Mathematical Modeling of Glaucomatous Optic Neuropathy--Toward Classification by Anatomical Features

Abstract

Purpose:: Confocal scanning laser microscopy (CSLM) provides detailed quantitative information about the anatomical structure of the optic nerve and peripapillary region. Mathematical modeling of these data can expose structural features useful for detection of disease and evaluation of progression. The purpose of this study was to evaluate the use of two related radial polynomial functions--Zernike and pseudozernike polynomials as well as two-dimensional B-splines--for modeling anatomical structural features of glaucomatous optic neuropathy (GON).

Methods:: Subjects at risk for GON (n = 111) and a comparison group (n = 161) were imaged using CSLM. The data from one eye of each subject were modeled using a series of Zernike and pseudozernike polynomials of varying complexity (0-256 coefficients) and two dimensional B-splines with similar dimensional complexity over a fixed 2500 µm² area. Computational time and model fidelity were compared using a one-way repeated measures ANOVA model. Stereo disc photos were graded by a panel of experts as GON or normal. Using these class labels as a gold standard, decision tree classification was performed based on these modeled features and areas under the Receiver Operating Characteristic (ROC) curves were compared for each modeling method.

Results:: The computational time required to generate the most complex model considered (256 coefficients) were identical for Zernike and pseudozernike polynomials: 61.3 ± 5.7 s, but B-spline models took only 0.065 ± 0.004 s. The residual model error (mean ±SD) for the Zernike model was 34 ± 13 µm, pseudozernike: 32 ± 12 µm and B-spline 60 ± 24 µm. There was no significant difference in residual RMS error between the two radial polynomial models, but both had significantly better fidelity than the B-spline representation (p<0.001). Classification performance estimated by ROC-curve areas were Zernike: 0.81, pseudozernike: 0.85, B-spline: 0.71.

Conclusions:: Radial polynomial models provide an efficient means of dimensional reduction that are 1) computationally feasible, 2) have good fidelity as evidenced by low residual RMS error and 3) enable GON classification based on structural features that results in very good classification performance. These methods may also permit new approaches to analysis of disease progression.

Keywords: optic nerve • computational modeling • microscopy: confocal/tunneling