Peter Heil

Leibniz Institute for Neurobiology, Magdeburg, Saxony-Anhalt, Germany

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Publications (72)211.65 Total impact

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    ABSTRACT: In the analysis of data from magnetoencephalography (MEG) and electroencephalography (EEG), it is common practice to arithmetically average event-related magnetic fields (ERFs) or event-related electric potentials (ERPs) across single trials and subsequently across subjects to obtain the so-called grand mean. Comparisons of grand means, e.g. between conditions, are then often performed by subtraction. These operations, and their statistical evaluation with parametric tests such as anova, tacitly rely on the assumption that the data follow the additive model, have a normal distribution, and have a homogeneous variance. This may be true for single trials, but these conditions are rarely met when ERFs/ERPs are compared between subjects, meaning that the additive model is seldom the correct model for computing grand mean waveforms. Here, we summarize some of our recent work and present new evidence, from auditory-evoked MEG and EEG results, that the non-normal distributions and the heteroscedasticity observed instead result because ERFs/ERPs follow a mixed model with additive and multiplicative components. For peak amplitudes, such as the auditory M100 and N100, the multiplicative component dominates. These findings emphasize that the common practice of simply subtracting arithmetic means of auditory-evoked ERFs or ERPs is problematic without prior adequate transformation of the data. Application of the area sinus hyperbolicus (asinh) transform to data following the mixed model transforms them into the requested additive model with its normal distribution and homogeneous variance. We therefore advise checking the data for compliance with the additive model and using the asinh transform if required. © 2015 Federation of European Neuroscience Societies and John Wiley & Sons Ltd.
    European Journal of Neuroscience 03/2015; 41(5):631-40. DOI:10.1111/ejn.12833 · 3.67 Impact Factor
  • European Journal of Neuroscience 03/2015; 41(5):515-7. DOI:10.1111/ejn.12832 · 3.67 Impact Factor
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    ABSTRACT: In mammalian auditory systems, the spiking characteristics of each primary afferent (type I auditory-nerve fiber; ANF) are mainly determined by a single ribbon synapse in a single receptor cell (inner hair cell; IHC). ANF spike trains therefore provide a window into the operation of these synapses and cells. It was demonstrated previously (Heil et al., 2007) that the distribution of interspike intervals (ISIs) of cat ANFs during spontaneous activity can be modeled as resulting from refractoriness operating on a non-Poisson stochastic point process of excitation (transmitter release events from the IHC). Here, we investigate nonrenewal properties of these cat-ANF spontaneous spike trains, manifest as negative serial ISI correlations and reduced spike-count variability over short timescales. A previously discussed excitatory process, the constrained failure of events from a homogeneous Poisson point process, can account for these properties, but does not offer a parsimonious explanation for certain trends in the data. We then investigate a three-parameter model of vesicle-pool depletion and replenishment and find that it accounts for all experimental observations, including the ISI distributions, with only the release probability varying between spike trains. The maximum number of units (single vesicles or groups of simultaneously released vesicles) in the readily releasable pool and their replenishment time constant can be assumed to be constant (∼4 and 13.5 ms, respectively). We suggest that the organization of the IHC ribbon synapses not only enables sustained release of neurotransmitter but also imposes temporal regularity on the release process, particularly when operating at high rates.
    The Journal of Neuroscience : The Official Journal of the Society for Neuroscience 11/2014; 34(45):15097-15109. DOI:10.1523/JNEUROSCI.0903-14.2014 · 6.75 Impact Factor
  • Peter Heil
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    ABSTRACT: Absolute auditory threshold decreases with increasing sound duration, a phenomenon explainable by the assumptions that the sound evokes neural events whose probabilities of occurrence are proportional to the sound's amplitude raised to an exponent of about 3 and that a constant number of events are required for threshold (Heil and Neubauer, Proc Natl Acad Sci USA 100:6151-6156, 2003). Based on this probabilistic model and on the assumption of perfect binaural summation, an equation is derived here that provides an explicit expression of the binaural threshold as a function of the two monaural thresholds, irrespective of whether they are equal or unequal, and of the exponent in the model. For exponents >0, the predicted binaural advantage is largest when the two monaural thresholds are equal and decreases towards zero as the monaural threshold difference increases. This equation is tested and the exponent derived by comparing binaural thresholds with those predicted on the basis of the two monaural thresholds for different values of the exponent. The thresholds, measured in a large sample of human subjects with equal and unequal monaural thresholds and for stimuli with different temporal envelopes, are compatible only with an exponent close to 3. An exponent of 3 predicts a binaural advantage of 2 dB when the two ears are equally sensitive. Thus, listening with two (equally sensitive) ears rather than one has the same effect on absolute threshold as doubling duration. The data suggest that perfect binaural summation occurs at threshold and that peripheral neural signals are governed by an exponent close to 3. They might also shed new light on mechanisms underlying binaural summation of loudness.
