INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Visual motion provides primates with a wealth of information about where objects are and how they move. In many situations, however, visual motion alone is ambiguous because only relative motions are seen. For example, rightward motion in the retinal image could be caused either by an object moving to the right or by a turn of the eyes or head to the left. In these situations, the visual system must rely on extraretinal signals containing information about eye and head movement to interpret visual motion correctly. Although a great deal is known about the neural structures that interpret visual motion when the gaze is fixed (Maunsell and Newsome 1987) as well as about the neural mechanisms that integrate visual and gaze-position signals (Andersen 1997), much less is known about motion processing during eye and head rotations.

How does the brain combine visual-motion and extraretinal gaze-rotation signals? We considered this question in the context of visual navigation (Gibson 1950; Warren 1995). When we move forward, the retinal image expands. The center or focus of this expansion (FOE) corresponds to the heading, or instantaneous direction of translation, when the gaze is fixed, and humans can use the FOE to estimate accurately their heading (Warren and Hannon 1988). However, when we smoothly shift our gaze, as during pursuit eye movements, the FOE on the retina is displaced from the true heading as illustrated in Fig. 1. Humans use an extraretinal pursuit signal to compensate for this displacement and, thereby, are able to judge their heading quite accurately even during pursuit (mean compensation of 90%) (Crowell et al. 1998a; Royden et al. 1992, 1994).

View larger version (16K): [in this window] [in a new window]   Fig. 1. Retinal image while moving forward and rotating gaze. When we move forward and hold our eyes still, the visual motion pattern (optic flow) on our retinae is radial expansion; focus of expansion (FOE) position indicates the heading. We recreated this retinal image motion on a computer screen (on screen). When we move forward but now rotate our eyes in our head or our head in the world, to track an object moving to the right for example, leftward rotational flow is added to the retinal image (on retinae). Rotational flow displaces the FOE to the right. Without correction, this displacement leads to large errors in self-motion estimates.

We recently reported that many neurons in macaque extrastriate cortical area MSTd (dorsal subdivision of the medial superior temporal area) use pursuit signals to compensate, at least partly, for the displacement of the FOE caused by pursuit eye movements (Andersen et al. 1996; Bradley et al. 1996). MSTd is well suited for such visual and nonvisual cue integration, which is essential for estimating heading, because of the following receptive field specializations and extraretinal contributions: 1) large receptive fields (RFs) (often >50° in diameter); 2) selectivity for the direction of laminar motion; 3) selectivity for expansion, contraction, rotation, or spiral optic-flow patterns (Duffy and Wurtz 1991a,b; Graziano et al. 1994; Komatsu and Wurtz 1988a,b; Lagae et al. 1994; Lappe et al. 1996; Orban et al. 1992; Raiguel et al. 1997; Saito et al. 1986; Sakata et al. 1985, 1994; Tanaka and Saito 1989; Tanaka et al. 1986, 1989); 4) optic-flow selectivity is typically invariant to the position of the pattern within the RF (Duffy and Wurtz 1991b; Graziano et al. 1994; Lagae et al. 1994; Orban et al. 1992); 5) optic-flow selectivity does not depend on the forms or cues of the moving objects (Geesaman and Andersen 1996); 6) optic-flow selectivity is typically invariant to the size of the visual pattern (Graziano et al. 1994); 7) responses are modulated by the position of the FOE in the RF (Duffy and Wurtz 1995); 8) responses are modulated by the rate of optic-flow expansion (Duffy and Wurtz 1997); 9) responses are modulated by stereoscopic disparity (Roy and Wurtz 1990; Roy et al. 1992); 10) smooth-pursuit signals are direction and speed tuned (Bradley et al. 1996; Erickson and Thier 1991; Kawano et al. 1984, 1994; Newsome et al. 1988); and 11) eye-position signals are present (Bremmer et al. 1997; Squatrito and Maioli 1996; Squatrito et al. 1997). Finally a recent report that microstimulating expansion-selective columns in macaque MSTd systematically biases heading estimates provides direct evidence that MSTd neurons contribute to the visual sensation of heading (Britten 1998; Britten and van Wezel 1998, Celebrini and Newsome 1995; Geesaman et al. 1997).

The question remains whether MSTd neurons also shift focus tuning to compensate for FOE displacements caused by smooth head rotations, which commonly occur during gaze tracking (see Fig. 1). Recent human psychophysical experiments indicate that self-motion judgments are quite accurate during active, smooth head rotations (observers smoothly rotate their heads while fixating a target moving with the head; mean compensation of 94%) (Crowell et al. 1998a). In this condition, there are three sources of extraretinal information that potentially drive compensation: proprioceptive information from the neck muscles, efferent information about the motor commands sent to the neck muscles, and vestibular canal information about head rotation.

As a first step, we asked if vestibular canal signals contribute to MSTd focus-tuning compensation during head-in-world rotations, as pursuit signals contribute to focus-tuning compensation during eye-in-head rotations. We suspected canal signals in MSTd because otolith signals recently were found in MSTd (Duffy 1998) and because canal signals have been reported in MSTl and in nearby areas of the posterior parietal cortex (Kawano et al. 1980, 1984; Sakata et al. 1994; Snyder et al. 1998; Thier and Erickson 1992a,b). To investigate this question, we trained two monkeys to perform a vestibulo-ocular reflex cancellation (VORC) task in which we mechanically rotated their bodies and heads while they fixated a target rotating with their bodies and heads. The eyes rotate in the world, but not in the head, during VORC. By measuring the response of MSTd cells to optic-flow patterns during both VORC and fixed gaze conditions, we could assess vestibularly induced focus tuning shifts. We found substantial focus tuning compensation during VORC. Interestingly although vestibularly-derived signals are essential for accurate self-motion estimates during active, smooth head rotation (Crowell et al. 1998a), humans do not judge their self-motion accurately during the VORC task where the only extraretinal signal available is vestibular in origin (mean compensation of 4%) (Crowell et al. 1998a). MSTd physiology results are compared with human psychophysical performance in the DISCUSSION.

