# Temporal modulation transfer functions derived from envelope following responses: what can they tell us about auditory midbrain tuning properties?

Emmanuel Ponsot, Victor Bauer, Nathan Goedseels, Clémence Basire,
Laurianne Cabrera

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## To cite this version:

Emmanuel Ponsot, Victor Bauer, Nathan Goedseels, Clémence Basire, Laurianne Cabrera. Temporal modulation transfer functions derived from envelope following responses: what can they tell us about auditory midbrain tuning properties?. Journal of Neurophysiology, 2025, 135 (1), pp.42-50. 10.1152/jn.00363.2025 . hal-05440930

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SHORT REPORT

Sensory Processing

Temporal modulation transfer functions derived from envelope following
responses: what can they tell us about auditory midbrain tuning properties?

ID Emmanuel Ponsot,¹ Victor Bauer,¹ ID Nathan Goedseels,¹,² ID Clémence Basire,¹,³ and
ID Laurianne Cabrera³

¹STMS Lab (CNRS/Ircam/Sorbonne Université/Ministère de La Culture), Paris, France; ²Research Group ExpORL, Department of Neurosciences, KU Leuven, Leuven, Belgium; and ³Integrative Neuroscience and Cognition Center (INCC-UMR 8002), Université Paris Cité-CNRS, Paris, France

Abstract

This study investigates how the properties of neural temporal modulation transfer functions (TMTFs) derived from envelope fol-
lowing responses (EFRs) to amplitude-modulated sounds relate to the hypothetical tuning of individual neurons in the midbrain.
We followed a joint modeling and empirical approach. We measured EFRs for young adults with normal hearing (n = 15) using
rectangular amplitude-modulated (RAM) tones with modulation frequencies varying between 70 and 160 Hz, to target the most
sensitive region of brainstem/midbrain neurons. These empirical data portrayed a large variability across individuals, both in
terms of TMTF shapes and gains; at the individual level, most individuals exhibited TMTFs band-pass or low-pass in shape, but
at the group level, there was no significant trend. We also conducted simulations using computational models of the auditory
periphery and midbrain to examine how simulated, EFR-derived TMTFs vary depending on hypothesized models of inferior-colli-
culus (IC) neurons, their parameters, and distributions. When considering a population of band-pass-tuned IC cells with varying
best modulation frequencies, simulations suggest that the magnitude of the TMTF, rather than its shape, might actually better
reflect a change in tuning. These experimental and simulation results are discussed in relation to previous works, along with
additional simulations showing that the type of stimulus envelope (sinusoidal vs. rectangular modulation) or subtle threshold var-
iations among individuals with normal hearing have only a limited impact on these trends. From these results, we derive several
considerations for the interpretation of EEG-based TMTFs and the potential information they provide regarding auditory midbrain
tuning.

**NEW & NOTEWORTHY** What do EEG-derived temporal modulation transfer functions (TMTFs) tell us about human auditory midbrain tuning? We found substantial individual variability in both the shapes and gains of empirically derived TMTFs. Computational model simulations suggest that the TMTF's magnitude, rather than its shape, might better reflect underlying neural tuning changes. These results provide new perspectives for modeling individual differences and for developing more sensitive clinical tests of subcortical temporal processing.

computational auditory models; computational modeling; envelope following responses; midbrain; temporal modulation transfer
functions

INTRODUCTION

The human brain's capacity to encode temporal envelope
information in auditory signals is crucial for processing nat-
ural sounds such as speech. This processing involves distinct
neural substrates that are progressively tuned to slower tem-
poral modulations along the auditory pathway, from the

cochlea and auditory nerve to the brainstem/midbrain and
up to the cortex (1). The envelope-following response (EFR),
which captures the overall ability of auditory neurons to
phase-lock to the envelope of sound, can be recorded using
electroencephalography (EEG) and provides an objective
tool to probe the characteristics of temporal modulation
processing. The EFR has been widely used to study the

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auditory processing of relatively fast modulation frequencies around ~80–200 Hz. Within this frequency modulation range, the EFR is primarily thought to result from neural generators in the auditory brainstem and midbrain, and therefore reflects the combined processing of auditory nerve (AN) and brainstem/midbrain functions (1–4).

One of the current challenges in hearing science is to develop an efficient measure of temporal processing that could be used to probe an individual's hearing status, beyond sensitivity. To objectively characterize the temporal processing fidelity of the auditory system, EFR-based temporal modulation transfer functions (TMTFs) have been derived for over 30 yr, following either static, that is, testing one modulation frequency at a time (5, 6), or dynamic approaches, that is, using sweeps of modulation frequencies (4, 7–9). Such an assay (either following a static or a dynamic approach) is appealing for at least two reasons. First, it is objective and therefore constitutes a direct characterization of sensory neural coding less hampered by subjective psychophysical measurements, inherently shaped by attentional and cognitive factors. Second, it can be deployed identically across participants of all ages, from newborns to older adults. It can also be used with patients for whom it is difficult or impossible to obtain behavioral responses, as well as in animals, paving the way to translational research.

