Vergence Fusion Sustaining Oscillations

Abstract

Introduction: Previous studies have shown that the slow, or fusion sustaining, component of disparity vergence contains oscillatory behavior as would be expected if fusion is sustained by visual feedback. This study extends the examination of this behavior to a wider range of frequencies and a larger number of subjects.

Methods: Disparity vergence responses to symmetrical 4.0 deg step changes in target position were recorded in 20 subjects. Approximately three seconds of the late component of each response were isolated using interactive graphics and the frequency spectrum calculated. Peaks in these spectra associated with oscillatory behavior were identified and examined.

Results: All subjects exhibited oscillatory behavior with fundamental frequencies ranging between 0.37 and 0.55 Hz; much lower than those identified in the earlier study. All responses showed significant higher frequency components. The relationship between higher frequency components and the fundamental frequency suggest may be harmonics. A correlation was found across subjects between the amplitude of the fundamental frequency and the maximum velocity of the fusion initiating component probably due to the gain of shared neural pathways.

Conclusion: Low frequency oscillatory behavior was found in all subjects adding support that the slow, or fusion sustaining, component is mediated by a feedback control.

Keywords: feedback control; fusion sustaining component; oscillations; slow component; vergence.

Figure 1:

A schematic model of the dual-mode control strategy showing pathways for fusion initiating and fusion sustaining components (from Semmlow et al., 21).

Figure 2:

Left graph: An ensemble of 4 vergence eye movements in response to a step stimulus from 4.0 to 8.0 deg convergent. Right graph: Fusion sustaining components isolated from 2 of the responses on the left showing the last 3 seconds of the recorded responses.

Figure 3:

The plots on the left show two examples of fusion sustaining components isolated from vergence responses. The plots on the right show the magnitude frequency spectra associated with these components. The ‘*’ marks indicate frequency peaks.

Figure 4:

Bar graph showing the fundamental frequencies, in Hz, found for the 20 subjects. The filled section of each bar indicates the frequency (units of Hz) averaged over all responses with error bars indicating one standard deviation Top numbers indicate number of responses.

Figure 5:

The amplitude of the fundamental frequency spectral peaks presented in the same order and format as in Figure 4. Averaged peak amplitudes varied widely between 0.04 and 0.18 deg rms.

Figure 6:

Mean amplitudes (squares) of the first 5 spectral peaks averaged across all subjects. The large standard deviations reflect the large variability in the amplitude of the oscillation. A least squares algorithm was used to fit an exponential to the data.

Figure 7:

Average frequency in Hz of the fundamental frequency (n = 1) and the first 4 harmonics averaged across all subjects. The small standard deviations reflect the relative constancy of the fundamental (i.e., first) frequency across the subjects. Note that the middle three peaks fall very close to a straight line (dotted blue line).

(Eq. 1)

Figure 8:

Average frequency in Hz of the fundamental frequency (n = 1) and the first 4 harmonics plotted as in Figure 7 except the frequencies are normalized to f₁, the fundamental frequency. The slope of the first 3 harmonics is 0.62 Hz averaged across all subjects.

Figure 9:

Relationship between the amplitude of the fundamental frequency peak in the fusion sustaining component and the maximum velocity of the fusion initiating component for all responses from all subjects.