The oculomotor mechanisms engaged during VORC are not well understood. There appear to be three possibilities. First, during VORC the vestibular ocular reflex (VOR) could be shut down, thereby allowing fixation of the VORC target without any eye movement commands. Second, it is possible that the VOR is active during VORC and that a pursuit signal is generated to oppose the VOR signal, thereby enabling VORC-target fixation. Finally a combination of these mechanisms could underlie VORC-task performance. Recordings from the brain stem appear to implicate both ocular and vestibular sources of VORC signals, consistent with this last possibility (Cullen and McCrea 1993; Cullen et al. 1991, 1993; Tomlinson and Robinson 1984). Posterior parietal cortex (PPC) studies also appear to be consistent with this view. Robust responses have been reported in MSTl, the lateral subdivision of MST, during sinusoidal VORC (Thier and Erickson 1992a,b). These responses persisted, though at roughly half the strength, during sinusoidal rotation in complete darkness, which isolates the vestibular canal component of the signal. Regardless of the exact origin, VORC signals are present naturally during tracking head movements and are viable extraretinal cues for heading estimation.

Brief reports of this material have appeared previously (Shenoy et al. 1996, 1997).

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Animal preparation

Experiments were conducted in two hemispheres of two adult, male Rhesus monkeys (Macaca mulatta), and all protocols were approved by the Caltech Institutional Animal Care and Use Committee. In a sterile surgical procedure under sodium pentabarbitol anesthesia, stainless steel bone screws were implanted in the skull, and a fixture for immobilizing the head was constructed with methylmethacrylate. In the same procedure, a Teflon-insulated, 50-gauge stainless steel wire coil was implanted between the conjuctiva and the sclera for the measurement of eye position (Judge et al. 1980; Robinson 1963). The coil was connected electrically to a coaxial connector embedded in the methylmethacrylate.

Behavioral training on oculomotor tasks began no sooner than 1 wk after surgery. Monkeys received juice rewards for correct performance during both behavioral training and experimental sessions. Adequate performance levels, typically >90% on all tasks, were reached after several weeks of training. A subsequent surgery was performed to open a craniotomy and to implant a Lucite cylinder (5 mm posterior, 17 mm lateral, dorsoventral orientation), which provided chronic access to cortical area MSTd for electrophysiological recording.

Recording techniques

Extracellular action potentials were monitored with varnish-coated tungsten microelectrodes, with ~1 M impedance at 1 kHz. A stainless steel guide tube was advanced manually dorsoventrally through the dura and the electrode was extended further into the brain with a hydraulic micropositioner. Action potentials were amplified and single neuron waveforms were isolated with a time-voltage discriminator. MSTd was identified based on the following criteria: 1) depth below the dura; 2) position relative to gray and white matter boundaries; 3) location relative to the middle temporal (MT) cortical area; 4) receptive field size (typically >50° diam with both contra- and ipsilateral visual responses); 5) selectivity for optic-flow type (e.g., expansion); and 6) position invariance of optic-flow selectivity within the receptive field. Neurons tuned for the type of optic flow, by visual inspection and in at least one location in the RF, were tested in all experiments and are included in our database. Action potential event times and behavioral states were stored for subsequent analysis.

Visual stimuli

All experiments were conducted in a sound-insulated room, which was totally dark except for the visual stimuli. We generated expanding random dot optical flow fields by simulating forward translation at 16.5 cm/s toward a fronto-parallel wall held 38.1 cm distant. One thousand dots were placed randomly in computer memory representing an 82 × 82° area, and each dot was assigned a random age. Dots moved at constant velocity for the remainder of their 300-ms lifetime or until they crossed the area perimeter, in which case they were extinguished and reborn at a random location. Dot speeds were proportional to the eccentricity from the FOE, reaching 9.2°/s at 24° eccentricity. The direction of dot motion was rotated by 90, 180, or 270° from the expansion stimuli to create counterclockwise rotation, contraction, or clockwise rotation stimuli, respectively. Dots were white (~10 candela/m²) on a completely black background and were not anti-aliased. Displays were viewed binocularly.

We displayed an 18 × 18° subregion (window) of the total area simulated on a computer monitor operating in 640 × 480 pixel resolution and 60 frames/s mode. This was the largest possible stimulus area due to monitor size (50 × 38° at 38.1 cm), monitor weight (the monitor moved with the vestibular chair), stimulus movement, and stimulus position constraints. Such display windows contained 48 dots (0.15 dots/deg²) with each dot subtending 0.08 × 0.08° of visual angle (1 pixel). Display windows, including the optic flow and the invisible window frame, were presented: at a fixed location in the room, moving with the fixation target, which moved in the room, or drifting across the room (see Behavioral tasks).

Pursuit targets moved an integral number of pixels/frame resulting in smooth motion (e.g., 2 pixels/frame = 9.2°/s); consequently, horizontal and vertical pursuit targets moved at 9.2°/s while 45° diagonal pursuit targets moved times faster. Fixation and VORC targets remained stationary on the display, but during VORC trials the entire display moved at 9.2°/s or times faster for diagonal trials. The direction and speed of pursuit- and VORC-tracking targets were identical in all experiments. Fixation, pursuit, and VORC targets subtended 0.24 × 0.24° of visual angle.

To simulate different headings, we created nine optic-flow patterns with varying focus (origin) positions by shifting the origin of the 82 × 82° pattern behind the 18 × 18° window (aperture). Focus positions varied from 32 to 32° in 8° increments along an axis either parallel to the neuron's preferred-null axis (see Data analysis) for expansion/contraction neurons, or orthogonal to this axis for rotation neurons. Different axes are required because the direction of origin shift depends on both the visual pattern and on the direction of gaze rotation (Andersen et al. 1996; Bradley et al. 1996). For example, rightward pursuit across an expansion pattern shifts the focus rightward (parallel to pursuit), whereas rightward pursuit across a clockwise rotation pattern shifts the origin of rotation upward (orthogonal to pursuit). Diagonal focus spacing and range was increased by to account for the increased real and simulated gaze-tracking speeds during diagonal trials.

