Practical model description of peripheral neural excitation in cochlear implant recipients: 1. Growth of loudness and ECAP amplitude with current

Hearing Research 247 (2009) 87–99

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Methodological paper

Practical model description of peripheral neural excitation in cochlear implant recipients: 1. Growth of loudness and ECAP amplitude with current Lawrence T. Cohen * Department of Otolaryngology, The University of Melbourne, 384-388 Albert Street, East Melbourne, Vic. 3002, Australia

a r t i c l e

i n f o

Article history: Received 31 March 2008 Received in revised form 18 November 2008 Accepted 18 November 2008 Available online 27 November 2008 Keywords: Cochlear implant Modeling of neural response ECAP NRT Loudness growth Temporal loudness summation

a b s t r a c t This is the first in a series of five papers, presenting the development of a practical mathematical model that describes excitation of the auditory nerve by electrical stimulation from a cochlear implant. Here are presented methods and basic data for the subjects, who were implanted with the NucleusÒ 24 cochlear implant system (three with straight and three with ContourTM electrode arrays), required as background for all papers. The growth of subjective loudness with stimulus current was studied, for low-rate pulse bursts and for single pulses. The growth of the amplitude of the compound action potential (ECAP) was recorded using the Neural Response TelemetryTM (NRTTM) system. An approximately linear relationship was demonstrated between ECAP amplitude and burst loudness, although this failed at the lower end of the dynamic range, to an extent that varied with subject and stimulated electrode. Single-pulse stimuli were audible below ECAP threshold, demonstrating that the audibility of burst stimuli at such low currents was not due solely to temporal loudness summation. An approximate function was established relating the curvature of the burst loudness growth function to the maximum comfortable level (MCL). Loudness at threshold was quantified, as a percentage of loudness at MCL. The relationship between loudness and ECAP growth functions, the curvature versus MCL function and the loudness associated with threshold are relevant to the development of a mathematical model of electrically evoked auditory nerve excitation. Ó 2008 Elsevier B.V. All rights reserved.

Abbreviations: CL, clinical current level (programming unit, Cochlear Limited); ECAP, electrically evoked compound action potential; ESF, effective stimulation field (usually expressed in CL); FEA, finite element analysis; FPE, first pulse effect, resulting in increased loudness of the first pulse of a burst; I20, I50, I80, currents required to achieve loudness 20%, 50% and 80% that of IMCL300; IMCL300, MCL current for 300 ms stimulus (mA); IMCLONE, MCL current for single pulse (mA); Imax300, maximum current used in fitting power law functions; ITBek300, Békésy threshold for 300 ms burst (at 250 pulses/s); ITBekONE, Békésy threshold for single pulse; I2%300, current for which power law function fitted to loudness growth function for 300 ms bursts is 2% of maximum; I2%ONE, current for which power law function fitted to loudness growth function for single pulses is 2% of maximum; I2%ECAP, current for which power law function fitted to ECAP growth function is 2% of maximum; IF5TM, computer interface card (Cochlear Limited); MCL, maximum comfortable level (CL); MCL300, maximum comfortable level for 300 ms burst at 250 pulses/s (CL); MCLONE, maximum comfortable level for single-pulse (CL); MP1, monopolar 1 (extracochlear ‘‘ball” reference electrode); MP2, monopolar 2 (extracochlear ‘‘plate” reference electrode); MP1+2, monopolar 1 plus 2 (‘‘ball” and ‘‘plate” reference electrode); MPI, masker probe interval (previously known as ‘‘masker advance”): interval between end of masker pulse and start of probe pulse (NRT term); Masker offset, current excess of masker relative to probe (CL, NRT term); NRTTM, Neural Response TelemetryTM (Cochlear Limited); PCITM, processor control interfaceTM (Cochlear Limited); Pl, percentage length along organ of Corti; Riw, radial distance of electrode band from inner wall of scala tympani (mm); RS, relative spread, ratio describing dynamic range of neural fiber relative to its threshold; SOE, spread of (neural) excitation, typically as determined by a specific NRT measure (Cohen et al., 2003a); SPrintTM, speech processor (Cochlear Limited). * Tel.: +61 3 9877 4693. E-mail address: [email protected] 0378-5955/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.heares.2008.11.003

1. Introduction The main objective of this series of studies was to develop a relatively simple mathematical characterization (model) of the peripheral neural response to electrical stimulation delivered through a cochlear implant. In addition, methods are provided to enable tailoring of the model to the individual patient, through a series of radiological, psychophysical and electrophysiological measures. The model developed makes provision, with differing degrees of initial sophistication, for patient-specific information regarding:  the positions of the ‘‘bands” of the array: both longitudinal and radial;  the neural density;  the distribution of neural thresholds: mean and standard deviation;  the ‘‘relative spread” (RS) of the neurons (Verveen, 1961): a measure of stochasticity;  the decay of the ‘‘effective stimulation field” as a function of longitudinal distance from a stimulated electrode band;  refractory properties of the neurons;  facilitatory properties of the neurons.

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 temporal loudness summation (seen as non-peripheral for the cochlear implant case) Other effects could be incorporated including, for example, adaptation. Once the parameters for a patient have been established, the model enables prediction of the peripheral neural response to any spatio-temporal pattern of electrical stimulation pulses. The value of such a patient-specific model is considerable. It embodies a practical understanding of the complex factors involved in electrical stimulation of the cochlea. Therefore, it could be a valuable tool for understanding observations and, indeed, for bringing order into an array of diverse and seemingly unrelated observations. It could be used to evaluate the function of existing speech processing strategies in individual patients, by predicting the detailed neural response to complex sounds. Furthermore, it could pave the way for the development of more advanced ‘‘neural behavior-aware” sound processing strategies. Improved speech perception results should be possible mainly because existing speech processing algorithms take only very limited account of actual neural behavior, either in the individual patient or even in a general sense, and they do not take adequate account of the spread of the stimulation field within the cochlea. It is a considerable advantage of the present approach that the model can be readily refined, including by the incorporation of additional aspects of neural behavior that may be considered useful in the future. Furthermore, the computational requirements of the model would be relatively modest. The development begins with the basic framework of the model of Bruce et al. (1999a). That model comprised a population of neurons distributed ‘‘along” the cochlea, with a range of thresholds (uniformly distributed ±5 dB around the mean), acted upon by an electric field that decayed exponentially with longitudinal distance of a neuron from the stimulated electrode band. Individual neurons were allowed a non-zero dynamic range, expressed as the relative spread (RS), which is proportional to the ratio of the dynamic range to the mean threshold of the fiber (Verveen, 1961). Bruce et al. (1999c) also introduced refractory behavior of the neurons. The present treatment differs in numerous respects from that of Bruce and colleagues, in an endeavor to make the model more realistic and more consistent with the data obtained from human subjects. The overall scheme and some initial results were introduced in Cohen et al. (2001a) and a recent summary of the work was given in Cohen et al. (2007a,b). The sequence of steps was essentially as follows. 1.1. Radiographic quantification of electrode position A radiographic method was developed to quantify the positions of individual electrode bands, longitudinally and radially (Cohen et al., 1996a, 2000; CViewÓ software). 1.2. Development of ECAP measure of spread of neural excitation An ECAP (electrically evoked compound action potential) measure of the spread of neural excitation was developed (Cohen et al., 2003a; also the earlier study Cohen et al., 2004). This ‘‘SOE” measure employed the Neural Response TelemetryTM (NRTTM) system. 1.3. Study of growth functions The growth of loudness and ECAP amplitude with current is studied; in particular, the curvature (degree of non-linearity) of such growth functions. Preliminary results have been reported concerning the relationship between loudness and ECAP growth functions (Cohen et al., 2001b) and a relationship has been noted

