Analytic methods in assessment of optic nerve cupping.

: The intent of this paper is to provide a systems-based analysis of the methods used to evaluate optic nerve cupping, identify potential flaws in these systems, and propose alternatives better to assess this anatomic quantity. Estimation of optic nerve cupping requires an analytic understanding of both the psychophysical as well as the mathematical bases inherent in this measure. When the (decimal-based) cup-to-disc ratio is used to quantitate optic nerve cupping, a one-dimensional, linear estimate is produced, which in turn is derived from two- or three-dimensional, non-linear physical quantities of area or volume, respectively. When extrapolating from volume, to area, to linear measures, due to the psychophysical constraints which limit this task, such a data-compressed estimate of optic nerve cupping may neither accurately reflect, nor correctly represent, the true amount of cupping actually present in the optic nerve head. This type of one-dimensional metric (when comparing calculations from two- or three-dimensional measures over a range of optic nerve cupping), appears to introduce errors which, while most pronounced earlier on in the disease progression, often overestimate the amount of relative cupping (percent cupping) present in a pathological process like glaucoma. The same systemic errors can also lead to overestimation of the progression in cupping, especially in optic nerves with low cup-to disc values. To provide clinically meaningful estimates of optic nerve cupping, the practitioner needs to be aware of psychophysical and mathematical limitations inherent in using a linear cup-to-disc ratio to estimate the amount of cupping observed in a physical structure like the optic disc. The resultant flaws introduced by observer extrapolation from three, to two, to one dimensions (volume, area, and linear); transposition from non-linear to linear quantities; and optical illusions, caused by factors like disc topology, morphology, and ametropia, can all influence subjective-based estimates of optic nerve cupping. To improve clinical outcomes, a non-linear mathematical technique is proposed which utilizes two- or three-dimensional objective measures of optic nerve cupping to describe, more accurately and more precisely, the anatomic quantities (disc, cup, and rim) under discussion. The authors acknowledge that any proposed technique is only a beginning to the work required to improve the clinical value of this type of measure.