Auditory brainstem responses with optimized chirp signals compensating basilar-membrane dispersion

This study examines auditory brainstem responses (ABR) elicited by rising frequency chirps. The time course of frequency change for the chirp theoretically produces simultaneous displacement maxima by compensating for travel-time differences along the cochlear partition. This broadband chirp was derived on the basis of a linear cochlea model [de Boer, "Auditory physics. Physical principles in hearing theory I," Phys. Rep. 62, 87-174 (1980)]. Responses elicited by the broadband chirp show a larger wave-V amplitude than do click-evoked responses for most stimulation levels tested. This result is in contrast to the general hypothesis that the ABR is an electrophysiological event most effectively evoked by the onset or offset of an acoustic stimulus, and unaffected by further stimulation. The use of this rising frequency chirp enables the inclusion of activity from lower frequency regions, whereas with a click, synchrony is decreased in accordance with decreasing traveling velocity in the apical region. The use of a temporally reversed (falling) chirp leads to a further decrease in synchrony as reflected in ABR responses that are smaller than those from a click. These results are compatible with earlier experimental results from recordings of compound action potentials (CAP) [Shore and Nuttall, "High synchrony compound action potentials evoked by rising frequency-swept tonebursts," J. Acoust. Soc. Am. 78, 1286-1295 (1985)] reflecting activity at the level of the auditory nerve. Since the ABR components considered here presumably reflect neural response from the brainstem, the effect of an optimized synchronization at the peripheral level can also be observed at the brainstem level. The rising chirp may therefore be of clinical use in assessing the integrity of the entire peripheral organ and not just its basal end.     

Frequency specificity of chirp-evoked auditory brainstem responses

This study examines the usefulness of the upward chirp stimulus developed by Dau et al. [J. Acoust. Soc. Am. 107, 1530-1540 (2000)] for retrieving frequency-specific information. The chirp was designed to produce simultaneous displacement maxima along the cochlear partition by compensating for frequency-dependent traveling-time differences. In the first experiment, auditory brainstem responses (ABR) elicited by the click and the broadband chirp were obtained in the presence of high-pass masking noise, with cutoff frequencies of 0.5, 1, 2, 4, and 8 kHz. Results revealed a larger wave-V amplitude for chirp than for click stimulation in all masking conditions. Wave-V amplitude for the chirp increased continuously with increasing high-pass cutoff frequency while it remains nearly constant for the click for cutoff frequencies greater than 1 kHz. The same two stimuli were tested in the presence of a notched-noise masker with one-octave wide spectral notches corresponding to the cutoff frequencies used in the first experiment. The recordings were compared with derived responses, calculated offline, from the high-pass masking conditions. No significant difference in response amplitude between click and chirp stimulation was found for the notched-noise responses as well as for the derived responses. In the second experiment, responses were obtained using narrow-band stimuli. A low-frequency chirp and a 250-Hz tone pulse with comparable duration and magnitude spectrum were used as stimuli. The narrow-band chirp elicited a larger response amplitude than the tone pulse at low and medium stimulation levels. Overall, the results of the present study further demonstrate the importance of considering peripheral processing for the formation of ABR. The chirp might be of particular interest for assessing low-frequency information.     

Ear-canal acoustic admittance and reflectance effects in human neonates. I. Predictions of otoacoustic emission and auditory brainstem responses

This report describes the extent to which ear-canal acoustic admittance and energy reflectance (YR) in human neonates (1) predict otoacoustic emission (OAE) levels and auditory brainstem response (ABR) latencies, and (2) classify OAE and ABR responses as present or absent. Analyses are reported on a subset of ears in which hearing screening measurements were obtained previously [Norton et al., Ear. Hear. 21, 348-356 (2000a)]. Tests on 1405 ears included YR, distortion-product OAEs, transient-evoked OAEs, and ABR. Principal components analysis reduced the 33 YR variables to 5-7 factors. OAE levels decreased and ABR latencies increased with increasing high-frequency energy reflectance. Up to 28% of the variance in OAE levels and 12% of the variance in ABR wave-V latencies were explained by these factors. Thus, the YR response indirectly encodes information on inter-ear variations in forward and reverse middle-ear transmission. The YR factors classify OAEs with an area under the relative operating characteristic (ROC) curve as high as 0.79, suggesting that middle-ear dysfunction is partly responsible for the inability to record OAEs in some ears. The YR factors classified ABR responses less well, with ROC areas of 0.64 for predicting wave-V latency and 0.56 for predicting Fsp.     

