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Department of Biomedical Engineering, McGill University, Montreal, Quebec, Canada
Submitted 14 August 2006; accepted in final form 9 November 2006
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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). As depicted schematically in Fig. 2, the gaze saccade is generated by activity in the excitatory (EBNs) and inhibitory (IBNs) burst neurons, classified as medium-lead burst neurons (MLBNs) in the brain stem that cause, respectively, excitation of the agonist motor neurons and inhibition of the antagonist motor neurons (for review, see Moschovakis et al. 1996). OPNs project inhibitory connections to these premotor burst neurons (Curthoys et al. 1984; Kaneko and Fuchs 1982), thereby releasing their discharge during fast phases and inhibiting it during slow phases of gaze shifts. The afferent inputs to OPNs that dictate their tonic discharges and pauses in activity are however uncertain. Accordingly, the switching mechanism coordinating slow and fast phases of orienting gaze shifts that needs to be implemented in models of eye-head coordination is still one of the least-understood aspects in oculomotor control.
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) compares the actual eye position 
to the desired target position T to produce a motor error signal that drives the burst cells. The switching activity of OPNs, then referred to as suppressor cells, is modeled as a switch that gates the burst pathway. No explicit signal is responsible for closing the switch during the saccade; it is rather activated by a "supranuclear command" in the form of a trigger pulse. At the end of the saccade, once 
T, the end in burst activity reopens the switch suggesting reactivation of OPNs. Many improvements to the Robinson model and new models inspired by it have been proposed. They all rely on a dynamic motor error signal produced by a "comparator" that drives the burst neurons during the saccadic fast phase. The anatomical location of the comparator still remains a controversial issue. Most models either attribute its role to the superior colliculus (SC) or place it downstream of the SC. The SC receives visual inputs from the retina and the spatial location of neural activity on identified collicular output cells is believed to encode the dynamic gaze position error (Bergeron and Guitton 2002; Bergeron et al. 2003; Munoz et al. 1991), the distance between current gaze position and the final target gaze position, also referred to as gaze motor error (GME). Moreover, cellular recordings on the SC motor map are found to reflect perturbations in the gaze trajectory (Choi and Guitton 2006; Matsuo et al. 2004), which could be taken as evidence for gaze feedback to the SC as originally proposed by Galiana and Guitton (1992). Alternatively, the SC is thought to be functioning open loop and providing only a static desired gaze displacement; the motor error is then computed directly at the burst neurons. Other than the SC, the frontal eye fields and the fastigial oculomotor region in the cerebellum project to the burst generator in the brain stem and could therefore also be sources of gaze-related commands (for review, see Scudder et al. 2002).
The proposed models, and their subsequent improvements, have given little consideration to the OPN switching mechanism. Some only simulate the saccadic burst generator and ignore the logic responsible for initiating and terminating saccades (Freedman 2001; Tweed and Vilis 1985; Zee et al. 1976). OPNs are completely absent in these models, and a nonlinear burst generator gain prompts the start and end of saccades (fast phases) by itself. Most other models simply replicate Robinson's switching strategy (Goossens and Van Opstal 1997; Pélission et al. 1988; Phillips et al. 1995; Scudder 1988; Tomlinson 1990; Van Gisbergen et al. 1981; Van Opstal and Van Gisbergen 1989). In the latter case, to initiate a gaze displacement, an external trigger pulse inhibits OPNs at saccade start, and reciprocal and inhibitory connections between OPNs and EBNs/IBNs form a "latch" circuit that maintains OPN inhibition until saccade end. Intracellular recordings from OPNs during saccade inhibition reveal that the time course of OPN membrane hyperpolarization greatly resembles that of MLBN (EBN and IBN) firing (Yoshida et al. 1999). Both OPN hyperpolarization and MLBN firing amplitudes correlate closely with eye saccade velocity (or presumably gaze velocity for head-free gaze shifts). However, EBN output is excitatory and IBNs do not seem to project to OPNs directly (Strassman et al. 1986). The inhibitory latch signal that keeps OPNs silenced during fast phases thus seems to be conveyed from MLBNs to OPNs via inhibitory interneurons. The study of Yoshida et al. (1999) also demonstrates that the OPN inhibition is induced by an early abrupt hyperpolarization prior to the EBN/IBN burst. This makes sense because the burst is initiated by a pause in OPNs, and therefore it cannot be itself responsible for inducing the OPN pause in the first place. The necessity of a trigger signal to initiate the saccadic fast phase in Robinson's switching strategy is hence consistent with this finding.
