Figure 5.

Linear extrapolation significantly underestimates neural threshold values in the PD. A, Illustration showing why linear extrapolation would underestimate the neural discrimination threshold at PD. Left, Schematic of the fore–aft (FA) and lateral (Lat) axes of translation (black arrows) as well as the PD of an example afferent (green line and arrows). Right, Discrimination threshold (T_min−max) of this afferent as a function of direction (i.e., the absolute difference between the axis of translation and the PD of the afferents: |PD − 2D|) calculated using the sensitivity tuning curve (inset). The black circles show measured sensitivities (inset) and corresponding threshold values (main panel). The gray circles were obtained using a cosine fit (solid black line in inset) for sensitivity (inset) and estimating the corresponding threshold values. The predicted threshold at PD (dashed circle) based on a linear extrapolation (dashed line) is much smaller than the actual value measured by direct stimulation along the PD of the afferent (filled green circle, green arrow). Based on the fact that the discrimination threshold is inversely proportional to sensitivity, we would expect that the threshold as a function of direction would be well fit by a 1/cosine function (solid black line in main panel). Extrapolating the discrimination threshold at PD using this fit gives rise to a correct estimate. B, Discrimination threshold values T_min−max as a function of direction for regular (blue) and irregular (red) afferents during 5 Hz sinusoidal stimulation. We used a 1/cosine fit (solid lines; see Materials and Methods) to extrapolate the threshold at PD (red and blue arrows). The R² values quantifying the goodness-of-fit are also shown. We then compared the extrapolated threshold values (open bars in the inset) with the actual measured values (filled bars in the inset) and found no significant differences (t test, p = 0.14 and 0.09 for regular and irregular afferents, respectively). C, Same data as in B except that we instead used a linear fit to extrapolate discrimination threshold values at PD. The best fits are shown (dashed lines) along with goodness-of-fit as quantified by R². We note that fitting a straight line gave rise to lower R² values than using a 1/cosine function. We also compared the linearly extrapolated discrimination threshold values (red and blue arrows, open bars in the inset) with the actual measured values (filled bars in the inset) and found that the former significantly underestimated the latter (t test, p < 0.0001 for both regular and irregular afferents).