Spread of the intracochlear electrical field: Implications for assessing electrode array location in cochlear implantation

The electrode-generated intracochlear electrical field (EF) spreads widely along the scala tympani surrounded by poorly-conducting tissue and it can be measured with monopolar transimpedance matrix (TIMmp). Bipolar TIM (TIMbp) allows estimations of local potential differences. With TIMmp, the correct alignment of the electrode array can be assessed, and TIMbp may be useful in more subtle evaluations of the electrode array's intracochlear location. In this temporal bone study, we investigated the effect of the cross-sectional scala area (SA) and the electrode-medial-wall distance (EMWD) on both TIMmp and TIMbp using three types of electrode arrays. Also, multiple linear regressions based on the TIMmp and TIMbp measurements were used to estimate the SA and EMWD. Six cadaver temporal bones were consecutively implanted with a lateral-wall electrode array (Slim Straight) and with two different precurved perimodiolar electrode arrays (Contour Advance and Slim Modiolar) for variation in EMWD. The bones were imaged with cone-beam computed tomography with simultaneous TIMmp and TIMbp measurements. The results from imaging and EF measurements were compared. SA increased from apical to basal direction (r = 0.96, p < 0.001). Intracochlear EF peak negatively correlated with SA (r = -0.55, p < 0.001) irrespective of the EMWD. The rate of the EF decay did not correlate with SA but it was faster in the proximity of the medial wall than in more lateral positions (r = 0.35, p < 0.001). For a linear comparison between the EF decaying proportionally to squared distance and anatomic dimensions, a square root of inverse TIMbp was applied and found to be affected by both SA and EMWD (r = 0.44 and r = 0.49, p < 0.001 for both). A regression model confirmed that together TIMmp and TIMbp can be used to estimate both SA and EMWD (R2 = 0.47 and R2 = 0.44, respectively, p < 0.001 for both). In TIMmp, EF peaks grow from basal to apical direction and EF decay is steeper in the proximity of the medial wall than in more lateral positions. Local potentials measured via TIMbp correlate with both SA and EMWD. Altogether, TIMmp and TIMbp can be used to assess the intracochlear and intrascalar position of the electrode array, and they may reduce the need for intra- and postoperative imaging in the future.


Introduction
Hearing rehabilitation with a cochlear implant (CI) is an established treatment for severely-to-profound hearing loss. The sound processor of a CI gathers sound waves, which are converted into a digital signal to be transmitted to the internal parts of the CI via a magnetic coil. The processed information is then passed on to the intracochlear electrode array to generate electrical impulses that The ST is bordered by bone and the basilar membrane, whose conductivity is approximately one-tenth of the conductivity of perilymph ( Briaire and Frijns,20 0 0 ), causing a wide spread of the electrode-generated EF along the ST. The EF can be recorded with versatile objective back-telemetry tests of a CI by measuring the potential differences between the intracochlear electrode contacts and an extracochlear reference electrode. The CI manufacturers have diverse methods to visualize the spread of EF either as a one-dimensional longitudinal course of the EF along the electrode array or as two-dimensional heatmaps or voltage matrices across all possible combinations of the intracochlear electrode contacts. Measuring the spread of the EF has been proven to be useful in diverse situations, including incomplete insertion of the electrode array; it has been successfully used to detect both extracochlear electrode contacts ( de Rijk et al., 2020 ) and electrode array tip fold-overs ( Zuniga et al., 2017 ;Hoppe et al., 2022 ). To this end, measurements of the intracochlear EF can be employed to avoid intra-or postoperative imaging and reduce the patient's exposure to radiation. Modeled electric potential distributions and neural excitation profiles have also been shown to depend on individual cochlear morphology and the location of the electrode array in the cochlea ( Malherbe et al., 2016 ). Information about the EF spread is therefore useful in estimating physiological parameters, such as psychophysical loudness ( Berenstein et al., 2010 ) and the extent of SGN activation ( Söderqvist et al., 2021 ).
Recently, different configurations to measure the intracochlear EF have become clinically available allowing for the estimation of local potential differences between the intracochlear electrode contacts. These recordings include a bipolar four-point impedance measurement in which the current is led from electrode contact n to contact n + 3, and the potential difference is measured between contacts n + 1 and n + 2. Tan et al. (2014) hypothesized based on the higher conductivity of the perilymph than bone that bipolar impedance would increase in the proximity of the ST's medial wall. Tan et al. (2014) found that bipolar impedances are higher after stylet removal of a perimodiolar electrode array (i.e., the array was assumed to move closer to the medial wall) in cadaver temporal bones. These results were later confirmed by Pile et al. (2017) . Sijgers et al. (2022) found in their cadaver temporal bone study that the electrode-medial-wall distance (EMWD) can be predicted with great accuracy with the surgeon's inspected linear insertion depth and simultaneously measured four-point impedance. However, they did the four-point impedance experiment with just one temporal bone, which may limit the generalizability of their outcome.
In our earlier study, we found that with a lateral-wall electrode array the spread of the intracochlear EF is narrower in larger than in smaller cochleae and that there is more than a two-fold increase in the width of the EF when comparing a basal electrode contact to middle and apical electrode contacts ( Söderqvist et al., 2021 ). Also, in 3D-printed cochleae, steep slopes of the EF were found in cochleae with large basal lumen and in cochleae whose ST narrows rapidly towards the apex ( Lei et al., 2021 ). In the present study, six temporal bones were implanted with both lateral-wall and perimodiolar electrode arrays, imaged with a novel cone-beam computed tomography (CBCT) device with a protocol optimized for inner-ear imaging, and the intracochlear EF was recorded with monopolar transimpedance matrix (TIM mp ) together with bipolar TIM (TIM bp ) using the four-point configuration. Our primary object was to assess the effect of the cross-sectional scala area (SA) and EMWD on the intracochlear EF. Our secondary objective was to utilize the regression model by Sijgers et al. (2022) for predicting SA and EMWD with both monopolar and bipolar recordings to assess to what extent cochlear size and the intracochlear location of the electrode array can be estimated from electrical measurements without intra-or postoperative imaging.  1. A temporal bone in the 3D-printed plastic bone holder and the measurements from the cone-beam computed tomography (CBCT) images. A) A temporal bone before the implantation with a Contour Advance electrode array placed in a 3D-printed plastic temporal bone holder. B) The same temporal bone placed in the CBCT for simultaneous transimpedance matrix (TIM) measurements and imaging. C) The measurements of the electrode-medial-wall-distance (orange line) as well as scala height and width (blue dashed lines). D) and E) together with C) illustrates the orientation of the cochlea.