A direct approach for the design of chirp stimuli used for the recording of auditory brainstem responses

A recent study evaluates auditory brainstem responses (ABRs) evoked by chirps of different durations (sweeping rates) [Elberling et al. (2010). J. Acoust. Soc. Am. 128, 215-223]. The study demonstrates that shorter chirps are most efficient at higher levels of stimulation whereas longer chirps are most efficient at lower levels. Mechanisms other than the traveling wave delay, in particular, upward spread of excitation and changes in cochlear-neural delay with level, are suggested to be responsible for these findings. As a consequence, delay models based on estimates of the traveling wave delay are insufficient for the design of chirp stimuli, and another delay model based on a direct approach is therefore proposed. The direct approach uses ABR-latencies from normal-hearing subjects in response to octave-band chirps over a wide range of levels. The octave-band chirps are constructed by decomposing a broad-band chirp, and constitute a subset of the chirp. The delay compensations of the proposed model are similar to those found in the previous experimental study, which thus verifies the results of the proposed model.     

The importance of cochlear processing for the formation of auditory brainstem and frequency following responses

A model for the generation of auditory brainstem responses (ABR) and frequency following responses (FFRs) is presented. The model is based on the concept introduced by Goldstein and Kiang [J. Acoust. Soc. Am. 30, 107-114 (1958)] that evoked potentials recorded at remote electrodes can theoretically be given by convolution of an elementary unit waveform (unitary response) with the instantaneous discharge rate function for the corresponding unit. In the present study, the nonlinear computational auditory-nerve model recently developed by Heinz et al. [ARLO 2(3), 91-96 (2001)] was used to calculate the instantaneous discharge rate ri(t) for fibers i in the frequency range from 0.1 and 10 kHz. The summed activity across frequency was convolved with a unitary response which is assumed to reflect contributions from different cell populations within the auditory brainstem, recorded at a given pair of electrodes on the scalp. Predicted potential patterns are compared with experimental data for a number of stimulus and level conditions. Clicks, chirps as defined in Dau et al. [J. Acoust. Soc. Am. 107, 1530-1540 (2000)], long-duration stimuli comprising the chirp, as well as tones and slowly varying tonal sweeps were considered. The results demonstrate the importance of considering the effects of the basilar-membrane traveling wave and auditory-nerve processing for the formation of ABR and FFR. Specifically, the results support the hypothesis that the FFR to low-frequency tones represents synchronized activity mainly stemming from mid- and high-frequency units at more basal sites, and not from units tuned to frequencies around the signal frequency.     

Analysis of the click-evoked brainstem potentials in man unsing high-pass noise masking

Brainstem electrical responses (BSER) to 60-dB-SL click in noise high passed at various cutoff frequencies separated b 1/2-octave steps were recorded in normal-hearing adult subjects. By applying a derived response technique, narrow-band contributions to the BSER from specific portions of the basilar membrane were revealed. Latencies and amplitudes of the various waves in the derived BSER were recorded. Results indicate that nearly the whole cochlear partition can contribute to the brainstem response. The shifts in latency of waves I, III, and V and amplitude changes of waves I and III as a function of CF appear to be fully comparable to those of the AP. In contrast, the amplitude behavior of wave V as a function of CF is different from waves I and III depending upon frequency range. The discrepency in the behavior of wave V with respect to the earlier waves suggests some sort of neural reorganization at the level where was V is generated. The fact that there are contributions to the brainstem response from apical portions of the cochlea opens the possibility for extending the brainstem technique in assessing the higher cochlear turn function.     

Auditory brainstem responses to chirps delivered by an insert earphone with equalized frequency response

Recently it has been demonstrated that auditory brainstem responses, ABRs, to chirps are larger with the ER-2 than with the ER-3A insert earphone due to differences between the corresponding amplitude-frequency responses. Therefore a modified chirp, which equalizes the amplitude-frequency response of the ER-3A, is constructed and subsequently compared to the unmodified chirp. ABRs are recorded from 20 normal-hearing subjects in response to the two chirps delivered by the ER-3A earphone at a wide range of levels. The results confirm that the modified chirp generates significantly larger ABRs than the unmodified chirp at levels below 60?dB nHL.     

