Population responses to multifrequency sounds in the cat auditory cortex: One- and two-parameter families of sounds

Population responses to multifrequency sounds in the cat auditory cortex: One- and two-parameter families of sounds
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  HWRlflC RESBlRCH ELSEVIER Hearing Research 72 (1994) 223-236 Population responses to multifrequency sounds in the cat auditory cortex: Four-tone complexes I. Nelken *, Y. Prut, E. Vaddia, M. Abeles Drpurtmcxt of hysiolo~, The Iludassah Medical Scl~ool. emralem 91010, Irrael (Received 27 February 1993; Revision rrceived 1 September 1903: Accepted 15 September IYYi) Abstract Population responses to two-tone and four-tone sounds were recorded in primary auditory cortex of anesthetized cats. The stimuli were delivered through a sealed, calibrated sound delivery system. The envelope of the neural signal (short time mean absolute value, MABS) was recorded extracellularly from six microelectrodes simultaneously. A new method was developed to describe the responses to the four-tone complexes. The responses were represented as sums of contributions of diffcrcnt orders, The first order contributions described the effect of the single frequencies appearing in the stimulus. The second order contributions described the modulatory effect of the pairs of frequencies. Higher order contributions could in principle bc computed. This paper concentrates on the mean onset responses. The extent to which the first and second order contributions described the onset responses was assessed in two ways. First, the actual rcsponscs to two-tone stimuli were compared with those predicted using the contributions computed from the four-tone stimuli. Second, the residual variance in the responses, after the substraction of the first and second order contributions. was computed and compared with the variability in the rcsponscs to repetitions of the same stimulus. The first type of analysis showed good quantitative agreement between the predicted and the measured two-tone responses. The second type of analysis showed that the first and second order contributions wcrc often sufficient to predict the responses to four-tone stimuli up to the level of the variability in the rcsponscs to rcpctitions of a single stimulus. In conjunction with the results of the companion paper (Nelken et al., 1994a) it is concluded that the onset rcsponscs to multifrcquency sounds are shaped mainly by the single frequency content of the sound and by two-tone interactions, and that higher order interactions contribute much less to the responses. It follows that single-tone cffccts and two-tom interactions arc necessary and sufficient to explain the mean population onset rcsponscs to the four-tone stimuli. Marc information can bc coded in the temporal evolution of the responses. Keq’ scuds: Primary Auditory Cortex; Complex Sounds; Non-linear modeling: Cat 1 Introduction The study of the coding of complex sounds in the activity of the central nervous system is still in its infancy. On the one hand, it is known that the re- sponses of neural elements (nerve fibers, neurons and populations of neurons) to complex stimuli often can- not be predicted on the basis of their responses to simple stimuli (e.g. Oonishi and Katsuki, 1965; Whit- field and Evans, 1965; Abeles and Goldstein, 1972; Newman and Wollberg, 1973; Smolders et al., 1979, * Corresponding author. The Johns Hopkins School of Medicine. Center for Hearing Sciences. 720 Rutland Avenue, Baltimore. MD 21205. USA Eggermont et al., 1981; Phillips and Cynader. 1985: Ehret and Merzenich 1988; Sutter and Schreiner. 1991; Spirou and Young, 1991; Nelken et al.. 1994a; Shamma et al., 1993). On the other hand, once beyond the use of simple stimuli, i.e. those described by one or two parameters, the wealth of possible sounds is enormous. It is impossible to map the responses of a neuron or a population of neurons to all possible stimuli; on the other hand, since there is no clear understanding of the processing of complex sounds by neural elements. it is hard to choose apriori a subset of all possible sounds which would completely characterize the rc- sponses of these neural elements, in the sense that their response to any other sound can be predicted from their responses to this subset. Previous work studying the coding of complex sounds can usually be categorized into one of three groups. 