Institute for Systems Research

The collection of responses to all elementary ripples is the spectro-temporal transfer function. Previous experiments using ripples with downward drifting spectra suggested that the transfer function is separable, i.e., it is reducible into a product of purely temporal and purely spectral functions.

Here we compare the responses to upward and downward drifting ripples, assuming separability within each direction, to determine if the total bi-directional transfer function is fully separable. In general, the combined transfer function for two directions is not symmetric, and hence units in AI are not, in general, fully separable. Consequently, many AI units have complex response properties such as sensitivity to direction of motion, though most inseparable units are not strongly directionally selective.

We show that for most neurons the lack of full separability stems from differences between the upward and downward spectral cross-sections, not from the temporal cross-sections; this places strong constraints on the neural inputs of these AI units.

In this paper, the relationship betweenthe spectro-temporal structure of any given stimulus and the quality ofthe STRF estimate is explored and exploited. Invoking the Fouriertheorem, arbitrary dynamic spectra are described as sums of basicsinusoidal components, i.e., "moving ripples." Accurate estimation isfound to be especially reliant on the prominence of components whosespectral and temporal characteristics are of relevance to the auditorylocus under study, and is sensitive to the phase relationships betweencomponents with identical temporal signatures.

These and otherobservations have guided the development and use of stimuli withdeterministic dynamic spectra composed of the superposition of many"temporally orthogonal" moving ripples having a restricted, relevant rangeof spectral scales and temporal rates.

The method, termedsum-of-ripples, is similar in spirit to the "white-noise approach," butenjoys the same practical advantages--which equate to faster and moreaccurate estimation--attributable to the time-domain sum-of-sinusoidsmethod previously employed in vision research. Application of the methodis exemplified with both modeled data and experimental data from ferretprimary auditory cortex (AI).

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.