Eye movement instabilities and nystagmus can be predicted by a nonlinear dynamics model of the saccadic system

The study of eye movements and oculomotor disorders has, for four decades, greatly benefitted from the application of control theoretic concepts. This paper is an example of a complementary approach based on the theory of nonlinear dynamical systems. Recently, a nonlinear dynamics model of the saccadic system was developed, comprising a symmetric piecewise-smooth system of six first-order autonomous ordinary differential equations. A preliminary numerical investigation of the model revealed that in addition to generating normal saccades, it could also simulate inaccurate saccades, and the oscillatory instability known as congenital nystagmus (CN). By varying the parameters of the model, several types of CN oscillations were produced, including jerk, bidirectional jerk and pendular nystagmus. The aim of this study was to investigate the bifurcations and attractors of the model, in order to obtain a classification of the simulated oculomotor behaviours. The application of standard stability analysis techniques, together with numerical work, revealed that the equations have a rich bifurcation structure. In addition to Hopf, homoclinic and saddlenode bifurcations organised by a Takens-Bogdanov point, the equations can undergo nonsmooth pitchfork bifurcations and nonsmooth gluing bifurcations. Evidence was also found for the existence of Hopf-initiated canards. The simulated jerk CN waveforms were found to correspond to a pair of post-canard symmetry-related limit cycles, which exist in regions of parameter space where the equations are a slow-fast system. The slow and fast phases of the simulated oscillations were attributed to the geometry of the corresponding slow manifold. The simulated bidirectional jerk and pendular waveforms were attributed to a symmetry invariant limit cycle produced by the gluing of the asymmetric cycles. In contrast to control models of the oculomotor system, the bifurcation analysis places clear restrictions on which kinds of behaviour are likely to be associated with each other in parameter space, enabling predictions to be made regarding the possible changes in the oscillation type that may be observed upon changing the model parameters. The analysis suggests that CN is one of a range of oculomotor disorders associated with a pathological saccadic braking signal, and that jerk and pendular nystagmus are the most probable oscillatory instabilities. Additionally, the transition from jerk CN to bidirectional jerk and pendular nystagmus observed experimentally when the gaze angle or attention level is changed is attributed to a gluing bifurcation. This suggests the possibility of manipulating the waveforms of subjects with jerk CN experimentally to produce waveforms with an extended foveation period, thereby improving visual resolution.     

Spectral analysis of dual jerk waveforms in congenital nystagmus

Congenital nystagmus (CN) is a disorder of the ocular motility characterized by oscillatory eye movements preventing the correct fixation of a target. Many typical waveforms of eye position recordings have been recognized and classified in the literature: in jerk CN a slow phase eye movement is followed by a fast phase, giving rise to a typical saw-tooth waveform, while in pendular CN the eyes exhibit a periodic motion, giving rise to an approximately sinusoidal waveform. Dual jerk waveforms seemed to show small, rapid oscillations superimposed on a jerk-like waveform, thus being originary classified as a mixture of jerk and pendular CN. On the contrary, a theoretical model of CN has appeared recently, which suggests a possible interpretation of the small amplitude oscillations in dual jerk waveforms as consecutive pieces of growing and decaying exponentials.By spectral analysis of dual jerk waveforms in a number of patients with CN, we show that the oscillations are truly sinusoidal in nature, thus suggesting the possibility of a different explanation of dual jerk waveforms in CN.Preliminary results of this work were presented at XIV ICMP —International Congress of Medical Physics, Espoo, Finland, 11–16 August 1985     

Visual loss as initial presentation of chronic myelogenous leukemia

A previously healthy 17-year old girl presented with sudden visual loss in both eyes. Visual acuity on the right eye was 0.3 and on the left eye 0.1. Fundoscopic examination showed bilateral optic disc edema, retinal venous tortuousity and dilatation, retinal blot and flame-shaped hemorrhages, Roth spots and on the left eye dark blot preretinal hemorrhage covering the fovea. Laboratory evaluation showed white blood cell count of 455 x 10(9) L. Bone marrow biopsy confirmed the diagnosis of chronic myelogenous leukemia. Chemotherapy was initiated and led to the improvement of visual acuity. Fundus changes had resolved except for the preretinal hemorrhage on left eye which decreased in size. Preretinal hemorrhage in fovea caused maculopathy on the left eye. Three months after admisson visual acuity was 1.0 on the right eye and 0.3 on the left eye. Leukemia should always be included in the differential diagnosis of optic disc edema and retinal hemorrhages.     

