Psychophysics studies the relationship between physical stimuli and their evoked sensations. In contrast, tinnitus is an auditory percept in the absence of external sounds. It is not surprising that we face a conceptual dilemma in studying the tinnitus sensation directly. This dilemma is best exemplified by the inconsistent subjective estimate of tinnitus, which can be unusually loud, but often matched to a soft external sound that is only 10–20 dB above the sound threshold (e.g., Moore, 2012). Alternatively, we can study the effect of tinnitus on perception of external sounds indirectly. This alternative approach would have the same psychophysical foundation while allowing examination of neural mechanisms underlying tinnitus.

An active loudness model took such an approach to decompose loudness growth into an additive noise source that determines loudness at thresholds and a nonlinear gain that determines the slope of loudness growth (Zeng, 2013). The active loudness model allows psychophysical investigation into the neural mechanisms underlying tinnitus and other related disorders. For example, if tinnitus increases the central noise, then one would predict increased loudness at the threshold. While previous studies found greater than normal loudness at the threshold in individuals with hearing loss (Buus and Florentine, 2002), no studies measured loudness at the sound threshold in tinnitus subjects. Also note that it is routine to use an external sound to match tinnitus loudness or measure the upper loudness level (e.g., Tyler and Conrad-Armes, 1983; Vernon and Meikle, 2003; Gu et al., 2010; Zeng et al., 2020), but few studies obtained the entire loudness function and none explicitly measured loudness at thresholds (Penner, 1986; Hebert et al., 2013; Erinc and Derinsu, 2022). On the other hand, if tinnitus increases the central gain, then one would predict a steepened loudness growth function. Although previous studies found steepened loudness growth in tinnitus subjects, these subjects had either hearing loss or hyperacusis that might confound the result (Penner, 1986; Hebert et al., 2013).

Conceptually, both the central gain and noise are well defined. First, the gain is the slope of an input-output function, which can be measured in terms of the relative change in evoked neural activities or behavioral outcomes such as loudness and reaction time in response to a given range of input. The increased central gain model is based on the observation that the peripheral output is reduced but the central output restored or even enhanced in response to apparent or hidden hearing loss (e.g., Norena, 2011; Schaette and McAlpine, 2011; Auerbach et al., 2014; Sedley, 2019). Second, the increased central noise may manifest itself in terms of both spontaneous and evoked activities. Similar to the central gain model, hearing loss reduces the spontaneous activity in the auditory nerve (Liberman and Kiang, 1978) but increases it in the central pathway (Kaltenbach and Afman, 2000). Different from the central gain model, the central noise may not change the gain in terms of the average spike rate but affect the evoked response in terms of impaired temporal coding, e.g., reduced phase locking to an external stimulus, bursting or oscillation activities independent of the external stimulation (e.g., Norena and Eggermont, 2003; Chambers et al., 2016; Knipper et al., 2020).

Here we used absolute magnitude estimation to measure systematically loudness growth in tinnitus and control subjects. Our hypothesis was that, compared with the control, tinnitus would increase loudness at the threshold but not the slope of loudness growth. The present study minimized the potential hearing loss confounding factor by collecting all data at frequencies with normal hearing. The study also controlled the hyperacusis factor by selecting tinnitus subjects with unremarkable hyperacusis.

Figure 1 shows all individual data points from the control (black dots; n = 103) and tinnitus (red dots; n = 78) groups, as well as the fitted power function to each group (thick black line = control; thick red line = tinnitus). The fitted function found that at the threshold, the control group produced a loudness estimate of 0.26, whereas the tinnitus group produced 2.4 times greater loudness of 0.62. The slope of loudness function was similar between the two groups (0.09 for the control vs. 0.08 for the tinnitus).