Previous studies consistently observed that EFR-derived TMTFs, covering a large range of frequencies, for example, from ~10 to 1,000 Hz (9), exhibit an overall low-pass morphology. Such a function provides an overall image of how the entire auditory system is able to phase-lock at different input frequencies. It is widely assumed that different auditory structures are predominantly involved in specific frequencies with a certain overlap: responses to frequencies above 200 Hz resulting mainly from AN neurons, and responses to frequencies below 70 Hz resulting mainly from cortical neurons. Indeed, a sinusoidal amplitude-modulated (SAM) tone, for instance, modulated at 120 Hz, will stimulate a broad range of neurons in the inferior colliculus (IC) and brainstem. This includes neurons with a best modulation frequency (BMF) of 120 Hz and also the “tails” of tuning curves from neurons with lower and higher BMFs. In other words, the EFR to a specific modulation frequency provides a compound measure of all neurons responding to this given frequency. As a consequence, EFR-derived TMTFs obtained by varying the modulation frequency of the input AM sound lead to a function exhibiting a low-pass morphology. Similarly, TMTFs obtained in psychophysics, which exhibit clear band-pass tuning when probed using notched-noise paradigms (e.g., Ref. 10), exhibit low-pass shapes when considering detection thresholds for amplitude modulation (11).

Nonetheless, a number of studies observed that, in addition to this overall decreasing trend with modulation frequency, EFR-based TMTFs also exhibit local peaks at modulation frequencies around 15 Hz, 40–50 Hz, and 80–100 Hz (5–7, 12). These peaks are thought to reflect dominantly cortical processing for modulations below 70 Hz, and subcortical processes (brainstem/midbrain) for modulations between 80–100 Hz. EFR-based TMTFs are thought to reflect

the total phase-locking activity of a population of units with varying BMFs. Peak activity in the 80–100 Hz region is qualitatively consistent with the known filtering properties of neurons in the auditory midbrain, in particular in the inferior colliculus (IC), where the majority of units exhibit band-pass tuning with BMFs close to 100 Hz (13). Yet, the putative relationships between the local peaks in EFR-based TMTFs and the filtering properties of underlying subcortical units discussed here remain qualitative, and further study is required to establish a quantitative link between the two.

Importantly, both the paradigm and the nature of the modulation have been shown to impact the EFR-based TMTF. Although most previous research has focused on the EFR to SAM sounds, studies specifically addressing cochlear synaptopathy have considered the EFR to rectangular amplitude-modulated (RAM) tones (14–16). RAM-EFRs are proposed to be potential candidates for characterizing the neural coding of temporal fluctuations because they lead to stronger responses than SAM-EFRs and are less affected by concomitant losses in outer-hair cells (OHCs), as suggested by computational simulations and empirical measurements (14). Parthasarathy and Bartlett (17) empirically investigated the influence of envelope asymmetry (sinusoidal/ramped/damped) of AM sounds on EFRs in rats, by assessing their respective sensitivity to aging for different modulation frequencies. To the best of our knowledge, no previous studies have used RAM sounds to derive neural TMTFs in humans. It is therefore relevant to ask whether the use of rectangular, compared with sinusoidal, envelopes would yield different results in this context.

Finally, psychophysical data show that the shape of TMTFs differs according to the listeners' intrinsic characteristics, such as age (10), aligning with neuroimaging studies showing poorer temporal selectivity in older listeners (18). Previous studies in animals and humans have shown that EFR-based TMTFs evidenced band-pass tuning in the 80–100 Hz region that gradually sharpens during the early stages of development, specifically during infancy (19, 20). The impact of aging on EFRs has been documented at very high modulation frequencies (~1,000 Hz) and is presumably linked with the loss of auditory nerve (AN) fibers (21). Surprisingly, however, we are lacking a direct assessment of the effect of aging on neural TMTFs in the midbrain range (~100 Hz) of modulation frequencies.<fnref n="1" />

In addition to these maturation effects, EFR differences are still observed among young adult listeners with clinically normal audiograms. These differences likely reflect supra-threshold coding variations beyond cochlear processing. Gransier et al. (6) demonstrated substantial interindividual differences in TMTFs across listeners, but their characterization remained limited up to 100 Hz. In studies characterizing TMTFs across a larger range of modulation frequencies, a large variability across individuals was observed, but it was not specifically assessed or discussed (4, 9).

