Download Spatial and temporal frequency selectivity of neurons in

European Journal of Neuroscience, Vol. 25, pp. 1780–1792, 2007
doi:10.1111/j.1460-9568.2007.05453.x
Spatial and temporal frequency selectivity of neurons in
the middle temporal visual area of new world monkeys
(Callithrix jacchus)
Leo L. Lui, James A. Bourne and Marcello G. P. Rosa
Department of Physiology, Monash University, Clayton, VIC 3800, Australia
Keywords: extrastriate cortex, motion selectivity, primate, receptive fields, response properties
Abstract
Information about the responses of neurons to the spatial and temporal frequencies of visual stimuli is important for understanding
the types of computations being performed in different visual areas. We characterized the spatiotemporal selectivity of neurons in the
middle temporal area (MT), which is deemed central for the processing of direction and speed of motion. Recordings obtained in
marmoset monkeys using high-contrast sine-wave gratings as stimuli revealed that the majority of neurons had bandpass spatial and
temporal frequency tuning, and that the selectivity for these parameters was largely separable. Only in about one-third of the cells
was inseparable spatiotemporal tuning detected, this typically being in the form of an increase in the optimal temporal frequency as a
function of increasing grating spatial frequency. However, most of these interactions were weak, and only 10% of neurons showed
spatial frequency-invariant representation of speed. Cells with inseparable spatiotemporal tuning were most commonly found in the
infragranular layers, raising the possibility that they form part of the feedback from MT to caudal visual areas. While spatial frequency
tuning curves were approximately scale-invariant on a logarithmic scale, temporal frequency tuning curves covering different portions
of the spectrum showed marked and systematic changes. Thus, MT neurons can be reasonably described as similarly built spatial
frequency filters, each covering a different dynamic range. The small proportion of speed-tuned neurons, together with the laminar
position of these units, are compatible with the idea that an explicit neural representation of speed emerges from computations
performed in MT.
Introduction
The aim of the present study was to characterize the spatial and
temporal filtering properties of neurons in the middle temporal area
(MT, or V5), a key cortical field for the analysis of visual motion
(Dubner & Zeki, 1971; see Britten, 2003 for review). Interest in the
spatial and temporal transfer functions of neurons in different stations
of the visual pathway originates from the suggestion that images can
be coded and analysed by the brain in terms of different Fourier
components (Campbell & Robson, 1968; Glezer et al., 1973; Maffei &
Fiorentini, 1973). While at one stage this may have been seen as
incompatible with feature-based representations (Hubel & Wiesel,
1962, 1968), physiological and psychophysical studies have since
indicated that different Fourier channels, present at early stages of the
visual pathway, can be combined in specific ways to form featurebased representations (Hess, 2003).
Here, we were interested in establishing the extent to which the
neural representations of spatial and temporal frequency by cells in
area MT are scale-invariant. This type of information sheds light on
the type of information being extracted by neural populations, and
allows parallels with human perception. For example, it has been
reported that MT cells behave as invariant, logarithmically scaled
detectors of stimulus speed: the shape of the neuronal tuning functions
Correspondence: Dr Marcello Rosa, as above.
E-mail: [email protected]
Received 9 December 2006, revised 29 January 2007, accepted 31 January 2007
remain constant even though different cells have peaks corresponding
to different optimal speeds (Nover et al., 2005). There is psychophysical evidence to suggest that motion detection is based on parallel
spatial frequency lines, each presumably corresponding to an interconnected population of neurons analysing a corresponding region of
the spectrum (Hess et al., 1998). In addition, studies of MT neurons
have established a strong correlation between the preferred spatial
frequency (revealed in tests using sine-wave gratings) and the
preferred speed (revealed in tests using random dot fields, which
comprise a number of spatial frequencies; Priebe et al., 2003). This
could suggest that spatial frequency is represented as a separable
parameter at the level of MT, as is the case for most cells in the
primary visual area (V1; Tolhurst & Movshon, 1975; Priebe et al.,
2006). In contrast, it is unclear whether temporal frequency per se is
represented in the responses of MT neurons. Indeed, given that speed
can be defined as a ratio between the temporal and spatial frequencies
of a stimulus, an explicit neural representation of this parameter can
only be achieved if a neuron’s temporal frequency tuning curves
change as a function of the stimulus spatial frequency (Simoncelli &
Heeger, 2001). While evidence of the existence of such ‘inseparable’
spatiotemporal tuning in MT has been presented (Perrone & Thiele,
2001), the issue of speed selectivity has remained more controversial,
primarily due to methodological issues (Priebe et al., 2003, 2006;
Perrone, 2006). Thus, as part of the present study we also addressed
the separability of spatial and temporal frequency tuning in MT, and
its relationship to the coding of speed.
ª The Authors (2007). Journal Compilation ª Federation of European Neuroscience Societies and Blackwell Publishing Ltd
Spatiotemporal selectivity in area MT 1781
Materials and methods
Animals
Single-unit recordings were obtained from MT of 14 adult New World
monkeys (Callithrix jacchus, the common marmoset). The boundaries,
topographic organization and connections of area MT have been
established by earlier studies in this species (Rosa & Elston, 1998; Lui
et al., 2005; Palmer & Rosa, 2006a,b). Experiments were conducted in
accordance with the Australian Code of Practice for the Care and Use
of Animals for Scientific Purposes, and all procedures were approved
by the Monash University Animal Ethics Experimentation Committee.
Some of these animals were also part of parallel anatomical
investigations, having received tracer injections in the auditory cortex
of the contralateral hemisphere.
Preparation
The methods for the preparation of marmosets for single-unit
recordings have previously been described in detail (Bourne & Rosa,
2003). Anaesthesia was induced with ketamine (50 mg ⁄ kg; Parnell,
Sydney, Australia) and xylazine (3 mg ⁄ kg; Ilium, Sydney, Australia),
allowing a tracheotomy, vein cannulation and craniotomy to be
performed. The dura mater overlying the dorsal cortical surface was
covered with a thin layer of silicone oil in order to prevent desiccation.
