Spectro-temporal interpretation of activity patterns of auditory neurons.

Sensory receptors transform an external sensory stimulus into an internal neural activity pattern. This mapping is studied through its inverse. An earlier paper showed that within the context of a neuron model composed of a linear filter followed by an exponential pulse generator and a Gaussian stimulus ensemble a unique "most plausible" first-order stimulus estimate can be constructed. This method, applicable only to neurons showing phase-lock, is extended to neurons without phase-lock. In this situation second-order spectro-temporal stimulus estimates are produced; examples are given from simulation. The method is applied to activity of neurons in the auditory system of the frog.

Representation of time-dependent correlation and recurrence time functions. A new method to analyse non-stationary point processes.

Correlation functions based on time averaging are not suited to study non-stationary point processes (e.g. the electric organ discharge activity of weakly-electric pulse fish). To overcome this problem, we present here a time-dependent correlation method, which can also be applied to study complicated correlations of moderately non-stationary point processes (e.g. neuronal spike trains). Indication of recurrence time aspects of the point processes provides a more complete representation of the correlation functions. In addition higher order correlations between two point processes are represented.

Directional hearing in the grassfrog (Rana temporaria L.). II. Acoustics and modelling of the auditory periphery.

In an earlier paper (Vlaming et al., 1984) we reported on optical measurements (laser-doppler interferometry) of the vibrations characteristics of the grassfrog's tympanic membrane. In the present paper these measurements were extended to include acoustic measurements concerning the functional role of the mouth cavity in frog hearing. Based on these measurements a model of the frog's acoustic periphery, consisting of three coupled linear oscillators with three entrance ports for sound, was developed and analyzed mathematically to give the various relevant transfer functions. The model is characterized by six parameters, all of which could be estimated from the available experimental data. For frequencies up to some 1500 Hz the model adequately describes the experimental data, both our own and earlier, seemingly conflicting data in the literature. For higher frequencies deviations occur, possibly due to nonuniform vibrations of the membranes. The model was used to evaluate the monaural directional sensitivity of the frog under free-field stimulation. Essentially it behaves as a combined pressure-gradient receiver, with highly frequency-dependent directional sensitivity. Directional sensitivity of the tympanic membrane could be modulated drastically by changing the resonance properties of the mouth cavity, without affecting the intrinsic membrane properties. This, theoretically, allows the frog to manipulate its direction sensitivity by actively tuning the volume of its mouth cavity. In order to account for discrepancies with known properties of low-frequency auditory nerve fibers an additional, extra-tympanic channel was included into the model. The extended model, the second-channel possibly involving the opercularis complex, provides a good quantitative fit to the available data on tympanic membrane movement as well as auditory nerve activity. Finally, the model enables to simulate a (moving) sound source in space, while stimulating the frog via closed couplers.

The master equation for neural interaction.

Based on neural interaction equations a random walk model for the stochastic dynamics of a single neuron is introduced. In this model the somatic potential corresponds to a state in the state space and action potentials provide the mechanism causing transitions. Time is made discrete, consisting of small finite increments delta t; assumptions are made about the transitions within such an increment and the associated probabilities are formulated. These quantities depend on delta t and on parameters derived from neural interaction equations. Moreover the model is chosen so that the sequence of somatic potentials is a Markov chain. By appropriately scaling the parameters, in the limit as delta t----0, a master equation for the probability in continuous time is obtained. Depending on the parameters, the master equation describes the evolution of a deterministic, a diffusion, or a discrete process. An interpretation for the diffusion and discrete processes is outlined. The conclusion is that the stochastic equations for neural interaction lead to a master equation representing a diffusion or a discrete process depending on the number, size of synaptic connectivity coefficients, and probability distribution of neural activity. An example is included describing how a master equation may be used to derive properties of the single neuron's output process.

Quantitative characterisation procedure for auditory neurons based on the spectro-temporal receptive field.

Studies dealing with auditory information processing often present the dynamic spectrum of the sound stimulus (sonogram) in addition to the stimulus waveform. The sonogram, presenting the spectral and temporal properties of the sound in a combined way, reflects properties that are assumed relevant in central information processing. For 12 neurons recorded from the midbrain of the grass frog the sonogram of a Gaussian wide-band noise stimulus was correlated with the output of the neuron to that noise. From this input-output correlogram the spectro-temporal receptive field (STRF) was calculated. The STRF reflects those spectral and temporal properties of the stimulus that influence the firing probability of the neuron. A quantitative procedure was developed to calculate the neuron's response as far as it could be derived from the STRF. This procedure basically consisted of a convolution between STRF and the sonogram of the stimulus followed by a summation over the various frequency bands. In this way it proved possible to estimate to what extent the STRF characterised the neuron's firing behaviour. Heuristic approaches, in which the neuron was modelled to a parallel series of band-pass filters, a summator and a static nonlinearity, representing a spike-generating mechanism, resulted in a considerable improvement of the characterisation.