    Journal of the Association for Research in Otolaryngology 01/2014; DOI:10.1007/s10162-013-0432-x · 2.95 Impact Factor
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    ABSTRACT: Grand means of time-varying signals (waveforms) across subjects in magnetoencephalography (MEG) and electroencephalography (EEG) are commonly computed as arithmetic averages and compared between conditions, for example, by subtraction. However, the prerequisite for these operations, homogeneity of the variance of the waveforms in time, and for most common parametric statistical tests also between conditions, is rarely met. We suggest that the heteroscedasticity observed instead results because waveforms may differ by factors and additive terms and follow a mixed model. We propose to apply the asinh-transformation to stabilize the variance in such cases. We demonstrate the homogeneous variance and the normal distributions of data achieved by this transformation using simulated waveforms, and we apply it to real MEG data and show its benefits. The asinh-transformation is thus an essential and useful processing step prior to computing and comparing grand mean waveforms in MEG and EEG.
    Psychophysiology 04/2013; DOI:10.1111/psyp.12047 · 3.18 Impact Factor
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    ABSTRACT: Our study estimates detection thresholds for tones of different durations and frequencies in Great Tits (Parus major) with operant procedures. We employ signals covering the duration and frequency range of communication signals of this species (40-1,010 ms; 2, 4, 6.3 kHz), and we measure threshold level-duration (TLD) function (relating threshold level to signal duration) in silence as well as under behaviorally relevant environmental noise conditions (urban noise, woodland noise). Detection thresholds decreased with increasing signal duration. Thresholds at any given duration were a function of signal frequency and were elevated in background noise, but the shape of Great Tit TLD functions was independent of signal frequency and background condition. To enable comparisons of our Great Tit data to those from other species, TLD functions were first fitted with a traditional leaky-integrator model. We then applied a probabilistic model to interpret the trade-off between signal amplitude and duration at threshold. Great Tit TLD functions exhibit features that are similar across species. The current results, however, cannot explain why Great Tits in noisy urban environments produce shorter song elements or faster songs than those in quieter woodland environments, as detection thresholds are lower for longer elements also under noisy conditions.
    Journal of Comparative Physiology 01/2013; DOI:10.1007/s00359-012-0789-z · 1.86 Impact Factor
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    ABSTRACT: Detection thresholds for auditory stimuli, specified in terms of their -amplitude or level, depend on the stimulus temporal envelope and decrease with increasing stimulus duration. The neural mechanisms underlying these fundamental across-species observations are not fully understood. Here, we present a "continuous look" model, according to which the stimulus gives rise to stochastic neural detection events whose probability of occurrence is proportional to the 3rd power of the low-pass filtered, time-varying stimulus amplitude. Threshold is reached when a criterion number of events have occurred (probability summation). No long-term integration is required. We apply the model to an extensive set of thresholds measured in humans for tones of different envelopes and durations and find it to fit well. Subtle differences at long durations may be due to limited attention resources. We confirm the probabilistic nature of the detection events by analyses of simple reaction times and verify the exponent of 3 by validating model predictions for binaural thresholds from monaural thresholds. The exponent originates in the auditory periphery, possibly in the intrinsic Ca(2+) cooperativity of the Ca(2+) sensor involved in exocytosis from inner hair cells. It results in growth of the spike rate of auditory-nerve fibers (ANFs) with the 3rd power of the stimulus amplitude before saturating (Heil et al., J Neurosci 31:15424-15437, 2011), rather than with its square (i.e., with stimulus intensity), as is commonly assumed. Our work therefore suggests a link between detection thresholds and a key biochemical reaction in the receptor cells.