between curvature of the loudness growth function and maximum comfortable level, MCL (Cohen et al., 2001b,c, 2003a, 2006). In the present paper these matters are considered in greater detail. 1.4. Development of measure of spread of stimulation field The ‘‘effective stimulation field” (ESF) was defined as a measure of the capacity of a stimulus to excite neurons at various longitudinal separations from the stimulated electrode band. An NRT measure was developed of the longitudinal decay of the ESF, complemented by results from finite element (FEA) models (Cohen et al., 2003b, 2005a). This work is presented formally and in more detail in Paper 2 (Cohen, 2009a). 1.5. Quantification of loudness as a function of burst duration Loudness was quantified as a function of low-pulse rate burst duration (Cohen and Cowan, 2005), which was done mainly to investigate the influence of non-peripheral (‘‘central”) neural effects, especially temporal loudness summation. While the present model predicts peripheral neural responses to single pulses, the loudness versus burst duration data provide complementary knowledge of how more central neural processing integrates those responses. These measurements were performed at three current levels spanning the dynamic range, rather than at threshold. This work is presented formally and in more detail in Paper 3 (Cohen, 2009b). 1.6. Establishment of representative parameters for model at low pulse rate Representative parameters are established in Paper 4 (Cohen, in press-a) for the model at low pulse rates, enabling the description of general trends in patient data. This development draws on results from the first three papers of the series. 1.7. Fitting of low-pulse rate model to individual subjects The model is fitted, also in Paper 4, to individual subject data at low pulse rates. The individual model fits allow prediction of spread of excitation (SOE) functions, which are compared with experimental results from Cohen et al. (2003a). This provides a validation of the model fit. 1.8. Establishment of refractory parameters in individual subjects Refractory recovery behavior is modeled for individual subjects in Paper 5 (Cohen, in press-b). Extensive NRT measurements of refractory recovery, employing numerous intensities of the masker relative to the probe, enable the establishment of parameters describing the refractory recovery of the neurons. The model is fitted to the recovery data for an intense masker, where facilitation is assumed negligible, making use of the individual low-rate parameters from Paper 4. The model predictions for weaker maskers are then compared with experimental data. The difference between the experimental and modeled results provides an estimate of the component of the ECAP attributable to facilitation, a temporary reduction of fiber threshold following a stimulation that does not produce an action potential. This sequence of steps leads to the establishment of a model, for the individual patient, that is able to describe the growth of loudness with current, the longitudinal spread of neural excitation and the refractory behavior. The model incorporates stochasticity of the neural response, which is essential if it is to describe, for example, the variation of ECAP amplitude with the current of a masker pulse relative that of a probe pulse. The methods quantify the facil-

L.T. Cohen / Hearing Research 247 (2009) 87–99

itatory component in the ECAP response and the model can therefore, in principle, incorporate facilitation. In summary, the papers present an integrative model that can describe the peripheral response to electrical stimulation in the individual patient. Innovative methods are employed to obtain the information required to construct the mathematical model. The work makes extensive use of the Neural Response Telemetry (NRT) system, which enables the measurement of numerous aspects of the peripheral neural response to electrical stimulation, via the ECAP. These NRT measures may be seen as providing a bridge between two traditional approaches to understanding the human neural response: human psychophysics and animal neurophysiology. A salient feature of the NRT measures is that they are entirely peripheral, which enables elimination of the central ‘‘contaminants” of psychophysical measures. Conversely, in comparison with the latter, it is possible, in principle, to quantify the central effects. NRT provides a rich additional source of information, which may be considered fundamental to the quantification of neural behavior in individual humans, and to the establishment of a mathematical model for its description. In this paper, the relationship between the growth functions of loudness and ECAP amplitude is studied, with respect to both their shapes and thresholds. In the first case, ECAP growth functions are compared with loudness growth functions for 300 ms pulse bursts at 250 pulses/s. It has been noted that temporal loudness summation is a likely contributory factor to the audibility of pulse bursts at currents lower than the ECAP threshold, the latter being measured for single-pulse stimuli. In order to remove the effect of temporal loudness summation, loudness growth functions are also measured for single pulses, and compared with both loudness growth functions for bursts and ECAP growth functions. In addition, the curvature (degree of non-linearity) of the growth functions is considered and, in particular, its relationship to MCL. The loudness at threshold is quantified as a percentage of the loudness at MCL. The relationship between growth functions of loudness and ECAP amplitude, the curvature versus MCL function and the loudness associated with threshold are all relevant to the subsequent development of the mathematical model of auditory nerve excitation produced by stimulation of the cochlear implant electrode array. 2. Methods and materials 2.1. Subjects Six profoundly hearing-impaired adult subjects from the Cochlear Implant Clinic of the Royal Victorian Eye and Ear Hospital, participated in the study. Subject background details are summarized in Table 1. All subjects were implanted with the NucleusÒ 24 cochlear prosthesis (Cochlear Limited): the straight (banded) array was used in subjects S1–S3, the ContourTM array in subjects C1–C3. These subjects were required to have NRT responses of reasonable quality. Intensive measurements were performed with a sub-group of the subjects, viz. S1–S3 and C1–C2. Although only limited data were available for C3, they were included because the extreme variation of the radial distance of electrode bands from the modiolus rendered the data very informative. Each array was inserted into scala tympani through a cochleostomy. Plain film radiographs were taken using the ‘‘Cochlear View” orientation (Marsh et al., 1993; Xu et al., 2000), and the individual positions of the electrode bands were determined using an extension (Cohen et al., 2000) of the method described by Cohen et al. (1996a). S1–S3 and C1–C3 also participated in an earlier study (Cohen et al., 2003a). The subject numbering convention employed in the present papers is the same as in that earlier paper. The loud-

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ness growth data used for C3 in the present study were from Cohen et al. (2006), in which she participated as ‘‘C2”, whereas her ECAP growth data were from about the same period but have not been published previously. 2.2. Apparatus The Nucleus 24 banded (‘‘straight”) electrode array has 22 conducting platinum electrode bands, placed at intervals of 0.75 mm, and ten basal stiffening rings. The Nucleus 24 Contour array has 22 approximately half-banded platinum electrodes, placed at intervals graduated from large at the basal end to small at the apical end, and no stiffening rings. The Contour array is designed to assume a peri-modiolar position after surgical insertion and withdrawal of the stylet wire, which initially holds the array almost straight. More detailed descriptions of both arrays are given in Tykocinski et al. (2001) and Saunders et al. (2002). For both arrays, the electrode bands are numbered in a basal to apical direction and two extracochlear electrodes are provided: a ball electrode, which is placed under the temporalis muscle, and a plate electrode, on the top of the receiver–stimulator package. The modes for monopolar stimulation are: MP1, which is referenced to the ball electrode; MP2, referenced to the plate electrode; and MP1+2, referenced to both extracochlear electrodes. Both power and data were delivered to the implanted receiver– stimulator by an external induction coil, driven by a SPrintTM speech processor in association with the Processor Control InterfaceTM (PCITM) and the IF5TM computer card (all provided by Cochlear Limited), controlled by a personal computer. Control of psychophysical stimuli was managed by custom software (‘‘Psychophysics Themepark”), which made use of the Nucleus Implant CommunicatorTM software to interface with the Cochlear Limited electronics and thus communicate with the implant. Intracochlear recordings of the ECAP were recorded using the Neural Response TelemetryTM (NRTTM) system with Version 3.0 of the NRT software. 2.3. Stimuli Charge-balanced biphasic current pulses were used for all stimuli, which were monopolar. The current was measured in Cochlear clinical current level (CL) units and converted to mA as required. The following conversion was used, where I is the current in mA and CL is the clinical current level:

