Period Histograms Research Articles

Characterizing inner-hair-cell specific dysfunction from spike-train-derived transduction functions using a phenomenological auditory-nerve model

The impact of outer-hair-cell damage on sensorineural hearing loss (SNHL) has been extensively studied compared with inner-hair-cell (IHC) damage (e.g., stereocilial). Pre-clinical SNHL animal models provide unique data to directly address IHC-specific deficits (e.g., carboplatin-exposed chinchillas). Spike-train data (period histograms) to low sound level tones can be used to derive IHC-transduction functions by mapping instantaneous spike rates to corresponding sinusoidal pressure values (Horst et al., 2018). However, this approach depends on sensation level and spontaneous rate, which are both affected by IHC dysfunction. To better understand the effect of these dependencies, we used a phenomenological auditory-nerve (AN) model (Bruce et al., 2018) that provides parametric control over IHC and OHC dysfunction allowing exploration of optimal experimental design. Here, we explore the utility of spike-train-derived IHC-transduction functions in capturing parametric changes in IHC dysfunction as currently implemented in the AN model. We used unsupervised methods and information-theoretic approaches to quantify the dependency of transduction functions on IHC dysfunction. We also compared model findings with AN-fiber data recorded from carboplatin-exposed chinchillas. Preliminary findings suggest that transduction functions obtained from the AN model can capture IHC-specific dysfunction within specific regimes of controllable model parameters, thus showing promise for characterizing IHC dysfunction.

Pulsation Analysis of High-Amplitude δ Scuti Stars with TESS

In this work, the pulsation analysis is performed on 83 high-amplitude δ Scuti stars (HADS), which have been observed by the Transiting Exoplanet Survey Satellite. The results show that 49 of these HADS show single-mode pulsation, 27 of them show radial double-modes pulsation (in which 22 of them pulsate with the fundamental and first overtone modes and five of them pulsate with the first and second overtone modes), and seven of them show radial triple-modes pulsation (three of which are newly confirmed triple-mode HADS). The histogram of the fundamental periods and the ratios between the fundamental and first overtone periods show bimodal structures, which might be caused by the stellar evolution in this specific phase. Most of the radial triple-mode HADS have a fundamental amplitude of 41–54 mmag, and 50% of them have similar amplitudes of the fundamental and first overtone pulsation modes. All these hints require further confirmation not only in observations with more HADS samples, but also in theoretical models with suitable treatments of stellar evolution and pulsation.

Comprehensive listing of 156 reliable orbital periods for novae, including 49 new periods

ABSTRACT I report on a large-scale search for the orbital periods (P) of most known nova systems, by looking for significant, coherent, and stable optical photometric modulation in two or more independent light curves taken mostly from the large surveys of TESS, Kepler, AAVSO, SMARTS, OGLE, ASAS, and ZTF. I have discovered 31 new orbital periods. Further, I have measured new periods for 18 novae with evolved companions, to 30 per cent accuracy, as based on their spectral energy distribution. Also, I have confirmed, improved, and rejected prior claims for P in 46 novae. (As part of this effort, I recognize that 5 novae display 1–3 coherent, significant, and transient periodicities 0.12–4.1 d, with these being mysterious as not being the orbital, spin, or superhump periods). In all, I have compiled a comprehensive list of 156 reliable P values for novae. The histogram of nova periods shows a minimum P at 0.059 h (85 min), and a Period Gap from 0.071 to 0.111 d (1.70–2.66 h). The upper edge of the Period Gap is significantly different between novae (0.111 d), nova-like systems (0.131 d), and dwarf novae (0.141 d). A further issue from the histogram is that 31 per cent of nova systems have evolved companions, for which there has been no models or understanding for their current state or evolution. For the novae with red giant companions, 15-out-of-20 are in the bulge population, despite novae with main-sequence and subgiant companions having bulge fractions near 0.11–0.32.

Theoretical Relationship Between Two Measures of Spike Synchrony: Correlation Index and Vector Strength.

