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Group in Vision Science, School of Optometry, University of California, Berkeley, California 94720-2020
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ABSTRACT |
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 Abstract
 Introduction
Methods
Results
Discussion
References
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Cai, Daqing, Gregory C. DeAngelis, and Ralph D. Freeman. Spatiotemporal receptive field organization in the lateral geniculate nucleus of cats and kittens. J. Neurophysiol. 78: 1045-1061, 1997. We have studied the spatiotemporal receptive-field organization of 144 neurons recorded from the dorsal lateral geniculate nucleus (dLGN) of adult cats and kittens at 4 and 8 wk postnatal. Receptive-field profiles were obtained with the use of a reverse correlation technique, in which we compute the cross-correlation between the action potential train of a neuron and a randomized sequence of long bright and dark bar stimuli that are flashed throughout the receptive field. Spatiotemporal receptive-field profiles of LGN neurons generally exhibit a biphasic temporal response, as well as the classical center-surround spatial organization. For nonlagged cells, the first temporal phase of the response dominates, whereas for lagged neurons, the second temporal phase of the response is typically the largest. This temporal phase difference between lagged and nonlagged cells accounts for their divergent behavior in response to flashed stimuli. Most LGN cells exhibit some degree of space-time inseparability, which means that the receptive field cannot simply be viewed as the product of a spatial waveform and a temporal waveform. In these cases, the response of the surround is typically delayed relative to that of the center, and there is some blending of center and surround during the time course of the response. We demonstrate that a simple extension of the traditional difference-of-Gaussians (DOG) model, in which the surround response is delayed relative to that of the center, accounts nicely for these findings. With regard to development, our analysis shows that spatial and temporal aspects of receptive field structure mature with markedly different time courses. After 4 wk postnatal, there is little change in the spatial organization of LGN receptive fields, with the exception of a weak, but significant, trend for the surround to become smaller and stronger with age. In contrast, there are substantial changes in temporal receptive-field structure after 4 wk postnatal. From 4 to 8 wk postnatal, the shape of the temporal response profile changes, becoming more biphasic, but the latency and duration of the response remain unchanged. From 8 wk postnatal to adulthood, the shape of the temporal profile remains approximately constant, but there is a dramatic decline in both the latency and duration of the response. Comparison of our results with recent data from cortical (area 17) simple cells reveals that the temporal development of LGN cells accounts for a substantial portion of the temporal maturation of simple cells.
Classically described as simply a relay station, the lateral geniculate nucleus (LGN) is an important processing stage within the central visual pathways. The LGN is currently thought to play a major role in regulating the flow of information from the retina to the primary visual cortex (for a review, see Casagrande and Norton 1991 All experiments were performed with adult cats or kittens at ages 4 and 8 wk postnatal. All of the animals were reared in a normal environment. Kittens at 4 and 8 wk postnatal weighed 320-400 g and 750-1,000 g, respectively. Adult cats ranged in weight from 2.2-4.2 kg. The methods and procedures used in this study are quite similar to those we used to study spatiotemporal RF properties in the visual cortex (see DeAngelis et al. 1993a Experimental preparation
Under general anesthesia, the animal is connected to equipment for life support and for continuous monitoring of vital signs (EEG, ECG, CO2 level and intratracheal pressure). Standard surgical procedures (see DeAngelis et al. 1993a Recording procedures
After isolating spikes from an LGN neuron, a three stage experimental protocol is followed. 1) A preliminary search is conducted to localize the cell's RF and to determine its preferred spatial frequency (SF). 2) Quantitative measurements are obtained, with the use of drifting sinusoidal gratings, to assess the cell's selectivity for orientation, spatial frequency, and temporal frequency, as well as to classify the cell as X or Y, lagged or nonlagged. 3) A detailed spatiotemporal RF profile is obtained using the reverse correlation technique (described below). For each neuron, this three-step experimental protocol requires approximately 1.5-2.5 h to complete.
Reverse correlation analysis
To characterize the spatiotemporal RF organization of LGN cells, we used a one-dimensional (1-D) version of the reverse correlation algorithm (Jones and Palmer 1987
In this study, complete spatiotemporal receptive field profiles (X-T profiles) have been obtained for 144 LGN neurons. This population consists of 67 cells from 3 adult cats, 41 cells from 3 kittens at 8 wk postnatal, and 36 cells from 6 kittens at 4 wk postnatal. There are 56 X cells and 11 Y cells among the population from the adult cats, 34 X cells and 7 Y cells in the 8 wk population, and 32 X cells and 4 Y cells in the 4 wk population. The proportions of X and Y cells in all three age groups are similar to those reported in other studies (see Lennie 1980 General aspects of spatiotemporal RF structure
Figure 2 shows a spatiotemporal receptive field profile (X-T plot) for an ON-center LGN neuron from an adult cat (see METHODS for details concerning the construction of X-T profiles). Spatial position (X) is plotted along the horizontal axis and time (T) is plotted on the vertical axis. As described earlier, the areas enclosed by solid contour lines have positive values and represent bright-excitatory subregions; areas enclosed by dashed contours have negative values and represent dark-excitatory subregions.
Development of temporal receptive field structure
Figure 4 illustrates the analysis we have used to quantify differences in temporal RF structure between cats of different ages. First, we find the spatial position (X) at which the X-T profile has its largest positive value (for RFs with a bright-excitatory center response) or negative value (for RFs with a dark-excitatory center response). This position is indicated by a vertical line through the X-T profile of Fig. 4A. A temporal response profile, R(T), is then obtained by slicing through the X-T profile at this position (filled circles in Fig. 4B). The temporal profile is then fit with the following function:
Lagged and nonlagged cells
LGN cells in the cat can be divided into lagged and nonlagged types based on the temporal response pattern exhibited in response to a flashing spot stimulus (Humphrey and Weller 1988 Development of spatial receptive field structure
In this section, we examine how spatial aspects of LGN RFs mature during normal postnatal development. The spatial properties that we consider are RF center size, surround size, and the relative strengths of the center and surround responses.
