Output of the auditory image model for the <i>T</i>_1/2 = 4ms ramped and damped sinusoids.

<p>Auditory Image Models’ output for damped (a–c) and ramped (d–f) trains (<i>T</i>_1/2 = 4ms) at the time point of the same envelope height. Panels a) and d) show the stabilized auditory image (SAI) over time in each cochlear frequency channel. Panels c) and f) represent the spike probability averaged over time. Panels b) and e) show the summarised activity of all channels in the auditory image. The integration interval is the inverse of the carrier frequency applied [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0153947#pone.0153947.ref011" target="_blank">11</a>], thus it shows a peak at <i>τ</i> = −1ms in the figure. The height of this peak predicts the perceived carrier salience.</p

Schematic diagram of the Auditory Image Model and the Top-down Modulated Hierarchical Model of Pitch.

<p>a) Schematic view of the Auditory Image Model (AIM) [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0153947#pone.0153947.ref014" target="_blank">14</a>]. In the first stage, peripheral auditory filters transform the input waveform into a multi-channel representation of basilar membrane motion. The next stage applies a hair cell model and converts this motion into a neural activity pattern in the auditory nerve (NAP). In the final stage, this signal is used to produce a stabilised representation of the stimuli by means of strobed temporal integration. The output of this process is termed the stabilised auditory image (SAI) of the input stimulus. b) Schematic view of the top-down modulated Hierarchical Generative Model of pitch perception (GPM) [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0153947#pone.0153947.ref017" target="_blank">17</a>]. The peripheral processing is similar to the one in AIM (bottom). The next step consists of a coincidence detection process of auditory nerve activity patterns for different cochlear delay lines <i>l</i>, <i>A</i>₁(<i>t</i>, <i>l</i>). Further processing is carried out by two consecutive ensemble models <i>A</i>₂ and <i>A</i>₃ performing leaky integrations of input activity using time-varying integration windows. Such ensembles correspond putatively to pre-thalamic and central auditory areas. A top-down, stimulus-dependent mechanism modulates the size of the effective integration windows of bottom-up information.</p

Autocorrelation model’s predictions for the amplitude of the N100m peak.

<p>Predictions were computed following the same procedure as in the analysis of the top-down modulated model (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0153947#pone.0153947.g004" target="_blank">Fig 4d</a>). Predictions of the autocorrelation model do not show statistically significant correlations with the N100m values or the perceptual predictions. Moreover, the predicted amplitudes elicited by ramped and damped sinusoids with <i>T</i>_1/2 = 4,ms are not significantly different in this analysis.</p

Auditory fields evoked by the ramped and damped sinusoids.

<p>Grand mean source waveforms for the five different conditions of ramped and damped sinusoids. Average was taken over subjects (<i>n</i> = 27) for both hemispheres. The magnitude of the N100m increases for rising <i>T</i>_1/2 values of the stimuli. Note the maximal difference between ramped and damped sinusoids in the right hemisphere for the <i>T</i>_1/2 = 4ms condition.</p

Summary of the statistics of the fit between the N100m transient and the output of GPM.

<p>Left panel: Example of the model response derivative, normalized to the amplitude of the recording, for a ramped stimulus (<i>T</i>_1/2 = 0.5ms) and the corresponding recordings, averaged across right and left hemispheres and participants. Transparent shadows represent standard deviations. Right panel: Histograms of the Pearsons’s correlation coefficient and root-mean-square errors corresponding to the fittings between the GMP prediction and MEG recordings in an interval of 50 ms around the N100m peak. Each value corresponds to a single cross-validation instance for ramped and damped stimuli.</p

GPM raw output for the ramped and damped stimuli.

<p>Heat maps show the evolution in time (<i>x</i>-axis) of the activity of the different ensembles (<i>y</i>-axis) in the third layer of the GPM model for ramped (top) and damped (bottom) sinusoids with different <i>T</i>_1/2. In all cases, after a small period of instability, there is a maximum centred in the ensemble characterized by <i>δt</i> = 1ms, the frequency of the carrier sinusoid. Qualitative differences are noticeable between the output of ramped and damped stimuli, and also between stimuli with different envelope time constants.</p

Comparison of the perceived salience, N100m magnitude, and the prediction of the two models of pitch.

<p>Perceptual and neuromagnetic results for each of the five pairs of ramp and damp stimuli. The corresponding temporal asymmetry indices are drawn at the bottom of each plot (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0153947#pone.0153947.e002" target="_blank">Eq (2)</a>). (a) Perceived salience estimated by the BTL method and averaged across subjects (<i>N</i> = 13). (b) SAI mean ridge height at the frequency of the carrier (1 kHz). Ridge height was used to predict the perceived salience of the stimuli [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0153947#pone.0153947.ref014" target="_blank">14</a>]. (c) Magnitude of the N100 component averaged across subjects. (d) Top-down modulated model’s predictions for the amplitude of the N100m peak, computed as a linear transform of the derivative of the activation of the top layer population evaluated at the winning frequency. The linear relationship was cross-validated across subjects (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0153947#sec002" target="_blank">Methods</a>), yielding to a total of 702 predictions. The figure shows the average of the predictions. Significant correlations were found between perceived saliency 4a) and N100m magnitude (4c); between the perceptual observations 4a AIM responses (4b) and between the N100m magnitude 4c) and GPM predictions (4d). Error bars represent SME.</p

Inter-hemispherical differences observed between the fields evoked by ramped and damped sinusoids.

<p>Comparison between the fields evoked in left and right hemispheres for ramped and damped stimuli. N100m’s magnitude is plotted in the left panel. Corresponding asymmetry indices are displayed in the right panel.</p

Comparison between our results and previously reported measures of the perceptual asymmetry between ramped and damped sinusoids.

<p>Comparison between asymmetry preference of ventral cochlear nucleus [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0153947#pone.0153947.ref023" target="_blank">23</a>], inferior colliculus [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0153947#pone.0153947.ref024" target="_blank">24</a>], cortical neurons [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0153947#pone.0153947.ref025" target="_blank">25</a>], human psychophysical performance in discriminating the ramped and damped sinusoids in A1 [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0153947#pone.0153947.ref001" target="_blank">1</a>], the N100m magnitude temporal asymmetry, and psychophysical perceptual asymmetry measured in this work. Multiplicative factors (2 and 0.25, respectively) were applied to rescale the results of our study in order to improve visualisation. Note that the absolute values of the indices depend on the individual scale of each quantity.</p

Waveforms of the ramped and damped sinusoids.

<p>Ramped (left) and damped (right) sinusoidal waves with half-life times (<i>T</i>_1/2) of 0.5, 1, 4, 16, and 32 ms used in the experiment. Note the two periodicities present in the stimuli corresponding to the carrier (1000 Hz) and the repetition period (20 Hz) of the ramped/damped modulation.</p