Information processing in the nervous system critically relies on temporally precise spiking activity. In the auditory system, various degrees of phase-locking can be observed from the auditory nerve to cortical neurons. The classical metric for quantifying phase-locking is the vector strength (VS), which captures the periodicity in neuronal spiking. More recently, another metric, called the correlation index (CI), was proposed to quantify the temporally reproducible response characteristics of a neuron. The CI is defined as the peak value of a normalized shuffled autocorrelogram (SAC). Both VS and CI have been used to investigate how temporal information is processed and propagated along the auditory pathways. While previous analyses of physiological data in cats suggested covariation of these two metrics, general characterization of their connection has never been performed. In the present study, we derive a rigorous relationship between VS and CI. To model phase-locking, we assume Poissonian spike trains with a temporally changing intensity function following a von Mises distribution. We demonstrate that VS and CI are mutually related via the so-called concentration parameter that determines the degree of phase-locking. We confirm that these theoretical results are largely consistent with physiological data recorded in the auditory brainstem of various animals. In addition, we generate artificial phase-locked spike sequences, for which recording and analysis parameters can be systematically manipulated. Our analysis results suggest that mismatches between empirical data and the theoretical prediction can often be explained with deviations from the von Mises distribution, including skewed or multimodal period histograms. Furthermore, temporal relations of spike trains across trials can contribute to higher CI values than predicted mathematically based on the VS. We find that, for most applications, a SAC bin width of 50 ms seems to be a favorable choice, leading to an estimated error below 2.5% for physiologically plausible conditions. Overall, our results provide general relations between the two measures of phase-locking and will aid future analyses of different physiological datasets that are characterized with these metrics.

Phase Locking of Auditory Nerve Fibers: The Role of Lowpass Filtering by Hair Cells.

Phase locking of auditory-nerve-fiber (ANF) responses to the temporal fine structure of acoustic stimuli, a hallmark of the auditory system's temporal precision, is important for many aspects of hearing. Previous work has shown that phase-locked period histograms are often well described by exponential transfer functions relating instantaneous stimulus pressure to instantaneous spike rate, with no observed clipping of the histograms. The operating points and slopes of these functions change with stimulus level. The mechanism underlying this apparent gain control is unclear but is distinct from mechanical compression, is independent of refractoriness and spike-rate adaptation, and is apparently instantaneous. Here we show that these findings can be accounted for by a model consisting of a static Boltzmann transducer function yielding a clipped output, followed by a lowpass filter and a static exponential transfer function. Using responses to tones of ANFs from cats of both sexes, we show that, for a given ANF, the period histograms obtained at all stimulus levels for a given stimulus frequency can be described using one set of level-independent model parameters. The model also accounts for changes in the maximum and minimum instantaneous spike rates with changes in stimulus level. Notably, the estimated cutoff frequency is lower for low- than for high-spontaneous-rate ANFs, implying a synapse-specific contribution to lowpass filtering. These findings advance our understanding of ANF phase locking by highlighting the role of peripheral filtering mechanisms in shaping responses of individual ANFs.SIGNIFICANCE STATEMENT Phase locking of auditory-nerve-fiber responses to the temporal fine structure of acoustic stimuli is important for many aspects of hearing. Period histograms typically retain an approximately sinusoidal shape across stimulus levels, with the peripheral auditory system operating as though its overall transfer function is an exponential function whose slope decreases with increasing stimulus level. This apparent gain control can be accounted for by a static saturating transducer function followed by a lowpass filter. In addition to attenuating the AC component, the filter approximately recovers the sinusoidal waveform of the stimulus. The estimated cutoff frequency varies with spontaneous rate, revealing a synaptic contribution to lowpass filtering. These findings highlight the significant impact of peripheral filtering mechanisms on phase locking.

Modeling of spike trains in auditory nerves with self-exciting point processes of the von Mises type.

This article presents the modeling of spike trains in auditory nerve fiber (ANF) models with a one-memory self-exciting point process (SEPP) of the von Mises type. The ANF models were acoustically stimulated by a synaptic current of inner hair cells, or electrically stimulated by sinusoidally amplitude-modulated pulsatile waveforms. It has been shown that the parameters of one-memory SEPP of the von Mises type could be estimated by numerically maximizing the likelihood function from sample realizations of the spike trains in response to acoustic or electric stimulus. Furthermore, it was found that period histograms of the one-memory SEPP generated artificially on the basis of the estimated von Mises parameters agreed well with those of acoustic or electric stimulus, by performing the uniform-scores test. It implies that the waveforms of pulsatile electric stimuli should be selected such that the spike trains can be represented by one-memory SEPP of the von Mises type with appropriate parameters, efficiently carrying information to the cochlear implant user's brain, like that in acoustic stimulation of the healthy ear. The findings presented in this paper may play an important role in determining optimal parameters of pulsatile electric stimuli by using one-memory SEPP of the von Mises type, and further in the design of better cochlear prostheses.

