134
Peter M. Narins
further characterize the fiber without the need for histological tracing methods;
however, for this promise to be realized, putative origins based on S-V offset must
first be confirmed for bimodal fibers by dye-filling methods.
3.1.3 How do we Characterize Bimodal Fibers?
Most studies of tuning (Frishkopf et al. 1968; Feng et al. 1975; Capranica
1976;Capranica and Moffat 1980), adaptation (Megela and Capranica 1981;
Megela 1984), two-tone suppression (Liff and Goldstein 1970; Benedix et a!.
1994), one-tone suppression (Christensen-Dalsgaard and J0rgensen 1996) and
dynamic range (Feng 1980, 1982; Narins 1987; Dunia and Narins 1989) for
amphibian low-frequency auditory fibers have been accomplished using
traditional methods of analysis. These include frequency-threshold curves (FTCs)
or tuning curves, PST, lSI, and period histograms in response to pure tones, clicks,
and natural sounds, and rate-level functions. Nevertheless, this plethora of experimental techniques has not yielded a model of auditory unit function capable of
accurately predicting the temporal response of these units to novel stimuli.
Recently, there has been rekindled interest in characterizing the filtering properties
of acoustic units in terms of Wiener kernel analysis (Wiener 1958). This analysis
is applicable to the investigation of nonlinear systems with unknown
characteristics, and is inherently a stochastic one- often relying on the use of
Gaussian white noise as the test input ensemble. The experimental possibilities of
this analysis were much advanced by Lee and Schetzen's discovery that the
Wiener kernels could be derived by cross-correlation of the system's output with
its Gaussian white noise input (Lee and Schetzen 1965; Marmarelis and
Marmarelis 1978).
The Wiener series is capable of predicting the response of spontaneously active
auditory units to novel and arbitrarily complex sounds (first-order series: de Boer
and de Jongh 1978; Wolodkin et al. 1997; second-order series: van Dijk et al.
1994, 1997a,b; Yamada and Lewis 1999). Thus, the Wiener kernels embody properties of the auditory filter such as suppression, adaptation, separable AC and DC
responses, and spectro-temporal filtering (Yamada 1997; Yamada and Lewis
2000). The kernels can be analyzed to describe these properties. For example, the
amplitude ofthe discrete Fourier transform (DFT) of the first-order Wiener kernel
(K 1 ) of an auditory unit with a low CF will approximate that unit's pure-tonederived tuning curve or FTC (Evans 1977), while the DFT of the significant
singular vectors of the second-order Wiener kernel (K2) of a fiber with a high CF
will approximate its FTC (Yamada 1997). K2s have been gaining favor as the
preferred method for characterization of auditory system non-linearities; as such
we are attempting to apply them to the understanding of cross-modality interaction
in the eighth nerve.
Peter M. Narins
further characterize the fiber without the need for histological tracing methods;
however, for this promise to be realized, putative origins based on S-V offset must
first be confirmed for bimodal fibers by dye-filling methods.
3.1.3 How do we Characterize Bimodal Fibers?
Most studies of tuning (Frishkopf et al. 1968; Feng et al. 1975; Capranica
1976;Capranica and Moffat 1980), adaptation (Megela and Capranica 1981;
Megela 1984), two-tone suppression (Liff and Goldstein 1970; Benedix et a!.
1994), one-tone suppression (Christensen-Dalsgaard and J0rgensen 1996) and
dynamic range (Feng 1980, 1982; Narins 1987; Dunia and Narins 1989) for
amphibian low-frequency auditory fibers have been accomplished using
traditional methods of analysis. These include frequency-threshold curves (FTCs)
or tuning curves, PST, lSI, and period histograms in response to pure tones, clicks,
and natural sounds, and rate-level functions. Nevertheless, this plethora of experimental techniques has not yielded a model of auditory unit function capable of
accurately predicting the temporal response of these units to novel stimuli.
Recently, there has been rekindled interest in characterizing the filtering properties
of acoustic units in terms of Wiener kernel analysis (Wiener 1958). This analysis
is applicable to the investigation of nonlinear systems with unknown
characteristics, and is inherently a stochastic one- often relying on the use of
Gaussian white noise as the test input ensemble. The experimental possibilities of
this analysis were much advanced by Lee and Schetzen's discovery that the
Wiener kernels could be derived by cross-correlation of the system's output with
its Gaussian white noise input (Lee and Schetzen 1965; Marmarelis and
Marmarelis 1978).
The Wiener series is capable of predicting the response of spontaneously active
auditory units to novel and arbitrarily complex sounds (first-order series: de Boer
and de Jongh 1978; Wolodkin et al. 1997; second-order series: van Dijk et al.
1994, 1997a,b; Yamada and Lewis 1999). Thus, the Wiener kernels embody properties of the auditory filter such as suppression, adaptation, separable AC and DC
responses, and spectro-temporal filtering (Yamada 1997; Yamada and Lewis
2000). The kernels can be analyzed to describe these properties. For example, the
amplitude ofthe discrete Fourier transform (DFT) of the first-order Wiener kernel
(K 1 ) of an auditory unit with a low CF will approximate that unit's pure-tonederived tuning curve or FTC (Evans 1977), while the DFT of the significant
singular vectors of the second-order Wiener kernel (K2) of a fiber with a high CF
will approximate its FTC (Yamada 1997). K2s have been gaining favor as the
preferred method for characterization of auditory system non-linearities; as such
we are attempting to apply them to the understanding of cross-modality interaction
in the eighth nerve.