This study was approved by the Ethics Committee of Cologne University’s Faculty of Medicine. Written informed consent was obtained from all subjects according to the Declaration of Helsinki and Good Clinical Practice. Participants were 18 individuals with subjective bilateral chronic tonal tinnitus (15 males and 3 females). Individuals with pulsatile, buzzing, roaring, or hissing tinnitus and subjects with a history of auditory hallucinations, Ménière’s disease, middle ear disorders, and diagnosed neurological or mental disorders, as well as individuals taking CNS-acting medication or using hearing aids, were excluded. The mean age was 45.89 (±12.97 standard deviation, SD) years, and the mean tinnitus duration was 9.83 (±7.08) years. Otoscopic examination was performed in all participants. Additional details can be found in (Adamchic et al., 2017).

Extended high-frequency air conduction audiometry was performed in all subjects, ranging from 125 Hz to 16 kHz, with thresholds measured in dB HL. While estimates of the frequency distribution of the tinnitus pitch match (f _T ) vary across studies (Reed, 1960; Meikle and Taylor-Walsh, 1984; Savastano, 2004), the prevalence of f _T above 4,000 Hz in these studies is consistently sizeable. Thus, in order to comprehensively estimate hearing in the ranges possibly affected by the tinnitus, a five-frequency pure tone average (5-PTA) was calculated for each subject as the average of thresholds at 500, 1,000, 2000, 4,000, and 8,000 Hz.

The tinnitus pitch was determined by means of a pure tone matching procedure (from 0.5 to 13 kHz) (Adamchic et al., 2017). Starting from either well above or well below the subject’s tinnitus frequency, subjects had to adjust the frequency of a pure tone to the perceived pitch of their tinnitus. The tinnitus pitch matching procedure required patients to confirm the best matching pitch twice with a maximum modulus of the difference between two matched tones <100 Hz. Tinnitus pitches obtained ranged from 675 to 9,800 Hz. Audiometric data, tinnitus pitch, and tinnitus duration can be found in Supplementary Table S1.

Figure 1A illustrates the stimulation patterns for aCR. The aCR stimulation comprises the four tones whose frequencies are specified as fixed percentages relative to f T   . There are two forms of aCR, referred to as “regular” and “noisy.” In regular aCR, two tones are placed below f T   and two are placed above f T     ( f 1 = 0.76 ⋅ f T   ,   f 2 = 0.9 ⋅ f T   , f 3 = 1.1 ⋅ f T   , f 4 = 1.4 ⋅ f T ) (Figure 1B). For the noisy aCR stimulation, prior to each cycle, four frequencies f 1   , … . ,   f 4 are randomly chosen out of a set of frequencies c 1   to c 12   with equal probability (Figure 1B) in the following way: f 1   is chosen from the set S 1 = { c 1 , c 2 , c 3 } ,   f 2   is chosen from the set S 2 = { c 4 , c 5 , c 6 } , f 3   is chosen from the set S 3 = { c 7 , c 8 , c 9 } , and f 4   is chosen from the set S 4 = { c 10 , c 11 , c 12 } , where c j = d j f T and d 1 = 0.69 ,     d 2 = 0.728 ,     d 3 = 0.766 ,     d 4 = 0.810 ,     d 5 = 0.855 ,     d 6 = 0.900 ,     d 7 = 1.100 ,   d 8 = 1.182 ,   d 9 = 1.265 ,   d 10 = 1.400 ,   d 11 =   1.505 ,   d 12 = 1.610 . The duration of the acoustic tones is 150 ms for both protocols.

