Beat-to-beat control of human optokinetic nystagmus slow phase durations

This study provides the first clear evidence that the generation of optokinetic nystagmus (OKN) fast phases is a decision process that is influenced by performance of a concurrent disjunctive reaction time task (DRT). The slow phase (SP) durations are consistent with a Gaussian basic interval generator and multiple interval SP durations occur more frequently in the presence of the DRT. Hence, OKN shows dual-task interference in a manner observed in voluntary movements, such as saccades.

Abstract

This study provides the first clear evidence that the generation of optokinetic nystagmus fast phases (FPs) is a decision process that is influenced by performance of a concurrent disjunctive reaction time task (DRT). Ten subjects performed an auditory DRT during constant velocity optokinetic stimulation. Eye movements were measured in three dimensions with a magnetic search coil. Slow phase (SP) durations were defined as the interval between FPs. There were three main findings. Firstly, human optokinetic nystagmus SP durations are consistent with a model of a Gaussian basic interval generator (a type of biological clock), such that FPs can be triggered randomly at the end of a clock cycle (mean duration: 200–250 ms). Kolmogorov-Smirnov tests could not reject the modeled cumulative distribution for any data trials. Secondly, the FP need not be triggered at the end of a clock cycle, so that individual SP durations represent single or multiple clock cycles. Thirdly, the probability of generating a FP at the end of each interval generator cycle decreases significantly during performance of a DRT. These findings indicate that the alternation between SPs and FPs of optokinetic nystagmus is not purely reflexive. Rather, the triggering of the next FP is postponed more frequently if a recently presented DRT trial is pending action when the timing cycle expires. Hence, optokinetic nystagmus FPs show dual-task interference in a manner usually attributed to voluntary movements, including saccades.

NEW & NOTEWORTHY This study provides the first clear evidence that the generation of optokinetic nystagmus (OKN) fast phases is a decision process that is influenced by performance of a concurrent disjunctive reaction time task (DRT). The slow phase (SP) durations are consistent with a Gaussian basic interval generator and multiple interval SP durations occur more frequently in the presence of the DRT. Hence, OKN shows dual-task interference in a manner observed in voluntary movements, such as saccades.

optokinetic reflexes are assessed by measuring optokinetic nystagmus (OKN). Like vestibular nystagmus, the eye movements have two alternating components, slow phases (SPs) and fast phases (FPs) (Leigh and Zee 1991; Purkinje 1819). SP eye movements compensate for the velocity of movement of the head or visual surround relative to the head. Hence, they may be considered to be a period of visual information sampling during maintenance of gaze on a point in visual space relative to that of the head. By contrast, the FPs (or quick phases) typically move the eye in the direction opposite the SPs. FPs are ballistic eye movements with similar trajectories to saccades and are thought to maintain mean eye position in a particular region of visual space and within the orbit. The alternation between SPs and FPs produces a controlled, repetitive pattern of movement of the eye in the orbit that is regarded generally as “reflexive” or automatic.

Three basic models have been proposed to explain control of the regular alternation between FPs and SPs. An eye position control hypothesis proposed that extraocular proprioception (an eye position signal) during SPs triggers FPs to maintain nystagmus within a particular location relative to the orbit (ter Braak 1936). An internal timing (or clocking) hypothesis, developed by Ohm (1928-9), proposed that the duration of SPs is governed by a central interval generator. ter Braak's (1936) hybrid position-interval generator hypothesis is a third approach; it posits that the SP-FP alternation is governed by coordinated actions of both a proprioceptive-driven control system and a central temporal pattern generator.

The internal timing hypothesis was supported by the observation of multimodal distributions of SP durations in human nystagmus (Cheng and Outerbridge 1974) and by an analysis of turtle OKN by Balaban and Ariel (1992). The timing of SP durations (or intervals between FPs) was consistent with the existence of a basic interval generator, which elapsed to permit generation of the FP. However, FP generation was not obligatory at the end of a basic interval generator cycle. Rather, the probability of FP generation reflected an internal decision process with eye position sensitivity. If eye position deviated in the SP direction, with regard to mean eye position, when the SP began, the FP was generated after a single interval generator cycle. However, if the eye was deviated initially in the FP direction, with regard to mean eye position, a proportion of the SP durations were produced by two or more cycles of the basic interval generator. In essence, the end of a discrete interval generator cycle provides an opportunity for a decision to interrupt the SP by generating the FP or to continue the SP for another cycle of the internal interval timer (i.e., “skipping a beat”).

The usage of the terms “interval generator” and “clock” requires brief clarification. A physical clock operates on metric time, with units or cycles of precisely equal length, based on an oscillator that generates events at a fixed interval and an integrator to provide an estimate of the period of the oscillator (clock ticks or beats). Our use of the term “interval generator cycle” denotes a biological timing interval with statistical properties. We have assumed a Gaussian distribution for simplicity, recognizing that the explanatory capability of a model demonstrates that such a Gaussian timer is sufficient to explain the data, rather than a proof that the process is from that statistical distribution.

Nystagmus performance is known to be affected by vigilance and alerting. The early descriptions of “vestibular habituation” (Dodge 1922) and vestibular “response decrement” (Hood and Pfaltz 1954) cited decrements in the duration and number of FPs during vestibular-evoked nystagmus with repeated exposures to optokinetic or vestibular stimuli (Dodge 1922; Griffith 1920, 1924; Hood and Pfaltz 1954) and a transient reversal of such changes by either behavioral or pharmacological arousal (Hood and Pfaltz 1954). Drowsiness, “alerting” tasks, or “mental set” produces a change in nystagmus during vestibular stimulation (Collins and Guedry 1961; Collins and Poe 1962; Crampton and Schwalm 1961; Furman et al. 1981; Kasper et al. 1992). For example, vestibular nystagmus had fewer FPs and a reduced SP eye velocity when subjects attended to sensations of movements, compared with when the same subjects performed mental arithmetic (Collins and Guedry 1961). These studies provide motivation for investigating the effects of cognitive tasking on the timing of alternating SPs and FPs of nystagmus.