037X-5955/94/ 07.00 0 1994 Elsevier Science B.V. All rights reserved SSDI 037X-5’)55(93)E0157-7  The first group consists of studies in which a low-di- mensional subspace of all possible stimuli was exam- ined. These subspaces included sets of two-tone stimuli (Oonishi and Katsuki, 196.5; Abeles and Goldstein, 1972; Ehret and Merzenich, 1988; Sutter and Schreiner, 1991; Nelken et al., 1994a; Shamma et al., 19931, sets of harmonic or quasi-harmonic complexes (Schreiner et al., 1983; Schwartz and Tomlinson, 1990; Nelken et al., 1994a), combinations of a tone and wideband noise (Phillips and Cynader, 1985; Phillips and Hall, 1986), or simple amplitude or frequency modulation schemes (Whitfield and Evans, 1965; Phillips, 1988; Schreiner and Urbas, 1988). The second group of studies of complex sounds consists of studies in which a small set of sounds, that the experimenters believed to be interesting, was used. Such a set can be natural calls (Newman and Wollberg, 1973), vowel-like and syllable-like stimuli (Sachs, 1984; Steinschneider et al., 1990), or a complete ‘acoustic biotope’ (Aertsen et al., 1979). Finally, studies in the third group are those in which some sort of invariant description of the response properties of a neuron or a population of neurons to all possible sounds is attempted. This is traditionally accomplished through the use of system-theoretic tools like the Wiener-Volterra expansion (Victor and Knight, 1979; Eggermont et al., 1983~). In this ‘black-box’ approach, the responses to an appropriately chosen set of stimuli are used to compute a description of a (generally nonlinear) system which would give rise to those responses. Because of computational problems and noise in the measurements, the expansion is usu- ally limited to quadratic terms. It is anticipated that this description can be used to predict the responses to all possible sounds, or at least to a larger set of sounds than the one used to compute it. Aertsen introduced the term spectra-temporal receptive field (STRF) to describe the resulting characterization based on the Fourier transform of the second order Wiener kernels (Aertsen et al., 1981). Wickesberg et al., (1984) used time-domain Wiener-Volterra expansion to study the responses of neurons in the cochlear nucleus of cats; Epping (1985) used similar methods in the Torus Semi- circularis of grassfrogs, the analog of the Inferior Col- liculus (IC) of mammals. Yeshurun et al., (1985) used the responses to natural calls in the Medial Geniculate Body (MGB) of squirrel monkeys to fit a limited ver- sion of a second-order multi-band system. They showed that the response properties of at least some of the cells in the MGB can be approximated by such a system. Recently there was a renewed interest in the STRF (Clopton and Backoff, 1991; Kim and Young, 1993). All three approaches have limitations. The first per- mits the study of relatively simple stimuli only. The second permits the study of stimuli of arbitrary com- plexity, but only of few of those. In both cases it is difficult to generalize the results to different classes of stimuli. In particular, it is essentially impossible to generate a predictive model for large sets of sounds. The third gives a presumably complete description of the system, but in most of those studies, the estimated system predicts only very partially the responses to stimuli outside the set used to estimate it (Johnson 1980; Eggermont et al., 1983a,b; Wickesberg et al.. 1984; Epping, 198.5, Yeshurun et al., 1985). Previous parametric studies showed that non-linear effects in the responses to two-tone stimuli in the auditory cortex play an important role in shaping single unit and population responses to complex sounds (cats: Oonishi and Katsuki, 1965; Abeles and Goldstein 1972; Sutter and Schreiner, 1991; Nelken et al., 1994a; fer- rets: Shamma et al., 1993; bats: Suga, 1990). The aim of the present work is to extend these observations to a larger family of sounds, and to find out to what.extent additional mechanisms, beyond the non-linear summa- tion of the responses to pairs of tones, are needed to quantitatively explain the resulting patterns of re- sponses. This is achieved by studying parametrically the responses to four-tone stimuli. The methodology used is based on a combination of the first and the third approaches described above. The set of four-tone sounds is more complicated than those usually used in parametric studies. Thus, a system-theoretic approach is used to represent the responses. On the other hand, the method of describing the responses is simpler than the STRF or the time-domain Wiener-Volterra expan- sions. It is possible therefore to make rigorous valida- tion tests of the resulting model. In our view, the cortical activity is an emergent result of the cooperative interactions of a large popula- tion of neurons with an enormous number of feedback loops. Therefore we took the approach of studying the representation of sound by population activity in the auditory cortex, rather than the single-unit responses. It is much easier to study the population, rather than single-unit, responses to large sets of complex sounds in the auditory cortex (Nelken et al., 1994a). Ulti- mately, we would like to relate the single-unit re- sponses to the population responses, and both of them to the computational tasks performed by the auditory cortex on the one side, and to the neurophysiological mechanisms which