A spatiotemporal RF model for LGN cells
Having characterized the spatiotemporal RFs of LGN neurons, we wish to construct a simple model that can account for the main features of the data. It is well established that a difference of Gaussians (DOG) function (Rodieck 1965
In this study, we have applied a one-dimensional version of the reverse correlation technique to examine the spatiotemporal RF organization of LGN neurons in adult cats, as well as in kittens at the ages of 4 and 8 wk postnatal. The reverse correlation technique is well-suited to reveal important basic features of the LGN RF. We have investigated the center-surround organization, spatial symmetry of the center and the surround, temporal response profiles of lagged cells and nonlagged cells, and the interactions between space and time (i.e., separability). Our spatiotemporal maps of LGN RFs consist of clear center and surround regions. As reported previously (e.g., Dawis et al. 1984 The spatiotemporal organization of LGN receptive fields
The RFs of neurons in the retino-geniculo-cortical pathway were originally described simply as functions of space (e.g., Hubel and Wiesel 1962 Development of LGN receptive field organization
Postnatal development of neuronal response properties in the cat's visual system has been the subject of numerous studies (for reviews, see Fregnac and Imbert 1984 Comparison with cortical simple cells
We reported previously (DeAngelis et al. 1993a
INTRODUCTION
Abstract
Introduction
Methods
Results
Discussion
References
). Although the LGN provides the primary afferent input to striate cortex, the receptive field (RF) organization of cortical neurons in the cat (including those in the input layers) differs dramatically from that of their LGN inputs (e.g., Hubel and Wiesel 1962). To understand the transformations that take place at the geniculo-cortical synapse, it is necessary to have a detailed understanding of the RF structure of both LGN neurons and cortical neurons.
; Emerson et al. 1987; Jacobson et al. 1993; Jones and Palmer 1987; McLean et al. 1994; Shapley and Reid 1991). A major advantage of these techniques is that they provide a characterization of RFs in the joint domain of space and time, and this representation yields a more comprehensive understanding of response properties than traditional static RF profiles. Thus far, nearly all of the work undertaken using these techniques has concentrated on elucidating the RF dynamics of cortical cells (see DeAngelis et al. 1995 for a review). For example, it has been shown that the RFs of simple cells can be either space-time separable or inseparable (DeAngelis et al. 1993a; McLean and Palmer 1989; McLean et al. 1994). For the latter type, the positions of RF subregions change smoothly during the time course of the response; thus, there is no unique spatial or temporal RF profile. Moreover, it has been shown that space-time inseparability constitutes a quasilinear mechanism for direction selectivity in simple cells (DeAngelis et al. 1993b; Jagadeesh et al. 1993; McLean and Palmer 1989; McLean et al. 1994; Reid et al. 1987).
initially proposed that the RF of a simple cell is constructed from a group of geniculate cells having RFs appropriately arrayed in space, a hypothesis that has recently received some direct experimental support (Chapman et al. 1991; Ferster et al. 1996; Reid and Alonso 1995). The recent characterization of simple cell RFs in the joint space-time domain has raised new questions concerning the genesis of these RFs. For example, how might LGN afferents be combined to construct the space-time inseparable RFs of direction-selective simple cells? One possibility (Saul and Humphrey 1992) is that direction-selective simple cells receive inputs from two physiologically distinct groups of LGN cells, the lagged and nonlagged cells, that have markedly different temporal response properties (Humphrey and Weller 1988; Mastronarde 1987; Saul and Humphrey 1990). Alternatively, there could be classes of LGN cells that exhibit a form of space-time inseparability similar to simple cells. Another possibility is that space-time inseparable RFs are constructed within the cortex, by combining the outputs of simple cells with separable RFs that differ in spatial and temporal phase (e.g., Adelson and Bergen 1985; Watson and Ahumada 1985).
performed an extensive study of the organization of LGN RFs; however, their response-plane technique did not have sufficient temporal resolution to reveal the intrinsic dynamics of the RFs. Methods utilized more recently (Eckhorn et al. 1993; Golomb et al. 1994; Reid and Shapley 1992) have overcome this problem, but data from only a few cells were presented in these reports. Hence, a major goal of the present study is to provide a detailed characterization of LGN RFs in the space-time domain.
; Ikeda and Tremain 1978; Tootle and Friedlander 1989), relatively little is known about development of temporal response properties in the LGN (Daniels et al. 1978; Mangel et al. 1983). In a recent study of the postnatal development of cortical RFs in the cat (DeAngelis et al. 1993a), we found that the temporal structure of simple cell RFs matures much more slowly than the spatial structure. Thus it is of interest to determine if this difference may be accounted for at the level of the LGN.
; Jones and Palmer 1987) to map the spatiotemporal RFs of LGN cells recorded from adult cats and from kittens at 4 and 8 wk postnatal. Our results from adult cats reveal interesting properties of the LGN RF that can only be demonstrated in the joint space-time domain. The spatiotemporal RF profiles of most LGN cells are shown to be spatiotemporally inseparable, although the pattern of space-time inseparability shown by LGN cells is markedly different from that observed for cortical simple cells (DeAngelis et al. 1993a; McLean and Palmer 1989; McLean et al. 1994). Temporal response profiles of both the center and surround are typically biphasic, but the response of the surround is usually delayed with respect to that of the center. Moreover, the first temporal phase of the surround typically merges into the second temporal phase of the center. We show that this behavior is consistent with a simple spatiotemporal model of the LGN receptive field, in which both the center and surround profiles are space-time separable but temporally offset. RFs of lagged and nonlagged cells can be distinguished by the phase of their temporal responses, and we demonstrate that this difference can account for the characteristic response patterns of lagged cells, namely their long latency and "anomalous" offset discharge (Humphrey and Weller 1988; Mastronarde 1987).
) is partially accounted for by the development of subcortical structures.
METHODS
Abstract
Introduction
Methods
Results
Discussion
References
). An abbreviated version of these methods is given here with emphasis on aspects that are specific to the LGN.
