Scaling the structure--function relationship for clinical perimetry.

PURPOSE: The full ranges of glaucomatous visual field defects and retinal ganglion cell losses extend over several orders of magnitude and therefore an interpretation of the structure-function relationship for clinical perimetry requires scaling of both variables. However, the most appropriate scale has not been determined. The present study was undertaken to compare linear and logarithmic transformations, which have been proposed for correlating the perimetric defects and neural losses of glaucoma.
METHODS: Perimetry, by behavioural testing, and retinal histology data were obtained from rhesus monkeys with significant visual field defects caused by experimental glaucoma. Ganglion cell densities were measured in histologic sections of retina that corresponded to specific perimetry test locations for the treated and control eyes. The linear (percentage) and logarithmic (decibel) relationships for sensitivity loss as a function of ganglion cell loss were analysed.
RESULTS: With decibel scaling, visual sensitivity losses and ganglion cell densities were linearly correlated with high coefficients of determination (r(2)), although the parameters of the functions varied with eccentricity. The structure-function relationships expressed as linear percentage-loss functions were less systematic in two respects. Firstly, the relationship exhibited considerable scatter in the data for small losses in visual sensitivity and, secondly, visual sensitivity losses became saturated with larger losses in ganglion cell density. The parameters of the percentage-loss functions also varied with eccentricity, but the variation was less than for the decibel-loss functions.
CONCLUSIONS: Linear scaling of perimetric defects and ganglion cell losses might potentially improve the structure-function relationship for visual defects associated with small amounts of cell loss, but the usefulness of the relationship is limited because of the high variability in that range. With log--log co-ordinates, the structure--function relationship for clinical perimetry is relatively more accurate and precise for cell losses greater than about 3 dB. The comparatively greater accuracy and precision of decibel loss functions are a likely consequence of the logarithmic scale of stimulus intensities for perimetry measurements and because the relationship between visual sensitivity and the number of neural detectors is a form of probability summation.