I ¼ 0:01  ð1:02046ÞCL

ð1Þ

In psychophysical testing, the MP1+2 stimulation mode was employed. In ECAP measurements, stimulation was delivered in the MP1 mode, while recording was performed between a given intracochlear electrode band and the extracochlear plate electrode (MP2). Different reference electrodes for stimulation and recording were used to help minimize artifact. For psychophysical and ECAP measures the pulse duration was 25 ls/phase and the inter-phase gap was 25 ls. For psychophysical measures the burst duration was 300 ms and the pulse rate was 250 pulses/s, whereas, for ECAP measures of this paper, it was either 55 or 80 pulses/s. 2.4. Estimation of longitudinal and radial positions of electrode bands from radiographs The 2D ‘‘Cochlear View” radiographs (Xu et al., 2000) were analyzed using CViewÓ software1 (Cohen et al., 1996a, 2000). This analysis of a Cochlear View radiograph enables specification of the

1 CViewÓ software available from: The HEARing CRC, Melbourne, Australia (http:// www.hearworks.com.au/).

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Table 1 Subject information. Subject

Gender

Age

Bilateral deafness (years)

Hearing aid impl. ear (years)

Implant (years)

Aetiology

Electrode insertion angle

CID sentences % words correct

CNC words % correct

S1 S2 S3

F M F

59 65 70

>50 46 14

50 46 10

3 2 3

371° 399° 389°

100 95 99

66 38 44

C1

F

56

3

10

2

340°

100

68

C2

M

70

19

3

2

425°

97

78

C3

F

30

5

21

2

Maternal rubella Unknown-progressive Mumps age 35progressive Unknown-progressive since age 35 Unknown-progressive since age 59 Unknown-progressive since age 4

414°

100

66

positions of the electrode bands both longitudinally, in terms of angle or percentage length along the organ of Corti (Pl), and radially, in terms of distance from the inner wall of the scala (Riw). The method makes use of a registered set of template shapes describing the outer wall of the otic capsule and the outer and inner walls of scala tympani. The latter wall functions were derived from SilasticÒ molds of scala tympani, whereas the function describing the outer wall of the otic capsule was produced by combining data from a sectioned cochlea with that from the molds of scala tympani (Cohen et al., 2000). The x–y position and size of the template spiral for the outer wall of the otic capsule are adjusted to provide a best fit to the image of that feature on the radiograph, making use, in addition, of a reference line passing through the tip of the superior semi-circular canal and the vestibule. The positions of the electrode bands of the array can then be specified objectively within a cochleo-vestibular framework. Riw is the radial distance from the ‘‘center of gravity” of the radiographic image of a given electrode band to a modeled inner wall of scala tympani, which is predicted on the basis of the image of the outer wall of the otic capsule observed on the radiograph. The characteristic frequencies associated with the bands can be calculated from Pl, using the equations of Greenwood (1990). This frequency calculation does not allow for the angular offset that exists between a basilar membrane location and the associated spiral ganglion cells (Ariyasu et al., 1989; Sridhar et al., 2006). This offset increases towards the apex and would result in the excitation of ganglion cells with lower characteristic frequencies than suggested by the electrode location. In Cohen et al. (2006), it was demonstrated that a small shift of the cochlear model (comprising the spirals for the outer wall of the otic capsule and the outer and inner walls of scala tympani), could dramatically enhance the correlation between threshold and Riw for an individual subject. It had been estimated previously (Cohen et al., 2000) that an error of up to about 0.2 mm would be possible in the position of the cochlear model, when analyzing a good quality X-ray. Accordingly, for the present radiographs, the shift was determined (with magnitude up to 0.2 mm) that optimized the correlation between threshold and Riw. 2.5. Loudness measurements 2.5.1. Threshold and maximum comfortable level (MCL) Behavioral thresholds were determined using two methods. The first was the Hughson–Westlake ascending/descending technique (Carhart and Jerger, 1959), henceforth referred to as ‘‘general” threshold. Threshold was also measured using an adaptive Békésy (von Békésy, 1947) procedure, as applied in Cohen et al. (2005b, 2006). Stimuli were continuously presented at a rate of one every 650 ms. The subject responded by depressing a computer mouse button as soon as the sound was audible, and releasing the button as soon as the sound was inaudible. A total of eight ascending and eight descending turn-points were obtained, and threshold was de-

fined as the mean of the final six ascending and six descending turn-points. Maximum comfortable level (MCL) was determined by increasing the current until the onset of discomfort, then reducing it a small amount until the loudness was acceptable. In this paper, clinical T-level was approximated by the Hughson–Westlake technique. This measure, in S1–S3 and C1–C3, was used in order to compare, approximately, the Békésy threshold with the clinical T-level. 2.5.2. Numerical estimation of loudness, as function of current Magnitude estimates of loudness were obtained from each subject at 17 current levels spaced at approximately equal intervals of current level between 15% below threshold and MCL (where threshold corresponded to 0% and MCL to 100%). These thresholds were obtained using the Békésy adaptive technique, described above. Stimuli were presented in two randomized blocks, each containing five presentations of each stimulus. The subject was asked to give a numerical estimate of the loudness of each presentation (fractions were allowed), with the suggestion that a sound of medium loudness would be ‘50’. It was stated that a sound twice as loud as another would result in a loudness estimate that was twice as large, that there was no upper limit on the magnitude estimate and that a loudness of ’0’ would correspond to an inaudible stimulus. Loudness growth data were collected in two sets, [A] and [B]. In set [A], collected from S1 to S3 and C1 to C3 on electrodes 6, 12 and 18, the stimuli were 300 ms bursts of pulses at a rate of 250 pulses/ s. ECAP amplitude growth functions were collected, in addition (see below). In set [B], collected from S1 to S3 and C1 to C2 on the same three electrodes, loudness growth data were collected for single-pulse stimuli, in addition to burst stimuli. Again, ECAP growth functions were collected. Thus, the data from set [B] allowed single-pulse loudness growth functions to be compared with ECAP growth functions, thereby eliminating the factor of temporal loudness summation present in the data for bursts. In data set [A], MCLs, Békésy thresholds and clinical T-levels were obtained for the pulse bursts. In data set [B], MCLs and Békésy thresholds were obtained for the pulse bursts. In addition, MCLs and Békésy thresholds were obtained for the single pulses, although there was less confidence regarding MCL for these stimuli. 2.5.3. Curve fitting and establishment of reference currents The use of a power law function to fit the shape of loudness growth functions has been described previously (Cohen et al., 2001c). A power law function of the following form was used:

L ¼ A  ðI  I0 ÞP

ð2Þ

where L is the loudness, A is a scaling factor, P is the power, I is the current (in mA) and I0 is an offset of the current. This form has the necessary attribute that it has sufficient degrees of freedom to

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describe differing amounts of curvature in the loudness growth function, whereas an exponential function does not. (Two endpoints define the exponential function and the amount of curvature it will exhibit between those points.) The fitting of the power function to the loudness data involved minimization of an RMS error. The contributions from the errors for the individual data points were weighted by the inverse root of the value of the power function, in order to reduce the influence of the louder values on the fitting process. Although the subjects had the freedom to employ loudness estimates of their choosing, each resulting loudness growth function was normalized so that the fitted power function had a value of 100 at IMCL. (Thus, the actual normalized data point at IMCL might not have a value of exactly 100.) The power law functions enabled the calculation of reference currents, I20, I50 and I80, associated with loudness 20%, 50% and 80% of the loudness at IMCL (data set [A] for 300 ms pulse trains at a pulse rate of 250 pulses/s). These reference currents were obtained for each subject at electrodes 6, 12 and 18. Fig. 1 illustrates different loudness growth curvatures in two subjects and the use of power functions to obtain the reference currents I20, I50 and I80. The test electrodes 6, 12 and 18 were used throughout the five papers of the series. These electrodes were chosen, conservatively, to span a reasonable percentage of the electrode array, while avoiding any possible end effects. Further, they had been used in