The main candidate for the input to OPNs that initiates the fast phase inhibition and acts as the source of the trigger signal seems to be the SC. As already suggested, the SC might be the anatomical location of the comparator that produces the GME signal that drives the burst cells. Electrical stimulation of the saccade-related neurons in the caudal SC is not only shown to excite MLBNs monosynaptically in cats (Chimoto et al. 1996; Sugiuchi et al. 2005) and disynaptically in primates (Raybourn and Keller 1977) but to also induce disynaptic inhibition of OPNs (Kaneko and Fuchs 1982; Raybourn and Keller 1977; Yoshida et al. 2001). It is therefore reasonable to assume that the trigger signal that initiates fast phases is at least partially provided by the SC to OPNs via inhibitory interneurons as well. As already mentioned, the inhibitory trigger does not seem to be relayed by MLBNs (IBNs) to OPNs. Instead, long-lead burst neurons (LLBNs) are most likely to accomplish this task as originally suggested by Keller (1981). LLBNs are monosynaptically activated from the SC (Raybourn and Keller 1977), and their stimulation produces short-latency inhibition of OPNs (Kamogawa et al. 1996). A recent study by Kaneko (2006) furthermore states that discharge characteristics of a particular group of LLBNs (termed dorsal LLBNs) is well suited to subserve uniquely the "trigger" function and rules out their involvement in other saccadic functions that are traditionally attributed to these neurons. Similarly, as the fast phase is terminated and slow phase initiated, the end of the OPN pause is not believed to simply be triggered by the inhibitory release as burst activity ends. It could instead be explained by known afferent connections emanating from neurons in the rostral SC that pause during most fast phases and discharge during fixation (slow phases) (Munoz and Guitton 1989; Munoz and Wurtz 1993). Specialized superior colliculus fixation neurons (SCFNs) located at its rostral pole are demonstrated to have direct excitatory connections with OPNs (Büttner-Ennever et al. 1999; Paré and Guitton 1994; Sugiuchi et al. 2005; Takahashi et al. 2005), and electrical stimulation of SCFNs interrupts ongoing fast phases of both eye saccades (Munoz et al. 1996) and head-free gaze shifts (Paré and Guitton 1994). The decreased activity of SCFNs during fast phases could also contribute to triggering saccades through disfacilitation of OPNs.
A gaze control model where the SC is explicitly responsible for both the initiation and termination of fast phases was put forward by Galiana and Guitton (1992). OPNs switch the model structure between slow and fast phase operating modalities based on a gaze motor error input encoded by the SC. When GME exceeds an ON threshold (caudal SC is activated), OPNs turn off (inhibited by neurons in the caudal SC) and the circuit enters saccade mode (OPNs release the burst generator from inhibition). As gaze approaches the target, GME decreases below an OFF threshold (SCFNs start discharging), OPNs turn back on (excited by SCFNs) and switch the circuit to the slow phase operating modality (OPNs inhibit the burst generator). The inhibitory projection from burst neurons to OPNs (latch signal) is not present in the model, but it is implicitly implied that the activity of the burst generator is what keeps OPNs inhibited during fast phases. The switching strategies implemented in all other existing saccade or gaze control models are functionally identical to this one. Despite their differences in the neural derivation of trigger or latch signals, the initiation and termination of slow and fast phases ultimately rely only on the visually induced GME (or eye motor error for head-fixed saccade models).
OPN pauses can be triggered during pure vestibular stimulation as well. In vestibular nystagmus induced by whole body rotation, OPNs pause during fast phases and resume firing during slow phase movements (Cohen and Henn 1972; Paré and Guitton 1998), which are present even after chemical lesion of the SC (Hepp et al. 1993) as well as after combined ablation of the SC and the frontal eye field (Schiller et al. 1980). The occurrence of fast phases during nystagmus is observed to be well correlated with periods of high head velocity. Furthermore, passive rotation of the head on a stationary body in the dark and in absence of any visual stimuli, performed on cats (Paré and Guitton 1998) and humans (Barnes 1979; Guitton and Volle 1987), induces a saccadic gaze movement and an associated pause in OPN activity. The gaze shift is subsequently ended, and OPNs resume firing only after the head becomes nearly immobilized. Signals that drive OPNs in these two behavioral conditions clearly seem to be of vestibular rather than visual origin.
Vestibular inputs to OPNs are thought to control their operation even during visually triggered gaze shifts. This was first suggested in the study conducted by Barnes (1979) in human subjects where during visual acquisition of a target flash in the dark, there was a significant positive latency between the start of the head acceleration and the onset of the saccadic eye movement (head movement preceded eye movement) for large target eccentricities (>45°). The same observation was confirmed elsewhere in cats (Guitton et al. 1984): when the head began to move in response to a visual target, the eyes first appeared to compensate for the head movement in a slow phase preceding the saccade onset. This observation led Barnes to suggest that for large target offsets (those where the head significantly contributes to the gaze displacement), gaze shifts are generated as an automatic response to head rotation. In these studies, the eyes lag head movement systematically in cats (Guitton et al. 1984) but the same is not true for human (Barnes 1979; Goossens and Van Opstal 1997; Tweed et al. 1995) and monkey subjects (Freedman and Sparks 1997; Phillips et al. 1995). The lag between eye and head movement onset was variable, and negative lags (eyes preceding head) were also observed. Based on these observations, the hypothesis that head movement contributes to the OPN pause at fast phase onset is inconclusive. However, experiments in which the head is mechanically stopped after initiation of the gaze shift and subsequently released (Guitton and Volle 1987; Paré and Guitton 1998), clearly seem to point toward vestibular control of OPN switching even during visually triggered gaze shifts. As can be observed in Fig. 5, braking the head movement during the fast phase of the gaze shift results sequentially in a termination of the gaze shift that enters the slow phase fixation before the visual target has been reached and GME nulled. Gaze eventually reenters fast phase mode and nulls the gaze motor error but only after the head has been released. Based on behavioral recordings of eye and head movements in monkeys, during visually triggered gaze shifts interrupted by a head brake, we propose in this paper that the gaze related activity of OPNs is controlled by signals of vestibular origin as well, presumably the head-velocity signal.
