Modeling the Electrode-Neuron Interface of Cochlear Implants: Effects of Neural Survival, Electrode Placement, and the Partial Tripolar Configuration

Abstract

The partial tripolar electrode configuration is a relatively novel stimulation strategies that can generate more spatially focused electric fields than the commonly used monopolar configuration. Focused stimulation strategies should improve spectral resolution in cochlear implant users, but may also be more sensitive to local irregularities in the electrode-neuron interface. In this study, we develop a practical computer model of cochlear implant stimulation that can simulate neural activation in a simplified cochlear geometry and we relate the resulting patterns of neural activity to basic psychophysical measures. We examine how two types of local irregularities in the electrode-neuron interface, variations in spiral ganglion nerve density and electrode position within the scala tympani, affect the simulated neural activation patterns and how these patterns change with electrode configuration. The model shows that higher partial tripolar fractions activate more spatially restricted populations of neurons at all current levels and require higher current levels to excite a given number of neurons. We find that threshold levels are more sensitive at high partial tripolar fractions to both types of irregularities, but these effects are not independent. In particular, at close electrode-neuron distances, activation is typically more spatially localized which leads to a greater influence of neural dead regions.

1. Introduction

Cochlear implants (CIs) transmit spectral information with multiple electrodes that stimulate the auditory nerve in a place-specific manner along the frequency gradient of the cochlea. The electric fields generated by adjacent electrodes may stimulate overlapping populations of neurons. This overlap is thought to reduce spectral resolution in CI listeners by limiting the independence of multiple electrodes. For instance, past studies have shown that speech recognition does not improve when the number of active electrodes is increased beyond seven in quiet listening conditions (Fishman et al., 1997; Friesen et al., 2001) and ten in the presence of background noise (Friesen et al., 2001).

In theory, stimulating with spatially selective electric fields should reduce overlapping neural activation and increase the number of independent electrodes. Experimental configurations intended to focus electric fields include the tripolar (TP) or quadrupolar configuration (Jolly et al., 1996), the partial tripolar (pTP) configuration (Kral et al., 1998; Litvak et al., 2007; Bonham and Litvak, 2008) and the phased-array configuration (Rodenhiser and Spelman, 1995; van den Honert and Kelsall, 2007). Volume conduction models and physical measurements show that these configurations produce more spatially restricted electric fields than the commonly used monopolar (MP) and bipolar configurations. A recent study by Berenstein et al. (2008) showed that the pTP configuration, when compared to the MP configuration, significantly improves CI users’ discrimination of spectral ripples, which relies on the use of spatial information. In addition, a study by Bierer and Faulkner (2010) used a forward masking paradigm to demonstrate that the pTP configuration sharpens forward-masked tuning curves.

Improved spatial selectivity and spectral resolution should lead to improved speech and music perception in CI users. It appears, however, that CI users do not fully realize the expected benefits of spatially-restricted strategies. The Berenstein et al. (2008) study showed that, despite improved spectral resolution when using a pTP configuration, subjects did not show significant improvements in the perception of speech in noise and did not report a greater music appreciation or satisfaction in everyday use. One possible explanation for these findings is that focused stimulation strategies are sensitive to local irregularities in the electrode-neuron interface (Pfingst and Xu, 2004; Bierer and Faulkner, 2010). This explanation is motivated by two observations. First, perceptual threshold levels tend to vary from electrode to electrode for the TP configuration yet remain relatively constant across the array for the MP configuration (Mens and Berenstein, 2005; Bierer, 2007). Second, increased channel-to-channel variability in thresholds is correlated with poorer speech recognition (Pfingst and Xu, 2004; Bierer, 2007). Possible causes of local irregularities include degeneration of spiral ganglion (SG) neurons (Terayama et al., 1979; Spoendlin, 1984; Moore and Glasberg, 1997; Finley and Skinner, 2008), variations in the position of the CI electrodes and their proximity to SG neurons (Cohen et al., 1996a; Ketten et al., 1998; Skinner et al., 2002; Cohen et al., 2003; Wardrop et al., 2005a,b), and variations in tissue impedance throughout the cochlea (Kawano et al., 1998; Somdas et al., 2007) that can alter current pathways (Vanpoucke et al., 2004). In addition, channels with elevated thresholds could adversely impact speech perception if sufficient loudness levels cannot be reached due to voltage compliance limitations. The higher current levels required may also lead to greater spread of neural activation and thus poorer spatial selectivity (Morris and Pfingst, 2000; Bierer and Middlebrooks, 2002; Snyder et al., 2004).

This study simulates intracochlear potential fields and neural activation using a modeling framework similar to Litvak et al. (2007), Bonham and Litvak (2008), and Cohen (2009). As in Bonham and Litvak (2008), we use a simplified cochlear geometry with two regions of different resistivity to describe the fluid-filled scala tympani and the surrounding bone. While Bonham and Litvak (2008) used finite element numerical methods to compute the intracochlear electric field, here we present an analytic solution to the potential field problem and the associated neural activating function. The resulting simulations show that, as expected, higher pTP current fractions lead to more spatially focused stimulation. We then systematically investigate the effects of including a discrete neural dead region, as we vary electrode-neuron distance and pTP current fraction. While threshold levels increase with dead region size, pTP fraction, and electrode-neuron distance, we find that sensitivity to dead regions increases for more focused stimulation. In particular, the effect of dead regions is greatest at close electrode-neuron distance and high pTP fraction. The model demonstrates, therefore, that variations in electrode position and neural survival can explain the greater channel-to-channel variability in threshold levels measured using pTP configurations. The model also illustrates a potential clinical use of spatially focused stimulation strategies: since high TP thresholds can be caused by neural dead regions, the results support the idea that TP configuration can be used to probe the cochlea to identify regions of the cochlea with poor neural survival.

2. Method

The following sections describe the three stages of the computer model. First, the potential field is computed in a simplified cochlear geometry (Sec. 2.1). Next, neural excitation is simulated using an activating function (Sec. 2.2). Lastly, the total number of activated neurons is computed and used to predict perceptual threshold levels and growth of loudness (Sec. 2.3).

2.1. Potential Field Model

The potential field model uses a simplified cochlear geometry that is depicted in Fig. 1. The model consists of an inner cylinder representing the scala tympani that is surrounded by an outer region representing the osseous spiral lamina. The cochlear implant electrode array is located in the inner region and the SG neurons lie in the outer region. Following the model of Rattay et al. (2001), we set the resistivity of the inner region to 70 Ω cm and the outer region to 6400 Ω cm. The ratio of the inner to outer resistivity is therefore approximately 1:90. The work of Whiten (2006) showed that this ratio of resistivity is a key parameter controlling the spread of neural activation and that a large ratio (1:100 in his work) led to closer fits of psychophysical data than a homogeneous volume conduction model.

