Practical model description of peripheral neural excitation in cochlear implant recipients: 2. Spread of the effective stimulation field (ESF), from ECAP and FEA

Hearing Research 247 (2009) 100–111

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Methodological paper

Practical model description of peripheral neural excitation in cochlear implant recipients: 2. Spread of the effective stimulation field (ESF), from ECAP and FEA Lawrence T. Cohen * Department of Otolaryngology, The University of Melbourne, 384-388 Albert Street, East Melbourne, Vic. 3002, Australia

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Article history: Received 31 March 2008 Received in revised form 18 November 2008 Accepted 18 November 2008 Available online 25 November 2008 Keywords: Cochlear implant Modeling of neural response ECAP NRT Current spread Spread of neural excitation

a b s t r a c t This second paper of the series considers the spread of the ‘‘effective stimulation field” (ESF) produced by monopolar biphasic stimulation of an electrode within scala tympani, in subjects implanted with the NucleusÒ 24 cochlear implant system (three with straight and two with ContourTM electrode arrays). A novel measure of the ECAP was employed, using the Neural Response TelemetryTM (NRTTM) system. The ESF provides a patient-specific measure of the ‘‘ability” of the stimulation field to excite neurons at differing locations around the cochlea. The results were interpreted with the aid of simple finite element computational models of the electric field. The finite element models were used to generate template field spread functions that differed with radial distance of the stimulated electrode from the modiolus. Relative to a template field function for the appropriate radial distance, the ESF spread on average approximately twice as broadly (a scaling factor of two). The magnitude of this scaling factor was considered to be indicative of the site of excitation on the neural fibers. The relationship between two ECAP measures, the spread of ESF and the ‘‘spread of excitation” (SOE), is discussed. Ó 2008 Elsevier B.V. All rights reserved.

1. Introduction In order to model the excitation of the neural population in the cochlea, it is necessary to quantify the spread of stimulation field produced by electrical stimulation of any electrode on the implanted electrode array. A detailed model of neural excitation, such as that of Frijns et al. (1995, 1996, 2001) or Rattay et al. (2001a, 2001b), requires a full three-dimensional specification of the potential field, in order to compute the firing of individual neural fibers. The firing may be initiated at different locations on a fiber, depending on the field distribution. The present model is

Abbreviations: ANOVA (GLM), Analysis of variance analysis (Generalized Linear Model); 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; I20, I50 and I80, Currents required to achieve loudness 20%, 50% and 80% that of IMCL300; IMCL300, MCL current for 300 ms stimulus (mA); MCL, Maximum comfortable level (CL); MCL300, Maximum comfortable level for 300 ms burst at 250 pulses/s (CL); 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); Pl, Percentage length along organ of Corti; Riw, Radial distance of electrode band from inner wall of scala tympani (mm); SF, Scaling factor for ESF (NRT relative to FEA model); 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.2008.11.004

less detailed: all that is required, regarding field spread, is a general function that will describe the capacity of the stimulation on a particular electrode to produce excitation at all locations along the electrode array. Other aspects of the model development, of which this is a part, are described in Cohen (2009a, b, in press-a, -b). The field spread problem was approached in two ways. First, simple axi-symmetric Finite Element Analysis (FEA) models were constructed to compute the spread of the potential field around the inner wall of scala tympani, as a function of distance from the stimulated electrode. This position at the inner wall of scala tympani was chosen as a simple ‘‘standard”, close to, although certainly not coincident with, the point of excitation on the neural fibers. How close it would be to the point of excitation would depend on many factors, including the state of preservation of the neural fibers. Second, a measure of the electrically-evoked action potential (ECAP) was devised that enabled estimation of the capacity of a stimulated electrode to excite neurons at various locations along the cochlea: the ‘‘effective stimulation field” (ESF). This was related to, but distinct from, the spread of excitation (SOE) produced by stimulation of an electrode (Cohen et al., 2003a). The patient ESF data were compared with the predictions of the FEA models, drawing some tentative conclusions regarding the site of excitation on the neural fibers. In addition, as the FEA potential functions had been found to describe the ESF shapes quite well, slightly modified versions of the former were employed to smooth the individual patient ESF data.

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The detailed models of Frijns et al. (1995, 1996, 2001), using Boundary Element Analysis (BEA), and Rattay et al. (2001a, 2001b), using FEA, naturally include information regarding the potential at the inner wall of scala tympani, although that information is not available directly from the papers. The variation of the potential along scala tympani has been estimated in earlier simple models as the potential in a leaky transmission line (e.g., Black and Clark, 1980), which decays exponentially along the scala and is characterized by a length constant. Such a treatment does not allow for variations of potential radially, across the scala. While it may give reasonable estimates at longitudinal locations far from the stimulated electrode, it would be expected otherwise to be in error, especially if the stimulated electrode band was not in a mid-scalar position. Some error would be expected also from the assumption of a linear scalar duct of infinite length. Some cochlear implants allow measurement, simultaneous with stimulation, of the voltage at all the electrodes of the array (ClarionÒ II, Vanpoucke et al., 2004; NucleusÒ CI24RE receiver-stimulator, Patrick et al., 2006). Such voltages should be related to the FEA predictions of the potential at the inner wall of scala tympani, although they would differ in that the electrodes are not exactly at the inner wall. Indeed, the distances of individual bands from the inner wall could be quite variable and the effect of this on the sharpness of the stimulation field would not be well represented by voltages measured on the electrode bands. It is important to recognize that no simple potential in scala tympani, whether modeled or recorded, can be taken as a measure of the capacity of the stimulation to produce neural excitation. The ESF, in contrast, is a measure of this capacity. Nevertheless, the potential at the inner wall of the scala was a quantity of practical utility.

