, wall height and slope, pit depth and width were derived from the best-fitting model curve. Ten variations of Gaussian and Difference of Gaussian models were fitted to the same scans and compared with the SPG model for goodness of fit (by Root mean square error, RMSE), model complexity (by the Bayesian Information Criteria) and model fidelity.

The SPG model produced excellent goodness of fit (mean RMSE = 4.25 and 3.89 μm; 95% CI: 4.20, 4.30 and 3.86, 3.93 for fitting horizontal and vertical profiles respectively). The SPG model showed pit asymmetry, with average nasal walls 17.6 (11.6) μm higher and 0.96 (0.61)^° steeper than temporal walls and average superior walls 7.0 (12.2) μm higher and 0.41 (0.65)^° steeper than the inferior walls. The SPG model also revealed a continuum of human foveal shapes, from round bottoms to extended flat bottoms (up to 563 μm). 49.1% of foveal profiles were best fitted with a flat bottom >30 μm wide. Compared with the other tested models, the SPG was the preferred model overall based on the Bayesian Information Criteria.

The SPG is a new parsimonious mathematical model that improves upon other models by accounting for wall asymmetry and flat pit bottoms, providing an excellent fit and more faithful characterisation of typical foveal pit shapes and their known variations. This new model may be helpful in distinguishing normal foveal shape variations by refractive status as well by other characteristics such as sex, ethnicity and age.