We selected the gaze rotation and display parameters described above to shift the focus (origin) during gaze rotation by 24°. Physical geometry and gaze rotation lead to the following governing equations:

(1)

where  (rads) is the visual angle to a particular point on the simulated wall that the observer is approaching, (rads/s) is the rate at which  increases, x (cm) is the linear distance from the center of the wall to the point being considered, z is the distance from the observer to the wall (38.1 cm), and T_z is the simulated forward translation speed of the observer (16.5 cm/s). Substituting the experimental parameters into these equations reveals that a point on the simulated wall 24° eccentric travels outward at a speed of 9.2°/s. Therefore when the eyes rotate at 9.2°/s, the point 24° eccentric does not move on the retinae, which is the definition of a focus (origin). Thus the focus (origin) shifts 24° during gaze rotation as compared with when the eyes are still (focus at 0°). To detect tuning curve shifts smaller than the theoretical shift during gaze rotation (24°), we spaced the foci (origins) every 8° to generate tuning curves with sufficient sampling resolution.

Vestibular stimuli

Monkeys were seated comfortably in a primate chair which we attached to a vestibular chair (Acutronic, Pittsburgh, PA). Precise horizontal plane (yaw) and sagittal plane (pitch) rotations were executed by the feedback control system. Vestibular chair sensors reported real-time position information, which was monitored and used to trigger visual stimulus onsets during VORC trials. We fixed the monkeys' heads to the primate chair such that the axis of yaw rotation passed through the midline (medial/lateral), midway between the ear canals and the center of the eyes (anterior/posterior). The pitch rotation axis was positioned midway between the ear canals and the center of the eyes (anterior/posterior), in the plane of the ear canals and the center of the eyes (dorsal/ventral). This arrangement is intermediate between the natural eye rotation axes, passing roughly through the center of the eyes, and the natural head rotation axis, passing through the neck. This compromise produces rotations that approximate natural head rotations but without creating excessive visual translation during VORC conditions, which is not present during eye pursuit.

A computer monitor and electromagnets also were mounted on the vestibular chair. The electromagnetic coils were attached to the vestibular chair to improve eye position accuracy by maintaining a more uniform local magnetic field during large-angle body rotations. Even with such measures, it was not possible to maintain a perfectly constant magnetic field because the position and orientation of various vestibular chair components in the magnetic fringe fields changed through the course of a vestibular chair rotation. The resulting systematic drift in eye position measurement over the range of vestibular chair rotations (±20° yaw and/or pitch) was ~1° and was substantially <1° over the smaller rotation range traveled during visual stimulus presentation and data collection (±4.6° yaw and/or pitch).

Although the on-line eye position tolerance (demand box) was enlarged slightly to account for this variation (typically ±4° square), inspection of the eye traces revealed accurate pursuit (very few, small catch-up saccades), accurate VORC (very few, small VOR/OKN drifts), accurate simulated gaze rotation (fixation), and accurate fixed gaze (fixation). Off-line analysis consisted of selecting 16 heading experiments at random, 8 from each monkey and totalling 20% of all heading experiments, and calculating the deviation of the eye from the average fixation position (simulated gaze rotation and fixed gaze trials), from the average VORC position (VORC trials), or from a line regressed through the eye trace (pursuit trials). The average standard deviation across all trials was quite small in all conditions: horizontal (0.31°) and vertical (0.32°) channel VORC, horizontal (0.30°) and vertical (0.31°) channel pursuit, horizontal (0.18°) and vertical (0.30°) channel simulated gaze rotation, and horizontal (0.18°) and vertical (0.30°) channel fixed gaze.

We reproduced the retinal image seen during pursuit by generating head, body, and eye rotations using the VORC paradigm. Both pursuit and VORC conditions require an ~2 s constant angular rotation period (9.2°/s, times faster during combined yaw and pitch rotations), during which time the visual stimulus is displayed and neural data are collected. This constant angular velocity period was embedded in the middle of a trapezoidal speed trajectory: 307 ms, 30°/s² constant acceleration phase; ~2 s constant velocity phase; and a 307 ms, 30°/s² deceleration phase. To verify that this protocol effectively generates VORC signals, we recorded the response of two representative MSTd neurons in a pursuit and VORC paradigm in which only a pursuit or VORC target was present and in which the constant rotation period lasted 4 s. Robust responses persisted out to 4 s in both conditions, indicating that the velocity signal, which is integrated from rotational acceleration cues by the vestibular canal apparatus and which ultimately drives the MSTd VORC signal, has a time constant of at least a few seconds (Wilson and Jones 1979).

Behavioral tasks

Monkeys were trained to perform three types of behavioral tasks: fixation, pursuit, and VORC. One or more of these behavioral tasks were employed in three sequential, blocked experiments: preferred optic flow, preferred direction, and heading.

Preferred-optic-flow experiment trials consist of fixating (less than ±2.5° eye box) a target for 1.7 s, during which time a 1.2-s optic-flow display appears. To determine the preferred type of optic flow, expansion, contraction, clockwise rotation, and counterclockwise rotation stimuli were presented pseudorandomly (stimuli randomly drawn without replacement and blocked by repetition number). Optic-flow stimuli were centered at 0°,0°; 10°,+10°; 10°,10°; 10°,10°; and 10°,10° (horizontal, vertical pairs; + indicates either ipsilateral or up) while gaze was fixed at 0°,0°. An additional configuration with gaze fixed at 10°,0° and optic flow centered at +15°,0° also was included to test for far ipsilateral responses. Receptive field sizes were estimated using this timing and hand-positioned patterns.