2. Materials and methods 2.1. General (summary) Methods and materials are presented in Paper 1 (Cohen, in press-a), regarding subjects, apparatus, stimuli, radiographic estimation of electrode positions and various measures and methods relating to the loudness of pulse-burst and single-pulse stimuli. In summary, six profoundly hearing-impaired adult subjects from the Cochlear Implant Clinic of the Royal Victorian Eye and Ear Hospital, participated in the study. All subjects were implanted with the NucleusÒ 24 cochlear prosthesis (Cochlear Limited): the straight array was used in subjects S1–S3, the ContourTM array in subjects C1–C3. Intensive measurements were performed with these subjects, excepting C3. 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. Both power and data were delivered to the implanted receiverstimulator by an external induction coil, driven by a SPrintTM speech processor in association with a suite of hardware provided by Cochlear Limited and a personal computer. Control of psychophysical stimuli was managed by custom software (‘‘Psychophysics Themepark”). Intracochlear recordings of the ECAP were recorded using the Neural Response TelemetryTM (NRTTM) system with Version 3.0 of the NRT software (unless otherwise stated). Charge-balanced biphasic current pulses were used for all stimuli, which were monopolar. The positions of the electrode bands of the array were specified objectively within a cochleo-vestibular framework, by analysis of 2D ‘‘Cochlear View” radiographs (Xu et al., 2000) using CViewÓ software (Cohen et al., 1996a, 2000). This analysis enables specification of the positions of the electrode bands both longitudinally, in terms of angle or percentage length along the organ of Corti

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(Pl), and radially, in terms of distance from the inner wall of the scala (Riw). Power law functions fitted to loudness growth functions for 300 ms pulse trains at a pulse rate of 250 pulses/s enabled the calculation of reference currents, I20, I50 and I80, corresponding to 20%, 50% and 80% of the loudness at IMCL300, the current associated with a 300 ms burst at maximum comfortable level, MCL (Paper 1, Section 3.1.2). A method was described for measurement of the curvature of growth functions. 2.2. Finite element analysis ANSYS Multiphysics (Release 5.7) finite element software was used to compute the spread of the electric field in simple axi-symmetric models of the human cochlea implanted with Nucleus electrode arrays. The geometry of the models is shown in Fig. 1, the gross structure being illustrated in (a). An axi-symmetric structure was created by rotating this section around the modiolar axis. A bony sphere surrounded a structure comprising: scala tympani, a simple neural structure and a well of cerebrospinal fluid. The structure comprised only a single turn and scala media and scala vestibuli were absent, as was any representation of neural fibers passing from the organ of Corti to the modiolus. Scala tympani contained perilymph and also an electrode array, constructed of Silicone but on which a single conductive electrode band was placed. The tissue resistivities were taken from Frijns et al. (1995): bone 6.41, perilymph 0.70 and nerve 3.33 (Xm). The resistivities used for platinum and Silicone were 1E-7 and 1E12 (Xm), respectively. The same resistivity was used for cerebrospinal fluid as for perilymph. Stimulation was monopolar: current was injected into the electrode and the outer surface of the bony sphere was maintained at a uniform potential of zero volts. Two Nucleus array types were modeled: the banded (‘‘straight”) array, which normally adopts a position against the outer wall of scala tympani; and the Contour, which lies considerably closer to the modiolus. More detailed descriptions of both arrays are given in Tykocinski et al. (2001) and Saunders et al. (2002). Whereas the electrodes of the straight

Fig. 1. Geometry of axi-symmetric FEA models. This section was rotated around the modiolar axis to create a simple cochlear model embedded in a bone sphere. (a) Gross structure. (b) Detailed structure. Four electrodes are shown within scala tympani: a banded ‘‘straight” electrode near the outer wall and three half-banded Contour electrodes in positions ranging from near the outer wall to near the inner wall. Only two positions were modeled: the ‘‘straight” electrode near the outer wall and the Contour in mid-scalar position. The vertical dashed lines represent approximate ‘‘center of mass” of the metal on the electrodes (essentially the centre of the X-ray image of an electrode contact).

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array are full bands, those of the Contour are approximately half bands. In Fig. 1(b), which provides greater detail, a straight array is shown close to the outer wall and the Contour array is shown at three locations ranging from close to the outer wall to close to the inner wall. Heavy lines indicate the conductive metal of the electrodes: the half bands of the Contour are on the medial side. While the FEA model computed the potential field in the entire model, data was extracted only for the (scalar) potential on a circular path around the inner wall of scala tympani, created by rotation of the medial dot in the figure (marked ‘‘measure potential”). The geometry of scala tympani, including distance of inner wall from modiolar axis and cross-sectional area, was taken from detailed analysis of a sectioned human cochlea, which had been found to be representative of mean cochlear dimensions (Cohen et al., 2000). The distance of the scala tympani inner wall from the modiolar axis and the cross-sectional areas of scala tympani and the electrode arrays were based on estimates for a cochlear angle of approximately 180° relative to the basal end of the organ of Corti. This angle corresponds approximately to the position of electrode 12 in the present subjects. The Contour array appears large relative to the size of scala tympani. However, this is approximately the worst case: more basally, the area of the scala increases while the area of the Contour remains the same; and more apically, while the area of the scala decreases, that of the Contour decreases more rapidly. Further, for scala tympani with the area shown, the height of the scala would generally be greater towards the modiolus, which would allow the Contour to fit more easily than the figure suggests. The field spread was modeled for the Contour array at a midscalar location and for the straight array at an outer wall location. The radiographic measure of the distance of an electrode from the inner wall of scala tympani (Riw) was taken from the ‘‘center of gravity” of the image of the electrode band (or half band) on the X-ray. In the two FEA models, M1 and M2 on the figure, the corresponding values of Riw were 1.216 and 0.573 mm. In a recent study (Cohen et al., 2006) mean Riw values of 1.368 and 0.614 mm were reported for the straight and Contour arrays, so that the modeled values were fairly representative. The straight array would be expected to have a somewhat larger Riw than has been modeled because, in penetrating into the spiral ligament, it can actually pass a little beyond the outer wall of scala tympani. (Also, a small gap was left between the modeled straight array and outer wall in order to facilitate meshing.) For a Contour array Riw can vary considerably, even within a patient (e.g., Paper 1, Fig. 2 C3). In the present study, mean values of Riw were found to be 1.445 mm for the straight array (S1–S3) and 0.659 mm for the Contour (C1–C3). While the two modeled cases, for straight array near outer wall and Contour in mid-scalar location, provided useful information, there was, in addition, the need for a family of field functions suitable for the Contour array at all possible radial distances from the modiolus (Riw). Such functions were approximated by performing a mathematical transformation, for a given Riw, based on the two functions that had been modeled. This family of functions had the appropriate characteristic that, while they differed systematically close to the electrode (in terms of Pl), they converged towards a common function at a large longitudinal distance from it (because the two modeled functions did so).