Phase Locking of Auditory-Nerve Fibers Reveals Stereotyped Distortions and an Exponential Transfer Function with a Level-Dependent Slope.

Phase locking of auditory-nerve-fiber (ANF) responses to the fine structure of acoustic stimuli is a hallmark of the auditory system's temporal precision and is important for many aspects of hearing. Period histograms from phase-locked ANF responses to low-frequency tones exhibit spike-rate and temporal asymmetries, but otherwise retain an approximately sinusoidal shape as stimulus level increases, even beyond the level at which the mean spike rate saturates. This is intriguing because apical cochlear mechanical vibrations show little compression, and mechanoelectrical transduction in the receptor cells is thought to obey a static sigmoidal nonlinearity, which might be expected to produce peak clipping at moderate and high stimulus levels. Here we analyze phase-locked responses of ANFs from cats of both sexes. We show that the lack of peak clipping is due neither to ANF refractoriness nor to spike-rate adaptation on time scales longer than the stimulus period. We demonstrate that the relationship between instantaneous pressure and instantaneous rate is well described by an exponential function whose slope decreases with increasing stimulus level. Relatively stereotyped harmonic distortions in the input to the exponential can account for the temporal asymmetry of the period histograms, including peak splitting. We show that the model accounts for published membrane-potential waveforms when assuming a power-of-three, but not a power-of-one, relationship to exocytosis. Finally, we demonstrate the relationship between the exponential transfer functions and the sigmoidal pseudotransducer functions obtained in the literature by plotting the maxima and minima of the voltage responses against the maxima and minima of the stimuli.SIGNIFICANCE STATEMENT Phase locking of auditory-nerve-fiber responses to the temporal fine structure of acoustic stimuli is important for many aspects of hearing, but the mechanisms underlying phase locking are not fully understood. Intriguingly, period histograms retain an approximately sinusoidal shape across sound levels, even when the mean rate has saturated. We find that neither refractoriness nor spike-rate adaptation is responsible for this behavior. Instead, the peripheral auditory system operates as though it contains an exponential transfer function whose slope changes with stimulus level. The underlying mechanism is distinct from the comparatively weak cochlear mechanical compression in the cochlear apex, and likely resides in the receptor cells.

Input-output curves of low and high spontaneous rate auditory nerve fibers are exponential near threshold

Input-output (IO) properties of cochlear transduction are frequently determined by analyzing the average discharge rates of auditory nerve fibers (ANFs) in response to relatively long tonal stimulation. The ANFs in cats have spontaneous discharge rates (SRs) that are bimodally distributed, peaking at low (<0.5 spikes/s) and high (∼60 spikes/s) rates, and rate-level characteristics differ depending upon SR. In an effort to assess the instantaneous IO properties of ANFs having different SRs, static IO-curves were constructed from period histograms based on phase-locking of spikes to the stimulus waveform. These curves provide information unavailable in conventional average rate-level curves. We find that all IO curves follow an exponential trajectory. It is argued that the exponential behavior represents the transduction in the IHC and that the difference among ANFs having different SRs is predominantly a difference in gain attributed most likely to synaptic drive. © 2018 The authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Analysis of a purely conductance-based stochastic nerve fibre model as applied to compound models of populations of human auditory nerve fibres used in cochlear implant simulations.

The study presents the application of a purely conductance-based stochastic nerve fibre model to human auditory nerve fibres within finite element volume conduction models of a semi-generic head and user-specific cochleae. The stochastic, threshold and temporal characteristics of the human model are compared and successfully validated against physiological feline results with the application of a mono-polar, bi-phasic, cathodic first stimulus. Stochastic characteristics validated include: (i) the log(Relative Spread) versus log(fibre diameter) distribution for the discharge probability versus stimulus intensity plots and (ii) the required exponential membrane noise versus transmembrane voltage distribution. Intra-user, and to a lesser degree inter-user, comparisons are made with respect to threshold and dynamic range at short and long pulse widths for full versus degenerate single fibres as well as for populations of degenerate fibres of a single user having distributed and aligned somas with varying and equal diameters. Temporal characteristics validated through application of different stimulus pulse rates and different stimulus intensities include: (i) discharge rate, latency and latency standard deviation versus stimulus intensity, (ii) period histograms and (iii) interspike interval histograms. Although the stochastic population model does not reduce the modelled single deterministic fibre threshold, the simulated stochastic and temporal characteristics show that it could be used in future studies to model user-specific temporally encoded information, which influences the speech perception of CI users.