Prediction of the responses of auditory neurons in the midbrain of the grass frog based on the spectro-temporal receptive field.

The spectro-temporal receptive field (STRF) of an auditory neuron represents those characteristics of the sound stimulus in both the time and frequency domain that affect the firing probability of the neuron. The STRF is determined under stationary stimulus conditions for Gaussian wide-band noise. It has been demonstrated that for some neurons the response to that noise could to a considerable extent be derived from the STRF. In the present study the usefulness of the STRF is tested to predict responses to other stimuli such as noise with different frequency content and to species-specific vocalisations. It appears that the predicted response to vocalisations is at best in qualitative agreement with the actual response.

Spectro-temporal characteristics of single units in the auditory midbrain of the lightly anaesthetised grass frog (Rana temporaria L.) investigated with tonal stimuli.

Responses were obtained from 112 auditory neurons in the midbrain of the grass frog in response to sequences of tones. Their spectro-temporal sensitivities (STS) were determined by a second-order cross-correlation technique. For the majority of units the shape of their action potentials, the degree of timelock to the stimulus and the recording sites were obtained. Two stages of information processing could be distinguished. One was characterized by short latencies (less than 30 ms), strong timelock to the stimulus and many of these units had axon-like action potential waveforms. They were localised in the ventral part of the principal nucleus from the torus semicircularis and in the transition region between laminar and principal nucleus. The other stage comprised units, found all over the torus, with longer latencies, and a weaker timelock to the stimulus. Several units which were predominantly found in the central part of the torus, especially the magnocellular nucleus, showed a broad or multiple STS. Within the principal nucleus a weak tonotopy was found, the dorsoposterior part being sensitive to lower frequencies, the ventroanterior part to the higher frequencies. Binaural-interaction properties are discussed with respect to the eardrum coupling through the mouth cavity. An organisational plan for the torus semicircularis is proposed.

Spectro-temporal characteristics of single units in the auditory midbrain of the lightly anaesthetised grass frog (Rana temporaria L) investigated with noise stimuli.

About 30% of the auditory units in the midbrain of the lightly anaesthetised grass frog respond in a sustained way to stationary pseudorandom noise. This response is described by the spectro-temporal receptive field (STRF), the regions in the spectro-temporal domain where the average second-order functional of those parts of the stimulus ensemble that precede the action potentials differ from the average second-order functional of the stimulus ensemble. By means of the STRF frequency selectivity, postactivation suppression and lateral suppression can quantitatively be studied under one and the same experimental condition. Auditory units that respond to stationary noise are localised in those parts of the torus where fibres enter from the olivary nucleus. They are characterised by relatively short latencies to tones and probably represent the first information-processing stage in the torus semicircularis.

Spectro-temporal characterization of auditory neurons: redundant or necessary.

For neurons in the auditory midbrain of the grass frog the use of a combined spectro-temporal characterization has been evaluated against the separate characterizations of frequency-sensitivity and temporal response properties. By factoring the joint density function of stimulus intensity, I (f, t), preceding a spike, into two marginal density functions I1(f) and I2(t) one may under the assumption of statistical independence reconstruct the joint density by multiplication: I1(f).I2(t). The reconstructed I(f, t) is compared to the original I(f, t) for 83 neurons: in 23% thereof the I(f, t) appeared to be vastly different from I(f, t). These units appeared to be located dominantly in the ventral parts of the auditory midbrain and had a latency exceeding 30 ms. On the basis of the action-potential wave forms the absence of non-separable I(f, t) in the incoming nerve fiber population is concluded. A spectro-temporal characterization of auditory neurons seems mandatory for investigations in and central from the auditory midbrain.

The spectro-temporal receptive field. A functional characteristic of auditory neurons.