the response and artifact from the masker can be eliminated, leaving only the response to the probe. Additional methods are described in the subsequent papers of the series. 2.3.2. NRT measure of effective stimulation field (ESF) Attenuation of the effective stimulation field (ESF) was measured, using the NRT system (software version 3.0) in subjects S1–S3 and C1–C2, about electrodes 6, 12 and 18. The method employed the standard subtraction algorithm (Brown et al., 1990; Abbas et al., 1999; Lai and Dillier, 2000). The MPI (interval between the end of masker pulse and the start of probe pulse, in ls) was 500 ls. A fixed probe stimulus, applied to one of the three test electrodes, used a current low within the recordable NRT dynamic range but sufficient to produce a clear NRT trace. The current I20, corresponding to 20% of the loudness at maximum comfortable level (MCL) for a 300 ms pulse-burst at 250 pulses/s (Paper 1, Section 3.1.2), was used if it resulted in a satisfactory trace; otherwise the level was increased until a clear trace was obtained. A low-intensity probe current was used for two reasons: first, to produce, ideally, a localized region of neural excitation; and second, because the masker current would in some cases be much larger than that for the probe and the overall loudness needed to be kept within acceptable limits. NRT recordings were made, using maskers at many locations along the array. One series of runs was performed for each masker location. The first series was for the masker on the same electrode as the probe. The masker offset (the current level of the masker relative to that of the probe) was varied from 10 to +25 CL: an example is shown for S1 at electrode 12 in Fig. 2. As the masker current is increased, the amplitude obtained from the standard subtractive algorithm increases because the partially-masked response of the ‘‘B component”, that is, in the masker + probe condition, decreases. When masking is essentially complete, a plateau of amplitude is reached in the subtractive algorithm. In this example, masking is complete when the current of the masker is larger than that of the probe by about 10 CL (1.76 dB). The ESF measure now considers the masking produced for stimulation of the same probe electrode by a masker on a different electrode. If the region of neural excitation produced by the probe is very localized, the current required to achieve a given amount of masking should differ from the original situation, where probe and masker were coincident, by a constant scaling factor. This would result in a simple shift of the amplitude versus masker offset function along the masker offset axis, because masker offset is proportional to the logarithm of

2.3. ECAP methods 2.3.1. NRT methods (summary) General NRT methods and offline processing techniques have been described in Paper 1, Section 2.6. The general methods include derivation of the ECAP from recordings made in response to a probe, a masker and a masker + probe combination. Using a ‘‘standard” subtraction technique, the artifact from the probe and

Fig. 2. Variation of standard subtractive NRT response amplitude with masker offset (current level of the masker relative to that of the probe). When the response reaches a plateau, it is indicative of complete masking. Example for S1, electrode 12.

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masker current. The larger the longitudinal separation between the masker and probe electrodes, the larger this shift should be. The effect is illustrated in Fig. 3, for S1 with probe at electrode 12 and maskers at electrodes 2–21. For maskers other than M12, the dashed curve replicates the function for M12, while the heavy solid curve indicates the position of that function required to match, approximately, the experimental data for the different masker electrode (i.e., it shows the required shift). For maskers more basal than electrode 12 (i.e., <12), there is indeed a simple shift, which increases with separation of masker and probe. Note that masker offsets as large as 40 CL were used for some masker electrodes,

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in order to attain (or approach) the plateau amplitude. In the NRT series for each masker location, the masker current was increased progressively. If the subject considered a stimulus too loud, the run would be terminated immediately, which in some cases compromised the ability to find the plateau current. In the example shown Fig. 3, there is not a simple shift, however, for masker electrodes more apical than electrode 12. The slope of the amplitude versus masker offset function becomes shallower for the apical maskers and it is not clear what shift to attribute relative to the (dashed) function from M12. This effect might be explained by considering the ECAP-derived spread of neural

Fig. 3. Main data: Growth of standard NRT subtractive response amplitude for maskers at different locations (e.g., M6 signifies masker at electrode 6). These results are for S1, with probe at electrode 12. For maskers other than M12, the dashed curve replicates the function for M12 (‘‘*”), while the heavy solid curve indicates the position of that function required to match, approximately, the experimental data for the different masker electrode (i.e., it shows the required shift). For M19–M21 (‘‘?”), no attempt was made to estimate the shift required for the M12 function. Bottom right frame: SOE data that may assist interpretation (described in text).