Figure 1.

Diagrams of the model cochlea. A: Radial cross-section view. The osseous spiral lamina has a higher resistivity (ρ₂) and surrounds the cylindrical scala tympani. The scala tympani has a lower resistivity (ρ₁) and its radius is denoted r_s. Electrode position is measured by its distance from the center of the scala tympani (r_e). Spiral ganglion nerve cells are located in the spiral lamina, a distance of a from the interface of the two layers and a distance d from the electrode array. B: Longitudinal view. The length of the cochlea is 33 mm with the auditory nerve extending along the entire distance. The cochlear implant array consists of 16 electrodes numbered from apex to base. The most basal electrode (number 16) lies 30 mm from the apical end of the cochlea and a mid-array electrode (number 8) is 21.2 mm from the apex.

The bottom panel of Fig. 1 shows a longitudinal view of the model cochlea. The cochlear implant array is represented by sixteen point sources of current located within the scala tympani region. The radial displacement of an electrode from the center of the inner region, denoted by r_e, can vary from −1 mm (2.3 mm from the closest SG neuron) to +1 mm (0.3 mm from the closest SG neuron). To simplify the mathematical derivation of the potential field solution, the cylinder is assumed to have an infinite length, but in all simulations we compute the potential field in a 33 mm subsection of this infinite domain. This 33 mm span of the domain defines the length of the model cochlea and the most basal electrode (electrode 16) is defined to be 30 mm from the apex. The spacing between electrodes is 1.1 mm, consistent with the design of the Advanced Bionics HiFocus-I electrode array (Advanced Bionics, Sylmar, CA).

In this simplified two-layer domain, it is possible to derive an exact solution for the potential field. This problem was first considered by Peskoff (1974) and, in the context of CI stimulation, by Rubinstein (1988). The potential induced by a point current source of intensity I placed at r = r_e, z = z₀, and θ = θ₀ in a medium of resistivity ρ₁ is the solution to the partial differential equation:

$$\frac{1}{r}\frac{\partial }{\partial r}(r\frac{\partial V}{\partial r})+\frac{1}{r^2}\frac{{\partial }^{2}V}{\partial {\theta }^2}+\frac{{\partial }^{2}V}{\partial z^2}=-\frac{{\rho }_{1}I}{r}\delta (r-r_e)\delta (\theta -{\theta }_0)\delta (z-z_0)$$ (1)

where r, θ, and z are radial coordinates. The potential field must be continuous and bounded in z and r and the radial current flow across the boundary between the two regions must also be continuous. This last condition can be expressed as:

$$\underset{r\to r_s^{-}}{\text{lim}}\frac{\partial V}{\partial r}=\epsilon \underset{r\to r_s^{+}}{\text{lim}}\frac{\partial V}{\partial r},$$ (2)

where ε is the ratio of resistivity of the scala tympani to the spiral lamina $\left(\frac{{\rho }_1}{{\rho }_2}\right)$.

To simplify the calculations we only consider electrode displacements in the direction toward (θ₀ = 0) or away (θ₀ = π) from the location of the auditory nerve. Moreover, by symmetry, the solution for θ₀ = π can be obtained by a reflection of the solution for θ₀ = 0 and the solution for an electrode positioned anywhere along the implant array can be obtained by translating the solution in the z-direction. It suffices, therefore, to consider the solution for θ₀ = 0 and z₀ = 0.

Following Peskoff (1974), we note that the solution is an even function of θ and z so we apply a double cosine transform to Eq. 1 to obtain a system of ordinary differential equations:

$$\frac{1}{r}\frac{\partial }{\partial r}\left(r\frac{\partial {\psi }_n}{\partial r}\right)-\left(\frac{n^2}{r^2}+k^2\right){\psi }_n=-\frac{{\rho }_{1}I}{r}\delta (r-r_e)$$ (3)

where n = 0, 1, 2, … and k are the spatial frequencies in the θ and z directions, respectively, arising from the double cosine transform. The double cosine transform must also be applied to the boundary condition in Eq. 2. The resulting transformed boundary conditions are

$$\underset{r\to r_s^{-}}{\text{lim}}\frac{\partial {\psi }_n}{\partial r}=\epsilon \underset{r\to r_s^{+}}{\text{lim}}\frac{\partial {\psi }_n}{\partial r}.$$ (4)

By solving these ordinary differential equations for ψ_n(r, k), we can recover the unique solution for the potential field by applying the inverse transform:

$$V(r,\theta ,z)=\frac{1}{2{\pi }^2}{\displaystyle {\int }_0^{\infty }dkcos(kz){\displaystyle \sum _{n=0}^{\infty }{\gamma }_{n}cos(n\theta ){\psi }_n(r,k),}}$$ (5)

The coefficient γ_n is one for n = 0 and two otherwise.

In practice, the integral and series in Eq. 5 must be approximated numerically. We approximate the integral as a definite integral with sufficiently large upper bound and use the adaptive Lobatto quadrature function (quadl in Matlab). The infinite series is truncated when higher order terms do not significantly alter the computed solution. This typically required using the first five terms in the series.

In order to determine ψ_n(r, k), note that Eq. 3 is a Modified Bessel’s Equation so the solution can be expressed as a sum of Modified Bessel functions of the first and second kind (denoted I_n and K_n, respectively) (Watson, 1952). The Fourier coefficients, therefore, are of the form:

$${\psi }_n(r,k)={\alpha }_n{I}_n(kr)+{\beta }_n{K}_n(kr).$$ (6)

The solution is assumed to be bounded as r approaches infinity, so α_n is zero for r > r_s. In the case of an off-center electrode (r_e > 0), the solution is also assumed to be bounded at the center of the inner region so β_n = 0 for r < r_e. The coefficients in the remaining regions can be determined by ensuring that the solution satisfies the boundary conditions Eq. 4. The coefficients are found to be (see Supplementary Materials for details):

$${\alpha }_n=\{\begin{array}{cc}{K}_n(k{r}_e)+(1-\epsilon )I_n(k{r}_e)K_n(k{r}_s)K_n^{\prime }(k{r}_s)F_n(k{r}_s)\hfill & \text{if}r<r_e\hfill \\ (1-\epsilon )I_n(k{r}_e)K_n(k{r}_s)K_n^{\prime }(k{r}_s)F_n(k{r}_s)\hfill & \text{if}{r}_e<r<r_s\hfill \\ 0\hfill & \text{if}r>r_s\hfill \end{array}$$ (7)

and

$${\beta }_n=\{\begin{array}{cc}0\hfill & \text{if}r<r_e\hfill \\ I_n(k{r}_e)\hfill & \text{if}{r}_e<r<r_s\hfill \\ \frac{I_n(k{r}_e)F_n(k{r}_s)}{k{r}_s}\hfill & \text{if}r>r_s\hfill \end{array}$$ (8)

where $F_n(k{r}_s)={[\epsilon K_n^{\prime }(k{r}_s)I_n(k{r}_s)-K_n(k{r}_s)I_n^{\prime }(k{r}_s)]}^{-1}$. These equations for the coefficients together with Eqs. 5 and Eqs. 6 completely determine the potential field.