Preferred-direction experiment trials consist of pursuit or VORC of a moving target (9.2°/s or faster) for 1.5 s, during which time a 1.2-s preferred-optic-flow display appears and moves with the target (less than ±4.0° eye box). Trial illustrations and timing diagrams are shown in Fig. 2. During VORC trials, the target remains fixed on the screen (screen moved with the vestibular chair), and there is no eye-in-head rotation (confirmed by monitoring eye position). Also there is nominally no head-on-body rotation, promoted by seating the monkeys comfortably and noting his relatively constant seating position in the primate chair (Lucite box). Eye pursuit and VORC trials were presented pseudorandomly (monkey FTZ) or blocked (monkey DAL) in eight directions in the fronto-parallel plane (0, 45, ... , 315°; 0° indicates eye rotation or chair yaw to the right; 90° indicates upward eye rotation or chair pitch). Gaze trajectories were centered on the same room location for both tasks to equalize all gaze angles on average. Gaze rotated by ±4.6° about the central location during the 1.0-s data-analysis period.

View larger version (30K): [in this window] [in a new window]   Fig. 2. Schematic illustrations and timing diagrams for the 2 behavioral tasks in the preferred-direction experiment. Rightward gaze rotation conditions are shown in this example, although gaze rotations in 8 directions in the fronto-parallel plane were performed in the experiment. Left: all arrows refer to movement in the room and indicate conditions during the data-collection interval. A: pursuit task requires pursuing a moving target (filled circle with filled arrow) while viewing the preferred optic flow stimulus (e.g., expansion; dashed motion vector arrows) which moves with the pursuit target (3 filled arrows). B: vestibulo-ocular reflex cancellation (VORC) task requires fixating a target moving in register with the head and body while viewing the preferred-optic-flow stimulus that moves with the fixation target. Right: timing diagrams plot the experimental conditions and behavioral requirements as a function of time. Lines represent physical positions in the room, hence parallel lines indicate no relative movement (only horizontal and yaw positions are shown for simplicity). Presence of a line indicates the presence of a stimulus (fixation and optic flow) or a positional requirement being enforced (eye and vestibular chair). For room lights, the line position indicates the light status. Times are aligned on the middle (0.0 s) of the 1.0-s data-analysis period, shown in gray. Onset times for pursuit trials are as follows: 700 ms, optic-flow stimulus; 1.0 s, proper eye position required; and 2.2 s, fixation target appears. Onset times for VORC trials are as follows: 700 ms, optic-flow stimulus; 1.0 s, proper eye position required; 1.6 s, fixation target appears; and 2.2 s, chair begins sweep. At 2.7 s, the chair arrives at the ready position and the room lights are extinguished.

We presented and moved the preferred-optic-flow stimulus (e.g., expansion) along with the pursuit and VORC target in this experiment for two reasons. First, optic flow significantly increases the neural response and allowed us to better determine gaze-rotation directional tuning. Second, we sought to select the axis along which the gaze-rotation signal varies maximally. As long as the retinal stimulus is comparable between pursuit and VORC trials, the presence of a visual stimulus is acceptable. That the results of the heading experiment reported here are similar to the results we reported previously (Bradley et al. 1996), where a visual stimulus was not present during pursuit-axis selection, suggests that directional tuning largely is unaffected by the presence of the optic-flow pattern.

Heading experiment trials consist of fixation, pursuit or VORC of a target (less than ±4.0° eye box) for 1.5 s, during which time a 1.2-s preferred-optic-flow display appears. Nine optic-flow stimuli, with differing focus (origin) positions, and four behavioral tasks were presented pseudorandomly. Trial illustrations and timing diagrams are shown in Fig. 3. Pursuit and VORC tasks are identical to those in the preferred-direction experiment except that the optic-flow stimuli are stationary in the world in this experiment. Gaze tracking almost always occurred along the VORC preferred-null axis with small differences occurring if the pursuit and VORC preferred-null axes differed; we split the difference. Gaze rotations were performed in both the preferred and the null directions. The fixed gaze task was identical to the gaze tracking tasks except that the eye, head, and body were stationary in the room. The simulated gaze-rotation condition was identical to the fixed gaze condition except that the visual stimulus drifted in the direction opposite to the direction tracked in the gaze tracking tasks. This created a retinal stimulus identical to the retinal stimuli in the gaze-tracking tasks to the extent that eye movements were performed perfectly. Counter drifting the visual stimulus approximates counter rotating the visual stimulus quite well for the small, centrally located stimuli used in these experiments. Gaze trajectories were centered on the same room location across all tasks to equalize all gaze angles on average. Gaze rotated by ±4.6° ( more for diagonal gaze rotations) about the central location during the 1.0-s data-analysis period. The gaze trajectory center was located within 7.07° of the screen center, and the visual stimuli were centered within 14.1° of the gaze trajectory center. Gaze and stimulus centers were offset to position the optic-flow stimuli in the RF "hot spot."

View larger version (27K): [in this window] [in a new window]   Fig. 3. Schematic illustrations and timing diagrams for the 4 behavioral tasks in the heading experiment. Rightward gaze rotation conditions are shown in this example, although gaze rotations were performed in the preferred and null directions in the experiment. Left: all arrows refer to movement in the room and indicate conditions during the data collection interval. A: fixed gaze task requires fixating a stationary target (solid circle) while viewing optic flow stimuli (dashed motion vector arrows). B: pursuit task requires pursuing a moving target (filled circle with filled arrow) while viewing optic-flow stimuli. C: VORC task requires fixating a target moving in register with the head and body (filled circle with filled arrow) while viewing optic-flow stimuli. Optic-flow stimulus location does not move in the room. D: simulated gaze rotation task requires fixating a stationary target while viewing optic-flow stimuli being counter drifted across the screen (stimulus movement indicated by 3 solid leftward arrows). Nine focus positions within the stimulus frame were presented to simulate a span of headings (an expansion pattern with a heading of 0° is shown here). Stimulus remains fixed in the world (A-C) or is drifted in the world (D). Right: timing diagrams plot the experimental conditions and behavioral requirements as a function of time. Lines represent physical positions in the room, hence parallel lines indicate no relative movement (only horizontal and yaw positions are shown for simplicity). Presence of a line indicates the presence of a stimulus (fixation and optic flow) or a positional requirement being enforced (eye and vestibular chair). For room lights, line position indicates the light status. Times are aligned to the middle (0.0 s) of the 1.0-s data-analysis period, shown in gray. Gaze rotated by ±4.6° about the central location during the 1.0-s data-analysis period. Onset times are as follows: 700 ms, optic-flow stimulus; 1.0 s, proper eye position required; and 2.2 s, fixation target appears. For VORC trials, onset times are as follows: 700 ms, optic-flow stimulus; 1.0 s, proper eye position required; 1.6 s, fixation target appears; and 2.2 s, chair begins sweep. At 2.7 s, the chair arrives at the ready position and the room lights are extinguished.

