Nonlinear dynamics of cellular vibrations in the organ of Corti.
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Animals↗
Biomedical subjects
M C Teich
Publications and source records attributed to M C Teich.
Multinomial pulse-number distributions for neural spikes in primary auditory fibers: theory.
We previously reported experimental short- and long-counting-time pulse-number distributions (PND's) for the neural spike train in cat primary auditory nerve fibers. Data were obtained for spontaneous activity, pure-tone stimuli with a wide range of frequencies and intensity levels, and Gaussian noise. The irregular shapes of the PND's are an indication of the presence of spike clusters of various sizes in the neural impulse train. We develop a family of theoretical cluster counting distributions and examine their suitability for describing the experimental PND's. The reduced-quintinomial distribution provides theoretical results that describe the characteristics of the PND's quite well, accounting for the smooth or scalloped behavior of short-counting-time data, the jagged nature of long-counting-time data, and the Poisson-like character of very-short-counting-time data. This family of distributions admits values for the spike-number mean-to-variance ratio that are independent of stimulus level, in agreement with experimental observation. A number of procedures for fitting the theoretical distributions to the experimental PND's are studied. These include the use of a minimum mean-square error criterion, the factorial moments of the data, and the discrete Fourier transform of the PND. The first of these techniques appears to be the most useful.
Animals↗
Multiplication and refractoriness in the cat's retinal-ganglion-cell discharge at low light levels.
Measurements of the pulse-interval distribution and pulse-number distribution for cat retinal ganglion cells in darkness and light have been carried out by Barlow, Levick, and Yoon. The experimental results for an on-center brisk-sustained cell are in accord with a mathematical model incorporating four features: Poisson quantum fluctuations, additive dark noise, multiplication noise (random multiple neural spikes per absorbed quantum), and refractoriness. The data cannot be properly explained by a model lacking any one of these features. Parameters extracted from the model are in good agreement with physiological values.
Animals↗
Pulse-number distribution for the neural spike train in the cat's auditory nerve.
Pulse-number distributions (PNDs) were recorded from primary afferent fibers in the auditory nerve of the cat, using standard extracellular microelectrode recording techniques. Pure-tone and broadband-noise stimuli were used. The number of neural spikes (pulses) n was measured in a set of contiguous intervals, each of duration T seconds. The quantity n varies from one interval to another. These data were then used to determine the PND, which is the probability p(n,T) of occurrence of n spikes in the time T, versus the number n. The estimated mean and variance of p(n,T) were obtained. Two different values of T were used. An unexpected observation was that the count mean-to-variance ratio R is relatively constant and independent of the stimulus intensity. Use of the PND as a statistical measure of the underlying neural point process has a number of virtues. For example, the PND readily exhibits the existence of spike clusters (e.g., pairs) for some units. The PND is essentially unaffected by time jitter and time quantization and provides a statistically significant measure for units firing at low rates. A study of the scaled and unscaled pulse-interval distributions (PIDs), under conditions of spontaneous firing, demonstrates that the occurrences of neural events are generally not describable by a renewal process. Our investigation shows that none of the point processes customarily used to model the auditory neural spike train is consistent with all of the data. It appears that the encoding of acoustic information into nerve spikes in the peripheral auditory system takes the form of a cluster point process similar to the Neyman-Scott type. For pure-tone excitation, the PND will be well represented as a multinomial distribution in this case.
Animals↗
Multiplication noise in the human visual system at threshold: 2. Probit estimation of parameters.
A mathematical technique is described that relates detection model parameters to stimulus magnitude and experimental probability of detection. The normalizing transform is used to make the response statistics approximately Gaussian. Conventional probit analysis is then applied. From measurements at M stimulus levels, a system of M equations is solved and estimates of M unknown parameters of the detection model are obtained. The technique is applied to a threshold vision model based on additive and multiplicative Poisson noise. Results are obtained for the parameter estimates for individual subjects, and for the standard deviation of the estimates, for various values of the stimulus energy and number of trials. A frequency-of-seeing experiment is performed using a point-source stimulus that randomly assumes 3 energy levels with 200 trials per level. With a central efficiency of 50%, the estimated ocular quantum efficiency for our four subjects lies between 12% and 23%, the average dark count at the retina lies between 8 and 36 counts, and the threshold count for our (low false-report rate) data lies between 11 and 32. The theoretical results reduce to those obtained by Barlow (J. Physiol. London 160, 155-168, 1962), in the absence of dark light and multiplication noise.