In sum, although the EFR-derived TMTF is a promising tool for monitoring individual differences in temporal processing, the quantitative link between human TMTFs and the underlying tuning properties of midbrain neuron

<footnote n="1">¹One notable exception comes from extracellular recordings in the rat IC by Parthasarathy et al. (22). Their study found an increase in modulation sensitivity with aging in the 100 Hz region, which they interpreted as an effect of increased central gain.</footnote>
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populations remains poorly understood. The present study addresses this gap through a joint empirical and computational modeling approach designed to bridge the EEG and single-neuron levels of tuning consideration. First, we empirically characterize RAM-based TMTFs within a cohort of young adults with normal hearing. These data provide a crucial reference point for the extent and type of variability that models must explain. Second, we use computational simulations to address how specific features of these EEG-based TMTFs—namely their overall magnitude and band-pass/low-pass shape—relate to changes in the hypothesized tuning properties of the underlying IC neuron population. By analyzing the empirical variability in light of model predictions, we discuss which neural tuning parameters are most plausibly reflected in the human EFR data. Finally, we use the developed modeling pipeline to evaluate the practical impact of key methodological and individual factors, such as the use of RAM versus SAM sounds and subtle differences in audiometric thresholds. This combined strategy allows us to derive principled considerations for interpreting EEG-based TMTFs and the information they provide about auditory midbrain function in individuals.

# MATERIALS AND METHODS

## Participants and Audiometric Testing

A group of 15 young participants with normal hearing [13 females; age (means ± SD), 24 yr ± 5] was recruited for this study. Pure-tone audiometry in quiet was conducted bilaterally at conventional frequencies (0.125, 0.25, 0.5, 1, 2, 4, and 8 kHz). The participant's best ear was chosen for further testing. All individuals had normal or close-to-normal hearing thresholds in their best ear (≤30 dB hearing level, HL). Among the 15 participants, 11 had hearing thresholds equal to or better than 20 dB HL at all frequencies, 3 participants had a threshold equal to 25 dB HL at one frequency, and 1 participant had a threshold equal to 30 dB HL at one frequency. Individual audiograms are displayed in Supplemental Fig. S1.

## EEG Measurements

### RAM stimuli.

Rectangular amplitude-modulated (RAM) stimuli of various modulation frequencies were created following Vasilkov et al. (14); a rectangular envelope modulation with 95% modulation depth and a duty cycle of 25% was imposed on a 4-kHz tone carrier. The modulation frequency could take one of five values: 70, 90, 110, 130, and 160 Hz. Stimuli duration was 400 ms.

### FFR protocol and data acquisition.

All stimuli were generated using MATLAB at a sampling frequency of 48 kHz with 24-bit resolution and then sent to an external sound amplifier to which nonshielded ER3A inserts (Etymotic Research) were connected. Participants were seated in a comfortable armchair in a soundproof booth. Stimuli were presented monaurally to the participant's best ear at 70 dB sound pressure level (SPL, rms). Measurements were conducted during a single session

split into five different blocks, each corresponding to a given modulation frequency condition and lasting ~30 min. The order of blocks was randomized across participants. Each block contained 2,000 stimuli of a given modulation frequency with alternating polarities, separated with an inter-stimulus interval randomly distributed between 100 and 110 ms. EFRs were recorded with a 32-channel system, BioSEMI Active2 system, using the auditory brainstem response (ABR) module, with a sampling frequency of 16,384 Hz. Active electrodes were placed in the EEG recording cap at Cz and each mastoid. The common mode sense (CMS) and driven right leg (DRL) electrodes, which form the active ground, were placed on the forehead, 1 cm on either side of Fpz. All electrodes had offsets <50 mV. Following previous studies and recommendations, the response at Cz referenced to the average response of the two mastoids was considered for analyses (21, 23). The recordings were epoched based on triggers directly obtained from the audio signal that was converted and fed to the BioSemi Ergo channel via an optical cable.

### FFR preprocessing and analysis.

Data were processed using MATLAB. All recordings were first band-pass filtered between 40 and 1,000 Hz and divided into epochs corresponding to each stimulus presentation. We first performed baseline correction by removing the mean computed over all responses. We then performed epoch rejection using a sliding window; the range of the signal (max-min) was extracted for each epoch, and epochs with ranges exceeding three times the median value computed over 200 epochs were rejected. Responses to both positive and negative stimulus polarities were added together to emphasize the envelope component of the response. A bootstrap procedure was used to remove noise and compute the mean EFR spectral magnitude across the available epochs (see Ref. 14). Importantly, this noise-removal bootstrap-based procedure ensured an unbiased comparison of EFR strength corresponding to different modulation frequencies, which would be differently affected by the 1/f distribution of neural noise. For each modulation frequency, EFR strength was estimated by summing the amplitude of the FFT at frequencies corresponding to the first five harmonics of the modulation frequency (only for peaks 2 dB above noise floor level), as it contained most of the power related to the modulation envelope of the stimuli (see Supplemental Figs. S2 and S3). Similar results as those presented here were obtained using phase-locking values (e.g., Ref. 24) instead of the magnitude of peaks in the FFT of the average EFR (see Supplemental Fig. S4).