Nonlinear time series analysis of jerk congenital nystagmus

Nonlinear dynamics provides a complementary framework to control theory for the quantitative analysis of the oculomotor control system. This paper presents a number of findings relating to the aetiology and mechanics of the pathological ocular oscillation jerk congenital nystagmus (jerk CN). A range of time series analysis techniques were applied to recorded jerk CN waveforms, and also to simulated jerk waveforms produced by an established model in which the oscillations are a consequence of an unstable neural integrator. The results of the analysis were then interpreted within the framework of a generalised model of the unforced oculomotor system. This work suggests that for jerk oscillations, the origin of the instability lies in one of the five oculomotor subsystems, rather than in the final common pathway (the neural integrator and muscle plant). Additionally, experimental estimates of the linearised foveation dynamics imply that a refixating fast phase induced by a near-homoclinic trajectory will result in periodic oscillations. Local dimension calculations show that the dimension of the experimental jerk CN data increases during the fast phase, indicating that the oscillations are not periodic, and hence that the refixation mechanism is of greater complexity than a homoclinic reinjection. The dimension increase is hypothesised to result either from a signal-dependent noise process in the saccadic system, or the activation of additional oculomotor components at the beginning of the fast phase. The modification of a recent saccadic system model to incorporate biologically realistic signal-dependent noise is suggested, in order to test the first of these hypotheses. Action Editor: Peter Latham     

The two axes of the human eye and inversion of the retinal layers: The basis for the interpretation of the retina as a phase grating optical,cellular 3D chip

The question of why the human eye has two axes, a photopic visual axis, and an eye axis, is just as justified as the one of why the fovea is not on the eye axis, but instead is on the visual axis. An optical engineer would have omitted the second axis and placed the fovea on the eye axis. The answer to the question of why the design of the real eye differs from the logic of the engineer is found in its prenatal development. The biaxial structure was the only possible consequence of the decision to invert the retinal layers. Accordingly, this is of considerable importance. It, in turn, forms the basis of the interpretation of the retina as a cellular 3D phase grating, and can provide a grating-optical interpretation of adaptive effects (Purkinje shift) and aperture phenomena (Stiles-Crawford effects I and II, Bezold-Brücke phenomenon) and visual acuity data in photopic and scotopic vision.     

A Gene for Autosomal Dominant Congenital Nystagmus Localizes to 6p12

Congenital nystagmus is an idiopathic disorder characterized by bilateral ocular oscillations usually manifest during infancy. Vision is typically decreased due to slippage of images across the fovea. As such, visual acuity correlates with nystagmus intensity, which is the amplitude and frequency of eye movements at a given position of gaze. X-linked, autosomal dominant, and autosomal recessive pedigrees have been described, but no mapping studies have been published. We recently described a large pedigree with autosomal dominant congenital nystagmus. A genome-wide search resulted in six markers on 6p linked by two-point analysis at θ = 0 (D6S459, D6S452, D6S465, FTHP1, D6S257, D6S430). Haplotype analysis localizes the gene for autosomal dominant congenital motor nystagmus to an 18-cM region between D6S271 and D6S455.     

Factors Affecting Reading Speed in Patients with Diabetic Macular Edema Treated with Laser Photocoagulation

Purpose

To study the factors that may affect reading speed in patients with diabetic macular edema previously treated with laser photocoagulation.

