INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

As we move our head in the world, we experience both gravitational and translational accelerations. Both acceleration components are sensed by primary otolith afferents that innervate the utricular and saccular maculae. These linear acceleration signals are transmitted to the CNS, primarily to the vestibular nuclei and vestibulo-cerebellum. Otolith signals related to changes of the head relative to gravity or translatory head movements have been shown to be critical for the control of the eyes, head, body, and limb movements (Ikegami et al. 1994; Lacour et al. 1987; Lacquaniti et al. 1984; Pozzo et al. 1990; Watt 1976; Wilson and Schor 1999) as well as for perceptual orientation responses (Clark and Graybiel 1964, 1966; Glasauer 1995; Schone and Lechner-Steinleitner 1978; Seidman et al. 1998; Stockwell and Guedry 1970). More recently, head tilt signals have also been shown to be important for the autonomic control of the respiratory and cardiovascular systems (Uchino et al. 1970; Yates 1992; Yates and Miller 1994; Yates et al. 1999).

One of the most challenging aspects in understanding the function of the otolith system is determining the nature of central processing of gravitational and translational accelerations. Even though this has never been directly investigated, it is generally thought that primary otolith afferents respond similarly to both head tilts relative to gravity and to translational movements (Dickman et al. 1991; Fernandez and Goldberg 1972, 1976a; Loe et al. 1973; Si et al. 1997). Despite indiscriminate primary otolith afferent information, eye movement responses to head tilts and translations have been shown to be different (Angelaki et al. 1999a). How and where the discrimination between gravitational and translational components of acceleration takes place remains illusive (Angelaki et al. 1999a; Glasauer and Merfeld 1997; Guedry 1974; Mayne 1974; Merfeld 1995; Merfeld et al. 1999; Paige and Tomko 1991; Telford et al. 1997; Young 1974).

Despite the diverse functional demands of the otolith system, primary otolith afferents exhibit relatively stereotypic responses, demonstrating dynamic properties consistent with encoding of linear accelerations over a broad frequency range (Dickman et al. 1991; Fernandez and Goldberg 1976a-c; Fernandez et al. 1972; Goldberg et al. 1990; Loe et al. 1973; Si et al. 1997; Tomko et al. 1981). Afferent response dynamics have been shown to vary across a continuum from purely tonic to phasic-tonic (regularly and irregularly discharging afferents, respectively) with a phase distribution in squirrel monkeys that reflects small phase lags or leads relative to linear acceleration (Fernandez and Goldberg 1976c). The functional correlate of the characteristic distribution of response dynamics has been a matter of speculation in recent years. For example, the diversity in vestibular afferent dynamics has been suggested to be related to different roles in vestibulo-ocular versus vestibulo-spinal systems (Boyle et al. 1992; Highstein et al. 1987; Minor and Goldberg 1991), constant velocity rotations (Angelaki and Perachio 1993; Angelaki et al. 1992b, 2000a) and viewing distance-dependence changes of the rotational VOR (Chen-Huang and McCrea 1998). Different roles of tonic and phasic-tonic afferents have also been proposed for VOR adaptation and recovery after lesions (Lasker et al. 1999; Lisberger and Pavelko 1988; Minor et al. 1999). An involvement of irregularly firing otolith afferents in producing the viewing distance dependence and dynamics of the translational VOR has been suggested from reversible ablation studies (Angelaki et al. 2000a).

The diversity in response dynamics of the otolith afferent population, in particular, has also been proposed to facilitate spatiotemporal processing of sensory information. Spatiotemporal convergence (STC) between primary otolith afferents that differ in both their spatial and temporal response properties represents a means of spatiotemporal filtering. Thus STC may be an alternative to distinct spatial and temporal channels of information in the central otolith system (Angelaki 1993a). Even the simplest form of a linear, spatiotemporal summation of otolith afferents could result in central neurons with different dynamic properties that might be dependent on movement direction (Angelaki 1992, 1993a,b). Since primary otolith afferents differ in their polarization vector direction, as well as response dynamics (Fernandez and Goldberg 1976a-c; Fernandez et al. 1972; Loe et al. 1973; Si et al. 1997), spatiotemporal convergence might be the rule rather than the exception in the central otolith system. In fact, evidence of spatiotemporal processing of otolith signals in the majority (78%) of vestibular nuclei neurons of decerebrate rats has been previously reported (Angelaki et al. 1993; Bush et al. 1993).

The implications of spatiotemporal processing of linear acceleration have remained unexplored, largely due to the lack of direct evidence regarding the presence of two-dimensional (2-D) spatial tuning in the otolith system of alert animals. Furthermore because of the diverse motor correlates of the otolith system, it is possible that distinct populations of response dynamics should exist centrally, with neurons exhibiting high-, low-, or band-pass filter properties. The present study was undertaken to directly investigate the spatiotemporal properties of central otolith neurons in the vestibular nuclei of alert rhesus monkeys. Specifically, we investigated the following questions: first, do central otolith neurons exhibit 2-D tuning to linear acceleration? Second, are the dynamics of central otolith neurons different from those of the afferent population and are they suggestive of a central integration of linear acceleration? Finally, the ability of afferent and central neurons to discriminate between different sources of linear acceleration was also directly investigated here by comparing neural responses during sinusoidal pitch oscillations and fore-aft displacements. The data confirm the commonly used assumption that neither primary otolith afferents nor central-otolith-only neurons can discriminate tilt from translation.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Animals

