The dependence of auditory nerve rate adaptation on electric stimulus parameters, electrode position, and fiber diameter: a computer model study

Abstract

This paper describes results from a stochastic computational neuron model that simulates the effects of rate adaptation on the responses to electrical stimulation in the form of pulse trains. We recently reported results from a single-node computational model that included a novel element that tracks external potassium ion concentration so as to modify membrane voltage and cause adaptation-like responses. Here, we report on an improved version of the model that incorporates the anatomical components of a complete feline auditory nerve fiber (ANF) so that conduction velocity and effects of manipulating the site of excitation can be evaluated. Model results demonstrate rate adaptation and changes in spike amplitude similar to those reported for feline ANFs. Changing the site of excitation from a central to a peripheral axonal site resulted in plausible changes in latency and relative spread (i.e., dynamic range). Also, increasing the distance between a modeled ANF and a stimulus electrode tended to decrease the degree of rate adaptation observed in pulse-train responses. This effect was clearly observed for high-rate (5,000 pulse/s) trains but not low-rate (250 pulse/s) trains. Finally, for relatively short electrode-to-ANF distances, increases in modeled ANF diameter increased the degree of rate adaptation. These results are compared against available feline ANF data, and possible effects of individual parameters are discussed.

FIG. 1

Schematic summary of the computational model. A Anatomical features of a typical cat ANF, using data from Liberman and Oliver (1984). The peripheral axon has an unmyelinated terminal and smaller diameter than does the central axon. Details of the myelinated cell body are provided in the Methods. B Equivalent circuit diagram of an internode and two adjacent active nodes. Only the active nodes have Na and K stochastic channels as well as the resistances and capacitances.

FIG. 2

Example of the membrane potentials recorded from each node in response to a single monophasic current pulse. The offsets in the responses correspond to propagation delays. The stimulus electrode was positioned over a peripheral node (A) or a central node (B) to demonstrate site-of-excitation effects.

FIG. 3

Summary of model responses to single-pulse stimuli (200 repeated presentations of single monophasic 40 μs cathodic pulses). The stimulus electrode is positioned at each of five locations (panels A–E) to explore effects of distance and site of excitation. The distances between the stimulus electrode and axon are 0.235 mm (B and E), 0.925 mm (A and D), and 2.025 mm (C). Electrode positions in A and B overlie the peripheral process while the positions for C–E overlie the central axon. Individual (dots) and mean (circles) spike latencies are plotted vs. stimulus level (top graph of each set) and firing efficiency is also plotted vs. level. Relative spread (RS) and threshold (θ) are indicated for each case. The bubble plots indicate the incidence and location of spike initiation for three values of FE (10%, 50%, and 90%).

FIG. 4

Electrode-to-axon distance greatly affects threshold, particularly for small distances. Threshold levels for two stimuli (single pulses and 5,000 pulse/s trains) are plotted for electrode-to-axon distances ranging from 0.235 to 2.025 mm. Single-pulse thresholds were defined by the level evoking a firing efficiency of 50%, while a criterion of 300 spike/s within an onset window (i.e., 0–12 ms) was used for the pulse-train stimuli. The arbitrariness of these thresholds advises against comparisons of the two curves' absolute values. The distances are defined from the center of the 0.45 mm diameter spherical electrode and the axon surface. To obtain measures of the space between electrode and neuron, a radius (0.225 mm) should be subtracted from the x-axis values.

FIG. 5

Temporal responses to modeled ANFs vary with level for 5,000 pulse/s stimuli. Transmembrane potentials in response to 20 repeated trains are shown for three stimulus current levels. Stimulus levels were chosen to elicit onset rates of 150, 250, and 450 spike/s. Each panel plots an initial interval of 0–10 ms and a late interval of 190–200 ms so that initial and “steady-state” response patterns can be readily seen.

FIG. 6

PSTHs produced by the [K⁺]_ext model (columns 2, 3, and 4) demonstrate rate adaptation not seen using an analogous model lacking the adaptation component (column 1). Three stimulus parameters are explored over the 18 PSTHs of columns 2, 3, and 4. The effects of stimulus pulse rate are contrasted by the upper set of PSTHs (A, 250 pulse/s) and the lower set (B, 5,000 pulse/s). Three electrode-to-fiber distances are examined across the three columns and the effect of changing stimulus level is demonstrated across the PSTHs within 1 column. While the no-adaptation model results (leftmost column) demonstrate an initial decrease in spike rate, it is attributed to refractoriness and no further decrements are evident. The current level (i) for each PSTH is expressed in microampere units. Each graph has two histograms, with the vertical bars representing 1 ms bin widths and filled circles representing long intervals. Onset rates are indicated and have units of spike/s.

FIG. 7

Characterization of rate adaptation across response rates indicates that modeled responses to 5,000 pulse/s trains (A) result in greater adaptation than do the 250 pulse/s trains (B), although axon-to-electrode distance produces an interaction. Spike-rate decrements from cat ANFs are plotted using dots and the line and dashed line plots indicate results obtained by the model with the adaptation component deactivated, essentially indicating a noise floor. Different symbols indicate data from the adaptation model for different electrode-to-fiber distances. The model axon diameter was fixed at 2.3 mm, and the electrode was positioned close to 9th active node.

FIG. 8

Summary of model sensitivity to rate adaptation with changes in axon diameter and electrode-to-axon distance. The degree of adaptation represents the slope of the linear regression computed for each data set of Figure 7. A “degree of adaptation” value of 1 corresponds to complete loss of spikes in the final, steady-state analysis window. Note the non-linear scale for the electrode-to-axon distance.

FIG. 9

A Schematic representation of the curved axon-model according to Shepherd et al. (1993). A stimulus electrode is positioned at x_E = 0.0, y_E = 0.67, and z_E = 0.85 mm in a homogeneous isotropic conducting medium (ρ_e = 0.3 kΩ cm). B Example of spike latency at three response levels (FE = 0.3, 0.7, and 0.99, respectively) using the conditions indicated in the diagram of panelA. The PSTH in response to 400 repeated single monophasic pulses at a level of 4.9 mA is plotted in panelC.