Humans↗
Multiplication noise in the human visual system at threshold. 3. The role of non-Poisson quantum fluctuations.
Several kinds of light used in vision experiments produce photon statistics that are distinctly non-Poisson. Representative examples are light from a cathode-ray tube and an image-intensifier device. For the class of vision experiments in which the photon statistics play an important role, excess fluctuations produced by such light sources can alter the observed results and obscure the visual mechanisms being studied. They must therefore be accounted for in a proper way. We use the results of a Hecht-Shlaer-Pirenne type experiment, carried out with modulated Poisson light, to illustrate the point. Sensitivity and modulation depth, as well as sensitivity and reliability, are shown to be traded against each other. Finally, we demonstrate that number-state light, which is comprised of photons of an ideal kind, provides the ultimate tool for extracting information about the intrinsic noise distribution in the visual system at threshold. The state of the art in producing such light is discussed.
Humans↗
Multiplication noise in the human visual system at threshold: 1. Quantum fluctuations and minimum detectable energy.
We have carried out a series of frequency-of-seeing experiments similar to those performed by Hecht, Shlaer, and Pirenne [J. Gen. Physiol. 25, 819-840 (1942)], using an Ar+ laser operated at 514.5 nm as the source of light. In certain blocks of trials, our subjects were encouraged to report as seen those trials in which the stimulus might have been present. It was determined that sensitivity and reliability were traded against each other over a broad range: for our subjects, the detection of 147 photons at the cornea with 60% frequency of seeing entailed, on the average, a 1% false-positive rate (FPR), whereas the detection of 34 photons at the cornea with 60% frequency of seeing was accompanied by a 33% FPR. A new neural-counting model has been developed in the framework of signal-detection theory. It combines Poisson stimulus fluctuations with additive and multiplicative neural noise, both of which are known to be present in the visual system at threshold. The resulting probability-of-detection curves, derived from the Neyman Type-A counting distribution, are in good accord with our experimental frequency-of-seeing data for sensible values of the model parameters. We deduce that, on the average, our four subjects are able to detect a single photon at the retina with 60% frequency of seeing, at the expense of a 55% FPR. In Part 2 of this set of papers [P.R. Prucnal and M.C. Teich, Biol. Cybern. 43, 87-96 (1982)], we use the normalizing transform, together with probit analysis, to provide improved estimates of threshold parameters, whereas in Part 3 [M.C. Teich, P.R. Prucnal, G. Vannucci, M.E. Breton, and W.J. McGill, submitted to Biol. Cybern.], we consider the effects of non-Poisson quantum fluctuations.
Adult↗
A neural-counting model incorporating refractoriness and spread of excitation. II. Application to loudness estimation.
In previous paper [Teich and Lachs, J. Acoust. Soc. Am 66, 1738--1749 (1979)] we demonstrated that an energy-based neural counting model incorporating refractoriness and spread of excitation satisfactorily described the results of pure-tone intensity discrimination experiments. In this paper, we show that the identical linear filter refractoriness model (LFRM) also provides proper results for pure-tone loudness estimation experiments at all stimulus levels. In particular, as the stimulus intensity increases from very low to moderate values, the model predicts that the slope of the intensity discrimination curve will climb from 1/2 toward 1, whereas the slope of the loudness function will gradually decline below 1 in this same region. For sufficiently high values of the stimulus intensity, the slopes calculated from a simplified (crude saturation) version of the model are found to be 1--1/4N for the intensity discrimination curve and 1/2N for the loudness function. The quantity N is the number of poles associated with the tuned-filter characteristic of the individual neural channels; it is the only important free parameter in the model. Appropriate values for N appear to lie between 2 and 4, providing an asymptotic slope for the intensity discrimination curve bounded by 7/8 and 15/16 (the near miss to Weber's Law), and an asymptotic slope for the loudness function bounded by 1/4 and 1/8. The results follow from the assumption that the neural concomitant of loudness is the number of impulses observed on a collection of parallel neural channels during a fixed observation time. Our calculations are supported by Hellman and Zwislocki's [J. Acoust. Soc. Am. 33, 687--694 (1961)] observation of unit slope for the loudness function at low intensities and provide a theoretical foundation, based on spread of excitation, for Stevens' power law at high intensities.