The frequency span for regular aCR stimulation reads   f 4 − f 1 = 0.63 ⋅ f T . For noisy aCR stimulation, the frequency span ranges from   c 12 − c 1 = 0.920 ⋅ f T to   c 10 − c 3 = 0.634 ⋅ f T with an average (over stimulation cycles) of S 4 ¯ − S 1 ¯ = 0.777 ⋅ f T . Thus, the average frequency span of noisy aCR stimulation is approximately 23% greater than that of aCR stimulation, which means an even higher total span for the ERBs centered at the stimulation tone frequencies. In the case of aCR stimulation, the distances between adjacent tones are   f 2 − f 1 = 0.134 ⋅ f T ,   f 3 − f 2 = 0.2 ⋅ f T ,   f 4 − f 3 = 0.3 ⋅ f T . For the noisy aCR stimulation, the average distance between adjacent sets of tones is given by   S 2 ¯ − S 1 ¯ = 0.127 ⋅ f T ,   S 3 ¯ − S 2 ¯ = 0.327 ⋅ f T ,   S 4 ¯ − S 3 ¯ = 0.323 ⋅ f T   , where   S 1 ¯ , .. , S 4 ¯ are the mean frequencies of the corresponding sets defined above. Thus, the distance between the inner sets of tones of the noisy aCR stimulation is on average 64% greater than the distance between the inner CR tones f 2 and f 3 . Accordingly, aCR stimulation is more closely spaced around the tinnitus frequency f T than is noisy aCR. More details about the frequency spacing for both protocols can be found in the article (Adamchic et al., 2017). For both stimulation protocols in this study, stimulation tones were equally loud. The loudness of the stimulation tones was set using the following procedure: First the intensity of the stimulation tone with the lowest frequency was set at threshold +20 dB. Loudness of the other stimulation tones was set so that they were perceived by the participant as equally loud as the first tone. Participants who were not able to hear all stimulation tones were excluded from the study.

The first part of each experimental session consisted of a 10-min period of silence (Figure 1C). The participants sat still and listened to their tinnitus. At the end of this baseline period, the participants were asked to indicate the mean tinnitus loudness and annoyance during the baseline resting period on a 100 mm long visual analogue scale (VAS) verbally anchored at the endpoints (Adamchic et al., 2012). VAS for loudness (VAS-L; tinnitus is not audible = 0, tinnitus is extremely loud = 100) and annoyance (VAS-A; tinnitus is not annoying = 0, tinnitus is extremely annoying = 100) were obtained. After the rating, CR stimulation (Figure 1B) was presented for exactly 16 min. At the end of this stimulation period, the participants were asked to indicate the mean tinnitus loudness and annoyance during the stimulation period on the VAS-L and VAS-A. The stimulus presentation was followed by a 2-min-long resting period with eyes closed, followed by a final VAS-L and VAS-A rating between 2 and 4 minutes after the stimulation. The order of the experimental sessions—whether regular aCR first or noisy aCR first—was pseudorandomly counterbalanced across subjects. The subjects thus underwent both types of aCR. The sequence of events in a typical experimental session is also illustrated in Figure 1C. Since the VAS-A and -L scores were measured both for the right and left ears, we used their arithmetic mean values normalized to their baseline values (Adamchic et al., 2017). Since the values were normalized to their baseline, the final score used in the analysis is a proportion (with 1.0 indicating a score unchanged from baseline). From this point on, all reference to VAS-A and VAS-L refers to the normalized score unless indicated otherwise. All subjects’ normalized VAS-L and VAS-A scores during and after therapy for regular and noisy aCR can be found in Supplementary Table S2.

In the present study, we used a frequency scale based on the equivalent rectangular bandwidth (ERB) of the auditory filter, as determined from masking experiments using notched noise or spectrally rippled noise with human listeners (Moore and Glasberg, 1983; Glasberg and Moore, 1990). The average value of the ERB for young listeners with normal audiometric thresholds measured at moderate sound levels is denoted as ERB_N. Its value in Hz is given by   E R B N = 24.7 ⋅ ( 0.00437 ⋅ f + 1 ) , (1) where f is the center frequency in Hz (Glasberg and Moore, 1990). This equation provides a good prediction of E R B values estimated psychoacoustically using masking experiments for center frequencies spanning almost the entire range of human hearing from about 50 to 15,000 Hz (Zhou, 1995). The edges of the ERB-wide frequency intervals were estimated at low sensation levels using data presented by Moore and others, where the value of the ERB was provided for center frequencies 2,000, 4,000, and 6,000 Hz and audiometric thresholds from 0 to 80 dB HL (Moore et al., 1999). From these data, the following equation was generated for hearing loss h in the range of 0–50 dB HL (Tass et al., 2019): E R B ( h ) = E R B N ⋅ ( 1 + h / 50   d B   H L ) , (2) The values of frequencies at the upper edges a T and lower edges b T of the ERB-wide band centered around f T   are defined by a T = f T − 0.5 ⋅ E R B ( h ( f T ) ) , (3) b T = f T + 0.5 ⋅ E R B ( h ( f T ) ) , (4) Analogously, the frequencies at the upper and lower edges of the E R B band centered at the frequency of CR tone j, a j , and b j , read a j = f j − 0.5 ⋅ E R B ( h ( f j ) ) , (5) b j = f j + 0.5 ⋅ E R B ( h ( f j ) ) , (6) Figure 2 illustrates the alignment of CR tones f 1 , … f 4 , tinnitus tone f T   together with the corresponding ERBs for the case when the ERBs of neighboring CR tones are not overlapping.

