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Basic and Translational Research

“Leaky” and “Unstable” Neural Integrator Can Coexist—Paradox Observed in Multiple Sclerosis

Gupta, Palak BTech; Shaikh, Aasef G. MD, PhD

Editor(s): Bennett, Jeffrey L. MD, PhD; Shindler, Kenneth S. MD, PhD

Author Information
Journal of Neuro-Ophthalmology: June 2020 - Volume 40 - Issue 2 - p 226-233
doi: 10.1097/WNO.0000000000000955
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Two fundamental requirements serve gaze control: rapid eye movements (i.e., saccades) shift the eyes to the object of interest, and gaze-holding keeps the eyes stable at a new position. The neural command encoding the speed at which the eyes are moved (i.e., saccade velocity) is encoded by the pulse of neural discharge called “burst.” The burst causes phasic contraction of the extraocular muscles that rapidly rotate the eyes toward the point of interest. The elastic restoring forces within the orbit, however, tend to drag the eyes back to the central (neutral) position. Therefore, steady gaze-holding at eccentric positions requires tonic contraction of the extraocular muscles that can resist the elastic restoring forces. The cellular network called the neural integrator converts the burst to tonic firing—a correlate for stable gaze position (1–4). The flawless function of the neural integrator requires external feedback from multiple sensory systems such as vision and proprioception as well as internal sources such as the cerebellum (5,6). Disruption in any of the feedback sources results in impaired neural integration and subsequent disabling eye oscillations called nystagmus.

Various patterns of nystagmus due to neural integrator dysfunction have been characterized. If the eye positions are tracked in real time, the waveform of these oscillations may be sinusoidal, as in acquired pendular nystagmus, or assume the shape of a saw tooth, as in gaze-evoked jerk nystagmus. The waveform characteristics provide a helpful framework for distinguishing the underlying pathophysiology. Well-accepted hypothesis explaining the most typical features of the acquired pendular nystagmus predicts the involvement of the neural integrator. It was suggested that excessive feedback, in mathematical terms—increased feedback gain, leads to an unstable neural integrator resulting in sinusoidal eye oscillations, that is, acquired pendular nystagmus (7). Previous studies suggested that acquired pendular nystagmus has approximately 4- to 6-Hz frequency, and the saccades occurring in the midst of the oscillatory train reset the phase of the sinusoid (7). It is believed that the burst of neural activity generated by the saccade transiently silences neural integrator neurons that would otherwise fire periodically, causing nystagmus.

The second form of neural integrator impairment, gaze-evoked nystagmus, is believed to be due to suboptimal feedback—in mathematical terms decreased feedback gain to the integrator. Mutually excitatory connection within each neural network performing the function of neural integrator must have precisely calibrated synaptic strengths. Unfortunately, in the biological systems, the synaptic strengths are not optimally tuned to guarantee the perfect output. As a result, the neural integrators become inherently “leaky.” The output of the “leaky” integrator is characterized by slow drifts where eye velocity exponentially decreases. The drifts are physiologically compensated by the external feedback loops around the neural integrator. The cerebellar projections serve as one of the feedback sources to the integrator that improves its function under normal circumstances (4,8–10). A deficit in cerebellar feedback in form of decreased gain to the neural integrator reveals its inherently imperfect behavior causing velocity decreasing drifts in the eye position followed by visually driven corrective saccades (i.e., quick phases) that realign the eyes toward the target of interest. The drift velocity increases as the eyes move away from the center. The phenomenology of alternating drifts and corrective movements, and their gaze position dependence define gaze-evoked nystagmus (8–10). On rare occasions, the slow-phase velocity of the drifts exponentially increased; the phenomenon called velocity-increasing or “run-away” nystagmus is also explained by increased feedback gain leading to unstable neural integrator (11–13).

