Downbeat nystagmus: evidence for enhancement of utriculo-ocular pathways by ocular vestibular evoked myogenic potentials?

Abstract

Downbeat nystagmus (DBN) is caused by an impairment of Purkinje cells in the flocculus. The decreased cerebellar inhibitory input affects otolith pathways. Since ocular and cervical vestibular evoked myogenic potentials (o-/cVEMP) test the otoliths, the VEMP were measured in DBN patients and in controls. Sixteen patients with DBN, 14 cerebellar oculomotor disorder patients without DBN (COMD), and 16 healthy controls were examined with o-/cVEMP. Computational modeling was used to predict VEMP differences between groups. DBN patients had significantly higher oVEMP peak-to-peak (PP) amplitudes than COMD patients without DBN and controls. Cervical VEMP did not differ. The computational model of DBN predicted a twofold oVEMP increase for DBN patients. These findings suggest an enhancement of the utriculo-ocular response. The unchanged cVEMP indicate no effect on the otolith-cervical reflex in DBN. Computational modeling suggests that the utriculo-ocular enhancement is caused by an impaired vertical neural integrator resulting in the increased influence of utricular signals. This also explains the gravitational dependence of DBN.

Appendix

The previously published model ([18], see their Figure 1) can be slightly simplified for the present simulations by setting several inputs to zero.

In particular, for the oVEMP simulation we can neglect saccadic eye movements, there is no semicircular canal input, the visual input can be neglected due to the open-loop character of oVEMP, and the eye plant equation describing mainly the dynamics of the eyeball is not required, since oVEMP are measured at the level of the extraocular eye muscles. Consequently, the remaining equations aredepends on the PC gain

• 1. the utricular input $u = g_{u} \cdot \sin \alpha + \delta_{\text{tap}}$ with α being the pitch angle of the head and δ _tap the oVEMP stimulus (“otoliths” in [18] Figure 1),

• 2. the brainstem integrator (“INC” in [18] Figure 1) in Laplace notation (s is the complex frequency) can be written as $e_{i} = \left( { - p + c_{\text{ft}} - u} \right) \cdot \frac{{\tau_{\text{b}} - \tau_{\text{e}} }}{{1 + \tau_{\text{b}} s}}$ with τ _b and τ _e being the time constants of brainstem integrator and eye plant, p being the PC output, and c _ft a bias term compensating for the PC resting discharge,

• 3. the motor command $m = \left( { - p + c_{\text{ft}} } \right) \cdot \tau_{\text{e}} + e_{i}$ sent to the eye muscles (input to “eye plant” in [18] Figure 1),

• 4. the floccular loop yielding the PC output $p = g \cdot v_{\text{e}} + p_{\text{rest}}$ (“FL-Purkinje-cells” in [18] Figure 1) with g being the PC gain factor, v _e being the internal estimate of eye velocity $v_{\text{e}} = \frac{s}{{1 + \tau_{\text{e}} s}} \cdot m$, and p _rest being the PC resting discharge (normally p _rest = c _ft).

Given these equations, we can now solve for the motor command following an oVEMP tap δ _tap. First, we set $p = g \cdot \frac{s}{{1 + \tau_{\text{e}} s}}m + p_{\text{rest}}$ and plug (2) into (3) as $m = ( - p + c_{\text{ft}} ) \cdot \tau_{\text{e}} + ( - p + c_{\text{ft}} - u)\frac{{\tau_{\text{b}} - \tau_{\text{e}} }}{{1 + \tau_{\text{b}} s}}$. Ignoring the bias terms (assuming they cancel out) we can simplify and get $m = - p \cdot \frac{{(1 + \tau_{\text{e}} s)\tau_{\text{b}} }}{{1 + \tau_{\text{e}} s}} - u\frac{{\tau_{\text{b}} - \tau_{\text{e}} }}{{1 - \tau_{\text{b}} s}}$. Now we can insert p and solve for m: $m = - \frac{{\tau_{\text{b}} - \tau_{\text{e}} }}{{1 + \tau_{\text{b}} (1 + g)s}}u$. The oVEMP input to the utricle can be approximated as impulse with amplitude d resulting in a muscle response of $m = - \frac{{\tau_{\text{b}} - \tau_{\text{e}} }}{{\tau_{\text{b}} (1 + g)}}d$, which depends on the PC gain g. As in [18], to simulate healthy subjects, the gain is set to g = 10, while for an average DBN patient the gain can be set to about g = 5. If the oVEMP amplitude d is the same in both healthy subjects and patients, independently of the other constants we thus get $m_{\text{DBN}} = \frac{{1 + g_{\text{healthy}} }}{{1 + g_{\text{DBN}} }} \cdot m_{\text{healthy}} = 1.83 \cdot m_{\text{healthy}}$, i.e. a motor command to the eye muscles which is about 180 % of the amplitude in DBN patients. Note that this analytical derivation assumes upright position and gaze straight ahead. Due to the nonlinear Purkinje cell activation function, the relation changes to lower values with upward gaze and pitch-back position.