Linear ensemble-coding in midbrain superior colliculus specifies the saccade kinematics

Recently, we proposed an ensemble-coding scheme of the midbrain superior colliculus (SC) in which, during a saccade, each spike emitted by each recruited SC neuron contributes a fixed minivector to the gaze-control motor output. The size and direction of this 'spike vector' depend exclusively on a cell's location within the SC motor map (Goossens and Van Opstal, in J Neurophysiol 95: 2326-2341, 2006). According to this simple scheme, the planned saccade trajectory results from instantaneous linear summation of all spike vectors across the motor map. In our simulations with this model, the brainstem saccade generator was simplified by a linear feedback system, rendering the total model (which has only three free parameters) essentially linear. Interestingly, when this scheme was applied to actually recorded spike trains from 139 saccade-related SC neurons, measured during thousands of eye movements to single visual targets, straight saccades resulted with the correct velocity profiles and nonlinear kinematic relations ('main sequence properties' and 'component stretching'). Hence, we concluded that the kinematic nonlinearity of saccades resides in the spatial-temporal distribution of SC activity, rather than in the brainstem burst generator. The latter is generally assumed in models of the saccadic system. Here we analyze how this behaviour might emerge from this simple scheme. In addition, we will show new experimental evidence in support of the proposed mechanism.     

Optimal control of saccades by spatial-temporal activity patterns in the monkey superior colliculus

A major challenge in computational neurobiology is to understand how populations of noisy, broadly-tuned neurons produce accurate goal-directed actions such as saccades. Saccades are high-velocity eye movements that have stereotyped, nonlinear kinematics; their duration increases with amplitude, while peak eye-velocity saturates for large saccades. Recent theories suggest that these characteristics reflect a deliberate strategy that optimizes a speed-accuracy tradeoff in the presence of signal-dependent noise in the neural control signals. Here we argue that the midbrain superior colliculus (SC), a key sensorimotor interface that contains a topographically-organized map of saccade vectors, is in an ideal position to implement such an optimization principle. Most models attribute the nonlinear saccade kinematics to saturation in the brainstem pulse generator downstream from the SC. However, there is little data to support this assumption. We now present new neurophysiological evidence for an alternative scheme, which proposes that these properties reside in the spatial-temporal dynamics of SC activity. As predicted by this scheme, we found a remarkably systematic organization in the burst properties of saccade-related neurons along the rostral-to-caudal (i.e., amplitude-coding) dimension of the SC motor map: peak firing-rates systematically decrease for cells encoding larger saccades, while burst durations and skewness increase, suggesting that this spatial gradient underlies the increase in duration and skewness of the eye velocity profiles with amplitude. We also show that all neurons in the recruited population synchronize their burst profiles, indicating that the burst-timing of each cell is determined by the planned saccade vector in which it participates, rather than by its anatomical location. Together with the observation that saccade-related SC cells indeed show signal-dependent noise, this precisely tuned organization of SC burst activity strongly supports the notion of an optimal motor-control principle embedded in the SC motor map as it fully accounts for the straight trajectories and kinematic nonlinearity of saccades.     

On identification of saccades from sinusoidal eye movement signals

Sinusoidal eye movements and potential saccadic eye movements are examined using the syntactic pattern recognition method presented previously. A few computer tests are presented for the verification of potential saccades from signals of sinusoidal eye movements. The technique was developed and tested with electro-oculographic signals. The verification of saccades consists of three tests: the estimation of average noise peaks in an eye movement signal; an angular velocity threshold; and the comparison between a sinusoidal eye movement signal and the corresponding stimulus signal. The technique is also efficient for noisy signals of eye movements, which were stimulated by both predictive and non-predictive sinusoidal stimulus movements.     