## Computational Simulations of EFRs

To simulate EFRs, we used a biophysically inspired model of the auditory periphery and midbrain, following the approach recently described by Temboury-Gutierrez et al. (25). All models were taken from the UR_2025a toolbox (MATLAB codes were downloaded from the UR OSF space: https://osf.io/6bsnt/).

The auditory periphery of Bruce et al. (26) was first used to simulate the population response of AN fibers. We only considered AN fibers with high-spontaneous rates (HSR). This
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modeling choice was based on the physiological considera-
tion that low and medium spontaneous rate (LSR/MSR) of
AN fibers do not project directly onto IC neurons, but rather
connect to the efferent pathway controlling the MOC system
(27; but see Ref. 28). However, we controlled how much our
simulations relied on this hypothesis; we observed that at 70
dB SPL, the only impact on TMTFs was an increase in gain of
~2 dB (see Supplemental Fig. S5). Therefore, for all the simu-
lations discussed here, only activity in HSR-AN fibers was
considered. For all simulations, we considered the summed
responses of fibers tuned to 50 characteristic frequencies
(CFs), log-spaced between 125 Hz and 8 kHz.

The mean response of HSR-AN fibers was then given as input to an IC model. We considered and compared two IC models: a band-pass model (BP model) made of a population of band-pass filters mimicking cells from the IC, and the same-frequency inhibition-excitation model (SFIE model), which is a more physiologically plausible account of IC mimicking inhibition and excitation between cells (see Refs. 13, 29). The SFIE model can return the output of band-pass or band-suppressed neurons. In this work, we considered in particular the output of band-enhanced neurons from the SFIE model; additional simulations based on the output of band-suppressed neurons from the SFIE model showed that these were simply offset from those based on band-enhanced neurons. We compared different implementation scenarios for the BP model to assess the extent to which our results relied on the choices of filter parameters for modeling IC responses. Different distributions of band-pass filters were tested: 1) a single best modulation frequency (BMF) value of 100 Hz, or 2) a likely more realistic bank of filters drawn from a Gaussian distribution of BMFs centered on 100 Hz with a standard deviation of 50. We also compared filters with different quality factors (Q-values of 0.5, 1, or 2). Only the original configuration of SFIE model parameters (default values in the toolbox) was tested. In all scenarios, the simulated EFR was taken as the sum of the whole population of band-pass neurons (for the BP model) or band-enhanced neurons (for the SFIE model). Exactly as with the empirical measurements, for each tested modulation frequency, the summed power of the first five harmonics of the simulated EFR was taken as a measure of strength.

RESULTS

Figure 1 shows the simulated EFRs using the proposed (HSR-only AN + IC) modeling pipeline described above. We simulated the EFRs to RAM tones (Fig. 1A) for different modulation frequencies (70–160 Hz) using different IC filter parameters and distributions (Fig. 1B). FFTs of an example simulated EFR are shown in Fig. 1C, highlighting the strongly periodic structure of the responses, where peaks in the responses correspond to multiples of the first harmonics of the input modulation frequency (see Supplemental Fig. S2). We derived the EFR strength by summing the power of the first five harmonics (then dB-scaled) of these representations for different stimulus modulation frequencies. This allowed us to derive TMTFs for different model parameters tested (Fig. 1D). For simulations assuming IC cells as simple band-pass modulation filters, all with a BMF of 100 Hz, these

TMTFs exhibit band-pass tuning at ~100 Hz (Fig. 1D, left). In this condition, the recovered band-pass behavior is clear and its sharpness appears to be directly related to the quality factor of the cells: as expected, cells with higher Q-values led to TMTFs exhibiting sharper tuning. For simulations with IC cells having BMFs more realistically drawn from a Gaussian distribution centered at 100 Hz, TMTFs had different shapes, from low-pass to band-pass, depending on the Q-value considered (Fig. 1D, right). Another difference was that the Q-values of IC cells more strongly impacted the overall gain of the derived TMTFs than their sharpness, with a difference in magnitude of ~20 dB between Q-values of 0.5 and 2. This is illustrated in Fig. 2C, which plots the normalized gains and the slopes (in top and bottom panels, respectively) estimated from linear fits on simulated TMTFs. In comparison, for the SFIE model, TMTFs with a clear low-pass shape were obtained, whether a single cell or a population of cells with different BMFs was considered (Fig. 1D, red curves), with a mean slope from linear best fits at approximately –0.1 dB/Hz (see Fig. 2C, bottom).