    Advances in Experimental Medicine and Biology 01/2013; 787:21-29. DOI:10.1007/978-1-4614-1590-9_3 · 2.01 Impact Factor
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    Benedikt Zoefel, Peter Heil
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    ABSTRACT: Low-frequency oscillations in the electroencephalogram (EEG) are thought to reflect periodic excitability changes of large neural networks. Consistent with this notion, detection probability of near-threshold somatosensory, visual, and auditory targets has been reported to co-vary with the phase of oscillations in the EEG. In audition, entrainment of δ-oscillations to the periodic occurrence of sounds has been suggested to function as a mechanism of attentional selection. Here, we examine in humans whether the detection of brief near-threshold sounds in quiet depends on the phase of EEG oscillations. When stimuli were presented at irregular intervals, we did not find a systematic relationship between detection probability and phase. When stimuli were presented at regular intervals (2-s), reaction times were significantly shorter and we observed phase entrainment of EEG oscillations corresponding to the frequency of stimulus presentation (0.5 Hz), revealing an adjustment of the system to the regular stimulation. The amplitude of the entrained oscillation was higher for hits than for misses, suggesting a link between entrainment and stimulus detection. However, detection was independent of phase at frequencies ≥1 Hz. Furthermore, we show that when the data are analyzed using acausal, though common, algorithms, an apparent "entrainment" of the δ-phase to presented stimuli emerges and detection probability appears to depend on δ-phase, similar to reports in the literature. We show that these effects are artifacts from phase distortion at stimulus onset by contamination with the event-related potential, which differs markedly for hits and misses. This highlights the need to carefully deal with this common problem, since otherwise it might bias and mislead this exciting field of research.
    Frontiers in Psychology 01/2013; 4:262. DOI:10.3389/fpsyg.2013.00262 · 2.80 Impact Factor
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    ABSTRACT: Detection thresholds for pairs or multiple copies of sounds are better than those for a single sound, an observation commonly interpreted as indicating temporal integration by the auditory system. Detection thresholds for pairs of brief tones depend on the delay between the tones (if short) and on frequency, suggesting frequency-dependent temporal overlap of auditory-filter responses elicited by the two successive stimuli (Krumbholz and Wiegrebe, 1998). The model presented by Krumbholz and Wiegrebe did not account for all aspects of their data, despite its complexity. This study shows that a simple probabilistic model based on Neubauer and Heil (2008) predicts the increase in threshold for short temporal delays as well as the asymptotic behaviour towards longer delays. The model entails (i) a 4(th)-order gammatone filter with a brief impulse response and thus broad bandwidth (shorter and broader than those of a filter normally assumed), (ii) the formation of stochastic 'spikes' or 'events' whose probability of occurrence is proportional to the filter output (half-wave rectified fine-structure or amplitude envelope), raised to a power of 3, and (iii) probability summation. The same model with the same front-end filter also predicts thresholds for pairs of clicks presented in band-reject noise, measured by Hall and Lummis (1973). The model accurately predicts the magnitudes and the decay of the alternating increase and decrease of thresholds as the delay between the click varies, the small effects of click polarity, and the dependence of thresholds for pairs of clicks with unequal intensities on their temporal order. Finally, we show that this model also correctly predicts the decrease in threshold with increasing number of temporally separated brief sounds, reported in several studies. While the latter data do not constrain the characteristics of the front-end filter, they do confirm the exponent of 3 in the model. Our paper stresses the viability of the model and raises the possibility that the bandwidths of filters estimated with psychophysical techniques may depend more strongly on the experimental paradigms and stimuli than hitherto thought.
    Hearing research 12/2012; DOI:10.1016/j.heares.2012.12.002 · 2.85 Impact Factor
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    ABSTRACT: The build-up of auditory stream segregation refers to the notion that sequences of alternating A and B sounds initially tend to be heard as a single stream, but with time appear to split into separate streams. The central assumption in the analysis of this phenomenon is that streaming sequences are perceived as one stream at the beginning by default. In the present study, we test the validity of this assumption and document its impact on the apparent build-up phenomenon. Human listeners were presented with ABAB sequences, where A and B were harmonic tone complexes of seven different fundamental frequency separations (Δf) ranging from 2 to 14 semitones. Subjects had to indicate, as promptly as possible, their initial percept of the sequences, as either "one stream" or "two streams," and any changes thereof during the sequences. We found that subjects did not generally indicate a one-stream percept at the beginning of streaming sequences. Instead, the first perceptual decision depended on Δf, with the probability of a one-stream percept decreasing, and that of a two-stream percept increasing, with increasing Δf. Furthermore, subjects required some time to make and report a decision on their perceptual organization. Taking this time into account, the resulting time courses of two-stream probabilities differ markedly from those suggested by the conventional analysis. A build-up-like increase in two-stream probability was found only for the Δf of six semitones. At the other Δf conditions no or only minor increases in two-stream probability occurred. These results shed new light on the build-up of stream segregation and its possible neural correlates.
