The fine structure of the recovering auditory detection threshold

Objective Estimation of Sensory Thresholds Based on Neurophysiological Parameters

Reliable determination of sensory thresholds is the holy grail of signal detection theory. However, there exists no assumption-independent gold standard for the estimation of thresholds based on neurophysiological parameters, although a reliable estimation method is crucial for both scientific investigations and clinical diagnosis. Whenever it is impossible to communicate with the subjects, as in studies with animals or neonates, thresholds have to be derived from neural recordings or by indirect behavioral tests. Whenever the threshold is estimated based on such measures, the standard approach until now is the subjective setting-either by eye or by statistical means-of the threshold to the value where at least a "clear" signal is detectable. These measures are highly subjective, strongly depend on the noise, and fluctuate due to the low signal-to-noise ratio near the threshold. Here we show a novel method to reliably estimate physiological thresholds based on neurophysiological parameters. Using surrogate data we demonstrate that fitting the responses to different stimulus intensities with a hard sigmoid function, in combination with subsampling, provides a robust threshold value as well as an accurate uncertainty estimate. This method has no systematic dependence on the noise and does not even require samples in the full dynamic range of the sensory system. We prove that this method is universally applicable to all types of sensory systems, ranging from somatosensory stimulus processing in the cortex to auditory processing in the brain stem.

Threshold vs duration for Gaussian-shaped tone-pips of one to four periods duration

Detection thresholds were obtained for Gaussian-shaped tone-pips of 1, 2, 3, or 4 periods duration for 20 frequencies spanning 50-3,000 Hz, in quiet, and in high-pass noise, for a single exceptionally patient and experienced listener. Thresholds were fitted by straight lines in decibels SPL versus the logarithm of duration. Slopes fell into 3 distinct regimes of frequency-dependence under both listening conditions. Models of Garner and of Formby, et al. do not account for this relation.

Effects of peripheral nonlinearity on psychometric functions for forward-masked tones

Psychometric functions (PFs) for forward-masked tones were obtained for conditions in which signal level was varied to estimate threshold at several masker levels (variable-signal condition), and in which masker level was varied to estimate threshold at several signal levels (variable-masker condition). The changes in PF slope across combinations of masker frequency, masker level, and signal delay were explored in three experiments. In experiment 1, a 2-kHz, 10-ms tone was masked by a 50, 70 or 90 dB SPL, 20-ms on-frequency forward masker, with signal delays of 2, 20, or 40 ms, in a variable-signal condition. PF slopes decreased in conditions where signal threshold was high. In experiments 2 and 3, the signal was a 4-kHz, 10-ms tone, and the masker was either a 4- or 2.4-kHz, 200-ms tone. In experiment 2, on-frequency maskers were presented at 30 to 90 dB SPL in 10-dB steps and off-frequency maskers were presented at 60 to 90 dB SPL in 10-dB steps, with signal delays of 0, 10, or 30 ms, in a variable-signal condition. PF slopes decreased as signal level increased, and this trend was similar for on- and off-frequency maskers. In experiment 3, variable-masker conditions with on- and off-frequency maskers and 0-ms signal delay were presented. In general, the results were consistent with the hypothesis that peripheral nonlinearity is reflected in the PF slopes. The data also indicate that masker level plays a role independent of signal level, an effect that could be accounted for by assuming greater internal noise at higher stimulus levels.

Afferent response parameters derived from postmasker probe-detection thresholds: 'the decay of sensation' revisited

The classical model of forward masking postulates that the detection threshold for a tone probe that follows a stimulus of similar frequency content is elevated relative to the quiet threshold because the probe must evoke a just-detectable increment in a decaying postmasker sensation. That postmasker decay is charted by probe-detection thresholds if the sensation increment is small and constant. This model was examined for a 2-kHz Gaussian-shaped probe and a 2-kHz forward masker, based on the model's assumption that a just-detectable increment in sensation results from a just-detectable increment in level. Psychometric functions for detection were obtained at 2.5-30 ms postmasker. Their means and standard deviations generally decreased with delay. It was assumed that standard deviation is related to the putative just-detectable level increment by a simple monotonic transformation. Thus, if the standard deviation of the psychometric function for probe detection is neither small nor constant, then the corresponding just-detectable increment in level is neither small nor constant, and the just-detectable increment in sensation is neither small nor constant. The classical model also fails to allow for the variability of internal events. The concept of detection threshold as a sensation increment was preserved in a Signal Detection model, that does allow for internal variability. In this model the postmasker residual is the input to a probe detector. The new model produces an equation for the just-detectable level increment as a function of probe delay. Comparison data were generated by again assuming some relation between the standard deviation of the psychometric function for detection, and the just-detectable increment in level. The fit of equation to data yields robust values for the probe detector's maximum firing rate, dynamic range, and spike-counting time. All that is required to account for the decay of sensation, for a pure tone, is a single neuron operating at some higher center.

The intensity-difference limen for Gaussian-enveloped stimuli as a function of level: tones and broadband noise

Van Schijndel et al. [J. Acoust. Soc. Am. 105, 3425-3435 (1999)] have proposed that the internal excitation evoked by an auditory stimulus is segmented into "windows" according to the stimulus spectrum and stimulus length. This "multiple looks" model accounts for the mid-duration hump they observed in plots of intensity-difference limens (DLs) versus pip duration for Gaussian-shaped 1- and 4-kHz tones, an effect replicated by Baer et al. [J. Acoust. Soc. Am. 106, 1907-1916 (1999)]. However, van Schijndel et al. and Baer et al. used few levels. A greater number of levels were used by Nizami (1999) for Gaussian-shaped 2-kHz tone-pips whose equivalent rectangular duration (D) was 1.25 ms. The DLs show the mid-level hump known for clicks [Raab and Taub, J. Acoust. Soc. Am. 46, 965-968 (1969)]. At some duration this pattern must become the "near-miss to Weber's law." To determine this duration, as well as the level-dependence of the mid-duration hump, DLs were established for Gaussian-shaped 2-kHz tone-pips of D = 1.25, 2.51, and 10.03 ms at levels of 30-90 dB SPL. The across-subject average DLs for the tone-pips rise up at mid-levels for D= 1.25 and D = 2.51 ms. The DLs for D=2.51 ms are larger, creating the mid-duration hump. At all durations, the new DLs are smaller at high levels than at low levels, consistent with the near-miss to Weber's law. DLs were also obtained here for Gaussian-shaped broadband-noise pips of D=0.63, 1.25, 2.51, 5.02, and 10.03 ms. The DLs for the noise-pip show a mid-level hump for all pip durations. The noise-pip DLs decrease as the pip lengthens, such that the plot of DL versus log duration shows a linear decline, with no mid-duration hump. Analysis of variance reveals that the mid-level hump coexists with the classical patterns of level-dependence, perhaps reflecting the existence of two level-encoding mechanisms, one that depends on firing-rates counted over single neurons and which is responsible for the classical patterns, and one that depends on the initial coordinated burst of neuronal spikes caused by rapid ramping, and which presumably causes the mid-level hump.

The periodicity of forward-masked auditory pip-detection thresholds, predicted from the output power of the auditory filter during ringing

The plot of detection thresholds vs. time for a forward-masked Gaussian-shaped 2 kHz pip (S.D.=0.5 ms) shows a noisy 'fine structure' that disappears with across-subject averaging. The averaging uncovers a slower threshold periodicity, that can be predicted from the output power of the auditory filter during extended ringing.