After all surgical procedures were completed the animal was
administered an intravenous infusion of pancuronium bromide
(0.1 mg ⁄ kg ⁄ h; Organon, Sydney, Australia) combined with sufentanil
(6 lg ⁄ kg ⁄ h; Janssen-Cilag, Sydney, Australia) and dexamethasone
(0.4 mg ⁄ kg ⁄ h; David Bull, Melbourne, Australia), after which it was
artificially ventilated with a gaseous mixture of nitrous oxide and
oxygen (7 : 3). The electrocardiogram, SpO2 level and level of
cortical spontaneous activity were continuously monitored. Administration of atropine (1%) and phenylephrine hydrochloride (10%) eye
drops (Sigma Pharmaceuticals, Melbourne, Australia) resulted in
mydriasis and cycloplegia. Appropriate focus and protection of the
corneas from desiccation were achieved by means of hard contact
lenses selected by streak retinoscopy. These lenses brought into focus
the surface of a computer monitor located 40 cm in front of the
animal. Visual stimuli were presented to the eye contralateral to the
hemisphere from which the neuronal recordings were obtained.
Electrophysiological recordings and receptive field mapping
Parylene-coated tungsten microelectrodes, with exposed tips of 10 lm
(WE3001XXF; MicroProbe, Fremont, CA, USA), were directed
towards area MT based on stereotaxic coordinates and sulcal
morphology (Rosa & Elston, 1998). Provisional attribution of
recording sites to MT during the experiment was based on mapping
of multiunit receptive fields, using electrodes that penetrated vertically.
The dorsoventral trajectory of the electrodes resulted in a gradual shift
of MT receptive field centre positions, from the lower quadrant
towards the upper quadrant, and a gradual decrease in the eccentricity
of receptive fields (Rosa et al., 2000). These trends allowed us to
estimate the dorsal and ventral borders of MT during the recording
session. Confirmation of the location of the recording sites was based
on histological examination of the electrode tracks (see below).
Amplification and filtering of the electrophysiological signal was
achieved via a Model 1800 Microelectrode AC amplifier (AM
Systems, Everett, WA, USA) and a 50 Hz eliminator (HumBug;
Quest Scientific, Vancouver, Canada). The processed signal was fed
into a waveform discriminator (SPS-8701; Signal Processing Systems,
Adelaide, Australia), allowing the isolation of single-unit signals by
means of a template-matching algorithm. The neural activity was
continuously monitored by means of loud speakers, an oscilloscope
(raw signal) and computer displays (processed signal, corresponding
to the unit under investigation). For quantitative analyses, the spike
trains processed by the SPS-8701 system were collected via a highfidelity interface (ITC-16; Instrutech Corp., Great Neck, NY, USA)
into a Macintosh computer, which also controlled the visual stimulus
generation and displayed the accumulated peristimulus time histograms in real time.
The initial exploration of the receptive field boundaries was
conducted using hand-held stimuli moved at various speeds, orientations and directions of motion across the screen of a 20-inch monitor
(resolution 1024 · 768 pixels). Estimates of receptive field borders
were then refined by presenting computer-generated moving bars or
gratings while listening to the cell’s activity. Finally, in order to ensure
that the stimuli used for quantitative tests were appropriately centred
on the receptive fields we employed small stimuli (such as a 1
crosshair or square), flashed or moved at different points in the
receptive field, in order to determine the point that elicited maximal
response. Reflecting previous observations in the macaque (Raiguel
et al., 1995), we found that this usually coincided with the geometrical
centre of the excitatory receptive field. Repeated estimations of the
receptive field centre of the same cell typically yielded estimates
within 1 of each other, and never exceeded 2. This margin of error is
small relative to the dimensions of the receptive fields (Lui et al.,
2007).
Quantitative tests
Following the determination of the receptive field centre, neuronal
response properties were studied quantitatively using computercontrolled stimuli. The stimuli for these tests consisted of rectangular
patches of drifting sine-wave gratings presented against a grey
background of average luminance (2.6 cd ⁄ m2). Each trial started with
a 0.5-s presentation of the grey screen, during which measurements of
spontaneous activity were obtained. Gratings were then presented for
2 s, with the phase varied from trial to trial, at constant speed. An
intertrial interval of 4 s, during which the grey screen was presented,
separated trials.
The testing of each unit started with a qualitative assessment of
response selectivity, conducted with the objective of finding a stimulus
configuration that was capable of eliciting robust responses. Using
these estimated parameters, the cell was tested for direction of motion
selectivity using gratings that drifted in directions 20 apart, allowing
the determination of optimal direction by vector sum (Bourne et al.,
2002); all subsequent tests employed gratings that drifted in this
optimal direction. Responses to different spatial frequencies (at a
constant temporal frequency of 1.8 or 2.7 Hz, selected on the basis of
the qualitative test) and temporal frequencies (at the preferred spatial
frequency) were then examined in sequence. In addition, a subset of
neurons (94 ⁄ 220 cells; 42.7% of the sample) was tested with a matrix
of independently varied, logarithmically scaled spatial and temporal
frequencies (Perrone & Thiele, 2001; Priebe et al., 2003). Size
summation tests were also conducted for most units, as reported
separately (Lui et al., 2007). The protocol was then concluded with a
test of contrast sensitivity and a re-test of selectivity to direction of
motion, using optimal spatiotemporal parameters (Lui et al., 2005).
With the exception of the contrast-sensitivity test, all other gratings
had a Michelson contrast of 66%, which elicited near-maximal
(average 90% of peak) responses from most cells but did not result in
ª The Authors (2007). Journal Compilation ª Federation of European Neuroscience Societies and Blackwell Publishing Ltd
European Journal of Neuroscience, 25, 1780–1792
1782 L. L. Lui et al.
supersaturation (Li & Creutzfeldt, 1984). This relatively high contrast
was chosen to match empirically determined typical contrasts in
natural scenes (Bex & Makous, 2002) and to address the possibility
that ‘inseparable’ spatiotemporal tuning may be masked at nearthreshold contrasts (Priebe et al., 2003).
entire matrix of single-trial responses rather than the mean responses
to each stimulus condition. Confidence intervals for parameter
estimates were computed from the Jacobian matrix and the residuals
using the Matlab function ‘nlparci’. As detailed in the Results section,
nonparametric statistical tests were used in most analyses due to the
non-normal distributions of data.
Histology
At the end of the experiment the animal was administered an overdose
of sodium pentobarbitone (Rhone-Merieux, Brisbane, Australia) and
perfused transcardially with 0.9% saline, followed by 4% paraformaldehyde in 0.1 m phosphate buffer (pH 7.4). After cryoprotection by
increasing concentrations of sucrose, and sectioning, alternate slides
(40 lm) were stained for Nissl substance and myelin, allowing for
reconstruction of electrode tracks relative to histological borders.