Four juvenile rhesus monkeys were chronically implanted with a circular molded, lightweight dental acrylic ring that was anchored by stainless steel inverted T-bolts secured under the skull. For single unit recordings from the vestibular nerve (3 of the animals) and the vestibular nuclei (3 of the animals), a platform (3 × 3 × 0.5 cm) constructed of plastic delrin was stereotaxically secured to the skull and fitted inside the head ring. The platform had staggered rows of holes (spaced 0.8 mm apart) that extended from the midline to the area overlying the vestibular nerves bilaterally. In separate surgeries, all animals were also implanted with dual eye coils on both eyes (cf. Angelaki 1998; Angelaki et al. 2000a,b). Eye coils were calibrated both prior to implantation and daily during experiments, as explained in detail elsewhere (Angelaki 1998; Angelaki et al. 2000b). Subsequent to the eye coil surgeries, animals were sufficiently trained to fixate visual targets. Next labyrinthine stimulating electrodes were implanted in both ears of one of the animals to be used for vestibular nuclei neuron recordings (c.f., Angelaki et al. 2000a). All surgical procedures were performed under sterile conditions in accordance to institutional and National Institutes of Health guidelines.

Experimental set-up and protocols

During experiments, the monkeys were seated in a primate chair with their heads statically positioned 18° nose-down, which aligned the major plane of the utricle and horizontal canals with an earth-horizontal plane. The animal's body was secured with shoulder and lap belts, while the extremities were loosely tied to the chair. The primate chair was then secured inside the inner frame of a vestibular turntable consisting of a three-dimensional (3-D) rotator on top of a 2-m linear sled (Acutronics).

For each recording session, the eight voltage signals of the two eye-coil assemblies, the three output signals of a 3-D linear accelerometer (mounted on fiberglass members that firmly attached the animal's head ring to the inner gimbal of the rotator), as well as velocity and position feedback signals from the linear sled and/or rotator were low-pass filtered (200 Hz, 6-pole Bessel), digitized at a rate of 833.33 Hz (Cambridge Electronics Design, model 1401, 16-bit resolution), and stored on a PC for off-line analysis.

Extracellular recordings from single primary otolith afferents or vestibular nuclei neurons were obtained with epoxy-coated, etched tungsten microelectrodes that were inserted into the brain through a 26-gauge stainless steel guide tube (457 µm OD). Electrodes were inserted into guide tubes, then advanced through a predrilled hole in the recording platform and manipulated vertically with a remote-control mechanical microdrive. After neural activity was amplified and filtered (300 Hz to 6 kHz), it was directed to an audiomonitor as well as passed through a BAK Instruments dual time-amplitude window discriminator whose output was displayed on an oscilloscope. For each recorded cell, acceptance pulses from the BAK window discriminator were used to trigger the event channel of a Cambridge Electronics Design (model 1401) data-acquisition system, which stored the time of the spike at a 10-µs resolution. Both stimulus presentation and recording protocols were computer-controlled with the CED using scripts written for the Spike2 software environment.

Vestibular nuclei neuron recordings

Initial experiments in each animal were performed to identify the abducens nuclei based on the characteristic burst-tonic activity of motoneurons (Fuchs and Luschei 1970). Subsequent penetrations explored an area that extended 0.8-4 mm lateral and 0.0-3 mm posterior to the abducens nucleus. Recordings were concentrated in rostral areas of the vestibular nuclei, mainly in the rostral portions of the medial subdivision and around the ventral lateral vestibular nucleus. All neurons reported here were recorded either in the same penetrations as eye-movement-related cells or within an area extending no more than 1.6 mm lateral or posterior from penetrations where eye-movement-sensitive cells were recorded. No electrode tracks were identified in the caudal medial or descending vestibular nuclei. In the animal that was implanted with bilateral labyrinthine stimulating electrodes, the location of the vestibular nuclei was also guided by vestibular field potentials evoked with electrical stimulation of the ipsilateral vestibular nerve (0.1-ms monophasic pulses, 50-400 µA). A few cells in this animal (6) were also tested for mono- or polysynaptic inputs from the ipsilateral labyrinth based on orthodromic activation with monophasic single pulses (0.1-ms duration, 50- to 400-µA amplitude) delivered at a frequency of 2 or 5 Hz. Two of the three cells that were positively identified as receiving monosynaptic input from the ipsilateral labyrinth (latency less than 1.2 ms) belonged to the "flat" dynamics category (the 3rd cell was not tested at sufficient frequencies to allow identification of its dynamics). The three cells that were not activated at monosynaptic latencies belonged to the high-pass category.

Once a vestibular nuclei neuron was isolated, the responsiveness of each cell was characterized by examining its sensitivity to eye movement as well as rotational and translational motion. The responses during horizontal and vertical smooth pursuit (0.5 Hz, ±10°), as well as fixation and visually guided saccades, were first obtained. Only cells that did not exhibit any eye-velocity or -position sensitivity [termed vestibular-only (VO) neurons] (e.g., Scudder and Fuchs 1992) were included in the present study. Isolated VO cells were tested during lateral and fore-aft motion at 0.5, 2, or 5 Hz. Cells that did not respond during translation were excluded. Neurons that responded to linear acceleration were further tested during (0.5 Hz, ±10°) rotations about different head axes. The axis of rotation always remained earth-vertical during the classification protocol to avoid simultaneous dynamic otolith activation and to investigate if the cell exhibited any rotational sensitivity due to activation of the semicircular canals. Earth-vertical axis rotations were first delivered with the animal upright as well as pitched 30° nose-up and 30° nose-down (eliciting horizontal or combinations of horizontal and torsional VOR). If neural isolation was maintained, the cell was further tested during earth-vertical axis rotations in additional planes (by re-orienting the animal relative to the rotation axis). Only translation-sensitive VO neurons that did not modulate during any earth-vertical axis rotation and whose firing rate was unrelated to eye movements were further investigated in the present study.