According to the American Speech-Language-Hearing Association (ASHA), the hearing thresholds relevant to our study can be classified with the following descriptors: normal hearing (0–15 dB), slight hearing loss (16–25 dB), mild hearing loss (26–40 dB), and moderate hearing loss (41–55 dB) (Goodman, 1965; Clark, 1981). Due to deterioration in estimates of the ERB width beyond hearing thresholds of 50 dB, we do not plot severe-to-profound hearing loss here. Nine of the eighteen subjects had at least one threshold above 50 dB in at least one ear at the frequencies included in the 5-PTA.

To illustrate how the range of possible gap index values for aCR stimulation depends on tinnitus frequency f T   and hearing loss, we plot the gap index against tinnitus frequency f T   , assuming homogenous hearing loss, where 0, 16, 26, and 41 dB hearing loss applies to all corresponding CR frequencies, respectively (“HL 0dB”, …, “HL 41dB” in Figure 3A). In these cases, h ( f 1 ) , … , h ( f 4 ) =   0, 16, 26, and 41 dB, respectively. This is to illustrate maximum ranges of the gap index belonging to normal hearing as well as slight, mild, and moderate homogenous hearing loss. Analogously, we plot the same curves for noisy aCR stimulation (Figure 3B). The maximum range of possible gap index values increases with increasing tinnitus frequency and begins to broaden even for milder degrees of homogenous hearing loss. The tinnitus frequency-dependent increase is more pronounced for aCR stimulation than for noisy aCR stimulation. In general, the values of the gap index for aCR stimulation are smaller than for noisy aCR stimulation.

However, the gap index not only depends on the average hearing loss in the vicinity of the tinnitus frequency f T (i.e., the frequency range between f 1 ,   the lowest CR tone, and f 4 ,   the highest CR tone) but may strongly vary depending on the actual shape of the audiogram in that frequency range. For illustration, for aCR stimulation we consider different types of non-homogenous hearing impairment. For this, we introduce the mean hearing impairment belonging to all four CR tones by h ¯ ( f T ) = 1 4 ∑ j = 1 4 h ( f j )   . We consider different shapes of (model) audiogram with the same mean h ¯ ( f T ) as for the homogenous hearing impairment at 26 dB shown in Figure 3A:

On average 26 dB hearing loss:

For h ¯ ( f T ) = 26  dB we consider three different cases with non-homogenous (model) hearing impairment (Figure 3A):

1) Lower-frequency hearing loss (“HL 26 dB LF”): h ( f 1 ) = h ( f 2 ) = 50  dB, h ( f 3 ) = 4  dB, h ( f 4 ) = 0 dB.

As shown in Figure 3A, the lower-frequency (model) hearing impairment has the greatest gap values, even exceeding the HL 16 dB curve for homogenous hearing impairment. Conversely, for frequencies between 800 Hz and 1,500 Hz the gap index of the higher-frequency (model) hearing impairment approaches gap index values of the HL 41 dB curve for homogenous hearing impairment. Similar audiogram-shape dependent variations of the gap index were also observed for h ¯ ( f T ) = 16  dB and h ¯ ( f T ) = 41  dB, as described in the Supplementary Methods. In summary, the gap index does not simply depend on the average hearing impairment around f T . The gap index rather strongly depends on the actual shape of the audiogram in the vicinity of the tinnitus frequency f T .

To compute the distances between adjacent ERBs and the overall gap index (Eq. 9, above) for the aCR tones used in the clinical study, we used the following procedure:

1) The audiogram of every tinnitus patient was linearly interpolated on a logarithmic frequency axis.