A novel interpretation for the collicular role in saccade generation

Recently, we found evidence that the activity of neurons in the deep layers of the monkey superior colliculus (SC) is modulated by initial eye position (gain fields). In this paper, we propose a quantitative model of the motor SC which incorporates these new findings. Inputs to the motor map represent the desired eye displacement vector (motor error), as well as initial eye position. A unit's activity in the motor map is described by multiplying a weak linear eye position sensitivity with a gaussian tuning to motor error. The motor map projects to several sets of output neurons, representing the coordinates of the desired eye displacement vector, the desired eye position in the head, and the three-dimensional ocular rotation axis for saccades in Listing's plane, respectively. All these signals have been hypothesized in the literature to drive the saccade burst generator. We show that these signals can be extracted from the motor map by a linear weighting of the population activity. The saccadic system may employ all coding strategies in parallel to ensure high spatial accuracy in many complex sensorimotor tasks, such as orienting to multimodal stimuli.     

Blink Perturbation Effects on Saccades Evoked by Microstimulation of the Superior Colliculus

Current knowledge of saccade-blink interactions suggests that blinks have paradoxical effects on saccade generation. Blinks suppress saccade generation by attenuating the oculomotor drive command in structures like the superior colliculus (SC), but they also disinhibit the saccadic system by removing the potent inhibition of pontine omnipause neurons (OPNs). To better characterize these effects, we evoked the trigeminal blink reflex by delivering an air puff to one eye as saccades were evoked by sub-optimal stimulation of the SC. For every stimulation site, the peak and average velocities of stimulation with blink movements (SwBMs) were lower than stimulation-only saccades (SoMs), supporting the notion that the oculomotor drive is weakened in the presence of a blink. In contrast, the duration of the SwBMs was longer, consistent with the hypothesis that the blink-induced inhibition of the OPNs could prolong the window of time available for oculomotor commands to drive an eye movement. The amplitude of the SwBM could also be larger than the SoM amplitude obtained from the same site, particularly for cases in which blink-associated eye movements exhibited the slowest kinematics. The results are interpreted in terms of neural signatures of saccade-blink interactions.     

A competitive integration model of exogenous and endogenous eye movements

We present a model of the eye movement system in which the programming of an eye movement is the result of the competitive integration of information in the superior colliculi (SC). This brain area receives input from occipital cortex, the frontal eye fields, and the dorsolateral prefrontal cortex, on the basis of which it computes the location of the next saccadic target. Two critical assumptions in the model are that cortical inputs are not only excitatory, but can also inhibit saccades to specific locations, and that the SC continue to influence the trajectory of a saccade while it is being executed. With these assumptions, we account for many neurophysiological and behavioral findings from eye movement research. Interactions within the saccade map are shown to account for effects of distractors on saccadic reaction time (SRT) and saccade trajectory, including the global effect and oculomotor capture. In addition, the model accounts for express saccades, the gap effect, saccadic reaction times for antisaccades, and recorded responses from neurons in the SC and frontal eye fields in these tasks.     

On automatic diagnosis of pathological saccadic eye movements

A syntactic technique is described for the recognition of saccadic eye movements to distinguish normal saccades from those distorted by brain stem lesions. A digitalized eye movement signal is transformed into a sequence of symbols. Eye movements are then found from this sequence by using a parser. This recognition method appropriately enlarged could be applied as a classifier of saccades to aid in diagnosis     

A model that integrates eye velocity commands to keep track of smooth eye displacements

Past results have reported conflicting findings on the oculomotor system’s ability to keep track of smooth eye movements in darkness. Whereas some results indicate that saccades cannot compensate for smooth eye displacements, others report that memory-guided saccades during smooth pursuit are spatially correct. Recently, it was shown that the amount of time before the saccade made a difference: short-latency saccades were retinotopically coded, whereas long-latency saccades were spatially coded. Here, we propose a model of the saccadic system that can explain the available experimental data. The novel part of this model consists of a delayed integration of efferent smooth eye velocity commands. Two alternative physiologically realistic neural mechanisms for this integration stage are proposed. Model simulations accurately reproduced prior findings. Thus, this model reconciles the earlier contradictory reports from the literature about compensation for smooth eye movements before saccades because it involves a slow integration process. Action Editor: Jonathan D. Victor     

Two types of eye movements during electrical stimulation of the rostral and caudal parts of the medial frontal "oculomotor" area in cats

