The VOR Simulator: How It Works

A white paper on the physiology model and 3D visualisation behind this app

1. What this app simulates

The Vestibulo-Ocular Reflex (VOR) is the reflex that keeps your gaze fixed on a target while your head moves — it's why you can read a street sign while walking, or keep eye contact while shaking your head "no". This simulator drives a real-time, physiologically grounded model of that reflex from live device rotation (phone/tablet gyroscope) or mouse-drag input, and renders the downstream effects: fluid movement in the inner ear's semicircular canals, changes in vestibular nerve firing rate, and the resulting eye movement (nystagmus).

2. The pipeline, end to end

Every animation frame runs the same five-stage pipeline:

1. Head angular velocity is read from the device gyroscope (or synthesised from mouse-drag velocity, or played back from a scripted maneuver such as Dix-Hallpike or the Epley repositioning sequence).
2. Vector projection resolves that 3D angular velocity onto each of the six semicircular canals' individual sensing axes.
3. Cupular fluid dynamics convert each canal's projected velocity into a deflection signal using a damped-pendulum model.
4. Neural firing converts cupular deflection into a vestibular nerve firing rate for each canal, obeying Ewald's Laws.
5. Eye mechanics compute the slow-phase drift and fast-phase saccades (nystagmus) that the brainstem would command from the difference in firing rate between paired canals.

3. Vector projection: six canals, three planes

The six semicircular canals aren't aligned with simple up/down/left/right axes — each is tilted, and they work as three functional pairs:

• Horizontal pair (left/right horizontal canals) — primarily sense yaw (turning your head side to side).
• LARP pair (left anterior + right posterior) — a diagonal plane.
• RALP pair (right anterior + left posterior) — the mirror diagonal plane.

Each canal is represented by a unit vector n̂ pointing along its sensing axis. The stimulation a canal receives is the dot product of the head's angular velocity vector ω with that canal's axis: ω_canal = ω · n̂_canal. This is why tilting your head changes which canals respond to a given rotation — you're changing the alignment between the rotation axis and each canal's fixed sensing direction.

4. Cupula fluid dynamics: a damped pendulum, not a bucket of water

Each canal is a fluid-filled ring with a gelatinous membrane (the cupula) that bows in response to fluid inertia. Physiologically this behaves like a heavily overdamped torsion pendulum (the Steinhausen model): it responds promptly to acceleration, then relaxes back toward zero even during sustained constant-velocity rotation, with a biological time constant around 6 seconds. The app models this as a discrete high-pass filter run every frame — cupular deflection decays a little each tick while being driven by the canal's current angular velocity. This decay is the reason a prolonged constant-speed spin eventually stops producing a sensation of turning, and why stopping abruptly produces a strong after-sensation in the opposite direction.

5. Neural firing and Ewald's Laws

Each vestibular nerve has a resting discharge rate of roughly 90 spikes/second even with no head movement at all — this baseline is what makes the reflex directionally sensitive, since a rate can go up or down from rest. Cupular deflection pushes the firing rate up or down from that baseline:

• Horizontal canals: fluid movement toward the ampulla (ampullopetal) excites; movement away from it (ampullofugal) inhibits.
• Vertical canals (anterior/posterior): the rule flips — ampullofugal flow excites, ampullopetal flow inhibits.
• Ewald's Second Law: firing rate can rise well above baseline (modelled up to roughly 400 Hz) but can never fall below 0 Hz. This floor is the physiological root of many clinical asymmetries: a canal being maximally inhibited saturates at zero, while its excited partner keeps climbing, so a given real rotation does not produce symmetric left/right neural signals.

The canal panel's colour coding shows this directly — canals shift toward red as firing rises above baseline (excitation) and toward blue as it falls below baseline (inhibition), with neutral grey at rest.

6. From firing-rate asymmetry to eye movement (nystagmus)

The brainstem doesn't read absolute firing rates — it reads the difference between a canal pair's left and right members (e.g. Δf = f_LH − f_RH for the horizontal pair). That difference drives a smooth, involuntary slow-phase eye drift in the direction opposite the head's rotation, at a velocity (SPV) proportional to Δf — this is the reflex actually doing its job of holding gaze steady on the world while the head moves under it.

Because the eye can't drift indefinitely in one direction, once the accumulated slow-phase displacement crosses a mechanical threshold (about 15°), the eye snaps back rapidly in a fast-phase saccade before resuming slow-phase tracking. This slow-drift/fast-reset sawtooth is nystagmus, and it's what the simulator renders in the eye panels — by convention, the fast phase's direction is used clinically to name the nystagmus.

7. Live input: how head motion gets into the model

On a phone or tablet, the app requests access to the device's rotation-rate sensor (DeviceMotionEvent) and reads angular velocity directly in degrees/second, converting to radians for the physics. On desktop, mouse-drag gestures are converted into an equivalent synthetic angular velocity so the same downstream pipeline runs unmodified. A library of scripted diagnostic and repositioning maneuvers (Dix-Hallpike, Epley, Semont, BBQ-roll, Zuma, roll-test) can also drive head orientation directly, useful for demonstrating canalithiasis (BPPV) scenarios where free-floating otoconia debris in a canal generates its own transient stimulation independent of real head motion.

8. The 3D visualisation

The inner-ear geometry (semicircular canals, ampullae, utricle) is not a stylised cartoon — it's built from real anatomical geometry sourced from the IE-Map in-vivo inner-ear atlas (Ahmadi et al., 2021, Scientific Reports). Individual canal and ampulla meshes are identified during asset load and their materials are recoloured every frame from the neural firing engine's output, so the 3D model becomes a live readout of which canals are excited or inhibited for the current head motion. A separate "micro fluid view" zooms the camera onto an individual ampulla to demonstrate cupular deflection and endolymph flow directly, and a neural firing-rate plot mode shows the same signals numerically alongside the 3D view.

9. Why this matters clinically

This model is the same reasoning clinicians use at the bedside: a rotation is decomposed onto the six canal axes, cupular dynamics determine how briskly each canal responds, firing-rate asymmetry (bounded below by zero per Ewald's Second Law) explains why some maneuvers produce strong nystagmus and others don't, and the resulting slow/fast-phase eye movement pattern is exactly what's observed during Dix-Hallpike testing, caloric testing, and head-impulse testing. The simulator exists to make that normally invisible chain — from a millisecond of angular velocity to a visible beat of nystagmus — something you can see happen in real time.