Study design and ethics
The study fulfilled the Helsinki Declaration for ethical use of human material. Institutional Review Board at Helsinki University Hospital approved the study protocol and the use of anonymous cadaveric temporal bones in the study (Approval No. §14 HUS/126/2021

Preparation of the temporal bones
Six fresh frozen temporal bones (TB1-6) were thawed and mastoidectomy and posterior tympanotomy were performed and the round window niche was drilled to expose the round window in a similar way as in clinical practice with CI recipients. To fill the cochleae with fluid similar to the perilymph, the temporal bones were submerged in Ringer's solution bath and subsequently placed in a vacuum chamber. The pressure was gradually decreased to 50 mbar for a complete fill and removal of any air bubbles inside the cochlea while maintaining the soft tissue as intact as possible. After confirming the absence of air bubbles in the cochlea via CBCT imaging, the temporal bones were placed in a 3D-printed plastic temporal bone holder ( Figs. 1A and B ) and implanted consecutively with a Cochlear Slim Straight (SS; Cochlear Ltd, Sydney, Australia), Contour Advance (CA), and Slim Modiolar (SM) electrode arrays using the round window approach. The bone holder allowed a fixed position of the extracochlear reference electrode in the Ringer's solution bath. Every other cochlea was implanted first with a SS and every other with a SM electrode array, CA being always the second electrode array implanted. After each implantation, the temporal bones were placed in the CBCT scanner (see Section 2.5 below; Fig. 1B ) for simultaneous imaging and TIM recordings. One SS (in TB3) and one CA (in TB1) electrode array had open circuits in the apical section of the electrode array. Thus, TIM bp measurements were unrecordable for these electrode arrays.

Intracochlear EF recordings via TIM
The electrode arrays were provided with DB25 connectors to allow them to be connected to a CI24RE Implant Emulator (Cochlear Ltd) receiver/stimulator mounted in a box. A Cochlear Nucleus CP910 sound processor was connected to the implant-in-a-box allowing for TIM recordings similar to clinical settings. All measurements were performed using the Custom Sound EP 6.0 (Cochlear Ltd) software. Before the TIM recordings, the electrode array was conditioned by sweeping the contacts with 230 current level (CL) to reduce contact impedances and to avoid running out of compliance in the subsequent measurements.
Initially, each electrode contact was sequentially stimulated in the monopolar mode using the extracochlear reference electrode as a ground and the resulting voltage was recorded from all intracochlear electrode contacts. Further, the recorded voltage was normalized by the stimulating current, resulting in a 22 × 22 transimpedance matrix in ohms ( Ω ), which represents the intracochlear electric potential at different parts of the electrode array ( Klabbers et al., 2021 ). The stimulating current was selected automatically by the clinical Custom Sound EP software to be the maximum value at or below 230 CL that does not result in out of compliance or channel saturation. The current used for TIM mp recordings varied from 180 to 230 CL, being 208 ± 14 CL (mean ± SD) on average. The pulse width and interphase gap were always 25 and 9 μs, respectively.
After the monopolar recordings TIM bp was measured. At first, electrode number n was stimulated, and electrode number n -3 was used as a reference electrode, and the resulting potential difference between electrodes n -1 and n -2 was measured (recording depth 1). All possible locations of these four adjacent electrodes along the electrode array were measured. Subsequentially, the distance between the stimulated and reference electrodes was increased by two electrode contacts at a time (recording depth 2, 3, 4…) while maintaining the recording electrode contacts next to each other in the middle between stimulating and reference electrode contacts. All possible locations for each configuration of stimulating and recording electrode contacts along the array were measured. Finally, electrode 22 was stimulated using electrode 1 as the ground, and the potential was recorded between electrodes 11 and 12 (recording depth 10). Similarly to the monopolar recordings, the current used for TIM bp varied in Custom Sound EP being between 149 and 216 CL with an average of 193 ± 17 CL. As the magnitude of the EF is proportional to the inverse of squared distance, we used 1 TIMbp ( TIM − 1 2 bp ) in further analyses to allow for linear comparison of the EF with the obtained anatomic dimensions.