Theoretical descriptions of acquired pendular nystagmus and gaze-evoked nystagmus depict that both disorders are caused by an impairment in the function of neural integrator; however, theoretically, the deficits in the feedback circuit that leads to such impairments are mutually exclusive—in one form, the feedback is suboptimal, whereas in the other, the feedback is excessive. We found a scenario, in patients with multiple sclerosis, where both forms of deficits seem to coexist. These deficits account for the hypothesis that integrator can be simultaneously leaky and unstable. Mechanistically, some parts of network are served by increased feedback gain (unstable network), whereas other part would be decreased feedback gain (leaky). Both leaky and unstable the networks converge on the ocular motor plant, leading to simultaneously present gaze-evoked jerk and sinusoidal nystagmus.



We studied 7 patients (6 women, 1 man, 31–55 years in age) with clinical and imaging diagnosis of multiple sclerosis. All of them had nystagmus, 2 had predominant jerk nystagmus while 5 had mixture of jerk and pendular oscillations. The clinical appearance of nystagmus in our patients was consistent with traditionally described pendular nystagmus in disorders of central myelination (5). Visual function was previously described in pathophysiology, various forms of pendular nystagmus (14–16). However, the visual afferent function in our patients was unremarkable, except optic disc pallor, in all subjects. One patient had internuclear ophthalmoplegia. At the time of examination, 5 patients were not taking any pharmacotherapy for nystagmus or any other drug that affects brainstem saccade generation; one patient was on quinine, and the other was taking alprazolam. Table 1 depicts the clinical summary.

Clinical features of multiple sclerosis patients with nystagmus

Experiment Protocol

The experiments were performed at the Louis Stokes Cleveland Veterans Affairs Medical Center (LSCVAMC). All patients gave written, informed consent in accordance with the Institutional Review Board of the LSCVAMC and the Declaration of Helsinki. We measured binocular eye positions in horizontal and vertical planes using the magnetic search coil technique (Skalar, Delft, the Netherlands). Each patient's head was securely stabilized with the chair to prevent head movement. Search coil annuli were calibrated before the experiment and then placed on each sclera after local anesthesia with oxybuprocaine 0.4%. Eye positions were recorded when looking at a target and in a completely dark room at straight ahead, 5, 10, 15, and 20° to the right and left and 5, 10, 15° up and down.

Data Analysis

The angular position of the search coil with respect to the magnetic fields was digitized at 500 Hz, and the data were processed to compute the vertical and horizontal eye positions using MATLAB (The Mathworks, Natick, MA) (17). For the analysis of eye drifts, the raw signal was first filtered to remove the sinusoidal eye oscillations. MATLAB algorithm to implement a fourth-order Butterworth low-pass filter with zero-phase shift correction was used for such data processing. The beginning and the end of eye drifts were interactively identified on the eye position trace. The epochs of eye positions comprising drifts were further differentiated to compute drift velocity (i.e., slow-phase velocity). The analysis of filtered high-frequency eye oscillations was separately performed. Cycle-by-cycle analysis was performed on smoothed horizontal and vertical eye position signals (18,19).


We tested the hypothesis that integrator can be simultaneously leaky and unstable. Both leaky and unstable networks converge on the ocular motor plant, leading to simultaneously present gaze-evoked jerk and sinusoidal nystagmus. Figure 1 depicts an example where horizontal position of the right eye (y-axis) is plotted vs the time (x-axis) when the eyes are located in rightward orbital position. The eye positions are characterized by sinusoidal oscillations of 5.28 ± 0.59-Hz frequency (Fig. 1A, C, gray traces); they are present in both horizontal and vertical planes and are present in both eyes (although for clarity, the Fig. 1 only shows right eye horizontal position). The sinusoidal oscillations are superimposed on the drifts in eye position (black trend line, Fig. 1A), which is then corrected by rapid eye movements (saccade comprising the quick phase, arrow, Fig. 1B). The drift in the eye position followed by correction is consistent with the feature of gaze-evoked jerk nystagmus due to “leaky” integrator, while the sinusoidal oscillations are consistent with the pendular nystagmus due to “unstable” integrator. The subsequent analysis objectively examined the quantitative features of both sinusoidal and jerky oscillations in all patients, addressing a specific question whether these oscillations can be objectively described by “leaky” integrator (i.e., gaze-evoked nystagmus) and “unstable” integrator (i.e., pendular nystagmus).