The solution is valid for a single current source and therefore describes the MP configuration. In the pTP configurations, current is returned through the two electrodes that are adjacent to the central active electrode. The fraction of current that is returned through the adjacent electrodes, denoted σ, can range from 0 for MP to 1 for the TP configuration. Intracochlear electric fields from multiple electrodes are thought to sum linearly (Spelman et al., 1982), so the potential field solutions for pTP configurations can be written as linear combinations of the MP solution. If the potential for the i^thelectrode is denoted by V⁽ⁱ⁾ (i = 1, 2, …, 16 numbered from apex to base), then the potential produced by a configuration with pTP fraction σ is:

$$V_{\sigma }^{(i)}=V^{(i)}-\frac{\sigma }{2}(V^{(i-1)}+V^{(i+1)}).$$ (9)

2.2. Auditory Nerve Model

To model the auditory nerve, we define 330 clusters of 100 SG cells for a total of 33, 000, typical for the human cochlea. The array of SG cells extends 33 mm in the longitudinal direction; each cluster is therefore 1 mm. The SG cells are placed in a linear array at a fixed distance from the boundary between the scala tympani and the osseous spiral lamina. The model can simulate nerve loss by reducing the number of SG cells in any of the 330 neural clusters. The number of consecutive clusters with fewer than 100 neurons defines the width, in millimeters, of the neural dead region. For simplicity, the number of neurons in a cluster is restricted in this study to be either 100 (no dead region) or 0 (dead region).

The goal of the model is to efficiently simulate the spatial pattern of neural activation in the cochlea. In order to achieve this, the model does not include a number of biophysical and anatomical details such as voltage-sensitive ion channels and multiple possible sites of action potential initiation along the central and peripheral processes of the neurons. Instead, we adopt the activating function method developed by Rattay (1999), which relates neuronal excitability to the velocity of the change in membrane potential induced by an applied electric field. As in Litvak et al. (2007), we define the activating function to be the second spatial derivative of the potential field in the direction of the peripheral processes. The peripheral processes are assumed to be orthogonal to the longitudinal coordinate z, so the value of the activating function in a Cartesian coordinate system is

$$A(z)={\frac{{\partial }^{2}V(x,y,z)}{\partial y^2}|}_{(x=r*,y=0)}$$ (10)

where r* = r_s + a is the radial distance to the spiral ganglion neurons. Although the potential field is defined anywhere in space, the activating function only requires local information at the site of the SG cells. To compute A(z), we must convert V(r, θ, z) from Eq. 5 into Cartesian coordinates via the transformation x = r cos(θ) and y = r sin(θ) and then differentiate V(x, y, z) in the z-direction. The result is:

$$A(z)=\frac{1}{2{\pi }^2}{\displaystyle {\int }_0^{\infty }dkcos(kz){\displaystyle \sum _{n=0}^{\infty }{\gamma }_n}\left(-\frac{n^2}{r^{*2}}{\psi }_n(r^{*},k)+\frac{1}{r^{*}}\frac{\partial {\psi }_n}{\partial r}(r^{*},k)\right).}$$ (11)

Term-by-term differentiation in this case is not rigorously justified so we checked the validity of this expression by using a finite difference scheme to numerically approximate the second derivative in Eq. 10. The results from the finite difference scheme (not shown) are identical to the activating function values computed using Eq. 11. The infinite sum and integral in this equation are approximated numerically with the same methods used to compute V(r, θ, z) in Eq. 5.

Our method for simulating the activity of a population of neurons using the activating function is similar to the method used by Bruce et al. (1999b), Litvak et al. (2007), and Bonham and Litvak (2008). In particular, we define the probability p(z) that a neuron at position z will fire to be

$$p(z)=\frac{1}{2}\left[1+\text{erf}\left(\frac{|A(z)|-A_{thr}}{\sqrt{2}{A}_{thr}RS}\right)\right].$$ (12)

The value of the activating function will be identical for all neurons in a given cluster, but the probability of firing will vary depending on the parameters describing the individual neuron: threshold (A_thr) and relative spread (RS). The relative spread is a measure of the variability in the neural response to CI stimulation and A_thr is the value of A(z) at which the probability of activating the neuron is 0.5. A_thr and RS are determined by intrinsic properties of the SG nerve cells such as distributions of ion channels, demyelination of the peripheral processes, and other forms of neural degeneration. To simulate a full population of SG cells, therefore, each model neuron is typically assigned different values for A_thr and RS (Bruce et al., 1999a; Litvak et al., 2007). In Fig. 2, the x-marks show realizations for five repeated simulations of the model in which these parameters are randomly distributed. Panel A shows the number of active neurons in a single cluster of 100 neurons and Panel B shows the number of neurons activated across the entire model cochlea (33,000 total neurons). A_thr has a mean of −31 dB, this value is chosen so that the perceptual threshold predicted by the model is relatively consistent with psychophysical measures obtained in our lab using the MP configuration. The standard deviation of A_thr is 4.8 dB, based on data from Miller et al. (1999). RS values are drawn from a normal distribution with mean 6.28% and standard deviation 4.4% (Miller et al., 1999).

Figure 2.

Comparison of five repeated simulations of the fully stochastic model (x) with the deterministic approximation method (black line). A: Number of activated neurons in a single cluster of 100 neurons as a function of stimulus level. B: Number of activated neurons in the entire model cochlea (33000 total) as a function of stimulus level.