Electrode tracks were reconstructed with the aid of small electrolytic
lesions (4 lA, 10 s), which were placed at various sites during the
experiment. Only cells confirmed as belonging to MT, on the basis of
the pattern of myelination observed in sections stained with the
method of Gallyas (1979), were included in the present report. The
laminar distribution of the recorded units was also determined, based
on cytoarchitectural criteria illustrated by Bourne & Rosa (2006).
Data analysis
The responses of each cell were converted into peristimulus time
histograms with a 10-ms bin width; these formed the basis of all
subsequent analysis. A single trial response was computed as the mean
firing rate over the entire duration of stimulus presentation. Spontaneous activity was calculated from the mean firing rate during the
500 ms before stimulus onset. The results to be reported here only
include cells which responded to near-optimal stimuli at a level at least
2 SD above the mean spontaneous activity. The mean spontaneous
activity was subtracted from the activity measured during the
presentation of a stimulus as a preliminary step in all analyses
described below. Tuning functions for different stimulus parameters
were then fitted using the Matlab function ‘lsqcurvefit’ (MathWorks,
Natick, MA, USA); different functions (specified in the ‘Results’
section) were used to describe the variation of different stimulus
parameters. In each case the best fit for each neuron was obtained by
minimizing the sum-squared error between the neuronal response and
the values obtained by the function. Curve fitting was based on the
Results
We have characterized the responses of 220 neurons confirmed to
be in MT by histological reconstruction. The receptive fields
encompassed both the upper and lower visual quadrants, and were
centred on eccentricities ranging between 3 and 33 (median
eccentricity 13).
Were the spatial and temporal tuning properties of MT neurons
separable?
Ninety-four neurons were tested with a matrix of independently varied
spatial and temporal frequencies in an attempt to clarify the extent to
which the responses of MT cells to these parameters are separable
(Fig. 1A). This stimulus set was constructed after initial experiments
which determined the approximate range of spatial and temporal
frequencies to which neurons in the explored part of marmoset MT
respond, so that it covered the dynamic range of the vast majority of
the units studied. As summarized in Fig. 1, surfaces describing the
spatiotemporal tuning (‘spectral receptive fields’; Perrone & Thiele,
2001) of separable units (i.e. those characterized by preference for
stimuli of a defined optimal temporal frequency, irrespective of their
spatial frequency) can be identified by isoresponse contours which are
aligned with the vertical and horizontal axes (Fig. 1B). In contrast, the
spectral receptive fields of inseparable units are characterized by
contours which are tilted in such a way that the optimal temporal
frequency depends on the spatial frequency of the stimulus. In the case
illustrated in Fig. 1C, the model neuron also shows perfect tuning to
the grating speed, with increments of spatial frequency being matched
by a corresponding increase in temporal frequency (Perrone & Thiele,
2001). Studies in the macaque monkey area MT have shown some
disagreement regarding the proportion of neurons that show true speed
tuning (Perrone & Thiele, 2001; Priebe et al., 2003), so we were also
interested in determining the existence of such cells in a different
primate species.
Fig. 1. (A) Combinations of spatial frequencies and temporal frequencies in our stimuli set (circles). The diagonal lines link combinations of spatial and temporal
frequency which result in the same speed. The numbers along the top and right of this panel indicate the corresponding speeds in degrees per second. (B and C)
Spectral receptive fields of two model neurons, illustrating the hypothetical separable and inseparable response patterns. The model neuron illustrated in C would
also be considered speed-tuned. The value of parameter Q, which indicates the dependency of temporal frequency tuning on spatial frequency, is indicated.
ª The Authors (2007). Journal Compilation ª Federation of European Neuroscience Societies and Blackwell Publishing Ltd
European Journal of Neuroscience, 25, 1780–1792
Spatiotemporal selectivity in area MT 1783
Following the study of Priebe et al. (2006) we fitted a variant twodimensional Gaussian function (Eqns 1 and 2) to the data obtained
from each neuron. This model represented the data well, with a
median r2 of 0.89.
!
ðlog2 ðsf Þlog2 ðsf opt ÞÞ2
Rðsf ;tf Þ¼Aexp
2rsf
!
"
#
ðlog2 ðtf Þlog2 ðtf opt ðsf ÞÞÞ2
1
exp 2
exp
f
2ðrtf fðlog2 ðtf Þlog2 ðtf opt ðsf ÞÞÞÞ2
ð1Þ
where
log2 ðtf opt ðsf ÞÞ ¼ Qðlog2 ðsf Þ log2 ðsf opt ÞÞ þ log2 ðtf opt Þ ð2Þ
Here R(sf,tf) is the response with respect to spatial frequency (sf) and
temporal frequency (tf). Free parameters were A, sfopt, tfopt, rsf, rtf, f
and Q, where A accounts for the size of the peak response, sfopt and
tfopt relate to the position of the peak (preferred average spatial
frequency and temporal frequency, respectively), the r parameters
represent the bandwidth of the Gaussian along the spatial and temporal
frequency dimensions, and f relates to the skew of the temporal
frequency tuning curve (the relevance of this parameter is discussed
below, where we present the temporal frequency selectivity). Parameter Q (the exponent of power function relating the optimal temporal
frequency to spatial frequency) forms the basis the present analysis. A
value of Q ¼ 0 denotes temporal frequency tuning that is spatial
frequency-invariant (Fig. 1B) whilst Q ¼ 1 denotes perfect ‘speed
tuning’, where temporal frequency tuning varies in proportion to
changes in the stimulus spatial frequency (Fig. 1C). Confidence
interval estimates (95%) for parameter Q were computed; from these
we could classify cells into categories as detailed below.
The results obtained in four of the units were inconclusive, by virtue
of yielding confidence intervals for Q which included both 0 and 1.
For three of these units the peak of the Gaussian was not adequately
captured within the range of temporal frequencies tested, while one
cell had a Q value of 0.56 and unusually high variance. These cells
were excluded from further analyses. As illustrated in Fig. 2, the
Fig. 2. Distribution of parameter Q, which describes the dependency of
temporal frequency tuning on the stimulus spatial frequency, for 90 MT
neurons. Black bars, corresponding to the majority of the sample, represent the
population of neurons for which the confidence interval of Q included 0 but did
not extend to 1. These units were deemed to be temporal frequency (TF)-tuned.
White bars, indicating cells for which the confidence interval of Q included 1
and did not overlap with 0, correspond to speed-tuned units.
majority of neurons in MT (57 ⁄ 90; 63.3% of the sample) were tuned
to the temporal frequency of a drifting grating stimulus, with
confidence intervals for parameter Q overlapping 0 and excluding 1.