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; Galiana 1991) rely on vestibular control of OPNs. Chun and Robinson propose a switching strategy where the quick phases are initiated after an eye motor error exceeds a head-velocity-dependent threshold. In Galiana's model, pauses in OPN activity are triggered by inhibitory connections from the vestibular nucleus. In existing gaze control models, however, OPN activity is modulated uniquely by a visual motor error signal. These models can explain the OPN discharges during active single step gaze shifts but cannot account for their behavior during passively generated saccades or during gaze movements interrupted by a head brake. An improved switching strategy is proposed here for the coordination of slow and fast phases of gaze shifts, which relies on the combined effect of visual (GME) and vestibular (head velocity) inputs on OPN behavior. The approach is based on known physiology and behavioral observations described in the literature and is implemented in an anatomically based model of combined eye-head gaze control. Furthermore, all types of combined eye-head movements are considered to be composed of a strategic succession of the same two basic mechanisms; the slow and fast phases of gaze. Saccades and vestibular quick phases are therefore considered to be equivalent, and the proposed switching strategy allows the model to reproduce a variety of movements. As a result, with the proposed visual-vestibular control of OPNs, the model is shown to correctly simulate single step gaze shifts, head-fixed saccades, gaze shifts interrupted by a head brake, VOR nystagmus, and VOR cancellation behavior using a single parameter set. The discussion and model applications are focused on eye-head rotations in the horizontal plane only, and eye position is limited to the conjugate deviation of left and right eyes.
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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Omnipause neurons are modeled with a system that outputs a binary signal whose value is based on the system's inputs. The two output levels describe the OPNs as either discharging at a regular rate or completely ceasing their activity even though intermediate discharge rates during "perisaccadic slow movements" have been reported (Paré and Guitton 1998). In these cases, the brain stem burst generator would be less inhibited than during fixation resulting in slow gaze displacements not considered as true fast phases (saccades). In our modeling approach, OPNs are considered to possess only ON or OFF discharge characteristics; intermediate discharge rates are not represented. The inputs to the OPN system are the gaze motor error (GME) encoded by the "comparator," the head-velocity signal (
) sensed by the semi-circular canals (SCC) of the inner ear and encoded by the activity of vestibular neurons (Chubb et al. 1984; Fuchs and Kimm 1975; Tomlinson and Robinson 1984), and the eye (or gaze) velocity signal (
) provided by the activity of burst neurons (Fig. 3). The GME signal does not have to be visually induced; it is generalized for all sensory (auditory, somatosensory etc.) or cognitive errors. Rather than having each of these signals independently initiate and terminate gaze shifts, the implemented switching strategy depends on a weighted sum of the visual and vestibular inputs to OPNs. The OPN behavior functions as follows.
When the sum of afferent signals exceeds a threshold Ton, the OPN system turns off, signaling a pause in activity. This can be monitored with a weighted sum mGME + n + k where burst cell activity is represented by eye velocity head-fixed or gaze velocity head-free.
When this sum decreases below a threshold Toff, the OPN system turns on and indicates reactivation of its tonic discharge and the slow phase fixation.
The weighted sum input is also normalized with respect to the intended gaze shift amplitude prior to being compared with OPN thresholds. This operation is necessary because otherwise constant thresholds would end fast phases at the same offset angle from the intended target for all gaze shift amplitudes. For instance, for a particular threshold the fast phase would be ended at 65° for a 70° target eccentricity and at 5° for a target at 10° (at a 5° offset in both cases). In that case, gaze would be displaced by >90% of the desired deviation for the 70° target, but only by 50% for the 10° target. Also, a nonnormalized input would trigger fast phases for different target amplitudes at different latencies, which is inconsistent with behavioral results. The normalization on the other hand allows fast phases to displace gaze near the target for all amplitudes, at identical latencies and using constant OPN thresholds. The normalization could be implemented with a simple recruitment effect either on the visuo-motor map or in its projection to the premotor brain stem circuits.
At fast phase onset, this weighted sum input to OPNs corresponds to the trigger signal. The fast phase is therefore triggered by a combined inhibition of OPNs from the caudal SC (increasing GME) and the vestibular neurons (increasing ). The eye-velocity input does not contribute to the initial inhibitory signal because the eye movement is initiated and the burst generator released only after the OPNs turn off. At fast phase end, the OPN pause is ended by a decrease of the same weighted sum. In this case, OPNs are both excited by an excitatory input from SCFNs and disinhibited by reduced firing in the caudal SC (decreasing GME) combined with a decreased inhibition from the burster (decreasing ) and the ongoing inhibition from vestibular neurons (concurrent ). Therefore the implemented control of OPNs shown in Fig. 3 is intended to simulate only the triggering of OPN pause onset and end. The inhibitory latch provided by EBNs/IBNs that keeps OPNs inhibited during fast phases and a bias input that maintains their tonic discharges during slow phase fixation (Scudder 1988) are implicit.