For this fully stochastic implementation, there are two sources of variability in the number of activated neurons on each trial: the randomly assigned threshold and relative spread values and the probabilistic responses determined, in part, by those parameters. The goal of this model is to characterize the population response of thousands of neurons in a computationally efficient manner so these trial-to-trial sources of variability are not critical. We therefore make additional simplifications which allow us to perform deterministic simulations. First, the values of A_thr are distributed identically in all clusters. Second, the values of A_thr within a cluster are determined by partitioning the normal distribution into 100 equal areas and assigning value of A_thr based on the midpoint of each area. Third, RS values are identical and set to the mean reported in Miller et al. (1999) (6.28%) for all model neurons. Lastly, rather than simulating whether each neuron fires via a random number draw, we compute p(z) in Eq. 12 and define the number of activated neurons in the cluster at position z to be p(z) times the total number of neurons in the cluster.

The results of the deterministic approximation are shown by the solid lines in Fig. 2. The approximation adequately captures the population response within a single cluster (Panel A). Panel B shows that for stimulus levels that activate more than 100 neurons in the entire population, the deterministic approximation and the fully stochastic model are nearly identical. At stimulus levels that activate fewer than 100 neurons, the deterministic approximation underestimates the total number of activated neurons. These low stimulus levels, however, are not relevant in this study because we assume that at least 100 neurons must be activated to reach perceptual threshold.

2.3. Prediction of Psychophysical Measures

The output of the electrostatic and neural activation stages of the model is the spatial pattern of active neurons. Counting the total number of active neurons across the cochlea gives a measure of overall neural activation. Although it is not known how the total number of active neurons is related to psychophysical measurements, it is commonly assumed that perceptual threshold is achieved when some small number of neurons is activated. Typical values used in past studies range from one (Bruce et al., 1999a) to 125 (Whiten, 2006); we define perceptual threshold to be 100 active neurons. As in Bruce et al. (1999a) and Cohen (2009), we assume the total number of active neurons is proportional to the loudness of the stimulus.

CIs are primarily used to convey speech and sound information at audible levels, so it is of practical importance to consider spatial patterns of activation at suprathreshold levels of stimulation. We analyze activation patterns for 1000 activated neurons; this number of activated neurons requires current levels well above threshold, but at current levels that would still be within the dynamic range of a typical cochlear implant listener.

3. Results

3.1. Electric Field Patterns

Figure 3 displays the potential field solutions for monopolar stimulation of a single electrode at three radial positions. The potentials were calculated in the radial 2-D cross-section that encompasses the electrode and the nearest portion of the spiral ganglion (i.e. perpendicular to the longitudinal z-axis). In each of the three examples, the current was set to the threshold level determined by the model (see next subsection) at the respective radial position of the electrode (d = 1.3, 0.8, and 0.5 mm). Note that, because the scala tympani is modeled as an infinite cylinder of constant radius, these examples represent stimulation at any of the 16 electrodes of the cochlear implant.

Figure 3.

Radial potential fields produced by monopolar stimulation at three electrode positions, d = 1.3 (top), 0.8 (middle), and 0.5 mm (bottom). The applied current for each panel is set to achieve a threshold activation of 100 neurons; the current and resulting voltage at the level of the SG neurons (double-headed arrow at r = 1.3 mm) are shown at the top left corner of each panel. Computed potentials were interpolated to a fine grid and then rendered as a gray-scale image overlaid with a set of linearly-spaced contour lines. The contour lines range from −25% to +25% with respect to the SG voltage, in steps of 5%, such that the 6^th contour always passes through the SG neurons. Shading ranges from −50% (black) to +50% (white) in the same manner.

The top panel of Fig. 3 shows the potential field for an electrode located in the center of the scala tympani, corresponding to an electrode-neuron distance of 1.3 mm. The applied current level and the resulting voltage at the place of the spiral ganglion (depicted by a black double-headed arrow pointing in the direction of the auditory nerve fibers) are indicated in the upper right corner of the panel. Only the top portion of the cylinder is displayed, and the black regions at r > 1.8 are outside of the boundaries of the solution grid. As expected from the symmetric geometry, the contour lines spread out concentrically from the center. In a homogeneous medium, the voltage would fall off as the inverse of the distance from the current source, resulting in contour lines that are more spread apart. However, because of the abrupt decrease in conductivity from the inner scalar region to the outer bone region (white dashed line), the contour lines become closer together when r > 1. The result is that the voltage at the spiral ganglion as well as its 2^nd spatial derivative, which determines activation of the model neurons is higher than it would be without the higher resistance of the osseous spiral lamina.

The middle and bottom panels of Fig. 3 depict the potential fields for electrode-neuron distances of 0.8 and 0.5 mm, respectively. To facilitate comparison across images, in each panel the 6th contour line is drawn through the level of the spiral ganglion. The five contour lines on either side of this reference contour range from 25% above to 25% below in voltage; likewise, the gray-scale coloring ranges from 50% above to 50% below in voltage. As the electrode moves closer to the bony outer region, the contour lines on either side of the spiral ganglion become closer together. In the neural portion of the model (see Eq. 10), this larger potential gradient translates to a higher degree of activation. Consequently, progressively less current is required to achieve perceptual threshold at the smaller electrode-neuron distances, as will be demonstrated in more detail in the next subsection.

A series of potential fields calculated in the longitudinal plane, parallel to the axis of the cochlea, is shown in Figure 4. The contour lines and image coloring are scaled similarly to Fig. 3, but the spiral ganglion at the middle contour is now marked by a black circle (the nerve fibers project out of the plane of the images).From top to bottom, the electrode configuration was varied from monopolar (σ = 0), to partial tripolar (σ = 0.5), to true tripolar (σ = 1). In each case, stimulation was centered at the 8th electrode (z = 21.2 mm) using an electrode-neuron distance of 0.8 mm. The top panel represents the same stimulus condition as the middle panel of the previous figure. As before, the spiral lamina region of lower conductivity results in a bending and compression of the iso-voltage contours. Observed along the longitudinal dimension, the spread of current along the cochlea is somewhat more limited in the bone than in the fluid-filled scala tympani, based on the number of field lines in the two regions over the same distance along the cochlea.

Figure 4.

Longitudinal potential fields produced by partial tripolar stimulation at flanking currents of σ = 0 (top), 0.5 (middle), and 1.0 (bottom), with the electrode position fixed at d = 0.8 mm. Currents are set to the respective threshold levels, and the formatting and contour normalization are the same as in Fig. 3. The z-axis of the modeled cochlea appears along the abscissa and the radial x-axis appears along the ordinate. The spiral ganglion at the middle contour is now marked by a black circle (the nerve fibers project out of the plane of the images).