Prefrontal cortical involvement in nystagmus FP generation was reported in 1968 by Bizzi (1968), who demonstrated that neurons in primate frontal eye fields discharged in a similar manner before saccades and either OKN or vestibular nystagmus FPs. An extensive cortical network, including prefrontal cortex, shows increased functional MRI activation during both OKN (Bucher et al. 1998; Dietrich et al. 1998; Konen et al. 2005) and during larger field optic flow stimulation (Smith et al. 2006).

This paper provides the first evidence that the human decision process for generating a nystagmus FP is affected by performance of a concurrent cognitive task. We demonstrate that the durations of the SPs of human OKN are consistent with a model consisting of a basic interval generator, with a random probability of generating an FP at the end of a timing cycle. We also show that the probability of generating an FP at the end of each timing cycle decreases significantly during performance of a DRT task. These findings indicate that the alternation between SPs and FPs of OKN is not purely reflexive. Rather, the generation of the FP, at the conclusion of a biological timing cycle, shows a dual-task interference effect.

MATERIALS AND METHODS

The protocol for this study was approved by the Institutional Review Board of the University of Pittsburgh. Each subject provided informed consent. Subjects received payment for participation in the experiment. Exclusionary criteria to participate were a history of neurological or otologic disease, significant abnormalities on neurological examination, a binocular visual acuity with corrective lenses worse than 20/40 in both eyes, abnormal, age-corrected audiometric function, and abnormal ocular motor testing results [i.e., spontaneous or gaze-evoked nystagmus, saccadic dysmetria, abnormal ocular pursuit, or abnormal OKN, or abnormal vestibular function defined by a significant persistent positional nystagmus, abnormal caloric responses, or a significant directional preponderance (asymmetry) on earth-vertical axis rotation]. Data are reported from 10 subjects (21–81 yr, mean 63.3 ± 20.9 yr, 5 females, 5 males).

Subjects were seated upright while viewing full-field vertical optokinetic stripes moving at either 30 or 60°/s at constant velocity. The stripes had a uniform thickness of five degrees and were projected onto a cylindrical screen 1 m from the subject. Eye movements were measured using a dual scleral search coil (Skalar) placed in either eye (Schor and Furman 2001). Two sets of magnetic field coils, one producing a vertical field, the other a transverse horizontal field, were bolted to the test chair, with the subject's head near the center of the two fields. The four currents induced in the two scleral coils by these fields were amplified and detected, resulting in a voltage proportional to the strength of the signal (CNC Engineering). Before or after each recording session, each dual eye coil assembly was calibrated by placing it on a fixture that permitted precise positioning of the coil. Scleral coil voltages were digitized at 1,000 Hz. These voltages were converted into horizontal, vertical, and torsional eye position using a Fick coordinate system (Schor and Furman 2001).

Subjects viewed moving optokinetic stripes for two sets of four 90-s trials: 30 and 60°/s horizontal velocity with and without a concurrent RT task. The DRT task was a disjunctive (“go-no go”) task in which subjects held a response button in either their dominant or nondominant hand, assigned randomly, and were presented with either of two tones every 1.5–4.0 s via insert earphones binaurally. The two tones were a low-frequency (560 Hz) or high-frequency (980 Hz) tone with an intensity of 80 dB SPL. These frequencies were chosen based on tabled values of center frequencies of critical bands (Zwicker et al. 1957). One of these tones was randomly designated as the target tone, the other the nontarget tone. Subjects were instructed to press the button when they heard the target tone and not to respond when they heard the nontarget tone. The number of presentations for the target tone and the number of presentations for the nontarget tones were equal. Each subject practiced the RT task during a nontest day that preceded the test day. During training, a qualified technician assured that error levels remained between 5 and 10%.

Eye movement data were analyzed by first identifying the onset and endpoint of each SP of OKN. Initially, an automatic custom-designed nystagmus algorithm flagged all slow-component-fast component transitions based on the horizontal, vertical, and torsional eye position. A qualified technician, blinded to whether or not a concurrent DRT task was being performed, subsequently reviewed each dataset and manually corrected any errors in the identification of transitions. The times associated with each transition were output to a file that contained synchronized time base information regarding the DRT task and the subject's responses.

For purposes of clarity, a detailed description of each component of the approach for modeling and parameter estimation from the SP duration data is included with presentation of the results.

RESULTS

Figure 1 shows an example of the alteration of the pattern of OKN during the presentation of a DRT. Note that the nystagmus is stationary during the stimulus presentations and that longer duration SPs in this example appear during the stimulus presentation, particularly for the button presses to the “go” condition.

Fig. 1.

Optokinetic nystagmus (OKN) during a disjunctive reaction time (DRT) task. Data were recorded with a scleral search coil at a sampling rate of 1 kHz. Top: horizontal eye position between 52 and 62 s of a 90-s trial. Middle: times of presentation of tones. Bottom: times of button presses. Note the alteration in the pattern of nystagmus when the subject responds to the “go” stimulus with a button press.