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excitation function (SOE)1 for this probe electrode at the same current (Cohen et al., 2003a, Fig. 6), equal to the 20% level, inset bottom right in Fig. 3. Although this SOE function is quite well localized on the basal side, it spreads considerably on the apical side and, most likely, extends well beyond the apical end of the electrode array. While this tendency for SOE to spread more in an apical direction was present to some extent in all subjects (S1–S3 and C1–C3), it was very pronounced for S1. Where the effect is pronounced, especially for a probe electrode at, or apical of, the middle of the array, it is possible that some ‘‘cross-turn excitation” is taking place (e.g., Frijns et al., 2001; Cohen et al., 1996b). Here, excitation occurs of axons descending from more apical turns. However, the interpretation presented below for electrode 12 in S1 does not involve cross-turn excitation. Here, in addition to example results, we present a limited discussion in order to allow a detailed understanding of the method used to measure the spread of the ESF. The results obtained by applying the method can then be presented in an uncluttered manner in Section 3.2. Because, for S1 at electrode 12, the excitation pattern is not very localized, we are not concerned simply with a single point on a function of field voltage spread along the scala. In the bottom right frame of the figure are shown hypothetical excitation patterns associated with stimulation at locations shifted basally and apically by 7.5% of the length along the organ of Corti (solid lines). If, now, we imagine the (masker) current being increased at these locations, whereas complete masking may require only a small current increase at the basal masker location, it may require a considerably larger increase at the apical location. In fact, with increase of current comes not only increase in amplitude of the excitation profile but also additional broadening. For example, the dashed line shows the SOE at the 50% current level (217 CL), from Cohen et al. (2003a), shifted by 7.5% of the length along the organ of Corti. If this function is scaled (dotted line) so that its peak amplitude equals that of the function for 20% level, in comparison to the latter it does exhibit greater spread basally, although not apically. Nevertheless, the unsymmetrical shape of the SOE function might explain the non-ideal behavior of the growth functions for the maskers apical of the probe location in Fig. 3. The unsymmetrical SOE function implies, however, an unsymmetrical spread of stimulation field. As will be discussed below, the true spread of excitation for the probe may not be as broad or as asymmetrical as the ECAP-derived SOE measure suggests. The method for measuring the stimulation field spread is somewhat compromised by spread of excitation for the probe, especially if there is a lack of symmetry (and also, more fundamentally, by non-uniformity in the spread of the ESF). Probe 12 in S1 represents a fairly bad case. Nevertheless, in order to implement the measure of ESF, it was necessary to determine effective shifts along the masker offset axis for each masker electrode. When the shape of the ECAP amplitude versus masker offset function closely resembled that for the reference case (masker and probe on the same electrode), the task was fairly straightforward. For example, the reference function has been shifted to align with the rise of the function for the masker at electrode 9. These two functions also reach a plateau at essentially the same point. In this case, as in most, the growth function does not quite reach the plateau amplitude for the reference function (perhaps indicating a difficulty in achieving complete masking or a adaptation effect). The main criterion for determining an offset for the reference function was that the growth function for a given masker should reach a plateau at

1 The SOE measure is based on masker-probe interaction. The probe current and location are fixed, while, for the masker, the current is equal to that of the probe and the location is varied across the array. When the masker and probe are coincident, masking is maximal, the partially-masked amplitude is minimal and a peak results in the standard NRT subtractive algorithm.

approximately the same value of masker offset as for the shifted reference function. This criterion was applied also to the problematical apical masker electrodes. The offset was estimated visually and could only be approximate in cases such as shown in Fig. 3 for a masker at electrode 17. Here, the plateau point was judged in the context of the functions for maskers at electrodes 15 and 16, for which a plateau was considered to have been achieved, although at level a little below that of the reference function. The estimation of the plateau point might be improved in future by use of the ‘‘Miller” method, described in Paper 3, Section 2.2.2 (Cohen, in press-b). That method allows the measurement of the partially-masked probe response and, rather than a function such as Fig. 2 rising to a slightly uncertain upper limit, would result in a function falling to zero (e.g., Paper 4, Fig. 5(b) (Cohen, in press-a)). Note that the ESF data obtained are for spread of field towards the probe electrode, rather than away from it, which would have been the ideal (see Section 4). The measure was done in this way mainly because of the importance of maintaining a uniform fiber population excited by the probe. 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. Finite element analysis 3.1.1. Model results The modeled potential distributions for a straight array placed near the outer wall of scala tympani and for a mid-scalar Contour array are shown in Fig. 4(a). The FEA model computed the potential around the inner wall of a toroidal scala tympani. While the field was computed around a circle of radius 1.585 mm, where the corresponding distance of the organ of Corti from the rotational axis was 2.8 mm, the figure expresses the data relative to the percentage length along the organ of Corti, assuming a cochlear length of 34 mm. The dashed lines display the raw model data, which are confounded and limited in range by the finite size of the modeled cochlear ‘‘turn”. Whereas the field would be able to ‘‘dissipate” basally and apically in a spiral structure, that cannot happen in the present model, and the field at the position 180° away from the stimulated band represents a summation of the field ‘‘arriving” from both directions. This effect was removed approximately, on assumption of an exponential decay far from the electrode, resulting in the corrected functions shown as solid lines in the figure. Note that the functions for straight and Contour arrays limit to a single function far from the stimulated electrode: this is so for both the raw and corrected functions. The corrected functions can be plotted as clinical programming units (Current Level: CL), rather than volts (Fig. 4(b)), which is possible because CL is a logarithmic unit (1 CL = 0.176 dB). Plotting these and subsequent functions in units of CL arguably gives a better sense of the results in a clinical context. The data have been normalized to 0 CL at the peak of the straight array case. Approximate functions were derived to describe, for arbitrary Riw, the variation of the potential around the inner wall of scala tympani, based on the two modeled functions. It was assumed that the potential would vary in inverse proportion to the distance from the electrode. At a point on the inner wall of scala tympani (at angle h relative to the position of the stimulated electrode) the potential was assumed to take the form A=ðR0 þ R0iw Þ, where R0iw was the distance from the point representing the electrode location (at 0° and Riw out from the inner wall) to the point on the inner wall. For each value of Pl (percentage length along the organ of Corti)