Data analysis

Horizontal and vertical eye positions were sampled every millisecond and yaw and pitch head positions were sampled every 8 ms. Action potential event times were stored for off-line analysis with microsecond resolution. Neurons from two monkeys were recorded. Data trends are similar and significant in both monkeys so the data were pooled for analysis.

We analyzed the preferred-optic-flow experiment data with a nonparametric, one-way ANOVA (Kruskal-Wallis) to test for optic-flow pattern tuning. Each of the six locations was considered separately. Mean firing rates from three (DAL) or four (FTZ) replicates during the last 1.0 s of the 1.2-s stimulus presentation were used for the ANOVA.

We analyzed the preferred-direction experiment data to determine the preferred pursuit and VORC directions. We estimated these directions as the angle of the response-weighted vector sum (Fisher 1993; Geesaman and Andersen 1996). The preferred direction () is equal to arctan(S/C), where S is the sum of F_i sin _i and C is the sum of F_i cos _i over all eight gaze-rotation directions (i = 1, 2, ... , 8). F_i and _i correspond to the average firing rate and specified gaze-rotation angle, respectively, associated with each of the eight gaze-rotation directions. The preferred direction was adjusted to the proper quadrant based on the signs of S and C. We also calculated the trigonometric mean which we used as a selectivity index (SI). SI is equal to divided by the sum of F_i over all eight gaze-rotation directions. Unlike other selectivity measures, such as 1  (null/pref), which only indicate the modulation along a single axis, SI reaches unity (perfect selectivity) only if all nonpreferred directions are totally suppressed. An SI of zero indicates the complete lack of tuning.

Circular, nonparametric statistics were used to assess preferred-direction biases (Rayleigh) and cell-by-cell preferred-direction correlation (angular-angular correlation). We determined the significance of SIs with boot-strap methods: we created directional tuning curves by drawing (without replacement) eight mean firing rates from a given cell's response database, we randomly assigned the firing rates to the eight directions, and finally calculated the SI for this tuning curve. We repeated this procedure 1,000 times for pursuit and VORC for all cells. If the measured SI exceeded the 95% point of the simulated distribution, we considered the SI significant. We found that the Rayleigh test, which has been used previously for determining SI significance (Geesaman and Andersen 1996), is overly conservative. Finally a nonparametric correlation test (Spearman) was used to test for relationships between SIs in the population. All analyses used the mean firing rates from two (FTZ) or three (DAL) replicates during the last 1.0 s of the 1.2-s stimulus presentation.

We analyzed the heading experiment data to determine the influence of gaze tracking on the visual response. We constructed seven focus tuning curves for each neuron, one for each gaze tracking condition in both tracking directions, using mean firing rates and variances from three (DAL) or four (FTZ) replicates during the last 1.0 s of the 1.2-s stimulus presentation. We used Kruskal-Wallis analyses to assess the tuning significance for each focus tuning curve.

To understand the effects of preferred- and null-direction VORC, pursuit, and simulated gaze rotation, it is necessary to compare tuning curves in the different gaze-rotation conditions with the fixed-gaze condition tuning curve. In general, we found that gaze rotations preserved the primary shapes of the fixed-gaze tuning curves, which are often sigmoidal or Gaussian (examples will be presented in RESULTS). This observation led to our approach for comparing tuning curves: the relationship between two tuning curves with similar shapes can be characterized approximately by two parameters, one reflecting horizontal effects and one reflecting vertical effects.

Figure 4 shows three possible alignments of two focus tuning curves. Figure 4A illustrates a horizontal, or independent variable, offset between two tuning curves with related structures. We calculated this offset with a cross-correlation analysis, which provides a measure of tuning curve alignment at each relative horizontal offset, as one curve is shifted past the other. The optimal shift is identified as the relative horizontal offset with the maximum correlation coefficient. Parameterizing the vertical, or dependent variable, relationship is more difficult because the tuning curves are not necessarily functions (single valued) of the dependent variable, ruling out cross-correlation techniques. Moreover, as shown in Fig. 4B, the relationship between the curves may be described as multiplicative, additive, linear, or even nonlinear. Distinguishing between these possibilities has inherent difficulties and is beyond the scope of this report. Instead, we attempted to quantify the vertical relationship with a single parameter to describe the basic effect and to compare this effect across conditions. We compared multiplicative and additive measures and found that the ² goodness-of-fit values were comparable across gaze-rotation conditions and across the population of cells. We chose the multiplicative measure for two reasons: multiplicative gain, or the ratio between two responses, is normalized automatically for firing rate so comparison between conditions and cells is straighforward and multiplicative gain commonly is used for characterizing modulatory effects (Brotchie et al. 1995; Snyder et al. 1998). To calculate the gain, we used the mean discharge rates during visual stimulus presentation as opposed to the difference between the peristimulus and the prestimulus discharge rates. Such subtraction would remove the additive contributions of the gaze-rotation signals, which is an influence we wish to consider.

View larger version (7K): [in this window] [in a new window]   Fig. 4. Three possible alignments of 2 focus tuning curves. , hypothetical fixed-gaze tuning curve; - - -, hypothetical gaze-rotation tuning curve. A: horizontal, or independent variable, offset between 2 tuning curves with similar structures. B: vertical, or dependent variable, changes in tuning curves caused by modulatory cues often are approximated as multiplicative. C: general case of 2 tuning curves related by both a horizontal shift and a vertical gain. These curves are related by the combined horizontal offset shown in A and the vertical gain shown in B.