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a previous study with the same subjects, which provided relevant data (Cohen et al., 2003a). 2.5.4. Curvature of growth functions The method used to quantify the curvature of the growth functions has been described in Cohen et al. (2001c). In order to quantify the degree of curvature (departure from linearity) in the growth functions, the area under fitted power law functions was considered, between currents corresponding to the loudness at MCL (IMCL) and to a loudness five percent of that value. The percentage difference in area, relative to a linear function between these two end-points, was used as a measure of curvature. A concave growth function was deemed to have positive curvature. The following exact expression, applicable to a power law function, relates curvature to the power:

Curvature ¼ 100 n o ð1þ1=PÞ ð1=PÞ  1  2  ½ð1  k Þ=ð1  k Þ=½ð1 þ PÞ  ð1 þ kÞ ð3Þ where k = 0.05, since the curvature is calculated for loudness between 5% and 100% of that at MCL. The curvature equals zero for a linear function (P = 1). Curvature is more easily related to the appearance of a growth function than is the power, and has proved a more tractable quantity in the analysis of data. Further, curvature can be computed directly for functions other than power law functions. (The logarithm of power is also a convenient quantity for use in data analysis.) The same method was used to calculate the curvature for ECAP growth functions, as well as loudness growth functions from bursts and single-pulse stimuli. 2.6. ECAP methods

Fig. 1. Examples of loudness growth functions with different curvatures. Power law functions have been fitted to the data. From those functions, currents have been derived corresponding to 20%, 50% and 80% of the loudness at MCL. Conversely, the loudness associated with a given current can be computed from the power function: the ‘‘loudness yardstick” (Paper 3, Section 3.2).

2.6.1. General NRT methods The ECAP was measured using the NRT system as described by Abbas et al. (1999) and Lai and Dillier (2000). The NucleusÒ 24 implant system allows the recording of the intracochlear potential, subsequent to stimulation, at any of the intracochlear electrode bands, and uses telemetry to communicate the measurement via the SPrint speech processor and the PCI to the host computer. The NRT software supports the recording of the ECAP using this method. The ‘‘subtraction” algorithm was used (Brown et al., 1990; Abbas et al., 1999; Lai and Dillier, 2000), which will be referred to as the ‘‘standard NRT subtraction algorithm”. In this method both ‘‘masker” and ‘‘probe” pulses are employed, usually with the sole intention of minimizing artifact. The standard subtraction method makes use of four separate recordings of the potential at a chosen intracochlear band: (A) following the probe pulse; (B) following the probe pulse, preceded by the masker pulse; (C) following the masker pulse; and (D) in a no-stimulus condition. The D component is obtained in order to determine the settling artifact produced following the un-shorting of the preamplifier input, and is not relevant to this description. What is usually desired is the response to the probe pulse. This is present in the A component, which contains also an electrical artifact due to the probe pulse. The B component contains, in addition to the partiallymasked response to the probe plus the probe artifact, some residual response and artifact due to the masker pulse. The C component contains only the residual response and artifact due to the masker pulse. It follows that [A  (B  C)] yields the response to the unmasked probe minus the response to the partially-masked probe. If the partially-masked probe response is negligible, as would be the case for a masker much more intense than the probe, this expression yields the response to the probe alone. There are,

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however, circumstances in which the masker does not fully mask the probe, and where it is useful to obtain the response to the partially masked probe (as in Papers 3–5). Amplitude measurements were made between the negative (N1) and positive (P1) peaks of the response waveform (Lai and Dillier, 2000). For ECAP measures the pulse duration was 25 ls/phase, the inter-phase gap 25 ls. In this paper, the pulse rate was either 80 pulses/s (for data set [A]) or 55 pulses/s (for data set [B]), a compromise value lying between the two standard rates of 80 and 35 pulses/s, resulting in less adaptation2 than the former but faster data collection than the latter. The number of sweeps was 200. The preamplifier gain was 60 dB and the delay differed across subjects but was not less than 60 ls. In this paper, the masker offset (the current level of the masker relative to that of the probe) was 10 CL. The MPI (interval between the end of masker pulse and the start of probe pulse, in ls) was 500 ls. 2.6.2. Custom off line NRT methods Custom software, previously described in Cohen et al. (2003a), was used to perform off line processing of NRT results files. The software allowed calculation of either the standard subtraction, [A  (B  C)], or the ‘‘Miller” subtraction, [(B2  C2)  (B1  C1)] (Miller et al., 2000), which is described in Paper 3, Section 2.2.2. It had three additional features not provided by the NRT software: (1) Quadratic fitting of the N1 peak allowed finer estimation of the peak latency. (2) Curve fitting in the vicinity of the P1 peak allowed improved estimation of the peak amplitude and finer estimation of the peak latency. (3) In order to achieve an effective sampling rate of 20 kHz, two sets of measurements are performed by NRT, one offset relative to the other by 50 ls. The amplitudes of the two sets of samples are offset by an amount that is not constant throughout the measurement time-window. Whereas the NRT software allowed registration of the two sets of samples by providing a linear regression correction, the custom software allowed a quadratic correction. These differences resulted in slightly different waveforms, as well as peak amplitudes and positions, than would have been produced by the NRT software. Note that an automated amplitude measurement system was used, which did not necessarily distinguish an artifactual (or noise) response from a true response. Such a method has advantages in speed and convenience. The waveforms could be monitored, however, to avoid errors of the automation. Further NRT methods are described in the subsequent papers of the series. This work was conducted under the clinical approval and oversight of the Human Research and Ethics Committee of the Royal Victorian Eye and Ear Hospital (Projects 93/226H, 92/193H and 02/504H). 3. Results 3.1. General 3.1.1. Estimation of longitudinal and radial positions of electrode bands from radiographs Reconstructed radiographs are shown, inset, in Fig. 2 for six subjects, S1–S3 and C1–C3. For the present group of subjects, the mean insertion angles for the most apical electrode bands were similar for subjects with Contour (395°, sd 44°) and straight arrays (390°, sd 17°). These angles correspond to characteristic frequencies of approximately 839 and 864 Hz, respectively. The Contour

2 In the present paper, the effect of adaptation at 80 pulses/s would have been small, however.

Fig. 2. General threshold (open circles) and MCL (filled circles) measurements for all subjects (in CL units) plotted against electrode. Subjects with straight arrays are indicated by S1–S3, those with Contour arrays by C1–C3. Later dedicated measurements of MCL at electrodes 6, 12 and 18 in some cases yielded higher values. Reference current levels at 20%, 50% and 80% of the loudness at MCL (later value) are shown as open squares, filled triangles and filled squares, respectively (only 50%, approximately, for C3). Radial distances of electrode bands from the inner wall of scala tympani are displayed as vertical bars. Processed X-ray data are shown in the inset, arrays indicated by solid lines with filled circles. Estimated inner and outer walls of scala tympani (Cohen et al., 1996a, 2000) are given as solid lines. The angle, h, used to specify the longitudinal position is shown for S1, and the angles for electrodes 6, 12 and 18 are tabulated for each subject. The position of cochlear model relative to electrode has been modified slightly to enhance correlation of threshold with radial distance of electrode contact from inner wall of scala tympani, as discussed in Cohen et al. (2006). The angles for electrodes 6, 12 and 18 differ slightly, as a result, from those provided in Cohen et al. (2003a).

