Increment and decrement contrast discrimination thresholds measured with the Δ-pedestal-to-test delays from −106.7 to 1213.3 ms are plotted in
Figure 1 as a function of the delay. The three panels show data of three observers. The dashed line shows the average Δ-pedestal threshold measured in the second protocol. Observers CS and IY showed minimal difference (< 0.1 log unit) in these thresholds but HK was 0.2 log unit less sensitive in the temporal paradigm and showed more scatter in thresholds. Thresholds rose at Δ-pedestal onset, reached their maximum, and returned to near baseline sensitivity within 100 ms. Thresholds then rose again at the Δ-pedestal offset, and then returned to baseline within 100 ms. The time course for increments and decrements differed subtly but consistently among observers. The increment thresholds reached their first peak about 25 ms before Δ-pedestal onset but their second peak coincided with Δ-pedestal offset. In comparison, the decrement thresholds reached their first peak at Δ-pedestal onset but their second peak occurred about 25 ms before the Δ-pedestal offset.
The data could be described by modifying an equation to describe contrast saturation in the MC-pathway (
Pokorny & Smith, 1997;
Smith, Sun, & Pokorny, 2001). This equation describes contrast discrimination as dictated by a product of the threshold term, steady-state gain to the pedestal, and saturation to the Δ-pedestal:
where |
C| represents the absolute value of the Δ-Pedestal Weber contrast (Δ
P/
Ip,
Csat represents the saturating contrast,
KC represents the criterion increment firing rate (comparable to Δ/
Rmax of a single cell), and
K represents the overall scaling constant. The overall scaling constant,
K, incorporates threshold sensitivity and gain for the presumed MC-pathway. We can incorporate time dependence by adding an exponential time constant at onset and at offset to describe the recovery from saturation:
where
Gp represents the gain term at 162td and (Δ
G) represents the added gain (1.15 fold) caused by the 24-td Δ-pedestal. This equation gives an instantaneous change in contrast at onset (or offset), which recovers exponentially with time constant
τ. The peak advances can be described by replacing exp(−
t/
τ) by exp(−(
t+
k)/
t) where
k is a constant.
The solid lines show fits of
Equation (2) to the data of the three observers. For these fits, we allow variation of
τ, k,
Csat, and
K. The value of
τ varied from 23 – 40 ms. The values of
k varied from 17 – 30 ms. The advance was required to fit the increment thresholds measured at Δ-pedestal onset and to fit the decrement thresholds measured at Δ-pedestal offset. The values for
Csat, were 0.12 – 0.14. These values are consistent with values for contrast saturation in retinal ganglion cell data in the MC-pathway. In general, the quality of the fits was good. The use of a single exponential implies that the onset of saturation was instantaneous. However, data for early light adaptation show a more gradual rise. This could be modeled if the pathways mediating detection involved an average over cells with slightly varying time constants. There was no expectation that the time constant of the gain change should match the time constant of the contrast saturation. However, because the expected gain change was so small, there was no rationale to adjust the time constant.
Figures 2–
4 show the results of varying contrast at three fixed delays for the three observers. The upper panel shows data for increments and the lower panel shows data for decrements. Also shown on the graphs are data from the Steady-Pedestal Paradigms previously collected on all three observers (
Smith et al., 2001). The data were fit by
Equation (2). The parameters
t, k, C
sat, were those used to fit the delay data. The scaling
K was varied to account for day-to-day variability. Data were similar for all three observers. There was a steep V-shape at 0 delay, flattening at 26.7-ms delay. The thresholds at 506.7-ms delay corresponded well with the previous data from the Steady Pedestal Paradigm (
Smith et al., 2001). The three observers were well practiced, having participated in a variety of contrast discrimination experiments over a one-year period. Their thresholds were low. The smallest fixed Δ-pedestal was approximately twice threshold. There was no indication of facilitation (dipper effect) or inhibition (bumper effect) (
Bowen, 1997). The minimum of the V-shape occurred primarily for the zero Δ-pedestal, although there was some scatter among observers.