Vestibulo-Ocular Reflex: Gaze Stabilization

Head Rotation

Oscillation frequency 0.50 Hz

Oscillation amplitude 20°

Reflex Parameters

VOR gain (eye / head) 1.00

VOR suppression — fixate a head-fixed target

Live Readouts

Head velocity

0.0°/s

Eye velocity

0.0°/s

Retinal slip

0.0°

Measured gain

0.00

How it works

The horizontal semicircular canals sense head angular velocity, not position. The cupula — an elastic membrane deflected by inertial lag of the endolymph fluid — behaves like a heavily damped torsion pendulum. Ignoring its ~3 ms short time constant, its transfer function relating cupula deflection Δ to head velocity Ω is a high-pass filter:

Δ(s)/Ω(s) = T1·s / (1 + T1·s),   T1 ≈ 5–7 s

implemented here as: dz/dt = (Ω_head − z)/T1   (low-pass state)
                     Δ = Ω_head − z             (cupula/canal signal)

Because T1 is long, Δ ≈ Ω_head for any head movement faster than about 1/T1 — the canal reports velocity accurately during ordinary head turns — but decays toward zero during sustained constant-velocity rotation, which is why a spinning sensation fades even though you're still turning.

The vestibular nuclei convert Δ into a three-neuron-arc command that drives the extraocular muscles at gain g:

ω_eye = −g · Δ         (ideal g = 1.0 → perfect gaze stabilization)
gaze angle = θ_head + θ_eye-in-head
retinal slip = −(gaze angle)   [target fixed at 0°]

VOR gain slider — g < 1 under-compensates (vestibular hypofunction, causes oscillopsia — the world appears to jump during head movement); g > 1 over-compensates.
VOR suppression — when you deliberately track a target that moves with your head (reading a phone while walking), smooth pursuit overrides the reflex and drives eye-in-head offset back toward zero instead of counter-rotating.
Eye-in-head rotation is clamped to ±40°, the approximate physiological range of horizontal ocular motility before a real eye would need a saccadic reset (the fast phase of nystagmus), simplified away here to keep the slow-phase compensation visible.

Clinical relevance: the head-impulse test measures exactly this gain at the bedside — a corrective catch-up saccade after a fast head turn indicates g well below 1, a hallmark of vestibular neuritis or ototoxic canal damage.

Gaze on target Small retinal slip Large retinal slip

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Vestibulo-Ocular Reflex: Gaze Stabilization During Head Rotation