Improving structure-function relationship by optimizing mathematical retinal nerve fiber layer models on perimetric data.

Abstract

 

Purpose

 

To present a method to optimize mathematical retinal nerve fiber layer (RNFL) models on perimetric data of glaucomatous eyes to increase the structure-function relationship; to illustrate how to use an optimized RNFL model for spatial averaging of visual fields.

 

Methods

 

Visual fields of 103 eyes with moderate glaucoma (MD between -12 and -6 dB) were included (available at http://orgids.com). The correlation coefficient was calculated for deviation values of each pair of locations in the visual field. The generalized distance of each location pair was determined in two ways: the regular Euclidean distance, and the distance across RNFL fibers from a mathematical RNFL model (Airaksinen, PNAS, 2008). Each set of distances and correlation coefficients was fitted by a monotonically decreasing function, such that larger distances resulted in smaller correlation coefficients. A small root mean square error (RMSE) of the fit then implied a strong structure-function relationship. The RNFL model's shape parameters were therefore optimized by minimizing the resulting RMSE. Visual fields were then spatially averaged according to the optimized RNFL model.

 

Results

 

The RMSE for the Euclidean distance was 0.30. Our initial values for the RNFL model (A=0.8, B=0.015) resulted in an RMSE of 0.23. Optimized values for A and B were 0.4 and 0.02, respectively, resulting in an RMSE of 0.14. Correlation coefficients and distances are shown in Figure 1, together with the fiber bundles' course. Figure 2 shows an example of sensitivity deviation values and the result of averaging based on Euclidean distances or the optimized RNFL model. Averaging along the RNFL bundles leaves important visual field details intact.

 

Conclusions

 

The presented method enables the optimization of a mathematical RNFL model to perimetric data of glaucomatous eyes. These optimized structural models exhibit a strong relationship with functional visual field measurements. One application is the spatial averaging of visual fields to reduce noise without removing clinically relevant patterns.

 

 

Figure 1. Pairwise correlation coefficient as a function of their distance. (top) Euclidean distance. (bottom) Angle according to RNFL model (the inset shows the modeled course of fibers).

 

 

Figure 2. Spatial averaging of visual field data. (top) Threshold deviation values. (middle) Euclidean averaging. (bottom) RNFL model based averaging.

 

Keywords: 758 visual fields • 610 nerve fiber layer • 642 perimetry