Effective intracochlear EF
To estimate the electrode-tissue interface without bulk tissue impedance, an effective transimpedance (Z eff ) at the stimulating electrode contact was modeled similarly as in Berenstein et al. (2010) from the TIM mp measurements. The model is based on the measurements from the non-stimulating electrode contacts and the exponential decay of the intracochlear EF. In this model, it is assumed that transimpedances (Z) measured from the non-stimulating electrode contacts represent the intracochlear EF and can thus be used to derive Z eff in the proximity of the stimulating electrode contact. As the intracochlear EF decays exponentially ( Briaire and Frijns, 20 0 0 ), Z generated by the stimulating electrode contact in each location along the electrode array can be parametrized to: where A is amplitude (in Ω ), x is a distance (in mm) between the recording electrode contact and the stimulating contact, λ is a length constant (in mm; separately for the apical and basal direction from the stimulating electrode contact), and dc (in Ω ) is a direct current offset. The parameters were obtained using MAT-LAB (MathWorks, Natick, MA, USA) using the function fminsearch , which minimizes the sum of squared deviations between the measured Z values and values derived with Eq. (1) . The magnitude of the effective EF at the location of the stimulating electrode contact (Z eff , when x = 0 mm) can be expressed as follows: Further, the measured Z at the stimulating contact was substituted with the Z eff and a dc offset was subtracted from the measured TIM mp with the Z eff substitution to create an effective TIM (TIM eff ), which allowed a comparison between the intracochlear EF and the extent of neural activation in an earlier study ( Söderqvist et al., 2021 ). A TIM 50% width, where the peak amplitude of the TIM eff is halved, was estimated similarly as in Söderqvist et al. (2021) with the function findpeaks in MATLAB using halfheight as a reference. The function findpeaks finds the location and the amplitude of the peak in a curve, the locations where the maximum amplitude is halved from either side of the peak, and finally, gives the distance between the two locations as an output.
Modeling was considered successful when Z eff -dc was 0-2500 Ω as fminsearch may give unrealistic values in the extremities of the electrode array due to scarcity of the measurement points. The Z eff -dc limits were chosen based on a visual inspection of outliers in an earlier EF study ( Söderqvist et al., 2022 ). In the present study, the modeling was unsuccessful for electrode contacts 10-13 for the SS electrode array in TB1. In addition, modeling was not attempted for electrode contacts within four contacts of the contact containing an open circuit (SS in TB3 and CA in TB1).
The estimations of TIM 50% widths under two or over 20 electrode contacts were evaluated as unrealistically narrow or wide, respectively. As TIM 50% width could not be reliably determined from the most basal electrode contact, both TIM 50% width and Z eff from electrode 1 were excluded from the further analyzes.
Another method to examine the intracochlear EF is to evaluate its decay rate or slope at a given location along the electrode array. The slope of the intracochlear EF (EF slope ) can be approximated as a derivative of Eq. (1) : Similarly as in Lei et al. (2021) , EF slope was evaluated 1 mm both in the apical and basal direction from the stimulating electrode contact to estimate the extent of current spread along the ST. When x = 1 mm and A = Z eff -dc, Eq. (3) becomes: The relationship between effective transim pedance (Z eff ), decay rate of the intracochlear electrical field (EF slope ), and width of the EF (TIM eff 50% width). The Z eff depicts the peak of the intracochlear EF. As the EF decays to both basal and apical directions from the stimulating electrode contact, basal and apical EF slopes were calculated 1 mm from the stimulating electrode contact. TIM eff 50% width is determined to be the distance between the locations in the electrode array where the maximum amplitude in the EF is halved.
where the unit of EF slope is Ω /mm. The EF slope was calculated for electrode contacts with both basal and apical λ under 100 mm.
Thus, the EF slope was not calculated for electrode contacts shown in Supplemental Table 1. In the following analyses, the EF slope was averaged across the apical and basal EF slopes . The relationship between Z eff , EF slope and TIM 50% width is illustrated in Fig. 2 , where Z eff represents the peak, EF slope the decay rate, and TIM eff 50% width the extent of the intracochlear effective EF along the electrode array.
As TIM bp is recorded between two adjacent electrode contacts, a corresponding SA and EMWD was designated to be the mean SA and EMWD between the recording electrode contacts. Also, to compare TIM mp with TIM bp , means of Z eff and EF slope were calculated in a similar fashion.
To investigate the effect of recording depth on TIM bp , correlation coefficients were computed between measured TIM bp and the corresponding SA and EMWD from each electrode contact pair with post-hoc pairwise comparisons corrected with the Bonferroni method.
Finally, multiple linear regressions (MLRs) were conducted in SPSS 27 to evaluate the EF predictors of SA and EMWD. A stepwise selection method for MLR in SPSS was applied to obtain the regression parameters. At first, we evaluated the usability of the TIM mp measurements. At the location of the recording electrode contact, SA was the dependent variable and Z eff , EF slope , insertion angle, and EMWD independent variables, as outlined in Eq. (5) below: Further, the MLR model was supplemented with TIM To assess the usefulness of the MLR model in a situation where information from imaging is not available, e.g., in an intraoperative setting, the EMWD was discarded from the analysis and the insertion angle was replaced with a calculated linear insertion depth (LID), which correlates with angular insertion depth ( Aebischer et al., 2021 ). The distance between the center of each electrode contact was computed based on implant specifications (0.85-0.95 mm between adjacent electrode contacts for SS, 0.80 to 0.40 mm from the proximal end to the distal end of CA, and 0.60 mm for SM electrode arrays).
When the EMWD was excluded and insertion angle was replaced by LID in the models Eqs. (5) and (6) , the regression equations Eqs. (7) and (8) and Further, for EMWD, the MLR equations with and without TIM − 1 2 bp Eqs. (9) and (10) were: respectively. The MLR equations Eqs. (11) and (12) for EMWD without information from imaging were: and Finally, Eqs. (8) and (12) were used to estimate SA and EMWD, respectively, at individual electrode contacts. Two-way ANOVAs were conducted to analyze the differences between measured and estimated SAs and EMWDs. Either SA or EMWD was used as a dependent variable and electrode contact and acquisition type (measured or predicted) as independent variables. The post-hoc comparisons were corrected with the Tukey method.

