Ocular oscillations generated by coupling of brainstem excitatory and inhibitory saccadic burst neurons

Abstract

The human saccadic system is potentially unstable and may oscillate if the burst neurons, which generate saccades, are not inhibited by omnipause neurons. A previous study showed that combined saccade vergence movements can evoke oscillations in normal subjects. We set out to determine: 1) whether similar oscillations can be recorded during other paradigms associated with inhibition of omnipause neurons; 2) whether lesions of the fastigial nuclei disrupt such oscillations; and 3) whether such oscillations can be reproduced using a model based on the coupling of excitatory and inhibitory burst neurons. We recorded saccadic oscillations during vergence movements, combined saccade-vergence movements, vertical saccades, pure vergence and blinks in three normal subjects, and in a patient with saccadic hypermetria due to a surgical lesion affecting both fastigial nuclei. During combined saccade-vergence, normal subjects and the cerebellar patient developed small-amplitude (0.1–0.5°), high-frequency (27–35 Hz), conjugate horizontal saccadic oscillations. Oscillations of a similar amplitude and frequency occurred during blinks, pure vergence and vertical saccades. One normal subject could generate saccadic oscillations voluntarily (~0.7° amplitude, 25 Hz) during sustained convergence. Previous models proposed that high-frequency eye oscillations produced by the saccadic system (saccadic oscillations), occur because of a delay in a negative feedback loop around high-gain, excitatory burst neurons in the brainstem. The feedback included the cerebellar fastigial nuclei. We propose another model that accounts for saccadic oscillations based on 1) coupling of excitatory and inhibitory burst neurons in the brainstem and 2) the hypothesis that burst neurons show post-inhibitory rebound discharge. When omnipause neurons are inhibited (as during saccades, saccade-vergence movements and blinks), this new model simulates oscillations with amplitudes and frequencies comparable to those in normal human subjects. The finding of saccadic oscillations in the cerebellar patient is compatible with the new model but not with the recent models including the fastigial nuclei in the classic negative-feedback loop model. Our model proposes a novel mechanism for generating oscillations in the oculomotor system and perhaps in other motor systems too.

Appendix

The model of coupled burst neurons was simulated in Simulink/Matlab. The structure of the model included OPN and two EBN/IBN pairs, connected as shown in Fig. 7. Individual neurons contained an adaptation element (as in Fig. 8a) and a synaptic delay (τ). Values for the cross-coupling coefficients and other dynamic properties are given in Table 2. The final common path (i.e., neural integrator and orbital tissues) was modeled with an integrator and one uncompensated, single-pole filter (time constant Teye).

The medium lead burst neurons were represented by bilateral pairs of inhibitory and excitatory burst neurons. Both EBN and IBN were modeled like the OPN, except that a soft-saturating nonlinearity was added to the output. The equation for this element comes from Zee and Robinson (1979):

$$B(e){\rm{ }} = {\rm{ }}\left\{ \matrix{ B_m (1 - e^{ - (e - e_0 )/b} ),e > e_0 \hfill \cr 0,e \le e_0 \hfill \cr} \right.$$

(1)

This element was added to reduce the harmonic distortion in the saccadic oscillations that was present when a hard saturation element was used. In this equation the input variable e represents motor error for the Robinson model, whereas in our model e represents an input in terms of the frequency of discharge rate, which is related to eye velocity. The values for the parameters in these equations were therefore derived from those in the original model and scaled to reflect the different input variables (cf. Table 2). The EBN and IBN were reciprocally coupled across the midline. EBN projected to ipsilateral IBN with a gain of 1.0. IBN projected to contralateral EBN with a gain of 1.0 and to contralateral IBN with a gain of either ibnLR (Left to Right side) or ibnRL (Right to Left side). These gain values were not perfectly symmetric, to ensure that the system would start oscillating as soon as the OPN shut off. When equal gains were used, the system was quasi-stable, and would only begin to oscillate after a few hundred milliseconds.