Methods

Consecutive patients with type II diabetes treated with laser photocoagulation for diabetic macular edema (DME) at least twelve months previously, with best corrected visual acuity of better than 65 letters (approximately 20/40) measured with Early Treatment Diabetic Retinopathy Study (ETDRS) charts were included in this study. Patients previously treated with pan-retinal photocoagulation, vitrectomy, intravitreal steroid or anti-VEGF therapy were excluded. Any other ocular co-morbidities that may influence reading ability such as cataract, glaucoma or macular degeneration were also excluded. All patients were refracted by a certified examiner, the following measurements were collected: best corrected visual acuity (BCVA), contrast sensitivity with Pelli-Robson chart, reading speed with MNREAD chart, microperimetry with Nidek MP1, and central subfield thickness with Zeiss spectral domain optical coherent topography.

Results

The slow reading group had poorer contrast sensitivity (p = 0.001), reduced retinal sensitivity (p = 0.027) and less stable fixation (p = 0.013). Most interestingly the reduced retinal sensitivity findings were driven by the microperimetry value on the right subfield (p = 0.033), (nasal to the fovea in the right eye and temporal to the fovea in the left eye). Multiple linear regression analysis showed that contrast sensitivity is probably the most important factor that affects reading speed (p = 0.001).

Conclusion

Reduced retinal sensitivity after laser treatment is associated with reduced reading speed in patients with diabetic macular edema.     

Retinal pigmentation, visual acuity and brightness levels.

This study investigates the hypothesis that the degree of retinal pigmentation in the human eye is adaptive as it relates to the maintenance of visual acuity in optically stressful environments, deserts and snowfields. Eighty-four subjects were examined, an estimation of their degree of retinal pigmentation made by ophthalmoscopic examination and their binocular visual acuity tested over ten levels of brightness. The general level of retinal pigmentation did not influence mean visual acuity within the levels of brightness used in this study. The hypothesis was, therefore, rejected, but with the proviso that this study should be extended to even higher levels of brightness than were obtained here. There was no difference in mean pupil size at various levels of illumination between individuals grouped by degree of retinal pigmentation.     

Characterisation of baseline oscillation in congenital nystagmus eye movement recordings

Congenital nystagmus is an ocular–motor disorder that develops in the first few months of life; its pathogenesis is still unknown. Patients affected by congenital nystagmus show continuous, involuntary, rhythmical oscillations of the eyes. Monitoring eye movements, nystagmus main features such as shape, amplitude and frequency, can be extracted and analysed. Previous studies highlighted, in some cases, a much slower and smaller oscillation, which appears added up to the ordinary nystagmus waveform. This sort of baseline oscillation, or slow nystagmus, hinder precise cycle-to-cycle image placement onto the fovea. Such variability of the position may reduce patient visual acuity. This study aims to analyse more extensively eye movements recording including the baseline oscillation and investigate possible relationships between these slow oscillations and nystagmus. Almost 100 eye movement recordings (either infrared-oculographic or electrooculographic), relative to different gaze positions, belonging to 32 congenital nystagmus patients were analysed. The baseline oscillation was assumed sinusoidal; its amplitude and frequency were computed and compared with those of the nystagmus by means of a linear regression analysis. The results showed that baseline oscillations were characterised by an average frequency of 0.36 Hz (SD 0.11 Hz) and an average amplitude of 2.1° (SD 1.6°). It also resulted in a considerable correlation (R² scored 0.78) between nystagmus amplitude and baseline oscillation amplitude; the latter, on average, resulted to be about one-half of the correspondent nystagmus amplitude.     

Visual Function and Cortical Organization in Carriers of Blue Cone Monochromacy

Carriers of blue cone monochromacy have fewer cone photoreceptors than normal. Here we examine how this disruption at the level of the retina affects visual function and cortical organization in these individuals. Visual resolution and contrast sensitivity was measured at the preferred retinal locus of fixation and visual resolution was tested at two eccentric locations (2.5° and 8°) with spectacle correction only. Adaptive optics corrected resolution acuity and cone spacing were simultaneously measured at several locations within the central fovea with adaptive optics scanning laser ophthalmoscopy (AOSLO). Fixation stability was assessed by extracting eye motion data from AOSLO videos. Retinotopic mapping using fMRI was carried out to estimate the area of early cortical regions, including that of the foveal confluence. Without adaptive optics correction, BCM carriers appeared to have normal visual function, with normal contrast sensitivity and visual resolution, but with AO-correction, visual resolution was significantly worse than normal. This resolution deficit is not explained by cone loss alone and is suggestive of an associated loss of retinal ganglion cells. However, despite evidence suggesting a reduction in the number of retinal ganglion cells, retinotopic mapping showed no reduction in the cortical area of the foveal confluence. These results suggest that ganglion cell density may not govern the foveal overrepresentation in the cortex. We propose that it is not the number of afferents, but rather the content of the information relayed to the cortex from the retina across the visual field that governs cortical magnification, as under normal viewing conditions this information is similar in both BCM carriers and normal controls.     