generate them on the other. How- ever, the current state of understanding of the neural circuitry in the cortex makes it very difficult to eluci- date these neurophysiological mechanisms. The results presented in this paper may be seen as contraints on such more advanced theories. In this spirit, we concen- trated on studying steady-state sounds rather than on time-varying sounds. Therefore, temporal phenomena, which are obviously important in the auditory system, are not explicitly addressed in this paper. On the other  I. Nelken et al. Hearing Research 12 (1994) 223-236 175 hand, the dependence of the responses on the spectral characteristics of the sound was studied to a great depth; in particular, it is shown that single tone and two-tone responses are enough to quantitatively pre- dict the population responses to more complex steady- state stimuli. 2. Methods Experiments were conducted on three adult cats, weighing 2-4 kg. Details of the surgical preparation, recording procedures, and stimulus generation and de- livery are given in the companion paper (Nelken et al., 1994a). The experiments were performed in accor- dance with the guidelines of the Declaration of Helsinki Single tone responses were measured at 30 frequen- cies, equidistant on a logarithmic scale with l/6 octave resolution, between 100 Hz and 5500 Hz. They were delivered at 3 sound levels (3 dB, 27 dB and 51 dB above the threshold levei of the MABS signal from the electrode with the highest threshold). The tone bursts were usually long: 600 ms, with rise and fall times of 5 ms, shaped by multiplication with a linear ramp, and a silent period of 1100 ms between bursts. Sometimes short bursts (100 ms, with 5 ms rise/fall times and a 600 ms interval between bursts) were used. They were given in blocks of 50 stimuli at each sound level, and the levels alternated cyclically. The frequencies were chosen by a randomly selected permutation of the frequency table. To obtain a map, at least 5 blocks of stimuli were presented at each level (750 stimuli in total). Thus, each frequency and amplitude combina- tion was presented 8 or 9 times. Two-tone combinations were presented in one of the experiments. They were also presented in blocks of 50 stimuli alternating between the 3 sound presenta- tion levels. The two frequencies were selected inde- pendently of each other, and each was chosen by a randomly selected permutation of the frequency table. As a result, the sequence of stimuli was not a permuta- tion of all the two-tone combinations, but nevertheless the number of stimuli in which an individual frequency appeared was approximately the same for al1 frequen- cies. All tones started with the same phase (approxi- mately sine phase). The energy of the equal-frequency combinations was therefore 3 dB above the energy of the other stimuli. In this experiment, a 1Zfrequency table was used, and there were 78 different two-tone combinations. Four-tone stimuli were mapped in a different way. The set of all possible combinations is much too large to be mapped in its entirety: for the table of 30 frequencies used in some of these experiments, there are 40920 possible four-tone combinations (the number of ordered 4-tuples from a table of 30 possible choices, allowing repetitions). The goal of the experiment was to measure once the response to as many combinations as practically possible. In two of the experiments, there were about 1900 stimulus presentations at each of the three levels. In the third experiment, there were more than 5600 stimulus presentations at each level, spread over more than 20 h. Mapping the responses to the complex sounds sets required long periods of time, and therefore the stabil- ity of the responses during that time was monitored. Both spontaneous and evoked activity were examined. For each stimulus presentation, the mean MABS dur- ing the 300 ms preceding stimulus onset was computed and used as a measure of the spontaneous activity. This sequence of values, one for each stimulus presen- tation, was arranged in the order in which the stimuli were presented, and further analyzed as a time series. The mean MABS after stimulus onset, in 50 ms sec- tions with 25 ms overlap, was computed to measure the stability of the evoked responses. These sequences of values, one for each time section, were aIso arranged in the order of the stimulus presentations. All the time series were smoothed with a running window of SO points (the length of a block of stimuli at a single level, duration 85 s>, downsampled by a factor of 10 and displayed graphically. To qualify as stable, the time series for the spontaneous activity and the time series for at least the first two sections of the evoked activity (0 ms - 50 ms after signal onset and 25 ms - 75 ms after signal onset) had to have stable features as judged by eye. 2.2. Analysis of the responses to the four-tone stimuli The individual MABS responses to the various four-tone combinations were used in the analysis. The response was averaged over 50 ms sections with 2.5 ms overlap between successive sections, beginning with stimulus onset (see Nelken et al., 1994a). The analysis was applied to each time section separately. The term ‘data set’ is used below to refer to the responses to all the stimuli, recorded from one of the electrodes, dur- ing one of the time sections. Each data set was described as srcinating from terms of ascending orders. Formally, r flTfZYf35f4) = b +rl fl~f2d.i9fJ) -+r2 firf2tf3tfdJ + ..