Modeled auditory nerve responses to amplitude modulated cochlear implant stimulation

Cochlear implants encode speech information by stimulating the auditory nerve with amplitude-modulated pulse trains. A computer model of the auditory nerve's response to electrical stimulation can be used to evaluate different approaches to improving CI patients' perception. In this paper a computationally efficient stochastic and adaptive auditory nerve model was used to investigate full nerve responses to amplitude-modulated electrical pulse trains. The model was validated for nerve responses to AM pulse trains via comparison with animal data. The influence of different parameters, such as adaptation and stochasticity, on long-term adaptation and modulation-following behavior was investigated. Responses to pulse trains with different pulse amplitudes, amplitude modulation frequencies, and modulation depths were modeled. Rate responses as well as period histograms, Vector Strength and the fundamental frequency were characterized in different time bins. The response alterations, including frequency following behavior, observed over the stimulus duration were similar to those seen in animal experiments. The tested model can be used to predict complete nerve responses to arbitrary input, and thus to different sound coding strategies.

Drosophila Preparation and Longitudinal Imaging of Heart Function In Vivo Using Optical Coherence Microscopy (OCM).

Longitudinal study of the heartbeat in small animals contributes to understanding structural and functional changes during heart development. Optical coherence microscopy (OCM) has been demonstrated to be capable of imaging small animal hearts with high spatial resolution and ultrahigh imaging speed. The high image contrast and noninvasive properties make OCM ideal for performing longitudinal studies without requiring tissue dissections or staining. Drosophila has been widely used as a model organism in cardiac developmental studies due to its high number of orthologous human disease genes, its similarity of molecular mechanisms and genetic pathways with vertebrates, its short life cycle, and its low culture cost. Here, the experimental protocols are described for the preparation of Drosophila and optical imaging of the heartbeat with a custom OCM system throughout the life cycle of the specimen. By following the steps provided in this report, transverse M-mode and 3D OCM images can be acquired to conduct longitudinal studies of the Drosophila cardiac morphology and function. The en face and axial sectional OCM images and the heart rate (HR) and cardiac activity period (CAP) histograms, were also shown to analyze the heart structural changes and to quantify the heart dynamics during Drosophila metamorphosis, combined with the videos constructed with M-mode images to trace cardiac activity intuitively. Due to the genetic similarity between Drosophila and vertebrates, longitudinal study of heart morphology and dynamics in fruit flies could help reveal the origins of human heart diseases. The protocol here would provide an effective method to perform a wide range of studies to understand the mechanisms of cardiac diseases in humans.

Linewidth measurement of mid infrared quantum cascade laser by optical feedback interferometry

We estimated experimentally the linewidth (0.28 MHz) of a distributed feedback quantum cascade laser emitting at 6.2 μm using optical feedback interferometry. The method is simply based on the analysis of the histogram of laser self-mixing fringe periods measured directly as voltage variation across the laser terminals. We assessed the optimal experimental conditions estimating the influence of the optical feedback strength on the interferometric phase noise and compared our results with those reported using conventional interferometric methods based on the analysis of the frequency noise power spectral density.

Encoding frequency contrast in primate auditory cortex

Changes in amplitude and frequency jointly determine much of the communicative significance of complex acoustic signals, including human speech. We have previously described responses of neurons in the core auditory cortex of awake rhesus macaques to sinusoidal amplitude modulation (SAM) signals. Here we report a complementary study of sinusoidal frequency modulation (SFM) in the same neurons. Responses to SFM were analogous to SAM responses in that changes in multiple parameters defining SFM stimuli (e.g., modulation frequency, modulation depth, carrier frequency) were robustly encoded in the temporal dynamics of the spike trains. For example, changes in the carrier frequency produced highly reproducible changes in shapes of the modulation period histogram, consistent with the notion that the instantaneous probability of discharge mirrors the moment-by-moment spectrum at low modulation rates. The upper limit for phase locking was similar across SAM and SFM within neurons, suggesting shared biophysical constraints on temporal processing. Using spike train classification methods, we found that neural thresholds for modulation depth discrimination are typically far lower than would be predicted from frequency tuning to static tones. This "dynamic hyperacuity" suggests a substantial central enhancement of the neural representation of frequency changes relative to the auditory periphery. Spike timing information was superior to average rate information when discriminating among SFM signals, and even when discriminating among static tones varying in frequency. This finding held even when differences in total spike count across stimuli were normalized, indicating both the primacy and generality of temporal response dynamics in cortical auditory processing.