In conclusion, these simulations provide novel information regarding how EFR-based TMTFs are theoretically related to the tuning of individual IC cells. Taken together, they show that this relationship is indirect and opaque; the tuning recovered from the TMTFs appears to be related to the tuning of IC band-pass neurons only when assuming a single (or narrow) distribution of IC BMFs. If we assume a more realistic Gaussian distribution of IC BMFs, or band-enhanced neurons from a SFIE model, 1) the TMTFs exhibit a low-pass or even a rather flat shape, and 2) the tuning has a strong impact on the magnitude of the EFRs and, as a result, on the TMTFs.

Figure 2 shows the empirical results obtained in the present study. Figure 2A plots the average, noise-corrected, RAM-EFRs for the five different modulation frequencies tested. Figure 2B shows the individual TMTFs (derived as explained in *EEG Measurements*), and the average TMTF. First, it can be observed that RAM stimuli led to EFRs showing clear phase-locking to the first five harmonics of the stimulus modulation frequencies (Fig. 2A). The power of these first five harmonics was summed to assess EFR strength and therefore derive the resulting TMTF for each participant, shown in Fig. 2B Descriptively, the average TMTF appears to be low-pass (slope approximately –0.02 dB/Hz), but paired *t* tests comparing EFR strength obtained for different modulation frequencies showed no significant effect of modulation frequency (all *Ps* > 0.05, after correction). A look at individual trends portrayed a diversity of shapes, from low-pass to band-pass. The overall magnitude of TMTFs varied strongly across individuals, with a difference of ~15 dB across extreme individuals (Fig. 2C, top). To capture the diversity of TMTFs gain and shape with simple metrics, we first examined the parameters returned by the best linear fits of individual functions. Figure 2 plots the mean and slope of individual empirically derived TMTFs. In particular, the slope values provide a first approximation of the diversity of TMTF shapes across individuals. A *t* test showed no significant difference between these slope values and zero (*P* = 0.15), again providing no support to an overall low-pass behavior. For comparison, the same slopes and gains metrics inferred
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<figure><img src="image_9.png" /><figcaption>**Figure 1.** Simulating EFRs and TMTFs. A: modeling pipeline used to simulate EFRs to RAM tones. RAM tones of different modulation frequencies are used as input signals. The models used are Bruce et al. (26) AN model (HSR neurons only) fed to an IC model. B: two types of IC models were considered; the band-pass (BP) model and band-enhanced neurons from the same-frequency inhibition-excitation (SFIE) model (see the MATERIALS AND METHODS for details). For the BP model, band-pass modulation filters of different Q-values, based on a single filter or a population of Gaussian-distributed filters with varying BMFs around 100 Hz. The simulated EFR was taken as the overall response of the population of IC neurons. C: example FFT of simulated EFR in a specific condition (see text in the *inset*). EFR strength was computed by summing the power of the first five harmonics ($a_1-a_5$), and was then dB-scaled. D: EFR strength was computed for different stimulus modulation frequencies to derive TMTFs. We compared the predictions obtained using band-enhanced (BE) neurons from the SFIE model (red) to those obtained using the BP model based on a single or a population of Gaussian-distributed IC filters BMFs (**left/right panel**), and for different Q-values (color lightness). In each panel, black arrows indicate the mean BMF of the population of IC neurons. AN, auditory nerve; BMF, best modulation frequency; EFRs, envelope following responses; HSR, high-spontaneous rate; IC, inferior-colliculus; RAM, rectangular amplitude-modulated; TMTFs, temporal modulation transfer functions.</figcaption></figure>

from fitting different model configurations on the simulated TMTFs were added to the empirical estimates in Fig. 2C. Note that the TMTF gain of the different models was normalized, so they cannot be compared directly with the obtained data. However, these simulations show that the range of variations between extreme individual cases can be captured by different model implementations. Regarding the TMTF slope, where we could directly compare the simulation results with the empirical data, we observed that model predictions fall with the region covered by our empirical measurements, although these conditions do not fully capture the differences between “extreme” individual results. A finer descriptive analysis of individual variability was attempted by considering individuals’ TMTF shapes. We observed that only 2 out of 15 individuals had indeed “flat” TMTFs with values across modulation frequencies comprised within a 5-dB range; all other individuals exhibited more band-pass or low-pass behavior, but with various shapes and maxima positions. Running a hierarchical clustering of individual functions did not yield any clear clusters of individuals with similar shapes, limiting a more quantitative assessment of this variability.