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Fig. 4. (a) FEA model scalar potential around inner wall of modeled scala tympani, for a straight array near outer wall and a Contour array placed mid-scala. Dashed curves show raw model calculations, while solid curves have been corrected for finite size and axi-symmetric nature of models. (b) FEA modeled potential curves (corrected as in (a)) plotted as CL (current level: programming units). One CL is equivalent to 0.176 dB.

and corresponding angle h around the toroidal model, values for A and R0 were found that satisfied the two modeled cases, enabling functions to be estimated for any value of Riw. The resulting functions for potential around the inner wall of scala tympani are shown in Fig. 5(a). Again the data have been normalized to 0 CL at the peak of the modeled straight array case (Riw = 1.216 mm). In this figure, in contrast to Fig. 4, the peak is located at 40% of the distance along the organ of Corti, approximating the longitudinal position from which the axi-symmetric model was derived. Finally, the results are presented for a larger range of Riw values, including the mean values for straight (1.445 mm) and Contour (0.659 mm) arrays in this study (Fig. 5(b)). The transformed functions, as described above, are shown as dashed lines. In addition, in the light of ESF data to be presented below, the functions were modified slightly to incorporate a sharpening of the peaks (4 CL increase at the peaks). The modifications were as shown for the modeled cases (Riw = 0.573 and 1.216 mm). The functions for other values of Riw were then generated by the same transformation process as described above. These modified functions were employed in the subsequent model developments, normalized to 0 CL for Riw equal to 1.445 mm, as shown in Fig. 5(b). Note that the function used to mediate transformation to an arbitrary value of ðRiw ; A=ðR0 þ R0iw Þ, simply provided an approximate means to interpolate between the two modeled cases and to extrapolate beyond them, with some degree of physical validity. The transformed potential functions would be increasingly unreliable for Riw values

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Fig. 5. (a) FEA model field spread functions for different values of Riw, obtained by interpolation between and extrapolation beyond the two FEA models actually run, i.e., for Riw = 1.216 mm and Riw = 0.573 mm. See text for description of the interpolation method. The curves have been normalized to 0 CL at peak of modeled ‘‘straight array” case, i.e., Riw = 1.216 mm. In this figure the peak is located at 40% of the distance along the organ of Corti, approximating the longitudinal position from which the axi-symmetric model was derived. (b) Similar to (a), but further developed. FEA model field spread functions for different values of Riw, obtained by interpolation between and extrapolation beyond the two FEA models actually run, i.e., for Riw = 1.216 and 0.573 mm. Riw values presented include the means for the present straight and Contour groups (1.445 and 0.659 mm). In addition, in light of the ‘‘ESF” results, a sharpening of 4 CL was added to the FEA model curves for Riw = 1.216 and 0.573 mm. The curves have been normalized to 0 CL at peak of mean straight array case, i.e., Riw = 1.445 mm. Solid curves have this peak modification, dashed ones do not.

approaching zero. For Riw = 0.210, the modeled Contour electrode would be in contact with the inner wall. 3.1.2. Threshold predictions as function of electrode distance from modiolus (Riw) In Fig. 6 the model is used to estimate the relationship between threshold and Riw. Here, model threshold is approximated by the reciprocal of the potential at the peak of the field function (Fig. 5(b)). Behavioral threshold is plotted against Riw for C1 – C3: individual and mean regression lines are shown. The model function was scaled to match the mean subject regression line. The model function is linear because it was based, originally, on only two points (the two FEA models). The slope of the model function is approximately 30% larger than for the mean subject regres-

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The ESF data for the Contour subjects were treated in a more refined manner in Fig. 8. Here, the Riw values used for the model functions were different for each probe electrode and on the basal and apical sides of each. The value of Riw on a given side of a probe electrode was the mean Riw for the masker electrodes used. This approximation very much simplified the determination of the SF. In addition, the modified version of the model functions was used, with the sharpened peak (Fig. 5(b)). Fig. 8 indicates the merit of the sharpened function in representing the ESF data. This refinement was incorporated in the further development of the general model of neural excitation. The use of these SFs did not alter the statistical conclusions stated above.