The more limited spread of current along the bony portion of the cochlea is also apparent with the partial-tripolar and tripolar configurations (middle and bottom panels), but the spread becomes even more restricted as the amount of flanking current is increased. In the middle panel (σ = 0.5), the two flanking electrodes cause the voltage in their immediate vicinity to decrease because their polarity is opposite of the center electrode. This forces the central contours to compress along the longitudinal z-axis. While this compression is most evident near the center electrode, its effect continues several millimeters down the cochlea (e.g. at z = 18 mm) where the voltage is proportionally lower than in the monopolar condition. Note that negative potential contours are not plotted in this panel and the bottom panel of Fig. 4 in order to simplify comparisons across configurations. Negative potentials are contained within the black shaded region, which represents the lowest range of voltages in each panel.

In the bottom panel, which displays the potential field for tripolar stimulation (σ = 1), the potential field lines are extremely compressed. Indeed, most of the 7 mm of cochlea that is represented in the panel is shaded black, indicating voltages less than 50% of the value at the central spiral ganglion position. This steep fall-off in voltage follows from the known volume conduction properties of a charge dipole (in this case, two colinear dipoles with a common pole), which in a homogenous medium produces a voltage null along the axis joining the poles (Hayt and Buck, 2004). In the remainder of this section, the effects of electrode configuration and electrode-neuron distance on current spread evident in Figure 3 and Figure 4 are examined in the context of neural activation.

3.2. Neural excitation patterns at threshold

Fig. 5 demonstrates the spatial spread of neural excitation along the cochlea and the influence of electrode configuration, electrode-neuron distance, and neural survival. Each panel shows the number of active neurons as a function of cochlear place measured in millimeters from the apex. Current levels (indicated in each panel) are set to activate 100 total neurons, the definition of perceptual threshold in the model. The effect of electrode configuration is evident by comparing neural excitation patterns from top (MP) to bottom (TP) in Fig. 5. For both the 0.8 mm electrode-neuron distance (left column) and the 1.3 mm distance (center column), the population of activated neurons becomes more localized near the site of stimulation as the pTP fraction increases. Excitation patterns also become more spatially localized when the electrode is closer to the neurons, reflecting the potential field patterns in Fig. 3. This effect can be seen by comparing the left column (0.8 mm electrode-neuron distance) to the middle column (1.3 mm). In the right column, there is an absence of active neurons near the stimulating electrode due to a 1 mm SG dead region. To compensate for the neural loss, current levels must be increased to access viable neurons on either side of the nearby dead region, especially for large pTP fractions. Despite the increase in current levels, however, the activation patterns remain more focused for the higher pTP fractions.

Figure 5.

Spatial patterns of simulated neural excitation: 100 activated neurons. The central active electrode is number 8, in the middle of the array, 21.2 mm from the apex. Current level is shown in the upper left of each panel in units of dB re. 1 µA and pTP current fraction in the upper left. Electrode configuration is varied from MP (top row) to TP (bottom row). Central column: 1.3 mm electrode-neuron distance and full SG nerve survival; left column: 0.8 mm electrode-neuron distance and full SG nerve survival; right column: 1.3 mm electrode-neuron distance and a 1 mm SG dead region centered at the site of the stimulating electrode. The gray line indicates the width at half-maximum.

Threshold levels are greater for the more focused configurations and this difference is exacerbated at larger electrode-neuron distances. For instance, the difference between MP and TP thresholds is 10 dB at the 0.8 mm electrode-neuron distance (left column), but this difference increases to 20 dB at the 1.3 mm distance (middle column). This is primarily due to the fact that TP threshold increases substantially with electrode-neuron distance while MP thresholds increase only modestly. Threshold levels also increase when there is a dead region (right column), although again the change is relatively small for the MP configuration (less than 1 dB).

Fig. 6 illustrates the relationship between the width at half-maximum of the spatial pattern of neural activation and threshold levels (gray horizontal line in Fig. 5). Each electrode configuration is represented by a different symbol and, in Panel A, the symbol coloring indicates a different electrode-neuron distance. The MP threshold values (circles) are nearly constant with changes in electrode-neuron distance while the width increases from 1 mm to nearly 4 mm. As the pTP fraction increases, thresholds become more sensitive to electrode-neuron distance while activation spread becomes less sensitive. For instance, as electrode-neuron distance increases from 0.8 mm to 1.8 mm, the TP threshold (triangles) increases by more than 15 dB while the width at half maximum remains below 1.5 mm.

Figure 6.

Relationship between threshold current levels (abscissa) and width at half maximum of the spatial pattern of excitation at threshold (ordinate) for the MP (circle), pTP 0.5 (square), pTP 0.75 (diamond), and TP (triangle) configurations. A: Effect of varying electrode-neuron distance for complete neural survival. The three electrode-neuron distances are 0.8 mm (black), 1.3 mm (gray), and 1.8 mm (dotted). B: Effect of a neural dead region for an electrode-neuron distance is held at 1.3 mm. The different shadings represent the cases of no dead region (gray, identical to Panel A), 1 mm dead region (striped), and 3 mm (white).

Fig. 6B illustrates the effect of an expanding dead region with the electrode-neuron distance fixed at 1.3 mm. Simulation results are shown for no dead region (gray), a 1 mm dead region (striped), and a 3 mm dead region (white) centered at the site of the central active electrode. The gray symbols in both panels of Fig. 6 represent the same simulation conditions. Similar to Fig. 6A, thresholds are relatively constant for the MP configuration, but increase by more than 10 dB for the TP configuration.

Unlike the activation profiles for the no dead region and 1 mm dead region conditions, the widths for the 3 mm dead region increase from σ=0 to 0.75. This trend is the result of off-peak activation, which can arise with partial tripolar stimulation. As observed in Fig. 4 for σ = 0.5, the flanking electrodes produce non-monotonicities in the electric field pattern. The influence of the return current can, therefore, lead to increases in the electric field beyond the flanking electrodes which can generate greater spread of neural activation. In Fig. 6B, for the 3 mm dead region data, this phenomenon broadens the activation patterns for σ = 0.5 and 0.75 relative to MP because of the absence of surving neurons near the central electrode. At σ = 1.0, the excitation due to the flanking electrodes is sufficiently narrow to reduce the width below the MP value. In some model conditions, off-peak activation can become sufficiently pronounced as to create multimodal patterns of activation. Litvak et al. (2007) also observed such patterns in their model and termed them side lobes. Even in the absence of a dead region, an activation pattern may contain side lobes at the higher currents required for supratheshold stimulation, as seen in the next section.

