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Implications of gain modulation in brainstem circuits: VOR control system

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Abstract

Gain modulation is believed to be a common integration mechanism employed by neurons to combine information from various sources. Although gain fields have been shown to exist in some cortical and subcortical areas of the brain, their existence has not been explored in the brainstem. In the present modeling study, we develop a physiologically relevant simplified model for the angular vestibulo-ocular reflex (VOR) to show that gain modulation could also be the underlying mechanism that modifies VOR function with sensorimotor context (i.e. concurrent eye positions and stimulus intensity). The resulting nonlinear model is further extended to generate both slow and quick phases of the VOR. Through simulation of the hybrid nonlinear model we show that disconjugate eye movements during the VOR are an inevitable consequence of the existence of such gain fields in the bilateral VOR pathway. Finally, we will explore the properties of the predicted disconjugate component. We will demonstrate that the apparent phase characteristics of the disconjugate response vary with the concurrent conjugate component.

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Acknowledgements

Supported by grants from the Canadian 797 Institute of Health Research (CIHR).

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Authors and Affiliations

  1. Biomedical Engineering Department, McGill University, Montreal, Quebec, Canada

    Elham Khojasteh & Henrietta L. Galiana

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  1. Elham Khojasteh
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Correspondence to Elham Khojasteh.

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Appendix

Appendix

The addition of cerebellar pathways to the current model can improve the gaze holding time constant in darkness. To demonstrate this, two of the many possible scenarios are presented in Fig. 9. Dashed pathways in Fig. 9(a), (b) show postulated pathways to-from the cerebellum. Both (a) and (b) include the inhibitory pathway from cerebellar gaze-velocity Purkinje cells (PJ) to the EHV (or FTN) neurons. PJ neurons receive ipsilateral vestibular input from primary afferents. They also receive an input from the paramedian tract neurons in the brainstem. In (a) we assume that they receive the efference copy of eye position commands, and in (b), a copy of the motor neuron drive. This is only a simplistic assumption for the sake of demonstrating how adding cerebellar loops will improve gaze holding in the model. An extensive study of the literature will be needed to exactly determine the cell types that project to the PJ cells.

Fig. 9
figure 9

(a, b) show two possible alternatives for adding cerebellar pathways to the slow-phase structure.. Dashed lines show cerebellar connections

Full size image

The two gaze holding time constants from the new structure in Fig. 9(a) will be:

$$ T_1 \! = \! \frac{T_f(1\!-\!c)}{1\!-\!c\!-\!k_f(ad\!+\!q(1\!-\!c)\frac{\partial{g(.)}}{\partial{x}}\mid_{x_0}) \mathbf{-k_fmn(1\!-\!c)\frac{\partial{g(.)}} {\partial{x}}\mid_{x_0}}}\\ $$
(6a)
$$ T_2 \! = \! \frac{T_f(1\!+\!c)}{1\!+\!c\!-k_f(ad\!+\!q(1\!+\!c) \frac{\partial{g(.)}}{\partial{x}}\mid_{x_0})\mathbf{-k_fmn(1\!+\!c)\frac{\partial{g(.)}} {\partial{x}}\mid_{x_0}}} $$
(6b)

The two gaze holding time constants from the new structure in Fig. 9(b) will be:

$$ T_1 \! = \! \frac{T_f(1\!-\!c)(1\mathbf{-mn\frac{\partial{g(.)}}{\partial{x}}\mid_{x_0}})} {(1\!-\!c)(1\mathbf{-mn\frac{\partial{g(.)}}{\partial{x}}\mid_{x_0}})\!-\!k_f(ad\!+\!q(1\!-\!c) \frac{\partial{g(.)}}{\partial{x}}\mid_{x_0})}\\ $$
(7a)
$$ T_2 = \frac{T_f(1\!+\!c)(1\!\mathbf{-mn\frac{\partial{g(.)}}{\partial{x}}\mid_{x_0}})} {(1\!+\!c)(1\mathbf{-mn\frac{\partial{g(.)}}{\partial{x}}\mid_{x_0}})\!-\!k_f(ad\!+\!q(1\!+\!c)\frac{\partial{g(.)}} {\partial{x}}\mid_{x_0})} $$
(7b)

The effect of adding the cerebellar loop is emphasized with bold letters in the above equations. By comparing the new time constants (Eq. (6a), (6b), (7a), (7b)) with Eqs. (2a) and (2b), it can be shown that the model time constants will become larger in both structures of Fig. 9. However, as mentioned in the Discussion, adding new pathways may require adjustments to some model parameters to preserve the desired global performance.

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Khojasteh, E., Galiana, H.L. Implications of gain modulation in brainstem circuits: VOR control system. J Comput Neurosci 27, 437–451 (2009). https://doi.org/10.1007/s10827-009-0156-4

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