Figure 4C illustrates the general case of two tuning curves related by a horizontal shift and a vertical gain. We adopted the following approach to characterize such a relation: 1) calculate the optimal horizontal shift between the two curves by cross-correlation, which is insensitive to vertical gain and offset; 2) subtract the optimal shift thereby horizontally aligning the curves; and 3) calculate the gain over the range of tuning curve overlap. The effect of a given gaze-rotation condition thereby is characterized by two scalars, optimal shift and gain, and relates the gaze-rotation tuning curve to the fixed-gaze tuning curve.

Although cross-correlation has advantages and disadvantages compared with other methods, we adopted this method because the advantages are well suited for the specific questions we ask. Cross-correlation reduces to correlation at a given horizontal shift, as expressed

(2)

The mean response vectors for the two tuning curves are x and y, and and are the average responses of the two tuning curves.

Cross-correlation is well suited to our analysis approach for several reasons. First, it is quite sensitive to the tracking, or alignment, of two tuning curves regardless of the exact functional form of the curves. This allows us to avoid curve fitting (e.g., sigmoids or Gaussians), which would be appropriate for only a part of the data given the strict assumptions of parametric methods. Second, cross-correlation is insensitive to vertical shifts between the two tuning curves, which is apparent in the correlation equation by substituting x + k for y, where k is a scalar vertical offset: this case reduces to autocorrelation (independent of k). Finally, cross-correlation is insensitive to vertical, multiplicative gains between two tuning curves and is apparent in the correlation equation by substituting gx for y, where g is a multiplicative gain: this case also reduces to autocorrelation (independent of g).

However, we also must contend with two limitations. First, we restricted the total range of shifts tested so as to avoid situations where fewer than five data points overlap. We found that less than five overlapping points results in erroneously high correlation values due to alignment of the edges of the tuning curves not to the alignment of the prominent features of the tuning curves that we sought. This shift range is 8 to +56°, where 0° corresponds to retinal coordinates and 24° corresponds to screen coordinates. Screen coordinates, or equivalently room coordinates, is an operational term and alignment in screen coordinates indicates complete compensation for gaze rotation (Bradley et al. 1996). Alignment in retinal coordinates indicates no compensation for the visual effects of gaze rotation. Second, if the prominent features (e.g., minima, maxima, inflection points) of two tuning curves are aligned, but the shape of one or both of the two tuning curves is altered slightly, this can lead to misestimations of the alignment of the prominent features. However, this misestimation grows as the extent of the shape change increases, which means that the misestimation is small for small shape changes. Alternate methods also suffer from such misestimations, but cross-correlation deviates from what we consider proper alignment of prominent features in a graded manner.

We began the cross-correlation analysis by smoothing the tuning curves with a three-point moving average (twice; uniform weights) followed by a spline interpolation (1° sampling). Although all results are qualitatively similar without smoothing and interpolation, such methods provide reasonable intersample interpolation and reduce anomalous cross-correlogram peaks at the edges of the correlation range. Cross-correlation results also remained qualitatively similar for tuning curves formed by integrating activity as brief as 200 ms, centered on the midpoint of the data collection interval.

Nonparametric tests were used to analyze cross-correlation population data. Wilcoxon t-tests were used to determine the significance of optimal shifts in the various gaze tracking tasks across the population. Mann-Whitney t-tests were used to test if distribution means are different. Spearman correlation tests were used to determine if a significant correlation exists between optimal shifts in different gaze tracking conditions across the population. Nonparametric tests also were used to evaluate gain data.

Gaze tracking conditions along diagonal axes result in tuning curves with focus spacings of 8 ° instead of 8°. However, the theoretical shift along these axes also is expanded to 24 °. Because the focus spacing, theoretical shift, and tracking speeds all scale proportionally, the resulting shifts are readily remapped (i.e., divide shift by ) for inclusion with the rest of the population data.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

We recorded and analyzed data from 80 neurons in two monkeys, 56/80 from monkey FTZ and 24/80 from monkey DAL, in the preferred-optic-flow, preferred direction, and heading experiments.

Optic-flow tuning

We measured the response of MSTd neurons to expansion (EX), contraction (CO), clockwise rotation (CW), and counterclockwise rotation (CCW) optic-flow stimuli presented at six locations. We found most cells to be tuned significantly for the pattern of optic flow in at least one of the stimulus locations (54/80, 67.5%, P < 0.05/6, Kruskal-Wallis). Although additional trial replicates likely would increase the number of significantly tuned cells, we were able to identify clear tuning trends in all neurons. We conserved trials in this experiment, and in the preferred-direction experiment, because the heading experiment (the core experiment) required many long trials.

We noted the stimulus location eliciting the strongest tuning, and we refer to the preferred-optic-flow pattern at this location as the preferred-optic-flow pattern of the cell. The distribution of preferred-optic-flow patterns in the population is as follows: 43/80 (54%) EX, 24/80 (30%) CO, 9/80 (11%) CW, and 4/80 (5%) CCW. We also noted the preferred-optic-flow pattern at the location centered on fixation, which was typically the same as the cell's preferred-optic-flow pattern, for use in the preferred-direction experiment.

Although large optic-flow patterns elicit the strongest neural responses, we were restricted to 18 × 18° visual stimuli. However, we routinely found strong, tuned responses that were modulated by the position of the stimulus within the receptive field. These characteristics are indicative of well-activated MSTd neurons. We also found similar proportions of cells selective for expansion, contraction, and rotation (54, 30, and 16%, respectively) as compared with our previous study in a different monkey (41, 33, and 27%, respectively) which used 50 × 50° stimuli (Bradley et al. 1996). These similarities indicate that MSTd response characteristics persist as stimulus size decreases and are consistent with a previous report (Graziano et al. 1994).

