Effect of Pulse Rate on Loudness Discrimination in Cochlear Implant Users

Abstract

Stimulation pulse rate affects current amplitude discrimination by cochlear implant (CI) users, indicated by the evidence that the JND (just noticeable difference) in current amplitude delivered by a CI electrode becomes larger at higher pulse rates. However, it is not clearly understood whether pulse rate would affect discrimination of speech intensities presented acoustically to CI processors, or what the size of this effect might be. Intensity discrimination depends on two factors: the growth of loudness with increasing sound intensity and the loudness JND (or the just noticeable loudness increment). This study evaluated the hypothesis that stimulation pulse rate affects loudness JND. This was done by measuring current amplitude JNDs in an experiment design based on signal detection theory according to which loudness discrimination is related to internal noise (which is manifested by variability in loudness percept in response to repetitions of the same physical stimulus). Current amplitude JNDs were measured for equally loud pulse trains of 500 and 3000 pps (pulses per second) by increasing the current amplitude of the target pulse train until it was perceived just louder than a same-rate or different-rate reference pulse train. The JND measures were obtained at two presentation levels. At the louder level, the current amplitude JNDs were affected by the rate of the reference pulse train in a way that was consistent with greater noise or variability in loudness perception for the higher pulse rate. The results suggest that increasing pulse rate from 500 to 3000 pps can increase loudness JND by 60 % at the upper portion of the dynamic range. This is equivalent to a 38 % reduction in the number of discriminable steps for acoustic and speech intensities.

Appendix

The aim of this section is to mathematically demonstrate that the number of acoustic intensity JNDs (or the number of discriminable intensity steps) available to CI users is equal to the number of JND steps along the perceptual dimension of loudness.

Assume that Ψ is the psychophysical transformation between current amplitude A on a CI electrode and the perceived loudness L, and Ф is the function that maps envelope intensity I of the corresponding acoustic channel to current amplitude A. The perceived loudness of the stimulus is:

$$ L=\varPsi (A)=\varPsi \left(\Phi (I)\right) $$

(1)

Assume ΔL, ΔA, and ∆I are the just noticeable differences (JND) in loudness, current amplitude, and acoustic intensity respectively. Using Eq. (1), the relation between ΔL, ΔA, and ∆I can be described by:

$$ \varDelta L=\varPsi \left(A+\varDelta A\right)-\varPsi (A)=\varPsi \left(\Phi \left(I+\varDelta I\right)\right)-\varPsi \left(\Phi (I)\right) $$

After expanding the terms Ψ(A + ΔA) and Ψ(Ф(I + ∆I)), ΔL can be written as:

$$ \varDelta L=\varPsi (A)+\varDelta A\frac{d\varPsi (A)}{d A}+\mathrm{H}.\mathrm{O}.\mathrm{T}-\varPsi (A)=\varPsi \left(\Phi (I)\right)+\varDelta I\frac{d\varPsi \left(\Phi (I)\right)}{d I}+\mathrm{H}.\mathrm{O}.\mathrm{T}-\varPsi \left(\Phi (I)\right) $$

ΔL can be rewritten as:

$$ \varDelta L=\varDelta A\frac{dL}{dA}+\mathrm{H}.\mathrm{O}.\mathrm{T}=\varDelta I\frac{dL}{dI}+\mathrm{H}.\mathrm{O}.\mathrm{T} $$

The H.O.T (higher order terms) can be ignored if ΔA and ∆I are small and the current-to-loudness and intensity-to-current functions are approximately linear within the small range. Therefore:

$$ \varDelta L=\varDelta A\frac{dL}{dA}=\varDelta I\frac{dL}{dI}\kern0.5em $$

(2)

Equation (2) shows that ΔL can be described by ΔA and the slope of the current-to-loudness function $\left(\frac{dL}{dA}\right).$ ΔL can also be described by ∆I and the slope of the intensity-to-loudness function $\left(\frac{dL}{dI}\right).$ Equation (2) can be rewritten as:

$$ \frac{dL}{\varDelta L}=\frac{dA}{\varDelta A}=\frac{dI}{\varDelta I}\kern1em $$

(3)

The number of loudness JNDs (or the discriminable loudness steps) across the loudness range L₁ and L₂ can be mathematically formulated as (Allen and Neely, 1997):

$$ {N}_L={\int}_{L1}^{L2}\frac{dL}{\varDelta L} $$

Similarly, the number of current amplitude JNDs (or the discriminable current amplitude steps) within the amplitude range A₁ and A₂ that corresponds to the loudness range L₁ and L₂ can be written as:

$$ {N}_A={\int}_{A1}^{A2}\frac{dA}{\varDelta A.} $$

Similar to above, the number of acoustic intensity JNDs (or the discriminable intensity steps) within the intensity range I₁ and I₂ that corresponds to the loudness range L₁ and L₂ can be written as:

$$ {N}_I={\int}_{I_1}^{I_2}\frac{dI}{\varDelta I} $$

Using Eq. (3) it can be demonstrated that:

$$ {N}_L={N}_A={N}_I $$

The number of intensity and current amplitude JNDs is equal to the number of loudness JNDs only. The growth of loudness with current amplitude (Ψ), the acoustic-to-electric mapping (Ф), the absolute values of I₁, I₂, A₁, and A₂ and the dynamic ranges I₂ − I₁ and A₂ − A₁ are irrelevant to the number of discriminable level steps.