Features of the Retinotopic Representation in the Visual Wulst of a Laterally Eyed Bird,the Zebra Finch (Taeniopygia guttata)

The visual wulst of the zebra finch comprises at least two retinotopic maps of the contralateral eye. As yet, it is not known how much of the visual field is represented in the wulst neuronal maps, how the organization of the maps is related to the retinal architecture, and how information from the ipsilateral eye is involved in the activation of the wulst. Here, we have used autofluorescent flavoprotein imaging and classical anatomical methods to investigate such characteristics of the most posterior map of the multiple retinotopic representations. We found that the visual wulst can be activated by visual stimuli from a large part of the visual field of the contralateral eye. Horizontally, the visual field representation extended from -5° beyond the beak tip up to +125° laterally. Vertically, a small strip from -10° below to about +25° above the horizon activated the visual wulst. Although retinal ganglion cells had a much higher density around the fovea and along a strip extending from the fovea towards the beak tip, these areas were not overrepresented in the wulst map. The wulst area activated from the foveal region of the ipsilateral eye, overlapped substantially with the middle of the three contralaterally activated regions in the visual wulst, and partially with the other two. Visual wulst activity evoked by stimulation of the frontal visual field was stronger with contralateral than with binocular stimulation. This confirms earlier electrophysiological studies indicating an inhibitory influence of the activation of the ipsilateral eye on wulst activity elicited by stimulating the contralateral eye. The lack of a foveal overrepresentation suggests that identification of objects may not be the primary task of the zebra finch visual wulst. Instead, this brain area may be involved in the processing of visual information necessary for spatial orientation.     

Some results on translation invariance in the human visual system

Four experiments were conducted to study the nature of visual translation invariance in humans. In all the experiments, subjects were trained to discriminate between a previously unknown target and two non-target distractors presented at a fixed retinal location to one side of the fixation point. In a subsequent test phase, this performance was compared with the performance when the patterns were presented either centrally at the fixation point or at a location on the other side of the fixation point, opposite to the location where the patterns were learned, but where acuity was identical to what it was at the learned location. Two different experimental paradigms were used. One used an eye movement control device (Experiment 1) to ensure the eye could not move relative to the patterns to be learned. In the other three experiments, presentation duration of the patterns was restricted to a short enough period to preclude eye movements. During the training period in Experiments 1 and 2, presentation location of the patterns was centered at 2.4 deg in the periphery, whereas in Experiments 3 and 4 presentation eccentricity was reduced to 0.86 and 0.49 deg. In all four experiments performance dropped when the pattern had to be recognized at new test positions. This result suggests that the visual system does not apply a global transposition transformation to the retinal image to compensate for translations. We propose that, instead, it decomposes the image into simple features which themselves are more-or-less translation invariant. If in a given task, patterns can be discriminated using these simple features, then translation invariance will occur. If not, then translation invariance will fail or be incomplete.     

A hypothetical explanation of congenital nystagmus

Congenital nystagmus (CN) is a conjugate, rhythmic, eye movement disorder characterized by a wide variety of waveforms ranging from jerk to pendular types. No detailed mechanisms have been proposed to explain the generation of the CN wave-form This paper proposes a hypothetical mechanism for CN, and shows with computer simulations that a model based on this hypothesis can account for a variety of disparate waveforms. The basis of this model is a gaze-holding network, or neural integrator, that has both position and velocity feedback loops. The signals carried in these loops could arise from either afference or efference. In normal subjects, the position feedback would be positive and the velocity feedback would be negative. Both would help to increase the time constant of an imperfect neural integrator in the brain stem. We propose that in patients with CN the sign of the velocity pathway is reversed, making the neural integrator unstable. This instability could manifest as many different CN waveforms, depending on the direction and velocity of post-saccadic ocular drift and actions of nonlinearities within the position and velocity feedback loops. Thus a single underlying abnormality may be responsible for a variety of CN waveforms.     