3.3. Neural excitation patterns at suprathreshold levels

Fig. 7 demonstrates the spatial spread of neural excitation along the cochlea for current levels that activate 1000 SG neurons. As in Fig. 5, the left column shows results for a close electrode-neuron distance (0.8 mm), the center column shows results for a 1.3 mm electrode-neuron distance, and the right column shows results for a 1.3 mm distance and a 1 mm SG dead region. The suprathreshold activation patterns exhibit more spatial spread of excitation than the threshold patterns shown in Fig. 5. As in the case of threshold current levels, stimulation at smaller electrode-neuron distances produces narrower center peaks of activation. The left column of Fig. 7 also shows that high pTP fractions can produce side lobes, broadening the excitation beyond the central peak.

Figure 7.

Spatial patterns of simulated neural excitation: 1000 activated neurons. Conventions as in Fig. 5.

The differences between the current levels needed to activate 100 and and 1000 neurons are greater for the more spatially restricted configurations. For instance, comparing results from the central column of Fig. 5 to Fig. 7 indicates that, in the case of 1.3 mm electrode-neuron distance and full SG survival, an extra 5 dB of current is needed for the MP configuration to increase the number of active neurons from 100 to 1000, whereas a 10 dB increase is needed for the TP configuration. The left column shows that, consistent with the results shown Fig. 5, spatial spread of excitation and current levels are somewhat reduced at the closer electrode-neuron distances. The effect of a 1 mm dead region is shown in the right column. With the exception of the TP configuration, the populations of 1000 active neurons are broad relative to the dead region, so only a slight increase in current (<2 dB) suffices to maintain an active population of 1000 neurons. The TP configuration remains spatially focused as current levels increase, even as side lobes emerge. As a consequence, substantially higher current levels (an increase of 6 dB) are needed to recruit 1000 viable neurons when there is a 1 mm dead region.

Fig. 8 displays the number of active neurons as a function of current level measured in dB relative to 1 µA for varying pTP fraction (from top to bottom) and three levels of nerve survival. The primary effect of electrode configuration is that higher current levels are needed to activate a given number of neurons as the pTP fraction increases. The rate of growth of neural activation (i.e. the slopes of the curves in Fig. 8) is lowest for the TP configuration (bottom panel), while there is little difference among the rates when σ is less than one.

Figure 8.

Total number of activated neurons as a function of stimulus level for no neural dead region (black), 1 mm dead region (dashed), and 3 mm dead region (dotted). Electrode configuration is varied from top to bottom: MP, pTP 0.5, pTP 0.75, and TP. Electrode-neuron distance is 1.3 mm. The horizontal gray lines mark the activity levels previously shown in Fig. 5 (100 activated neurons) and Fig. 7 (1000 activated neurons).

The main effect of a local SG dead region is to decrease the total number of neurons activated by a given current level, as shown by the rightward shifts of the growth functions in Fig. 8 as dead region extent increases. The size of this rightward shift measures the amount of extra current needed to activate a given number of neurons. For the MP configuration (top panel), all three lines are nearly identical which shows that the same current levels activate approximately the same number of neurons regardless of whether there is a neural dead region. The TP configuration (bottom panel) is the most sensitive to loss of SG nerve cells since introducing dead regions produces the largest rightward shifts in the growth functions. In order for this configuration to maintain levels of activation that are equivalent to the full neural survival condition, current levels must increase by more than 5 dB if there is a 1 mm dead region and more than 10 dB if there is a 3 mm dead region. Fig. 8 also shows that growth functions for the TP configuration become steeper as the extent of the dead region increases. The steeper slope is likely a result of increases in off-peak activation at high currents, which cause a relatively greater rate of neural recruitment (per decibel change in current).

3.4. Channel-to-channel variability

To test the sensitivity of threshold measurements to localized SG dead regions, we computed threshold levels for all electrodes in the array and included a SG dead region, centered at electrode 8, of varying extent. Results for increasing pTP fraction are shown from top to bottom for a close (0.8 mm) electrode-neuron distance in the left column and a 1.3 mm electrode-neuron distance in the right column of Fig. 9. As expected, threshold levels are generally higher for the more distant electrode position. In addition, the threshold levels increase more due to the presence of SG dead regions at the close electrode position. For MP stimulation, the thresholds are identical for all channels when there is no dead region (dark circles). When a dead region is introduced, however, the threshold levels at the electrodes closest to the dead region slightly increase (striped and open circles). This effect becomes more pronounced as the pTP fraction increases, and is more exaggerated for the smaller electrode-neuron distance. For all configurations, there is no noticeable effect of the 1 mm and 3 mm local dead regions on thresholds at electrodes that are at least 2 positions (2.2 mm) away from the electrode at which the dead region is centered. In summary, Fig. 9 demonstrates that local loss of auditory neurons can produce a pronounced local elevation in threshold for spatially selective configurations.

Figure 9.

Threshold levels for each electrode in the simulated CI array. Electrodes are numbered from apex to base. Electrode-neuron distance is 0.8 mm in the left column and 1.3 mm in the right column. Electrode configurations are (from top to bottom): MP, pTP 0.5, pTP 0.75, and TP. Each panel includes simulated threshold levels in the case of no dead region (solid), a 1 mm dead region (striped), or a 3 mm dead region (white) centered at electrode number 8.

4. Discussion

We have presented a model of cochlear implant stimulation that computes intracochlear electrical potential and simulates neural activity in a simplified cochlear geometry. We have used this model to investigate the effects of electrode configuration, electrode-neuron distance, and spiral ganglion neural survival on spatial spread of excitation, threshold levels, and growth of neural activation. The computer model illustrates three key principles. First, the spatial pattern of neural activation becomes more localized as electrode configuration varies from monopolar to tripolar. Second, configurations that are more spatially selective require higher current levels to reach perceptual threshold, and the threshold current levels are more sensitive to variations in electrode-neuron distance and loss of auditory neurons. Lastly, the effect of variations in electrode-neuron distance and neural survival are not independent. At close electrode-neuron distances, excitation patterns become more spatially localized and, therefore, have a greater sensitivity to local neuron loss.