Monopolar transimpedances
The purpose of this study was to evaluate the effect of scala dimensions and the electrode contact's distance from the medial wall of the cochlea on the intracochlear EF. Fig. 3 presents the relationship between the monopolar EF peak (Z eff ), SA, and EMWD averaged over the six temporal bones. As seen in Fig. 3A , the mean SA increases towards the base of the cochlea while Z eff decreases in the same direction. With the electrode number decreasing from apical to basal direction, there was a statistically significant negative correlation between mean SA and electrode number ( r = -0.96, p < 0.001) and a positive correlation between mean Z eff and electrode number ( r = 0.93, p < 0.001). When analyzed with ANOVA, Z eff differed between the electrode array types (F(2361) = 3.1, p = 0.048). However, in the pair-wise comparisons, no significant differences were detected after the post-hoc correlation with the Tukey method (1140 ± 520, 1010 ± 410, and 1010 ± 510 Ω ; mean ± SD; for SS, CA, and SM, respectively, p > 0.05 for all comparisons). The mean and SD of Z eff for each electrode contact and each electrode array type are shown in Table 2 . In Fig. 3B , Z eff is presented including all three electrode array types in relation to the corresponding SA. The correlation coefficient between Z eff and SA was r = -0.55 ( p < 0.001), indicating that the injected current generates a higher local voltage in a smaller (or more apical) than in a larger (or more basal) point of the scala. Further, Fig. 3C shows that EMWD varies, as expected, between different electrode array types (1.7 ± 0.38, 0.79 ± 0.30, and 0.61 ± 0.26 mm; mean ± SD; for SS, CA, and SM, respectively, p < 0.001 for all comparisons), while Z eff remains similar across the electrode array types. No significant correlation was found between Z eff and EMWD ( Fig. 2D ; r = 0.04, p = 0.48) suggesting that the peak in the monopolar EF does not depend on the distance between the electrode contact and the modiolar wall.
To assess the longitudinal spread of the monopolar EF along the ST, TIM 50% width, and EF slope are illustrated in Fig. 4 . In Fig. 4A , the mean TIM 50% width and the mean EF slope across all three electrode array types are plotted at individual electrode contacts. The patterns of the means seem similar in the middle section of the electrode array, but they differ in the apical section and in the most basal section. The individual EF slope values seem to be independent of electrode contact number ( Fig. 4B ), as no correlation was found between the two ( r = 0.07, p = 0.230). Fig. 5 demonstrates the relation of EF slope to SA and EMWD. Fig. 5A shows that EF slope remains relatively constant in the apical and middle sections of the electrode array. In the base, EF slope gets steeper (higher absolute value in Ω /mm) for the SS electrode array. When averaged over electrode contacts, significant differences were detected in the EF slope values between the electrode array types (F(2337) = 83.5, p < 0.001). In pair-wise comparison, The EF slope s were different between each electrode array type: -96.2 ± 31.1, -157.0 ± 53.0, and -127.0 ± 33.4 Ω (mean ± SD) for SS, CA, and SM, respectively ( p < 0.001 for all comparisons). The mean and SD of the EF slope for each electrode contact and each electrode array type are shown in Table 2 . In contrast to Z eff , EF slope did not correlate with SA ( r = -0.09, p = 0.117; see Fig. 5B ). In Fig. 5C , EMWD and EF slope are shown at each electrode contact. Also, when EF slope values of individual contacts from all three electrode array types were plotted against EMWD ( Fig. 5D ), a weak correlation was found ( r = 0.35, p < 0.001). Altogether these results demonstrate that the monopolar EF decay is faster in the proximity of the medial wall than in more lateral locations.
To gain a better insight into how widely the monopolar EF is distributed, we analyzed TIM 50% width in relation to EMWD at individual electrode contacts for the lateral-wall SS electrode arrays ( Fig. 6 ). The correlation coefficient between TIM 50% width / EMWD ratio and the electrode number was positive ( r = 0.87, p < 0.001). In the apical section of the electrode array the TIM 50% width is approximately twelve times the distance between the electrode contact and the medial wall of the cochlea. This gradually decreases towards the base, being approximately eightfold in the middle and remaining around threefold in the basal sections of the electrode array. These results demonstrate that the monopolar EF is distributed longitudinally very widely from any given point in the cochlea when compared to the respective EMWD. The phenomenon is most pronounced in the apical section of the electrode array.