The hypothesized inputs are all anatomically relevant because afferent connections to OPNs have been shown to arise directly or indirectly from the SC and MLBNs (see INTRODUCTION) and also from neurons in the vestibular nucleus (Ito et al. 1986, 1987; King et al. 1978, 1980). The studies of Ito et al. and King et al. furthermore showed that the vestibular drive to OPNs is indeed inhibitory. The weighted sum hypothesis is also a conceptual representation of how neurons interconnect. Accordingly, the activation level of each incoming axon (GME, and connections) is multiplied by the strength of its synapse (represented by the m, n, and k weights). The OPN neuron sums these incoming levels and compares the sum to a threshold. A similar visual-vestibular interaction exists in the motor neuron drive during saccadic gaze movements. In addition to the visually activated burst cells, the participation of vestibular neurons in the saccadic drive has also been demonstrated (Baker et al. 1969; Galiana 1991; Galiana and Outerbridge 1984). It follows that the proposed weighted sum hypothesis implies a logical mechanism where gaze shifts are triggered and driven by analogous signals. The same applies for the slow phase fixation. Because the VOR response is controlled by a head-velocity input, it seems logical that its fast phases are also triggered by a signal of vestibular origin.
An eye-velocity signal is chosen as an input to OPNs in Fig. 3 to represent the inhibitory action of burst neurons at fast phase onset and end. Burst neurons are found to fire in relation to eye velocity during head-fixed saccades, but their firing rate seems to correlate with gaze velocity for head-free gaze shifts (Cullen and Guitton 1997a,b; Cullen et al. 1993). In the head-fixed condition, the weighted sum input to OPNs is equal to mGME + k, whereas for the head-free condition, it can be rewritten as mGME + (n – k) + k
, where (= + ) corresponds to gaze velocity. It follows that the velocity encoded input from burst neurons is correctly represented in both cases.
Model description
The proposed switching strategy is applied to a unilateral combined eye-head gaze shift model described in detail elsewhere (Galiana and Guitton 1992) and illustrated in Fig. 4. GME is produced in this model by the SC. As mentioned in the INTRODUCTION, whether the SC alone encodes GME and functions as a comparator is still a controversial issue. However, this controversy is not critical for our proposed switching strategy because it could be equally well implemented in any other gaze control model. The slow and fast phase movements were originally thought to be the outputs of two distinct neural systems. It is, however, impossible physiologically to find distinct neural circuits dedicated to specific tasks except for the activation of burst cells during saccades. The slow and fast phases of gaze shifts share identical sensory and premotor pathways (Krauzlis et al. 1997); they are hence generated in the model by different operating modalities of the same neural pathways.
In the fast phase operating modality, the gaze motor error projects to both burst and vestibular neurons (VN), drives both eye and head motor neurons and is nulled (gaze is brought to the desired target) by a negative gaze feedback loop configuration. The main contribution to the saccadic nature of the fast phase is the activation of the burst pathway. The latter considerably increases the forward gain in the feedback system, thereby reducing the system's time constants and bringing gaze quickly toward the target. Once the motor error is nulled, the slow phase modality should ensure gaze fixation by rotating the eyes in compensation to the head movement. As shown in the model schematic in Fig. 4, the SCC filters the head-velocity signal and projects to the VN. The VN provides the motor drive to the eye plant and receives an estimated feedback eye-position signal from the eye plant's internal model. For velocities of natural head movements, the canals operate in their high-pass bandwidth and the described circuit (with appropriate parameter values) produces an eye velocity such that the VOR gain / –1, which ensures perfect compensation for head rotation. A detailed mathematical analysis of this slow phase modality configuration can be found elsewhere in the context of a bilateral model of the vestibuloocular reflex (Galiana 1991).
The slow phase modality also incorporates gaze feedback to the SC and GME drives the eye and head plants. The only true structural difference between the slow and fast phase modes is the absence of the burst pathway in the former. Therefore if the saccade is interrupted in mid-flight and the slow phase is activated before the spatial target is reached, the slow phase modality must ensure fixation and not attempt to null the remaining gaze motor error. This is achieved, for the slow phase mode, by reducing the forward gain in the feedback system mainly by inactivating the burst pathway and reducing the sensitivity to the gaze motor error command (tv in Fig. 4). The lower gain ensures that the shortest time constant of the system is significantly longer than the gaze shift duration, thus producing a seemingly constant gaze even for nonzero motor error. Elsewhere, it has been reported that during the inter-saccadic plateau induced by a head brake the VOR does not have exactly unity gain and the visual axis is not fixed in space. The gaze rather continues to move toward the target in a slow ramp-like motion (Guitton et al. 1984; Paré and Guitton 1998). This can be accounted for in the slow phase model by appropriately increasing the forward gains that receive the motor error as an input. The slow phase mode can therefore also displace gaze in the model though with much slower dynamics than the fast phase mode. The VOR pathway is also not disconnected during fast phases. Therefore the head-velocity input to the VN acts as a second mechanism for the interaction of eye and head trajectories; it represents an active VOR that can enhance or suppress the gaze shift depending on the sign of gain P.
In the described gaze shift model, the OPN output signal gates the burst pathway and projects and modifies the gains of different premotor connections (see Fig. 4 legend for details), thereby alternating between the slow and fast phase modalities according to the proposed switching strategy. Unlike the connection with burst neurons, these projections do not have any anatomical relevance; they are conceptual. This change in gains in the unilateral model reflects the structural changes in the bilateral model configuration, where the activation and deactivation of EBN/IBN cells connects and disconnects certain loops that cross the midline (for details, see Galiana and Outerbridge 1984).