- 1) where r~~~,~~,~~,~~) is the response to the four-tone stimulus composed of the frequencies fl, fi, f3 and f4, r0 is the zeroth order term, r,(f,.fz,f3,f3) is the first order term, rz(f,,fz,fi,fJ is the second order term, and so on.  The zeroth order term, rO, was taken to be the mean MABS during the 300 ms before the stimulus onset, averaged over all the stimuli in the data set. Thus, this term described the baseline, or spontaneous, activity. The first order term described the effects of the single frequency content of the stimulus. Each first order term was written as a sum of four contributions corresponding to the frequencies of the tones compos- ing the stimulus. Formally, (2) where ai are the first order contributions of the four frequencies. For a frequency table of 30 frequen- cies, 30 first order contributions had to be estimated. This was done by finding the 30 numbers ai such that the first order error in the fit, - (ro + rr( f, Jz 7f3 7f4) ) (31 was smallest in the least square sense, that is, the sum of eKLLLfJ over all the stimulus presentations was smallest. In practice, the r0 term was substracted from each response in the data set, and then one linear equation, relating the sum of the appropriate first order contributions to the corresponding response, was written for each stimulus presentation. Since there were many more equations then first order contribu- tions, the resulting system was overdetermined, and was solved by the least squares method. The second order term described the effects of non-linear summation of the responses to pairs of tones in the stimulus. It was assumed that each pair of frequencies appearing in the stimulus could modify the response predicted by the first order contributions, and again, a least squares fit was computed. Formally, the 2nd order term in the response was written as + az(fsJ4) (4) where a,(fi,fjl are the second order contributions. As in the previous step, the zeroth order and first order terms were substracted from the responses, and then one equation, relating the sum of the appropriate six second order contributions to the corresponding resid- ual (the response minus the zeroth and first order terms), was written for each stimulus presentation. Even though there are many more second order contri- butions (465 for a 30-frequency table) than first order contributions, there were nevertheless many more stimulus presentations and the resulting linear system was still overdetermined, so that it could be solved by least squares. In this case, it was the square of the second order error in the fit, +rZ(fJ?JVf41) (5) which was minimized over all the data set. The higher order terms (for four-tone data, third and fourth order terms) could be computed in princi- ple. This was not done for practical reasons: the accu- mulation of noise in the estimation of the successive terms, and the lack of sufficient amounts of data to estimate the higher order contributions. 3. Results The responses to single tones and two-tone combi- nations, and comparison between the responses of well separated units, cluster activity and MABS were de- scribed in the companion paper (Nelken et al., 1994a). In this paper, the results of the analysis of the four-tone stimuli are reported. The results reported here are based on the MABS signal measured in 16 electrode penetrations in 3 cats (in one of the experiments, 2 electrodes showed nonstationary phenomena, as de- scribed above). This paper concentrates on the ON responses (the average MABS between 0 ms and 50 ms after signal onset). Although there were responses in later time sections, they were generally much weaker (Nelken, 1991; Nelken et al., 1994a). 50 40 30 > ZL 2o 10 0 -10 Frequency (kHz) Fig. 1. First order contributions at three levels (3 dB, 27 dB and 51 dB re threshold) for four-tone stimuli. The frequencies of the four tones were chosen pseudo-randomly from a 12-frequency table. The contributions were computed from the averaged MABS signal recorded between 0 ms and 50 ms after stimulus onset. The fre- quency axis is logarithmic. Continuous line - 51 dB level. Short dashes - 27 dB. Long dashes - 3 dB. Note that the contributions are similar to the expected single tone responses: the responses at BF increase to saturation within 27 dB from threshold, and with addi- tional increase in level the range of frequencies which evoke activity grows.  