The main experimental protocols consisted of an array of translational stimulus profiles (using a linear sled that moved in an earth-horizontal plane). At two different frequencies (0.5 and 5 Hz), the animal was re-oriented relative to the linear sled so that translations in different directions in the horizontal plane were provided. The orientations used varied through 180° in steps of 30°. Next, for a minimum of two different translational directions (usually during lateral and fore-aft motion), the frequency of the translational acceleration was varied between 0.16 and 5 Hz (0.16 and 0.2 at 0.1 G, all other at 0.2 G). An attempt was made to complete these experimental protocols in as many cells as possible. However, adequate isolation was maintained in only a subpopulation of the total number of cells tested. To determine if central otolith neurons discriminated between tilt and translational motion, pitch oscillations (0.5 Hz, ±10°) with the animal upright were also delivered to a few cells. During these pitch oscillations, a component of gravity modulated sinusoidally along the animal's naso-occipital axis. Since the neurons tested were known not to receive any semicircular canal inputs, comparison of the neural activity during pitch oscillations and fore-aft translation could be used as a direct test of whether or not cells distinguished between the gravitational and translational components of linear acceleration.

Otolith afferent recordings

Neural recordings from otolith afferents were obtained using similar techniques as those described in the preceding text for central neurons. Recordings were made as the fibers entered the brain stem proximal to Scarpa's ganglion. Electrode penetrations were made 8-10 mm from the midline at the level of A-P 0. Most tracks were made outside the boundary of the medulla, with several being histologically identified in cross-sections (e.g., Fig. 1). To identify primary vestibular afferents on-line, the fiber selectivity was carefully characterized through a combination of yaw/pitch/roll rotations and linear sled movements (e.g., Dickman 1996; Estes et al. 1975). Specifically, each afferent was tested with the following rotational stimuli (0.5 Hz, ±10°): yaw and pitch rotations, as well as rotations in the plane of the anterior and posterior semicircular canals (i.e., 45° away from the pitch and roll axes). Afferents were also tested during 0.5 Hz (0.2 G peak) translation along the lateral and fore-aft axes. All fibers were shown to receive input from only one sensory organ with spatial and dynamic properties consistent with those characterizing the vestibular nerve in squirrel monkeys (Fernandez and Goldberg 1971, 1976a-c). Once a recorded fiber was characterized as a primary otolith afferent (i.e., it responded during translation), units were tested at different frequencies (0.16-10 Hz) and different orientations. The peak amplitude and stimulus characteristics were identical to those described in the preceding text for central otolith neurons. This allowed a direct comparison between the properties of afferent and central neuron responses to translation.

View larger version (18K): [in this window] [in a new window]   Fig. 1. Electrode tracks into the VIIIth nerve for otolith afferent recordings. A representative cross-section with 2 electrode tracks where otolith afferents were recorded is illustrated. Most electrode tracks were observed at, or slightly anterior to, the location illustrated. FL, flocculus; IO, inferior olivary nucleus; MCP, middle cerebellar peduncle; PFL, paraflocculus; SCP, superior cerebellar peduncle; IV, fourth ventricle; VI, abducens nucleus; VII, facial nucleus; VIII, vestibulo-cochlear nerve. Scale bar = 1 mm.

Histology

At the completion of all recording experiments, the animals were deeply anesthetized (pentobarbital sodium) and perfused transcardially with a 2% paraformaldehyde/2% glutaraldehyde solution. The brain was removed, sectioned (80 µm), and counterstained (alternate sections with cresyl violet and Weil). An approximate recording location map was reconstructed for each animal, using the penetration records and known cell type location (e.g., abducens neurons) as well as identification of electrode tracks. The exact recording sites could not be verified based on histological examination (extensive marking lesions were not employed).

Data analyses

All data analyses were performed off-line using custom-written scripts in Matlab (Mathworks). Since none of the neurons examined exhibited any oculomotor sensitivity, the eye-movement signals (which were recorded and stored in each experimental run) were not used for quantitative analyses. For each neuron, the instantaneous firing rate (IFR) was computed as the inverse of interspike interval and assigned to the middle of the interval. For each experimental run, data were folded into a single cycle by overlaying neural IFR from each response cycle. A linear accelerometer mounted near the animal's head provided the stimulus measure during translation. The neural sensitivity (gain) and phase during translation were determined by fitting a sine function (1st and 2nd harmonics and a DC offset) to both response and stimulus using a nonlinear least-squares minimization algorithm (Levenberg-Marquardt). Silent portions of the neural activity, when present, were excluded from the least-square optimization. Neural sensitivity was then expressed as spikes · s¹ · G¹ (with G = 9.81 m/s²). Phase was expressed as the difference (in degrees) between peak neural activity and peak linear acceleration. Responses were considered significant if the second harmonic was less than 50% of the fundamental. As the animal was repositioned relative to the sled displacement, each stimulus direction was characterized by a polar angle , defined relative to the lateral (interaural) axis. During lateral motion (0° orientation), peak linear acceleration was to the right. During fore-aft motion (90° orientation), peak linear acceleration was backward.

A cell was considered to respond to either translation or rotation, if the following criteria were met: 1) the harmonic distortion was less than 20% during rotation/translation in at least one stimulus direction; 2) response gain was larger than a minimum (0.10 spikes/s per °/s for rotation and 15 spikes · s¹ · G¹ for translation) along the directions of minimum harmonic distortion. For the cells that fulfilled these two criteria, a clear modulation in firing rate was also heard through the audiomonitor.