In sum, the present empirical results showed a large variability in TMTFs across individuals, with most individuals showing a function low-pass or band-pass in shape, but once all aggregated, there was no statistical evidence for deviation from a flat function (Fig. 2B).

DISCUSSION

This study combined empirical EEG measurements with computational modeling to investigate the relationship between envelope-following response (EFR)-derived temporal modulation transfer functions (TMTFs) and the underlying processing in the auditory nerve and midbrain. Our empirical data revealed substantial interindividual variability and an average group-level TMTF that was rather flat in shape, contrasting with the band-pass or low-pass shapes often reported in previous works. This diversity may stem from experimental confounds or reflect genuine differences in inferior colliculus (IC) processing, as we discuss below. Computational models provide a framework for better understanding these differences. Our simulations suggest that TMTF magnitude may be a more informative metric than shape for reflecting population-level tuning in the inferior colliculus (IC).
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**A** Averaged EFRs (n=15)

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**B** TMTFs

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**C** Data vs. Models

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**Figure 2.** Empirical EFRs. **A:** average FFT of EFRs for the five modulation frequencies tested. **B:** average (blue, means ± SE) and individual (black) TMTFs derived from EFR strengths for different stimulus modulation frequencies (the blue dashed line shows the best linear fit). **C:** distribution of TMTF gains (top) and slopes (bottom) from the best linear fits inferred from the *n* = 15 individuals tested. To highlight the extent to which these variations of parameters could be captured by different models, we superimposed on this plot the normalized gains (removing the mean of all models) and slope values for different model configurations (see MATERIALS AND METHODS and Fig. 1 for nomenclature details). BP, band-pass; EFRs, envelope following responses; SFIE, same-frequency inhibition-excitation; TMTFs, temporal modulation transfer functions.

## The Shape of Neural TMTFs: Empirical Data and Model Predictions

A primary outcome of our empirical work is the absence of a clearly tuned, band-pass TMTF at the group level, which somehow contrasts with previous reports. Several methodological factors could account for this discrepancy.

First, we used rectangular amplitude-modulated (RAM) tones, not sinusoidal amplitude-modulated (SAM) tones. These signals have different modulation spectra and also recruit different cochlear frequencies. Compared with SAM tones, the modulation spectra of RAM tones not only contain a single fundamental frequency but also several harmonics (see Supplemental Fig. S2), which therefore result in the recruitment of a broader population of neurons. A comparison of the AN neurons recruited by the SAM versus RAM sounds across CFs shows that different cochlear regions are involved in the response (Supplemental Fig. S5). To investigate how these signal differences impact the resulting TMTF, we replicated our simulations using SAM tones and RAM-75 tones (75% duty cycle) as input signals, and compared the results with those obtained with the RAM-25 tones used in our experiment. Simulations comparing EFRs (Supplemental Fig. S3) and TMTFs based on SAM-EFRs versus RAM-EFRs (Supplemental Fig. S5) showed that the use of RAM tones leads to 1) superior magnitude of EFRs and thus of derived TMTFs for ~3–4 dB and 2) steeper TMTF slopes, either if these are computed from AN or IC responses (see Supplemental Fig. S5). This is particularly true for the RAM-25 tone, which produces low-pass TMTFs at the level of the AN, a shape that is not observed with the SAM tone, and much less with the RAM-75 tone. Thus, the type of sounds’ temporal envelope used to derive the TMTF is expected to result in a TMTF function with different shapes, but our simulations rather suggest that the use of RAM-25 tones in the present study should have reinforced the low-pass or band-pass shape observed. Therefore, these additional simulations suggest that the overall TMTF’s flat shape observed here is

likely not related to the envelope characteristics of the RAM stimuli. It is interesting to note that the gain or signal-to-noise ratio (SNR) advantage for RAM compared with SAM-derived EFRs inferred from these simulations is in line with previous empirical works investigating the stimulus envelopes providing optimal EEG responses (14, 30). This is also consistent with Parthasarathy and Bartlett (17), who experimentally studied the influence of the envelope shape of AM sounds on EFR magnitude. In this work, they found the highest amplitude for damped envelopes (fast attack/slow decay) compared with symmetric envelopes (sinusoidal).