In contrast, there were only nine speed-tuned cells (10% of the
sample) for which the confidence interval for Q included 1 and
excluded 0. The majority of the remaining units yielded confidence
intervals for Q lying between 0 and 1 (22 units, 24.4% of the sample),
while two units had negative Q values and confidence intervals that
did not extend to 0. Although these ‘unclassified’ units had
inseparable spatiotemporal tuning, they showed the opposite behaviour from that expected from speed-tuned cells (they preferred
progressively higher temporal frequencies as the spatial frequency of
the stimulus was decreased). The distribution of Q was unimodal and
had a median value of 0.18. In summary, the responses of
approximately two-thirds of the MT neurons were characterized by
separable spatiotemporal tuning. Among the cells which did show
inseparable spatiotemporal tuning, only a minority could be seen as
tuned to the speed of drifting gratings.
Perrone & Thiele (2001) reached the conclusion that a majority of
MT neurons have inseparable spatiotemporal tuning, including speed
selectivity, based on the comparison of different versions of a twodimensional Gaussian model fitted to the spectral receptive fields. An
‘oriented’ version of the model included a free parameter analogous to
Q which allowed rotation of the model around its peak, while in a
nonoriented version this parameter was constrained to a value
equivalent to Q ¼ 0. The rationale behind this analysis is that the
responses of units with inseparable spatial and temporal frequency
selectivities would necessarily be better described by the orientated
version of the model (e.g. Figures 3A and B), while those of units with
separable selectivities would be equally well described by the
nonoriented model (e.g. Figures 3E and F). For comparison, we
performed a similar analysis, fitting the matrix of single-trial responses
from each cell with two-dimensional log-Gaussian functions (for
details, see Lui et al., 2007). We compared the residuals to the
orientated and nonoriented fits using a sequential F-test (DeAngelis &
Uka, 2003; Nover et al., 2005), where the degrees of freedom were
adjusted according to the number of free parameters. According to this
analysis (Fig. 4), 40 units (44.4% of the sample) yielded an F-value
> 3.89 (i.e. indicating a significantly better fit by the orientated model,
at the level of P ¼ 0.05), while 25 units (27.8%) had an F-value
> 6.77 (significantly better fit at the level of P ¼ 0.01). The latter
estimate is arguably more appropriate, given that the sequential F-test
is best applied to functions that are linear in their parameters, hence
justifying a stringent criterion (compare, for example, Fig. 3C and D).
Moreover, there was good agreement (Table 1) between the classifications yielded by the confidence interval-based (Fig. 2) and residualsbased (Fig. 4) analyses. In Table 1, the columns indicate the category
of the unit according to the confidence interval-based method (Priebe
et al., 2003) while the rows indicate the classification according to the
residuals-based method (Perrone & Thiele, 2001). The figures along
each intersection correspond to the number of units that satisfied both
criteria; for example, each of the nine units classified as ‘speed tuned’
was also deemed inseparable, while 56 of the 57 temporal frequencytuned units were also deemed separable. In summary, irrespective of
the method of analysis used, the majority of MT neurons had
responses that reflected entirely, or nearly, separable spatial and
temporal frequency selectivity.
Neurons with inseparable spatial and temporal frequency tuning
were not homogeneously distributed across cortical layers. Considered
as a group, cells which were classified as either speed-tuned or
intermediate on the basis of confidence intervals of parameter Q were
significantly more common in infragranular layers (16 ⁄ 31; 51.6%)
ª The Authors (2007). Journal Compilation ª Federation of European Neuroscience Societies and Blackwell Publishing Ltd
European Journal of Neuroscience, 25, 1780–1792
1784 L. L. Lui et al.
Fig. 3. Examples of spectral receptive fields fitted to the data obtained in three MT neurons using different versions of two-dimensional log-Gaussian functions (Lui
et al., 2007). Left column: results obtained using an orientated version, which included a free parameter that allowed rotation of the model around its peak. Right
column: results obtained with a nonoriented (fixed) version of the model, in which this parameter was constrained to a value equivalent to Q ¼ 0. (A and B) A cell
with inseparable tuning. The fit obtained by (A) the free model was significantly better than (B) the one obtained by the fixed model. This neuron was also
classified as speed-tuned according to the analysis based on the confidence intervals of parameter Q. (C and D) A cell near the threshold between what we classified
as inseparable and separable tuning. (E and F) A cell with separable spatiotemporal tuning. The F-values and levels of significance are indicated for each
comparison, as are the values of parameter Q.
than in the granular (6 ⁄ 17; 35.3%) or supragranular (9 ⁄ 42; 21.4%)
layers (v22 ¼ 7.20,P ¼ 0.027). However, the majority of the neurons
classified as speed-tuned were located in layer 3 (five of nine such
units).
Selectivity for spatial frequency
We extended the study of spatial frequency selectivity to a further 120
neurons, each of which tested at a single temporal frequency. Thus, a
total sample of 214 units were used in this analysis. Typically, the
relationship between neuronal responses and grating spatial frequencies could be well described by log-Gaussian functions fitted to the
data (Eqn 3).
Rðsf Þ ¼ A expððlog2 ðsf Þ logs ðsf opt ÞÞ2 =2r2sf Þ
ð3Þ
Here, A, sfopt and r were free parameters which provided estimates of
the maximum firing rate above baseline, optimal spatial frequency and
ª The Authors (2007). Journal Compilation ª Federation of European Neuroscience Societies and Blackwell Publishing Ltd
European Journal of Neuroscience, 25, 1780–1792
Spatiotemporal selectivity in area MT 1785
Fig. 4. Comparison of the r2 values yielded by the orientated (free) and
nonoriented (fixed) two-dimensional models fitted to the spectral receptive
fields of MT neurons. The level of significance of the difference between the
fits using the orientated and nonoriented models is represented according to
shading of the circles. Black circles indicate cells for which the orientated
model provided a better fit to the data at a level of significance of P < 0.01,
while grey circles indicate those for which the fit was better only at a level of
P < 0.05.
spatial frequency tuning bandwidth, respectively (see, for example,
cells in Fig. 5). These functions provided accurate descriptions of the
data obtained from individual units, yielding a median r2 value of
0.94. In general, our sample of MT cells preferred low spatial
frequencies (median 0.18 cycles ⁄ degree; Fig. 6B) and had log-scaled
tuning bandwidths (represented by parameter r) distributed around
1.11 (Fig. 6C). Cells throughout the explored range of receptive field
eccentricities showed wide variation in terms of spatial frequency
selectivity (Fig. 7). As a result, although the optimal spatial
frequencies (Fig. 7A) were inversely correlated with eccentricity, this
relationship was relatively weak (r2 ¼ 0.035, P ¼ 0.008). In contrast,
the bandwidth of spatial frequency tuning (Fig. 7B) showed no
systematic variation with eccentricity (r2 ¼ 0.01, P ¼ 0.16).