All statistical analyses were performed using IBM SPSS Statistics (2020).

As shown in Table 1, in the linear models for VAS-L during both regular and noisy aCR, the gap index was the only significant predictor variable. Partial regression plots for the primary analysis are shown in Figure 4. It should be noted that partial regression plots demonstrate the residuals of the represented variables, rather than the variables themselves. For this reason, the y-axis in each subfigure of Figure 4 represents the residual of VAS-L during CR, and the x-axis represents the residual of the gap index after removing the linear effects of the residual variance of 5-PTA. The slope of each plot is the same as the unstandardized beta coefficient (B) for the gap index for each multiple linear regression, the values of which can be found in Table 1.

Coordinated reset was developed computationally to lead to desynchronization of populations of neurons with abnormal degrees of coincident firing (Tass, 2003; Tass and Popovych, 2012). However, the optimal values of overlap of spatial stimulation profiles for aCR—leading to maximal desynchronization and clinical benefit—remain an unknown in clinical practice. Several lines of evidence suggest that stimulus amplitudes and the intimately associated parameter of spatial stimulation profiles can have major impacts on the degree of desynchronization achievable. Tass et al. demonstrated that CR-DBS with one-third the stimulus amplitude of conventional DBS leads to more pronounced clinical effects in parkinsonian monkeys (Tass et al., 2012b). Additional computational studies have demonstrated the presence of the “spacing principle,” whereby spaced CR stimulation at weaker intensities can effectively induce anti-kindling (Popovych et al., 2015).

This study aims to shed light on the impact of tone spacing on clinical efficacy of regular and noisy aCR, as measured by the changes to self-reports of tinnitus loudness and annoyance during and after stimulation. The existing tone paradigms were transformed into an ERB-scale, which allowed for an analysis of the impact of aCR spatial stimulation profiles on clinical outcome. The gap index—or fraction of the target spectral range uncovered by stimulation—was introduced as a measure of spacing between adjacent auditory filters. We carefully analyzed several possible metrics, as described in the Methods, and found the gap index to be a useful composite measure that captures multiple relationships, both among the therapeutic tones and also between the therapeutic tones and the tinnitus frequency.

To that end, several multiple linear regression models were developed, using tinnitus duration, the gap index, and residual variance of 5-PTA (after controlling for multicollinearity with the gap index) as predictor variables. The primary outcome variable was VAS-L during therapy, with additional secondary analyses performed on the response variables of VAS-L after therapy and VAS-A during and after stimulation with the two CR paradigms. The gap index was found to be the primary predictor variable for the primary outcome variable of VAS-L during regular aCR and during noisy aCR. This suggests that, as the gap index becomes smaller, i.e., the ERBs corresponding to the CR tones have less space between them, there is a decrease in the response to treatment, with higher symptom scores during and after stimulation. Thus, higher gap indices—and thus loosely spaced CR tones—are associated with a more pronounced treatment response in the acute stage. These results hold true when controlling for both tinnitus duration and 5-PTA.

When examining VAS-L after regular aCR, only the duration was significant. When examining VAS-A after regular aCR, both gap index and duration were significant. The results of these exploratory analyses suggest that having had tinnitus for longer duration had a possible negative impact on therapeutic efficacy for the acute after-effect. In contrast, in a prospective, randomized, single-blind, placebo-controlled 12-week proof of concept study in 63 patients with chronic tonal tinnitus, up to 50 dB hearing loss and tinnitus duration characteristics comparable to the sample considered here, it was shown that tinnitus duration was not a confounding factor for patients treated with aCR stimulation for 4–6 hours per day (Tass et al., 2012a). Hence, while the acute effects studied in this paper may depend on tinnitus duration, long-term effects of aCR stimulation may evolve irrespective of tinnitus duration. The results of this study are applicable specifically to the acute effects of aCR during short, 16-min epochs. With these results in hand, it will be important to assess whether loosely spaced CR tones will also be favorable in a chronic stimulation setting, with the goal of inducing plastic changes furthering sustained long-term desynchronization and corresponding symptom relief. With regards to the other indices considered—mean relative gap and mean relative overlap—there were fewer models in which the VAS scores were explained solely by those variables, as summarized in Supplementary Table 6.