    Frontiers in Psychology 10/2012; 3:461. DOI:10.3389/fpsyg.2012.00461 · 2.80 Impact Factor
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    ABSTRACT: The amplitudes of the most prominent component of auditory evoked magnetic fields and electrical potentials, the M100 and N100, recorded from the human scalp depend on the duration of the stimulus onset interval (SOI). Here, we show, using magnetoencephalography, that the SOI dependence of the M100 amplitude strongly depends upon whether stimuli with different SOIs are presented in a conventional block design or in a random manner. This differential dependence reveals that the M100 is affected not only by the stimulus evoking it and by its predecessor, but by a longer-term history of stimulation. We provide a parsimonious model that accounts for our findings with both designs in a quantitative manner. It assumes a transient, temporally asymmetric reduction in the excitability of a fraction of potentially excitable neurons. A rather stereotyped response function may therefore underlie the stimulation-history effects in the human auditory cortex.
    Psychophysiology 04/2012; 49(7):909-19. DOI:10.1111/j.1469-8986.2012.01370.x · 3.18 Impact Factor
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    ABSTRACT: Acoustic information is conveyed to the brain by the spike patterns in auditory-nerve fibers (ANFs). In mammals, each ANF is excited via a single ribbon synapse in a single inner hair cell (IHC), and the spike patterns therefore also provide valuable information about those intriguing synapses. Here we reexamine and model a key property of ANFs, the dependence of their spike rates on the sound pressure level of acoustic stimuli (rate-level functions). We build upon the seminal model of Sachs and Abbas (1974), which provides good fits to experimental data but has limited utility for defining physiological mechanisms. We present an improved, physiologically plausible model according to which the spike rate follows a Hill equation and spontaneous activity and its experimentally observed tight correlation with ANF sensitivity are emergent properties. We apply it to 156 cat ANF rate-level functions using frequencies where the mechanics are linear and find that a single Hill coefficient of 3 can account for the population of functions. We also demonstrate a tight correspondence between ANF rate-level functions and the Ca(2+) dependence of exocytosis from IHCs, and derive estimates of the effective intracellular Ca(2+) concentrations at the individual active zones of IHCs. We argue that the Hill coefficient might reflect the intrinsic, biochemical Ca(2+) cooperativity of the Ca(2+) sensor involved in exocytosis from the IHC. The model also links ANF properties with properties of psychophysical absolute thresholds.
    The Journal of Neuroscience : The Official Journal of the Society for Neuroscience 10/2011; 31(43):15424-37. DOI:10.1523/JNEUROSCI.1638-11.2011 · 6.75 Impact Factor
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    ABSTRACT: MEG and EEG studies of event-related responses often involve comparisons of grand averages, requiring homogeneity of the variances. Here, we examine the possibility, implied by the nature of neural sources and the measuring principles involved, that the M100 component of auditory-evoked magnetic fields of different subjects, hemispheres, to different stimuli, and at different sensors differs by scaling factors. Such a multiplicative model predicts a linear increase in the standard deviation with the mean, and thus would have important implications for averaging and comparing such data. Our analyses, at the sensor and the source level, clearly show that the multiplicative model applies. We therefore propose geometric, rather than arithmetic, averaging of the M100 component across subjects and suggest a novel and superior normalization procedure. Our results question the justification of the common practice of subtracting arithmetic grand averages.