One question raised by the wide range of spatial frequency
selectivities observed in MT is whether or not each unit performs as a
similar spatial frequency filter, albeit optimized for a different dynamic
range. For example, Fig. 6A indicates a weak (r2 ¼ 0.035), but
significant (P ¼ 0.009) negative correlation between optimal spatial
frequency and log-scaled bandwidth, which could suggest that the
representation of spatial frequency in MT deviates systematically from
scale-invariance. In order to test this issue in a more rigorous manner,
we applied to the spatial frequency domain an analysis analogous to
that applied by Nover et al. (2005) to speed. The data from each unit
were fitted with a log-Gaussian model in which parameter r was
constrained to the median value of 1.11. The fits using this ‘fixed’
model were then compared to those in the ‘free’ model described
above, in which r was optimized for each cell. In theory, a scaleinvariant representation of spatial frequency would result in the
responses of most cells being equally well described by the fixed and
free models. Figure 8 summarizes the comparison of the r2 values
yielded by the fits to the fixed and the free log-Gaussian models.
Considering the entire sample, the free model yielded a higher median
Table 1. Comparison of the classification of spatiotemporal selectivity of 90 MT neurons according to two methods of analysis
Inseparable
Separable
Total (CI)
Speed-tuned
Intermediate
TF-tuned
Unclassified
Total (Residuals)
9
0
9
14
8
22
1
56
57
1
1
2
25
65
90
Columns indicate the classification of units according to the confidence interval-based method (CI; Priebe et al., 2003), while the rows indicate the classification
according to the residuals-based method (Residuals; Perrone & Thiele, 2001). The figures along each intersection correspond to the number of units that satisfied the
criteria defined by both methods of classification.
Fig. 5. Responses of two MT neurons as a function of the varying spatial frequency of a grating. For both cells, the log-Gaussian curve obtained by using the free
model (Eqn 3) is displayed in black. The optimal spatial frequency (opt) and bandwidth (r) estimates are displayed on the top right of each panel. The fits based on
the fixed model, in which parameter r was constrained to the sample median, are displayed in grey. Bars are ± 1 SEM. (A) A scale-invariant neuron, for which the
free function did not provide a significantly better fit than the fixed function. (B) A neuron which deviated significantly from the expectations of a scale-invariant
model.
ª The Authors (2007). Journal Compilation ª Federation of European Neuroscience Societies and Blackwell Publishing Ltd
European Journal of Neuroscience, 25, 1780–1792
1786 L. L. Lui et al.
of MT cells appearing to deviate from the expectations of a scaleinvariant model (e.g. Figure 5B).
Selectivity for temporal frequency
We were able to characterize the temporal frequency selectivity of 180
MT neurons, after excluding a group of units that were not tested with
sufficiently high temporal frequencies to fully define the shapes of
their tuning curves. We found that log-Gaussian functions similar to
those used to describe the spatial frequency selectivity (Eqn 3) did not
provide adequate fits to the data obtained in a substantial proportion of
cells. However, adding an extra parameter to allow skew provided a
much better description of the data. This modified function (Eqn 4)
accounted for 96% of the variance observed in over half of the sample
(median r2 ¼ 0.97).
"
Rðtf Þ¼ A exp
Fig. 6. (A) Relationship between optimal spatial frequency (SF) and tuning
bandwidth. Reliable estimates of tuning bandwidth could not be obtained for
cells having an estimated sfopt > 0.075 cycles ⁄ degree (the lowest spatial
frequency examined), as there were insufficient data points for modelling the
‘rise’ phase of the curve. These cells, which were not included in the
calculation of the regression line, are indicated by the grey points. (B and C)
Cumulative histograms of the distributions of optimal spatial frequency and
bandwidth, respectively, with the medians indicated by arrows.
r2 (0.94) value than the fixed model (0.87; Wilcoxon signed-rank test,
z ¼ )12.65, P < 0.0001). This was expected, as the r2 value from the
model with fewer free parameters (fixed) should not exceed the r2
value from the model with more parameters (free). However, a more
reliable indication of whether the free model provided a better
description of the response of individual neurons is given by the
results of the sequential F-test, where the number of free parameters is
taken into account. For the majority of neurons (75.7%), fixing
parameter r to the median did not cause a significant decline in the
quality of the fit (F £ 7.40; P ‡ 0.01; see for example the unit
illustrated in Fig. 5A), implying scale-invariant tuning. Using a less
stringent criterion (P < 0.05) still resulted in only a minority (31.3%)
ðlog2 ðtf Þlog2 ðtf opt ÞÞ2
2ðrtf fðlog2 ðtf Þlog2 ðtf opt ÞÞÞ2
!
#
1
exp 2
f
ð4Þ
Here R(tf) represents cell response with respect to varying temporal
frequency (tf), while parameters tfopt, r and f represent the optimal
temporal frequency, tuning bandwidth and the skew of the tuning
curve, respectively. Following this analysis, we found that the optimal
temporal frequencies were distributed around a median of 2.75 Hz
(Fig. 9B). All cells included in the sample displayed bandpass tuning,
with 87.2% having bandwidths of < 2 r units (median r ¼ 1.19;
Fig. 9C). In addition, most neurons (81.7%) displayed temporal
frequency tuning that was negatively skewed (median f ¼ )0.22; see
Figs 9E and 10). Significant negative correlations were found between
(logarithmically scaled) optimal temporal frequency and bandwidth
(r2 ¼ 0.15, P < 0.001; Fig. 9A) and between optimal temporal
frequency and skewness (r2 ¼ 0.19, P < 0.001; Fig. 9D). Thus, cells
preferring higher temporal frequencies also tended to be more
narrowly tuned, and to have more negatively skewed tuning curves.
This effect is illustrated by the tuning curves of three model neurons
(calculated on the basis of the regression lines shown in Fig. 9), which
represent the typical behaviour of cells with different optimal temporal
frequencies, in Fig. 11. A model incorporating the systematic variation
Fig. 7. Spatial frequency tuning as a function of receptive field eccentricity. (A) Relationship between optimal spatial frequency and eccentricity (r2 ¼ 0.035).