The orbits of subdwarf B + main-sequence binaries

The predicted orbital period histogram of an sdB population is bimodal with a peak at short (< 10 days) and long (> 250 days) periods. Observationally, there are many short-period sdB systems known, but only very few long-period sdB binaries are identified. As these predictions are based on poorly understood binary interaction processes, it is of prime importance to confront the predictions to observational data. In this contribution we aim to determine the absolute dimensions of the long-period sdB+MS binary system PG1104+243. High-resolution spectroscopy time-series were obtained with HERMES at the Mercator telescope at La Palma, and analyzed to obtain radial velocities of both components. Photometry from the literature was used to construct the spectral energy distribution (SED) of the binary. Atmosphere models were used to fit this SED and determine the surface gravity and temperature of both components. The gravitational redshift provided an independent confirmation of the surface gravity of the sdB component. An orbital period of 753 +- 3 d and a mass ratio of q = 0.637 +- 0.015 were found from the RV-curves. The sdB component has an effective temperature of Teff = 33500 +- 1200 K and a surface gravity of logg = 5.84 +- 0.08 dex, while the cool companion is found to be a G-type star with Teff = 5930 +- 160 K and logg = 4.29 +- 0.05 dex. Assuming a canonical mass of Msdb = 0.47 Msun, the MS component has a mass of 0.74 +- 0.07 Msun, and its Teff corresponds to what is expected for a terminal age main-sequence star with sub-solar metalicity. PG1104+243 is the first long-period sdB binary in which accurate physical parameters of both components could be determined, and the first sdB binary in which the gravitational redshift is measured. Furthermore, PG1104+243 is the first sdB+MS system that shows consistent evidence for being formed through stable Roche-lobe overflow.

TARP‐associated AMPA receptors display an increased maximum channel conductance and multiple kinetically distinct open states

Fast excitatory synaptic transmission in the CNS is mediated mainly by AMPA-type glutamate receptors (AMPARs), whose biophysical properties are dramatically modulated by the presence of transmembrane AMPAR regulatory proteins (TARPs). To help construct a kinetic model that will realistically describe native AMPAR/TARP function, we have examined the single-channel properties of homomeric GluA1 AMPARs in combination with the TARPs, γ-2, γ-4 and γ-5. In a saturating concentration of agonist, each of these AMPAR/TARP combinations gave rise to single-channel currents with multiple conductance levels that appeared intrinsic to the receptor-channel complex, and showed long-lived subconductance states. The open time and burst length distributions of the receptor complexes displayed multiple dwell-time components. In the case of γ-2- and γ-4-associated receptors, these distributions included a long-lived component lasting tens of milliseconds that was absent from both GluA1 alone and γ-5-associated receptors. The open time distributions for each conductance level required two dwell-time components, indicating that at each conductance level the channel occupies a minimum of two kinetically distinct open states. We have explored how these data place novel constraints on possible kinetic models of TARP-associated AMPARs that may be used to define AMPAR-mediated synaptic transmission.

A RADIAL VELOCITY STUDY OF COMPOSITE-SPECTRA HOT SUBDWARF STARS WITH THE HOBBY–EBERLY TELESCOPE

Many hot subdwarf stars show composite spectral energy distributions indicative of cool main sequence companions. Binary population synthesis (BPS) models demonstrate such systems can be formed via Roche lobe overflow or common envelope evolution but disagree on whether the resulting orbital periods will be long (years) or short (days). Few studies have been carried out to assess the orbital parameters of these spectroscopic composite binaries; current observations suggest the periods are long. To help address this problem, we selected fifteen moderately-bright (V~13) hot subdwarfs with F-K dwarf companions and monitored their radial velocities (RVs) from January 2005 to July 2008 using the bench-mounted Medium Resolution Spectrograph on the Hobby-Eberly Telescope (HET). Here we describe the details of our observing, reduction, and analysis techniques and present preliminary results for all targets. By combining the HET data with recent observations from the Mercator telescope, we are able to calculate precise orbital solutions for three systems using more than 6 years of observations. We also present an up-to-date period histogram for all known hot subdwarf binaries, which suggests those with F-K main sequence companions tend to have orbital periods on the order of several years. Such long periods challenge the predictions of conventional BPS models, although a larger sample is needed for a thorough assessment of the models' predictive success. Lastly, one of our targets has an eccentric orbit, implying some composite-spectrum systems might have formerly been hierarchical triple systems, in which the inner binary merged to create the hot subdwarf.