The spatial tuning at each tested frequency was characterized by applying the previously described 2-D spatiotemporal model to both the gain and phase data from each cell during fore-aft and lateral translation (Angelaki 1991; Angelaki et al. 1992; Schor and Angelaki 1992). If data were available at more than these two orientations, all tested directions contributed equally to the tuning estimate by fitting the following equations simultaneously to the gain and phase values as a function of stimulus direction,  (e.g., Fig. 4)

(1)

(2)

where G_la/G_fa and _la/_fa are the now computed (rather than directly measured) neural response gain and phase during lateral and fore-aft motions, respectively. In these equations,  is the heading direction ( = 0° and  = 90° for lateral and fore-aft motions, respectively). It was then these G_la/G_fa and _la/_fa estimates that were used to compute the maximum and minimum sensitivity directions (Angelaki 1991; Angelaki et al. 1992; Schor and Angelaki 1992).

In addition to the 2-D model, cells that were tested along at least five different directions were also fitted with the one-dimensional (1-D) cosine-tuning model. For both models, the goodness of fit was evaluated through two measures (see following text), the variance-accounted-for (VAF) and the mean square error (MSE) divided by the maximum gain (for a direct comparison of cells with a wide distribution of response sensitivities). Such a comparison was done to extend the results of Bush et al. (1993) that a 2-D model provides a more accurate description of the cell's spatial tuning.

Afferent cells were classified into "regular" and "irregular" according to the normalized coefficient of variation [CV* was computed as in Goldberg et al. (1984); regular afferents: CV*  0.1; irregular afferents: CV* > 0.1]. The coefficient of variation was also estimated for central neurons. It was found to be at least 0.9 with no systematic correlation with any aspect of response properties.

Transfer functions

Several functions were fitted to the mean dynamics (gain and phase simultaneously) of the afferent and central otolith neurons. For this and before the gain and phase averages were estimated, all neurons' response sensitivities were normalized by dividing with the respective response gain at 0.5 Hz (thus all cells had unity sensitivity at 0.5 Hz). To compare each model's ability to describe the gain and phase data for each group of neurons, two measures were used. First, VAF coefficients were computed as VAF = {1  [var (model - data)/var (data)]}. Separate VAF values were calculated for neuronal gain and phase (although the functions were fitted to both gain and phase simultaneously). The VAF provided a normalized measure of the goodness of fit. For example, a VAF = 0.50 indicates that 50% of the gain or phase dependence on frequency is described by the model. Second, the mean square error (MSE) was also computed as MSE = [model(f)  data(f)]²/(N  P), where data(f) represents the gain or phase values experimentally measured at each frequency f, model(f), the corresponding values estimated from the fit, N, the number of different frequencies tested, and P, the number of model parameters fitted. Whereas the VAF measure provides a goodness of fit criterion that is independent of the number of model parameters fitted, the MSE measure takes into account the number of parameters fitted. Thus MSE also serves to provide an index as to whether increasing the complexity of the model was warranted. VAF and MSE were also used for a quantitative description of the goodness of fit for the spatial tuning functions.

It should be stated that the goal behind these transfer function fits was not to reveal the underlying temporal processing, but merely to provide a quantitative description of the response dynamics of the neurons. This is particularly the case for 2-D central neurons whose properties might be shaped by spatiotemporal rather than purely temporal interactions (see DISCUSSION). In this case, the terms used to describe the neuron's dynamics need not necessarily correspond to actual temporal processing.

Simulations of spatiotemporal convergence

To simulate spatiotemporal convergence, a simple model was constructed based on the following assumptions: 1) a central otolith cell (whose dynamics were simulated) was assumed to receive inputs from two otolith afferents whose dynamics were described by the mean sensitivity and phase of the regular and irregular afferent populations; 2) summation was linear, with k_RE and k_IRR being the relative strengths of the two inputs; 3) there were no dynamics in the interaction of the two inputs (i.e., k_RE and k_IRR were frequency-independent); and 4) the vector of the "regular" afferent was oriented along the lateral axis (x axis), whereas the vector orientation of the "irregular" afferent formed an angle of ° (counterclockwise is positive).

A detailed description of the equations describing this interaction has been presented before (Angelaki 1993a,b). Briefly, if G_RE cos (t + _RE) and G_IRR cos (t + _IRR) describe the responses of the "regular" and "irregular" afferents at a frequency , the response of the target neuron along the lateral (x axis) and fore-aft (y axis) orientations can be calculated as

(3)

(4)

where


The gain and phase of the simulated target neuron along the lateral and fore-aft axes were computed at each frequency based on these equations. The maximum and minimum responses, as well as the tuning ratio were subsequently computed from G_la/G_fa and _la/_fa, as previously described (Angelaki 1991; Angelaki et al. 1992).

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Of 288 neurons in the rostral vestibular nuclei that were isolated long enough to be characterized, 129 exhibited eye-movement-related activity, 95 responded to activation of the semicircular canals (48% of which also responded to translation), whereas 64 were only activated during linear acceleration. The responses from these 64 vestibular nuclei neurons that responded exclusively during translational motion and 30 primary otolith afferents were used for the present analyses. None of the 64 central neurons responded during yaw rotation. None of the neurons had response components related to either fast or slow eye movements during fixations, visually guided saccades, or smooth-pursuit eye movements. The majority of the cells (47/64) were also tested during earth-vertical axis rotations in multiple head planes (see METHODS). None of the 47 cells received either horizontal or vertical canal input. The remaining 17 central otolith cells were lost before an extensive rotational protocol could be delivered, thus the possibility of vertical canal input could not be excluded. All quantitative data and frequency response properties were, therefore, confined to the 47 central cells that were positively characterized as receiving only otolith inputs.