Raw data analysis
Primate gaze shifts perturbed by a head brake were obtained from a previous approved animal study (Choi and Guitton 2006; Guitton and Choi 2002). The gaze shifts are memory guided and directed toward a remembered target flash after a fixation point has been turned off. The head movement is mechanically stopped following saccade initiation and released after a fixed time interval. The exact experimental paradigms are described in detail elsewhere (Choi and Guitton 2006). Data of head perturbed gaze shifts were obtained for three different target offset angles of 40° (12 trials), 50° (77 trials), and 60° (71 trials) from the initial fixation point. Gaze began initially deviated by 30° from straight-ahead in a direction contralateral to that of the movement (eyes started at –20° and head at –10°). All movement traces were digitized at 1 kHz and analyzed with Matlab. Eye-position traces were obtained by subtracting the recorded gaze and head signals. The gaze-position error or gaze motor error (the 2 terms are used interchangeably throughout the paper) is defined as the difference between the position of the visual target rather than the final position of the visual axis, and instantaneous gaze position. The motor error is thus not equal to zero at the end of the saccadic gaze component. Velocity profiles were obtained by approximating the derivative of position signals according to
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50 Hz which is appropriate for frequencies of natural eye (20–30 Hz) and head (0.5–6 Hz) movements. The start and end of saccadic fast phase components was determined according to the 20°/s velocity criterion. |
RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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Several common characteristics can be observed in all the recorded (160) head brake experiments illustrated with a typical trial in Fig. 5. First, following the head brake onset, head velocity quickly drops to zero but does not provoke a concurrent end in the on-going fast phase. While the head is immobile, gaze continues to be displaced by the ongoing eye saccade and even briefly accelerates during this period (Fig. 5, a). Gaze switches to slow phase mode only after the gaze motor error has been reduced below a certain threshold value but long before gaze has attained its intended target. The GME value at which gaze switches from fast to slow mode following head brake onset has been recorded for all the available equal amplitude (40, 50, and 60°) head brake trials and is observed to be normally distributed around mean values of 8.4 ± 3.0, 16.1 ± 4.2, and 25.4 ± 3.6° (means ± SD) for the 40, 50, and 60° target eccentricities, respectively. Second, after the head is released, the remaining motor error does not instantaneously trigger a fast phase (saccade). Rather, as best observed on the velocity traces in Fig. 5, the second gaze saccade is initiated only after head velocity reaches a certain threshold. Prior to this switching point, it can be seen that head and eye-velocity traces, respectively, increase and decrease by equal amounts producing a relatively stable gaze velocity (Fig. 5, b). Third, the second fast phase displaces gaze toward the intended spatial target and nulls the remaining motor error. The associated eye saccade is often observed to displace the eyes further than the position in the orbit they held during the inter-saccadic plateau (Fig. 5, inset).
As just mentioned, for the recorded brake trials of constant gaze amplitude, the inter-saccadic gaze plateau occurred at different GME values. It follows that if the proposed weighted sum hypothesis holds true, a negative correlation should be observed between the concurrent head velocity and gaze motor error values at the third switching point in Fig. 5. In other words, the threshold head velocity that needs to be reached following head brake release to initiate a saccadic fast phase by silencing OPNs should be lower for larger plateau GME and higher for lower plateau GME. For all recorded trials, the concurrent head velocity and gaze motor error data pairs at the onset point of the second gaze saccade (beginning of Fig. 5, c) are plotted in Fig. 6 for the three different target eccentricities. Indeed, a linear trend with a negative slope can be identified between the data pairs in all three cases. The deviations from the line of best fit can be attributed to the noisy estimates of gaze position error. The latter was defined as the difference between visual target position and instantaneous gaze position. As is readily observed in target flash memory-guided saccades, the final gaze position often overshoots or undershoots by roughly ±5° the flashed target. It is therefore difficult to estimate in such cases the exact gaze shift amplitude that the SC encodes and hence have an accurate evaluation of the neural estimate of GME. Neuronal recordings in SCFNs which should reach maximum activity when the target is foveated, also reveal this uncertainty; SCFNs peak in firing frequency when gaze is near the intended target, for a range of nonzero GME values (±5°) (Bergeron and Guitton 2002; Krauzlis et al. 2000).
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The proposed OPN switching strategy (Fig. 3) is applied to the described gaze control model (Fig. 4). The latter is implemented in SIMULINK (Mathworks) and simulated at a sampling rate of 1 kHz using a Runge-Kutta solver. For a 70° retinal error input to the SC, the generated eye, head and gaze position outputs are illustrated in Fig. 7A (see Table 1 for the detailed parameter set). These are characteristic of visually triggered combined eye-head gaze shifts and were obtained for any retinal error size with constant Ton and Toff thresholds (Fig. 7A, right). With the inputs to the head plant set to zero and for a retinal error input within the oculomotor range, the model also correctly simulates head-fixed eye saccades (Fig. 7B) using identical OPN synaptic weights and thresholds as in the head-free condition (Table 1). In this case, due to the absence of head movement a weighted combination of eye velocity and motor error is sufficient to inhibit OPNs at saccade start and excite/disinhibit OPNs at saccade end. Simulated traces of the weighted sum input that is compared against OPN thresholds are provided in Fig. 7 for all the different amplitude eye saccade and eye-head gaze shift simulations. These traces reveal that because the input to OPNs is normalized with respect to the intended gaze shift amplitude, as explained in the methods section, gaze shifts of all amplitudes can be triggered by using constant thresholds and are furthermore triggered with identical latencies. Microstimulations of OPNs are simulated for both head-free and -fixed conditions (Fig. 8) by briefly forcing the OPN output to the ON state during ongoing fast phases. Simulated results show that in both cases the model appropriately switches to the slow phase mode during OPN stimulation and that OPNs gate neither eye nor head but rather gaze movement. After the forced output is released, OPNs pause de novo and switch the model back to fast phase mode. The latter occurs only if the weighted sum input to OPNs has not decreased below Toff during the forced slow phase. Hence in the case of prolonged stimulations and those applied late in the saccade, OPNs will remain excited and maintain the slow phase after the stimulation ceases.