Differential Threshold↗
State-vector formalism for intrapersonal, interpersonal, and group interactions.
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Group Processes↗
A neural-counting model incorporating refractoriness and spread of excitation. I. Application to intensity discrimination.
We consider in detail a new mathematical neural-counting model that is remarkably successful in predicting the correct detection law for pure-tone intensity discrimination, while leaving Weber's law intact for other commonly encountered stimuli. It incorporates, in rather simple form, two well-known effects that become more marked in the peripheral auditory system as stimulus intensity is increased: (1) the spread of excitation along the basilar membrane arising from the tuned-filter characteristics of individual primary afferent fibers and (2) the saturation of neural counts due to refractoriness. For sufficiently high values of intensity, the slope of the intensity-discrimination curve is calculated from a simplified (crude saturation) model to be 1-1/4N, where N is the number of poles associated with the tuned-filter characteristic of the individual neural channels. Since 1 less than or equal to N less than infinity, the slope of this curve is bounded by 3/4 and 1 and provides a theoretical basis for the "near miss" to Weber's law.
Auditory Perception↗
Refractoriness in the maintained discharge of the cat's retinal ganglion cell.
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Animals↗
Work-function estimation with a single yield measurement.
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Crystallography↗
Investigating routes to chaos in the guinea-pig cochlea using the continuous wavelet transform and the short-time Fourier transform.
The continuous wavelet transform (CWT) and the short-time Fourier transform (STFT) were used to analyze the time course of cellular motion in the guinea pig inner ear. The velocity responses of individual outer hair cells and Hensen's cells to amplitude modulated (AM) acoustical signals applied to the ear canal displayed characteristics typical of nonlinear systems, such as the generation of spectral components at harmonics of the carrier frequency. Nonlinear effects were particularly pronounced at the highest stimulus levels, where half-harmonic (and sometimes quarter-harmonic) components were also seen. The generation of these components was consistent with the behavior of a dynamical system entering chaos via a period-doubling route. A negative-stiffness Duffing oscillator model yielded period-doubling behavior similar to that of the experimental data. We compared the effectiveness of the CWT and the STFT for analyzing the responses to AM stimuli. The CWT (calculated using a high-Q Morlet-wavelet basis) and the STFT were both useful for identifying the various spectral components present in the AM velocity response of the cell. The high-Q Morlet wavelet CWT was particularly effective in distinguishing the lowest frequency components present in the response, since its frequency resolution is appreciably better than the STFT at low frequencies. Octave-band-based CWTs (using low-Q Morlet, Meyer, and Daubechies 4-tap wavelets) were largely ineffective in analyzing these signals, inasmuch as the frequency spacing between neighboring spectral components was far less than one octave.
Animals↗
Fractal character of the electrocardiogram: distinguishing heart-failure and normal patients.
Statistical analysis of the sequence of heartbeats can provide information about the state of health of the heart. We used a variety of statistical measures to identify the form of the point process that describes the human heartbeat. These measures are based on both interevent intervals and counts, and include the interevent-interval histogram, interval-based periodogram, rescaled range analysis, the event-number histogram, Fano-factor, Allan Factor, and generalized-rate-based periodogram. All of these measures have been applied to data from both normal and heart-failure patients, and various surrogate versions thereof. The results show that almost all of the interevent-interval and the long-term counting statistics differ in statistically significant ways for the two classes of data. Several measures reveal 1/f-type fluctuations (long-duration power-law correlation). The analysis that we have conducted suggests the use of a conveniently calculated, quantitative index, based on the Allan factor, that indicates whether a particular patient does or does not suffer from heart failure. The Allan factor turns out to be particularly useful because it is easily calculated and is jointly responsive to both short-term and long-term characteristics of the heartbeat time series. A phase-space reconstruction based on the generalized heart rate is used to obtain a putative attractor's capacity dimension. Though the dependence of this dimension on the embedding dimension is consistent with that of a low-dimensional dynamical system (with a larger apparent dimension for normal subjects), surrogate-data analysis shows that identical behavior emerges from temporal correlation in a stochastic process. We present simulated results for a purely stochastic integrate-and-fire model, comprising a fractal-Gaussian-noise kernel, in which the sequence of heartbeats is determined by level crossings of fractional Brownian motion. This model characterizes the statistical behavior of the human electrocardiogram remarkably well, properly accounting for the behavior of all of the measures studied, over all time scales.
Electrocardiography↗