A “beat-to-beat” interval generator for optokinetic nystagmus

Abstract

An analysis of optokinetic responses was used to derive an iterative model that reproduces the duration of nystagmus slow phases and eye position control during optokinetic nystagmus. Optokinetic nystagmus was recorded with magnetic search coils from red-eared turtles (Pseudemys scripta elegans) during monocular, random dot pattern stimulation at constant velocities ranging from 0.25-63 degrees/s. The beat-to-beat behavior of slow phase durations was consistent with the existence of an underlying neural clock, termed the basic interval generator, that is based on an integrate-to-fire neuron model. This hypothetical basic interval generator produces an interval that is the product of the duration of the previous interval and a mean 1 truncated normal variate with variance sigma 2. Data analyses indicated that the initial value of the interval generator during a period of nystagmus, termed tau 0, is proportional to the inverse square root of slow phase eye velocity. Further, if the eye was deviated in the slow phase direction (re mean eye position) when the slow phase began, the slow phase duration was consistent with a single cycle of the basic interval generator. However, if the eye was deviated in the fast phase direction, the distribution of the durations of the ensuing slow phases indicated that a proportion of the slow phases were produced by more than one cycle of the basic interval generator. This phenomenon is termed "skipping a beat" and occurs with probability Ps. Finally, the amplitude of fast phases behaved as a linear function of eye position at the fast phase onset and the product of tau 0 and slow phase eye velocity. A computer simulation reproduced the observed distribution of slow phase durations, the proportion of fast phases in the fast phase and slow phase directions and the distribution of eye positions at the onset and end of fast phases. This novel model suggests that both timing and eye position information contribute to the alternation of nystagmus fast and slow phases.

On the correlation dimension of optokinetic nystagmus eye movements: computational parameters, filtering, nonstationarity, and surrogate data

“…Even so, there has been a problem in the modeling of the fast phases of vestibular and optokinetic nystagmus. Most models include a statistical or probabilistic component to create the timing and amplitude distribution of the fast phases (e.g., Cheng and Outerbridge 1974;Chun and Robinson 1978;Balaban and Ariel 1992; one notable exception is a model developed by Galiana 1991). The application of the tools of nonlinear dynamics, such as the correlation dimension presented here, might allow us to model the generation of nystagmus better.…”

Human optokinetic nystagmus: A stochastic analysis

“…SPs are slow movements made in the direction of stimulus motion with a gain (SP speed ‚ stimulus speed) less than unity, which decreases with stimulus speed (Fletcher, Hain, & Zee, 1990) so complete retinal stabilization is seldom achieved. SPs tend to bring the eye position to a more central location, but the timing and amplitude of both SPs and QPs are highly variable (Anastasio, 1996;Balaban & Ariel, 1992;Carpenter, 1993Carpenter, , 1994Cheng & Outerbridge, 1974;Trillenberg, Zee, & Shelhamer, 2002). This variability is intrinsic and implies either an embedded stochastic process or complicated deterministic behavior manifesting as chaos.…”

On the distribution of fast-phase intervals in optokinetic and vestibular nystagmus

“…Furthermore, their model requires the detection of outliers (excessively long or short IFPIs) after which the algorithm is reset to some default value. In summary, this model is much more complicated than the model underlying the IG distribution, and Anastasio (1996) noted that the data from Balaban and Ariel (1991) were fit equally well with the simpler IG law. A closer look at the experimental situation indeed shows that for a given mean IFPI of 0.30 s and variance of 0.01 s 2 (which are representative of the histograms we collected), the difference between the IG distribution and the lognormal distribution is extremely small.…”

“…All models assume a fixed threshold (thin line) that must be reached by a hypothetical activation parameter in order to trigger a fast phase. The time course of the activation parameter varies from fast phase to fast phase, and the diagrams show two examples (thick and shaded lines) for each model: A reciprocal Gaussian model (rise of the activation parameter with a slope that is normally distributed); B inverse Gaussian model (activation parameter is changed by random increments and decrements that are added to a fixed drift); C gamma model (activation parameter is increased by integer amounts, due to input impulses that arrive at exponentially distributed intervals) Balaban and Ariel (1991), studying OKN in three turtles, described IFPIs with a lognormal distribution. The model underlying this distribution does not fit the scheme above.…”

“…Balaban and Ariel (1991) fitted experimental fast-phase-interval histograms with a lognormal distribution function; the lognormal distribution results when a given fast-phase interval is the product of the previous fast-phase interval and a normally distributed random value. Carpenter (1993) suggested fitting IFPI histograms with the reciprocal Gaussian distribution, which assumes that each fastphase interval is the quotient of a constant threshold and a normally-distributed slope parameter.…”