Data Analysis

We measured the neuronal responses from successfully initiated trials until behav-ioral relevant events occured (i.e. color changes of the fixation square, or direction changes of peripherally attended stimuli), or the trial was terminated due to fixa-tion errors or lever releases prior to a change event. Apart from the MRC condifixa-tion mean firing rates were obtained by averaging spikes of every trial in time intervals adjusted to the respective conditions (see following sections).

Direction tuning

As noted previously, the attentional mapping experiment was only started when the initial estimate of direction selectivity showed fine Gaussian tuning based on periph-erally attended RDPs moving constantly throughout the trial in one of twelve direc-tions until a direction change occured at random times starting earliest 750msec after RPDP onset. For thisclassical direction tuning firing rates were averaged across the time intervals from 150msec after stimulus onset to 750ms. This allowed to exclude early transient responses and excluded time intervals in which direction changes could occur. Mean firing rates for twelve directions were fitted with circular Gaus-sians of the formrModel =baseline+dirGain∗e−0.5(dir/sigma)², where rModel is the predicted response,baseline corresponds to the lower asymptote of the Gaus-sian,dirGainis the height of the Gaussian,dirthe direction of motion relative to the preferred direction, sigma corresponds to the standard deviation of the Gaussian.

Gaussian fits were done with custom written software based on a non-linear least squares minimization algorithm (Press et al., 1988), which was given the standard deviation of the response at each direction as the variance measure. Goodness of fit was determined by computing first, theχ² statistics and the probability that the differences between fit and data could be due to noise, and second, the significance of the correlation of fitted and raw data values. The direction at maximum response of the fitted model was considered the preferred direction and the direction 180^o apart from it was considered the null direction. As a second measure of directional selectivity the directional index (DI) was computed as DI = 1−(rMax−rMin) with rMax/rMin constituting the response to the preferred and null directions of motion.

Motion reverse correlation

Directional tuning of the responses to the MRC stimulus was analyzed with a cus-tom program which reverse correlated each spike in a trial with the stimulus value

Figure 2.4: Illustration of the reverse correlation method: For each spike of the spiketrain the stimulus value (direction) at ±∆t is found. This is illustrated for a motion direction of 30^o: A spike occurring at ∆t before the stimulus will be added to the reverse correlogram matrix (bottom figure) at the respective positive time bin, while spikes occurring after the occurrence of the 30^o motion will increment values at the respective negative time bins of the matrix. The resulting matrix is then normalized to reflect the relative probability of motion direction occurrence preceding spike events.

(direction) at ± ∆ t with a bin size of 20msec (Eckhorn, Krause, and Nelson, 1993;

Mazer et al., 2002; Borghuis et al., 2003; Vajda, 2003). For this purpose the sequence of directions of the MRC stimulus was converted into a continuous stimulus vector (cf. figure 2.4 for an illustration). For each spike during a trial the stimulus values (direction of motion) from 400msec prior to the spike and up to 200msec after the spike were added to the corresponding cells of the stimulus-time matrix. The re-sulting rows (individual directions) were normalized by the number of presentations of the directions, and the whole matrix was normalized by the number of spikes that went into the analysis. The final matrix, i.e. the reverse correlogram, contains values which represent the probability of a motion direction occurrence at time ∆t given a spike of the neuron at time t. The analysis was restricted to stimulus values starting at 200msec after stimulus onset to reduce artifacts due to luminance onset.

Noise level and standard deviation was computed from the uncorrelated part at pos-itive t (i.e. when spikes preceded the stimulus value), because it is physiologically not possible that a stimulus triggers a spike before its onset and thus no correlation is expected to contribute to that part (Mazer et al., 2002). Units were considered for later analysis if values at any time exceeded the noise ± 2 times its standard

deviation. The correlogram was sliced at the time bin with maximum response and the directional index was computed as described above. In order to compare the quality of direction tuning of the MRC method and the classical approach circu-lar Gaussians were fit to the slice values according to Gaussian equation presented above, with goodness of fits determined as described above.

Receptive field: position and size parameters

RFs profiles were obtained by averaging spikes in response to the probe stimuli in a time interval of 60-220msec relative to probe onset. Spatial response maps were ob-tained by interpolating data points at adjacent positions with three to five positions (cubic spline interpolation, matlab, The Mathworks). We always derived RF shape at half maximum response (width at half height) and at two standard deviations above the baseline response to match procedures reported in the literature. Baseline was always the mean response to the virtual probe within the sequence of RF probes, i.e. when there were only S1 and S2 within the RF but no probe. All reported RF analyses were performed after subtracting the baseline response from the RF probe responses. RF center was indexed as peak response position and center-of-mass of the shape as described in the results section.