Bipolar transimpedances
When looking at the behavior of local potentials measured via TIM bp instead of the widely-spreading monopolar EF, we transformed TIM bp to TIM   . 3. The relationship between the intracochlear EF peak (Z eff ) and electrode-medial-wall-distance (EMWD) as well as scala area (SA) for Slim Straight (SS), Contour Advance (CA), and Slim Modiolar (SM) electrode arrays. A) The mean Z eff and SA plotted at individual electrode contacts, which are arranged from apical to basal direction. The Z eff decreases from apical to basal direction while the mean SA increases, which is apparent for all three types of electrode arrays. B) When measured from individual electrode contacts, Z eff decrease while SA increase ( r = -0.55, p < 0.001). C) Similarly as in A, the Z eff decreases from the apex to the base. However, the EMWD vary between the electrode arrays. D) No significant relationship was found between Z eff and EMWD. recording contacts (recording depth 1). In Fig. 7 A, the respective electrode contacts between different electrode arrays are located largely in the same insertion depth (similar SA) but TIM − 1 2 bp varies between different electrode arrays. The mean TIM − 1 2 bp averaged across electrode contacts was 0.0 6 6 ± 0.0 05, 0.059 ± 0.0 08, and 0.062 ± 0.007 Ω −1/2 (mean ± SD, p < 0.01 for all comparisons) for SS, CA, and SM, respectively. Table 3   The mean EF slope and SA plotted at individual electrode contacts, which are arranged from apical to basal direction. (B) No significant relationship was found between EF slope and SA. (C) The EMWD of the SS electrode array thoroughly greater than the EMWD of the perimodiolar arrays. Also, the EF slope appear to lower (steeper) especially in the basal section of the electrode array than with the perimodiolar electrode arrays. (D) When measured from individual electrode contacts, EF slope increase together with EMWD ( r = 0.35, p < 0.001).

Table 3
Correlation coefficients and the corresponding p-values between TIM − 1 2 bp and SA, and between TIM − 1 2 bp and EMWD in different TIM bp recording depths (1-10). The limit for significance after the Bonferroni correction is p < 0.005.