) are used to prepare the cat for single-unit recording. The animal is then secured in a stereotaxic apparatus and paralyzed with an injection of gallamine triethiodide (Flaxedil, 2%), which is subsequently infused at a rate of 10 mg·kg
1·h1 to maintain paralysis. Following the induction of paralysis, the animal is artificially respired with a gas mixture of 70% N2O, 29% O2, and 1% CO2. Sodium thiamylal (Surital) is also infused at 1 mg·kg1·hr1 to maintain adequate anesthesia. A round section of skull and dura (~5 mm in diam) is removed to allow insertion of tungsten-in-glass electrodes (Levick 1972), which have an impedance of 2-10 M
. For adult cats, the craniotomy is centered at Horsley-Clarke coordinates A6L9. For 4-wk-old kittens, the position of the craniotomy is set at coordinates A3L8, based on the data of Norman (1974). For 8-wk-old kittens, the craniotomy is centered halfway between the coordinates used for adult cats and 4-wk-old kittens. For kittens, we often had to adjust the position of our electrodes within the craniotomy, in order to enter the LGN near the representation of the area centralis. This is due to variation between animals in the position of the LGN within the head (Norman 1974). Pupils are dilated with atropine (1%) and nictitating membranes are retracted with 5% phenylephrine hydrochloride (Neo-Synephrine). Contact lenses (+2.0 diop.) with 3 mm artificial pupils are then positioned on each cornea.
; Wilson et al. 1976). Histological analysis and the characteristic sequence of eye dominance of the cells in each penetration confirmed that all cells included in this report were recorded from layers A and A1 of LGN.
; Olson and Freeman 1978). Upon lowering the electrodes into the LGN and isolating action potentials of single neurones, the RFs are initially explored with a bar of light that is moved manually.
), the stimuli are presented monocularly while the unresponsive eye views a blank CRT screen of the same mean luminance as the gratings (the CRT screens have a mean luminance of 45 cd/m2, subtense of 28 × 22°, resolution of 1,024 × 804 pixels, and are refreshed at 76 Hz). The stimulus is typically a round patch of drifting, sinusoidal-luminance grating with a diameter of 10-15° and a Michelson contrast of 50%. When spatial frequency or orientation is varied, the temporal frequency of the stimulus is fixed at 2.0 Hz. To measure spatial frequency tuning, a sequence of gratings having eight different spatial frequencies (0.14-1.5 c/deg) is presented in randomized order. Each grating is presented for 4 s, during which a peristimulus time histogram (PSTH) of the response is accumulated. Successive stimuli are separated by a period of 2 s during which the animal views blank screens of the same mean luminance as the gratings. After each different stimulus is presented once, the stimulus sequence is re-randomized and presented again, until each stimulus has been shown 4-6 times. To measure the orientation bias of LGN cells (Daniels et al. 1977; Vidyasagar and Urbas 1982), a sequence of gratings is presented that spans 360° of orientation (in 12 equally spaced steps). For the temporal frequency test, spatial frequency and orientation are set to the optimal values obtained previously. Typically, eight temporal frequencies are tested in the range from 0.26-38.0 Hz. To construct tuning curves, Fourier analysis is performed on the PSTHs. The mean firing rate and the first harmonic of the response are computed.
), counterphase-modulated sinusoidal gratings are presented at several positions across the RF. For this test, the spatial frequency is adjusted to be ~1.5 octaves above the optimal value, because this provides a more sensitive probe for the Y-type nonlinearity (Hochstein and Shapley 1976). The spatial phase of the grating is varied from 0 to 180° (in 15° steps) in blocks of randomly interleaved trials. At the spatial phase that elicits the smallest response, the ratio of the second harmonic to the first harmonic is calculated (after spontaneous firing rate is subtracted). Based on the criteria of Hochstein and Shapley (1976), cells are classified as X type if the ratio is less than or equal to 1.0, whereas cells with a ratio larger than 1.0 are classified as Y type. To classify cells as lagged or nonlagged, a high contrast (90%) flashing spot is presented within the center of the RF. The luminance of the spot is modulated over time by a 1 Hz square wave (see Fig. 7, inset), and cells are classified as either lagged or nonlagged based on the half-rise time of the response (Mastronarde 1987). Additional response features of lagged cells, such as the "anomalous" peak at stimulus offset, are also used in the classification (Hartveit and Heggelund 1992; Humphrey and Weller 1988; Mastronarde 1987; Saul and Humphrey 1990).
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FIG. 7.
This figure highlights the major differences between lagged and nonlagged cells in the temporal domain. On the left are X-T profiles for a lagged X-cell from an 8-wk kitten (A) and a nonlagged X-cell from an adult cat (B). To predict the cells' responses to a flashing spot, a portion of the X-T profile (delimited by the dashed lines), which corresponds to the size and location of the spot stimulus, is summed over space. Resulting temporal response profiles are shown in panels C and D. Notice that for the lagged cell, the amplitude of the second peak of the response is larger; whereas for the nonlagged cell, the first response peak dominates. Temporal response profiles in C and D are then convolved with the temporal waveform of the flashing spot stimulus (between panels E and F) to obtain linear predictions of the cells' flash responses. These predicted responses (thick curves) are shown in panels E and F, along with the measured responses (thin curves) to the flashing spot stimulus. The PSTHs shown in E and F are normalized and span one temporal cycle of the stimulus. Stimulation parameters for the X-T data in A: flash duration = 26 ms, bar size = 15° × 0.7°, bar orientation = 90°, right eye. For the X-T data in B: flash duration = 13 ms, bar size = 15° × 0.4°, bar orientation = 90°, left eye.