The mechanical waveform of the basilar membrane. III. Intensity effects

Mechanical responses in the basal turn of the guinea-pig cochlea were measured with broad-band noise stimuli and expressed as input-output cross-correlation functions. The experiments were performed over the full range of stimulus intensities in order to try to understand the influence of cochlear nonlinearity on frequency selectivity, tuning, signal compression and the impulse response. The results are interpreted within the framework of a nonlinear, locally active, three-dimensional model of the cochlea. The data have been subjected to inverse analysis in order to recover the basilar-membrane (BM) impedance, a parameter function that, when inserted into the (linearized version of that) model, produces a model response that is similar to the measured response. This paper reports details about intensity effects for noise stimulation, in particular, the way the BM impedance varies with stimulus intensity. In terms of the underlying cochlear model, the decrease of the "activity component" in the BM impedance with increasing stimulus level is attributed to saturation of transduction in the outer hair cells. In the present paper this property is brought into a quantitative form. According to the theory [the EQ-NL theorem, de Boer, Audit. Neurosci. 3, 377-388 (1997)], the BM impedance is composed of two components, both intrinsically independent of stimulus level. One is the passive impedance Zpass and the other one is the "extra" impedance Zextra. The latter impedance is to be multiplied by a real factor gamma (0 < or = gamma < or = 1) that depends on stimulus level. This concept about the composition of the BM impedance is termed the "two-component theory of the BM impedance." In this work both impedances are entirely derived from experimental data. The dependence of the factor gamma on stimulus level can be derived by using a unified form of the outer-hair-cell transducer function. From an individual experiment, the two functions Zpass and Zextra are determined, and an approximation (Zpass + gamma Zextra) to the BM impedance constructed. Next, the model response (the "resynthesized" response) corresponding to this "artificial" impedance is computed. The same procedure is executed for several stimulus-level values. For all levels, the results show a close correspondence with the original experimental data; this includes correct prediction of the compression of response amplitudes, the reduction of frequency selectivity, the shift in peak frequency and, most importantly, the preservation of timing in the impulse response. All these findings illustrate the predictive power of the underlying model.     

Influence of Polarization and Pulse Shape of Femtosecond Initial Laser Pulses on Spectral Broadening in Microstructure Fibers

We theoretically studied the influence of initial parameters of laser pulses, such as polarization, pulse shape and frequency chirp, on the broadening of spectrum during pulse propagation through microstructure fibers (MSFs). We utilized two coupled-mode equations based on the nonlinear Schrödinger equation using an intermediate-broadening model for a Raman response function, and the dispersion coefficients from 2nd to 7th orders for the slow and fast axes, respectively, of highly birefringent MSFs.     

Transient-evoked otoacoustic emission generators in a nonlinear cochlea

This study focuses on the theoretical prediction and experimental evaluation of the latency of transient-evoked otoacoustic emissions. Response components with different delay have been identified in several studies. The main generator of the transient response is assumed to be coherent reflection from cochlear roughness near the resonant place. Additional components of different latency can be generated by different mechanisms. Experimental data are re-analyzed in this study to evaluate the dependence of the latency on stimulus level, for each component of the response, showing that previous estimates of the otoacoustic emission latency were affected by systematic errors. The latency of the emission from each generator changes very little with stimulus level, whereas their different growth rate causes sharp changes of the single-valued latency, estimated as the time of the absolute maximum of the bandpass filtered response. Results of passive linear models, in which gain and bandwidth of the cochlear amplifier are strictly related, are incompatible with the observations. Although active linear models including delayed stiffness terms do predict much slower dependence of latency on the stimulus level, a suitable nonlinear model should be designed, capable of decoupling more effectively the dependence on stimulus level of amplitude and phase of the otoacoustic response.     

Short-time fractional Fourier methods for the time-frequency representation of chirp signals

The fractional Fourier transform (FrFT) provides a valuable tool for the analysis of linear chirp signals. This paper develops two short-time FrFT variants which are suited to the analysis of multicomponent and nonlinear chirp signals. Outputs have similar properties to the short-time Fourier transform (STFT) but show improved time-frequency resolution. The FrFT is a parameterized transform with parameter, a, related to chirp rate. The two short-time implementations differ in how the value of a is chosen. In the first, a global optimization procedure selects one value of a with reference to the entire signal. In the second, a values are selected independently for each windowed section. Comparative variance measures based on the Gaussian function are given and are shown to be consistent with the uncertainty principle in fractional domains. For appropriately chosen FrFT orders, the derived fractional domain uncertainty relationship is minimized for Gaussian windowed linear chirp signals. The two short-time FrFT algorithms have complementary strengths demonstrated by time-frequency representations for a multicomponent bat chirp, a highly nonlinear quadratic chirp, and an output pulse from a finite-difference sonar model with dispersive change. These representations illustrate the improvements obtained in using FrFT based algorithms compared to the STFT.     