Resolution of pseudophakic cystoid macular edema with combination therapy of topical corticosteroids and nonsteroidal anti-inflammatory drugs

A 69 years old women underwent uneventful cataract surgery of her left eye with phacoemulsification and posterior chamber intraocular lens implantation in topical anesthesia. Patient was postoperatively treated with combination of antibiotic and steroid in decreasing dosages during five weeks: one drop five times a day the first week, three times a day second to forth week and one time a day the fifth week. In each checkup, performed first postoperative day, 7 days, 5 weeks and 12 weeks after the operation, visual acuity with and without correction, tonometry, corneal transparency, biomicroscopy of posterior pole and measure of macular thickness by optical coherence tomography (OCT) were performed. At first day follow-up visit, the patient's visual acuity was 20/25 but 6 weeks after the operation, the patient's vision had worsened to 20/60 after a slow steroid tapper. At that time OCT showed foveal thickening and cystic changes specific for cystoid macular edema (CME). Combination of corticosteroid and non-steroidal anti-inflammatory drug four times daily was included in therapy. The dose was tapered off over the ensuing 8 weeks. The total treatment duration was 12 weeks. At the patient's 2-month follow-up visit, vision has improved to 20/20 and the fovea appeared flat. OCT showed complete resolution of foveal thickening and cystic changes. Combination of corticosteroid and NSAID is effective and safe therapy for treating pseudophakic CME. Patient showed significant improvement in visual acuity and retinal thickness at 2 months post treatment.     

Estimates of underwater and aerial visual acuity in the European beaver <Emphasis Type="Italic">Castor fiber</Emphasis> L. based on morphological data

The eye optics and topographic distribution of ganglion cells were studied using whole mount preparations from European beaver Castor fiber L. The beaver eye optics provides emmetropia in air and hypermetropia in water. The optometrical measurements predict retinal resolution of the beaver eye around 17′ in air and 9′ in water. In air, retinal resolution corresponds to the real visual acuity, whereas in water, visual acuity is below the retinal resolution because of the non-precise focusing.     

Different programming modes of human saccadic eye movements as a function of stimulus eccentricity: Indications of a functional subdivision of the visual field

1. Voluntary saccadic eye movements were made toward flashes of light on the horizontal meridian, whose duration and distance from the point of fixation were varied; eye movements were measured using d.c.-electrooculography.—2. Targets within 10°–15° eccentricity are usually reached by one saccadic eye movement. When the eyes turn toward targets of more than 10°–15° eccentricity, the first saccadic eye movement falls short of the target by an angle usually not exceeding 10°. The presence of the image of the target off the fovea (visual error signal) subsequent to such an undershoot elicits, after a short interval, corrective saccades (usually one) which place the image of the target on the fovea. In the absence of a visual error signal, the probability of occurrence of corrective saccades is low, but it increases with greater target eccentricities. These observations suggest that there are different, eccentricity-dependent modes of programming saccadic eye movements.—3. Saccadic eye movements appear to be programmed in retinal coordinates. This conclusion is based on the observations that, irrespective of the initial position of the eyes in the orbit, a) there are different programming modes for eye movements to targets within and beyond 10°–15° from the fixation point, and b_ the maximum velocity of saccadic eye movements is always reached at 25° to 30° target eccentricity. —4. Distributions of latency and intersaccadic interval (ISI) are frequently multimodal, with a separation between modes of 30 to 40 msec. These observations suggest that saccadic eye movements are produced by mechanisms which, at a frequency of 30 Hz, process visual information. —5. Corrective saccades may occur after extremely short intervals (30 to 60 msec) regardless of whether or not a visual error signal is present; the eyes may not even come to a complete stop during these very short intersaccadic intervals. It is suggested that these corrective saccades are triggered by errors in the programming of the initial saccadic eye movements, and not by a visual error signal. —6. The exitence of different, eccentricity-dependent programming modes of saccadic eye movements, is further supported by anatomical, physiological, psychophysical, and neuropathological observations that suggest a dissociation of visual functions dependent on retinal eccentricity. Saccadic eye movements to targets more eccentric than 10°–15° appear to be executed by a mechanism involving the superior colliculus (perhaps independent of the visual cortex), whereas saccadic eye movements to less eccentric targets appear to depend on a mechanism involving the geniculo-cortical pathway (perhaps in collaboration with the superior colliculus).     