RF size was indexed as the square root of the RF area at half-maximum response (after subtraction of responses from the baseline response, i.e. in the absence of the probe). This RF area was obtained from the interpolated maps and was defined by the vertices at half-maximum response. These vertices form a polygon and allow to apply standard geometric procedures to derive area and centroid parameters¹ . Our RF mapping involved the presence of three stimuli (S1, S2 and RF probe) simultaneously in the RF which has not been done before in area MT. We therefore encountered not always homogenous elliptical or circular shaped RF shapes at half-height but sometimes encountered an elliptical or circular central RF shape with one or more small satellite regions with responses above the half-maximum response.

These heterogenous RF maps were thus made of more than one polygonal shape.

For these cases we added the RF area of each polygonal region in order to derive the RF size. However, we always excluded conditions in which four or more satellite regions were present at half-maximum response.

We applied two major methods to index spatial tuning based on (i) the interpo-lated two-dimensional RF maps and (ii) on one-dimensional projection of activity along the S1-S2 axis. First, two-dimensional interpolated RF maps provided a po-sition with maximum response, and the RF size measured as the square root of the area within the RF (RF shape at half-height, or two standard deviations above baseline, see above). Second, two-dimensional RF maps were averaged along the

1The procedures used in this thesis were custom written matlab scripts adapted from informa-tion from the following website: http://www.me.psu.edu/sommer/me562/polygeom.doc.

attend S1 attend S2 attend S3, outside RF

response

0 5 10 15

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°visual angle (rel. to grid center)

20 40 60

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B

S1 S2

Figure 2.5: Illustration of one-dimensional RF projection. A: Example RF map of a neuron when stimulus 2 (S2) is attended. The RF is rotated to bring stimuli on the horizontal axis. Grey patches indicate the position of the stimuli presented inside the RF (S1 and S2). Coloured outlines indicate the half-height shape of the RFs when attention is directed to S1 (red), S2 (blue), and S3 (outside the RF, white).

The yellow outline reflects the area of the visual field which encompasses the RF in any of the attentional conditions. The analysis is based on an one-dimensional projection of activity averaged orthogonal to the S1-S2 axis (and encompassing only regions within the confines of the RF. B: Average activity, i.e. slice, for all three conditions (same color codes in A) orthogonal to the axis of S1-to-S2 across the yellow outlined area. Diamonds indicate the center of mass (centroid) of the curves and their 0.95 confidence limits which were estimated with a bootstrapping method (cf. p. 58). Vertical white lines indicate the position of S1 (left) and S2 (right) relative to the midline between S1 and S2 . A spatial shift towards the attended stimulus is evident in centroids that lie closer to the attended stimulus than to the unattended stimulus.

axis orthogonal to the axis made from S1 and S2 (the axis from S1 to S2 reflects the direction of the shift of attention in the attend inside conditions). The averaging of the RF took into account only those regions of the map that were lying within the RF in any of the conditions with peripheral attention. The resulting averaged one-dimensional projection of the RF allowed us to compute the center position of the curve (activity center of mass) and a peak position which were used to compare RFs across conditions (cf. figure 2.5).

Statistical analysis of one- and two-dimensional RF maps

In order to obtain a measure of variation of RF parameters after interpolation, which was based on the mean response to the RF probes at the positions of the virtual grid, we applied a bootstrapping method. For this test we repeated interpolation of the RF 200 times with responses to individual RF probe presentations drawn randomly from all occurences of the probe at a location in the grid (note that tests with 1000 repetitions did not change the overall result). For each single interpolated RF we obtained the centroid, the peak response, and the half-height RF size and computed the same parameters after the one-dimensional projection of the RF along the S1-S2 axis. which thus provided a means to estimate the statistical variation of the RF. Differences between RFs (i.e. their centroids, peak positions, or size) were statsitical tested with paired t-tests of the so obtained values.

Attentional modulation index

We computed an attentional index (AI) to index strength of modulation between conditions where attention was directed inside versus outside the RF as follows:

ai= (r1+r2/r1−r2), AI values can range between±1 with positive values indicating a stronger response for condition one (r1) than responses for condition two (r2) and negative values indicating a suppression.

Results

We recorded from neurons in the posterior bank of the superior temporal sulcus of the left hemisphere of a macaque monkey weigthing 8.2kg. Enough data for the mapping experiment could be collected for a set of 57 cells which fullfilled all inclu-sion criteria: (i) They could be held as well isolated single neurons throughout the experiment; (ii) they were recorded from a circumscribed area with highly direction-tuned neurons and had receptive field sizes that correspond to those expected for area MT; and (iii) sensory RFs of these neurons were all homogenous and allowed to position the potential target stimuli for the attentional mapping experiments at similarly activating regions within the confines of the RF. For some analysis only a smaller set of neurons could be used as indicated and explained in the respective sections. A detailed list of recorded neurons and experiments conducted with each cell is provided in appendix B.