The Spectro-Temporal Receptive Field (STRF) of an auditory neuron has been introduced experimentally on the base of the average spectro-temporal structure of the acoustic stimuli which precede the occurrence of action potentials (Aertsen et al., 1980, 1981). In the present paper the STRF is considered in the general framework of nonlinear system theory, especially in the form of the Volterra integral representation. The STRF is proposed to be formally identified with a linear functional of the second order Volterra kernel. The experimental determination of the STRF leads to a formulation in terms of the Wiener expansion where the kernels can be identified by evaluation of the system's input-output correlations. For a Gaussian stimulus ensemble and a nonlinear system with no even order contributions of order higher than two, it is shown that the second order cross correlation of stimulus and response, normalized with respect to the spectral contents of the stimulus ensemble, leads to the stimulus-invariant spectro-temporal receptive field. The investigation of stimulus-invariance of the STRF for more general nonlinear systems and for stimulus ensembles which can be generated by nonlinear transformations of Gaussian noise involve the evaluation of higher order stimulus-response correlation functions.

A comparison of the spectro-temporal sensitivity of auditory neurons to tonal and natural stimuli.

The spectro-temporal sensitivity of auditory neurons has been investigated experimentally by averaging the spectrograms of stimuli preceding the occurrence of action potentials or neural events ( the APES : Aertsen et al., 1980, 1981). The properties of the stimulus ensemble are contained in this measure of neural selectivity. The spectro-temporal receptive field (STRF) has been proposed as a theoretical concept which should give a stimulus-invariant representation of the second order characteristics of the neuron's system function (Aertsen and Johannesma, 1981). The present paper investigates the relation between the experimental and the theoretical description of the neuron's spectro-temporal sensitivity for sound. The aim is to derive a formally based stimulus-normalization procedure for the results of the experimental averaging procedure. Under particular assumptions, regarding both the neuron and the stimulus ensemble, an integral equation connecting the APES and the STRF is derived. This integral expression enables to calculate the APES from the STRF by taking into account the stimulus spectral composition and the characteristics of the spectrogram analysis. The inverse relation, i.e. starting from the experimental results and by application of a formal normalization procedure arriving at the theoretical STRF, is effectively hindered by the nature of the spectrogram analysis. An approximative "normalization" procedure, based on intuitive manipulation of the integral equation, has been applied to a number of single unit recordings from the grassfrog's auditory midbrain area to tonal and natural stimulus ensembles. The results indicate tha spectrogram analysis, while being a useful real-time tool in investigating the spectro-temporal transfer properties of auditory neurons, shows fundamental shortcomings for a theoretical treatment of the questions of interest.

Spectro-temporal receptive fields of auditory neurons in the grassfrog. III. Analysis of the stimulus-event relation for natural stimuli.

The stimulus-event relation of single units in the auditory midbrain area, the torus semicircularis, of the anaesthetized grassfrog (Rana temporaria L.) during stimulation with a wide ensemble of natural stimuli, was analysed using first and second order statistical analysis techniques. The average stimulus preceding the occurrence of action potentials, in general, did not prove to give very informative results. The second order procedure consisted in the determination of the average dynamic power spectrum of the pre-event stimuli, following procedures as described elsewhere (Aertsen and Johannesma, 1980' Aertsen et al., 1980). The outcome of this analysis was filtered with the overall power spectrum of the complete stimulus ensemble in order to correct for its non-uniform spectral composition. The "stimulus-filtered" average pre-event dynamic spectrum gives a first indication of the "spectro-temporal receptive field" of a neuron under natural stimulus conditions. Results for a limited number of recordings are presented and, globally, compared to the outcome of an analogous analysis of experiments with tonal stimuli.

Neural representation of the acoustic biotope. A comparison of the response of auditory neurons to tonal and natural stimuli in the cat.

Cats were stimulated with tones and with natural sounds selected from the normal acoustic environment of the animal. Neural activity evoked by the natural sounds and tones was recorded in the cochlear nucleus and in the medial geniculate body. The set of biological sounds proved to be effective in influencing neural activity of single cells at both levels in the auditory system. At the level of the cochlear nucleus the response of a neuron evoked by a natural sound stimulus could be understood reasonably well on the basis of the structure of the spectrograms of the natural sounds and the unit's responses to tones. At the level of the medial geniculate body analysis with tones did not provide sufficient information to explain the responses to natural sounds. At this level the use of an ensemble of natural sound stimuli allows the investigation of neural properties, which are not seen by analysis with simple artificial stimuli. Guidelines for the construction of an ensemble of complex natural sound stimuli, based on the ecology and ethology of the animal under investigation are discussed. This stimulus ensemble is defined as the Acoustic Biotope.