(B) Relationship between bandwidth and eccentricity (no significant trend).
ª The Authors (2007). Journal Compilation ª Federation of European Neuroscience Societies and Blackwell Publishing Ltd
European Journal of Neuroscience, 25, 1780–1792
Spatiotemporal selectivity in area MT 1787
Fig. 8. Comparison of the r2 values yielded by fitting the data from each
neuron with free and fixed log-Gaussian models. In the latter, the value of
parameter r, which describes the bandwidth of the curves, was constrained to a
value corresponding to the population median. Neurons indicated by s were
equally well fitted by free and fixed curves, while those indicated by d deviated
significantly from the expectations of a scale-invariant model (P < 0.01).
monkeys. Similar to the findings of Priebe et al. (2003) in the
macaque, our data in the marmoset were normally distributed over a
broad range encompassing both speed and temporal frequency tuning.
However, we have in fact observed an even lower proportion of cells
with inseparable spatiotemporal tuning, including speed tuning.
On one hand, our results do support the contention that some MT
cells ( 10% of the sample) are capable of spatial frequency-invariant
speed tuning (Perrone & Thiele, 2001), unlike the results of most
studies of V1 cells in both cats and primates (Holub & MortonGibson, 1981; Foster et al., 1985; Friend & Baker, 1993). On the other
hand, they also indicate that the majority of neurons in MT are
selective for a specific band of temporal frequencies, or at most show
relatively minor deviations from the expectations of a model based on
stable temporal frequency tuning. Thus, cue-invariant representation
of speed must emerge from the pooling of information obtained by
separate spatial frequency channels (Adelson & Bergen, 1985;
Simoncelli & Heeger, 2001; Hess, 2003) and is likely to require
nonlinear integration, such as the suppression of responses to certain
spatiotemporal combinations, in situations where stimuli composed of
multiple spatial frequencies are presented (Priebe et al., 2003, 2006).
of parameters r and f as a function of optimal spatial frequency
resulted in significantly higher r2 values, as compared to a model in
which these parameters were constrained to the population medians
(Wilcoxon signed-rank test, z ¼ )2.79, P < 0.01). This comparison is
particularly pertinent as both models have the same number of free
parameters. This indicates that the representation of temporal
frequencies in MT cannot be adequately described as scale-invariant;
rather, the shape of the tuning curve can be more accurately described
by a model in which tuning bandwidth and skewness vary systematically as a function of the optimal temporal frequency. Finally, our
results also indicate that the optimal temporal frequencies tend to
increase in parallel with receptive field eccentricity (r2 ¼ 0.12,
P < 0.001; Fig. 12A) but no corresponding variation was observed
with respect to the bandwidth or skewness of the temporal frequency
tuning functions (Fig. 12B and C).
Discussion
We have described the spatial and temporal frequency selectivity of
neurons in area MT using first-order sine-wave gratings drifting in
optimal directions. Our results indicate that, when tested with this
method, most MT neurons show separable spatial and temporal
frequency selectivity. Although interactions between spatial and
temporal frequency selectivity were evident in approximately onethird of the units, their magnitude was in most cases incompatible with
the existence of invariant speed tuning. Analysis of the data using
criteria based on confidence intervals (Priebe et al., 2003) vs.
comparison between a model incorporating spatiotemporal interactions and a model assuming separability (Perrone & Thiele, 2001)
resulted in very similar conclusions. In conducting the latter type of
analysis we accounted for the approximately logarithmic scaling of
both spatial and temporal frequency tuning curves in MT (Nover et al.,
2005; present results), and used a model that allowed for skewed
tuning surfaces with sharp peaks (Lui et al., 2007). We believe that
these modifications to the analysis technique removed some of the
possible criticisms of previous studies, thereby providing accurate
estimates of the spatiotemporal tuning in area MT of New World
Fig. 9. Quantitative analyses of the selectivity of MT neurons to the temporal
frequency of visual stimuli. (A) Relationship between optimal temporal
frequency (TF) and tuning bandwidth. (B and C) Distributions of the optimal
temporal frequencies and bandwidths in the population. Arrows indicates the
median values of the distributions. (D) Scatter plot indicating a correlation
between optimal temporal frequency and the skewness of temporal frequency
tuning curves (estimated by parameter f). (E) Distribution of parameter f in
the sample. Neurons preferring higher temporal frequencies tended to have
narrower and more negatively skewed temporal frequency tuning curves.
ª The Authors (2007). Journal Compilation ª Federation of European Neuroscience Societies and Blackwell Publishing Ltd
European Journal of Neuroscience, 25, 1780–1792
1788 L. L. Lui et al.
Fig. 10. Responses of four MT neurons to variations of the stimulus temporal frequency (TF). For each cell the best-fitting skewed log-Gaussian curve obtained by
using the free model (Eqn 4) is displayed in black. The optimal spatial frequency, bandwidth and skewness estimates are displayed on the top right of each panel. The
grey curves represent the best-fitting fixed model, in which parameters r and f were constrained to the population medians. Bars are ± 1 SEM. While the unit
illustrated in (A) can be adequately described by a curve constrained to median parameters, those shown in (B), (C) and (D) deviate significantly from the
expectations of a scale-invariant model.
Indeed, there is evidence to suggest that MT neurons show more
explicit speed tuning when tested with broadband spatial stimuli such
as bars and random dot fields (e.g. Maunsell & Van Essen, 1983;
Felleman & Kaas, 1984; Priebe et al., 2003; Nover et al., 2005).
We have conducted our measurements at a relatively high level of
contrast, making it unlikely that the predominance of temporal
frequency tuning in our results can be explained as the result of nearthreshold responses, which could in theory fail to activate the
mechanism responsible for such a nonlinearity (e.g. Priebe et al.,
2006). Moreover, we have focused on regions of the spatial and
temporal frequency spectra corresponding to the dynamic range of the
vast majority (> 90%) of the units, and excluded from analysis cells
for which both the rising and declining phases of the tuning curves
could not be adequately captured. Thus, it is also unlikely that the
existence of spatiotemporal interactions in some units may have been
masked by fitting surfaces or curves to points representing somewhat
less relevant portions of the units’ spatiotemporal spectra (e.g. Perrone,
2006). In addition to the improvements in the methods of analysis
mentioned above, these methodological precautions may explain the
lower proportions of neurons with inseparable tuning we report in the
marmoset in comparison to earlier reports in the macaque. However, it
is also possible that there are slight interspecific differences regarding
this aspect of visual motion processing. Whether the ‘true’ proportion
of speed-tuned cells in MT is closer to 10% or 25%, the basic
observations remain: these cells are in the minority, and they represent
one end of a continuum of response properties.