The distribution of SP durations during a session of constant velocity optokinetic stimulation is shown in Fig. 2. Note the multimodal appearance of the distribution, with peaks of decreasing size in the vicinity of 0.2, 0.4, 0.6, and 0.8 s. Unlike the behavior of turtles described previously (Balaban and Ariel 1992), scatterplots of our human data indicated that the distribution of SP durations was uncorrelated with horizontal, vertical, and torsional eye position at the start of the SPs. The FP magnitudes were also uncorrelated with the preceding SP durations.

Fig. 2.

Histogram of slow phase (SP) durations of human OKN data using a full-field stimulus rotating horizontally at a constant speed of 60°/s.

Kolmogorov-Smirnov tests rejected unimodal, single distribution fits for a Gaussian model for SP durations in 76/76 trial sessions, for a reciprocal Gaussian model for 71/76 trial sessions, for a log-normal model for 71/76 trial sessions, and for a best fit gamma distribution for 55/76 trial sessions across all subjects (P < 0.05). Hence, a model that produces a simple Gaussian mixture distribution was explored. The observed SP duration data from each trial were used to estimate the parameters of a simple Gaussian interval process (random variable X₀ with mean μ₀ and standard deviation σ₀), which serves as a discrete time interval for SP durations (Fig. 3). An FP may or may not be triggered at the expiration of the interval; a “skipped beat” (no FP generation) occurs with probability p. This simple timing model predicts that the SP durations can be simulated as a mixture of Gaussian distributions representing at least single intervals [N(μ₀, σ₀)], double intervals [N(2μ₀, √2σ₀)], triple intervals [N(3μ₀, √3σ₀)], quadruple intervals [N(4μ₀, 2σ₀)], five intervals [N(5μ₀, ⎷5σ₀)], and six interval cycles [N(6μ₀, ⎷6σ₀)] . Furthermore, the relative proportions of these components is 1-p for single interval cycles, p(1-p) for double interval cycles, p²(1-p) for triple interval cycles, p³(1-p) for quadruple interval cycles, p⁴(1-p) for five interval cycles, and p⁵ for six interval cycles. Therefore, the proportion of SPs with durations reflecting multiple interval cycles (or beats) is p.

Fig. 3.

Model and schematic nystagmus slow phase durations. The discrete time base for SP durations is a Gaussian interval generator (random variable X₀ with mean μ₀ and standard deviation σ₀). A choice process to generate the fast phase (FP) occurs after each timing cycle, which may be based upon factors that are independent of the interval generator parameters. For simplicity, it is assumed that the FP can be generated at the expiration of any timing interval with probability 1-p. Alternatively, the SP continues with probability P for another timing cycle. The distribution of SP durations produced by this model, shown schematically on the right side, will be a mixture of a proportion 1-p of SP durations distributed like X₀ (single interval generator cycle), a proportion p-p² of SP durations distributed like 2X₀ (two interval generator cycles), a proportion p²-p³ of SP durations distributed like 3X₀ (three clock cycles), a proportion p³-p⁴ of SP durations distributed like 4X₀ (four interval generator cycles) a proportion p⁴-p⁵ of SP durations distributed like 5X₀ (five interval generator cycles), and a proportion p⁵ of SP durations distributed like 6X₀ (six interval generator cycles).

The parameters μ₀, σ₀, and p were estimated by a two-stage process for each session. The first stage used an expectation maximization approach for a first order estimation of values for identifying the clock cycle parameters μ₀ and σ₀ and proportions of single and multiple clock cycle SPs for a mixture of two Gaussian distributions. These estimates were then used as initial conditions for nonlinear least squares estimation of the parameters as a mixture of six Gaussian components in the full model from Fig. 3.

Estimation of SP durations as a mixture of two Gaussians.

A first analysis used an expectation maximization method implementation in MATLAB (http://www.mathworks.com/matlabcentral/fileexchange/26184-em-algorithm-for-gaussian-mixture-model) to generate maximum likelihood estimates of the means and standard deviations of a mixture of two normal distributions [a smaller X₁∼N(μ₁, σ₁), a larger X₂∼N(μ₂, σ₂), and proportions of observations in each distribution] from the SP durations in each constant velocity OKN trial. The proportion of SP durations in the smaller of the Gaussians, in terms of the model, is 1-p; the proportion of SP durations in the larger of the Gaussians is an estimate of p. The hypothesis that μ₂ = 2*μ₁ was not rejected by a paired t-test [t(75) = 1.442, P > 0.14] across all trials and conditions. Similarly, linear regression analysis for the model μ₂ = a₁*μ₁ indicated a highly significant relationship [adjusted squared multiple R: 0.935, F(1,75) = 1072.35, P < 0.001] with a slope of 2.066 ± 0.063 (lower and upper 95% bounds: 1.940 and 2.192). These findings were consistent with the basic interval generator hypothesis.

The estimated SP basic interval cycle durations were on the order of 250 ms across trials. Repeated-measures ANOVA indicated that the estimates of the clock duration μ₁ did not differ in trials with no task vs. trials with a DRT task. However, the clock duration differed significantly with the speed of the OKN stimulus [F(1,9) = 50.0, P < 0.001]. The mean duration was slightly longer for 30°/s stimulation (no task trials: 0.266 ± 0.045 s; DRT task trials: 0.277 ± 0.048 s) than for 60°/s stimulation (no task trials: 0.249 ± 0.044 s; DRT task trials: 0.247 ± 0.039 s). The magnitude of these differences though was small; the 0.030-s range between the shortest (0.247 s) and longest (0.277) is less than the pooled standard deviation estimator for the comparisons of the data sets.