I. Nelken et al. /Hearing Research 72 I 9041 223-236 277 3.1. First and second order contributions An example of the first order contributions for the ON response (0 ms - 50 ms after signal onset) recorded from one electrode at 3 sound levels is shown in Fig. 1. In this experiment, a 12-frequency table was used. so that the first order contributions had to be estimated at 12 frequencies only. At 3 dB re threshold there were weak contributions around the best frequency (BF, 2783 Hz in this case), and no contributions to the response from other frequencies. At 27 dB re thresh- old, there was a large peak near BF, with some contri- butions from frequencies below BF. At 51 dB re threshold, the contributions near BF decreased slightly, while the low-frequency ‘tail’ became relatively more prominent. The first order contributions in this case reflected the single-tone behaviour of the cortical activ- ity in at least two measures: the BF, which was the same, and the QlO (width of the tuning curve at 10 dB Re threshold divided by the BF), which was slightly higher than 1. Another example of first order contributions, from another experiment, is shown in Fig. 2. In this case, the contributions from three different electrodes at 27 dB re threshold are shown. These electrodes had an ante- rior-posterior orientation in the cortex. The change in the BF with the location of the electrodes was reflected in the first order contributions for the three electrodes. The anterior-most electrode had the highest BF, the posterior-most electrode had the lowest BF, and the middle electrode had an intermediate BF. The single tone responses from these electrodes were measured 0.1 10 Fig. 2. First order contributions for the signal recorded simultane- ously from three electrode at 27 dB re threshold. The frequencies of the four tones were chosen pseudo-randomly from a 30.frequency table. The contributions were computed from the averaged MABS signal recorded between 0 ms and 50 ms after stimulus onset. The electrodes were positioned along the anterior-posterior axis in the cortex. Note the shift of BF with electrode location. The data was collected in the same experiment as Fig. 2 in (Nelken et al., 19931, from electrodes 1,4 and 6. Continuous line: 1st order contributions for the data from electrode 1. Dotted line: 1st order contributions for the data from electrode 4. Dashed line: 1st order contributions for the data from electrode 6. I+++++++----- ++++++------ G ++++++-----+ 5 ++++___+___- +- -++_+___+- -++---+++- 5 II__ -++-+++- 0:9 1 Freq2 (KHz) Fig. 3. Sign of the second order contributions for the S1 dB data whose first order contributions are presented in Fig. 1. Because of the symmetry of the second order contributions. the map is symmet- rical with respect to the main diagonal. Note the ordered organiza- tion of the contributions: negative contributions mostly along the diagonal and in its vicinity, positive contributions farther from it. No smoothing was applied to the data. also, and there is a good agreement between the two measurements of BFs (the single tone BFs were 2420 Hz, 1593 Hz and 523 Hz respectively). There is also good agreement in the bandwidth of the responses (see the companion paper, Nelken et al., 1994a, Fig. 5, for the single tone MABS data from these electrodes). Whereas the first order contributions are easily in- terpreted as the effect of single frequencies on the response, the second order contributions actually re- flect the modulation of the response caused by the presence of the pairs of tones in the stimulus, In consequence, they cannot be interpreted directly in terms of the observed responses. To get a feeling for their general characteristics, Fig. 3 presents the sign of the second order contributions as function of the two frequencies for the data set in Fig. 1, at 51 dB re threshold (the sign, rather than the magnitude, is used here to clearly separate between suppressory and facil- itatory interactions). It can be seen that there is a partition of the f,-fz plane into two parts: on the f, =f2 diagonal (from lower left to upper right) and in its vicinity there is a tendency of the second order contributions to be negative. This may be the result of saturation in the response, so that the response to a tone at twice the amplitude is less than twice the response at the srcinal amplitude, and of two-tone suppression. Farther from the diagonal, there is a clear block of positive contributions (most of the contribu- tions with f, < 2100 Hz and fZ > 2100 Hz). It is con- cluded that the second order contributions are orga- nized in ‘patches’ of suppression and facilitation in the f,-fz plane. Similar patches were seen for the ON responses in all cases at 27 dB and 51 dB re threshold (32 cases>. At 3 dB re threshold, the signal to noise ratio was usually too small to see any signs of such organization.
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