Spatiotemporal properties and tuning

The spatial tuning of primary otolith afferents and central otolith cells was characterized using the neural responses obtained during 0.5- and 5-Hz translation along six different directions in the horizontal plane. The responses to different directions of translation from one primary otolith afferent and a central otolith neuron are shown in Figs. 2 and 3, respectively. Stimulus orientations of 0° (and 180°) corresponded to lateral motion, whereas 90° corresponded to fore-aft motion. Stimulus directions of 30, 60, 120, and 150° corresponded to orientations in between lateral and fore-aft motion. All of the afferents tested were cosine-tuned. That is, the afferent's maximum modulation in firing rate occurred at a certain orientation (~60° for the afferent of Fig. 2) and the minimum modulation occurred at an orientation of approximately 90° away from the maximum. Translation along the minimum response direction typically elicited no response (null response direction). The afferent's response phase was the same for all stimulus directions, except for a 180° reversal that occurred at the minimum response direction.

View larger version (21K): [in this window] [in a new window]   Fig. 2. Instantaneous firing rate (IFR) of primary otolith afferent h18t during 0.5-Hz translation along different directions in the horizontal plane. Stimulus orientations of 0 and 180° correspond to lateral motion, whereas 90° corresponds to fore-aft motion. Stimulus directions of 30, 60, 120, and 150° correspond to in-between orientations. The superimposed solid line in each subplot is the best-fit sine function consisting of 1st and 2nd harmonics. The bottom traces represent the linear acceleration stimulus (in units of G; G = 9.81 m/s2).

View larger version (24K): [in this window] [in a new window]   Fig. 3. IFR of vestibular nuclei neuron p96f during 0.5-Hz translation along different directions in the horizontal plane. Stimulus orientations of 0 and 180° correspond to lateral motion, whereas 90° corresponds to fore-aft motion. Stimulus directions of 30, 60, 120, and 150° correspond to in-between orientations. The superimposed solid line in each subplot is the best-fit sine function consisting of 1st and 2nd harmonics. The bottom traces represent the linear acceleration stimulus (in units of G; G = 9.81 m/s2).

In contrast, the central otolith neurons were generally not cosine-tuned. For example, the neuron shown in Fig. 3 had no clear response null with some modulation occurring at all orientations. The neural response phase exhibited a more gradual dependence on stimulus direction, as observed in the responses to 90, 60, and 30° orientations. This noncosine behavior has previously been described as 2-D tuning (Angelaki 1991; Angelaki et al. 1992, 1993). To characterize the spatial tuning of these neurons, the gain and phase values of afferent and central otolith neurons were simultaneously fitted with a 2-D spatial tuning model (Angelaki 1991; Angelaki et al. 1992). Examples of 2-D fits for these central otolith neurons are illustrated in Fig. 4. These neurons were chosen to demonstrate the differences between 1-D (cosine-tuned) and 2-D neurons. Cell p90f () was cosine-tuned with a sensitivity that varied as a rectified cosine function and a response phase that abruptly shifted 180° at the zero sensitivity direction (33°). Cell p96f () also exhibited sensitivities that were dependent on stimulus orientation; however, the sensitivity was a complex sinusoidal function characterized by a broader peak and a narrower trough (see Eq. 1) and not a rectified cosine. An important characteristic of neurons exhibiting 2-D tuning was that the minimum response sensitivity was not zero. For cell p96f, the minimum gain was 26% of the maximum, corresponding to a tuning ratio (i.e., computed minimum response divided by the computed maximum response sensitivity) of 0.26. The response phase of cell p96f was not constant but decreased as the stimulus angle increased. The changing phase relationship was well described by Eq. 2. Cell p83d () is another example of a 2-D neuron where the minimum sensitivity was 66% of the maximum (tuning ratio of 0.66), and the response phase exhibited a strong dependence on stimulus direction. In general, the larger the tuning ratio, the greater the dependence of phase on stimulus orientation (Angelaki 1991; Angelaki et al. 1992).

View larger version (21K): [in this window] [in a new window]   Fig. 4. Neural sensitivity and phase values for 3 vestibular nuclei neurons. Tuning ratios were: p96f = 0.26 (), p83d = 0.66 (), and p90f = 0.02 (). , simultaneous fits of Eqs. 1 and 2 to the sensitivity and phase data (5 Hz).

To provide a quantitative comparison of the 2-D model with the more traditionally used 1-D (cosine-tuned) model, we also fitted 1-D, cosine-tuning functions to data from a subset of 17 neurons, which were tested along at least five different directions and were characterized by tuning ratios larger than 0.10. The VAF values for the 2-D fits have been plotted versus the corresponding values for the 1-D fits in Fig. 5A. For the majority of the cells, data points plotted above the unity-slope line ( · · · ), suggesting a substantial improvement in the ability of the 2-D model to describe the dependence of sensitivity and phase on stimulus direction. As we have also reported in the past, this improvement was larger for the phase than for the gain dependence on stimulus direction ( vs.  in Fig. 5). The improvement in VAF (VAF_2-D  VAF_1-D) and MSE [(MSE_1-D  MSE_2-D)/MSE_1-D] has been plotted versus the corresponding tuning ratio in Fig. 5B. For all but one cell, both of these values for the phase fits were positive (Fig. 5B, ). Thus, the 2-D model provides a significantly better fit (than the 1-D model) to the spatial tuning of the response phase for cells with tuning ratios larger than 0.10. For response gains, the improvement in the fit was generally smaller, particularly in relation to the MSE values which are a function of the number of fitted parameters (4 for 2-D tuning and 3 for 1-D tuning) (see also Bush et al. 1993).