Fig. 6. Comparison of thresholds for three Contour subjects, as function of Riw, and approximate thresholds suggested by modeled field potentials (Fig. 5(b)). Here, model threshold is approximated by inverse of potential at peak position. The model function has been scaled to match subject data. It is linear because it is based, originally, on only two points (two FEA models). The main comparison is between the slope of the model prediction and the slope of the mean regression for the subjects.

sion. However, basing the modeled threshold on the tip of the field function is rather simplistic. The reciprocal of the field function peak would tend to underestimate the threshold, more so for small Riw because of the greater sharpness of the function. Consideration of this effect would tend to reduce the slope of the model function. 3.2. ECAP measure of effective stimulation field (ESF) 3.2.1. Main results Effective stimulation field (ESF) functions for S1–S3 and C1–C2 are shown in Fig. 7. These were derived from data such as given in Fig. 3: the additional current level required at a masker electrode (separate from the probe) provided a measure of the attenuation of the ESF associated with the separation between the masker and probe electrodes. The model functions from Section 3.1 were used as an aid to interpretation of these results. The model functions for the straight and Contour array cases assumed the mean Riw values of 1.445 and 0.659 mm, respectively. The model functions shown here are the ‘‘standard” version, without peak-sharpening (see below). In order to fit the model functions to the ESF data, the model functions were scaled separately on the basal and apical sides of each probe electrode: the scaling factors (SFs) for the abscissa are shown. For example, an apical SF of 2.0 would mean that the model field spread function was stretched by that factor along the percentage length axis on the apical side of the test electrode. In addition, in order to obtain a good fit, it was appropriate to offset the ordinate of the model function: the mean offset was approximately 4 CL. The desirability of such an offset gave rise to the peak-sharpened version of the model functions given in Fig. 5(b). The mean SFs for the model functions to fit the experimental ESF data were 2.282 for the straight array and 1.992 for the Contour. Although the mean SFs were a little larger on the apical side (2.252) than the basal side (2.080), the difference was not significant by a paired t-test. The mean SF for basal and apical sides did not vary significantly with either probe electrode or subject (2-way ANOVA, GLM). Note that ESF was clearly narrower for the subjects with the Contour array but the SF was calculated with respect to a narrower modeled function.

3.2.2. Asymmetry of SOE and ESF: initial analysis In the ECAP-derived SOE measure of the spread of neural excitation (Cohen et al., 2003a, Fig. 6), there was a tendency, especially when using probe electrode 12, for the SOE function to spread more towards the apex. This was most pronounced for S1, S2 and C2 (subject numbering was the same in the previous study). One might expect that such a bias in the SOE function would be associated with—indeed, essentially caused by—a bias in the ESF function (a larger apical SF). The apical SF was clearly larger for S2 and C2, but only slightly larger for S1 (the case used for detailed discussion). For S1 at electrode 12, based on the ESF data, a substantial apical bias would not be predicted in the spread of neural excitation. This serves as a reminder that the present method for measuring ESF is approximate but, importantly, it may also point to limitations in the SOE measure. The SOE measure (Cohen et al., 2003a) employs a fixed probe and maskers of equal current but varied location. The spread of excitation is estimated from the amount of masking as a function of the separation between masker and probe. It is assumed that the excitation patterns for the maskers are similar to that for the probe, but longitudinally shifted. If that assumption is not correct, the SOE rendition of the excitation pattern for the probe can be considerably in error. For example, in the case of S1 (SOE shown bottom right in Fig. 3), the apical bias in the SOE could arise for a symmetrical excitation pattern around electrode 12 but a broadening of the excitation patterns for the maskers at more apical locations. In other words, the true excitation pattern for electrode 12 may not be nearly as biased as the SOE would suggest. In order to illustrate this effect and to indicate how the present modeling methods might be used to obtain deeper insight into both the spread of neural excitation and the ESF, an initial attempt to analyze the behavior in S1 is provided. In Fig. 9(a) the experimental SOE functions are plotted for 20% and 50% current levels at electrode 12. In addition, are plotted model emulations of these SOE functions (light solid lines) and the associated excitation patterns for (dashed lines). Here, the parameters derived for S1 in Paper 4, Section 5 (Cohen, 2008d) have been used, but SF has been allowed to vary with electrode. For electrodes below 12, basal and apical SFs are all 1.5. For electrodes 12 and above, SF increases linearly with electrode and the ratio of apical to basal SF is 2.0. At electrode 18, for example, the basal and apical SFs are 2.47 and 4.95. The main reason why the SF might change with electrode location and, indeed, be unsymmetrical is the spiral structure of the cochlea, which the (overall) model can only accommodate indirectly at the present stage of development. The resulting set of field spread functions produces a quite good emulation of the apical bias in the SOE data. However, the bias in the underlying excitation pattern is much less. The pronounced apical spread of the SOE occurs because the stimulation field is able to spread strongly from apical maskers to the region excited by electrode 12. In addition to allowing a plausible emulation of the SOE data, the above set of SFs was intended to allow emulation of the ESF data. In particular, the growth of ECAP amplitude with masker

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Fig. 7. Top three rows (S1–S3): Effective stimulation field (ESF) functions for, from left to right, probe electrodes 6, 12 and 18, derived from data such as illustrated in Fig. 3 (for S1, electrode 12). Fig. 3 gave rise, here, to the top center frame. The plain solid curves are approximate fits of the field function appropriate to Riw = 1.445 mm (mean straight value) in Fig. 5(a), although with peak set to 0 CL. This basic function was scaled along the abscissa, individually for the subject/electrode and also separately on either side of the electrode. Note that a good fit necessitated a vertical shift of the field function curve, by a mean of approximately 4 CL. Bottom two rows (C1–C2): The plain solid curves are approximate fits of the field function appropriate to Riw = 0.659 mm (mean Contour value) in Fig. 5(a), although with peak set to 0 CL. This basic function was scaled along the abscissa, as for S1–S3. Again, a good fit necessitated a vertical shift of the field function curve, by a mean of approximately 4 CL.

offset was considered, for maskers at electrodes 8, 12 and 16 (Fig. 9(c)). The (modified) model emulation of the growth function for masker at electrode 12 matches the experimental data. While

the emulations for maskers at electrodes 8 and 16 do not match the data as well, they do capture some of the difference between these two cases. Also shown, in Fig. 9(b), are the modeled growth