    Psychophysiology 02/2011; 48(8):1069-82. DOI:10.1111/j.1469-8986.2011.01183.x · 3.18 Impact Factor
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    Hearing research 11/2010; 271(1-2):1-2. DOI:10.1016/j.heares.2010.10.016 · 2.85 Impact Factor
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    Peter Heil, Heinrich Neubauer
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    ABSTRACT: Several recent studies of mature auditory and vestibular hair cells (HCs), and of visual and olfactory receptor cells, have observed nearly linear dependencies of the rate of neurotransmitter release events, or related measures, on the magnitude of Ca(2+)-entry into the cell. These relationships contrast with the highly supralinear, third to fourth power, Ca(2+)-dependencies observed in most preparations, from neuromuscular junctions to central synapses, and also in HCs from immature and various mutant animals. They also contrast with the intrinsic, biochemical, Ca(2+)-cooperativity of the ubiquitous Ca(2+)-sensors involved in fast exocytosis (synaptotagmins I and II). Here, we propose that the quasi-linear dependencies result from measuring the sum of several supralinear, but saturating, dependencies with different sensitivities at individual active zones of the same cell. We show that published experimental data can be accurately accounted for by this summation model, without the need to assume altered Ca(2+)-cooperativity or nanodomain control of release. We provide support for the proposal that the best power is 3, and we discuss the large body of evidence for our summation model. Overall, our idea provides a parsimonious and attractive reconciliation of the seemingly discrepant experimental findings in different preparations.
    Frontiers in Synaptic Neuroscience 01/2010; 2:148. DOI:10.3389/fnsyn.2010.00148
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    ABSTRACT: The analysis of electroencephalographic (EEG) and magnetoencephalographic (MEG) data commonly involves arithmetic averaging of the evoked magnetic fields across trials, but also across subjects (“grand average”), with subsequent comparisons of grand averages across stimuli or conditions. The classical, and most frequently used, model in the analysis of stimulus evoked brain responses in EEG and MEG is based on the assumptions that the arithmetic mean is a good estimator of the evoked responses, that the evoked responses are independent of background activity, and that the latter averages out. The comparison of evoked responses ideally requires homogeneity of the variance (homoscedasticity). Here, we explore the issue of homoscedasticity in a typical MEG experiment. Fifteen subjects were stimulated with tones of different onset intervals, while magnetic fields were measured with a whole-head MEG device. Our analyses revealed an approximately homogeneous standard deviation (SD) of the responses across repeated trials of the same stimulus, SDtrials, i.e. SDtrials was independent of the corresponding mean response amplitude. In contrast, the SDsubjects derived from averaging the trial-averaged responses across subjects increased approximately linearly with the corresponding mean amplitude. This result shows that the evoked responses, including the M100, from different subjects and stimulus conditions differed largely by scaling factors. The latter findings question the usefulness of the common practice of comparing arithmetic averages of trial-averaged responses across subjects to different stimuli or conditions, e.g. by subtraction of responses to different conditions, and thus have widespread implications. Keywordsauditory cortex-arithmetic averaging-standard deviation-magnetoencephalography-homoscedasticity
    12/2009: pages 179-182;
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    ABSTRACT: In vertebrate auditory systems, the conversion from graded receptor potentials across the hair-cell membrane into stochastic spike trains of the auditory nerve (AN) fibers is performed by ribbon synapses. The statistics underlying this process constrain auditory coding but are not precisely known. Here, we examine the distributions of interspike intervals (ISIs) from spontaneous activity of AN fibers of the barn owl (Tyto alba), a nocturnal avian predator whose auditory system is specialized for precise temporal coding. The spontaneous activity of AN fibers, with the exception of those showing preferred intervals, is commonly thought to result from excitatory events generated by a homogeneous Poisson point process, which lead to spikes unless the fiber is refractory. We show that the ISI distributions in the owl are better explained as resulting from the action of a brief refractory period ( approximately 0.5 ms) on excitatory events generated by a homogeneous stochastic process where the distribution of interevent intervals is a mixture of an exponential and a gamma distribution with shape factor 2, both with the same scaling parameter. The same model was previously shown to apply to AN fibers in the cat. However, the mean proportions of exponentially versus gamma-distributed intervals in the mixture were different for cat and owl. Furthermore, those proportions were constant across fibers in the cat, whereas they covaried with mean spontaneous rate and with characteristic frequency in the owl. We hypothesize that in birds, unlike in mammals, more than one ribbon may provide excitation to most fibers, accounting for the different proportions, and that variation in the number of ribbons may underlie the variation in the proportions.