For the trials with a DRT task, the maximum likelihood estimates of the mean and variance for a mixture of two Gaussian distributions were performed separately for SPs that occurred during the period between the stimulus and either the response or the period lasting 1 s after stimulus termination, vs. other SPs during epochs with no task. The mean clock duration did not differ within trials for SPs in the presence or absence of a stimulus-response period. However, there was a significantly larger proportion of long duration SPs during the stimulus-response periods [repeated-measures ANOVA, F(1,33) = 13.98, P < 0.01] across stimulus velocities. For epochs with no task, the estimated p was 0.259 ± 0.019 (SE). For DRT task epochs the estimated p was 0.454 ± 0.048 (SE). This finding suggests the probability of skipping a beat increases markedly during periods of processing a DRT task.

Estimation of SP durations as a mixture of multiple Gaussians (full model).

The second stage of the analysis used the expectation maximization (EM) algorithm estimates of the μ₁, σ₁, and p from X₁ as initial conditions for estimation from a full model of a single Gaussian clock with mean μ₀, standard deviation σ₀, and a proportion 1-p of single clock beats. The statistical approach was described in an earlier publication (McCandless and Balaban 2010) for fitting data to a mixture of circular Gaussian distributions. Parameters were estimated (using the MATLAB lsqnonlin.m algorithm) by least squares minimization of the error between the empirical cumulative probability function value of each ordered observation and the cumulative probability of that value for the model cumulative distribution function. This order statistics (David 1970) approach minimizes the differences between the model cumulative probability for each ordered observation and the function (i − 0.5)/N, which represents the empirical cumulative probability of the i^th ordered observation from a sample of size N. The model cumulative probability values were calculated during each iteration from a mixture of Gaussian distributions representing at least single interval cycles [N(μ₀, σ₀)], double interval cycles [N(2μ₀, ⎷2σ₀)], triple interval cycles [N(3μ₀, ⎷3σ₀)], quadruple interval cycles [N(4μ₀, 2σ₀)], five interval cycles [N(5μ₀, ⎷5σ₀)]. and six interval cycles [N(6μ₀, ⎷6σ₀)], using the MATLAB “cdf.m” function. The differences between the empirical and the model cumulative probability values for each observation were designated as the error term provided for least squares optimization of the Gaussian basic interval generator mean (μ₀), standard deviation (σ₀), and probability of skipping a beat, p. These three parameter estimates were stable when the initial conditions for μ₀ were varied ± 40%. The mean of residuals to each fit did not differ significantly from zero. Ranked sign tests for symmetry rejected a symmetric residual distribution for only 7/76 sets of observations with an uncorrected α = 0.05 but symmetry was not rejected for any set with a Bonferroni correction to α for multiple test comparisons.

Kolmogorov-Smirnov tests were performed on each of the 76 sets of observations, vs. expected values of the corresponding ordered observation from the model distribution, to assess goodness-of-fit of the model. In all cases one could not reject the hypothesis that model cumulative distribution function was the same as the empirical distribution function of the data (P > 0.20 in 75/76 cases, P > 0.10 in the remaining case, with no correction for repeated paired comparisons). Note that this three-parameter model is the most parsimonious (in terms of the number of free parameters) of mixture Gaussian models for these data. This was a marked improvement over the three-parameter model of a mixture of only two Gaussian distributions [N(μ₀, σ₀), N(2μ₀, ⎷2σ₀), and p] to describe the SP duration cumulative distribution; Kolmogorov-Smirnov tests rejected the adequacy of this reduced model for 59/76 of the trial sessions across all subject (P < 0.05).

For illustrative purposes, examples of probability distribution functions (with these estimated parameters from the SP duration cumulative distribution function) are shown in red on histograms from a set of four trials in Fig. 4. Note the large peak of single clock beat SPs and the increased proportion of longer duration SPs in the trials with a DRT task. There were no significant correlations 1) between the SP durations and subsequent FP amplitudes and 2) between the SP durations and initial eye positions. These relationships are shown in Fig. 5 across pooled data from two trials that presented the DRT during 30°/s OKN stimulation.

Fig. 4.

Histograms of OKN SP durations from one subject across four trials. The optokinetic stimulus was moving at 30°/s at top and at 60°/s at bottom. The no task trials are shown on the left and the DRT trials are shown on the right. Note an increased proportion of longer duration SPs in the DRT task trials.

Fig. 5.

Scatter plots illustrate the lack of correlations between the SP durations and subsequent FP amplitudes (left) and between the SP durations and initial SP eye positions (right). The data pooled from two trials for a single subject, during 30°/s OKN stimulation and intermittent DRT task presentation. Dotted vertical lines indicate the location of μ₀, 2μ₀, and 3μ₀ estimates for the SP interval generator model.

Repeated-measures ANOVA was used to assess the sensitivity of the full model estimates of the mean μ₀, standard deviation σ_0, and a probability of skipping a beat, p, to the speed of OKN and the presence of a DRT task across an entire trial. The clock cycle mean interval, μ₀, varied significantly with the speed of optokinetic stimulation [F(1,9) = 54.2, P < 0.001] but μ₀ was unaffected by the presence of a DRT task [F(1,9) = 1.5, P > 0.25]. The μ₀ values for 30°/s stimulation (no task trials: 0.257 ± 0.045 s; DRT task trials: 0.273 ± 0.049 s) were longer than for 60°/s stimulation (no task trials: 0.241 ± 0.044 s; DRT Task trials: 0.237 ± 0.040 s). The difference between the longest duration (30°/s OKN with DRT Task) and shortest duration (60°/s OKN with DRT task) condition means was small (0.036 s), less that one pooled standard deviation unit across these groups. The interval generator standard deviation estimates, σ₀, were unaffected by either stimulus speed or presence of the DRT task. The probability of skipping a beat across an entire trial, p, showed marginal effects for both OKN speed [F(1,9) = 4.894, P = 0.054] and the presence of a DRT task [F(1,9)=5.024, P = 0.052]. There were no interaction effects. The probability of skipping a beat tended to be lower for 30°/s stimulation trials (no task trials: 0.158 ± 0.064; DRT task trials: 0.212 ± 0.075) than for 60°/s stimulation trials (no task trials: 0.195 ± 0.084; DRT task trials: 0.242 ± 0.119) and smaller for no task trials than trials with a DRT task.