FIG. 1.
FIG. 1.:
A. Epoch of time series depicting horizontal eye position, an example of the gaze-evoked nystagmus in rightward eye-in-orbit position and superimposed pendular oscillations. The eye positions are plotted on y-axis while corresponding time is on the x-axis. The gray line is actual eye position data, whereas black superimposed trace is low-pass filtered signal showing gaze-evoked nystagmus. B, C. Separation of pendular and gaze-evoked nystagmus by low-pass and high-pass filtering, respectively. Such segregation is used for further quantitative analysis of gaze-evoked and pendular oscillations (SP: Slow-phase; QP: quick-phase). In the graph, positive value on y-axis depicts rightward position (and vice versa).

Analysis of Sinusoidal Oscillations

The sinusoidal oscillations comprising the pendular nystagmus were present in 5 patients. This analysis had primary aim to examine whether such oscillations follow the basic principles suggesting “unstable” neural integrator as their underlying cause.

Amplitude Analysis

The first prediction is that if the pendular nystagmus is due to unstable neural integrator, then its amplitude changes according to the eye-in-orbit orientation; at one orientation, the amplitude is minimal (i.e., null position), but it increases as the eyes move farther away from the null. Figure 2A depicts the effects of eye-in-orbit position on the amplitude of the sinusoidal oscillations. Inverse parabola depicts the presence of null, typically at straight-ahead orientation. The amplitude increases as the eye-in-orbit position changes to farther eccentric orientation (Fig. 2A).

FIG. 2.
FIG. 2.:
A. Dependence of the amplitude of pendular nystagmus (y-axis) on eye-in-orbit position (x-axis). Each data point depicts amplitude of oscillations; the solid line is parabolic fit, whereas dashed lines are the confidence interval around the fit. The parabola depicts increased amplitude at eccentric eye-in-orbit horizontal positions; the amplitude reduces to minimal (null) when eyes are directed straight ahead (eye-in-orbit position is zero degrees). B. Summary of oscillation frequency of horizontal and vertical pendular oscillations. The frequency is plotted on y-axis, the horizontal gray line in the center of box is the median value, while the length of the box is interquartile interval, and whiskers are the range. The plus symbols are outlier datapoints. C. The oscillation phase before saccade is plotted on the y-axis and after saccade on x-axis. The datapoints (plus signs) depict one pair. The cloud of datapoint depicting large scatter represents robust difference in presaccade and postsaccade phase of oscillation, hence suggesting a substantial phase shift. D. The relationship of the slow-phase velocity of gaze-evoked nystagmus (y-axis) on eye-in-orbit position (x-axis). Each datapoint depicts one drift, the solid line is the fit, while dashed lines depict the confidence interval.

Frequency Analysis

The second prediction is that if pendular nystagmus originates in the neural integrator, then the oscillation frequency ranges between 4- and 6-Hz, and it does not depend on the eye-in-orbit position. Figure 2B depicting the summary from 5 patients found that frequency of the vertical sinusoidal oscillations was 5.36 ± 0.88 Hz (mean ± SD). The horizontal sinusoidal oscillations had frequency of 5.28 ± 0.59 Hz. The frequency of horizontal or vertical oscillations did not change with the eye-in-orbit position.

Phase Reset

The third prediction for the “unstable” neural integrator as a cause of pendular nystagmus is that, after each saccade, there will be a shift or reset in the phase of the sinusoidal oscillations. We discovered robust phase reset of pendular nystagmus after visually guided saccade. Figure 2C depicting this phenomenon compares the phase of oscillation before and after the saccade. The phase shifts depicting reset is seen in the form of a robust dispersion in data points and poor correlation coefficient value of 0.089 in Figure 2C.