    Journal of Neurophysiology 05/2009; 101(6):3169-91. DOI:10.1152/jn.90779.2008 · 3.04 Impact Factor
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    ABSTRACT: Detecting sounds in quiet is the simplest task performed by the auditory system, but the neural mechanisms underlying perceptual detection thresholds for sounds in quiet are still not understood. Heil and Neubauer [Heil, P., Neubauer, H., 2003. A unifying basis of auditory thresholds based on temporal summation. Proc. Natl. Acad. Sci. USA 100, 6151-6156] have provided evidence for a simple probabilistic model according to which the stimulus, at any point in time, has a certain probability of exceeding threshold and being detected. Consequently, as stimulus duration increases, the cumulative probability of detection events increases, performance improves, and threshold amplitude decreases. The origin of these processes was traced to the first synapse in the auditory system, between the inner hair cell and the afferent auditory-nerve fiber (ANF). Here we provide further support for this probabilistic "continuous-look" model. It is derived from analyses of the distributions of the latencies of the first spikes of cat ANFs with very low spontaneous discharge rates to tones of different amplitudes. The first spikes in these fibers can be considered detection events. We show that, as predicted, the distributions can be explained by the joint probability of the occurrence of three independent sub-events, where the probability of each of those occurring is proportional to the low-pass filtered stimulus amplitude. The "temporal integration" functions of individual ANFs, derived from their first-spike latencies, are remarkably similar in shape to "temporal integration" functions, which relate threshold sound pressure level at the perceptual level to stimulus duration. This further supports a close link between the mechanisms determining the timing of the first (and other) evoked spikes at the level of the auditory nerve and detection thresholds at the perceptual level. The possible origin and some functional consequences of the expansive power-law non-linearity are discussed.
    Hearing Research 05/2008; 238(1-2):25-38. DOI:10.1016/j.heares.2007.09.014 · 2.85 Impact Factor
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    ABSTRACT: We examined effects of the task of categorizing linear frequency-modulated (FM) sweeps into rising and falling on auditory evoked magnetic fields (AEFs) from the human auditory cortex, recorded by means of whole-head magnetoencephalography. AEFs in this task condition were compared with those in a passive condition where subjects had been asked to just passively listen to the same stimulus material. We found that the M100-peak latency was significantly shorter for the task condition than for the passive condition in the left but not in the right hemisphere. Furthermore, the M100-peak latency was significantly shorter in the right than in the left hemisphere for the passive and the task conditions. In contrast, the M100-peak amplitude did not differ significantly between conditions, nor between hemispheres. We also analyzed the activation strength derived from the integral of the absolute magnetic field over constant time windows between stimulus onset and 260 ms. We isolated an early, narrow time range between about 60 ms and 80 ms that showed larger values in the task condition, most prominently in the right hemisphere. These results add to other imaging and lesion studies which suggest a specific role of the right auditory cortex in identifying FM sweep direction and thus in categorizing FM sweeps into rising and falling.
    Brain Research 04/2008; 1220:102-17. DOI:10.1016/j.brainres.2008.02.086 · 2.83 Impact Factor
  • Heinrich Neubauer, Peter Heil
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    ABSTRACT: Recent studies have shown a close correspondence between perceptual detection thresholds for sounds in quiet and a measure of neuronal thresholds derived from the stimulus-dependent timing of the first spike of auditory-nerve fibers. In addition, stimulus properties might be encoded by differences in first-spike timing of neurons in the central auditory system. Therefore, the physiological mechanisms underlying first-spike timing are of considerable interest, but are not thoroughly understood. Here, we present a physiological model which accurately explains the observed stimulus dependence of the first-spike latency of auditory-nerve fibers with a minimum number of physiologically plausible parameters. Two of the 5 parameters can be considered constant (at least for the vast majority of fibers), while the other 3 vary in meaningful ways with the fibers' spontaneous discharge rates. The elements of the model and some implications are discussed.
    Brain Research 10/2007; 1220:208-23. DOI:10.1016/j.brainres.2007.08.081 · 2.83 Impact Factor

Publication Stats

3k Citations
211.65 Total Impact Points


  • 2000–2015
    • Leibniz Institute for Neurobiology
      • • Department Auditory Learning and Speech
      • • Special Lab Non-Invasive Brain Imaging
      Magdeburg, Saxony-Anhalt, Germany
  • 2013
    • Bionics Institute
      East Melbourne, Victoria, Australia
  • 1992–1998
    • Monash University (Australia)
      • School of Psychology and Psychiatry
      Melbourne, Victoria, Australia
    • Tel Aviv University
      Tell Afif, Tel Aviv, Israel
  • 1985–1993
    • Technical University Darmstadt
      Darmstadt, Hesse, Germany