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– and head velocity increases while eye velocity decreases (Fig. 5, b). Therefore for the weighted sum to increase above Ton and trigger a fast phase, it is necessary that the synaptic weight n be larger than k so that an increasing vestibular inhibition can trigger by itself an OPN pause.
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; Galiana 1991), the present model configuration is also able to reproduce the generation of vestibular quick phases in response to passive sinusoidal head rotation. The head plant is stimulated with a 1/6 Hz sinusoid, and the generated eye, head and gaze position responses (Fig. 10) are characteristic of the classical vestibular nystagmus pattern where the eye produces alternating fast and slow velocity movements. Model parameters are identical to those used in the simulation of gaze shifts and retinal error is set to zero to simulate absence of any visual input. To direct the quick phases of VOR toward appropriate points in the orbit, a "virtual" target needs to be encoded by the SC. This is achieved by scaling the head-velocity feedback to the SC by a gain less than one, which results in an "internally derived" nonzero GME that directs gaze toward head position during quick phases. Interestingly enough, evidence for such an internally derived target exists because activity on the SC motor map related to vestibular quick phases has been reported (Schiller and Stryker 1972; Wurtz and Goldberg 1972). Also, ablation studies of the SC result in vestibular nystagmus where the goals of quick phases are significantly perturbed (Hepp et al. 1993; Schiller et al. 1980). However, a comprehensive study of the collicular motor map activity during vestibular nystagmus is yet to be done. In this case, the weighted sum input to OPN is not normalized with respect to a gaze shift amplitude and hence different values had to be chosen for the Ton and Toff thresholds than in the case of gaze shift simulations (Table 1). By appropriately adjusting Ton and Toff, nystagmus patterns with fewer or more quick phases can be reproduced. In this "virtual" target condition, the weighted sum switching strategy operates as follows: mGME + n 
Ton starts a quick phase and is mainly triggered by an absolute head-velocity increase. mGME + n 
Toff stops the quick phase and is mainly due to a decrease in gaze motor error.
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Similarly to the sinusoidal head displacement, passive head rotations can be simulated in the model by applying a ramp input to the head plant. The implemented switching strategy will trigger a fast phase as the head starts accelerating and switch back to the slow phase once the head movement ends; which corresponds to what is behaviorally observed (see INTRODUCTION). However, the GME signal is not suppressed in either of these two conditions because virtual targets need to be derived internally to direct gaze saccades during fast phases. The motor error can be suppressed by fixating a head-stationary target during rotation. This is called VOR cancellation (VORc) because in this case, slow phases are not used to hold gaze fixated in the orbit but instead to smoothly follow the moving target. To simulate VORc, visual feedback needs to be included in the model in Fig. 4 (represented in the figure by the leftmost summing junction). The latter is absent in all previous simulations because gaze shifts are too fast to be controlled by the visual system, and there is no visual input present for head rotations in the dark. The same model configuration is used as in the VOR simulation and in addition to the sinusoidal head stimulus, a spatial target set equal to head position provides a visual input. To keep gaze on the moving target during slow phases, the tvs gain receiving the motor error command is increased (Table 1). A second mechanism, independent of the visual feedback system, is argued to also displace gaze during VORc; it is believed to reduce the parametric gain of the head-velocity signal in the VOR pathway (Cullen et al. 1991; Lisberger 1990). Accordingly, to simulate VORc, a lower value for ps is also chosen in the model to contribute in lowering the VOR gain. Simulated results show that gaze is held very close to the head-stationary target throughout the movement, resulting in a near-zero GME (Fig. 10). Fast phases are not absent in this condition; they are fewer, shorter and result in smaller saccades compared with the VOR simulation. Because GME is suppressed and eye velocity is held near zero, fast phases are triggered in most part by the head-velocity input to OPNs. The simulated result indeed shows the occurrence of fast phases only during periods when head velocity is highest.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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Head brake behavior
In most studies of head perturbations during visually triggered gaze shifts (Cullen et al. 2004; Guitton and Volle 1987; Guitton et al. 1984; Tomlinson and Bahra 1986b), the goal is to investigate the interaction between saccades and the vestibuloocular reflex. It was reported that concomitant eye acceleration, deceleration, or no apparent change in the eye-velocity profile can all be associated with short head perturbations. These observations were found to be subject as well as task dependent. The three reported types of VOR-saccade interaction can be implemented in the gaze shift model by setting the vestibular gain during saccades (Pf in Fig. 4) to respectively a positive, negative, or zero value. Experimentally, applied head perturbations do not necessarily switch gaze from a fast to a slow phase mode despite completely stopping the head (0 head velocity). These observations imply that low head velocity is not the only factor responsible for stopping the visual axis in mid-flight during a visually induced gaze shift. The ongoing gaze is however systematically interrupted for prolonged head brakes and cases where the head is stopped late in the gaze saccade (Guitton and Volle 1987; Guitton et al. 1984; Paré and Guitton 1998). It follows that for visually triggered gaze shifts, a reduced gaze motor error, in conjunction with a decrease in head velocity, is necessary for the OPN activity to resume and switch the system to the slow phase mode.