; Palmer et al. 1991; see DeAngelis et al. 1993a for additional details). The algorithm is diagramed schematically in Fig. 1A. The visual stimulus is a pseudo-random sequence of bright and dark bars that are presented at 20 or 30 locations across the stimulus patch shown in Fig. 1A. This stimulus patch is positioned so that its center corresponds to that of the RF, as determined in the search procedure described previously. The width of the stimulus patch is adjusted so that it covers the entire width of the RF. Since many LGN neurons are known to have an orientation bias (Daniels et al. 1977; Vidyasagar and Urbas 1982), the orientation of the bars is adjusted to the preferred orientation of the cell, as determined from the orientation tuning curve obtained with gratings. The bar stimuli are typically 15 in length and 0.2-0.5 in width, and are usually presented for a duration of 13 ms (one video frame) or 26 ms. These parameters are varied somewhat from cell to cell, according to the spatial and temporal resolution of the RF (see DeAngelis et al. 1993a for details about choosing the spatial and temporal parameters of the reverse correlation stimulus). In general, the stimuli are chosen to be as narrow as possible in both space and time so that they still elicit a measurable response from the neuron. For cells that respond to high spatial frequencies, narrow stimuli must be used so that the spatial resolution of the reverse correlation technique is higher than that of the cell's RF, which can be determined from the spatial frequency tuning curve obtained using gratings. Similar considerations apply to the choice of stimulus duration, which can be guided by the measured temporal frequency tuning. Attention was paid to keeping the stimuli as brief as possible (13 ms for most cells from adults and 26 ms for most cells from kittens), so that temporal response profiles (e.g., Figs. 2 and 6) are not artificially extended in time (temporal blurring).
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FIG. 1.
To obtain detailed spatiotemporal recptive field (RF) profiles, a one-dimensional (1-D) reverse correlation algorithm is used. A: randomized sequences of long bright and dark bars (typically 15° length, 0.4-0.7° in width, and flashed for 13 or 26 ms) are presented in an area that is centered over the lateral geniculate nucleus (LGN) cell's RF. Orientation of the bars is adjusted to the optimal orientation of the cell, as estimated from stimulation with drifting sinusoidal gratings. Centers of the bars are positioned at discrete spatial locations (usually 20 or 30) along a line segment that transects the RF at an angle orthogonal to the optimal orientation (for clarity, only 15 bar positions are shown here). Assuming a correlation delay of T ms, for each spike in the recorded spike train, the position and polarity (bright or dark) of the causal stimulus is found and a histogram bin at that position is incremented. B: two histograms are initially constructed, one for responses to bright bars and one for responses to dark bars. Bins that are incremented are indicated in the graph. Bar heights in the two bins are drawn disproportionately for illustration purposes. A composite RF profile is then obtained by subtracting the dark bar responses from the bright bar responses. Composite RF profile shown here was obtained from an adult cat using a correlation delay of T = 30 ms. In this profile, positive values indicate excitation by a bright bar, negative values denote excitation by a dark bar.
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FIG. 2.
Construction and interpretation of a spatiotemporal RF profile (X-T plot). Panels A and B: spatial RF profiles determined at two different values (T = 25 ms and T = 60 ms) of the reverse correlation delay. By obtaining additional spatial RF profiles over a range of finely spaced values of T, we derive a comprehensive picture of how spatial RF structure evolves over the time course of the response. The resulting picture is shown as a contour plot in this figure. In the contour plot, areas enclosed by solid contours correspond to bright excitatory regions, areas enclosed by dashed contours correspond to dark excitatory regions. Tick marks along the horizontal and vertical axes are drawn at 1° and 50 ms intervals, respectively. Panels C and D: temporal response curves obtained by slicing through the X-T data at different spatial positions (indicated by the vertical lines through the X-T plot). The curve in panel C is derived by slicing through the center of the RF, whereas the curve in D is obtained by slicing through one flank of the surround. Values shown along side the temporal response curves indicate the time delays at which the curves have their first peak (25 ms for C) or trough (35 ms for D). Stimulation parameters for this X-cell were as follows: flash duration = 13 ms, bar size = 15° × 0.5°, bar orientation = 30°, left eye.
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FIG. 6.
Summary of developmental changes in temporal RF structure. A: temporal response profiles for populations of neurons (both ON- and OFF-center) from adult cats (solid curve), 8-wk kittens (dot-dashed curve), and 4-wk kittens (dashed curve). Each curve is generated by averaging the best-fitting temporal response curves for all cells within the same age group. In doing so, the sign of the responses was inverted for OFF-center cells, to avoid cancellation. Notice that from 4 wk to 8 wk, the predominant change is an increase in the strength of the second phase of the response, whereas from 8 wk to adulthood, the change is approximately a scaling in the time domain. B: comparison between ON and OFF center cells for each age group. Summary temporal profiles for the OFF center cells are inverted for easier comparison.
). In the composite profile, regions excited by bright stimuli are shown as positive histogram bins, whereas regions excited by dark stimuli are shown as negative histogram bins. This composite profile describes the one-dimensional spatial structure of the RF for one particular value of the reverse correlation delay (T = 30 ms).
; McLean and Palmer 1989; McLean et al. 1994). This is achieved by computing spatial RF profiles for a series of correlation delays (T) between stimulus and response. In Fig. 2, A and B, spatial RF profiles are shown for two different values of T (25 and 60 ms, respectively). By computing spatial profiles for a series of finely spaced values of T, we can construct a spatiotemporal response matrix which shows how RF structure evolves in the time domain after the onset of the stimulus. This spatiotemporal RF profile (or X-T plot), illustrated in Fig. 2, is a joint function of space (X) and time (T). Each X-T profile typically has a resolution of 20 to 30 points in both space and time. The X-T data are smoothed using a small Gaussian filter, which removes high frequency noise in the data. The parameters of this filter are chosen such that its roll-off does not substantially attenuate frequencies within the spatiotemporal pass-band of a given neuron. Once smoothed, the X-T data are interpolated and plotted as an isoamplitude contour map (see Fig. 2). Contours are drawn at 12 equally spaced amplitude levels ranging from 
A to +A, where A is the maximum absolute value of the data. In each X-T profile, the areas enclosed by solid contour lines have positive values and represent bright-excitatory RF subregions. Areas enclosed by dashed contours have negative values and represent dark-excitatory RF subregions. The relative strengths of different subregions can be judged by the number of contour lines which enclose these regions.