Recording depth
Distance between stimulating and reference electrode  The effect of the individual temporal bone, electrode array type, and insertion angle on the EF measurements was analyzed with MANCOVA. Significant main effects of insertion angle (Wilk's = 0.28, F(2281) = 367, p < 0.001), electrode type (Wilk's = 0.78, F(4562) = 19, p < 0.001), temporal bone (Wilk's = 0.45, F(10,562) = 28, p < 0.001), and an interaction between electrode type and temporal bone (Wilk's = 0.67, F(2281) = 6.2, p < 0.001) were detected. These results indicate that the EF measurements are different when using different electrode array types in the same temporal bone or the same electrode array type in different temporal bones. Also, the effect of the electrode array type on EF measurements is affected by an individual temporal bone.  Table 3 ). An increase of TIM − 1 2 bp with SA was apparent for every recording depth with an exception for the recording depth 10 ( r = 0.44-0.59, p < 0.001). In contrast, the correlation between TIM − 1 2 bp and EMWD weakens when the distance between stimulating and reference electrodes increase, and disappears, when the distance is over 5 electrode contacts.

Multiple linear regressions
To estimate SA at the location of the stimulated electrode contact from data acquired via imaging and the monopolar spread of EF recordings, MLRs were conducted. With Eq. (5), a statistically significant regression equation was found (F(3, 337) = 111.0, p < 0.001), with an R 2 of 0.50. The parameters accepted by the model were insertion angle, EMWD, and Z eff . Further, the MLR model for SA prediction was supplemented with TIM − 1 2 bp Eq. (6) , which improved the accuracy of the model (R 2 = 0.55, F(4282) = 85.7, p < 0.001). The significant parameters including their estimates and SDs are shown in Table 4 and their contribution in the regression models in Table 5 .
Further, the SAs were estimated with information acquirable in intraoperative settings without imaging. Thus, the EMWD was discarded and the measured insertion angle was replaced with the LID in the regression equations Eqs. (7) and (8) . There was a statistically significant correlation between the measured insertion angle and calculated insertion depth ( r = 0.94, p < 0.001, see Table 6 ), indicating that the measured insertion angle can be estimated by the inspected insertion depth. However, the relationship between the linear and angular insertion depths is dependent on the electrode array type and its intracochlear location.
With Eq. (7) , a statistically significant regression equation with an R 2 of 0.36 including LID and Z eff was found (F(2, 337) = 93.0, p < 0.001). The lack of radiologic information in the model includ-    Table 4 .
Further, MLRs were conducted to estimate the EMWD. At first, only monopolar EF recordings and imaging data were included in the model Eq. Finally, when SA was abandoned and insertion angle was replaced with LID Eqs. (11) and (12) , the parameters of the regression equations were EF slope , LID, and Z eff (F(3337) = 31.0, p < 0.001, R 2 of 0.22) as well as TIM − 1 2 bp , LID, and Z eff (F(3282) = 75.6, p < 0.001; R 2 = 0.45). To summarize, these results indicate that both SA and EMWD can be predicted with good accuracy without radiological information, and in the models TIM mp and TIM bp complement each other. The correlations between parameters used in the regression equations can be found in Table 6 .
Regression models including both the TIM measurements and the LID were also used to predict SA and EMWD for each electrode array type. The means and SDs of the measured and pre-  dicted SAs and EMWDs are shown in Table 7 . Fig. 8 illustrates the measured and predicted SAs and EMWDs across the electrode array types. Prediction of the SA ( Fig. 8A -D ) seems to be accurate regardless of the electrode array type. As seen in Fig. 8E , there was a discrepancy between the measured and predicted EMWD for the SS electrode array. For CA, there is a good agreement between the measured and predicted values ( Fig. 8F ). For SM, the pattern of the predicted EMWD resembles the measured EMWD especially in the apical and middle segments, but it differs in the basal segment ( Fig. 8G ). Across all electrode types, the predicted EMWD seems to follow the measured EMWD rather well in the absolute values ( Fig. 8H ). Two-way ANOVAs were conducted to evaluate the differences between the measured and predicted SAs and EMWDs. For both analyses, a significant main effect was detected only for electrode number (F(18,642) = 29.5 and F(18,642) = 0.66, p < 0.001 for both). However, the main effect of acquisition type ( p = 0.20 and p = 0.32) or the interaction between electrode contact and acquisition type ( p = 0.58 and p = 0.85) was insignificant in both analyses. The SA prediction seems to be accurate ( Fig. 8D ). However, the statistical insignificance of acquisition type for EMWD is likely due to the large SDs in both the measured and predicted EMWDs ( Fig. 8H ).
To assess the clinical usefulness of the EF measurements in the prediction of electrode array location at an individual level, the measured and predicted SAs and EMWDs were compared in Fig. 9 for each temporal bone. Note that there are missing data for TB1 with CA, as well as for TB1 and TB3 with the SS electrode array due to open circuits or unsuccessful Z eff modeling. The upper panels show the measured and predicted SAs. For TB2, TB5, and TB6, the prediction of SA is fairly accurate. The lower panels show the measured and predicted EMWDs. Prediction of the EMWD seems to be most accurate for the CA electrode array. Table 7 Measured and predicted SAs and EMWDs for each electrode array type and for all electrode arrays combined. The mean (SD) values measured and predicted at the location between the two electrodes are shown in each cell.   9. The measured and Predicted scala areas (SAs) and electrode-to-medial-wall distances (EMWDs) for each electrode array type in the individual temporal bones. The upper panel shows the measured and predicted SAs and lower panel the measured and predicted EMWDs.