Of note, acute desynchronizing effects (obtained during stimulation) are not necessarily predictive of long-term desynchronizing effects emerging after cessation of stimulation. For instance, a theoretical study in spiking neuronal networks with STDP receiving periodic stimulation revealed complex and counterintuitive stimulus-response relationships between acute (de)synchronization during stimulation and sustained, long-lasting (de)synchronization emerging as time evolves after cessation of stimulation (Kromer and Tass, 2020). In particular, synchronization during stimulation may be followed by long-lasting desynchronization, and desynchronization during stimulation may end up in long-lasting synchronization. From a computational standpoint, acute desynchronizing effects of CR stimulation are favorable but not predictive of long-term desynchronization (Manos et al., 2018; Kromer and Tass, 2020), for which reason the gap index is not necessarily predictive of long-term effects.

There are some important differences between regular and noisy aCR that are worth mentioning. First, regular and noisy aCR differ slightly with respect to acute after-effects. In the original Adamchic et al., 2017 study, while both stimulation protocols caused significant after-effects on tinnitus loudness, only noisy aCR led to a significant reduction of tinnitus annoyance after the end of stimulation. From an electrophysiologic standpoint, regular aCR caused a significantly longer and stronger decrease of the delta band power, longer and stronger increase of alpha band power, and significantly longer decrease of gamma band power (Adamchic et al., 2017). However, interestingly in the window of 80–90 s after stimulation, the reduction in gamma band power is superior after noisy aCR. There is evidence to suggest that the gamma band is more pertinent to the loudness of the tinnitus percept (Van Der Loo et al., 2009), so once again, this may be why only noisy aCR showed a statistically significant acute after-effect in VAS-L after therapy, while regular aCR does not (and hence also why the gap index is only a significant predictor for VAS-L after noisy aCR).

These electrophysiologic differences suggest a likely underlying mechanistic difference. The two protocols also differ with respect to long-term effects. While noisy aCR does have an acute on-effect, this effect is not long-lasting. After cessation of stimulation, only regular aCR has a lasting off-simulation effect, while noisy aCR does not (Tass et al., 2012a). Because regular and noisy aCR demonstrate marked differences in the duration of effect as well as in electrophysiologic changes induced, it stands to reason that the underlying mechanism of the two protocols may be different. For example, as described in (Adamchic et al., 2017), the reduction of delta band power after the end of regular aCR was more pronounced and lasted longer than that after noisy aCR. Noisy aCR may behave similar to a masker, suppressing the tinnitus via feed-forward inhibition rather than strictly via long-lasting desynchronization (Roberts, 2007), though this is not known. Despite the possible differences in underlying mechanism between regular and noisy aCR, we found in this study that wider ERB spacing was found to be beneficial for both regular and noisy aCR. The reason for this is yet unknown. One possibility is that wider ERB spacing in noisy aCR leads to a greater degree of masking. As shown in Supplementary Figure 5, the mean relative overlap of CR tones 2 and 3 is negative for noisy aCR, indicating greater spacing. Evidence suggests that masking may be most efficient for sounds of frequency just below the tinnitus frequency (Terry et al., 1983). With a higher degree of spacing between tones, it may be that the functional spectrum of noisy aCR is wider on average, thus possibly contributing to greater residual inhibition, but this is speculative and requires further investigation. Furthermore, as was seen in (Tass et al., 2012a), the pitch of patients’ tinnitus tended to shift downward over the course of therapy in regular aCR. One possible explanation for this may be evident from the relative gaps. As seen in Supplementary Figure 1, in regular aCR, the pairwise relative gaps increase with increasing tone frequency in regular aCR (i.e., in (A), G   ( 1,2 ) <   G ( 2,3 ) < G ( 3,4 )   on average), while in noisy aCR this is not true (i.e., in (B), G   ( 1,2 ) <   G ( 3,4 ) < G ( 2,3 ) on average). This may contribute to the lowering of the tinnitus pitch with therapy which has been observed with regular aCR only, on account of a possible downshifting of the tinnitus focus due to disproportionately effective desynchronization at higher stimulus frequencies in regular aCR.