; DeAngelis et al. 1993a; Eckhorn et al. 1993; Jones and Palmer 1987), we have chosen to use long, thin bars in our reverse correlation procedure. There are several benefits of using this one dimensional mapping technique. Compared with short bars or squares, long bars often elicit a much stronger response from the neuron being tested, allowing us to obtain X-T profiles from cells that respond poorly to the full 2-D stimulus ensemble (such as many cells from young kittens). Due to increased spatial summation, these long bars are also more effective in eliciting responses from the surrounds of LGN cells. Furthermore, by restricting the stimulus to one spatial dimension, a good X-T profile can be obtained in a fraction of the time required for the 2-D method. This is very helpful when obtaining data from young kittens since recording stability is more limited in these animals. The major disadvantage associated with our 1-D algorithm is that we lose information concerning the Y dimension of the RF. Thus, for example, the elliptical RFs of many LGN cells (Cleland and Enroth-Cugell 1968), which can be seen easily in two dimensional spatial RF maps, are not revealed using our stimulus. However, our main goal is to characterize the X-T profiles of LGN cells, so this loss of information is of little consequence.
RESULTS
Abstract
Introduction
Methods
Results
Discussion
References
). Because we limited our samples to laminae A and A1, we confined our investigation to X and Y cells and avoided W cells located in the C laminae (Cleland et al. 1976; Wilson et al. 1976). Statistically, we find no significant differences between X cells and Y cells with respect to several spatial and temporal parameters of the RF (described below). However, our population of Y cells in this study is rather small. Thus, data from X and Y cells are combined in this report.
; Mastronarde 1987; Saul and Humphrey 1990). This is likely to be due to differences in the impedance of the recording electrodes used in this and in previous studies (Mastronarde 1987; Saul and Humphrey 1990). For all cells included in this report, RFs were located within 20° of the area centralis.
; Derrington and Lennie 1982; Enroth-Cugell et al. 1983; Kaplan et al. 1979). Our results provide a direct demonstration of this effect.
for details). Like the ON-center cell of Fig. 2, virtually all nonlagged cells have a temporal response profile in which the first phase is dominant (see Fig. 5E). Thus, for ON-center cells, the temporal response (of the center region) has a bright-excitatory phase followed by a dark-excitatory phase (see Fig. 2C); OFF-center cells have a dark-excitatory phase followed by one that is bright-excitatory (see Fig. 3, A and B). For lagged cells, as discussed below, these simple rules do not usually apply.
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FIG. 5.
Postnatal development of temporal RF parameters. A: histogram showing distributions of Tpeak for the three age groups. Black, grey, and white bars denote data from adult cats, 8-wk kittens, and 4-wk kittens, respectively. Black, grey, and white arrows above the histograms indicate the geometric means for each population. B: mean values of Tpeak plotted as a function of age. Error bars represent 95% confidence intervals. By the Tukey criterion, if the error bars overlap, then two values are not significantly different (atP > 0.05 since 95% confidence intervals are used). C: distributions of response D for adult cats and kittens. Conventions as in A. D: mean duration plotted as a function of age. E: histogram of the biphasic indices of temporal response profiles. F: mean biphasic indices for the different age groups.
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FIG. 3.
X-T plots are shown for LGN cells from cats of different ages. The format of these contour plots is the same as that of Fig. 2, with horizontal and vertical tick marks corresponding to intervals of 1° and 50 ms, respectively. A: X-T profile for an OFF-center X-cell from an adult cat. Flash duration = 13 ms, bar size = 15° × 0.5°, bar orientation = 210°, left eye. B: data from another OFF-center X-cell from an adult. Flash duration = 13 ms, bar size = 20° × 0.5°, bar orientation = 200°, left eye. C: X-T profile for an ON-center X-cell from an 8-wk kitten. Flash duration = 26 ms, bar size = 15° × 0.3°, bar orientation = 0°, right eye. D: data from another ON-center X-cell from an 8-wk animal. Flash duration = 26 ms, bar size = 15° × 0.5°, bar orientation = 150°, left eye. E: RF profile for an OFF-centerX-cell from a 4-wk kitten. Flash duration = 26 ms, barsize = 20° × 0.6°, bar orientation = 270°, left eye. F: data from an ON-center X-cell from a 4-wk kitten. Flash duration = 26 ms, bar size = 15° × 0.7°, bar orientation = 0°, right eye.
, 1995; McLean and Palmer 1989; McLean et al. 1994). For these simple cells, the RF subregions are oriented along an oblique axis in the space-time domain.
![<IT>F</IT>(<IT>T</IT>) = <IT>K</IT><SUB>1</SUB> × <FR><NU>[<IT>c</IT><SUB>1</SUB>(<IT>T − t</IT><SUB>01</SUB>)]<SUP><IT>n<SUB>1</SUB></IT></SUP><IT>e</IT><SUP>−<IT>c</IT><SUB>1</SUB>(<IT>T−t</IT><SUB>01</SUB>)</SUP></NU><DE><IT>n</IT><SUP><IT>n<SUB>1</SUB></IT></SUP><SUB>1</SUB><IT>e</IT><SUP>−<IT>n<SUB>1</SUB></IT></SUP></DE></FR>](/content/vol78/issue2/fulltext/1045/img001.gif)
This function, F(T), is the difference of two Gamma functions. K1, K2, c1, c2, t01, t02, n1, n2 are free parameters. Our choice of this function is essentially arbitrary and is simply based on the fact that this formulation fits the data quite well (e.g., Fig. 4B), including the small minority of neurons that exhibit either triphasic or monophasic responses. Similar formulations have been used to model the temporal response characteristics of cortical neurons (Adelson and Bergen 1985
![− <IT>K</IT><SUB>2</SUB>× <FR><NU>[<IT>c</IT><SUB>2</SUB>(<IT>T − t</IT><SUB>02</SUB>)]<SUP><IT>n<SUB>2</SUB></IT></SUP><IT>e</IT><SUP>−<IT>c</IT><SUB>2</SUB>(<IT>T−t</IT><SUB>02</SUB>)</SUP></NU><DE><IT>n</IT><SUP><IT>n<SUB>2</SUB></IT></SUP><SUB>2</SUB><IT>e</IT><SUP>−<IT>n<SUB>2</SUB></IT></SUP></DE></FR>](/content/vol78/issue2/fulltext/1045/img002.gif)
(1)
; Watson and Ahumada 1985). A typical fit is shown as the solid curve in Fig. 4B. To quantitatively characterize the temporal response profile, and to facilitate comparisons between different age groups, we introduce three temporal response parameters: peak response latency (Tpeak), duration (D), and biphasic index (Rb = |PB/PA|) (see Fig. 4B).