Fig. 11. Temporal frequency tuning curves of three hypothetical MT units,
drawn to represent the mean bandwidth and skewness observed for cells with
different temporal frequency optima.
ª The Authors (2007). Journal Compilation ª Federation of European Neuroscience Societies and Blackwell Publishing Ltd
European Journal of Neuroscience, 25, 1780–1792
Spatiotemporal selectivity in area MT 1789
Fig. 12. (A) Relationship between receptive field centre eccentricity and optimal temporal frequency (r2 ¼ 0.12). There were no significant correlations between
(B) bandwidth or (C) skewness and eccentricity.
Whether the inseparable spatiotemporal tuning we observed in
approximately one-third of MT neurons reflects a transformation which
happens at the level of MT, or is simply relayed to this area by V1
afferents, remains open to debate. Priebe et al. (2006) have reported that
neurons with inseparable tuning also exist among the population of
complex cells in V1, including some speed-tuned cells, and Perrone
(2006) suggested that an even higher proportion of such units could
exist. Based on the fact that V1 and MT cells respond in an
approximately similar manner (in terms of spatiotemporal separability)
to stimuli formed by single sine-wave gratings, together with the notion
that inputs bypassing V1 are unimportant for sustaining the responses of
MT cells (Collins et al., 2003), Priebe et al. (2006) concluded that MT
cells almost certainly inherit their basic spatiotemporal properties from
V1. However, neurons in the koniocellular layers of the lateral
geniculate nucleus, some of which are known to project directly to
MT, have spatial properties that resemble those found in the magnocellular layers (White et al., 2001). Moreover, studies including the
exact determination of lesioned or inactivated portions of V1 have
repeatedly demonstrated that a proportion of MT neurons can respond to
moving stimuli in a direction-selective manner, even in the absence of
V1 inputs (Rodman et al., 1989; Girard et al., 1992; Rosa et al., 2000).
Thus, neural circuits that are intrinsic to MT are able to perform
relatively complex computations from inputs that show only mild
direction selectivity (White et al., 2001; Schoenfeld et al., 2002). The
present results, which demonstrate the predominance of separable
tuning in MT and suggest that units showing inseparable spatiotemporal
tuning are most commonly found in the infragranular layers, are equally
compatible with the idea that inseparable tuning emerges from
computations performed within MT. It is noteworthy that the
infragranular layers form the bulk of the MT projections to V1 (Perkel
et al., 1986; Sousa et al., 1991; Elston & Rosa, 2006), and hence the
possibility that a degree of spatiotemporal inseparability exists in V1
mainly as result of feedback connections should not be discounted.
Moreover, while the sample size remains too small for firm conclusions,
there is preliminary evidence to suggest that the relatively few neurons
which are tuned to grating speeds tend to reside in layer 3 (five out of
nine such units). Thus, it is possible that speed selectivity is encoded in
the output of MT to higher-order dorsal and ventral stream areas. This
output would be likely to reflect the integration of multiple spatial
frequency channels into a single representation which more accurately
reflects the movement of ‘real world’ objects (Priebe et al., 2006).
Spatial and temporal tuning of MT cells
Logarithmically scaled Gaussian functions modelled the spatial
frequency tuning curves well, and optimal spatial frequencies were
normally distributed over a logarithmic scale. Over 70% of the
neurons fitted the expectations of a scale-invariant model of spatial
frequency representation, a proportion which closely resembles the
result of the analysis performed by Nover et al. (2005) based on the
speed selectivity of MT neurons. Thus, at least to a first approximation, our results are compatible with a model whereby spatial
frequency is represented in a systematic manner in MT, as a result
of a similar neural operation involving combinations of inputs from
earlier stations of the visual pathway being performed in a modular
fashion. Although such a systematic mapping is in some cases
associated with columnar systems (Hubener et al., 1997; Issa et al.,
2000), to our knowledge there has been no investigation of the
existence of spatial frequency columns in MT. One significant
deviation from a strictly scale-invariant model of spatial frequency
processing is represented by the inverse correlation found between
optimal spatial frequency and tuning bandwidth (Fig. 6). This
correlation is also reflected in the tuning properties of V1 cells
(De Valois et al., 1982), hence probably reflecting a more general
limitation of the scale-invariant model when accounting for values
near the extremes of the distributions (Nover et al., 2005).
A reasonable expectation is that the spatial frequencies represented
by a neural population will be centred around a value determined by the
sampling properties of retinal ganglion cells representing the same
portion of space. However, one of the most striking characteristics of
our sample is the variability of optimal spatial frequencies for cells with
receptive fields located at a similar distance from the fovea (Fig. 7A; for
similar observations in V1 see Schiller et al., 1976; De Valois et al.,
1982). This could indicate that the information contained in the retinal
afference is recombined to generate spatial filters of multiple scales
covering each part of the visual field (De Valois et al., 1982). This
observation is in agreement with the substantial body of psychophysical evidence indicating that motion processing is closely linked to
spatial frequency channels (Hess, 2003).
Although MT neurons do resemble spatial frequency filters there are
important differences in comparison to V1. In our sample the median
value of parameter r was 1.11, which approximately equates to a halfheight tuning bandwidth of 2.5 octaves. This is rather broad in
comparison with results obtained in V1 of both cat and macaques,
where bandwidths of 1.4 octaves are typical (Movshon et al., 1978;
De Valois et al., 1982; Foster et al., 1985). Thus, MT neurons could
integrate information from different spatial frequency channels,
encoded in the V1 projections, in order to create a more robust
representation of motion, including the speed of broadband stimuli.
The responses of MT neurons are also dominated by frequencies
that are lower than those observed in marmoset V1 (Lui et al., 2006),
a finding that also appears to reflect observations in the macaque
ª The Authors (2007). Journal Compilation ª Federation of European Neuroscience Societies and Blackwell Publishing Ltd
European Journal of Neuroscience, 25, 1780–1792
1790 L. L. Lui et al.
Fig. 13. Comparison of optimal spatial frequencies of neurons in the near and
mid-peripheral representations of (A) MT and (B) V1. MT neurons had
receptive field centres located between 3 and 33 eccentricity (median 13)
while V1 cells included eccentricities between 6 and 25 (median 11). Only
cells showing strong direction selectivity, as assessed by the direction index
(Maunsell and Van Essen, 1983) were included in the V1 sample (n ¼ 36).