Analysis of Jerky Oscillations

The jerky oscillations comprising the gaze-evoked nystagmus were present in all 7 patients. This analysis had the primary aim to establish that the jerky oscillations that are seen in our patients follow the well-known principles of gaze-evoked nystagmus. These principles and steps of analysis were to examine and predict 1) “leaky” neural integrator leading to gaze-evoked nystagmus will cause eye-in-orbit position dependence of the slow-phase velocity of the jerky oscillations. 2) The slow-phase velocity of the jerky oscillations is minimal when the eyes are in one orientation called “null position.” 3) The drifts are directed toward the null, and its velocity increases as the eyes move farther away from the null. The trend of eye-in-orbit position dependence of slow-phase eye velocity depicts this phenomenon with a slope of 0.138 and intercept of 0.03 ± 0.002 (Fig. 2D). The intercept in Figure 2D depicts a “null” that is close to straight-ahead orientation.

Computational Model

The primary hypothesis addressed in our experiments is that neural integrator can be simultaneously leaky and unstable. Mechanistically, some parts of network are served by increased feedback gain (unstable network), while other part would be decreased feedback gain (leaky). Both leaky and unstable network converge on the ocular motor plant, leading to simultaneously present gaze-evoked jerk and sinusoidal nystagmus. Our experimental analyses supported this hypothesis by depicting that jerky oscillations seen in ocular motor waveforms follow the features of gaze-evoked neural integrator; although in the same patient, the pendular oscillations follow the features of “unstable” integrator. In subsequent analysis and computational model (Fig. 3A), we show: 1) Hypothetical organization of simultaneously present neural integrator dysfunction with coexistence of “leaky” and “unstable” feedback loops. 2) Model parameter(s) determining relative severity of “leaky” vs “unstable” integrator. There were 2 key features of this model; the “unstable” network comprised the integrator transfer function and the adaptation feedback loop, while the “leaky” network comprised integrator transfer function with feedback gain. Each of the 2 integrator networks confirmed independent forms of impairment, and their output gain determined their relative contributions. The organization and parameters of the models were determined by the experimental values derived from previous nonhuman primate studies (1–4).

FIG. 3.
FIG. 3.:
A. Schematic of computational model depicting segregated dysfunction of the feedback-dependent neural integrator. Two loops form feedback making the integrator unstable and leaky; the parameters such as adaptation loop gain (GAdap) determines the frequency of the pendular oscillations, while unstable pathway output gain (Gn) determines the amplitude of pendular oscillations—hence, the severity of impairment due to the unstable neural integrator. The leaky loop gain (GLeaky) determines the eye-in-orbit position dependence of slow-phase eye velocity characterizing the gaze-evoked nystagmus, hence the severity of leaky neural integrator impairment. B. The scatter plot depicting the dependence of the given individual's frequency on preset value of GAdap. C. The y-axis of the surface plot depicts the amplitude of pendular oscillations, while x-axis is eye in orbit position. The robustness of the parabolic curve forming this surface depends on the value of output gain (Gn); latter is shown in color code in jet scheme. D. The y-axis of the surface plot depicts the slow-phase velocity of the gaze-evoked nystagmus, while x-axis is eye-in-orbit position. The lines forming the surface have different slopes, the blue line depicting lowest value of leaky loop gain (GLeaky) has highest slope, and increase in gain reduces the slope of the line (i.e., red color). (S,S′ transfer functions, Gn' output gain of the leaky pathway).

Parameter Estimation

Sensitivity analysis using least-square estimation technique identified the most optimal free parameters in the model. Accordingly, the free parameters for the “leaky” network was feedback gain (GLeaky); “unstable” network was adaptation feedback gain (GAdap) and the output gain (Gn) (Fig. 3A).