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FIG. 4.
Quantitative analysis of temporal response profiles. X-T data are shown for the same cell as in Fig. 2. By slicing through the peak of the X-T profile, parallel to the T axis (indicated in panel A by the vertical line), a temporal response profile (filled circles in B) is obtained. Temporal response profile is fit with the difference of two Gamma functions (see Eq. 1). Solid curve in panel B shows the best fit of Eq. 1 to the data. Three parameters are extracted from the fit. Peak response time (Tpeak) is defined as the time at which the first peak occurs. The biphasic index is the absolute value of the ratio of the amplitude of the second peak (PB) to that of the first (PA). Duration (D) of the temporal response profile is obtained at 1/e (0.367) of the peak value of the temporal envelope (dashed curve).
for simple cells, we compute the duration (D) of the RF from the envelope of the best fitting temporal function, F(T). The envelope, E(T) (dashed curve in Fig. 4B), of the cell's temporal response profile is obtained as follows. First, the Hilbert transform of the temporal response function, H[F(T)], is obtained by shifting the phase of all frequency components in F(T) by 90 (Bracewell 1978; Gabor 1946). The temporal response function, F(T), and its Hilbert transform, H[F(T)], are said to form a quadrature pair. The envelope of the cell's temporal response, E(T), is then computed as the vector sum of these two quadrature components
The time duration, D, of the RF is then defined as the width of the envelope, E(T), at some criterion level. For convenience, we have computed the duration of the temporal envelope at the level which is 1/e (or 0.367) of the peak envelope value. For the cell of Fig. 4, the RF duration, measured in this manner, is D = 60 ms.
![<IT>E</IT>(<IT>T</IT>) = <RAD><RCD><IT>F</IT>(<IT>T</IT>)<SUP>2</SUP><IT>+ H</IT>[<IT>F</IT>(<IT>T</IT>)]<SUP>2</SUP></RCD></RAD>](/content/vol78/issue2/fulltext/1045/img003.gif)
(2)
2, P > 0.05) following logarithmic transformation. The black, gray, and white arrows above the histograms show geometric means of the data for the three populations.
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FIG. 9.
Quantitative summary of changes in spatial RF parameters with age. The format of this figure is identical to that of Fig. 5. A: histogram of RF center size (2 
c) for cats of different ages. B: RF center size plotted against age. Filled circles give the geometric mean and error bars represent the 95% confidence interval. C: distributions of the surround size, 2s, are shown in this histogram. D: changes in mean surround size (2s) for cats of different ages. E: histogram showing the ratio of the amplitudes (As/Ac) of the surround and center components of the RF for LGN cells from cats of different ages. F: the mean surround/center amplitude ratio (As/Ac) is plotted against age.
; Mastronarde 1987). Using a similar test (described below; see also METHODS), we also find it possible to distinguish lagged and nonlagged cells.
reached the same conclusion by inferring the temporal response profile from temporal frequency tuning curves. Our results show that the temporal phase shift is clearly revealed in the spatiotemporal RF profile. Given that our sample of lagged neurons is very small, however, further work will clearly be necessary to quantify differences in spatiotemporal RF structure between lagged and nonlagged cells.
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FIG. 8.
The fitting procedure used to quantify spatial aspects of LGN RF structure is illustrated here. A: an X-T profile is shown for an ON-center X-cell recorded from an adult cat (same cell as in Figs. 2 and 4). B: a 1-D spatial RF profile (filled circles) is obtained by taking a cross section through the X-T data at T = Tpeak, as indicated by the horizontal line through the X-T profile in A. Solid curve represents a difference of Gaussians (DOG) function that best fits the spatial profile. C: center and surround components of the best-fitting DOG function are shown here. Parameters 2 c and 2s (see Eq. 3) are used as metrics of the sizes of the RF center and surround, respectively.
). It has also been reported that the RF profiles of LGN cells may be asymmetric (e.g., Dawis et al. 1984). This can be seen in Fig. 8B, where the strengths of the two flanks of the surround are slightly dissimilar. Some degree of asymmetry is exhibited by many of the cells that we have studied. This behavior can be accounted for by a model in which the RF is described in terms of a difference of two Gaussian components that may be spatially offset (Dawis et al. 1984; Enroth-Cugell et al. 1983).
). We have not found any evidence that these nonlinear subunits are represented in the X-T data for Y cells. Thus we conclude that the X-T profiles that we obtain for Y cells represent only the linear response component. This issue will be addressed in considerably more detail in another paper (D. Cai, G. DeAngelis, and R. Freeman, unpublished results).
In this formulation, Ac and As are the amplitudes of the center and surround Gaussians, 2
(3)
c and 2s are the respective sizes of the center and surround (defined as the full width of the Gaussian at a criterion level of 0.367 times the amplitude), and xc, xs give the center positions of the two components. The solid curve in Fig. 8B shows the DOG function that best fits the spatial RF profile of this adult LGN X-cell. Figure 8C shows the two Gaussian components of the fit. Parameters of the best-fitting DOG function have been used to compare the RFs of LGN cells recorded from adult cats and kittens.
c; Fig. 9A), surround size (2s; Fig. 9C), and surround/center amplitude ratio (As/Ac; Fig. 9E). Data from adult cats, 8-wk kittens and 4-wk kittens are represented in black, gray, and white, respectively. Because most of the data in Fig. 9 are not normally distributed, statistical analyses were performed on the logarithm of the data. All distributions were indistinguishable from normal (2, P > 0.05) after logarithmic transformation. Figure 9A shows distributions of RF center size (2c) for the three age groups. The geometric means are 1.22°, 1.37°, and 1.15° for adult cats, 8-wk kittens, and 4-wk kittens, respectively. Figure 9B plots the (geometric) mean values of RF center size as a function of age. There is no significant trend for center size to change with age (ANOVA, F(2,141) = 1.53, P = 0.22). The mean values of RF center size for the different age groups are not significantly different (Tukey criterion, P > 0.05).
s) for the three age groups. The geometric means of surround size are 2.95°, 3.69°, and 3.98° for adult cats, 8-wk kittens, and 4-wk kittens, respectively. One-way ANOVA reveals a weakly significant trend for the surround size to decrease with age [F(2,141) = 3.14, P = 0.046], but the mean values of surround size for the three age groups are not significantly different (Tukey, P > 0.05).