4.1. Relation to Previous Work

Thresholds

In order to compare simulation results with psychophysical threshold data, we defined threshold as the minimum current level needed to activate a small number (100) of neurons. The range of threshold current levels obtained with the model, for current fractions from MP to TP, are generally consistent with those measured in psychophysical studies (Bierer, 2007; Litvak et al., 2007; Bierer and Faulkner, 2010). We also found that higher pTP fractions produce more spatially restricted patterns of neural excitation at threshold. This is consistent with neurophysiological studies in animals that have shown that pTP and TP configurations produce spectrally focused patterns of activation at multiple stages of the auditory pathway including the auditory nerve (Kral et al., 1998), the inferior colliculus (Snyder et al., 2004; Bonham and Litvak, 2008), and the auditory cortex (Bierer and Middlebrooks, 2002). The model predicts a trade-off between spatial selectivity and threshold levels since more current is needed to activate 100 neurons when stimulating the cochlea with spatially focused configurations. This finding is supported by previous psychophysical studies that found elevated thresholds when using the pTP and TP configurations (Mens and Berenstein, 2005; Bierer, 2007; Litvak et al., 2007; Bierer and Faulkner, 2010).

Studies that have measured perceptual threshold with spatially focused configurations typically have revealed a large amount of channel-to-channel variability (Pfingst and Xu, 2004; Mens and Berenstein, 2005; Bierer, 2007; Bierer and Faulkner, 2010). Local irregularities in the electrode-neuron interface that could cause this variability include local electrode-neuron distance (Saunders et al., 2002), degeneration of SG neurons (Miller et al., 2008), and other factors such as bone and tissue growth in the scala tympani (Kawano et al., 1998; Hanekom, 2005; Somdas et al., 2007). In human psychophysical studies, the relative contributions of any of these factors for a given listener are unknown. The model presented here can be used to investigate two of these factors: electrode-neuron distance and neural survival. The simulated thresholds indicate that SG nerve loss and greater electrode-neuron distances can both cause higher threshold levels (Fig. 6), and therefore may underlie observed channel-to-channel threshold variability. Indeed, Fig. 9 illustrates how a localized dead region can shift threshold levels at nearby electrodes while having no effect on the threshold levels recorded at other sites in the cochlea.

Loudness

To relate the simulation results to CI users’ perceptions of loud-ness, we assumed that the total number of active neurons is proportional to the loudness of a stimulus. Under this assumption, higher pTP fractions require additional current to reach a desired loudness level. Since spread of excitation increases with level, this raises the question of whether the pTP configuration remains more spatially selective than the MP configurations for current levels that are balanced to achieve equal loudness. Morris and Pfingst (2000), for instance, observed a small effect of configuration on level discrimination and reasoned that because spatially focused configurations require higher current levels, they may lose spatial selectivity. Our model suggests that the pTP configuration does remain spatially selective, even at suprathreshold levels of activation (Fig. 7). Understanding how the interaction of level and configuration affects psychophysical measures may require more detailed knowledge of the spatial and temporal patterns of neural responses (see, for example, discussion in Pfingst and Xu (2004)).

Simulated loudness growth functions (Fig. 8) are shallower for the TP configuration than the MP configuration. This finding is consistent with a psychophysical study using the bipolar configuration with variable separation between the stimulating electrodes (Chatterjee, 1999). In that study, the author observed shallower growth functions for decreasing separation of electrodes. Assuming that smaller electrode spacing produced more spatially selective neural activation, these results are consistent with our findings for the pTP configuration. Shallower loudness growth functions are associated with larger dynamic ranges, so the model predicts that dynamic ranges should increase with pTP fraction. Any predicted increase in dynamic range, however, would be negated if the maximum comfortable loudness levels cannot be achieved within the compliance limits of the CI device. Indeed, past studies of the TP configuration have frequently observed that maximum comfortable loudness levels lie beyond the compliance limits of contemporary CI devices (Mens and Berenstein, 2005; Bierer, 2007; Litvak et al., 2007). Fig. 8 illustrates this point since the TP configuration requires much higher current levels than MP to activate a large number of neurons.

The presence of a SG dead region did not appear to have a large effect on the rate of growth of neural activation for MP stimulation. This is inconsistent with animal studies which have shown that the degree of SG nerve survival is correlated with the slope of evoked potential growth functions (for review see Miller et al. (2008)). In this simulation study, however, we have only considered SG nerve degeneration in the form of a single discrete dead region which may not reflect the pattern or extent of nerve loss induced in animal models of deafness. Recent work from our lab has demonstrated that growth functions of both perceptual loudness and electrically evoked auditory brainstem responses are steepest for the channels with the highest TP threshold levels (Nye and Bierer, 2009; Faulkner et al., 2009). The model provides a plausible explanation for this finding: neural dead regions can lead to high TP thresholds as well as more rapid growth of neural activation (Fig. 8, bottom panel).

Modeling studies

The goal of the present modeling approach was to create a computationally tractable model with potential clinical utility. As a consequence, it was necessary to make a number of simplifying assumptions. These simplifications are considerable, but we believe the model represents a reasonable balance between biological realism and computational efficiency. The model does not include several details of the cochlear anatomy such as the coiled shape of the cochlea, changes in size and conductivity of the scala tympani along the length of the cochlea, and material properties of the CI electrode array that have been included in more detailed computer models. Despite the simplifications in the volume conduction model, the findings are broadly consistent with more sophisticated modeling studies. For instance, Rattay et al. (2001) developed a finite element model of the human cochlea and found that the TP configuration (referred to as quadrupolar) produced more spatially selective activation patterns. Briaire and Frijns (2006), using a similar modeling approach, demonstrated that decreasing electrode-neuron distance reduced thresholds and improved spatial selectivity. Both studies found that higher current levels were needed to activate neurons when there was degeneration of peripheral processes. While the anatomically realistic geometries of these models likely have an important role in predicting the current flow in the cochlea, there is some evidence that simplified volume conduction models adequately model current pathways in the cochlea. For example, Vanpoucke et al. (2004), using a lumped-parameter model of the cochlea, obtained relatively accurate fits of electrical field imaging data. Their parameter fitting procedure predicted that the resistivity in the direction transverse to the scala tympani is approximately two orders of magnitude larger than the resistivity in the longitudinal direction. Our two-region model, therefore, appears to capture the essential properties of volume conduction in the cochlea, with the ratio of resistivities between the two layers as a critical parameter. Using an anatomically realistic finite element model, Whiten (2006) also demonstrated that a spiral lamina-to-scala tympani resistivity ratio of approximately 100 to 1 was suitable to model intracochlear electric fields. With respect to the present model, the contribution of the high resistivity ratio ( 90:1) is evident in the potential field examples of Fig. 4, which shows relatively limited current spread in the outer bony region. Thus, although the cochlear bone forces current to flow mostly in the longitudinal direction, raising the threshold required to activate the closest SG neurons, it also focuses that current because it reduces the degree of spread to neighboring neurons.