arrays lay considerably closer to the modiolus. In the Contour subjects the radial distance from modiolus to electrode band (Riw) varied considerably along the array, especially in C3. The mean values of Riw were 1.445 mm (sd 0.119 mm) for the straight array and 0.659 mm (sd 0.290 mm) for the Contour (C1–C3). The positions of the electrodes in the X-ray reconstructions were shifted slightly relative to the template spirals, up to a maximum of 0.2 mm, according to a method described and discussed in Cohen et al. (2006). 3.1.2. Threshold, MCL and reference current measurements General thresholds and MCLs are also shown in Fig. 2 for the six subjects. Where Riw, indicated by the vertical bars, varied substantially across the array, there was a tendency for threshold, in particular, to be lower for bands lying nearer to the modiolus. Subsequent to the measurements of general threshold and MCL, made at all (or even numbered) electrodes across the array, additional measurements of MCL and Békésy threshold were performed at electrodes 6, 12 and 18. In these later MCL measurements, it was important to obtain the best possible estimates of the maximum acceptable level, which were in some cases a little higher than in the initial general measurements. These MCLs determined the maximum currents used in measurement of loudness growth functions for 300 ms pulse bursts (set [A]). The fitting of power law functions to these loudness growth functions enabled the calculation of reference currents, I20, I50 and I80, corresponding

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to 20%, 50% and 80% of the loudness at MCL, for electrodes 6, 12 and 18. The 20%, 50% and 80% levels are shown, in CL units, in Fig. 2. 3.2. Growth of loudness and ECAP amplitude with current 3.2.1. Relationship between curvature of burst loudness growth function and MCL Loudness growth functions were measured for 300 ms pulse bursts at a pulse rate of 250 pulses/s, in S1–S3 and C1–C3 (set [A]). It has been reported previously (Cohen et al., 2001b,c, 2003a, 2006) that the curvature of loudness growth functions for low-rate bursts of pulses was negatively correlated with MCL. It was necessary for the present study and, in particular, for the model development, to quantify as well as possible the relationship between curvature and MCL. Therefore, in addition to the data from set [A], use was made of similar loudness growth functions from a previous study, Cohen et al. (2006) (set [P]). The loudness growth functions [A] are shown in Fig. 3, for S1–S3 and C1–C3. In addition to the loudness estimates, the fitted power law functions are shown: the curves are normalized so that the fitted functions have a value of 100 at MCL. From left to right, the vertical dashed lines represent Békésy threshold, I20, I50, I80 and IMCL. Varying curvatures, i.e. departures from linearity, are apparent in these figures. S1/electrode six exhibits a clearly positive curvature, S3/electrode 12 has a slightly positive curvature (i.e. is close to linearity) and C3/electrode 18 has a clearly negative curvature. Curvature is plotted against MCL in Fig. 4 for the combined [A] and [P] data. Regression lines are shown for straight array data alone, Contour data alone and combined data. In these calculations, two data points for the Contour were deleted (shown as open inverted triangles): these were extreme outliers, especially in the context of the combined data. These data are consistent with our previous finding that curvature is negatively correlated with MCL. It is possible that some difference might exist between the curvatures of growth functions for patients with straight and Contour arrays. If so, it would likely be more pronounced for low MCLs, where neural excitation would be more localized and the differing stimulation field patterns of the two arrays would have more effect. As the curvatures for the two arrays did not appear very different for low MCLs, the data from the arrays were combined to produce a composite regression, shown as a heavy dashed line (R2 = 56.9%; p < 0.001; N = 31). The general form of the model, describing general trends in data, was required, therefore, to describe this regression relationship:

CurvatureBurst ¼ 121:76  0:5024  MCL

ð4Þ

3.2.2. Loudness at threshold, as percentage of MCL The power law functions, fitted to the loudness growth data, were used to calculate the loudness at the measured Békésy thresholds and clinical T-levels [A data]. This provides an indication of the loudness represented by these two threshold measures, relative to the normalized 100 at MCL. The mean loudness was found to be 1.72% (sd 1.36%) for the Békésy thresholds and 2.12% (sd 1.13%) for the clinical T-levels. This finding is of general interest but the loudness ratio of threshold to MCL is a parameter that is also required for development of the present mathematical model of neural stimulation. The following section provides further investigation of this ratio, confirming that it is approximately 2%. (It should be stressed, however, that MCL is a ‘‘subjective” quantity. Further, because clinical ‘‘C-level” is generally lower than MCL, the mean loudness ratio of threshold to clinical ‘‘C-level” would be expected to be in excess of 2%.)

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3.2.3. Growths of burst loudness, single-pulse loudness and ECAP amplitude: relationships A significant correlation between the curvatures of the loudness growth function for bursts and the ECAP amplitude growth function has been reported previously, which provided some evidence for similarity of their shapes (Cohen et al., 2001b). In the light of that result, and following Bruce et al. (1999b), it was hypothesized that the burst loudness and ECAP amplitude growth functions were similar in shape, the amplitudes of both being approximately proportional to the number of peripheral auditory neurons firing. It was clear, however, that there was a discrepancy at the low-current end of the dynamic range, as indicated by the lower behavioral thresholds. It was appropriate to consider the relationship between the two functions in more detail and, by measuring the loudness growth for single-pulse stimuli, to determine whether the lower behavioral thresholds for bursts were due simply to temporal loudness summation. 3.2.3.1. Data set [A]: burst and ECAP. ECAP growth functions were collected at a rate of 80 pulses/s. The ECAP growths, scaled in amplitude, are superimposed on the loudness growth functions in Fig. 3. There is apparent similarity between the shapes of the loudness and ECAP growth functions. For the data shown, an NRT response was present at I50, the 50% level for bursts, in all cases. In five cases out of 18, an NRT response was clearly not present at I20: C1/elec 6, C2/elec 6, C3/elec 6, C3/elec 12 and C3/elec 18. In one other case the NRT response was questionable at I20: C1/elec 18. In no case was an NRT response present at the Békésy threshold. Three subjects may be singled out for comment. In C3, while curvature was strongly negative for the loudness functions, especially for electrodes 6 and 18, it was negative also for the ECAP functions, although not as strongly so. The ECAP growth data were collected approximately six months earlier than the loudness growth data for C3, which might have accounted for some of the difference between the functions. The curvatures in all other subjects were positive. S1 showed a considerable discrepancy between curvatures of loudness and ECAP growth functions for elec 18, in particular, but also for elec 12. This subject was pre-lingually deafened. However, it appeared that the discrepancy between ECAP and loudness data for this subject was attributable to a subtle problem with the ECAP recording. Later inspection of the separate components of the NRT recording showed that there was an abrupt (negative, not response-like) increase in the magnitude of the B component (Section 2.6.1), for currents equal to or above about 0.78 mA for electrode 12 and 0.63 mA for electrode 18. (This issue is discussed in greater detail in Paper 4, Section 5.2.1.) In C1, it was not possible to record ECAP responses for electrode 6 over a considerable region of the behavioral dynamic range. In the present treatment, in contrast to that of Cohen et al. (2001b), power law functions were fitted to the loudness and ECAP growth functions using the same upper limit of current on a particular electrode in a given subject (thus minimizing the chance that any difference in curvature between the functions might be due, simply, to differing current ranges). This often meant discarding some data points for the ECAP fittings. Combining the data from [A] and [P], curvature of ECAP growth varied significantly with curvature of loudness growth (linear regression: R2 = 39.1%; p < 0.001; N = 29). 3.2.3.2. Data set [B]: burst, single pulse and ECAP. In order to explore further the relationship between the loudness and ECAP growth functions, the burst and ECAP growth measures were repeated (not including C3), with the addition of loudness growth for single-pulse stimuli (data set [B]). The psychophysical measure using a single pulse is more directly analogous to the NRT growth mea-