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FIG. 10.
Population summary of developmental changes in spatial RF structure. The format of this figure is identical to that of Fig. 6. A: summary spatial RF profiles are shown for populations of cells (including both ON- and OFF-center units) from adults and kittens. B: summary profiles are shown separately for ON- and OFF-center cells.
) provides a good fit to the spatial sensitivity profiles of retinal ganglion and LGN cells. However, to fit our data, we need an explicit formulation for the temporal RF profile. Moreover, we need to account for varying degrees of spatiotemporal inseparability in the data. Our initial observations (e.g., Fig. 2, C and D) suggested that this might be achieved by expanding the traditional DOG model to include a variable delay between center and surround responses. Similar formulations have been proposed (Dawis et al. 1984; Enroth-Cugell et al. 1983) to explain spatiotemporal coupling in the frequency domain (see DISCUSSION).
). The expressions for the model are as follows
where
(4)
(5)
![<IT>G</IT><SUB>center</SUB>(<IT>T</IT>) = <IT>K</IT><SUB>1</SUB> × <FR><NU>[<IT>c</IT><SUB>1</SUB>(<IT>T − t</IT><SUB>01</SUB>)]<SUP><IT>n<SUB>1</SUB></IT></SUP><IT>e</IT><SUP>−<IT>c<SUB><UP>1</UP></SUB></IT>(<IT>T−t<SUB>01</SUB>)</IT></SUP></NU><DE><IT>n</IT><SUP><IT>n<SUB>1</SUB></IT></SUP><SUB>1</SUB><IT>e</IT><SUP>−<IT>n<SUB>1</SUB></IT></SUP></DE></FR>](/content/vol78/issue2/fulltext/1045/img007.gif)
![− <IT>K</IT><SUB>2</SUB>× <FR><NU>[<IT>c</IT><SUB>2</SUB>(<IT>T − t</IT><SUB>02</SUB>)]<SUP><IT>n<SUB>2</SUB></IT></SUP><IT>e</IT><SUP>−<IT>c</IT><SUB>2</SUB>(<IT>T−t</IT><SUB><IT>02</IT></SUB><IT>)</IT></SUP></NU><DE><IT>n</IT><SUP><IT>n<SUB>2</SUB></IT></SUP><SUB>2</SUB><IT>e</IT><SUP>−<IT>n<SUB>2</SUB></IT></SUP></DE></FR>](/content/vol78/issue2/fulltext/1045/img008.gif)
(6)
(7)
Notice that the temporal function for the surround[Gsurround(T)] is the same as that for the center [Gcenter(T)] except for the time delay (td).
(8)
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FIG. 11.
This figure shows a simple model that accounts for the major features of the spatiotemporal RF profiles of LGN neurons. On the left are X-T profiles for three typical LGN neurons. In the middle are fits to the X-T data using the model of Eq. 4. On the right are the spatial and temporal components of the respective fits for each cell. Solid curves show the components of the center response and dashed curves are those for the surround. Vertical bars through the spatial components indicate the center position of the Gaussian functions. See text for further details.
DISCUSSION
Abstract
Introduction
Methods
Results
Discussion
References
), the two flanks of the surround are not of equal strength for many of the LGN RF maps. This asymmetry appears to be caused by a spatial offset of the center and surround (see below). Most of the RF maps show biphasic temporal response profiles for both the center and the surround. However, there are cells that have multiphasic temporal response profiles. Most of these cases involve lagged cells, for which the temporal response profile is phase shifted such that the second temporal phase dominates the response. Many of the LGN RF maps are spatiotemporally inseparable. The inseparability is primarily a result of the surround response being delayed relative to that of the center. In addition, the first temporal phase of the surround often converges toward the second temporal phase of the center. This kind of space time inseparability, shown in LGN neurons, is clearly different from that exhibited by cortical simple cells (see DeAngelis et al. 1993a, 1995; McLean and Palmer 1989; McLean et al. 1994).
). Therefore, the prolonged maturation of temporal response properties of cortical cells may be accounted for to some extent by the development of subcortical structures.
; Kuffler 1953). In recent years, technically advanced methods for RF mapping have allowed a complete characterization of RFs in the joint domain of space and time (see DeAngelis et al. 1995 for a review). The majority of this work has focused on elucidating the spatiotemporal RF structure of cortical neurons (DeAngelis et al. 1993a; Eckhorn et al. 1993; Emerson et al. 1987; Jacobson et al. 1993; McLean and Palmer 1989; Shapley and Reid 1991). However, to better understand the genesis of cortical RFs, it is also important to have a clear understanding of the spatiotemporal RF structure of the main cortical inputs, namely those from the LGN. Stevens and Gerstein (1976) first examined the space-time organization of LGN RFs in an elegant study; however, their "response-plane" technique did not have sufficient temporal resolution to reveal the intrinsic temporal dynamics of single neurons. Nevertheless, a number of their conclusions are consistent with ours. More recently, researchers have used "white-noise" techniques to characterize the RF dynamics of retinal ganglion cells (Citron et al. 1981, 1988) and LGN cells (Eckhorn et al. 1993; Golomb et al. 1994; Reid and Shapley 1992). However, in these studies, data from only a few neurons were presented. To our knowledge, the present study is the first systematic, quantitative investigation of spatiotemporal RF structure for a sizeable population of LGN neurons. Related work from other laboratories has appeared in abstract form, however (Alonso et al. 1995; Reid and Shapley 1990; Wolfe et al. 1994).
