Quantifying the Information in Auditory-NerveResponses for Level DiscriminationH. STEVENCOLBURN,1LAURELH. CARNEY,1ANDMICHAELG. HEINZ1,21Hearing Research Center and Department of Biomedical Engineering, Boston University, Boston, MA 02215, USA2Speech and Hearing Bioscience and Technology Program, Massachusetts Institute of Technology, Cambridge,MA 02139, USAReceived: 20 November 2000; Accepted: 4 December 2002; Online publication: 14 March 2003ABSTRACTAn analytical approach for quantifying the informa-tion in auditory-nerve (AN) fiber responses for thetask of level discrimination is described. A simpleanalytical model for AN responses is extended to in-clude temporal response properties, including thenonlinear-phase effects of the cochlear amplifier. Useof simple analytical models for AN discharge patternsallows quantification of the contributions of level-dependent aspects of the patterns to level discrimi-nation. Specifically, the individual and combinedcontributions of the information contained in dis-charge rate, synchrony, and relative phase cues areexplicitly examined for level discrimination of tonalstimuli. It is shown that the rate information providedby individual AN fibers is more constrained by in-creases in variance with increases in rate than by sat-uration. As noted in previous studies, there issufficient average-rate information within a narrow-CF region to account for robust behavioral perform-ance over a wide dynamic range; however, there is nomodel based on a simple limitation or use of AN in-formation consistent with parametric variations inperformance. This issue is explored in the currentstudy through analysis of performance based on dif-ferent aspects of AN patterns. For example, we showthat performance predicted from use of all rate in-formation degrades significantly as level increasesabove low–medium levels, inconsistent with Weber’sLaw. At low frequencies, synchrony information ex-tends the range over which behavioral performancecan be explained by 10–15 dB, but only at low levels.In contrast to rate and synchrony, nonlinear-phasecues are shown to provide robust information atmedium and high levels in near-CF fibers for low-frequency stimuli. The level dependence of the dis-charge rate and phase properties of AN fibers areinfluenced by the compressive nonlinearity of theinner ear. Evaluating the role of the compressivenonlinearity in level coding is important for under-standing neural encoding mechanisms and becauseof its association with the cochlear amplifier, which isa fragile aspect of the ear believed to be affected incommon forms of hearing impairment.Keywords: neural coding, intensity discrimination,nonlinear phase, signal detection theory, auditory-nerve modelingINTRODUCTIONThe focus of this article is the classical problem of levelencoding and its relation to the physiological responseproperties of auditory-nerve (AN) fibers. The pio-neering work in this area is a series of papers fromSiebert (1965, 1968). Siebert took a mathematicalmodeling approach to derive expressions for the sen-sitivity index for performance in intensity discrimina-tion. Siebert assumed that the action potentials on asingle AN fiber could be represented mathematicallyPresent address: Laurel H. Carney, Department of BioengineeringNeuroscience, Institute for Sensory Research, Syracuse University,Syracuse, NY 13244.Present address: Michael G. Heinz, Department of Biomedical En-gineering, Johns Hopkins University, Baltimore, MD 21205.Correspondence to: H. Steven ColburnÆBoston UniversityÆDe-partment of Biomedical EngineeringÆ44 Cummington StreetÆBoston, MA 02215. Telephone: (617)-353-4342; fax: (617)-353-6766; email: [email protected] 04: 294–311 (2003)DOI: 10.1007/s10162-002-1090-6294JAROJournal of the Association for Research in Otolaryngologyas a stochastic point process, specifically a Poissonprocess. He further assumed that the variability of thefiring times on each neuron was statistically inde-pendent from fiber to fiber, consistent with the resultsof Johnson and Kiang (1976). With these assumptions,the only additional information needed to specify themodel completely was the rate of firing for each fiberand, most important, the dependence of this firingrate on stimulus level. Siebert assumed a convenientform for this dependence that allowed an analytic so-lution for the performance of an ideal observer (ba-sically the best performance that could be achievedgiven the statistical nature of the firing patterns) basedon the complete set of neural firings. The currentstudy extends Siebert’s work with analytic expressionsthat allow explicit description of the level dependenceof the temporal response. A simple description of therate function for each nerve fiber is specified as afunction of time and level, and a nonstationary Pois-son process is assumed. Analytical performancemeasures are derived that allow comparisons amongthe different information sources regarding the levelof the stimulus, including the average rate of re-sponses, and the temporal synchronization and rela-tive phases of responses at low frequencies.Although many people have extended Siebert’swork with computations of performance based onmore detailed assumptions about peripheral coding(e.g., Goldstein 1980; Delgutte 1987; Viemeister 1988;Winslow and Sachs 1988; Winter and Palmer 1991;Huettel and Collins 1999; Heinz et al. 2001a,b; re-viewed by Delgutte 1996), most of these studies wereessentially computational in nature. The computa-tional approach does not take advantage of mathe-matical expressions that give insight into therelationship among the various sources of informa-tion and parameters of dependence. In addition,these studies have shown that the robust level-discrimination performance demonstrated by humanlisteners is not accounted for by the optimal use ofaverage-rate information in the AN. Thus, it is of in-terest to examine whether the optimal use of tem-poral information in AN responses provides a betteraccount of robust performance.In the following section, general results are de-rived that are used throughout the article. Then,analytical results based on average rate and on tem-poral information are presented in separate sections,followed by general discussion.THEORETICAL CALCULATIONSGeneral methods for characterizing performanceA convenient parameter for summarizing empiricalperformance and theoretical predictions is the sen-sitivity per decibel d¢(Heinz et al. 2001a;