The character of eye movements during electrical stimulation of the medial wall of the brain beneath the cruciate sulcus and of the inferior wall of the cruciate sulcus itself in the frontal cortex was investigated in waking cats. Stimulation of this part of the brain evoked two types of eye movements: unidirectional concomitant saccades, whose direction and amplitude were independent of the original position of the eyes in the orbits, and saccades into the central position (so-called centering saccades). Unidirectional saccades appeared in response to stimulation of the caudal part of the investigated zone, centering saccades in response to stimulation of its rostral part. Analysis of the directions and amplitudes of unidirectional saccades suggested the retinotopic organization of the caudal zone. Systematic changes in the magnitude and direction of vertical saccades during stimulation of the deep parts of the cruciate sulcus indicated previsely the projection of the vertical meridian of the retina. Reappearance of vertical saccades evoked by stimulation of certain parts of the medial wall of the brain suggests the existence of more than one retinotopically organized zone in this region. Inconstancy of stereotaxic coordinates of the oculomotor area, studied in different animals, was noted.Institute for Problems in Information Transmission, Academy of Sciences of the USSR, Moscow. Translated from Neirofiziologiya, Vol. 16, No. 6, pp. 761–766, November–December, 1984.     

A model of the saccade-generating system that accounts for trajectory variations produced by competing visual stimuli

Variable saccade trajectories are produced in visual search paradigms in which multiple potential target stimuli are present. These variable trajectories provide a rich source of information that may lead to a deeper understanding of the basic control mechanisms of the saccadic system. We have used published behavioral observations and neural recordings in the superior colliculus (SC), gathered in monkeys performing visual search paradigms, to guide the construction of a new distributed model of the saccadic system. The new model can account for many of the variations in saccade trajectory produced by the appearance of multiple visual stimuli in a search paradigm. The model uses distributed feedback about current eye motion from the brainstem to the SC to reduce activity there at physiologically realistic rates during saccades. The long-range lateral inhibitory connections between SC cells used in previous models have been eliminated to match recent physiological evidence. The model features interactions between visually activated multiple populations of cells in the SC and distributed and topologically organized inhibitory input to the SC from the SNr to produce some of the types of variable saccadic trajectories, including slightly curved and averaging saccades, observed in visual search tasks. The distributed perisaccadic disinhibition of SC from the substantia nigra (SNr) is assumed to have broad spatial tuning. In order to produce the strongly curved saccades occasionally recorded in visual search, the existence of a parallel input to the saccadic burst generators in addition to that provided by the distributed input from the SC is required. The spatiotemporal form of this additional parallel input is computed based on the assumption that the input from the model SC is realistic. In accordance with other recent models, it is assumed that the parallel input comes from the cerebellum, but our model predicts that the parallel input is delayed during highly curved saccadic trajectories.     

Tests of Models for Saccade–Vergence Interaction using Novel Stimulus Conditions

During natural activities, two types of eye movements - saccades and vergence - are used in concert to point the fovea of each eye at features of interest. Some electrophysiological studies support the concept of independent neurobiological substrates for saccades and vergence, namely saccadic and vergence burst neurons. Discerning the interaction of these two components is complicated by the near-synchronous occurrence of saccadic and vergence components. However, by positioning the far target below the near target, it is possible to induce responses in which the peak velocity of the vertical saccadic component precedes the peak velocity of the horizontal vergence component by approximately 75 ms. When saccade-vergence responses are temporally dissociated in this way, the vergence velocity waveform changes, becoming less skewed. We excluded the possibility that such change in skewing was due to visual feedback by showing that similar behavior occurred in darkness. We then tested a saccade-related vergence burst neuron (SVBN) model proposed by Zee et al. in J Neurophysiol 68:1624-1641 (1992), in which omnipause neurons remove inhibition from both saccadic and vergence burst neurons. The technique of parameter estimation was used to calculate optimal values for responses from human subjects in which saccadic and convergence components of response were either nearly synchronized or temporally dissociated. Although the SVBN model could account for convergence waveforms when saccadic and vergence components were nearly synchronized, it could not when the components were temporally dissociated. We modified the model so that the saccadic pulse changed the parameter values of the convergence burst units if both components were synchronized. The modified model accounted for velocity waveforms of both synchronous and dissociated convergence movements. We conclude that both the saccadic pulse and omnipause neuron inhibition influence the generation of vergence movements when they are made synchronously with saccades.     

