PMC

Responses of the same cell whose data are also displayed in and to a counter-phase in a centre and a surround stimulus. The size of the centre stimulus is varied. For details on the stimulus see the Methods and . The curves are fits of the DOG model to the data.

The influence of centre size (σ_C), surround size (σ_S) and the phase difference between centre and surround response (γ) on the goodness of fit in a complex plain The descriptions are optimal at the minima. The arrows indicate the parameters obtained from the fits to the additional set of recordings. These parameters are clearly close to the optimal values.

Original responses of an on-centre M-cell (unit 34u17) to stimuli presented at various displacements relative to the cell's RF In this data subset, centre and surround stimuli were modulated in counter-phase, at 5 Hz and 50% contrast. The radius of the central stimulus (r_o) was 0.26°. The response of this neuron is maximal at about zero displacement, and reaches a minimum at 0.36° stimulus displacement. For further displacements, the response amplitude increases again and the response phase shifts.

Goodness of model fits to the psychophysical data (F and F′) as a function of temporal frequency It was considered that values above 2.66 (horizontal lines) signify an adequate fit (α(1) < 0.05). It can be seen that the goodness of fit is better at low temporal frequencies. Furthermore, the introduction of the non-linear interactions between RF centre and surround improved the goodness of fit substantially for the conditions in which centre and surround stimuli contained different modulation contrasts.

Response amplitudes of the same on-centre M-cell as displayed in , as a function of the phase difference between centre and surround stimuli (S, deg) displayed for different spatial displacements between stimulus and RF (r′, °) The curves are descriptions of the difference of Gaussians (DOG) model of the data. The RF parameters of these descriptions are estimated from an independent set of data. The DOG model was fitted to the data with only the overall scaling (k) as free parameter.

An illustration of the model proposed in the present paper to link LGN physiological and psychophysical data on the lateral interactions between flickering stimuli The stimulus is projected upon a patch of the retina and is encoded by a corresponding array of LGN cells. The responses of the array are the input for a cortical mechanism, the output of which is proportional to difference between maximal and minimal response amplitudes within the LGN array. The signal of such a peak-to-trough detector undergoes saturation and threshold and leads to the flicker percept.

A three-dimensional plot depicting the model simulation of the response amplitudes of cells in an array of foveal LGN neurons The response amplitude is given as a function of cell location in the array (equivalent to the stimulus displacement, r′, relative to the RF) and as a function of the relative surround stimulus phase (S). The simulation considers a combined stimulus with 0.5° centre radius, modulated at 50% contrasts and 4 Hz temporal frequency in both subfields (see for the RF parameters).

Output of the cortical detector The left plot shows sections of the 3-D graph given in . Response amplitudes at four relative phases of the surround stimulus: 0, 180, –60, and +60 deg are shown as functions of displacement r′. A proposed peak-to-trough detector compares the largest and smallest response amplitudes within each profile. The outputs of the peak-to-trough detector are given in the inset. The right plot depicts the detector's output (R_d) as a function of relative stimulus phase (S). Note that the curve is not symmetric due to the phase delay in the RF surround.

Scheme of stimulus presentation and model The sketch is based upon a measurement that was performed on a K-off cell (m34u40). A, a sketch of the overall sizes of the RF (centre: σ_C: 0.216°; σ_S: 0.428° see also ) and the stimuli (centre radius (r_o): 0.46°; surround radius: 5.1°). The size and position of the stimuli match the RF. The surround stimulus is substantially larger than the centre stimulus and the RF. Furthermore, the centre stimulus (r_o) is substantially larger than the RF centre (σ_C). B, a magnification of the RF and the centre stimulus. The stimuli are displaced relative to the RF field. The maximal displacement is 2.45 r_o. In the measurements, the relative phases between the modulation in the central and surround stimuli varied, similar to the method used by . C, the responses of marmoset LGN cells were recorded to these stimuli. The response can be regarded as the sum of four subresponses: those of the RF centre and the RF surround to the centre and surround stimuli respectively. The response of the RF surround is delayed relative to the RF centre response. The RF centre and surround are assumed to have Gaussian responsivity profiles.

Perceived contrast in the centre stimulus as a function of the relative phase of the surround stimulus Centre size was 1.0°. The data are shown for two temporal frequencies (4 Hz and 8 Hz) and for different contrast combinations in the centre and surround stimulus. Averaged data from three subjects are depicted by means (•) and standard deviations (vertical bars). For each subject, the thresholds were measured six times. The continuous curves are the fits of the cortical peak-to-trough detector, including saturation and threshold, to the psychophysical data. The results of F tests are given next to respective graphs. Predictions with F > 2.66 were at the 5% level of significance and qualified as adequate. The dotted curves in the plots for which the centre and surround contrast were not equal (lower four plots) are fits after recalculations with corrected RF parameters; the goodness of these fits is given by the value of F′.