Estimation of signal and noise spectra by special averaging techniques with application to a posteriori "Wiener" filtering.

This paper deals with the problem of separating the spectra of signal and noise in ensembles where the signal can be considered as an invariant component and the noise as a stationary additive background. Several methods are discussed and compared on the basis of a statistical analysis of the first two moments of the estimators for signal and noise spectra. As a consequence a procedure is proposed which provides a flexible compromise between estimation accuracy and computational effort. The application of this procedure to a posteriori "Wiener" filtering is compared with a more common, but time consuming, technique.

Spectral and temporal characteristics of activation and suppression of units in the cochlear nuclei of the anaesthetized cat.

1. The responses are described of cochlear nucleus neurons of anaesthetized cats as a function of time in dependence on intensity and frequency of tonal stimuli. Depending on spectral properties three types are distinguished in the group of spontaneously active units: A type (activation only) AS type (activation and suppression) and S type (suppression only). The A(S) neurons have insufficient spontaneous activity to judge presence or absence of suppression. 2. Four temporal patterns of response are distinguished: transient, sustained, build up and complex. Units of the A type display a sustained time course of activation and have properties similar to those of auditory nerve fibres. S type units show sustained suppression. Temporal patterns of activation other than sustained were found only in the AS and A(S) units. 3. The recordings indicate that on suppression and off suppression are present more frequently in VCN neurons than previously found. The suppression phenomena in the DCN are, however, still more wide spread and more dramatic in appearance. 4. In contrast to earlier findings, off suppression was always observed and never seen to extent beyond the on activation band in A neurons. Data from AS neurons indicate that off suppression is neither simply an affect of high firing rates nor simply a continuation of on suppresion. 5. The relations between off suppression and spectral and temporal characteristics of on activation and suppression can be matched with a model featuring overlapping antagonistic inputs and postexcitatory inhibition.

Neurons in the cochlear nucleus investigated with tone and noise stimuli.

1. Responses of cochlear nucleus neurons to stationary and amplitude modulated noise stimulation are investigated and compared with responses to tonal stimuli. 2. Cross-correlation functions, computed from responses to stationary noise stimulation, showing a clear oscillation could be most easily obtained from low CF fibres presumed to be auditory nerve fibres and low CF cochlear nucleus neurons showing only activation response and a primarylike temporal pattern of response to tone bursts. This reflects good quality of phase locking in these neurons. 3. The CCF reflects strongly the frequency selectivity of the neuron as revealed in its response area but not the temporal pattern of response to tone bursts. 4. Responses to noise bursts are correlated with the responses to tone bursts of many different frequencies in both their sign (i.e. activation or suppression) and their temporal pattern. 5. The concept of two independently operating mechanisms, one depending on the fine time structure of the stimulus (the carrier) and the other on its amplitude, and determining respectively the fine time structure of the response pattern and its magnitude, is introduced. Experimental data are presented which lend support to the adequacy of the description in the majority of cases and reveal its shortcomings in others.

Statistical analysis and interpretation of the initial response of cochlear nucleus neurons to tone bursts.

1. Subject of investigation is the initial response of cochlear nucleus neurons and units presumed to be auditory nerve fibres to CF tone burst stimulation. 2. The initial response is characterized by computing the distribution of the latency of the first spike and of the duration of the first interval in the ensemble of responses to a large number of stimuli. 3. In many of the neurons the properties of both distributions appear to be related. The presumed auditory nerve fibres and spontaneously active cochlear nucleus neurons showing only activation responses to tonal stimuli (A type) exhibit irregularity in both response onset and intervals. Minimum latency and minimum first intervals are short. On the other hand, spontaneously active neurons with both activation and suppression in the response area (AS type) and silent neurons showing only activation (A(S) type) often show a more precisely timed onset of response and narrow interval distributions. In many neurons this leads to oscillations in the PSTH (chopping). In these neurons minimum latency and minimum first interval have higher values. The longer minimum latency cannot be attribute-d to longer pure time delays in these neurons. 4. The results are interpreted as speaking in favour of temporal integration as an important mechanism in many of the AS and A(S) neurons, particularly those in the DCN. The firing patterns of A neurons are thought to indicate virtual absence of this mechanism. 5. Using pure time delay estimates derived from cross-correlation functions, computed from the responses to stationary noise, an attempt is made to estimate the integration time in the cochlear and in the cochlear nucleus neurons.