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Fig. 3. Loudness growth functions (filled circles) for subjects S1–S3 and C1–C3, at electrodes 6, 12 and 18 from left to right. Stimuli were 300 ms bursts at 250 pps, for currents ranging from below threshold to MCL. Ten trials were conducted per stimulus. Power law fits are shown as solid lines. Subjects were free to adopt individual loudness scales but the data were then normalized to 100 at MCL (in the fitted function). Vertical lines show, from left to right, Békésy threshold, 20%, 50% and 80% of the loudness at MCL, and MCL. ECAP growth functions are superimposed (open squares). They are scaled to match approximately the magnitude of the loudness functions. ECAP amplitudes may be obtained by multiplying by factor at bottom right of each frame. Both loudness and ECAP data are from data set [A]. The asterisks for S1 electrodes 12 and 18 indicate a query regarding the accuracy of the ECAP data at higher currents (see Paper 4, Section 5.2.1). (The ECAP growth data were collected approximately 6 months earlier than loudness growth data for C3.)

sure, which effectively records the response to a single pulse. Measuring the loudness growth with single-pulse stimulation removes the effect of temporal loudness summation. The single-pulse

growth functions are shown in Fig. 5. The Békésy thresholds for single pulses (ITBekONE) and 300 ms burst stimuli (ITBek300) are shown as light vertical dashed lines: lines for single pulses are labeled

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Fig. 4. Curvature of loudness growth function plotted against MCL, for different data sets ([A] and [P]) and electrodes. Curvature was quantified from the difference in area under the fitted power law function compared to that under a linear function (Cohen et al., 2001c). It can be related simply to the ‘‘power” of the power law function (Eq. (2)). The heavy dashed line indicates the compromise function used to quantify, approximately, the relationship between curvature and MCL. Two data points were deleted from the regression calculation (open inverted triangles). The vertical dashed lines indicate approximate limits to the MCL range for patients with straight electrode arrays (Paper 4, Appendix 1).

with triangle symbols. The MCLs for single pulses (IMCLONE) and bursts (IMCL300) are indicated by heavier dashed lines, the former labeled with triangle symbols. Curvature, as calculated either over the full current range or only up to IMCL300, was smaller than for the burst stimuli: generally the single-pulse functions were closer to linearity. As with the [A] data above (Section 3.2.2), fitted power law functions were used to calculate the loudness at the Békésy thresholds for both bursts and single-pulse stimuli [B], relative to the normalized 100 at MCL. The mean loudness for the Békésy thresholds of the bursts was 1.96% (sd 1.35%), which was consistent with the [A] result (1.72%, sd 1.36%). The mean loudness for the Békésy thresholds of the single pulses was 2.58% (sd 1.57%), which was a little larger than for the bursts. The loudness of these Békésy thresholds for single pulses was calculated from power law functions fitted to the full range of range of currents used for the single pulses. It was less clear, however, that MCL (IMCLONE) had actually been achieved for the single pulses. Therefore, the maximum loudness might have tended to be low, causing the threshold percentage loudness to be higher. From the above results, primarily for the pulse bursts (both [A] and [B]), 2.0% was adopted as approximately representative of the loudness at Békésy threshold, relative to the loudness at MCL. Notwithstanding their higher mean loudness (2.58%, sd 1.57%), the Békésy thresholds for single pulses did not differ significantly from the currents at 2% loudness, as calculated from the fitted power functions (see below). In the following (unless otherwise stated), power law functions were fitted to growth data for bursts, single pulses and ECAP, all with the same upper limit of current, Imax300 (in almost all cases, equal to IMCL300). For all growth functions, burst, single-pulse and ECAP, the fitted functions were normalized to 100 at Imax300. The following are statistical findings regarding threshold, for the growth functions of burst and single-pulse loudness and ECAP amplitude. (1) ITBek300, the Békésy threshold for bursts, was not different from I2%300, the corresponding 2% current for fitted power law curves (paired t-test ‘‘not equal”: T = 0.97, p = 0.351, N = 15).

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Similarly, for single pulses, ITBekONE was not different from I2%ONE (T = 1.07, p = 0.302, N = 15). The single-pulse growth functions were fitted up to a maximum current of IMCLONE. These findings support the use of 2% loudness as a criterion for threshold as done, mainly, for the ECAP. (2) ITBek300 was lower than ITBekONE (T = 4.28, p = 0.001, N = 15). (3) ITBek300 was lower than I2%ECAP, the 2% current for power law curve fitted to ECAP (T = 5.28, p < 0.001, N = 15). It has commonly been observed that behavioral threshold for a burst is lower than the ECAP threshold. The present data show the same effect, even though the ECAP thresholds would be a little lower than usual, because of the 2% criterion (as discussed below). ITBekONE, also, was lower than I2%ECAP (T = 2.67, p = 0.018, N = 15). Thus, the behavioral threshold for a single pulse was lower than the ECAP threshold, although temporal loudness summation was absent. (4) ITBekONE was significantly correlated with ITBek300 (linear regression: R2 = 67.1%, p < 0.001, N = 15). (5) I2%ECAP was significantly correlated with ITBek300 (R2 = 27.0%, p = 0.047, N = 15). I2%ECAP was significantly correlated, also, with ITBekONE (R2 = 35.5%, p = 0.019, N = 15). The correlation of ECAP threshold was a little stronger, therefore, with single-pulse threshold than with burst threshold. I2% was used to indicate threshold for the ECAP growth function. This was based on its similarity to the Békésy threshold for the psychophysical growth functions. I2% would almost always be associated with an NRT voltage of less than 20 lV, which was the nominal noise floor for the CI24 system. Therefore, simple estimation of NRT threshold, based on visibility of a response waveform, would generally result in higher estimates than the 2% criterion. Linear regression methods, sometimes used to estimate NRT threshold, would also produce higher estimates, at least in the majority of cases, where the curvature of the growth function would be positive. In using the 2% criterion, the purpose was to judge the threshold of the three growth functions (burst loudness, single-pulse loudness and ECAP) by similar rules, which was important in the present context. (However, the 2% criterion would be inappropriate for general estimation of NRT threshold because it would be compromised by uncertainty of the upper current point. Nevertheless, the use of a power law function fit to ECAP growth data would still be preferable to a linear fit because it would take more account of the shape of the ECAP growth. For general application, a useful estimate of NRT threshold would be given by I0 (Eq. (2)).) Representative growth functions. In considering the three types of growth function (for burst, single pulse and ECAP), the objective was to compare both shapes and thresholds. In order to provide a visual framework for assessing the relative shapes and thresholds, representative growth functions were derived. These complement the statistical analyses of thresholds in individual subjects, given above. The representative growth functions were derived from the individual growth functions for 300 ms bursts, single pulses and ECAP. The data for each individual growth had been fitted with a power law function of the form given in Eq. (2). The process for derivation of the representative growth function was the same for each type of growth, and was as follows: (1) The current, I2%, was calculated for each individual fitted function, such that it gave an amplitude 2% of that at the maximum current, Imax300. (2) The mean value of I2% was calculated (for the set of individual functions). (3) The mean value of Imax300 was calculated (for the set of individual functions). (4) The mean curvature was calculated (for the set of individual functions).