Another simplifying assumption was modeling neural excitation with the activating function (Rattay, 1999). As a result, the model does not explicitly simulate fundamental features of neural responses to electric stimulation including stochastic dynamics, refractory effects, and adaptation. Numerous computer models have been developed that include these effects using, for instance, the Hodgkin-Huxley formalism (Frijns et al., 2001; Rattay et al., 2001; Whiten, 2006; Imennov and Rubinstein, 2009; Woo et al., 2009, e.g). The objective of this model was to simulate the general spatial pattern of neural activation so including detailed models of neural dynamics was unwarranted. Furthermore, Fig. 2 demonstrates that heterogeneity across the population of SG fibers and variability in individual neural responses can be well approximated by the average number of activated neurons within each cluster.

A final assumption in the neural model was the treatment of SG neurons as points in space, neglecting the fact that SG neurons are spatially extended with a cell body and multiple excitable nodes of Ranvier. In a more anatomically-detailed cochlear implant computer model, Briaire and Frijns (2006) have investigated how excitation patterns change depending on the presence of absence of excitable peripheral processes. They found that, at basal electrode positions, threshold levels and activation profiles are nearly identical, regardless of whether the model neurons included peripheral processes. They did, however, find substantial differences for more apical electrode positions. This suggests that our model may be suitable as a first approximation to an implanted cochlea with highly degenerated peripheral processes. Future work could extend the present dead region model to include a more detailed representation of neural degeneration as well as to consider potential sites of excitation along the axon of the neuron.

Our modeling approach is similar to the work of Litvak et al. (2007); Bonham and Litvak (2008) and Cohen (2009). Here, we have extended this modeling framework to include discrete SG dead regions and focused our analysis on how such local irregularities affect neural activation patterns while systematically varying electrode position and pTP fraction. Numerical values for threshold, relative spread, electrical resistivity in the two layers, and other key parameters were chosen based on past psychophysical, neu-rophysiological, and modeling studies, but the modeling framework should remain valid if future work suggests different values for these parameters. Auditory nerve excitation was based on the second spatial derivative of the potential field, but this approach could also be modified to incorporate other proposed approximations, such as the first spatial derivative used by Bonham and Litvak (2008).

4.2. Clinical Applications and Future Directions

The model illustrates how spread of neural activation can systematically decrease as the current fraction is raised from σ = 0 (MP) to σ = 1 (TP). Focused cochlear implant stimulation is predicted to have several benefits, including improved spectral resolution and decreased channel interaction. In most cases, neural activation patterns simulated with the TP configuration are the most spatially restricted, which indicates the potential value of this configuration. Several other findings in this study, however, illustrate challenges associated with implementing a TP speech processing strategy. TP thresholds are substantially higher than MP thresholds, and the difference in input current needed to excite a given number of neurons becomes even greater at suprathreshold activation levels. The large current requirements for the TP configuration indicate that it may be unable to transmit loud signals to CI users and would have much greater power requirements than the MP configuration. The model also illustrates situations in which the TP configuration may dramatically lose its high degree of spatial selectivity. For instance, when there are areas of low neural survival near an electrode, or when an electrode that is positioned close to the medial wall of the scala tympani is stimulated with suprathreshold current levels, the simulated neural activation patterns become multimodal. These side lobes of excitation reduce the spatial selectivity of the TP configuration and could transmit confounding pitch information to CI users. One possible strategy for avoiding these problems while preserving the benefits of focusing is to vary the configuration from channel to channel, depending on the state of the electrode-neuron interface. For example, focused pTP configurations could be used in regions of the cochlea with the most surviving SG neurons, and the MP mode could be used in the vicinity of a neural dead region.

In order for a multiple configuration stimulation strategy to be feasible, clinicians must be able to evaluate the electrode-neuron interface at each channel in order to determine the optimal pTP current fraction. At present, electrode-neuron distances can be estimated from CT scan data (Ketten et al., 1998) or x-rays (Cohen et al., 1996b), but there is no direct way to assess the spiral ganglion cell population. The results of this and similar studies point to the potential clinical utility of combining computationally tractable models with psychophysical data and focused stimulation strategies to probe the electrode-neuron interface. Litvak et al. (2007), for instance, used a similar model to estimate electrode-neuron distance and the amount of cross-channel interaction based on threshold measures and suprathreshold loudness balancing data. More recently, Cohen (2009) developed a practical computer model that could be used to estimate global nerve survival for individual patients based on psychophysical, electrophysiological, and radio-graphic measurements. Future work should seek to develop patient-specific fitting algorithms similar to Cohen (2009) that can identify localized areas of SG nerve loss. Our simulations show that spatially focused stimulation may be an essential tool for identifying such local irregularities since threshold levels become more sensitive to irregularities in the electrode-neuron interface at high pTP current fractions.

In addition to threshold, across site variability in psychophysical measures has also been observed for maximum comfortable loudness and modulation detection thresholds (Pfingst et al., 2008), and forward masked spatial tuning curves (Nelson et al., 2008; Bierer and Faulkner, 2010). Ideally, such psychophysical measures could be used to infer the extent of neural degeneration, and the spatial and temporal patterns of neural activation evoked at different sites in the cochlea. For instance, Bierer and Faulkner (2010) have observed a strong correlation between high TP thresholds and broad forward masked tuning curves. Since the model predicts that neural dead regions can cause higher TP thresholds and broader excitation patterns (see Fig. 6), it is reasonable to infer that channels with high TP thresholds and broad spatial tuning may be associated with poor neural survival. Finally, note that Bierer and Faulkner did not observe correlations between MP thresholds and tuning curve widths. This is consistent with the central finding of this study: local changes in the electrode-neuron interface have little effect on the neural activation patterns for the MP configuration and greater effects on the more spatially selective pTP configurations.

Abbreviations

a

distance from neuron to outer wall of scala tympani

A

activating function

CI

cochlear implant

d

electrode-neuron distance

dB

decibel

MP

monopolar

pTP

partial tripolar

r_e

electrode offset

r_s

radius of scala tympani

RS

relative spread

SG

spiral ganglion

TP

tripolar

V

electric potential

ε

ratio of resistivities of inner to outer region

ρ₁

resistivity of scala tympani

ρ₂

resistivity of osseous spiral lamina