The same studies report that after head brake release, the overall gaze shift is completed toward the original target. This movement is composed of an initial eye counter-rotation (see Fig. 5, b) compensating for the on-going head displacement followed by an eye saccade oriented in the same direction as the head (see Fig. 5, c). The latter was previously interpreted to be a vestibular quick phase (Guitton and Volle 1987; Guitton et al. 1984) completely dissociated from the initially present gaze shift. In other words, the head brake was long believed to completely suppress the visually triggered gaze shift and, after head release, an ensuing quick phase triggered by the vestibular system directs the eyes toward the head movement. This view is, however, now rejected by more recent head-perturbation studies (Matsuo et al. 2004; Paré and Guitton 1998) where it is found that after head release, the encoded gaze motor error still displaces gaze toward the visual target. Cell activity in the caudal and middle SC was found to be identical at the start and end of the brake-induced gaze plateau, whereas the silence of SCFNs was linearly prolonged with increasing plateau duration in cats (Matsuo et al. 2004). Identical experiments in monkey subjects reveal that the activity of SCFNs is not fully suppressed during the inter-saccadic plateaus but is instead significantly lower than for zero GME (Choi and Guitton 2006). Therefore during the head brake trials, the same gaze motor error signal is encoded by the SC as in the case of an equal amplitude single step gaze shift. The only difference is that the motor error is held constant during the plateau period and reduced toward zero only by the fast phases of gaze. This idea is further confirmed by studies of multiple step gaze shifts in the cat (Bergeron and Guitton 2002; Bergeron et al. 2003). It is observed that OPNs resume their tonic activity during the inter-saccadic slow phase (Paré and Guitton 1998) of the interrupted gaze shift even though the SCFNs remain silent. Paré and Guitton acknowledge that this OPN behavior is not solely modulated by a gaze motor error signal and must be under the control of head-related signals as well. They, however, fail to suggest any concrete switching strategy that could account for the observed activity of OPNs. Elsewhere, neurophysiologic studies have shown that horizontal saccades and vestibular quick phases are generated by the same neural circuitry (Cohen and Komatsuzaki 1972; Keller 1974) and moreover share the same temporal characteristics (Guitton and Mandl 1980; Kitama et al. 1995; Ron et al. 1972). They can therefore be considered as equivalent eye movements differentiated only by the type of stimulus that generates them. As demonstrated by simulated results (Figs. 7–10), both the horizontal saccade and vestibular quick phase movements can be generated by the same hereby described model using the proposed switching strategy.
The proposed fusion of sensory signals to control the switching strategy of OPNs is supported by the typical eye-head dynamics observed during head-interrupted gaze shifts (see RESULTS). The standard trigger and latch switching schemes, described in the INTRODUCTION, incorrectly predict that gaze will remain in fast phase mode after interruption of head movement. Because the GME has not been nulled, the burst cells should continue to discharge and inhibit OPNs in these models due to the enduring input from the "comparator." In agreement with our results, and in all examples of head-interrupted gaze shifts that can be found in the literature, the gaze displacement never resumes prior to head release. This is the case even when the head was held immobile for as long as 500 ms (Guitton et al. 1984). Standard control schemes again fail to predict correct OPN behavior in this case. Due to a nonzero motor error, there is no reason why the subsequent fast phase should not be initiated by the trigger signal prior to the release of head movement. Or if the trigger signal is too low (below the Ton threshold), a second OPN pause and an associated fast phase will never be evoked (even after head release), and gaze will remain fixed in the orbit and never reach the intended target. In our switching strategy, correct behavior is reproduced by having a head-velocity signal included in the sensory input to OPNs (Fig. 9). Therefore this experimental condition demonstrates the necessity of vestibular inhibition of OPNs even during visually evoked gaze movements. Obtained results, however, do not show sufficiency of the head-velocity signal to either trigger or end OPN pauses. The head brake does not evoke a concurrent end in the ongoing fast phase, which occurs only after GME has been reduced below a certain value as well (Fig. 5). Also, after head release, the second fast phase is not systematically triggered for the same concurrent head-velocity value (Fig. 6). The latter is instead observed to be negatively correlated with the remaining GME. Both observations are consistent with the hypothesis that a weighted sum of sensory signals controls OPNs, instead of each input being able to initiate and end OPN pauses independently of the others.
It should be mentioned that the correlations in Fig. 6 can be interpreted as a consequence of a known correlation between eye eccentricity and head drive. Accordingly, at low GME values, the eyes are further away from their central position in the orbit than at higher GME values. Higher eye eccentricity in turn increases the head drive and results in faster head movements (Freedman and Sparks 1997). This interpretation does not contradict our statement that, after head release, a higher head velocity is required for a lower plateau GME to trigger fast phases. It simply provides a mechanism by which the higher velocities could be achieved. Furthermore, because head immobilization does not instantaneously end the ongoing saccade, it could be argued that the gaze shift is subsequently interrupted because the eyes have reached their maximum deviation (end of Fig. 5, a). This is unlikely to be the case because the second saccade often reveals that the neural limit of eye position has not been reached by the initial saccade (Fig. 5, inset). Guitton and Volle (1987) have furthermore shown head-brake examples where gaze shifts are interrupted after the eyes have been rotated by only a few degrees (<10°).