Determinants of the Pendular Nystagmus

Our model simulations determined that GAdap in the “unstable” network was the most robust determinant of the frequency of the sinusoids comprising pendular nystagmus; the relationship was negative yet strongly correlated (slope = −5.89, correlation coefficient = 0.99, Fig. 3B). The output gain (Gn) of the “unstable” network strongly and positively correlated with the amplitude range of the pendular oscillations (Fig. 3C). The color code of the surface diagram in Figure 3C depicts the value of output gain of the “unstable” network. The larger output gain (red in the jet color scheme) corresponds with steeper parabola depicting larger oscillation amplitudes and more robust eye-in-orbit position dependence of the oscillation amplitude. As the value of output gain gets smaller (i.e., blue color in the jet color scheme), the oscillation amplitude gets smaller and parabola becomes nearly flat (i.e., lack of eye-in-orbit position dependence).

Determinants of Slow-Phase Velocity of Jerky Oscillations

GLeaky negatively and robustly correlated with the slow-phase velocity of jerk nystagmus and its eye-in-orbit position dependence (Fig. 3D). In the surface plot shown in Figure 3D, the lower value of GLeaky (blue in the jet color scheme) corresponds with higher slow-phase velocity (i.e., drift velocity) in eccentric eye positions, and the steeper slope of the line depicting slow-phase velocity to eye-in-orbit position dependence. By contrast, higher values of GLeaky (red in the jet color scheme) in Figure 3D represents minimal slow-phase velocity at eccentric orientation and much smaller slope of the line depicting the relationship of slow-phase velocity to eye-in-orbit position dependence.


The neural integrator is critical to hold gaze on the object of interest; dysfunction of this system leads to disabling oscillations called nystagmus (5). The most typical form of dysfunction is due to lack of adequate feedback to the integrator causing drifts in its output (i.e., “leaky” integrator) causing gaze-evoked nystagmus, while the other, rather uncommon form, is an abnormally excessive feedback causing “unstable” neural integrator and subsequent pendular oscillations (7). Given the opposing nature of the underlying deficits—lack of or excessive feedback—the coexistence of “leaky” and “unstable” neural integrator and corresponding gaze-evoked and pendular oscillations is not intuitive. However, in series of patients with common demyelinating disorder, multiple sclerosis, we found that both forms of nystagmus (gaze-evoked and pendular) were present. The observation suggested the possibility that “leaky” and “unstable” neural integrator may coexist. This observation motivated our hypothesis that neural integrator can be simultaneously leaky and unstable. Mechanistically, some parts of network are served by increased feedback gain (unstable network) while other part would be decreased feedback gain (leaky). Both leaky and unstable network converge on the ocular motor plant, leading to simultaneously present gaze-evoked jerk and sinusoidal nystagmus. To test this hypothesis, we first established that gaze-holding deficits seen in our patients followed all the characteristics of the gaze-evoked nystagmus that is due to “leaky” neural integrator and pendular nystagmus that is due to “unstable” neural integrator. The experimental validation was subsequently simulated in a computational model where the mathematical representation of “leaky” and “unstable” integrator was linked in parallel and identified the computational parameters that determine the frequency and amplitude of sinusoidal oscillations and the drift velocity that were seen in our patients. Our theoretical model supporting the experimental results is backed by strong anatomical realism. The medial vestibular nucleus, the key location for neural integration of horizontal eye movements receives feedback from the range of cerebellar and brainstem structures; the flocculus and nodulus are one of the key cerebellar regions providing the feedback to the neural integrator in the medial vestibular nucleus (20). The projection from the given area of the cerebellum is also divided in multiple zones. For example, the flocculus projection to the vestibular nuclei is divided in 3 zones that span through the folia. Each zone projects to discrete component of the vestibular nucleus complex, each having distinct function as a neural integrator (21).