To further explore the hypothesis that the clock duration and probability of skipping a beat parameters are sensitive within a trial to the secondary task, the SP duration data from the DRT task trials were analyzed separately for sets of SPs that 1) overlapped the period between the stimulus and either the response or a 1 s poststimulus limit, and 2) SPs unrelated temporally to the stimulus. Repeated-measures ANOVA showed that the estimates of the Gaussian cycle generator parameters μ₀ and σ₀ and the probability of skipping a beat, p, were affected by a concurrent DRT task within a trial. As shown in Fig. 6, the mean clock cycle length μ₀ increased slightly but significantly during the performance of the disjunctive reaction task [main effect: F(1,9) = 36.535, P < 0.001], paralleled by a slight but significant increase in σ₀ during the task performance [main effect: F(1,9) = 11.960, P < 0.01]. By contrast, there was a large magnitude change in the probability of skipping a beat during performance of the DRT task within a trial [main effect: F(1,9) = 23.795, P < 0.001]. However, the SP eye velocity did not vary significantly between periods with no DRT presentation and periods during DRT presentation at either optokinetic stimulus speed (repeated-measures ANOVA, not significant).

Fig. 6.

Mean (±SE; n = 10) values of the basic cycle generator parameters from DRT task trials. The data are compared for SP durations that overlapped the period between the stimulus and either the response or a 1 s poststimulus limit (DRT) vs. SP durations with no overlap (No Stim). Note that during the DRT performance period, there were small but significant increases in μ₀ and σ₀, as well as larger increase in p, relative to times when the task was not presented.

Mean values of the estimated basic cycle generator parameters from DRT task trials are shown in Fig. 6. The data are compared for SP durations that overlapped the period between the stimulus and either the response or a 1 s poststimulus limit (DRT) vs. SP durations with no overlap (No Stim). Note that during the DRT performance period, there were small but significant increases in μ₀ and σ₀, as well as larger increase in p, relative to times when the task was not presented.

The analysis to this point is consistent with the hypothesis (see Fig. 3) that a Gaussian basic interval generator is sufficient to simulate timing units for SP durations and that a context-sensitive decision process may govern the generation of the FP at the end of each interval. A fuzzy classification strategy permits examination of the distribution of single and skipped beat SPs in relationship to the stimulus onsets and responses in the choice reaction time trials. The normal mixture distribution model for SP durations provides an objective basis for defining a fuzzy membership mapping that classifies each of the SP durations as either a single interval cycle or a multiple interval cycles. The classifier for single interval cycle SPs was simply the ratio of the probability of a single beat of a given duration to the probability of a single or multiple beat at that duration (Fig. 7, green curve). Similarly, multiple cycle SPs (produced by skipped beats) are classified by the ratio of 1) the probability of a multiple beat of a given duration to 2) the probability of a single or multiple beat at that duration (Fig. 7, red curve). Hence, the membership function value (Fig. 7) represents the probability that a given SP has the duration of a single intervals or the duration of multiple interval beats.

Fig. 7.

The fuzzy classification membership functions are shown for a representative data set, superimposed on a histogram of the SP duration data. A membership function threshold value of 0.6 was used for classifying individual SP durations as either single beats (coded green in the histogram) or multiple beats (coded red in the histogram). Data with membership values between 0.4 and 0.6 on both maps were classified as indeterminate (coded yellow in the histogram).

Membership values were calculated for each SP, based on the full model estimates of μ₀, σ₀, and p for the trial. The cumulative distributions of the membership function values for individual SPs as single clock beats were pooled across all of the choice reaction time task trials in Fig. 8.

Fig. 8.

Cumulative distributions of the membership function values for individual SPs from the choice reaction time task trials. Data from all 30°/s OKN stimulation blocks are displayed at left and data from 60°/s OKN blocks are shown at right. Solid dots represent data from epochs when no stimuli were presented. Open circles represent the distribution for SPs that began before stimulus presentation and ended after stimulus presentation, these without regard to the timing of a button press response. Open squares represent similar data for SPs that began before and ended after a button press response, without regard to the timing of a stimulus onset (e.g., the SP could begin before or after stimulus onset, but end after the button press response). The single interval SPs (green), multiple interval cycle SPs (red), and indeterminate SPs (yellow) are color coded as in Fig. 7.

The increased prevalence of presumptive multiple beat duration SPs during the choice reaction task is documented by the analysis in Table 1. This analysis used all SP duration observations across subjects and choice reaction task trials, with single beat, multiple beat or indeterminate categories determined by the fuzzy classifier membership values (e.g., in Fig. 8). During epochs when the choice reaction task was not presented, approximately one-sixth of the SPs had a multiple interval cycle generator duration across the two OKN stimulus conditions. The prevalence of multiple interval generator cycle SPs roughly doubled during choice reaction task presentation [DRT (total)] and during task presentation, whether the task resulted in a button press response (DRT response) or there was no response (DRT stimulus-no response). The prevalence of multiple interval generator cycle SPs was approximately triple the no task epoch prevalence among SPs that either (1) began before stimulus onset and ended after stimulus termination or (2) began before and ended after the response to the stimulus. Fisher's exact tests demonstrated that there was a significantly higher prevalence of multiple interval beat duration SPs that included periods of either stimulus presentation or button-press responses (with regard to no task presentation periods). During 60°/s OKN stimulation, there was a greater likelihood of multiple interval cycle SPs in periods including a response (69.6%) than those including only the stimulus (52.7%). These findings are consistent with the interpretation that SPs are being prolonged preferentially for at least one interval timing cycle during performance of the choice reaction time task.