The same power function was fitted to each stimulus on an individual basis. Figure 2A shows the distribution of individually predicted loudness at thresholds (circles = individual data, bars = mean + std) between the tinnitus (left bar with orange circles; n = 78) and control (right bar with blue circles; n = 103) groups. On average, the loudness at thresholds was 2.3 times greater in the tinnitus than the control group (0.77 ± 0.72 vs. 0.34 ± 0.24; two-tailed t-test, df = 179, p = 0.002). In contrast, there was no significant difference in the slope of loudness function between the tinnitus and control groups (Figure 2B; 0.20 ± 0.11 vs. 0.23 ± 0.11; two-tailed t-test, df = 179, p = 0.08).

Following a classic absolute magnitude estimation technique, the present study found that the average loudness at the threshold was 2.3 times greater in 11 tinnitus subjects than in nine control subjects, while the average slope of their loudness functions was not significantly different. It is worthwhile to note several contexts surrounding the present study. First, the present result was obtained under normal audiometric thresholds and with unremarkable hyperacusis in both tinnitus and control subjects. Second, the present study did not control for age, nor did it complete data collection for all stimuli in all subjects. Third, the small sample size (11 tinnitus and nine control subjects) limits the generalization of the present results.

The present study can be compared to previous studies. Penner (1986) used a similar magnitude estimation technique to measure loudness growth at 1 kHz and tinnitus frequency (3.5–8.0 kHz) in 10 tinnitus subjects. She found that the slope of loudness function was much greater at the tinnitus frequency than the 1 kHz (0.74 vs. 0.28), but this difference was due to hearing loss at the tinnitus frequency because eight of her 10 subjects had hearing loss (25–69 dB SPL) while the remaining two without hearing loss had similar slope (0.20 and 0.36, see her Table 1). Hebert et al. (2013) used a scaling method to measure loudness growth at 1 and 4 kHz in 63 tinnitus and 53 control subjects. Controlling for hearing loss, they found that the tinnitus subjects had steeper than normal slope at both frequencies. Because the greater slope was a result of increased sensitivity to loud sounds and 60% of them had a hyperacusis score >10, they interpreted the steeper slope as an increased central gain. While hyperacusis and tinnitus are co-morbid, Erinc and Derinsu (2022) were able to find 20 subjects with mostly hyperacusis and additionally 20 with mostly tinnitus. They also used the scaling method to measure loudness growth at 0.5 and 2 kHz and found that only the hypercusis subjects had increased sensitivity. The present result is consistent with the Erinc and Derinsu finding that tinnitus does not increase sound sensitivity after controlling for hearing loss and hyperacusis.

To the extent that loudness reflects system-level neural processes, the present result supports the hypothesis that tinnitus increases the central noise but not the central gain (Zeng, 2013). The previously observed steeper than normal slope of loudness growth in tinnitus subjects reflects more likely the co-morbid hyperacusis (Penner, 1986; Hebert et al., 2013), which is a result of the increased central gain (Norena, 2011; Schaette and McAlpine, 2011).

Although the present study favors the central noise model in tinnitus, it remains to be worked out what central sources are involved and how they influence the central noise or gain in response to peripheral changes and their eventual system-level outcomes (e.g., Li et al., 2013; Wang et al., 2023). A potential means of separating the central noise and gain contributions is to examine the central variance, which should grow linearly with the additive central noise but nonlinearly with the multiplicative central gain (Zeng, 2020a). Psychophysically, the difference limen in intensity may serve as an indirect measure of the central variance (Zeng, 2020b).

The present study found that compared with the normal control, tinnitus subjects had increased loudness at the threshold, but unchanged slope of the loudness growth. This finding supports the increased central noise hypothesis in tinnitus. The strength of the evidence is limited by the uneven age, incomplete dataset and small sample size in the present study.

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

The studies involving humans were approved by University of California Irvine Institutional Research Board. The studies were conducted in accordance with the local legislation and institutional requirements. Written informed consent for participation in this study was provided by the participants' legal guardians/next of kin.

KT: Investigation, Data curation, Formal analysis, Methodology, Software, Writing—review and editing. F-GZ: Investigation, Conceptualization, Funding acquisition, Project administration, Supervision, Writing—original draft.