Discussion
The purpose of this study was to examine the effect of cochlear dimensions, namely SA, and EMWD on the spread of the intracochlear EF. In addition, the usefulness of both monopolar and bipolar EF measurements (TIM mp and TIM bp , respectively) in assessing SA and EMWD was investigated. To obtain variation in EMWD, the temporal bones were sequentially implanted with one lateral-wall (SS) and with two precurved perimodiolar electrode arrays with different positions in relation to the medial wall ( Mewes et al., 2020 ).
As the spread of the intracochlear EF is narrower in larger than in smaller cochleae ( Söderqvist et al., 2021 ) and it correlates with the peak of the intracochlear EF (Z eff , Söderqvist et al. 2022 ), the decrease of the peak amplitude Z eff with increasing SA is sensible. However, the location of the electrode array does not seem to affect the peak amplitude of the intracochlear EF in monopolar stimulation, as quantified by Z eff and EMWD. The decay rate of the EF was increased with the distance between the electrode contact and medial wall, indicating narrower monopolar EF profiles in the proximity of the modiolus. Also, higher TIM bp (lower TIM − 1 2 bp ) were found near the medial wall than from more lateral positions. These results suggest, that when the electrode contact is near poorly conducting bone ( Briaire and Frijns, 20 0 0 ), the decay of EF is faster and local potentials are higher. Faster decay of the intracochlear EF (steeper potential gradients; Kral et al. 1998 ) have been reported in the apical regions of the cochlea when comparing to the basal regions. In our study, EMWD does not decrease monotonically with electrode number or increased insertion angle, and the steeper EF slope cannot be explained by decreasing EMWD alone.
In a model of longitudinal (parallel to scala walls) and transverse (perpendicular to scala walls) resistances between electrode contacts based on Vanpoucke et al. (2004) and Aebischer et al. (2021) found that the longitudinal resistances are only a fraction of transverse resistances, and the transverse resistances in the most basal electrode contacts are only a fraction of transverse resistances measured from the other electrode contacts. Based on this finding they proposed that current in the ST mainly flows out from the base of the cochlea ( Aebischer et al., 2021 ), which could also explain our findings of the narrowest EF Fig. 10. The utility of TIM measurements in the clinical practice. In the upper left corner a normal TIM mp heatmap is presented. Row 1 of the heatmap shows the intracochlear EF generated by the stimulating electrode number 1. Other electrodes are sequentially stimulated one at a time and the measured EF is visualized on the corresponding row as the electrode number. The transimpedances are the highest in the diagonal and gradually decrease with the distance between the stimulating and recording electrode contacts, suggesting an insertion of the electrode array without any extracochlear electrode contacts, array tip fold-overs, or shunts between the electrode contacts. From TIM mp , the peak (Z eff ) can be modeled, and the rate of the EF decrease (EF slope) calculated. Together with TIM bp measurements, they can be used in the prediction of scala area (SA; dashed circle) and electrode-medial-wall-distance (EMWD; red line).
profiles and lowest peak amplitudes in the most basal section of the electrode array. In monopolar stimulation, these properties of the intracochlear EF may be linked with the amount and extent of the evoked potentials in the auditory nerve: a lower peak amplitude in the EF profile towards the base of the cochlea is associated with a higher threshold current for a measurable neural response ( Söderqvist et al., 2022 ), and there are similarities between the spread of the EF and SGN activation along the electrode array ( Söderqvist et al., 2021 ). In vivo , there is also a significant effect of EMWD on the thresholds of evoked responses in monopolar stimulation, which is more pronounced in bipolar stimulation ( Long et al., 2014 ). In line with earlier studies on bipolar EF measurements ( Tan et al., 2014 ;Pile et al., 2017 ;Sijgers et al., 2022 ), we found higher TIM bp (lower TIM − 1 2 bp ) values in the proximity of medial wall than from more lateral electrode contacts.
However, in our study, lower TIM bp (higher TIM − 1 2 bp ) values were found from larger than from smaller SAs. This is in contrast with Sijgers et al. (2022) , as they did not find a relationship between TIM bp and insertion depth, which may be unexpected given the decrease SA with increasing insertion angle ( Biedron et al., 2010 ).
With the information from TIM mp recordings and imaging, over one half of the SA variance may be predicted. When the information from imaging is discarded, the accuracy of the model for SA estimation is slightly decreased. After combining information from imaging with TIM mp and TIM bp , a good estimate with a regression equation (R 2 = 0.55) was found, which only slightly decreased (R 2 = 0.47) without the imaging information.