The effects of sensory hearing loss on cochlear filter times estimated from auditory brainstem response latencies.

Derived-band auditory brainstem responses (ABRs) were obtained in 43 normal-hearing and 80 cochlear hearing-impaired individuals using clicks and high-pass noise masking. The response times across the cochlea [the latency difference between wave V's of the 5.7- and 1.4-kHz center frequency (CF) derived bands] were calculated for five levels of click stimulation ranging from 53 to 93 dB p.-p.e. SPL (23 to 63 dB nHL) in 10-dB steps. Cochlear response times appeared to shorten significantly with hearing loss, especially when the average pure tone (1 to 8 kHz) hearing loss exceeded 30 dB. Examination of derived-band latencies indicates that this shortening is due to a dramatic decrease of wave V latency in the lower CF derived band. Estimates of cochlear filter times in terms of the number of periods to maximum response (Nmax) were calculated from derived-band latencies corrected for gender-dependent cochlear transport and neural conduction times. Nmax decreased as a function of hearing loss, especially for the low CF derived bands. The functions were similar for both males and females. These results are consistent with broader cochlear tuning due to peripheral hearing loss. Estimating filter response times from ABR latencies enhances objective noninvasive diagnosis and allows delineation of the differential effects of pathology on the underlying cochlear mechanisms involved in cochlear transport and filter build-up times.     

Auditory steady-state responses to chirp stimuli based on cochlear traveling wave delay

This study investigates the use of chirp stimuli to compensate for the cochlear traveling wave delay. The temporal dispersion in the cochlea is given by the traveling time, which in this study is estimated from latency-frequency functions obtained from (1) a cochlear model, (2) tone-burst auditory brain stem response (ABR) latencies, (3) and narrow-band ABR latencies. These latency-frequency functions are assumed to reflect the group delay of a linear system that modifies the phase spectrum of the applied stimulus. On the basis of this assumption, three chirps are constructed and evaluated in 49 normal-hearing subjects. The auditory steady-state responses to these chirps and to a click stimulus are compared at two levels of stimulation (30 and 50 dB nHL) and a rate of 90s. The chirps give shorter detection time and higher signal-to-noise ratio than the click. The shorter detection time obtained by the chirps is equivalent to an increase in stimulus level of 20 dB or more. The results indicate that a chirp is a more efficient stimulus than a click for the recording of early auditory evoked responses in normal-hearing adults using transient sounds at a high rate of stimulation.     

孤子源啁啾对光孤子传输的影响以及消啁啾的方法

本文提出了一种孤子源非线性啁啾的模型,利用解析和计算机模拟的方法从理论上分析了孤子源啁啾,特别是非线性啁啾对孤子传输的影响,并讨论了消啁啾的两种方法-正色散光纤消啁啾法和Fabry-Perot光谱窗消啁啾法,实验结果与理论分析基本一致.     

不同能量下环形高斯强激光光束在空气中的非线性传输

以线性传输模型为对比研究了不同初始能量的环形光束在空气中的非线性传输。结果显示,在传输初始阶段,非线性克尔效应减弱了线性空间啁啾导致的聚焦作用。线性聚焦使能量向光轴方向流动导致强光强核心,在光轴附近生成类高斯脉冲结构,增强了非线性自聚焦效应,导致光强急剧增加形成光丝。环形光束的初始能量的大小能够影响自聚焦焦距、光丝长度和光强通量。自聚焦焦距随着初始脉冲能量的增加而减小,但自聚焦焦距与初始功率的开方不成反比（这点与高斯光束不同）。光丝长度随着初始脉冲能量的增加而增加。轴上光强通量随初始脉冲能量的增加而增加。     

不同能量下环形高斯强激光光束在空气中的非线性传输

以线性传输模型为对比研究了不同初始能量的环形光束在空气中的非线性传输。结果显示,在传输初始阶段,非线性克尔效应减弱了线性空间啁啾导致的聚焦作用。线性聚焦使能量向光轴方向流动导致强光强核心,在光轴附近生成类高斯脉冲结构,增强了非线性自聚焦效应,导致光强急剧增加形成光丝。环形光束的初始能量的大小能够影响自聚焦焦距、光丝长度和光强通量。自聚焦焦距随着初始脉冲能量的增加而减小,但自聚焦焦距与初始功率的开方不成反比（这点与高斯光束不同）。光丝长度随着初始脉冲能量的增加而增加。轴上光强通量随初始脉冲能量的增加而增加。     