View larger version (24K): [in this window] [in a new window]   Fig. 5. Comparison of goodness of fit for 2-dimensional (2-D) and 1-dimensional (1-D) models. A: the variance-accounted-for (VAF) computed for 2-D fits is plotted vs. those for 1-D fits. A perfect model would have VAF = 1 ( · · · ). The other · · · is the unity-slope line. B: the improvement in VAF (VAF2-D  VAF1-D) and MSE [(MSE1-D -MSE2-D)/MSE1-D] has been plotted vs. the corresponding tuning ratio. , linear regressions (R2 = 0.11 and 0.10, top and R2 = 0.36 and 0.001, bottom). Parameters have been computed separately for gain and phase ( and , respectively).

The distributions of tuning ratios for all afferent and central neurons tested at multiple orientations at 0.5 and 5 Hz have been plotted in Fig. 6. All afferents were cosine (1-D)-tuned with tuning ratios that were less than 0.15. Even though the dependence of response phase on stimulus direction was significant even at smaller tuning ratios (Fig. 5) (see also Bush et al. 1993), we have chosen this value as a qualitative divider between what we have classified as 1- and 2-D central otolith neurons. Accordingly, the majority of central otolith neurons (22/37, 59% at 0.5 Hz and 16/23, 70% at 5 Hz) exhibited 2-D spatial tuning (tuning ratios more than 0.15). In contrast to what was reported in decerebrate rats (Bush et al. 1993), we found no linear correlation between the amplitude of the minimum and maximum sensitivities at 0.5 Hz in primate central otolith cells (R² = 0.04). At higher frequencies, the correlation improved but remained insignificant (R² = 0.39 at 5 Hz). Thus, no derivative relationship between the maximum and minimum sensitivity vectors exists in primate rostral vestibular nuclei neurons.

View larger version (42K): [in this window] [in a new window]   Fig. 6. Distribution of tuning ratios (minimum/maximum response sensitivity) for primary otolith afferents (hatched) and central otolith neurons (gray) during translation at 0.5 and 5 Hz.

Phase distribution

The phase distributions of afferent and central otolith neurons at 0.5 and 5 Hz have been illustrated in Fig. 7. Because of the dependence of response phase on stimulus direction in many of the central otolith neurons, only the phase computed along the maximum sensitivity direction was used to compare distributions across neurons. Similar to previous reports in other species, primary otolith afferents were characterized by response phases that slightly led head acceleration (Fig. 7). In contrast, central otolith neurons exhibited a broad phase distribution at 0.5 Hz (Fig. 7, top). Thirty-two percent of the neurons had phases that were similar to those of the afferents, i.e., closely in phase or slightly leading head linear acceleration. However, the majority of the central neurons (68%) lagged acceleration and were phase shifted 30-110° relative to the afferents (and to linear acceleration) at 0.5 Hz. It should be pointed out that phase values around 90° do not necessarily suggest that neuronal firing encodes the linear velocity of the head. In fact, as will be shown in the following text, data at multiple frequencies are not consistent with a temporal integration of linear acceleration in most central neurons.

View larger version (38K): [in this window] [in a new window]   Fig. 7. Distribution of the neuronal phase of the maximum sensitivity vector for primary otolith afferents () and central otolith neurons () during translation at 0.5 and 5 Hz. A phase of 0° corresponds to a response in phase with linear acceleration. A phase of 90° corresponds to a response in phase with linear velocity. Positive values represent phase leads.

When tested at 5 Hz, the phase distribution of central cells was narrower and the majority of central neurons exhibited phases that only slightly lagged linear acceleration at 5 Hz (Fig. 7, bottom). No systematic correlation between response phase and tuning ratio was found.

Response dynamics

The dependence of response gain and phase on frequency was very different for afferent and central otolith neurons. This was the case not only for 2-D but also for 1-D central neurons. It is also important to point out that characterization of the response dynamics for the otolith neurons that exhibited 2-D spatial properties is complicated by the fact that these cells typically should exhibit different dynamic properties depending on stimulus direction (Angelaki 1991, 1993a,b). The fact that this was indeed the case is illustrated in Fig. 8, which plots the neural sensitivity and phase across different frequencies for two directions of stimulation, i.e., lateral and fore-aft motion (, , , ,  and , , , ,  respectively). Two main results were further examined. First, central and afferent dynamics to linear acceleration were very different from each other. Second, 2-D neurons were found to differ in their response dynamics for different directions of linear acceleration.

View larger version (27K): [in this window] [in a new window]   Fig. 8. Response dynamics during lateral (, , , , ) and fore-aft motion (, , , , ) A: data from 2 primary otolith afferents, h18f ( and ) and h18r ( and ), with CV* = 0.12 and 0.10, respectively. B: data from 4 central otolith neurons, d61e ( and , left), d51b ( and , left), d53f ( and , right), and p90e ( and , right).

As the simplest example, Fig. 8A illustrates the responses from two otolith afferents ( and  and  and ) that were characterized by 1-D, cosine-tuned spatial properties. Afferent dynamics were the same during both lateral and fore-aft motion. Afferent response gains increased and phase leads were small, during both directions of motion. The dynamics of two cosine-tuned central neurons have been plotted in Fig. 8B (left). One of these central cells exhibited sensitivities and phase lags that increased with frequency, whereas the other exhibited sensitivities that decreased with frequency and phase leads that increased with frequency during both stimulus directions. Even though the dependence on frequency was very different from the afferent population, these two central 1-D neurons were characterized by relatively similar response dynamics during lateral and fore-aft motion (Fig. 8B, left; ,  and  and ).

