Non-linearity in gaze holding: Experimental results and possible mechanisms

Cerebellar impairment may cause deficits in horizontal gaze holding, leading to centrifugal gaze-evoked nystagmus during fixation of eccentric targets. Healthy individuals show a weak drift leading to physiological nystagmus only at large gaze angles. These drifts are due to imperfect memory of the neural circuitry generating the eye position signals by integration of velocity signals. The cerebellum plays a crucial role in reducing the "leakiness" of this neural integrator. This neural integrator has been traditionally modeled as a first order low-pass filter, implying a linear relation between drift velocity and eye eccentricity. Evidences of a non-linear behavior, however, can be found in the literature. In a recent series of papers we showed that the eye drift velocity (V) can be descriptively modeled as a tangent function of gaze eccentricity (P) with the following equation: V=k₂/k₁tan(k₁P). Notably, the two parameters have distinct roles: k₁ regulates the rate of compression of the tangent, exclusively determining the non-linearity; k₂ is a pure scaling factor. This descriptive model robustly fitted the data of healthy individuals both at baseline (n=50) and following transient cerebellar impairment induced by controlled amounts of alcohol [blood alcohol content 0.06% (n=15) and 0.1% (n=15)] and of patients with chronic cerebellar impairment of various origin (n=20). Interestingly, alcohol selectively changed the scaling factor k₂, evidencing that an overall, transient cerebellar impairment does not impact the non-linear behavior. Patients with cerebellar degeneration, on the other hand, showed a change in both k₁ and k₂, implying a role of the cerebellum in limiting the range of eye positions where the non-linearity becomes relevant. Non-linearity has been reported in literature for both the neural integrator and the eye plant. While previous models using a neural network attempted to reproduce the non-linear behavior of the brainstem, we propose a block diagram reproducing the observed PV tangent relation by introducing a position dependency in the parameters of the cerebellar feedback loop.