Detection thresholds of macaque otolith afferents

Abstract

The vestibular system is our sixth sense and is important for spatial perception functions, yet the sensory detection and discrimination properties of vestibular neurons remain relatively unexplored. Here we have used signal detection theory to measure detection thresholds of otolith afferents using 1 Hz linear accelerations delivered along three cardinal axes. Direction detection thresholds were measured by comparing mean firing rates centered on response peak and trough (full-cycle thresholds) or by comparing peak/trough firing rates with spontaneous activity (half-cycle thresholds). Thresholds were similar for utricular and saccular afferents, as well as for lateral, fore/aft, and vertical motion directions. When computed along the preferred direction, full-cycle direction detection thresholds were 7.54 and 3.01 cm/s(2) for regular and irregular firing otolith afferents, respectively. Half-cycle thresholds were approximately double, with excitatory thresholds being half as large as inhibitory thresholds. The variability in threshold among afferents was directly related to neuronal gain and did not depend on spike count variance. The exact threshold values depended on both the time window used for spike count analysis and the filtering method used to calculate mean firing rate, although differences between regular and irregular afferent thresholds were independent of analysis parameters. The fact that minimum thresholds measured in macaque otolith afferents are of the same order of magnitude as human behavioral thresholds suggests that the vestibular periphery might determine the limit on our ability to detect or discriminate small differences in head movement, with little noise added during downstream processing.

Figure 1.

Example otolith afferent response, shown as IFR. A, Modulation during three cycles of sinusoidal linear acceleration along the LR (top), NO (middle), and DV (bottom) axes. Stimuli (0.5 Hz) are shown below the IFR (LR, NO, 0.1 G; DV, 0.07 G). B, Experimental protocol used to measure detection thresholds. From top to bottom, Response to different magnitudes of 1 Hz LR linear acceleration. Gray lines illustrate Kaiser filter (see Materials and Methods) superimposed on top of the IFR.

Figure 2.

Summary of basic response properties of macaque otolith afferents (n = 49). A, Response gain (along the 3-dimensional PD) as a function of CV*. Marginal histograms show gain and CV* distributions (arrows illustrate geometric means). B, Response phase (measured during linear acceleration along the cardinal axis that elicited the largest response for each cell) as a function of CV*. C, PD vector distribution in three-dimensional space (all magnitudes have been normalized to a gain of 1). D, Scatter plot of the difference between response peak and spontaneous activity versus the difference between spontaneous activity and response trough (averaged over 100 ms; see Materials and Methods). Data are only shown for the largest response amplitude (1 data point per cell). Dotted line, Unity slope; solid line, type II linear regression. E, Distribution of spontaneous firing rates. Open symbols/bars illustrate neurons (all irregular fibers) with silencing of activity during the inhibitory response. Different symbols in A, B, and D are used for different animals (squares, monkey K; circles, monkey H).

Figure 3.

Quantification of full-cycle direction detection threshold for the cell in Figure 1. A, Example IFR (LR motion direction, 0.16 G) with superimposed gray line illustrating Kaiser filter response (see Materials and Methods). Bars mark 100 ms intervals used to compute mean firing rates for peak (filled bar) and trough (open bars) responses, analyzed cycle by cycle. B, Firing rate distributions for four pairs of stimulus magnitudes: 0.16, 0.04, 0.02, and 0.005 G. Data shown are during LR motion, with filled bars corresponding to rightward (peak) and open bars corresponding to leftward (trough) responses. C, Response magnitude tuning curves for three stimulus directions: LR, NO, and DV. Positive directions are rightward, forward, and upward, respectively. D, Example neurometric functions showing proportion rightward (LR, black circles), forward (NO, gray triangles), and upward (DV, gray inverted triangles) direction decisions of an ideal observer as a function of linear acceleration magnitude, computed from the magnitude tuning curve responses from C. Each data point corresponds to an ROC value computed from a pair of firing rate distributions like those shown in each row of B. Solid lines show cumulative Gaussian fits to the neurometric functions.

Figure 4.