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Fig. 5. Loudness growth functions for single pulse stimuli, for S1–S3 and C1–C2, at electrodes 6, 12 and 18 from left to right. Ten trials were conducted per stimulus. Power law fits (over full current range) are shown as solid lines. Subjects were free to adopt individual loudness scales but the data were then normalized to 100 at the maximum current used. Békésy thresholds for both single pulse and 300 ms burst are shown as light vertical dashed lines: lines for single pulse are labeled with triangle symbols. MCLs for single pulse and burst are shown as heavier vertical dashed lines, those for the single pulse labeled with triangle symbols. All thresholds and MCLs are from data set [B]: therefore, there are slight differences from results in Fig. 3.

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(5) The power (P) corresponding to the mean curvature was calculated, using Eq. (3). (6) The value of I0 (in Eq. (2)) was adjusted so that the ratio of loudness at the mean Imax300 to that at the mean I2% was 100/2 = 50. (7) The value of A (in Eq. (2)) was adjusted so that the loudness at the mean Imax300 was 100.

a

b

97

The result was a power law function approximately representative of the individual fitted functions (e.g. for loudness growth with 300 ms bursts). The representative functions for the three growth types were all scaled to 100 at Imax300. The representative functions are shown in Fig. 6(a). Also shown on the figure are vertical lines indicating the mean Békésy thresholds for 300 ms bursts and single pulses (solid lines), and the mean I2% for 300 ms bursts, single pulses and ECAP amplitudes (dashed lines). I2% for bursts (I2%300) is similar to the Békésy threshold for bursts (ITBek300). In Fig. 6(b), the amplitude of the single-pulse growth function (open circles) has been reduced by a factor of 2.216, corresponding to the mean ratio of the loudness for a burst relative to a single pulse (from Paper 3, Section 3.2). I2%ONE is then almost equal to ITBekONE. Both the statistics and the representative functions are consistent with the and, similarly, ranking: ITBek300 < ITBekONE < I2%ECAP I2%300 < I2%ONE < I2%ECAP. Growth function shapes. The shape of the single-pulse function differs from that for the burst, in Fig. 6(a), essentially in curvature. However, if the single-pulse function is scaled for equality at a burst loudness of 20 (dashed curve, Fig. 6(b)), the functions appear similar for loudness below 20. Presented in this way, there appears to be a progressive divergence between the burst and single-pulse growth functions for higher currents. Two possible mechanisms are suggested in the Discussion. The shape of the ECAP function, Fig. 6(a), seems similar to that of burst loudness for amplitude above about 25. The difference for lower currents can be interpreted as an attenuation of the ECAP amplitude at low currents. The attenuation (and disappearance) of the ECAP function at low currents cannot be explained simply by the effect of temporal loudness summation. Single pulses are clearly audible below I2%ECAP. Based on the findings, the following assumptions are made in the model development: (1) The ratio of loudness for a 300 ms pulse burst (250 pulses/s) to ECAP amplitude is approximately independent of current, both loudness and ECAP amplitude being proportional to the number of fibers firing, except that: (2) ECAP amplitude is attenuated at low currents, to an extent that differs across patients and electrodes. (3) The ratio of loudness for a 300 ms pulse burst (250 pulses/s) to loudness for a single pulse is approximately independent of current.

Fig. 6. (a) ‘‘Representative” growth functions (see text): loudness for 300 ms/250 pps bursts (filled circles), loudness for single pulses (open circles) and ECAP amplitude (filled squares) plotted against current. The single-pulse and ECAP functions were derived from data fitted over current ranging up to Imax300 (essentially IMCL300): ‘‘Lim” indicates this current limitation. The three functions have been scaled so that they are equal at the point of maximum current (see text). Solid vertical lines indicate Békésy thresholds for bursts and single pulses (labeled with filled and open circles, respectively). Dashed vertical lines show 2% currents for bursts, single pulses and ECAP functions (labeled with filled circles, open circles and filled squares, respectively). Horizontal dashed lines are shown for ordinate values of 100, 80, 50 and 2 (if 100 corresponds to MCL, we have suggested that 2 corresponds, approximately, to threshold). The burst and ECAP growth functions exhibit similar shapes at middle and high currents: the proposition is that ECAP ‘‘drops out” at low currents. Single pulses are audible to lower current than ECAP is measurable. (b) Exploration of scaling of single-pulse growth. The solid curve with open circles shows the single-pulse function scaled down by a factor of 2.216, which was an approximate loudness ratio for burst to single pulse (from Paper 3, Section 3.2). The corresponding vertical dashed 2% line is now very close to the Békésy threshold for a single pulse. The dashed curve shows the single-pulse loudness scaled to equal burst loudness at 20%.

The attenuation of ECAP amplitude at low currents was exhibited strongly for C1/elec 6: Fig. 7(a). I2%ECAP was much higher than either ITBek300 or ITBekONE. The difference between the ECAP and burst thresholds cannot be explained simply by temporal loudness summation for the bursts, as the burst and single-pulse thresholds are similar. In contrast are the growth functions for S2/elec 18, shown in Fig. 7(b). This case supports the assumptions that both the ratio of burst loudness to ECAP amplitude and the ratio of burst to single-pulse loudness are approximately independent of current. However, it must be recognized that these assumptions are only approximations that may differ in their validity across patients and electrodes. 4. Discussion This study has demonstrated a similarity between the growths with stimulus current of the ECAP amplitude and the loudness of a low-rate burst of pulses. This finding provides a basis for the development of the model of peripheral neural excitation. In the model development, a proportional relationship is assumed between the ECAP amplitude and the loudness, and both are assumed to be pro-

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a

b

Fig. 7. (a) Power law fits to growth data for C1, electrode 6: solid lines show loudness for 300 ms/250 pps bursts (filled circles), loudness for single pulses (open circles) and ECAP amplitude (filled squares) plotted against current. The ECAP function was derived from data fitted over current ranging up to Imax300, (‘‘Lim” indicates this current limitation) and has been scaled to equal the burst loudness function at Imax300. The single-pulse function (open circles) was obtained from a power law fit over the full current range (up to IMCLONE), and reaches a value of 100 at IMCLONE (cropped in figure). Solid vertical lines (Békésy thresholds), dashed vertical lines (2% currents) and dashed horizontal lines are as described in Fig. 6(a). Note severe dropout of the ECAP at low currents. The loudness ratio of burst to single pulse at Imax300 is 1.92, which is similar to the average ratio of 2.216 found in Paper 3. However, at low currents the two functions converge, which is consistent with the near-equality of the Békésy thresholds and of the 2% currents. Thus, in this case, the loudness ratio approaches unity at low currents. The dashed line shows the single-pulse data fitted up to Imax300 (‘‘Lim”) and scaled to equal the burst loudness at Imax300, as in Fig. 6(a). This allows visual comparison with the shapes of the burst and ECAP growth functions. (b) Power law fits to growth data for S2, elec 18, as in (a). Note ECAP sustained over most of the current range, with threshold only a little greater than for single pulse. The loudness ratio of burst to single pulse at Imax300 is 1.75, again fairly similar to the average ratio of 2.216 found in Paper3. There is some convergence of the burst and single-pulse functions (for example, the loudness ratio is 1.36 when the burst function equals 20) but not as much as in (a), above. However, when the three growth functions are compared (using the dashed curve for single pulse), the shapes are quite similar, consistent with the assumptions that both the ratio of burst loudness to ECAP amplitude and the ratio of burst to single-pulse loudness are approximately independent of current.