Basal Ganglia Neuronal Activity during Scanning Eye Movements in Parkinson’s Disease

The oculomotor role of the basal ganglia has been supported by extensive evidence, although their role in scanning eye movements is poorly understood. Nineteen Parkinsońs disease patients, which underwent implantation of deep brain stimulation electrodes, were investigated with simultaneous intraoperative microelectrode recordings and single channel electrooculography in a scanning eye movement task by viewing a series of colored pictures selected from the International Affective Picture System. Four patients additionally underwent a visually guided saccade task. Microelectrode recordings were analyzed selectively from the subthalamic nucleus, substantia nigra pars reticulata and from the globus pallidus by the WaveClus program which allowed for detection and sorting of individual neurons. The relationship between neuronal firing rate and eye movements was studied by crosscorrelation analysis. Out of 183 neurons that were detected, 130 were found in the subthalamic nucleus, 30 in the substantia nigra and 23 in the globus pallidus. Twenty percent of the neurons in each of these structures showed eye movement-related activity. Neurons related to scanning eye movements were mostly unrelated to the visually guided saccades. We conclude that a relatively large number of basal ganglia neurons are involved in eye motion control. Surprisingly, neurons related to scanning eye movements differed from neurons activated during saccades suggesting functional specialization and segregation of both systems for eye movement control.     

The control of gaze (3). Neurological defects

Eye movements serve vision, which has two different aims: changing images using saccades, i.e. rapid eye movements, and stabilizing new images on the retina using slow eye movements. Eye movements are performed by ocular motor nuclei in the brainstem, on which supranuclear pathways--originating in the cerebral cortex, cerebellum and vestibular structures--converge. It is useful for the neurologist to know the clinical abnormalities of eye movements visible at the bedside since such signs are helpful for localization. Eye movement paralysis may be nuclear or infranuclear (nerves), involving all types of eye movements, i.e. saccades as well as the vestibulo-ocular reflex (VOR), or supranuclear, in which case the VOR is usually preserved. Lateral eye movements are organized in the pons, with paralysis of adduction (and preservation of convergence) when the lesion affects the medial longitudinal fasciculus (internuclear ophthalmoplegia), paralysis of conjugate lateral eye movements when the lesion affects the abducens nucleus (VI) and the "one-and-a-half" syndrome when both these structures are involved. Vertical eye movements are organized in the midbrain, with ipsilateral oculomotor (III) paralysis and contralateral paralysis of the superior rectus muscle when the third nerve nucleus is unilaterally damaged, supranuclear upward gaze paralysis when the posterior commissure is unilaterally damaged and supranuclear downward gaze paralysis (often coupled with upward gaze paralysis) when the mesencephalic reticular formations are bilaterally damaged. Numerous types of abnormal eye movements exist, of which nystagmus is the most frequent and usually due to damage to peripheral or central vestibular pathways. Cerebral hemispheric or cerebellar damage results in subtle eye movement abnormalities at the bedside, in general only detected using eye movement recordings, because of the multiplicity of eye movement pathways at these levels and their reciprocal compensation in the case of a lesion. Lastly, eye movements can also help the neuroscientist to understand the organization of the brain. They are a good model of motricity allowing us, using eye movement recordings, to study the afferent pathways of the cortical areas that trigger them, and thus to analyze relatively complex neuropsychological processes such as visuo-spatial integration, spatial memory, motivation and the preparation of motor programs.     