; DeAngelis et al. 1993a; Reid et al. 1991) there is no unique spatial (or temporal) RF profile. Our data show that many LGN cells exhibit some degree of inseparability. This space-time coupling is manifested (e.g., Fig. 2) as a delay of the surround response relative to the center response and as a blending of the center and surround responses during the time-course of the response. This form of inseparability is quite different, however, from that exhibited by direction-selective simple cells (see DeAngelis et al. 1993a; McLean and Palmer 1989; McLean et al. 1994), which have RF subregions that are oriented obliquely in the X-T domain. A similar type of inseparability is not observed in the LGN. Thus, it remains to be understood exactly how the inseparable RFs of simple cells are constructed (see DeAngelis et al. 1995; Saul and Humphrey 1992 for further discussion).
). Having now extended the description of LGN RFs to the joint space-time domain, we sought to determine whether the classical DOG model can be generalized to describe the space-time data. In our modified DOG model (see Fig. 11 and related text), the center and surround components are each space-time separable, but the surround response may be delayed relative to that of the center. We have found that this simple modification provides for an excellent fit to the X-T profiles of most LGN cells.
to fit the spatiotemporal frequency spectra of retinal ganglion cells. Thus, the space-time inseparability exhibited by both ganglion and LGN cells appears to be well accounted for by a temporal delay of the surround response. A similar, but slightly more complicated, model was proposed by Dawis et al. (1984) to fit the spatiotemporal frequency response of ganglion and LGN cells. In this model, both the center/surround amplitude ratio and the temporal phase between center and surround were allowed to vary with temporal frequency. Dawis et al. (1984) concluded that their data were consistent with a separable center mechanism and an inseparable surround mechanism. Although we have not compared these models directly, the results of our simulations suggest that the simple "temporal delay" model is sufficient to account for the basic structure observed in our RF profiles.
; Mitchell and Timney 1984). Because the dorsal LGN provides the predominant input to the visual cortex, the spatiotemporal development of LGN RFs is of considerable interest. Previous physiological studies of LGN development (Daniels et al. 1978; Ikeda and Tremain 1978; Mangel et al. 1983; Tootle and Friedlander 1989) have focused almost exclusively, however, on spatial RF organization. In this study, we have directly compared the development of temporal and spatial properties for the same populations of neurons.
; Mangel et al. 1983). Interestingly, our population results (Fig. 6) suggest that temporal RF structure matures in two distinct stages. From 4 wk to 8 wk, there is a marked change in the shape of the temporal RF profile, with a substantial strengthening of the second response phase (Fig. 6A). However, there is little, if any, change in the response latency or duration during this time period. From 8 wk postnatal to adulthood, the shape of the response profile remains approximately the same, but there is a notable shortening of the time-scale of the response (i.e., temporal compression). This two-stage pattern of temporal development suggests that there may be different mechanisms at work during these two periods, although measurements at more finely spaced time intervals are required to fully address the "two-stage" hypothesis.
; Rusoff and Dubin 1977) and LGN cells (Daniels et al. 1978; Norman et al. 1977; Tootle and Friedlander 1989), particularly as regards X-cells. Consistent with previous studies, we do observe a modest decline (Fig. 9D) in the size of RF surrounds (Rusoff and Dubin 1977; Tootle and Friedlander 1989), as well as a concomitant increase (Fig. 9F) in the strength of surround inhibition (Daniels et al. 1978). We do not find any significant decrease in RF center sizes (Fig. 9B) after 4 wk postnatal. This is in agreement with some previous reports on X-cells (Rusoff and Dubin 1977 for ganglion cells; Daniels et al. 1978); however, other studies report a modest decline in RF center size after 4 wk postnatal (Ikeda and Tremain 1978; Tootle and Friedlander 1989). Since these differences are small, they may be attributable to sampling biases, to differences in the range of eccentricities studied, or to the degree of accuracy attained in measuring RF size.
), as discussed below.
) that the temporal RF structure of cortical cells continues to mature well past the age of 8 wk postnatal. A summary of these findings is plotted in Fig. 12, A and C, along with the comparable data for LGN neurons from the present study. Panels B and D of Fig. 12 show the mean differences between pools of simple cells and LGN cells, with respect to peak latency (Tpeak) and RF duration (D), as a function of age.
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FIG. 12.
Comparison of postnatal development of temporal response properties for LGN cells and cortical simple cells. A: change in peak response latency (Tpeak) as a function of age for populations of LGN cells (filled circles; replotted from Fig. 5B) and simple cells [open circles; replotted from Fig. 5C of DeAngelis et al. (1993a) ]. B: difference between mean values of Tpeak for simple cells and LGN cells is plotted as a function of age. C: developmental change in RF duration for populations of LGN cells (filled circles; replotted from Fig. 7B) and simple cells [open circles; replotted from Fig. 7B of DeAngelis et al. (1993a)]. D: difference in mean duration between simple and LGN RFs as a function of age.
and DeAngelis et al. (1993b) with Troy (1983); see also Hawken et al. (1996)]. The mechanisms underlying this loss of temporal resolution at the geniculo-cortical synapse are not entirely clear, but convergence of multiple geniculate inputs (of varying latencies) onto a simple cell may account for at least part of the effect.
; DeAngelis et al. 1993a). On the other hand, our present results show that RF center size in the LGN remains approximately constant from 4 wk postnatal to adulthood. This finding suggests that the LGN inputs to simple cells become more accurately aligned in space during postnatal maturation, an interpretation that is consistent with reports that geniculo-cortical axonal arbors go through extensive pruning after birth (e.g., Shatz 1990).
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ACKNOWLEDGEMENTS |
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We are grateful to A. Anzai for help in conducting these experiments and to Izumi Ohzawa for development of reverse correlation software, as well as assistance with data analysis.
This work was supported by research and CORE grants from the National Eye Institute (EY-01175 and EY-03176) and by a collaborative project of the Human Frontiers Science Program.
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FOOTNOTES |
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Present address of G. C. DeAngelis: Dept. of Neurobiology, Stanford University School of Medicine, Stanford, CA 94305-5401.
Address for reprint requests: R. D. Freeman, University of California, 360 Minor Hall, Berkeley, CA 94720-2020.
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REFERENCES |
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Abstract
Introduction
Methods
Results
Discussion
References
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