Pursuit and VORC tuning

We then recorded neural activity during the preferred-direction experiment and analyzed the responses to determine the preferred-pursuit and preferred-VORC directions. Figure 5A shows the basic result that individual MSTd neurons are tuned for the direction of both pursuit and VORC. The response of this neuron clearly is enhanced during rightward (ipsilateral) pursuit and VORC and clearly is suppressed during leftward (contralateral) pursuit and VORC. The estimated preferred pursuit and VORC directions are 0.7 and 344.8° (15.2°), respectively (angle of the response-weighted vector sum). Angles are measured counter clockwise from the ipsilateral direction. The preferred gaze-rotation directions are well aligned in this cell (15.9° difference), considering that the possible range of direction differences is 180°. The directions opposite the preferred directions are designated the null directions and also were noted for use in the heading experiment.

View larger version (16K): [in this window] [in a new window]   Fig. 5. Gaze-tracking activity in the preferred-direction experiment. A: response of a neuron during pursuit () and VORC (), in each of 8 directions. Data points are the mean firing rate of 2 replicates. - - -, spontaneous discharge rate of 2.4 spikes/s. Spontaneous discharge rate is the mean activity during the 500 ms preceding optic-flow presentation in the preferred-optic-flow experiment (96 repetitions). Preferred directions for pursuit and VORC are indicated by  and , respectively, located along the plot perimeter. Pursuit direction selectivity index (SI) is 0.527 and the VORC SI is 0.445; both are significant (P < 0.05, boot-strap). B: average response of all neurons (n = 80) as a function of gaze-rotation direction relative to the preferred directions. Pursuit and VORC preferred directions were selected as the measured directions with maximum response and were rotated (separately), along with the entire tuning curves, to 0°. All tuning curves were normalized to the preferred-direction firing rate (100%) before averaging across the population. , pursuit conditions (1 SD error bar); , VORC conditions (+1 SD error bar).

To visualize the degree of directional tuning in the population, Fig. 5B plots tuning curves averaged across the population. Pursuit and VORC tuning curves from each neuron were rotated (independently) to align preferred directions at 0°. The curves were normalized (separately) to the preferred-direction responses before averaging across the population. Mean pursuit and VORC tuning curve shapes are quite similar, indicating similar directional selectivities in the population. Pursuit has a slightly sharper mean tuning curve, but both pursuit and VORC have preferred:null response ratios of ~2:1 and both have tuning bandwidths (full width at half-maximum) of ~90°.

Does this similarity between pursuit and VORC tuning, seen in the population, arise from an equivalence at the single-cell level? To answer this question, we examined the distribution of preferred directions, the cell-by-cell difference in preferred directions and the cell-by-cell preferred-direction correlation, the population distribution of directional selectivity indices, and the cell-by-cell correlation of these indices.

Figure 6A shows population histograms of the pursuit and VORC preferred directions. Both distributions appear to favor some directions over others. The downward-ipsilateral direction is favored significantly for pursuit (P < 0.01, Rayleigh) and although VORC failed to reach significance (P = 0.31, Rayleigh), there appears to be a similar trend. Figure 6B is a population histogram of the cell-by-cell difference between the VORC and pursuit preferred directions. A single, strong peak occurs at ~0° (7.7 ± 80.1°, mean ± SD) and is significant (P < 0.001, Rayleigh). The preferred directions also are correlated significantly on a cell-by-cell basis (r_aa = 0.08, P < 0.01, nonparametric angular-angular correlation). These findings indicate that individual cells tend to have well-aligned pursuit and VORC preferred directions.

View larger version (43K): [in this window] [in a new window]   Fig. 6. Comparison of pursuit and VORC preferred directions and directional selectivity in the preferred-direction experiment. A: population histograms of the preferred directions for pursuit, plotted as downward bars, and VORC, plotted as upward filled bars. Histogram binwidth is 10°, and we broke the circular geometry at 40° for plotting purposes. B: population histogram of the cell-by-cell difference between the VORC- and pursuit-preferred directions. Positive differences were selected arbitrarily to indicate VORC-preferred directions counterclockwise relative to pursuit-preferred directions. Histogram binwidth is 10°. C: population histogram of the selectivity indices for pursuit, plotted as downward bars, and VORC, plotted as upward filled bars. Histogram binwidth is 0.05. VORC and pursuit distributions have 25th, 50th, and 75th percentile points of 0.09, 0.14, and 0.24 and 0.11, 0.19, 0.27, respectively. D: correlation plot of VORC against pursuit selectivity indices and best-fit line.

We quantified the pursuit and VORC directional tuning in each cell with a selectivity index (SI). Figure 6C plots population histograms of the SIs. Both populations are quite selective with pursuit slightly more selective on average. We found that 20/80 (25%) cells have significant pursuit tuning and 16/80 (20%) cells have significant VORC tuning (P < 0.05, boot-strap analysis of SIs). As with optic-flow pattern tuning, these percentages are likely underestimates due to the relatively low number of repetitions. Nevertheless, as Fig. 5B shows quite directly, there is clear evidence that pursuit and VORC signals are well tuned and we were able to identify clear tuning trends in all neurons.

Figure 6D plots VORC SIs versus pursuit SIs on a cell-by-cell basis. We found a significant correlation in these data (P < 0.001, r_s = 0.58, Spearman) and the best fit line has a slope of 0.89 (2-dimensional least mean squares fit). This indicates that pursuit and VORC directional selectivity is related, and is nearly equal, in individual neurons.

With evidence that pursuit and VORC gaze-tracking signals are similarly tuned in individual neurons, we now examine how these gaze-tracking signals interact with visual-motion patterns simulating translation through the world (i.e., heading experiment).

Focus tuning

The heading experiment consists of fixed gaze, pursuit, VORC, and simulated gaze-rotation conditions conducted along the cell's preferred-null axis. Figure 7 presents all neural and behavioral data collected from a single MSTd neuron in the heading experiment. The seven rows represent the seven behavioral/directional combinations while the nine columns represent the FOE positions on the screen. Comparisons of the relative alignment and magnitude of the various behavioral/directional tuning curves are presented in the following two sections, SHIFT COMPENSATION and GAIN MODULATION.