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Fig. 8. Similar to Fig. 7 (for Contour subjects), but more refined treatment for Contour subjects. The plain solid curves are fits of field functions from Fig. 5(b) (with sharpened peaks) and using values of Riw appropriate to the subject. See text for more detail. The model function was scaled along the abscissa, as before.

functions resulting from symmetrical field functions, equal for all three electrodes (unmodified model). Here, while the function for masker at electrode 12 matches the data, the curves for maskers 8 and 16 do not match the data and, indeed, show no difference from each other. 3.2.3. Effect of angular offset of ganglion cells relative to site of origin at organ of Corti The structure of the cochlea is such that there is an angular offset of ganglion cells relative to their dendritic sites of origin at the organ of Corti. This angular offset is minimal at the base but increases towards the apex, as has been known for a considerable time (e.g., Ariyasu et al., 1989) but has recently been analyzed in humans by Sridhar et al. (2006). A consequence is that, for electrical stimulation at a given longitudinal position, assuming neural excitation occurred in the vicinity of the soma, excitation would tend to be of fibers normally associated with lower pitch. Further, because the angular offset increases towards the apex, there could be an effective broadening of the region of fibers excited. Data provided by Patricia Leake enabled estimation of the influence of this effect in the present model. It was concluded that the magnitude of apical bias seen in S1, for example, would not be adequately explained by the angular offset effect. However, it will be appropriate to include the effect in future model development, particularly so as to describe accurately effects at the apical ends of electrode arrays. 4. Discussion In order to model the excitation of the neural population in the cochlea, it is necessary to quantify the spread of stimulation field produced by electrical stimulation of any electrode on the implanted electrode array. An ECAP-based method has been developed for measuring the spread of the ‘‘effective stimulation field” (ESF). The ESF provides a measure of the ‘‘ability” of the stimulation field to excite neurons at differing longitudinal locations

around the cochlea. In this, it differs from, and is arguably more useful than, any simple measure of the potential field in the cochlear duct. As an aid to the interpretation of the ESF measurements, simple finite element models were employed, from which predictions were extracted of the potential around the inner wall of scala tympani. From two such models, approximate functions were generated of the potential around the inner wall for electrodes placed at any distance (Riw) from the inner wall. The ECAP measure of ESF was related to, but distinct from, the spread of excitation (SOE) measure (Cohen et al., 2003a). The measure of ESF was an attempt to quantify the ability of the field to excite neurons, as a function of longitudinal distance from electrode to neuron. A probe stimulus was employed with fixed position and current and the current required at a series of masker locations along the array to achieve comparable masking of the probe was measured. Strictly, the measure was of the ability of the field to propagate towards the probe (from various locations), rather than away from it. However, it was considered preferable to do this, and to make a tacit assumption of local uniformity, because this method allowed the use of a common population of neurons associated with stimulation of the probe. A possible alternative method would involve estimation of the spread of ESF by using a masker at a fixed location and measuring the current required to mask probes presented at different locations. However, in this case, it would be difficult to determine appropriate currents for the various probe electrodes. The probe currents could not simply be equal, as some electrodes would be much closer to the modiolus than others, thus exciting more fibers. In some cases, particularly on the apical side of the probe electrode, the ESF measure appeared to be somewhat compromised by either the shape of the excitation pattern associated with the probe or by non-uniformity of the spread of ESF, or both, as in Fig. 3, (e.g., M16). Although the effect could perhaps be explained by an asymmetry in the probe excitation, ultimately that, in turn, would need to be explained in terms of spread of the ESF. Ideally, it should be possible to derive a solution that would explain both the SOE

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Fig. 9. (a) Illustration of a possible explanation for the bias in SOE measure in S1, electrode 12. SOE measurements for 50% level (filled squares) and 20% level (filled circles). Assuming a variation of field spread functions—for electrodes apical of 12, field spread scaling factors (SF) increase and have an apical bias (see text)—the experimental SOE can be approximated (solid lines). However, note that the corresponding excitation patterns (dashed lines) around electrode 12 have far less bias. Thus, the standard NRT SOE measure (Cohen et al., 2003a) can be misleading regarding the actual excitation pattern. (b) NRT amplitude as function of masker offset, for fixed probe location (12) and three different masker locations: 8 (open circles), 12 (filled circles) and 16 (filled squares). Note that the functions for maskers at electrodes 8 and 16 differ considerably from each other, although the maskers are equidistant from the probe. In this frame the model assumes a constant SF. The model function for masker at electrode 12 (fine dashed line) agrees well with the experimental data. The model functions for maskers at 8 (heavier dashed line) and 16 (unbroken line) are essentially the same, due to the constant and symmetrical SF, but are different from the experimental data. (c) Same as (b), except that the model employs the modified scheme for SF, as in (a). The model function for masker at electrode 12 again agrees well with experimental data. The model functions for maskers at 8 and 16 now differ from each other, and show an improved match to the experimental results.

function and the detailed ESF measurements, such as are illustrated in Fig. 3. Such a solution would, incidentally, circumvent

