Vestibulo-Ocular Gain

Integrate signed head and eye velocity over a supplied impulse window and compute compensatory area gain; corrective saccades must be excluded by the caller.

Description

Vestibulo-ocular area gain compares integrated eye and head velocities over an impulse window.

Vestibulo-ocular area gain compares integrated eye and head velocities over an impulse window. Compensation reverses eye direction, which accounts for the negative sign.

The tool returns headDisplacement (head displacement); eyeDisplacement (eye displacement); compensatoryGain (compensatory gain). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.

When to use Vestibulo-Ocular Gain

Use Vestibulo-Ocular Gain when you already have timesSeconds, headVelocities, eyeVelocities and want headDisplacement, eyeDisplacement, compensatoryGain. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.

How to use Vestibulo-Ocular Gain and understand its results

Enter timesSeconds, headVelocities, eyeVelocities using the field table below. Match the units, ordering and data boundaries described in the calculation.
Run the tool after checking the stated bounds and matching paired observations or categories. A malformed request gives a tool error rather than a usable measurement.
Read headDisplacement, eyeDisplacement, compensatoryGain. Use the calculation and interpretation below to distinguish amounts, ratios, signs and decision flags where applicable.
Review the supplied parameters and assumptions before using the result in a report or comparing it with another observation.

Input field	Meaning	Value type and bounds	Requirement
timesSeconds	Times seconds	list of number	Required
headVelocities	Head velocities	list of number	Required
eyeVelocities	Eye velocities	list of number	Required

Trapezoidally integrate both aligned traces on strictly increasing times. Require nonzero net head displacement and use consistent angular units.

gain = −∫eyeVelocity dt / ∫headVelocity dt

The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.

json

{
  "input": {
    "timesSeconds": [
      0,
      1,
      2
    ],
    "headVelocities": [
      1,
      1,
      1
    ],
    "eyeVelocities": [
      -0.8,
      -0.8,
      -0.8
    ]
  },
  "output": {
    "headDisplacement": 2,
    "eyeDisplacement": -1.6,
    "compensatoryGain": 0.8
  }
}

Limitations and assumptions

Bidirectional head motion can cancel in the denominator. No impulse segmentation, artifact rejection or clinical classification is performed.

Numerical inputs must be finite. The tool checks its declared input shape and calculation constraints; those checks do not verify the quality, calibration or representativeness of the supplied observations.

Alternative or Complementary methods

Saccade Velocity: Derive planar eye-path speeds from timestamped horizontal/vertical angles; finite-difference peaks are cadence-limited and not instantaneous physiological peaks. Smooth Pursuit Gain: Fit eye velocity against target velocity after caller-supplied saccade/blink exclusions; signed slope and intercept are preserved.

Methodological background: Digital Library of Mathematical Functions: Quadrature.^[1]

References

Digital Library of Mathematical Functions: Quadrature — National Institute of Standards and Technology

Similar or alternative tools

Saccade Velocity
Derive planar eye-path speeds from timestamped horizontal/vertical angles; finite-difference peaks are cadence-limited and not instantaneous physiological peaks.
Smooth Pursuit Gain
Fit eye velocity against target velocity after caller-supplied saccade/blink exclusions; signed slope and intercept are preserved.