A second factor that might explain the observed overall flat TMTF shape is the measurement paradigm. The coarse sampling of modulation frequencies in our static paradigm may lack the resolution to capture fine-grained tuning compared with dynamic sweeps used in other studies, which also covered a larger range of modulation frequencies (7, 9). In addition, averaging discrete curves obtained from different individuals, who exhibited a significant amount of variability in terms of both shape and peak frequencies, could have produced an overall flat shape. Consistent with this view, an analysis of individual TMTFs showed that the majority of individuals could be categorized as band-pass or low-pass in shape, and only two individuals exhibited flat functions (see RESULTS). In conclusion, there is a benefit of using RAM tones instead of SAM tones to derive TMTFs from a SNR perspective (14), but the relationship between the TMTF shape and the IC processing is probably less direct, so the use of SAM sounds may provide a more direct picture of underlying midbrain tuning properties.

## Beyond Confounding Factors of Interindividual Variability: Meaningful Differences in Midbrain Processing?

A striking feature of our data is the large variability in TMTF shape and gain across a rather homogeneous group of young individuals with normal hearing. We sought to
<figure><img src="image_14.png" /></figure>

determine whether this variability may stem from slight
peripheral coding differences or whether this could be
related to methodological confounds.

First, we asked whether slight differences in audiometric thresholds among individuals in our cohort could explain part of the observed variability. Additional simulations shown in Supplemental Fig. S6 indicated that the slight variations in audiometric thresholds within our cohort have only a minimal impact on EFRs and TMTF properties, effectively ruling out peripheral sensitivity as a major contributor. This is in line with the simulations of Vasilkov et al. (14), who showed that an advantage of using RAM tones instead of SAM tones for deriving synaptopathy-sensitive EFRs was that they were minimally impacted by concomitant OHC losses. Kale and Heinz (31) used the modulation response gain obtained from direct recordings in the AN in response to SAM tones to derive TMTFs for chinchillas with normal hearing or with a noise-induced hearing loss. In noise-exposed compared with normal AN fibers, the TMTF gain was enhanced, but the shape remained unaffected. Taken together with the observation that human RAM-EFRs are almost not affected by losses in OHCs, it is interesting to note that this paradigm could be deployed to compare brainstem tuning for listeners with or without hearing loss, without having to account for their differences in peripheral coding.

Finally, another potential confound is related to the directionality of neural generators: if directionality changes with varying modulation frequencies, measurements conducted with a single fixed electrode position would be biased. Interindividual differences in EFRs/TMTFs captured with only a few electrodes, generally thought to provide meaningful information regarding differences in temporal coding fidelity (9), could also reflect differences in directionality among individuals and modulation frequencies. To minimize potential confounds of neural directionality patterns, one solution might be to record neural activity using multiple electrodes and then average their activity (6). Large interindividual differences not only in overall EFR strength, but also regarding the relative strength of each harmonic, were already reported for frequency following responses (FFRs; 32). The large interindividual differences in FFRs are proposed to mainly result from the phase relationships of neural generators (33).

Having considered these confounds, the persistent vari-
ability likely reflects genuine individual differences in tem-
poral coding. A modeling approach provides a direct link to
the underlying processing parameters, showing that varia-
tions in IC parameters—such as the sharpness of tuning
or the balance of excitation and inhibition—naturally pro-
duce the range of TMTF patterns we observed empirically.

Theoretically, if the brainstem/midbrain is simply mod-
eled as a population of band-pass filters with BMFs restricted
to a somewhat narrow range, the resulting TMTF shape
should also exhibit a band-pass shape. This can be observed
in our simulations implementing the IC model with a single
band-pass filter (BP model) tuned to 100 Hz, more particu-
larly for Q-values of 1 and 2. However, when the same IC
model is made of band-pass filters having BMF varying over
a certain range, or for a single BMF with a Q-value of 0.5, our
simulations showed that the resulting TMTFs no longer

exhibit clear band-pass shapes: they appear rather low-pass
or even flat. When considering the SFIE model, the simu-
lated TMTFs exhibited a low-pass shape. Thus, TMTFs are
predicted to exhibit band-pass behaviors only under very
specific modeling hypotheses that are probably not realistic.
However, it is important to note that these simulations
rely on our assumption that frequency/envelope following
responses (FFRs/EFRs) can be approximated by the response
of HSR-AN neurons fed to band-pass neurons. At present, it
remains unclear how FFRs can be best simulated using a
computational model of the auditory periphery. It is then
relevant to address the influence of this modeling choice on
the results.

A possible alternative strategy for simulating EFRs is to
consider the summed AN response, or after convolution
with a unitary response, to simulate the transfer function
from the neurons to the scalp where the recordings are made
(25). We replicated our simulations with these two alterna-
tive implementations (not shown), and observed that the
simulated TMTFs resulted in a low-pass function similar to
the one obtained with the IC BP filter with the lowest Q-value
(Fig. 1D).