Other factors can also explain jerky oscillations in subjects with multiple sclerosis. Although considered in differential, these factors are less likely to cause jerky oscillations in our patients. One of such factors is the vestibular bias putatively due to the demyelinating plaque affecting the vestibular nuclei (22). The vestibular bias can lead to constant drift in the eye position, and it can lead to jerky oscillations; however, the consequent jerk nystagmus secondary to vestibular bias will not have characteristic of gaze-evoked nystagmus. Our patients had null position in the center (straight ahead). If vestibular bias coexists with the gaze-evoked nystagmus, it should lead to eccentric null. None of our patients had vestibular hypofunction or congenital forms of nystagmus. The manifest or latent nystagmus is another form of jerk nystagmus (5). The jerk nystagmus in our patients was unlikely to be a manifest or latent nystagmus because none of the patients had childhood onset of strabismus or amblyopia, the nystagmus was present at all the times, and it did not worsen while covering one eye. Above all, the jerk nystagmus followed all the characteristics of the gaze-evoked nystagmus.

There are other etiologies that can explain pendular oscillations. One possibility is saccadic oscillations, but their frequency is typically more than 10 Hz, and consistent with high-frequency profile, they have much faster eye velocity (23–26); all our patients had frequency in range of 4–6 Hz. The intensity of saccadic oscillations increase during saccades, (24,25) which was not the case in our patients—their oscillations transiently stopped during saccades, that is, phase reset. None of the patients had pathological lesions, such as inferior olive hypertrophy, that can explain other forms of pendular oscillations. Finally, the characteristics of pendular oscillations, such as 4- to 6-Hz oscillations, and phase reset after saccades in our subjects were typical of that explained by unstable neural integrator. In addition to phase reset after saccades, the pendular nystagmus subjects also have phase reset after blinks (5). To achieve best eye position data, our subjects were encouraged to blink as little as possible during experimental data collection session. As a result, although clinically observed, the blink-induced oscillation reset was not analyzed in this study.

Segregated dysfunction of neural integrator, particularly one form depicting excessive feedback leading to “unstable” neural integrator while the other abnormally reduced feedback causing “leaky” integrator, is not the only feature of gaze-holding deficits in multiple sclerosis. Similar dysfunction in the cephalomotor neural integrator affecting steady head holding was also described; it was proposed that deficits in the head movement neural integrator in midbrain causes common movement disorder called cervical dystonia (18,19,27,28). In patients with cervical dystonia 2 forms of head oscillations are prevalent, one form is jerky and is characterized by drifts followed by correction, the drift velocity is minimal at one position called “null,” and as the head turns farther away from the null, the drift velocity increases (18,27,28). In addition to the jerky oscillations, some patients with cervical dystonia also have sinusoidal head oscillations (resembling essential tremor) (19). These sinusoidal head oscillations follow the characteristics of pendular nystagmus due to unstable neural integrator, that is, the oscillations have 4- to 6-Hz frequency, and there is head-on-trunk dependent change in the amplitude of pendular head oscillations and reset of oscillation phase after rapid voluntary head turning (19). It was recently shown that both forms of head oscillations coexist in nearly all cervical dystonia patients—suggesting simultaneous dysfunction of head neural integrator due to different involvement in 2 forms of feedbacks. Another common disorder of eye movements, infantile nystagmus syndrome, also presents with 2 types of head oscillations—low-frequency (1–3 Hz) constant and high-frequency (5–7 Hz) episodic (29). Such coexisting head oscillations along with infantile nystagmus suggested coexisting pathological phenomenon (29). Our results provide an evidence for utility of waveform pattern analyses and mathematical simulation interrogating the underlying pathophysiological processes, as seen in a rare manifestation of demyelinating disease, in describing the pathogenesis of common neurological disorders.


Category 1: a. Conception and design: A. G. Shaikh; b. Acquisition of data: A. G. Shaikh and P. Gupta; c. Analysis and interpretation of data: A. G. Shaikh and P. Gupta. Category 2: a. Drafting the manuscript: A. G. Shaikh and P. Gupta; b. Revising it for intellectual content: A. G. Shaikh and P. Gupta. Category 3: a. Final approval of the completed manuscript: A. G. Shaikh and P. Gupta.


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