The estimation of EMWD based on TIM mp and imaging was not as accurate; with or without imaging, only one-fifth of the variance in EMWD was accounted for. However, with supplementing information from imaging and TIM mp with TIM bp, the accuracy of regression equation improved. When applying TIM bp and LID with no imaging data to the model, EMWD can be estimated with an R 2 of 0.44, which was unexpectedly greater than the prediction with the model including imaging information. This may be due to coincidentally better correlation between the estimated insertion depth (LID) and EMWD than between insertion angle and EMWD ( Table 6 ).
In clinical settings, TIM mp is currently used to reveal possible shunts between electrode contacts ( Vanpoucke et al., 2004 ), the presence of extracochlear electrode contacts ( de Rijk et al., 2020 ), and tip fold-overs or loops in the electrode array inside the cochlea ( Zuniga et al., 2017 ;Klabbers et al., 2021 ;Hoppe et al., 2022 ). Based on our results, TIM mp could also be used to reflect crosssectional SA and EMWD (see summary in Fig. 10 ). TIM bp is currently not in clinical use but according to our results, it could be used to estimate both the cross-sectional SA and EMWD ( Fig. 7 ). Combining TIM mp and TIM bp , SA and EMWD can be estimated with an R 2 of 0.47 and 0.44, respectively. Prediction of the SA seems to be fairly consistent and accurate and may be helpful for example when assessing the linear alignment of the electrode array. As SA narrows gradually towards the apex, similar decreasing trend in the predicted SAs indicate an insertion without substantial problems, which is further confirmed with a normal TIM mp heatmap ( Fig. 10 ). Nevertheless, even though generally providing promising results, the prediction of the electrode array location in respect to the medial wall of the scala may be inaccurate at an individual level. Our results are in line with Sijgers et al. (2022) , where most of the variation in EMWD was explained by inspected insertion angle and four-point TIM bp , and the model was only slightly improved when adding information from other impedance measurements.
Using cadaver temporal bones allows implantation of the cochlea sequentially using different electrode array types. However, the physical environment in the cadaver and living cochleae may not be entirely the same, even though the cadaver and clinical EF measurements appear similar ( de Rijk et al., 2020 ). First, it is unknown how the freezing and thawing of the temporal bones affect the delicate non-bony structures of the cochleae, such as the basilar and Reissner's membranes dividing the scala into scalae tympani, vestibuli, and media. Second, the low pressure needed to ensure fluid-filled cochlea after thawing, even when gradually decreased and slowly increased back to the atmospheric pressure, might further damage the intracochlear structures. Third, in vivo , the muscle/fascia plug inserted in on the round window scars and fibrous tissue forms around the electrode array affecting the impedance measurements ( Henkin et al., 2003 ). However, the postoperative tissue growth is not an issue in intraoperative settings. Fourth, the EF measurements were found to be affected by the electrode array type and individual temporal bone. The effect of the electrode array on EF measurements also varied between individual temporal bones. Fifth, while the scalae shape resembles an oval in the basal section of the cochlea, in more apical locations, the scalae are more triangle-shaped. Thus, the estimation of SA via fitting a constant shape into the scalae is not as accurate as measuring the area using segmentation of the structures ( Avci et al., 2014 ). Finally, the measured dimensions are small and may be hindered by the CBCT resolution. However, in our study the voxel size of the CBCT images were 25% smaller (75 vs. 100 μm) than CBCT image voxels in the temporal bone study by Sijgers et al. (2022) .
It is tempting to speculate that together with the knowledge of a decreasing SA with increasing insertion angle and typical behavior of the EMWD for each electrode array type, TIM mp and TIM bp could be used intra-or postoperatively to assess the intracochlear and intrascalar location of the electrode array without the need for intra-or postoperative imaging. Further studies in clinical settings are needed to verify these correlations in real-life situations, and what potential implications monopolar and bipolar EF measurements have on analyzing elicited neural responses, and ultimately, on hearing outcomes with CIs.

Conclusion
Our results suggest that TIM mp and TIM bp can be used to estimate SA and EMWD with good accuracy using linear regression models. Thus, EF measurements may be used to assess the intra-cochlear and intrascalar position of the electrode array, and they may reduce the need for intra-or postoperative imaging in the future.

Funding
The electrode arrays used in this study were funded by Cochlear Research & Development Ltd under reference number IIR-2342.

Declaration of Competing Interest
None.

Data availability
Data will be made available on request.

Supplementary materials
Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.heares.2023.108790 .