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the objection that the ESF measure was not strictly of the field propagating away from the probe electrode. An approximate solution was provided, as an example, in Fig. 9. This example indicated that the observations could be explained, approximately, by an asymmetry in the spread of ESF, the width of which increased apically. An inference from this solution was that the underlying spread of neural excitation for the probe may be much less asymmetrical than the associated SOE function. While the improvised set of SFs used in Fig. 9 was partially successful in modeling both SOE and ESF data, the systematic application of a model framework should allow self-consistent descriptions of both the field spread function and the spread of excitation. This would provide a measure of the spread of neural excitation considerably superior to that given by the existing SOE measure (Cohen et al, 2003a). When the spread of ESF was compared with the modeled spread of potential field (from the FE models), it was found that, although the ESF spread function was of a similar shape to the modeled function, it was on average approximately twice as broad (‘‘scaling factor”, SF  2). Why should the SF be substantially greater than unity? The FE models considered the distribution of the potential around the inner wall of scala tympani. While this was a convenient general location, it did not represent very accurately the site of any specific neural excitation, which may occur at the peripheral dendrite, in the vicinity of the ganglion cell body or at a more central axonal node. The latter two sites of excitation, in the context of Fig. 1(b), would be more medial than and, possibly, inferior to the point on the inner wall where the model potential was measured (i.e., to the left and down). If we were to measure the voltage distribution at such a location, in terms of angle around the rotational axis (or as percentage length along the organ of Corti), it would be broader than the distribution measured at the inner wall of the scala. Using a simple two-dimensional analytical model, it was estimated that the width of the distribution would double if the measurement point lay 0.66 mm medial of the modiolar wall for a straight array or 0.40 mm for a typically-placed Contour (Riw = 0.659 mm). An SF of about 2.0 appears consistent with excitation on the central side of the soma. However, SF differed considerably among subjects and across electrodes. It was as low as 1.37 for C1 at electrode 12. C1 had some residual hearing at low frequencies and it was possible that, due to better preservation of neurons even at more basal locations, excitation occurred at more peripheral sites on the fibers (i.e., closer to the FE-modeled location). If, generally, the principal site of excitation lay medial to the modiolar wall, the potential functions for differing values of Riw (Fig. 5(a and b)), based on potential at the modiolar wall, might exaggerate the effect of Riw. Threshold estimates, based simply on the peak maxima of these potential functions, did indeed predict a variation with Riw that was 30% larger than the mean experimental findings in the three subjects with the Contour array (Fig. 6). Some of this fairly small difference would be explained by the fact that this method of modeling threshold, using the peak maxima, would exaggerate the slope. However, the modeled slope agreed very well with that for C1, the state of preservation of whose neurons was perhaps better than average and for whom excitation might, therefore, have occurred closer to the modeled location. These results indicate that the peak amplitudes of the field spread functions shown in Fig. 5(a and b) vary appropriately with Riw, although, ideally, some allowance might be made for the effective site of neural excitation. Having found that the scaled model field functions fitted the ESF shapes well, but showed a consistent lack of sharpness at the peak, the modeled field functions were modified slightly as shown in Fig. 5(b). In subsequent modeling applications (in later papers), these modified functions were employed to smooth the individual

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patient ESF data. The peak-sharpening, relative to the potential measured around the inner wall of scala tympani, might be required because of more efficient excitation when the gradient of the field along the neural fiber is maximized. Whereas, adjacent to a stimulated electrode, the direction of maximum field gradient would be approximately perpendicular to the inner wall, at a location some distance along scala tympani from the electrode, the direction of maximum field gradient would not be perpendicular to the inner wall. As neural fibers generally lie approximately perpendicular to the inner wall, more efficient excitation might be expected adjacent to the electrode. The mean SF required to fit the modeled field spread functions to the experimental ESF data were fairly similar for the straight and Contour arrays (2.282 and 1.992, respectively). While the spread of ESF was clearly narrower for the subjects with the Contour array, the SF was similar because it was calculated with respect to a narrower modeled function. Although the mean SF was a little larger on the apical side (2.252) than the basal side (2.080), the difference was not significant. The mean SF for basal and apical sides did not vary significantly with either probe electrode or subject. In order to assess the variation of SF with electrode, however, it would be preferable to use FEA model functions calculated at different locations in the cochlea. The mean SF from the subjects with the straight array (2.282) was used in subsequent model development, Paper 4, Section 4, because of the greater uncertainties regarding Riw in those with the Contour, and because the mean SF for the latter did not differ greatly. However, in the model fits to individual subjects, Paper 4, Section 5, individual values of SF were used when available. More elaborate analysis of the FEA models could have been employed, for example calculating activating functions such as developed by Rattay (1999). A difficulty with more elaborate approaches, however, is that they embody assumptions about the degree and type of neural degeneration: arguably, the more detailed the model, the more dependence there is on the assumptions. The present approach in intended to be maximally open to what is measured in the individual patient, while building in a conservative scientific basis. As has been shown, the simple function of potential variation around the inner wall of scala tympani provides a useful, and rather informative, template for fitting the ESF functions obtained from NRT. The present approach represents a useful beginning. It should be emphasized that psychophysical or electrophysiological data obtained from subjects implanted with the Contour electrode need to be interpreted with considerable care. The effect of Riw, the distance of the individual band from the modiolus, can be large. Riw can vary not only across patients but also along the electrode array of an individual patient. The methods developed in this paper can be used to approximately quantify the effects of Riw. This is necessary for the present purpose, which is to describe mathematically the neural response in an individual implanted with either straight or Contour array, but it would be useful in a broader context. For example, it would be important in general psychophysical or ECAP studies to factor out the effect of Riw. Implicit here is the need for a radiographic method to quantify Riw in the individual patient. We developed such a method for use with plain film X-rays (see Paper 1, Section 2.4) but expect that CT technology will come to be used routinely for this purpose. Acknowledgements I wish to 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 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. I am indebted to Patricia Leake for provision of data that enabled estimation, in the model, of the influence of the angular offset of ganglion cells relative to their dendritic sites of origin at the organ of Corti. References Abbas, P.J., Brown, C.J., Shallop, J.K., Firszt, J.B., Hughes, M.L., Hong, S.H., Staller, S.J., 1999. 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