Summary of full-cycle direction detection thresholds (n = 49). A, Neuronal threshold as a function of CV*, color coded according to stimulus direction (LR, magenta; NO, blue; DV, green). Marginal histograms on the right show threshold distributions, separately for regular (black) and irregular (red) otolith afferents (arrows illustrate geometric means). B, Neuronal threshold as a function of the absolute difference between the tested direction and the three-dimensional PD of the cell, Δ(3D − PD), with data from each cell shown for one to three motion directions. Vertical dashed line marks Δ(3D − PD) = 90° (i.e., tested direction perpendicular to the PD of the cell). C, Distribution of neuronal threshold along the maximum response direction (i.e., the cardinal direction that was closest to the three-dimensional PD of the cell). Arrows illustrate geometric means. D, Data in B folded around 90°, such that type II linear regression (solid) lines can be fit to the data, separately for regular (black) and irregular (red) afferents. Black symbols/bars, Regular otolith afferents (CV* < 0.1); red symbols/bars, irregular otolith afferents (CV* > 0.1). Different symbols are used for different animals (squares, monkey K; circles, monkey H).

Figure 5.

Parameters influencing neuronal threshold. A, B, Dependence of neuronal threshold on linear acceleration magnitude tuning curve slope (A) and median variance (B), with data from each cell shown for one to three motion directions. Median variance is computed for each direction from multiple response amplitude distributions, like those in Figure 3B. C, Correlation of magnitude tuning curve slope and D, median variance with CV*. Black symbols, Regular otolith afferents (CV* < 0.1); red symbols, irregular otolith afferents (CV* > 0.1). Different symbols are used for different animals (squares, monkey K; circles, monkey H). Solid lines illustrate type II linear regressions plotted through all data (all directions, all neurons).

Figure 6.

Summary of half-cycle detection thresholds (n = 49). A, B, Neuronal threshold for excitatory (A) and inhibitory (B) responses as a function of CV*, color coded according to stimulus direction (LR, magenta; NO, blue; DV, green). Marginal histograms on the right show threshold distributions, separately for regular (black) and irregular (red) otolith afferents (arrows illustrate geometric means). C, Scatter plot comparing excitatory with inhibitory half-cycle detection thresholds. Dotted line marks unity slope. Solid line plots type II linear regression. D, Excitatory detection threshold as a function of the absolute difference between the tested direction and the three-dimensional PD, Δ(3D − PD), folded around 90°, such that type II linear regression (solid) lines can be fit to the data, separately for regular (black) and irregular (red) afferents (same format as in Fig. 4D). Black symbols/bars, Regular otolith afferents (CV* < 0.1); red symbols/bars, irregular otolith afferents (CV* > 0.1). Different symbols are used for different animals (squares, monkey K; circles, monkey H).

Figure 7.

A–F, Example magnitude tuning curves for six representative otolith afferents with significant nonlinearities, plotted for LR, NO, and DV directions (positive values: rightward, forward, and upward stimuli; negative values: leftward, backward, and downward stimuli). Solid lines illustrate quadratic fit. Horizontal dashed lines illustrate spontaneous (baseline) activity. Insets illustrate baseline ISI distribution.

Figure 8.

Summary of nonlinearities in magnitude tuning curves. A, Scatter plot of quadratic and linear correlation coefficients (R²_Q and R²_L, respectively) fitted to magnitude tuning curves of all cardinal directions tested (unity dotted line is also shown). B, Scatter plot of quadratic correlation coefficient (R²_Q) versus response gain along the respective direction. C, Bar graph of mean ± SD difference between the two correlation coefficients (R²_Q − R²_L) grouped according to maximum (Dir1) and minimum (Dir 3) cardinal response direction, summarized separately for regular (black bars) and irregular (red bars) afferents. D, Scatter plot of the difference between the two correlation coefficients (R²_Q − R²_L) versus the ratio of excitatory half-cycle to inhibitory half-cycle threshold (data from directions with gain < 10 spikes/s/G have been excluded). Solid line illustrates type II linear regression. For illustrative purposes, correlation coefficient differences < 0.001 have been set at R²_Q − R²_L = 0.001. Black symbols/bars, Regular otolith afferents (CV* < 0.1); red symbols/bars, irregular otolith afferents (CV* > 0.1). Different symbols are used for different animals (squares, monkey K; circles, monkey H).

Figure 9.

Dependence of population (geometric mean) full-cycle detection threshold (along the cardinal direction with the largest response) on analysis parameters, i.e., window size for computing mean firing rate (bars in Fig. 3A) and filtering method (Kaiser filter and spike density functions with different widths, σ; see Materials and Methods). Data are shown separately for regular (filled symbols, solid lines) and irregular (open symbols, dashed lines) otolith afferents. The analyses in previous figures used the Kaiser filter and a window size of 100 ms.