An example of two other central otolith neurons that exhibited 2-D tuning is shown in Fig. 8B, right (,  and  and ). These neurons both exhibited dynamics that differed during lateral and fore-aft motion. The phase difference between lateral and fore-aft motion responses in one of these two cells was ~90° (and not 180° as in Fig. 8A) at low frequencies and progressively decreased as frequency increased (Fig. 8B, right, , ). This dynamic behavior is very different from that of 1-D, cosine-tuned neurons that always exhibit similar phases (or shifted 180°) during lateral and fore-aft motion across all frequencies (e.g., Fig. 8, A and B, left). In the other cell (Fig. 8B, , ), response dynamics were also different during lateral and fore-aft motion. Phase leads increased versus frequency during fore-aft motion and decreased with frequency during lateral motion.

The lateral and fore-aft dynamics of the last two cells of Fig. 8B have been replotted in Fig. 9 along with the estimated dynamics that would occur for stimulation along the maximum and minimum sensitivity directions. The maximum sensitivity vector was computed to be closely aligned (but reversed in orientation) to the lateral motion direction for cell d53f (left) and the fore-aft direction for cell p90e (right). Because of the spatiotemporal properties of 2-D neurons, the phase of the minimum sensitivity vector always differed 90° from that of the maximum sensitivity vector at each frequency (Fig. 9, compare  and ; see also Angelaki 1991, 1993a,b).

View larger version (28K): [in this window] [in a new window]   Fig. 9. Response dynamics for 2 high-pass central otolith neurons, cell d53f (left) and p90e (right). The measured sensitivity and phase for lateral () and fore-aft () motion have been replotted from Fig. 8. The computed sensitivity and phase along the maximum (MAX) and minimum (MIN) sensitivity directions are represented by  and , respectively.

Because many of the central neurons had different response dynamics for different directions of movement, further examination of the frequency dependence of the sensitivity and phase was limited to only maximum sensitivity vector responses. Mainly cells whose responses were obtained for two or more movement directions in a minimum of three different frequencies were examined. A few cells whose dynamics were measured at a single orientation (lateral or fore-aft), but their maximum sensitivity direction was found to be less than ±10° of the lateral or fore-aft directions, were also included for analysis. For the 23 central otolith neurons studied, groups of cells with three distinctly different response dynamics were observed. As shown in Fig. 10 (left), the majority of cells (13/23, 57%), termed high-pass neurons, had gains that increased with frequency and phases that significantly lagged linear acceleration at low frequencies (phase, less than 60° at frequencies of up to 0.5 Hz). A second group of cells (7/23, 30%; Fig. 10, middle), termed flat neurons, were characterized by relatively constant sensitivities and phase lags (ranging from 55 to ~0°) for all stimulus frequencies. A third group of central otolith neurons (3/23, 13%; Fig. 10, right) exhibited maximum sensitivities that decreased with frequency and phase lags that increased with frequency. We refer to these cells as low-pass neurons.

View larger version (34K): [in this window] [in a new window]   Fig. 10. Sensitivity (in spikes · s1 · G1), phase (in °) and orientation (in °) of the maximum sensitivity vector as well as the tuning ratio (minimum/maximum) as a function of frequency for 13 high-pass, 7 flat, and 3 low-pass central otolith neurons. A phase of 0° (linear acceleration) and 90° (linear velocity) has been illustrated with · · · .

The difference in the response dynamics between these groups of central neurons and in relation to those of primary otolith afferents is better illustrated in Fig. 11 where mean sensitivity (normalized to unity at 0.5 Hz) and phase have been plotted versus frequency. It is apparent that although there is a large range in central otolith dynamics, none of the three groups have responses that are characteristic of primary otolith afferents. The changes in sensitivity as a function of frequency were usually more extreme and phase lags were larger than those of otolith afferents at nearly all frequencies. The large diversity in the low frequency dynamics among the three different groups of central otolith neurons explains the wide phase distribution observed across the larger central cell population sampled at 0.5 Hz (Fig. 7, top). Conversely, at high frequencies, the phase for all central cells was more similar, as evidenced by the tighter phase distribution observed at 5 Hz (Fig. 7, bottom).

View larger version (23K): [in this window] [in a new window]   Fig. 11. Response dynamics for otolith afferents and central neurons. Mean (±SD) gain and phase from high-pass (red circles, n = 13), flat (blue squares, n = 7), and low-pass (cyan triangles, n = 3) central neurons (Fig. 10) as well as regular (gold circles, CV* < 0.1, n = 6) and irregular (brown circles, CV* > 0.1, n = 15) primary otolith afferents (CV* computed as in Goldberg et al. 1984). For all groups of neurons, sensitivity has been normalized relative to a unity value at 0.5 Hz. Solid lines represent transfer function fits (Tables 1 and 2).

Transfer functions

To quantitatively describe the central neuron response dynamics, several functions were fit to the average gain and phase data for each group of afferent and central otolith neurons. This analysis was performed merely to specify the simplest function that would describe the maximum sensitivity vector dynamics of the central neurons and was not intended to define functional parameters related to specific temporal filtering (as will be discussed later, such a concept cannot be applicable for spatiotemporal processing of signals). Initially, the simplest model that would qualitatively describe the frequency dependence was tried. Then, the complexity of the model was increased guided by two goodness of fit measures, the VAF and the MSE (see METHODS). The complexity of the model was increased only if it resulted in an increase of VAF and a decrease of MSE.

For primary otolith afferents, the simplest function used was a first-order model that corresponded to the peripheral mechanics of the otolith system (Grant and Cotton 1990), cascaded by a frequency-independent adaptation operator (s^k). However, the simple model did not provide good fits for either the gain or phase of regular afferents (Table 1, 1st row). In fact, the variance of the model's fit error was larger than the variance of the data (as indicated by the negative value of VAF). Making the adaptation operator frequency-dependent yielded positive VAF values but only slightly improved the MSE (Table 1, 2nd row). A function consisting of only zeros and no poles was equally bad in adequately describing the frequency dependence of primary otolith afferents (Table 1, 3rd row). However, when a first-order function consisting of one pole and two cascaded, fractional adaptation operators was used, the model satisfactorily described the regular afferent data (Table 1, 4th row; see also Fig. 11, dashed lines). The same results were also obtained when describing irregular otolith afferent dynamics (Table 1). For both afferent groups, increasing the model complexity further did not significantly increase VAF while concurrently keeping constant or reducing MSE.