Head-velocity contribution at the onset of gaze shifts
Head movements are not necessary to trigger head-fixed eye saccades, and they also seem unnecessary to trigger head-free gaze shifts. As mentioned in the INTRODUCTION, for visually triggered gaze shifts, the latency between eye and head movement onsets is found to be highly variable for human and monkey subjects. First of all, it is consistently found that the head movement starts contributing to the gaze displacement for target offsets >25–30° (Freedman and Sparks 1997; Phillips et al. 1995) and increases linearly thereafter. Goossens and Van Opstal (1997) only rarely found negative latencies (head precedes eye movement) because their analysis was limited to 35°, whereas Tweed et al. (1995) observed gaze displacements to 70 and 90° targets and noticed negative latencies "in a significant proportion of movements." For gaze amplitudes between 40 and 90°, Freedman and Sparks (1997) noted that eye and head begin almost synchronously with positive latencies on average. Barnes (1979), however, found that head onset consistently leads eye onset for target eccentricities >45° and that the latency increases negatively as the target amplitude is increased. Barnes then suggested that his results indicate that for gaze shift amplitudes where the head contributes to the overall displacement, fast phases are initiated by the head movement in addition to retinal error information. The control strategy of OPNs that we propose indeed suggests that both the motor error and head velocity contribute to the onset of gaze shifts. This, however, does not preclude gaze shifts with either positive or negative latencies between eye and head movement onsets to be simulated by the model. In the case of a positive lag, the motor error input is simply large enough to alone exceed the OPN threshold prior to head movement onset; which is generally the case. Increasing the same threshold would additionally require a head-velocity contribution to inhibit OPNs and evoke a fast phase, producing as such a negative latency between eye and head onsets. The modification of OPN thresholds could result from biological noise in these cells, which translates into the high variability that is observed in relative onset times of eye and head movements.
It has been suggested that such varied movement latencies can only be explained by independent signals controlling eye and head movements separately (Freedman and Sparks 1997; Goossens and Van Opstal 1997; Phillips et al. 1995; Tweed et al. 1995), whereas a common gaze control model (such as the one in Fig. 4) should always produce stereotyped eye-head coordination. On the basis of the same observation, it is also presumed that eye and head movements must be triggered by separate processes. Goossens and Van Opstal (1997) furthermore speculate that this might be achieved by different subpopulations of OPNs. We argue on the contrary that the variable timing of eye and head movements can simply be explained by a visual-vestibular control of OPNs with noisy thresholds in a shared gaze control circuit.
Sufficiency of vestibular stimulation to trigger OPN pauses
Head velocity is neither necessary nor sufficient to trigger visually evoked single-step gaze shifts. As discussed in a previous paragraph, gaze shifts interrupted by a head perturbation demonstrate necessity but not sufficiency of vestibular inhibition of OPNs. Finally, OPN pauses induced by passive head rotation or in vestibular nystagmus during whole body rotation in the dark might additionally be controlled by an internally derived error signal. However, pure vestibular stimulation is applied in the VOR-cancellation experimental paradigm, where the subject is rotated in the dark, and any motor error signal is suppressed by forcing the subject to fixate a head-stationary target. Investigations of VORc show that fast phases are not absent in this condition either (Belton and McCrea 2000; Cullen et al. 1993; Meng et al. 2005; Roy and Cullen 2002; Takeichi et al. 2000). They occur less frequently and result in smaller saccades compared with VOR nystagmus obtained for the same vestibular stimulus. Our simulated results for the VOR and VORc conditions (Fig. 10) concur with these behavioral observations. Head velocity is therefore shown to be sufficient to trigger OPN pauses in this experimental paradigm because vestibular inhibition is the only input that could act on OPNs in this case (both motor error and eye velocity are held near 0). Indeed, if the head-velocity input to OPNs is removed in the model, fast phases will be completely absent in the VORc simulation in Fig. 10. It follows that the traditional trigger and latch control of OPN switching again incorrectly predicts that OPNs remain activated throughout the VORc stimulus and force a sustained slow phase modality. In this case, the "trigger" would be inactivated during the movement due to a nonexistent error signal, and thus there would be nothing to initiate OPN pauses. Our proposed switching strategy also implies that for faster rotation velocities, fast phases should occur more frequently in the VORc trials. However, we did not find any VORc study that methodically compares response dynamics for different frequencies or amplitudes of rotation, and this could test our prediction.
Multiple step gaze shifts
When shifting gaze to highly eccentric targets, it is occasionally observed that the gaze movement is composed of a series of smaller saccades separated by periods of slow phase plateaus. Such behavior is readily observed in cats (Bergeron and Guitton 2002; Bergeron et al. 2003) for large gaze shifts and is believed to be due to the cat's restrained oculomotor range. Multiple step gaze shifts have been observed in primates as well (Tomlinson and Bahra 1986a) and are believed to be the result of decreased alertness in the subject. A recorded multiple step gaze shift in a cat is shown in Fig. 7 (A. Bergeron and D. Guitton, personal communication). Bergeron and Guitton (2002) dem
Gd), implemented as the integrator's initial condition. The 
, period of head brake duration. It can be seen that interruption of the head movement together with a decreasing GME reduces the weighted sum signal below Toff which ends the OPN pause in mid-flight. After head release, an increasing head velocity brings the weighted sum above Ton and triggers a second fast phase which brings gaze to target. Compare with 