A Mathematical Model of Optimal Saccadic Eye Movement by a Pair of Muscles

This paper presents a model of saccadic eye movements. Eye movements are considered as being ballistic, since saccades (rapid concurrent movements of both eyes) occur several hundred thousand times per day; visual perception of the environment is interrupted by a saccade. The optimal control was constructed for the motion considered in three consecutively refined assumptions. The controls included in the time-optimal problem were the resultant moment of force exerted by the extraocular muscles, individual moments of force exerted by either muscle of the agonist–antagonist pair, and finally, the rate of change of these moments. This approach is consistent with the view that is currently upheld by physiologists, who believe that a saccade is programmed by the central nervous system before the beginning of an eye movement and is scarcely adjusted during the movement itself. The solution of the optimal control problem and the results obtained by subsequent numerical modeling of saccadic trajectories were compared with the published experimental data. The saccadic trajectories were compared based on the main sequence, the known consistent relationship between saccade amplitude and duration, which is the most widely applied and commonly accepted way of describing saccade data. The main sequence of saccades obtained from the solution of the optimal control problem formulated in the most complete form agreed well with published experimental results.     

Afferent signals from pigeon extraocular muscles modify the vestibular responses of units in the abducens nucleus.

Although the extraocular muscles contain stretch receptors it is generally believed that their afferents exert no influence on the control of eye movement. However, we have shown previously that these afferent signals reach various brainstem centres concerned with eye movement, notably the vestibular nuclei, and that the decerebrate pigeon is a favourable preparation in which to study their effects. If the extraocular muscle afferents do influence oculomotor control from moment-to-moment they should exert a demonstrable effect on the oculomotor nuclei. We now present evidence that extraocular muscle afferent signals do, indeed, alter the responses of units in an oculomotor nucleus (the abducens, VI nerve nucleus, which supplies the lateral rectus muscle) to horizontal, vestibular stimulation induced by sinusoidal oscillation of the bird. Such stimuli evoke a vestibulo-ocular reflex in the intact bird. The extraocular stretch receptors were activated by passive eye movement within the pigeon's saccadic range; such movements modified the vestibular responses of all 19 units studied which were all, histologically, in the abducens nucleus. The magnitude of the effects, purely inhibitory in 15 units, depended both on the amplitude and the velocity of the eye movement and most units showed selectivity for particular combinations of plane (e.g. horizontal versus vertical) and direction (e.g. rostral versus caudal) of eye movement. The results show that an afferent signal from the extraocular muscles influences vestibularly driven activity in the abducens nucleus to which it carries information related to amplitude, velocity, plane and direction of eye movement in the saccadic range. They thus strongly support the view that extraocular afferent signals are involved in the control of eye movement.     

An improved neural-network model for the neural integrator of the oculomotor system: More realistic neuron behavior

The discharge rates of premotor, brain-stem neurons that create eye movements modulate in relation to eye velocity yet firing rates of extraocular motoneurons contain both eye-position and eyevelocity signals. The eye-position signal is derived from the eye-velocity command by means of a neural network which functioins as a temporal integrator. We have previously proposed a network of lateral-inhibitory neurons that is capable of performing the required integration. That analysis centered on the temporal aspects of the signal processing for a limited class of idealized inputs. All of its cells were identical and carried only the integrated signal. Recordings in the brain stem, however, show that neurons in the region of the neural integrator have a variety of background firing rates, all carry some eye-velocity signal as well as the eye-position signal, and carry the former with different strengths depending on the type of eye movement being made. It was necessary to see if the proposed model could be modified to make its neurons more realistic.By modifying the spatial distribution of afferents to the network, we demonstrate that the same basic model functions properly in spite of afferents with nonuniform background firing rates. To introduce the eye-velocity signal a double-layer network, consisting of inhibitory and excitatory cells, was necessary. By presenting the velocity input to only local regions of this network it was shown that all cells in the network still carried the integrated signal and that its cells could carry different eye-velocity signals for different types of eye movements. Thus, this model stimulates quantitatively and qualitatively, the behavior of neurons seen in the region of the neural integrator.     