Additional studies are required to validate the findings of this acute effects clinical study. To that end, there are several important considerations discussed herein that impact the interpretation of these results and the design of future experiments. Firstly, the ERB model itself utilizes several assumptions, which may limit the generalizability of this approach to specific subgroups of tinnitus patients. Secondly, various cochlear nonlinearities can impact the frequency specificity and thus the frequency-to-place match of auditory tonotopy which are unaccounted for in the existing ERB-transformation of CR tones. Thirdly, peripheral estimations of frequency selectivity are reasonable but imperfect representations of cortical tuning, i.e., the ERB model represents the behavior at the level of the basilar membrane more closely than it may represent the auditory cortex in full, which is more difficult to probe non-invasively. And finally, ascertaining an accurate pitch match is a necessity of aCR in order to determine the correct f _T around which to place the therapeutic tones, whether using fixed spacing or ERB-based spacing. Each of these considerations is discussed in detail in the Supplementary Discussion.

Auditory filter widths tend to broaden in individuals with cochlear deficits (Florentine et al., 1980; Glasberg and Moore, 1986), with the bandwidth typically increasing with increasing threshold. As described in Eq. 2, the ERB widths for hearing-impaired listeners can be estimated as a function of threshold at a given center frequency. However, there are some limitations to this approach. Firstly, this relationship does not hold for thresholds greater than 50 dB HL (Moore et al., 1999). Secondly, the relationship between ERB width and center frequency is best established for frequencies from 2,000 to 6,000 Hz (Moore et al., 1999), thus it is harder to comment on relationships outside of this spectral range. The tinnitus frequency in this cohort ranged from 675 to 9,800 Hz. Of the 36 ears across 18 patients, seven ears had a tinnitus pitch match between 2,000 and 6,000 Hz.

Notably, there is a weak correlation between threshold elevation on audiometry and the widening of the filter bandwidth, as there is variability on an individual level in the degree of broadening and in the asymmetry of the filter, possibly due to varying patterns of cochlear damage (Moore, 1995). This points to a need for measuring the ERB directly rather than estimating it from the absolute threshold, as was done in Eq. 2, in order to attain truly perceptually relevant tone spacing for aCR in any given individual.

Furthermore, the analysis was done on previously acquired data. As a result, it was not possible to manipulate the spacing of CR tones independently of the hearing thresholds, for which reason the 5-PTA demonstrated multicollinearity, i.e., high intercorrelation, with the gap index, mean relative gap, and mean relative overlap. In each of these multiple linear regressions, the 5-PTA variable was residualized to help reduce the effect of multicollinearity, as described in Primary Analysis. This involves regressing the two predictor variables and using the resulting residual variance in the overall multiple linear regression instead of one of the original predictors. However, this is a statistical estimation of the residual variance of the 5-PTA, and as a result, it is not possible within the framework of this re-analysis to definitively eliminate the relationship of hearing loss to each of these measures of tone spacing. In the future, additional experiments would require a within-subject approach to vary the tone spacing on the frequency axis (rather than the estimated ERB axis alone) while holding the underlying hearing thresholds constant in order to eliminate the effect of hearing loss on the ERB spacing arrangements. Ultimately, on account of these limitations, direct measurements of auditory filters may be required in individual patients rather than estimations based on tinnitus pitch and hearing thresholds. In the Supplementary Methods, we describe several methods by which the ERB widths may be directly measured in future studies. Additionally, in the Supplementary Discussion, we describe in further detail several other limitations and considerations unique to the ERB model, as introduced in Overall Findings.

Based on the results of this study, we hypothesize that a larger gap index—and thus more loosely spaced CR tones—may improve the ability of tinnitus patients to respond positively to aCR acutely. Follow-up studies would involve the direct measurement of the ERBs of the auditory filters centered at the therapeutic tone frequencies, such as with one or more of the “rapid” methods described above. A first experiment may involve traditional, fixed spacing aCR compared head-to-head with aCR with some specified larger gap index between the ERBs of the therapeutic tones, on both an acute and chronic stimulation basis. Furthermore, our study at present was limited to the analysis of self-reported questionnaire data. Subsequent experiments should consider electrophysiologic measures of desynchronization as well, to assess the power changes that may result from different ERB-based aCR paradigms.