Table 1.

Distribution of presumptive single and multiple basic interval SP durations, identified by a fuzzy classifier, for trials that included the disjunctive reaction time task

OKN Speed/Epoch	Single Basic Interval Cycle	Multiple Basic Interval Cycles	Indeterminate
30°/s
Epochs with no task	1,988 (77.8%)	406 (15.9%)	160 (6.3%)
DRT trials (total SPs)	1,216 (58.8%)	711 (34.4%)*	142 (6.9%)
All SPs in DRT response window	577 (56.2%)	349 (34.0%)*	100 (9.7%)
SP begins before and ends after stimulus	214 (41.1%)	261 (50.2%)*	45 (8.7%)
SP begins before and ends after response	108 (37.2%)	166 (57.2%)*	16 (5.5%)
DRT stimulus-no response	639 (59.6%)	362 (33.7%)*	72 (6.7%)
60°/s
Epochs with no task	2083 (75.7%)	481 (17.5%)	189 (6.8%)
DRT trials (total SPs)	1,302 (54.3%)	768 (34.6%)*	152 (6.8%)
All SPs in DRT response window	525 (58.3%)	376 (38.9%)*	65 (6.7%)
SP begins before and ends after stimulus	219 (42.8%)	259 (50.6%)*	34 (6.6%)
SP begins before and ends after response	75 (27.3%)	186 (67.6%)*†	14 (5.1%)
DRT stimulus-no response SPs (1 s poststimulus window)	777 (61.9%)	392 (31.2%)*	87 (6.9%)

OKN, optokinetic nystagmus; DRT, disjunction reaction time; SP, slow phase.

^*P < 0.001 by Fisher's exact test with regard to corresponding no task SP proportions. †P < 0.001 by Fisher's exact test with regard to stimulus onset referenced SP proportions.

The ability to identify single and multiple basic interval SPs enables an examination of the temporal relationship between DRT task events (e.g., stimulus presentation or button press responses) and changes in the likelihood of skipping a beat at end of the current SP interval generator cycle. In terms of the model in Fig. 3, one can test the hypothesis that SPs reflecting multiple interval generator cycles are likely to be predominant during the DRT task.

To test the hypothesis that the presence of a disjunctive reaction task results in extending the current SP to another interval generator cycle, the time base for each subject and trial was transformed into “basic interval cycles” defined by the mean interval cycle duration (μ₀) for that trial. The prevalence of single and multiple interval duration SPs, defined by the fuzzy classifier described above, was then assessed relative to the DRT task stimulus presentations. The relative prevalence of multiple beat SPs was then estimated directly as the proportion of the number of multiple interval beat SPs, relative to the sum of the numbers of single and multiple beat SP in 0.1 cycle time intervals (Fig. 9).

Fig. 9.

Plot of the estimated likelihood of skipping beats, defined as the number of multiple interval generator cycle SPs identified by the fuzzy classifier, relative to the sum of the all SPs over 0.1 beat time intervals. The time base is in clock cycle beats relative to the stimulus onset time, which is indicated by the vertical dashed line. The median reaction time (RT) latency in the DRT task trials is indicated by the heavy vertical line at 1.75 interval generator beats. Note that SPs that are on-going at the time of stimulus presentation (i.e., they start approximately one interval generator cycle before the stimulus) had a markedly increased likelihood of extending for multiple clock cycles, rising from a baseline proportion of ∼0.21 (0.2050 average, thick line) to a peristimulus proportion of ∼0.5 (0.4925 average, thin line). This increment in the proportion of multiple interval cycle SPs persisted until about two interval beats after the stimulus, which delimits the period for processing and generating in a button press in the DRT task trials requiring a response.

The simple model in Fig. 3 assumes that the increased probability of multiple basic interval cycle SP durations is tantamount to a decision to delay FP generation until the expiration of the next interval generator cycle. In the case of the choice reaction time task, one predicts that stimulus presentation will result in a higher probability of multiple basic interval cycle SPs for any on-going or newly initiated SP. These predictions are confirmed by the data for DRT task auditory stimulus presentations, independent of whether a button press response was required (Fig. 9). For SPs beginning between one basic interval generator beat before the stimulus to nearly two basic interval generator beats after the stimulus, the proportions of multiple clock cycle SPs (relative to all SPs) were elevated significantly from earlier and later baseline values (Fisher exact tests, P < 0.05), at either speed of OKN stimulation. The time window for increased likelihood of skipping a beat corresponds well to the time course of DRT response generation; the median interval between an auditory DRT stimulus and response was 1.79 ± 0.07 (SE) interval generator cycle units across all subjects and conditions (30°/s OKN: 1.68 ± 0.09 cycles; 60°/s OKN 1.90 ± 0.09 cycles).

