Institute for Systems Research Technical Reports

The ripples parameters that characterize cortical cells are distributed somewhat evenly, with the characteristic ripple frequencies ranging from 0.2 to over 2 cycles/octave and the characteristic angular frequency typically ranging from 2 to 20 Hz. Many responses exhibit periodicities not found in the spectral envelope of the stimulus. These periodicities are of two types. Slow rebounds with a period of about 150 ms appear with various strengths in about 30 % of the cells. Fast regular firings, with interspike intervals of the order of 10 ms are much less common and may reflect the ability of certain cells to follow the fine structure of the stimulus.

Responses to ripples were parametrized in terms of characteristic ripple Wo(ripple frequency where the magnitude of the ripple transfer function is maximal, i.e., where the cell responds best) and characteristic phase Fo (intercept of the phase of the ripple transfer function, i.e., phase where the cell responds best). The response area (measured with tones) was parametrized in terms of its excitatory bandwidth at 20 dB above threshold (BW20), and its asymmetry as reflected by the directional sensitivity index (C) to frequency-modulated (FM) tones. Columnar organization for the above four parameters was investigated in 66 single units from 23 penetrations. It was confirmed for Wo, Fo, and the C index, but it appeared to be ambiguous for BW20. The response parameters measured from multiunit recordings corresponded closely to those obtained from single units in the same cluster. In a local region, most cells exhibited closely matched, response fields (RFs, inverse Fourier transformed ripple transfer function) and response areas (measured with two-tone stimuli), and had correspondingly similar response parameters to ripples and tones. The topographic distribution of the response parameters across the surface of AI was studied with multiunit recordings in four animals. In all maps, systematic patterns or clustering of, response parameters could be discerned along the isofrequency planes.

The distribution of the characteristic ripple Wo exhibited two trends. First, along the isofrequency planes, it was largest near the center of AI, gradually decreasing towards the edges of the field where often a secondary maximum was found.

The second trend occurred along the tonotopic axis where the maximum Wo found in an isofrequency range increases with increasing BF. The tonal bandwidth BW20, which was inversely correlated with Wo, exhibited a similar topographic distribution along the tonotopic axis and the isofrequency planes. The distribution of the characteristic ripple phase, Fo which reflects the asymmetry in the response field, showed a systematic order along the isofrequency axis. At the center of AI symmetric responses (Fo 0) predominated. Towards the edges, the RFs became more asymmetric with Fo < 0 caudally, and Fo > 0 rostrally. The asymmetric response types tended to cluster along repeated bands that paralleled the tonotopic axis. The FM directional sensitivity (C index, reflecting asymmetry of tonal response areas) tends to have similar trends along the isofrequency axis as Fo.

Using frequency-modulated (FM) tones, we also determined a directional sensitivity index for the cell. Using broadband stimuli (1-20 kHz) with sinusoidally modulated spectral envelopes (ripples), we measured the response magnitude of each cell as a function of ripple frequency (W) and ripple phase (F), and then reconstructed the magnitude and phase of a ripple transfer function. Most cells (approximately 90 %) were tuned to a specific ripple frequency, denoted as a characteristic ripple frequency (Wo) . Most cells also exhibited a linear ripple phase as a function of W. The intercept of the phase function defined as the characteristic ripple phase (Fo), and is interpreted as the best ripple phase to drive the cell; the slope of the phase function reflects the location of the response area of the cell along the tonotopic axis. By inverse Fourier transforming the transfer function, we obtain the response field (RF) of the cell, an analogue of the response area measured with tonal stimuli. Like the response area, the RF was parametrized by the following measures: BFRF, which is the location of the maximum of the RF along the tonotopic axis, Wo , which is roughly inversely proportional to the width of the RF, and Fo which reflects the asymmetry of the RF. In the ferret Wo , ranges from 0.2 to 3 cycles/octave, with the average of the distribution around 1.0. Fo , ranges over the full cycle in a Gaussian-like distribution around 0o. For a subgroup of cells the sinusoidal modulations of the spectrum were presented both on linear and logarithmic amplitude scale. The responses were not notably different. The effect of the variations of amplitude of the sinusoidal modulation was studied. The largest effect was observed for the magnitude transfer function, which increased with amplitude and then saturated. The parameters Wo and Fo did not vary significantly with ripple amplitude. Typically, cells respond best to intermediate sound levels of the ripple stimulus, i.e., the magnitude transfer function shows a nonmonotonic dependence on overall stimulus level. The phase function and Wo do not depend much on level. The effects of a few nonlinearities on the responses are examined briefly. Effects of nonlinearities as threshold and saturation of the neural firing rates are examined. It is found that (non)monoticity of the rate level function of a cell could be distinguished from its ripple response characteristics. The RF of a cell closely corresponds to the response area measured with tone stimuli. Regression analysis shows that: (A) BFRF is, very similar to the tonal BF; (B) Wo is inversely correlated to the excitatory bandwidth; (C) Fo is correlated to the asymmetry of the response area.

Responses to rippled spectra in AI resemble closely the response properties to sinusoidal gratings in the primary visual cortex (VI). This provides a unified framework within which to interpret the functional organization of both corticies. Basic differences between the two systems, however, are also evident as the lack in AI of a substantial simple/complex distinction in the responses.

It is hypothesized that AI effectively analyzes an arbitrary input spectrum into a weighted sum of ripple components of different ripple frequencies and phases. This analysis is performed locally around each BF by a two-dimensional bank of filters tuned to different Wo and Fo values. Psychophysical support and implications of this hypothesis are also discussed in relation to the perception of timbre and other auditory tasks.