High speed photometry of faint Cataclysmic Variables: A progress report

AbstractWe summarise the results of observing faint cataclysmic variables from the Catalina Real-Time Transient Survey, resulting in confirming the theoretically predicted maximum in the orbital period histogram near a period of 80 minutes.

Formation and evolution of W Ursa Majoris stars: fallacies and corrections

Period histograms of eclipsing binaries generated with data from the All-Sky Automated Survey cannot be interpreted only using orbital evolution. Eclipse probabilities, selection effects and space distributions in the solar neighbourhood should be considered before any interpretations are made. Depending upon the physical dimensions (the total mass and the period) of the progenitor stars and the efficiency of the angular momentum loss mechanism, a newly formed W Ursa Majoris type binary can be at any age up to several Gyr. Also, the evolution in the contact stage is controlled not only by angular momentum and mass loss but also by mass transfer between the component stars. Thus, the mean life of the contact stages should be about 1.6 Gyr. A different time-scale would cause inconsistencies.

Dynamic Amplitude Coding in the Auditory Cortex of Awake Rhesus Macaques

In many animals, the information most important for processing communication sounds, including speech, consists of temporal envelope cues below approximately 20 Hz. Physiological studies, however, have typically emphasized the upper limits of modulation encoding. Responses to sinusoidal AM (SAM) are generally summarized by modulation transfer functions (MTFs), which emphasize tuning to modulation frequency rather than the representation of the instantaneous stimulus amplitude. Unfortunately, MTFs fail to capture important but nonlinear aspects of amplitude coding in the central auditory system. We focus on an alternative data representation, the modulation period histogram (MPH), which depicts the spike train folded on the modulation period of the SAM stimulus. At low modulation frequencies, the fluctuations of stimulus amplitude in decibels are robustly encoded by the cycle-by-cycle response dynamics evident in the MPH. We show that all of the parameters that define a SAM stimulus--carrier frequency, carrier level, modulation frequency, and modulation depth--are reflected in the shape of cortical MPHs. In many neurons that are nonmonotonically tuned for sound amplitude, the representation of modulation frequency is typically sacrificed to preserve the mapping between the instantaneous discharge rate and the instantaneous stimulus amplitude, resulting in two response modes per modulation cycle. This behavior, as well as the relatively poor tuning of cortical MTFs, suggests that auditory cortical neurons are not well suited for operating as a "modulation filterbank." Instead, our results suggest that <20 Hz, the processing of modulated signals is better described as envelope shape discrimination rather than modulation frequency extraction.

Modeling auditory-nerve responses for high sound pressure levels in the normal and impaired auditory periphery

This paper presents a computational model to simulate normal and impaired auditory-nerve (AN) fiber responses in cats. The model responses match physiological data over a wider dynamic range than previous auditory models. This is achieved by providing two modes of basilar membrane excitation to the inner hair cell (IHC) rather than one. The two modes are generated by two parallel filters, component 1 (C1) and component 2 (C2), and the outputs are subsequently transduced by two separate functions. The responses are then added and passed through the IHC low-pass filter followed by the IHC-AN synapse model and discharge generator. The C1 filter is a narrow-band, chirp filter with the gain and bandwidth controlled by a nonlinear feed-forward control path. This filter is responsible for low and moderate level responses. A linear, static, and broadly tuned C2 filter followed by a nonlinear, inverted and nonrectifying C2 transduction function is critical for producing transition region and high-level effects. Consistent with Kiang's two-factor cancellation hypothesis, the interaction between the two paths produces effects such as the C1/C2 transition and peak splitting in the period histogram. The model responses are consistent with a wide range of physiological data from both normal and impaired ears for stimuli presented at levels spanning the dynamic range of hearing.