As a result of the afore mentioned cochlear nonlinearities and the related effect of stimulus level used to probe the auditory system’s frequency selectivity, it is evident that the desynchronization ability of individual CR tones may depend on more than simply the degree of overlap or gap between the corresponding ERBs. Upward and/or downward spread of masking, as well as lateral suppression, may have additional effects on CR efficacy, dependent on the magnitude and perhaps directionality of the individual inter-tone effects. As an example, if in fact there is pathologic downward spread of masking in SNHL, then higher frequency tones above f _T may themselves to some extent mask the tinnitus frequency. High-frequency CR tones may in theory also decrease the efficacy of lower-frequency CR tones. The inverse could be seen in excess upward spread of masking. To parse out these effects, follow-up experiments in tinnitus subjects may involve pairs of tones above and below the tinnitus frequency. The distance between the CR tones themselves and the distance between the CR tones and f _T could be varied systematically in order to determine degree of subjective tinnitus relief as well as degree of electrophysiologic desynchronization resulting from various spacing configurations. Considering as well that CR tones may be susceptible to the effects of forward masking, in which a probe tone is masked by a preceding masker tone, the temporal spacing of CR—in addition to frequency spacing—may also be an avenue of further exploration.

It should be noted that when reversing the residualization procedure in the methods, such that the residual variance of the gap index is calculated toward the 5-PTA, the model yields the same adjusted R ² and p-value as the original analysis, as shown in Supplementary Table 3. However, the only significant predictor variable now is the 5-PTA, rather than the residual variance of the gap index. From this, one could ask whether the hearing loss is the true predictor variable of the effect on VAS-L during aCR, rather than the tone spacing driving the effect. However, as shown in Figure 3A, the gap index does not simply depend on the average hearing impairment around f T . The gap index strongly depends on shape of the audiogram around f T . To that end, several studies will be necessary in further disentangling the impact of hearing loss versus the impact of tone spacing on clinical outcome.

As shown in Figure 3A, the largest values of the gap index are, on average, for normal hearing, and the gap span (or the range of gap values dependent on the hearing impairment) increases with increasing f _T . If normal hearing is more favorable, rather than inherently larger gap indices, we could provide a normal hearing subject with a relatively high f _T , such as on the order of 8 kHz, regular CR tones (in which the predicted gap index would be low for this patient). If the acute effect is favorable with significant tinnitus suppression during therapy, it may be that the absence of hearing impairment, rather than the tone spacing, is associated with clinical improvement. Further, if we were to provide wider tone spacing to this subject (essentially the spacing one would expect for an individual with moderate hearing loss) and the patient does not have clinical benefit, again this would suggest that the absence of hearing impairment is associated with improved outcomes, rather than loosely spaced tones on the ERB scale. The same effect should be observable throughout the f _T range. However, due to the fact that the gap span increases with increasing f _T , we hypothesize that the difference between regular CR tone spacing and the mimicked hearing impairment spacing would be greatest when f _T is on the higher end of the spectrum (such as in the aforementioned hypothetical patient with an f _T of 8 kHz).

In an additional related experiment, one could test a patient with moderate hearing loss. With hearing loss, the gap index tends to decrease. To compensate for hearing impairment, we could increase the spacing and thereby the gap index. If the patient has a clinical reduction in tinnitus loudness during CR, this could mean the tone spacing is the more salient predictor than the hearing loss. In each of these cases, whether normal hearing or moderate hearing loss, we could provide the aCR tone spacing expected in the opposite scenario to differentiate the effects of hearing threshold and tone spacing. Furthermore, it would be of immense utility to test patients whose audiograms demonstrate hearing loss above the f _T , hearing loss below the f _T , and hearing loss in the vicinity of f _T, thereby directly measuring outcomes with differently shaped audiograms, as was done in Figure 3A for the 26 dB hearing loss.

Overall, the results of this study are a first step in the clinical optimization of tone spacing for aCR in order to obtain maximal anti-kindling and long-term therapeutic benefit. Broader spatial stimulation of CR tones, as indicated by higher gap indices, may result in improved relief from tinnitus loudness and annoyance in the acute stage of therapy. Additional studies are required to determine electrophysiologic correlation of these findings, to assess the impacts of chronic stimulation, and to correlate measured rather than estimated auditory filter widths with symptom and electrophysiologic data.