Ecomorphology of eye shape and retinal topography in waterfowl (Aves: Anseriformes: Anatidae) with different foraging modes

Despite the large body of literature on ecomorphological adaptations to foraging in waterfowl, little attention has been paid to their sensory systems, especially vision. Here, we compare eye shape and retinal topography across 12 species representing 4 different foraging modes. Eye shape was significantly different among foraging modes, with diving and pursuit-diving species having relatively smaller corneal diameters compared to non-diving species. This may be associated with differences in ambient light intensity while foraging or an ability to tightly constrict the pupil in divers in order to facilitate underwater vision. Retinal topography was similar across all species, consisting of an oblique visual streak, a central area of peak cell density, and no discernible fovea. Because the bill faces downwards when the head is held in the normal posture in waterfowl, the visual streak will be held horizontally, allowing the horizon to be sampled with higher visual acuity. Estimates of spatial resolving power were similar among species with only the Canada goose having a higher spatial resolution. Overall, we found no evidence of ecomorphological adaptations to different foraging modes in the retinal ganglion cell layer in waterfowl. Rather, retinal topography in these birds seems to reflect the ‘openness’ of their habitats.     

Ocular albinism type 1: more than meets the eye

Ocular albinism type 1 (OA1) is an X-linked recessive disorder characterized by a severe reduction of visual acuity, and hypopigmentation of the retina that leads to nystagmus, strabismus, and photophobia/photodysphoria. Microscopic examination of both retinal pigment epithelium and skin melanocytes in OA1 reveals the presence of macrome-lanosomes, suggesting that the OA1 gene product plays a role in melanosome biogenesis. Studies of mutations identified from OA1 patients and an Oa1 knock-out mouse model further implicate OA1 protein function in the late stage of melanosome development. Because its effects are primarily limited to the eye, OA1 represents an ideal model system to study the relationship between pigmentation and visual development. Based upon sequence homology and biochemical studies, OA1 may represent a novel intracellular G-protein coupled receptor. Understanding the function of OA1 will contribute greatly to our understanding of melanosome biogenesis and the role of pigmentation in visual development.     

Self-motion-induced eye movements: effects on visual acuity and navigation

Self-motion disturbs the stability of retinal images by inducing optic flow. Objects of interest need to be fixated or tracked, yet these eye movements can infringe on the experienced retinal flow that is important for visual navigation. Separating the components of optic flow caused by an eye movement from those due to self-motion, as well as using optic flow for visual navigation while simultaneously maintaining visual acuity on near targets, represent key challenges for the visual system. Here we summarize recent advances in our understanding of how the visuomotor and vestibulomotor systems function and interact, given the complex task of compensating for instabilities of retinal images, which typically vary as a function of retinal location and differ for each eye.     

Ocular changes accompanying eye loss in the spider family uloboridae

In uloborid spiders, eye loss is accompanied by increased visual angles, optical material investment, and potential visual acuity of the retained eyes. Relative to carapace volume, the six-eyed Hyptiotes cavatus and two four-eyed Miagrammopes species have greater retinal hemisphere areas and lens volumes than do the eight-eyed uloborids Waitkera waitkerensis, Uloborus glomosus, and Octonoba sinensis. In Waitkera, in which the eyes have little visual overlap, and in Miagrammopes, in which eye loss simplifies the spiders' patterns of visual overlap, increased retinal cell density enhances potential visual acuity. However, this occurs at the expense of potential retinal cell sensitivity.