For the low-pass central neurons, the simplest model allowed was a first-order function. Even though the first-order model could account for 77% of the gain and 64% of the phase variance, MSE values were quite large for both (Table 2C). When the order of both the numerator and denominator was increased simultaneously, the goodness of fit was improved, yet a significant portion of the dynamics was unexplained (VAF values of 88% for gain and 63% for phase). A third-order model (Table 2C) was the best in describing the dynamics of low-pass neurons (Fig. 11, solid cyan line). Further increasing the order and the parameters of the model did not improve the goodness of fit.

For the other two groups of central otolith neurons, identifying a function that would adequately describe the dependence of both gain and phase on frequency was more difficult. Unlike the dynamic behavior of otolith afferents, the flat and high-pass neurons exhibited frequency dependencies of phase that did not parallel those of the gain. For example, flat gains would usually be accompanied with nearly zero phase values across all frequencies. In contrast, flat neurons were characterized by significant phase lags, which could be as large as 50-60° (Figs. 10, middle, and 11, ). Similarly, the gain increases observed in high-pass neurons would usually also be accompanied by small phase leads rather than large phase lags (Figs. 10, left, and 11, ). Dissociation between gain and phase in this manner is referred to as nonminimum phase system behavior. Nonminimum phase system behavior could be explained by a term of the form (1  s)/(1 + s), which is characterized by unity gain and a phase that equals 2 tan¹ (2f) (varying between 0 and 180° as a function of frequency) (cf. Ogata 1980). This simple nonminimum phase function was used to best describe the dynamics of flat neurons with a large time constant that was outside the frequency range tested (thus fixed to  = 100 s). Since the largest phase lags observed did not exceed 90°, a fractional exponent had to be incorporated (Table 2).

For the high-pass neurons, it was necessary that a nonminimum phase system equation also be used. Within a decade of frequency, the phase of these cells changed more than 90° (in some neurons the change was closer to 180°; see Fig. 10, left). A minimum phase system function would require that the gain also increase with frequency with a very steep slope (larger than unity). As shown in Figs. 10 and 11, the gain for high-pass neurons usually increased with a lesser slope. Therefore the same nonminimum phase term used to describe the flat neurons was also utilized for the high-pass neurons with a preset time constant of 100 s (Table 2). The transfer function also included additional high-pass terms with corner frequencies more than 2 Hz that reproduced the high-frequency gain and phase properties. A single high-pass term was sufficient to explain the gain changes, but two high-pass terms were necessary to reproduce the phase behavior (Table 2). Whereas the function used is sufficient to adequately account for the high-frequency behavior, it probably falls short of describing the neural properties at low frequencies (less than 0.3-0.5 Hz). In the few neurons tested at 0.16 Hz, gain continues to drop with decreasing frequency (Fig. 10, left), whereas the transfer function used to fit the data asymptotes to a flat gain at low frequencies. Since insufficient data were available at low frequencies, the present analysis cannot specify the low-frequency transfer function of these neurons.

Maximum and minimum vector distributions

The distribution of the maximum vector directions for the 56 central otolith cells and 18 primary otolith afferents that were tested at different orientations are shown in Fig. 12. Four groups of central otolith neurons have been plotted. High-pass neurons (n = 25) included the 13 cells shown in Fig. 10, plus 12 additional neurons that had phase lags at least 60° at 0.5 Hz (but were not tested across a broad enough frequency range to be included in the transfer function analysis). Flat and low-pass central neurons were those displayed in Fig. 10 (n = 7 and n = 3, respectively). The remaining (n = 21) central otolith neurons were tested at only one or two frequencies and had sensitivity and phase values that would not allow sufficient characterization in terms of response dynamics. They were thus termed "unidentified central OTO neurons."

View larger version (38K): [in this window] [in a new window]   Fig. 12. Distribution of the maximum sensitivity vectors in the horizontal plane. Different symbols and colors are used for the different groups of central neurons (high-pass, flat, and low-pass). Cells whose dynamics could not be identified have been labeled as unidentified central OTO neurons. Afferent vectors are shown with  and · · ·. "Contralateral" refers to acceleration toward the contralateral ear (corresponding to an ipsilateral head tilt).

As shown in Fig. 12, the majority of the afferent and central cells had vectors pointing toward the contralateral ear. As a general rule, the high-pass and the few low-pass neural vectors were split between ipsilateral and contralateral. In contrast, the vectors of flat central neurons tended to point mostly contralaterally. We did not encounter any neuron whose maximum sensitivity direction was pointing within ±15° from the ipsilateral ear.

Responses during static and dynamic pitch tilts

Fourteen otolith afferents and 12 central otolith-only cells were also tested during dynamic pitch oscillations at 0.5 Hz (±10°). These pitch oscillations elicited a sinusoidally varying gravitational acceleration along the animal's naso-occipital axis with a peak amplitude of 0.17 G. The peak firing rates of these cells during pitch oscillation has been plotted versus that during fore-aft translation (0.5 Hz, ±0.2 G) in Fig. 13. Data points for both afferents and central neurons were closely aligned with a 0.87-slope line (corresponding to the ratio of peak fore-aft gravitational acceleration during pitch over peak fore-