Comparison of Linear vs. Non-linear Methods for Analysing the Vestibulo-ocular Reflex (VOR)

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Abstract
The vestibulo-ocular reflex (VOR) is traditionally evaluated by the gain (sensitivity) and offset (bias) of nystagmus slow phases during sinusoidal, passive, head rotation in the dark. The analysis methods used are typically only truly applicable to linear systems, but are widely used despite the fact that the VOR has been known to be non-linear since the 19th century. We show here that the parameters obtained by linear methods, with data derived from a non-linear system, can be very noisy and unreliable. The questions are: under what conditions can linear approximations be tolerated, or justified, and can an analysis approach be devised which inherently tolerates non-linearities? Using both simulated and experimental data, it is found that assuming linear analysis methods can produce variable VOR gains and erroneous estimates of the VOR bias. changing with the selected oscillation protocol. Examples of' parameter distortions in bias and VOR gain are first given using simulated data relating slow phase eye velocity to head velocity, at different peak velocities. The relevance of these distortions is then illustrated with selected examples from a database of recordings on normals and unilateral vestibular patients, during rotations in the dark 1/6 Hz and maximum speeds of 90 to 180 degrees/s. More consistent estimates of the gain and bias can be found by properly correcting for phase differences between head and eve velocity, and allowing for non-linear reflex properties. Special indices are suggested to decide whether a particular subject's VOR should be considered non-linear, in order to select the appropriate representation in each case, before estimating VOR characteristics. Selecting the appropriate model (linear or non-linear) will contribute to a better unmasking of parametric trends in the VOR, when comparing normal vs. acute-lesioned subjects, or acute vs, compensated patients. These results have many implications for the design of clinical vestibular protocols and in the evaluation of patient functional deficits.