portional to the number of fibers firing. This study has, in addition, established a relationship between the curvature of the loudness growth function and MCL, and obtained an estimate of the ratio

of the loudness at threshold to that at MCL, both important to the model development, and introduced some of the methodology employed in the series of papers. It is clear, however, that the ECAP amplitude departs from proportionality to the loudness at the lower end of the current dynamic range, to an extent that varies with subject and stimulated electrode. The low-current attenuation of the ECAP amplitude is a phenomenon for which some possible mechanisms have been discussed previously (e.g. Cohen et al., 2004). One plausible mechanism is a loss of neural synchrony at low currents. This attenuation phenomenon results in a failure to obtain useful NRT responses in some patients. The ECAP growth function for C1/elec 6 (Fig. 7(a)) illustrates the effect: this function cannot be said to resemble the loudness growth function for the burst. It is concluded that the ECAP growth does not necessarily represent the growth of neural firing with any fidelity. It is assumed, in the subsequent model development, that the burst loudness growth is a more reliable source of information on the shape of the underlying growth of neural excitation. By obtaining loudness growth data for single pulses, in addition to pulse bursts, it was possible to show that the relative attenuation of the ECAP growth function at low currents was not solely due to temporal loudness summation occurring with bursts. Behavioral thresholds for single pulses, although higher than for bursts, were significantly lower than ECAP thresholds. However, it should be noted that the results of Paper 3, Section 3.2 suggest that an isolated or initial pulse is louder than a pulse occurring later in a pulse train. This ‘‘first pulse effect” (FPE) may lower the threshold for a single pulse. (The similarity of the burst and single-pulse thresholds for C1/elec 6 (Fig. 7(a)) is consistent with the corresponding data in Paper 3, Section 3.2 (Fig. 5), where the loudness of burst and single-pulse stimuli is similar at I20.) Although temporal loudness summation would not be present for the single pulse, its loudness might be increased by the FPE. Thus, the large difference for C1/elec 6 between I2%ECAP and both ITBek300 and ITBekONE could be due, at least in part, to the FPE. The differing shapes of loudness growth functions for bursts and single pulses, such that the loudness ratio appeared to vary with current, could be contributed to by level-dependence of the FPE (i.e. more pronounced at low levels). However, too much weight should not be placed on a comparison between loudness growth functions, separately obtained, for bursts and single pulses. The method of Paper 3, Section 3.2, based on loudness balancing, allows a comparison between bursts of differing duration (including single pulses). For both pulse bursts and single pulses, the loudness corresponding to threshold was found to be approximately 2% of the loudness at MCL. This was found by fitting a power law function to the growth data and calculating the loudness at the known threshold current. The 2% current (I2%ECAP) was used to estimate threshold for the ECAP growth functions, for consistency with the behavioral threshold measures. ECAP thresholds estimated in this way would tend to be lower than those obtained using conventional methods. For general estimation of ECAP threshold, the fitting of a power law function was suggested, using I0 as the threshold measure (see Eq. (2)). Such an approach would be analogous to the use of the intercept for a linear fit but would take more account of the curvature of the ECAP growth function. The previous finding (Cohen et al., 2001b,c, 2003a, 2006) of a negative correlation between the curvature of burst loudness growth function and MCL was confirmed. The linear regression describing this correlation is given by Eq. (4). Although such a correlation has been observed consistently, the regression line described by Eq. (4) was derived from a quite small group of subjects. Future work should allow the determination of a more precise relationship.

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The model development of Paper 4, drawing on the present study, assumes that ECAP amplitude and loudness, of both single-pulse and burst stimuli, are proportional to the number of fibers firing, and that the curvature of the growth function is related to MCL according to Eq. (4). The loudness at threshold, as a percentage of that at MCL, 2%, is used as a guide to the number of modeled fibers firing at threshold, as a percentage of the number at MCL. Acknowledgements I acknowledge support provided by the Commonwealth of Australia through the Co-operative Research Centre for Cochlear Implant and Hearing Aid Innovation. I acknowledge, also, additional support provided by the Department of Otolaryngology (University of Melbourne, Australia) and the Bionic Ear Institute (Melbourne, Australia). Thanks are due to the subjects, to Cochlear Limited and to the staff of the Cochlear Implant Clinic at the Royal Victorian Eye and Ear Hospital, Melbourne, for their assistance. I am grateful for the encouragement of Mark White. I thank Anthony Burkitt, David Grayden, Barbara Cone-Wesson, Robert Cowan and Ian Jakovenko for their critical reading of the manuscript, and acknowledge the support of the following in reading and discussing early versions of this work: Mark White, Richard van Hoesel and Stephen O’Leary. References Abbas, P.J., Brown, C.J., Shallop, J.K., Firszt, J.B., Hughes, M.L., Hong, S.H., Staller, S.J., 1999. Summary of results using the Nucleus CI24M implant to record the electrically evoked compound action potential. Ear Hear. 20, 45–59. Ariyasu, L., Galey, F.R., Hilsinger Jr., R., Byl, F.M., 1989. Computer-generated threedimensional reconstruction of the cochlea. Otolaryngol. Head Neck Surg. 100, 87–91. Brown, C.J., Abbas, P.J., Ganz, B., 1990. Electrically evoked whole-nerve action potentials: data from human cochlear implant users. J. Acoust. Soc. Am. 88, 1385–1391. Bruce, I.C., Irlicht, L.S., White, M.W., O’Leary, S.J., Dynes, S., Javel, E., Clark, G.M., 1999a. A stochastic model of the electrically stimulated auditory nerve: pulsetrain response. IEEE Trans. Biomed. Eng. 46, 630–637. Bruce, I.C., White, M.W., Irlicht, L.S., O’Leary, S.J., Clark, G.M., 1999b. The effects of stochastic neural activity in a model predicting intensity perception with cochlear implants: low-rate stimulation. IEEE Trans. Biomed. Eng. 46, 1393– 1404. Bruce, I.C., White, M.W., Irlicht, L.S., O’Leary, S.J., Dynes, S., Javel, E., Clark, G.M., 1999c. A stochastic model of the electrically stimulated auditory nerve: singlepulse response. IEEE Trans. Biomed. Eng. 46, 617–629. Carhart, R., Jerger, J., 1959. Preferred method for clinical determination of pure tone thresholds. J. Speech Hear. Disord. 24, 330–345. Cohen, L.T., Xu, J., Xu, S.-A., Clark, G.M., 1996a. Improved and simplified methods for specifying positions of the electrode bands of a cochlear implant array. Am. J. Otol. 17, 859–865. Cohen, L.T., Xu, J., Tykocinski, M., Saunders, E., Raja, D., Cowan, R.S.C., 2000. Evaluation of X-ray analysis method: comparison of electrode position estimates with information from phase contrast X-ray and histology. In: Fifth European Symposium on Paediatric Cochlear Implantation, Antwerp, Belgium, 4–7 June 2000. Cohen, L.T., O’Leary, S.J., Saunders, E., Knight, M., Cowan, R.S.C., 2001a. Modelling methods tailored to human psychophysical and ECAP data: practical applications to sound processing. 2001 Conference on Implantable Auditory Prostheses, Asilomar, Pacific Grove, California, USA, 19–24 August 2001. Cohen, L.T., Saunders, E., Knight, M., Cowan, R.S.C., Busby, P.A., 2001b. Comparison of subjective loudness growth and NRT amplitude growth with stimulus current. In: Second International Symposium and Workshop on Objective Measures in Cochlear Implantation, Lyon, France, 16–18 March 2001.

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