DISCUSSION

This study provides the first clear evidence that the generation of OKN FPs is a decision process that is influenced by performance of a concurrent auditory go-no go cognitive task. A model of a Gaussian basic interval generator (a biological timing process), such that a FP can be triggered randomly at the end of a cycle, is sufficient to fit the distribution of durations of the SPs of human OKN. We also show that, within the framework of this model, the probability of generating a FP at the end of each interval generator cycle decreases significantly during performance of a disjunctive RT task. These findings indicate that the alternation between SPs and FPs of OKN is not purely reflexive. Rather, as shown in Fig. 8, triggering the next FP is postponed more frequently if a recently presented task is pending action when the interval generator cycle expires. Hence, OKN FPs show dual task interference in a manner usually attributed to voluntary movements, including saccades (Pashler 1994).

The dilemma of model selection is implicit in any data analysis. Multiple models may describe a data set to a strong goodness-of-fit criterion with very different underlying structures. In his classic paper, “Statistical Modeling: The Two Cultures,” the eminent statistician Leo Breiman (2001) reminded colleagues that: “The goals in statistics are to use data to predict and to get information about the underlying data mechanism. Nowhere is it written on a stone tablet what kind of model should be used to solve problems involving data.” In fact, the models are tested by extending their application to more generalized paradigms and scenarios until they fail. This is precisely the point raised nearly two decades ago in Malcolm Forster's seminal article (2000), “Key Concepts in Model Selection: Performance and Generalizability,” which distinguished between assessing models 1) purely in terms of errors of parameter estimation (or goodness-of-fit) versus 2) errors of generalizability. Unification of explanations and simplicity in the breadth of explanatory capability are important determinants of the parsimony of a model.

One investigative approach has been to assume that nystagmus timing is produced by a process with a single skewed underlying distribution, such as the inverse Gaussian (or Wald) distribution (Anastasio 1996), reciprocal Gaussian distribution (Carpenter 1993), and a gamma distribution (Trillenberg et al. 2002). The model presented in Fig. 3 differs fundamentally because it regards the observed SP durations as the product of a discrete timing process that produces a mixture of single and multiple quantal intervals. The simplifying assumption of a Gaussian distribution for an interval generator has facilitated examination of the quantal, temporal structure of OKN. The ability to skip a beat generates the multimodal and skewed distribution of SP durations as a mixture of Gaussian distributions with predicted means, standard deviations, and proportions. Kolmogorov-Smirnov tests demonstrated robust goodness-of-fit for data from every trial. Furthermore, it is parsimonious because a single parameter (the likelihood of not making the FP at the end of an interval; skip a beat) is sufficient to explain changes in the shape of the SP durations during performance of a concurrent DRT task (Fig. 9). By contrast, model fits to skewed distributions such as gamma, reciprocal Gaussian, and lognormal distributions were rejected by Kolmogorov-Smirnov tests for a large majority of trials.

The Gaussian interval generator approach was sufficient to model SP durations for constant velocity OKN, which has constant SP eye velocity. No model fits could be rejected by Kolmogorov-Smirnov tests, despite simplifying assumptions that the probability of skipping a beat, p, can be considered as a constant throughout a trial and that repeated iterations at that fixed p determine the proportions of multiple interval cycle SP durations. It is now important to test whether this Gaussian interval generator model will generalize to nystagmus with time-varying eye velocity, such as vestibular nystagmus or sinusoidal OKN.

The interval generator approach in this study parallels our earlier approach to modeling turtle nystagmus with a skewed clock distribution that was produced by a threshold autoregression process, a special case of an “integrate-to-fire” process (Balaban and Ariel 1992). These statistical modeling approaches can each describe the time interval outputs of neural oscillators, ramping models and/or state dependent networks (Goel and Buonomano 2014; Karmarkar and Buonomano 2007). By analogy with the wave-particle duality in quantum mechanics, each model approach may be useful as a tool (and heuristic framework) to gain further insight into properties of the underlying mechanisms that produce nystagmus timing.

The modeled interval generator parameters for the duration of SPs during OKN (“SP dwell times”) are remarkably similar to the published findings for SPs in congenital nystagmus, durations of saccadic intrusions, the timing of square wave jerks that intrude during fixation, and the saccade dwell time for sequential saccades during scene scanning or reading (the “interval between saccades”). The estimates of basic interval generator cycle durations for OKN SPs varied between 160 and 328 ms across subjects and sessions during 30 and 60°/s OKN stimulation. The same range of durations has been reported for nystagmus frequency in individuals with congenital jerk nystagmus and normal visual acuity (Bosone et al. 1990; Hertle and Dell“Osso 1999; Hertle et al. 2002). The mean frequencies for nystagmus, from individual values published in each publication [Table 2 in Hertle and Dell'Osso (1999) and Table 2 in Hertle et al. (2002)] were 2.6 ± 0.8 Hz during binocular and 4.1 ± 0.9 Hz during monocular viewing. Similar timing properties (median duration of 249 ms) have been reported for square wave jerks in children and adolescents, (Salman et al. 2008), with a range of mean durations from 201 to 370 ms for subject groups ranging from young to elderly adults under different viewing conditions (Herishanu and Sharpe 1981; Shallo-Hoffman et al. 1990). Abadi and Gowan (2004) examined different patterns of saccadic intrusions during fixation and reported that monophasic square wave saccadic intrusions showed durations spanning the same range. Their published histogram of the duration of the saccadic intrusion durations indicates that the distribution of pooled data from 47 subjects is consistent with the model in Fig. 3, with a mean interval cycle of 179 ms, a standard deviation of 95 ms, and a 0.23 probability of skipping a beat. A similar range of durations characterize saccade dwell times during multiple target visual search tasks (e.g., Wu and Kowler 2013). Similar interval-like, spontaneous saccade behavior occurs in one type of saccadic dysmetria, macrosaccadic oscillations, which is characterized by conjugate saccades at ∼200-ms intervals (Averbuch-Heller et al. 1996; Hoyt and Daroff 1971; Selhorst et al. 1976). Finally, ocular tracking with sequential saccades at 200- to 250-ms intervals has been reported in step ramp tracking task in both normal subjects given low-dose barbiturates (Rashbass 1961) and schizophrenic subjects with low smooth pursuit gain (Levin et al. 1988; Ross et al. 1996); a similar intersaccade interval was illustrated for corrective saccades during normal smooth pursuit by Collewijn and Tamminga (1984).