Neural mechanisms potentially contributing to the intersegmental phase lag in lamprey

Factors contributing to the production of a phase lag along chains of oscillatory networks consisting of Hodgkin-Huxley type neurons are analyzed by means of simulations. Simplified network configurations are explored consisting of the basic building blocks of the spinal central pattern generator (CPG) generating swimming in the lamprey. It consists of reciprocally coupled crossed inhibitory C interneurons and ipsilateral excitatory E interneurons that activate C neurons and other E neurons. Oscillatory activity in the model network can, in the simplest case, be produced by a pair of reciprocally coupled C interneurons oscillating through an escape mechanism. Different levels of tonic excitation drive the network over a wide burst frequency range. In this type of network, powerful frequency-regulating factors are the effective inhibition produced by the active side, in combination with the tendency of the inactive side to escape from the inhibition. These two mechanisms can be affected by several factors, e.g. spike frequency adaptation (calcium-dependent K(+) channels), N-methyl-D-aspartate membrane properties as well as presence of low-voltage activated calcium channels. A rostrocaudal phase lag can be produced either by extending the contralateral inhibitory projections or the ipsilateral excitatory projections relatively more in the caudal than the rostral direction, since both an increased inhibition and a phasic excitation slow down the receiving network. The phase lag becomes decreased if the length of the intersegmental projections is increased or if the projections are extended symmetrically in both the rostral and the caudal directions. The simulations indicate that the conditions in the ends of an oscillator chain may significantly affect sign, magnitude and constancy of the phase lag. Also, with short and relatively weak intersegmental connections, the network remains robust against perturbations as well as intrinsic frequency differences along the chain. The phase lag (percentage of cycle duration) increases, however, with burst frequency also when the coupling strength is comparatively weak. The results are discussed and compared with previous "phase pulling" models as well as relaxation oscillators.     

Computer simulation of overshoot in saccadic eye movements.

The human horizontal eye movement system produces quick, precise, conjugate eye movements called saccades. These are important in normal vision. For example, reading tasks exclusively utilize saccadic eye movements. The majority of saccades have dynamic overshoot. The amplitude of this overshoot is independent of saccadic amplitude, and is such that it places the image of the stimulus within the retinal region of maximum acuity within a minimum of time. A computer based model of the saccadic mechanisms was used to study the origin of this overshoot. It was discussed that dynamic overshoot cannot be attributed to biomechanism properites of the eye movement mechanism, but must instead be explained by variations in the controlling nervous activity. The form of this neural controller signal is very similar to that required for a time optimal response of an inertial system.     

Unequal saccades generated by velocity interactions in the peripheral oculomotor system

Experiments with precision eye movement recordings show binocularly unequal saccades to be present under several stimulus conditions having as a common theme ongoing low velocities at the times of the saccades. Simulations using a model of eye muscles and eyeball dynamics reproduce these unequal saccades in quantitative agreement with the experimental findings. The model uses equal innervation for the saccades, and demonstrates a peripheral interaction between the muscle forces and the eye velocities to be the cause of the large inequality of the simulated binocular saccades. Thus, the simulations provide evidence that Hering's law continues to describe the innervation patterns to corresponding muscles producing these binocularly unequal saccades found in the experimental situation.     

Modeling dynamical interactions between fast and slow movements: fast saccadic eye movement behavior in the presence of the slower VOR

An ongoing controversy has to do with the interactions between “fast” (saccadic, quick phase) and “slow” (all other) eye movements. By attacking such issues with both experimental and especially simulation studies using our nonlinear sixth order reciprocally innervated model of the eye mechanical system, insights can be gained into the nature of these nontrivial phenomena. In our present study we relied both (1) on simulation of saccades under a wide range of experimental conditions [vestibular ocular reflex (VOR) velocities from -100 to 100 deg/sec, VOR induced position ranges from -30 to 30 degrees, time-optimal saccades ranging from 2 to 40 degrees], and (2) on using a wide variety of computer simulation of eye movement models, ranging from nonlinear ones with first and especially second order multipulse step controller signal structures, to different controller signal interaction schemes, to simulation using linearized models. We have isolated two important nonlinear phenomena: a level I nonlinear mechanical interaction, dependent not only on the initial velocity but also on the “position effect,” a new finding; and a level II nonlinear neurological interaction, close to “squelching” of the VOR controller signals by the dominating saccadic signal. Furthermore, we have used our simulation findings to reinterpret others' experimental data on eye movement interactions, including saccadic-smooth pursuit, saccadic-vergence, and vestibular nystagmus.