A mathematical description of nerve fiber bundle trajectories and their variability in the human retina

Abstract

We developed a mathematical model wherein retinal nerve fiber trajectories can be described and the corresponding inter-subject variability analyzed. The model was based on traced nerve fiber bundle trajectories extracted from 55 fundus photographs of 55 human subjects. The model resembled the typical retinal nerve fiber layer course within 20 degrees eccentricity. Depending on the location of the visual field test point, the standard deviation of the calculated corresponding angular location at the optic nerve head circumference ranged from less than 1 degrees to 18 degrees , with an average of 8.8 degrees .

Fig. 1

Illustration of the superimposition process. First, images are translated in order to center the foveolae. Next, the images are zoomed and rotated in order to center the optic disks (A). Illustration of the modified polar coordinate system (B); for details see Appendix A.

Fig. 2

Superimposition of all 1660 sampled fibers (A). Example of a fit by Eq. (1) of a single fiber with c = 0.5, φ₀ = 68°, n = 9 and RMS = 0.69 (B).

Fig. 3

Parameter c (as defined in Eq. (1)) as a function of φ₀ for the superior (A) and the inferior (B) hemifield. The continuous lines represent the corresponding fits as described in Eqs. (3) and (4).

Fig. 4

Parameter b (as defined in Eq. (1)) – raw data – as a function of φ₀ for the superior (A) and the inferior (B) hemifield.

Fig. 5

Parameter b – fitted data – as a function of φ₀ for the superior (A) and the inferior (B) hemifield. Datapoints from both the original (diamond) and the independent (+) sample. The lines represent the average values and the 95% limits of the corresponding fits as described in Eqs. (5) and (6).

Fig. 6

Final model, average trajectories in 10° steps (A) and upper and lower limits of trajectories in 30° steps (B).

Fig. 7

Final model, reciprocal representation, with points from the 30–2 6° × 6° grid of the Humphrey Field Analyzer connected to the corresponding parts of the optic nerve head. The optic nerve head is presented upright; the visual field grid as projected on the retina, i.e., mirrored along the x-axis.