View larger version (56K): [in this window] [in a new window]   Fig. 7. Neural and behavioral data collected from a single MSTd neuron in the heading experiment. Rows: seven behavioral/directional combinations; columns: FOE positions on the screen. Preferred-direction conditions are grouped in the top 3 rows and null-direction conditions are grouped in the bottom 3 rows. Optic-flow illustrations are drawn at one-third scale, referenced to the abscissa scale, and the FOE is beyond the stimulus frame for all but the central 3 FOE positions. Action potential raster plots (4 repetitions), action potential peristimulus time histograms (PSTHs; 100-ms time bins), horizontal and vertical eye position traces (1-ms sample period, + indicates right or up), and yaw and pitch head position traces (8-ms sample period, + indicates yaw right or pitch up) are shown for each condition. The 1.2-s stimulus period (thick bar on time scale) is indicated by vertical dotted lines, and the last 1.0 s of this period was analyzed to construct focus tuning curves for each of the seven behavioral/directional conditions. The 500-ms periods before and after the visual stimulus are indicated by thin bars on the time scale. This neuron is selective for expansion patterns and the preferred gaze-rotation direction is rightward. Tuning curves for this cell are shown in Fig. 8.

The fixed-gaze response (Fig. 7, middle) is a typical example of how the neural response changes as the focus position is varied along the cell's preferred-null gaze-rotation axis (Fig. 7, schematic illustrations). The preferred-optic-flow pattern for this cell is expansion and the preferred gaze-rotation direction is rightward. The fixed-gaze response is tuned for the FOE position (P < 0.001, Kruskal-Wallis), responding vigorously to leftward FOE positions but hardly at all to rightward FOE positions. Although this neuron was classified as expansion selective, because it responded better to expansion patterns than to contraction or rotation patterns, it also responds to nearly laminar motion. This is evident in the fixed-gaze response because the 32° FOE stimulus (nearly rightward laminar flow) elicits a strong response. That FOE tuning arises from the combination of expansion (or contraction or rotation) and laminar motion selectivities is not surprising. Moreover by varying the FOE positions along the preferred-null gaze-rotation axis, we expect to couple into the neuron's laminar flow response because it has been reported that most MSTd neurons have laminar motion selectivities that align with the preferred-null pursuit axis (Komatsu and Wurtz 1988b).

The fixed-gaze response appears to reliably encode the FOE position, but does it represent the FOE position on the retinae or the FOE position on the screen (in the world)? Retinal and screen coordinates are identical when the gaze is fixed. To dissociate retinal FOE position tuning from true heading tuning, which requires the cell to encode the FOE position on the screen, we must consider the neuron's focus tuning while gaze is rotating because the retinal focus is shifted then relative to the screen (see Fig. 1). Constant-velocity pursuit, VORC, and simulated gaze rotations introduce a constant FOE position difference, or displacement, between the retinal and screen images. Cell-by-cell comparisons of pursuit, VORC, and simulated gaze-rotation focus tuning curves with the fixed gaze focus tuning curve are discussed below.

To verify that MSTd neurons are sensitive to the dimension of visual motion that we varied, we tested the significance of FOE position tuning for each behavioral/directional tuning curve. The number of neurons in the population with significant tuning is as follows: 53/80 (66%) fixed gaze; 34/80 (43%) preferred-direction VORC; 40/80 (50%) null-direction VORC; 45/80 (56%) preferred-direction pursuit; 34/80 (43%) null-direction pursuit; 45/80 (56%) preferred-direction simulated gaze rotation; and 45/80 (56%) null-direction simulated gaze rotation (P < 0.05, Kruskal-Wallis). We expected to find fewer significantly tuned cells in the gaze-rotation conditions than in the fixed gaze condition because gaze rotation adds laminar flow to the retinal image, thereby causing more stimuli to have essentially laminar retinal flow. Neurons respond more similarly to visual patterns with only slight variations from laminar flow than to visual patterns that span both directions of laminar flow and, for example, expansion (see Fig. 7). Few cells are tuned significantly for focus position in all seven behavioral/directional conditions (12/80, 15%, P < 0.05, Kruskal-Wallis), but most cells are for at least one of the seven conditions (59/80, 74%, P < 0.05/7, Kruskal-Wallis).

Influence of gaze rotation

SHIFT COMPENSATION. Figure 8 plots tuning curves constructed from the heading experiment data presented in Fig. 7. Rows represent the three gaze-tracking conditions, which are retinally identical except for the visual effects caused by extremely small eye-movement deviations during fixation, pursuit, and VORC. The curves are plotted in both the coordinates of the screen and the retinae to help visualize the alignment of features.

View larger version (33K): [in this window] [in a new window]   Fig. 8. Response of a single "heading" neuron in the heading experiment. Focus tuning curves from the 3 gaze rotation conditions (rows) are plotted in the coordinates of the screen (left) and the retinae (right). Fixed gaze curve (thick solid line) is identical in all panels. Preferred (solid lines) and null (dashed lines) tuning curves are displaced by the theoretical shift offsets of +24 and 24°, respectively, with respect to the fixed gaze curve to plot the curves in retinal coordinates. Data points are means ± SE for 4 replicates (see Fig. 7 for rasters, PSTHs, eye traces, and head traces).

View larger version (19K): [in this window] [in a new window]   Fig. 9. Population cross-correlograms and histograms of compensatory shifts for the 3 gaze-rotation conditions. In all panels, preferred- and null-direction data are pooled. A: population average cross-correlograms for VORC (solid curve), pursuit (dashed curve), and simulated (dot-dashed curve) conditions. Gray bands represent the ±1 SE range. B: population histograms of VORC, pursuit, and simulated compensatory shifts (line styles as in A). Binwidth is 8.0°. Table 1 lists all distribution parameters and hypothesis test values. C: population histograms of VORC shifts minus simulated shifts (solid curve) and pursuit shifts minus simulated shifts (dashed curve). Binwidth is 8.0°. Subtraction was performed on a cell-by-cell basis, and Table 1 contains all distribution and test values.