(De Valois et al., 1981; Priebe et al., 2003, 2006). This conclusion is
upheld by an analysis restricted to a sample of marmoset V1 cells
characterized by high direction selectivity and with a median
eccentricity matching that of the present sample of MT neurons
(Fig. 13). It is probable that this difference reflects the dominance of
MT by the magnocellular (Maunsell et al., 1990) and koniocellular
(Morand et al., 2000) channels. It is apparent from Fig. 13 that,
although the ranges of optimal spatial frequencies represented in V1
and MT overlap significantly, the ranges are not exactly matching,
with MT cells showing tuning to lower spatial frequencies than those
represented among the V1 optima. Indeed, it can be argued that the
larger receptive fields of MT neurons may be in a better position to
process the motion information contained in very low spatial
frequency channels. In theory, the sensitivity to very low spatial
frequencies could arise in MT from the nonlinear recombination of
signals originating from V1, for example by a mechanism that
suppresses the information contained in the responses of V1 cells to
high spatial frequencies, while preserving the weak inputs corresponding to their responses to low spatial frequencies. On the other
hand, it is also possible that this extension of the dynamic range
represents the contribution of alternate pathways to MT, involving
direct thalamic innervation (Stepniewska et al., 1999; O’Brien et al.,
2001; Sincich et al., 2004) or parallel medial extrastriate pathways,
which target the peripheral representation of this area (Palmer & Rosa,
2006a). In our sample, the periods of the optimal gratings (calculated
as the inverse of their spatial frequency) nearly doubled between 5
and 30 eccentricity, a relationship that approximately parallels the
increase in receptive field size centres of magnocellular geniculate
neurons in the marmoset (Kremers, 1998) over a similar range of
eccentricities. The distribution illustrated in Fig. 6 also reveals that the
peak spatial frequency represented at a given eccentricity range (as
indicated by the optimal spatial frequency of the most sensitive
neuron) declines gradually with eccentricity, with similar observations
being obtained with regards to the high cutoffs (not illustrated). These
measures may be more directly related to the limits of motion
perception in different parts of the visual field. In a study of the
marmoset lateral geniculate nucleus, White et al. (2001) reported a
similar change in the spatial resolution power of magnocellular and
koniocellular neurons as a function of eccentricity.
Although the shapes of spatial frequency tuning curves are
approximately the same throughout the range represented in MT
(with the exception of a slight broadening of bandwidth at low
frequencies), the same generalization does not apply to temporal
frequency selectivity as our results show that the shapes of the
tuning curves vary systematically as a function of optimal temporal
frequency. One possible interpretation of this finding is that temporal
frequency is not a critical parameter for the role of MT in motion
perception; rather, temporal frequency tuning could emerge for
different cells simply as a result of computations aimed at extracting
velocity. Relationships between temporal frequency optima and
bandwidth, such as the one apparent in our data (Fig. 11), have not
been reported in studies of primate V1 and V2 (Foster et al., 1985),
and hence these may emerge as an indirect consequence of other
computations (such as speed tuning) which, as discussed above,
could represent emergent properties of MT neurons. It has been
demonstrated that MT is important for speed perception (Liu &
Newsome, 2005; Nover et al., 2005) and that there is only a weak
correlation between optimal temporal frequencies and speeds
among MT cells (as opposed to spatial frequencies; Priebe et al.,
2003).
Comparisons between marmoset and macaque
Understanding common physiological features across species of
different size, phylogenetic history and habits is an important
requirement for the accurate interpretation of the relationship between
studies in humans and animal models (Rosa & Tweedale, 2005). It is
fair to expect that size differences between the macaque and marmoset
will be accompanied by differences in response properties, as the
decoding of information coming from the same amount of visual space
(both species have frontalized eyes) has to rely on fewer neurons in the
smaller animal. The brain of the marmoset is 12 times smaller than
that of the macaque (Stephan et al., 1981), a difference that is known
to translate into some differences in the pattern of afferent connections
to MT (Palmer & Rosa, 2006b).
The smaller eye of the marmoset somewhat limits the Nyquist
frequencies despite the high densities of photoreceptors and ganglion
cells (Wilder et al., 1996). Correspondingly, minimum response fields
of cortical neurons centred on similar eccentricities are approximately
twice as large in the marmoset (Rosa & Elston, 1998) as in the
macaque (Albright & Desimone, 1987; Maunsell & Van Essen, 1987).
In the present sample, the optimal spatial frequencies of MT neurons
were on average lower than those reported in the macaque, an
observation that could be explained in terms of an approximately
constant relationship between the resolution power of the retinal
mosaic and the spatial frequency selectivity of cortical cells in the
different primate species. However, it remains unclear to what extent
this is really the case, given that spatial frequency selectivity varies
with eccentricity and that the distribution of receptive field
eccentricities has not been reported in most of the studies published
to date.
ª The Authors (2007). Journal Compilation ª Federation of European Neuroscience Societies and Blackwell Publishing Ltd
European Journal of Neuroscience, 25, 1780–1792
Spatiotemporal selectivity in area MT 1791
References
Fig. 14. (A) Estimates of optimal speed for the population of MT neurons,
obtained by the ratio of the optimal spatial and temporal frequencies, as a
function of eccentricity. (B) Histogram showing the distribution of optimal
speeds in the present sample. The median is indicated by an arrow.
Our results also reveal that cells in marmoset area MT tend to
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Acknowledgements
The authors would like to acknowledge the contribution of Rowan Tweedale in
correcting the text for style and grammar. Funded by a research grant from the
National Health and Medical Research Council. Equipment items purchased
with funds provided by the Clive and Vera Ramaciotti Foundation and by the
ANZ Charitable Trust were vital for the completion of this project.
Abbreviations
A, size of the peak response; MT, middle temporal area (or V5); Q, the
exponent of the power function relating the optimal temporal frequency to
spatial frequency (Q ¼ 0 denotes exclusive temporal frequency tuning whilst
Q ¼ 1 denotes perfect speed tuning); sf, spatial frequency; rsf and rtf,
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ª The Authors (2007). Journal Compilation ª Federation of European Neuroscience Societies and Blackwell Publishing Ltd
European Journal of Neuroscience, 25, 1780–1792