Previous studies have noted that the frequency of nystagmus FP (or the SP duration) varied nonlinearly with the SP eye velocity in both turtle horizontal OKN (Balaban and Ariel 1992) and human torsional vestibular nystagmus (Schneider et al. 2003) and with optokinetic stimulus velocity in cats (Honrubia et al. 1971). Consistent with these reports, the estimated clock cycle duration was slightly, but significantly, prolonged during 30°/s stimulation vs. 60°/s stimulation. Within subject designs can be used in the future to assess the effects of multiple factors on the nystagmus timing cycle.

It is noteworthy that the durations of saccade dwell times, the durations of saccadic intrusions (or monophasic square wave jerks), macrosaccadic oscillations, and nystagmus SP dwell times (intervals between FPs) are consistent with the ∼200-ms sampled data period for control of eye movements, proposed in 1963 by Young and Stark. Consistent with this “programming latency” view, Nichols and Sparks (1995) demonstrated that extremely hypometric saccades are elicited by electrical stimulation of the superior colliculus immediately after a spontaneous saccade. However, they found that the response magnitude and direction recover exponentially with a time constant of ∼45 ms in macaques. Expressed in terms of the recovery time for these central stimulation-evoked saccades, the estimated interval cycle for SP durations is ∼5 ± 1 time constants of the time needed to generate a full amplitude saccade by a site in the superior colliculus. Based on these considerations, we propose the unifying hypothesis that SP interval generator durations should be considered as both data sampling and rapid eye movement programming epochs of “visual fixation.” The eye velocity merely follows a nonzero optic flow velocity during SPs but is governed by the same clock times as visual target search under zero optic flow velocity conditions. This view is an extension of the proposal by Dell'Osso et al. (1997) that fixation periods in congenital, acquired, and latent nystagmus may represent normal fixation reflex intervals in the absence of optic flow.

Dual-task interference is a well-known phenomenon in human performance (Pashler 1994). Saccade reaction times show dual task interference effects in the presence of a simple reaction time task (Pashler et al. 1993), such that mean saccadic reaction times were prolonged significantly by presentation of a choice reaction task during a time window extending from at least 150 ms before presentation of a visual target until a period at least 150 ms after presentation of the visual target. Because only summary statistics for reaction time values are reported, the distribution of the times cannot be tested for correspondence to the analysis of single and multiple interval cycle generator events shown in Fig. 9.

Skipping a beat of nystagmus may be regarded as suppression (or disfacilitation) of FP generation during a time interval that permits initiation. This phenomenon in the DRT task during OKN may be analogous to the latencies associated with suppression of saccades directed to a target (prosaccades) during an antisaccade task. Specifically, the distributions of prosaccadic error latencies relative to correct antisaccade latencies in an antisaccade task (e.g., Fig. 3 in Noorani and Carpenter 2013) suggest that the prosaccades have single interval generator cycle latencies and the antisaccades, which require suppression and target calculations, have multiple interval cycle latencies. Evidence from nonhuman primates indicates that saccades and nystagmus FPs are initiated when a variable threshold firing rate is exceeded, by signals combining premotor and visual information, in either the frontal eye fields or the superior colliculus (Bizzi 1968). Inhibition of saccade generation is mediated by inhibitory contributions of several frontal cortex regions, basal ganglia modulation of GABAergic output from substantia nigra, and pars reticulata to the superior colliculus and thalamus (Munoz and Everling 2004). A parsimonious hypothesis is that the same pathways govern triggering of nystagmus FPs.

This line of reasoning implies that the duration of an OKN SP is a quantized, discrete sampling behavior that is specialized to allow time for visuospatial information processing and FP target selection. Previous studies have noted that the targets of FPs have a deterministic component that is likely related to directing gaze toward regions of interest in extrapersonal space (Chun and Robinson 1978; Shelhamer 1997). The quantal biological timing interval, then, represents a temporal unit of data sampling for eye movement control. The expiration of the interval generator cycle enables saccade or FP generation to the next sampling region in extra-personal space, based on additional factors that may include current eye position, completion of FP target selection, changes in the sensory environment, and urgency of other (on-going) cognitive tasks. Hence, skipping a beat in a dual-task experiment may be regarded as “holding one's place” for visuospatial information processing vis-à-vis the current environment: visual sampling is extended into the next quantal period of time (interval generator cycle) while a high priority action is taken. The target of the next rapid eye movement can then be informed by the updated visual information.

GRANTS

This study was supported by National Institutes of Health Grants AG-10009, AG-14116, AG-024827, and DC-05205.

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the author(s).

AUTHOR CONTRIBUTIONS

C.D.B. and J.M.F. conception and design of research; C.D.B. and J.M.F. performed experiments; C.D.B. and J.M.F. analyzed data; C.D.B. and J.M.F. interpreted results of experiments; C.D.B. prepared figures; C.D.B. drafted manuscript; C.D.B. and J.M.F. edited and revised manuscript; C.D.B. and J.M.F. approved final version of manuscript.