Click- and chirp-evoked human compound action potentials

In the experiments reported here, the amplitude and the latency of human compound action potentials (CAPs) evoked from a chirp stimulus are compared to those evoked from a traditional click stimulus. The chirp stimulus was created with a frequency sweep to compensate for basilar membrane traveling wave delay using the O-Chirp equations from Fobel and Dau [(2004). J. Acoust. Soc. Am. 116, 2213-2222] derived from otoacoustic emission data. Human cochlear traveling wave delay estimates were obtained from derived compound band action potentials provided by Eggermont [(1979). J. Acoust. Soc. Am. 65, 463-470]. CAPs were recorded from an electrode placed on the tympanic membrane (TM), and the acoustic signals were monitored with a probe tube microphone attached to the TM electrode. Results showed that the amplitude and latency of chirp-evoked N1 of the CAP differed from click-evoked CAPs in several regards. For the chirp-evoked CAP, the N1 amplitude was significantly larger than the click-evoked N1s. The latency-intensity function was significantly shallower for chirp-evoked CAPs as compared to click-evoked CAPs. This suggests that auditory nerve fibers respond with more unison to a chirp stimulus than to a click stimulus.     

亚强非局域介质中的超高斯空间光孤子族研究

研究了亚强非局域介质中超高斯光束的传播特性.运用变分法,对任意实对称响应函数泰勒级数展开取至四阶,得到了1+1维亚强非局域非线性介质中光束传输的超高斯光束的近似分析解.分析结果表明：束宽解是椭圆雅可比双周期函数,相移、空间啁啾以及临界输入功率都正比于超高斯光束的阶数.提出了超高斯空间光孤子族模型和准方波形空间光孤子的实现可能性.     

强非局域非线性介质中的超高斯空间光孤子族

运用变分法,对任意实对称响应函数泰勒级数展开取至二阶,得到了1 1维强非局域非线性介质中光束传输的超高斯光束的近似分析解,提出了超高斯空间光孤子族模型。分析结果表明:束宽解是三角函数型,相移、空间啁啾以及临界输入功率都正比于超高斯光束的阶数,束宽振荡周期不仅与介质材料有关,而且还与光束和相位因子的阶有关。提出了准方波形空间光孤子的可能性。     

The mechanical waveform of the basilar membrane. II. From data to models--and back

Mechanical responses in the basal turn of the guinea-pig cochlea are measured with low-level broad-band noise as the acoustical stimulus [for details see de Boer and Nuttall, J. Acoust. Soc. Am. 101, 3583-3592 (1997)]. Results are interpreted within the framework of a classical three-dimensional model of the cochlea that belongs to a very wide class of nonlinear models. The use of linear-systems analysis for this class of nonlinear models has been justified earlier [de Boer, Audit. Neurosci. 3, 377-388 (1997)]. The data are subjected to inverse analysis with the aim to recover the "effective basilar-membrane impedance." This is a parameter function that, when inserted into the model, produces a model response, the "resynthesized" response, that is similar to the measured response. With present-day solution methods, resynthesis leads back to an almost perfect replica of the original response in the spatial domain. It is demonstrated in this paper that this also applies to the response in the frequency domain and in the time domain. This paper further reports details with regard to geometrical properties of the model employed. Two three-dimensional models are studied; one has its dimensions close to that of the real cochlea, the other is a stylized model which has homogeneous geometry over its length. In spite of the geometric differences the recovered impedance functions are very similar. An impedance function computed for one model can be used in resynthesis of the response in the other one, and this leads to global amplitude deviations between original and resynthesized response functions not exceeding 8 dB. Discrepancies are much larger (particularly in the phase) when a two-dimensional model is compared with a three-dimensional model. It is concluded that a stylized three-dimensional model with homogeneous geometric parameters will give sufficient information in further work on unraveling cochlear function via inverse analysis. In all cases of a sensitive cochlea stimulated by a signal with a stimulus level of 50 dB SPL per octave or less, the resulting basilar-membrane impedance is found to be locally active, that is, the impedance function shows a region where the basilar membrane is able to amplify acoustic power or to reduce dissipation of power by the organ of Corti. Finally, the influence of deliberate errors added to the data is discussed in order to judge the accuracy of the results.