Considering the IC model to consist only of a population
of band-pass filters is clearly a crude model of midbrain
processing. Animal physiological studies showed that the IC
is composed of multiple populations of neurons, with low-
pass, high-pass, band-pass, and band-suppressed behaviors,
the latter being the most representative category (see Refs. 13
and 29). We therefore tested the same-frequency inhibition-
excitation (SFIE) model as a more complex account of IC
including inhibition and excitation between cells (proposed
in the same toolbox), which can return the output of band-
enhanced and band-suppressed neurons. The simulated
TMTFs were low-pass with a similar slope for both band-
enhanced and band-suppressed outputs (the two functions
primarily differed in magnitude). In conclusion, these simu-
lations showed that a band-pass TMTF is only predicted with
a specific modeling choice of band-pass cells all with the
same (or very similar) BMFs.

At present, we still lack human and animal studies com-
paring directly simulated and measured IC responses.
Further research in that direction is important to assess how
empirical EFRs can be best accounted for by computational
models.

Clinical Implications and Cautious Interpretation of EFR
Strength

The translation of EFR measures into clinical biomarkers, particularly for cochlear synaptopathy, requires careful consideration of the present findings. EFR strength is currently proposed as a marker for cochlear synaptopathy (14, 34, 35). Although EFR strength is directly linked to the remaining number of AN fibers (36), our simulations demonstrate that it is also profoundly influenced by the tuning properties of IC neurons, which are presumably also contributing to neural responses for modulation frequencies at ~100 Hz. This dual dependency complicates the interpretation of EFR strength as a direct marker of cochlear synaptopathy. For instance, in an aging individual, the expected decline in EFR strength due to cochlear synaptopathy (modeled as a
<figure><img src="image_15.png" /></figure>

reduction of both L/MSR and HSR AN fibers; see Refs. 14 and 16) could be counteracted by an age-related broadening of IC tuning, which might artificially bolster the response. This opposing effect could mask underlying pathology, making EFR strength to sounds modulated at ~100 Hz a less sensitive and transparent marker of cochlear nerve integrity than previously assumed. Works using EFRs with tones modulated at higher frequencies (500–1,000 Hz) to assess cochlear synaptopathy are presumably much less contaminated by these potential changes in midbrain processes, because their contributions at these higher modulation frequencies would be minimal (37). Furthermore, an increase in EFR gain could also result from maturational processes occurring at the cochlear and AN level (axonal myelination; 20).

In conclusion, although EFR strength is potentially an interesting marker to assess age-related changes, these analyses highlight the need to consider the potential multiple contributions of peripheral and central stages.

## Future Directions: Toward a Model-Based Assay of Brainstem/Midbrain Function, and Relationship with Behavior

Once confounding factors related to interindividual differences across modulation frequencies are adequately addressed, the potential of the current approach lies in developing an objective assay to probe an individual's brainstem/midbrain auditory processing characteristics. The combination of EFR-based TMTFs with computational modeling is a powerful step in this direction. A compelling future application is to invert this approach: using an individual's empirical TMTF to find the best-fitting parameters of an IC model. Depending on the IC model considered, this fitting process could yield quantitative estimates of parameters such as the distribution of neural tuning (BP model) or the strength and time constants of excitatory/inhibitory circuits (SFIE model). Such model-based analysis would be valuable for tracking developmental maturation in infants and for objectively quantifying the specific contributions of peripheral and central deficits to auditory processing disorders in older adults. By moving beyond a simple consideration of magnitude toward a computational characterization of neural tuning, the EFR could become a precise tool for diagnosing the functional integrity of the auditory pathway across the lifespan.

Another interesting direction for the present line of research is to study the link between interindividual differences in TMTFs and related psychophysical performance. Only few previous studies discussed the link between EFR-based TMTFs and perception, either regarding the maximum modulation frequency that can be detected (7) or the minimal amplitude modulation that can be detected at a given modulation frequency (see Ref. 6). Regev et al. (10) recently provided psychophysical evidence of broader frequency selectivity in the temporal envelope domain with aging in humans, in particular for processing temporal modulations at 64 and 128 Hz, which is likely constrained by the temporal filtering properties of subcortical units. Future studies should determine whether EFR-based TMTFs corroborate these psychophysical observations of less sharp band-pass TMTFs with aging.

## ETHICAL APPROVALS

All experiments were approved by the Institut Européen d'Administration des Affaires. The study was conducted in accordance with the Declaration of Helsinki. All subjects were informed about the experimental procedures, provided written informed consent, and received financial compensation for their participation.

## DATA AVAILABILITY

The data are available from the authors upon reasonable request. The MATLAB codes used in this manuscript are available from the authors upon reasonable request.

## SUPPLEMENTAL MATERIAL

Supplemental Figs. S1–S6: https://doi.org/10.6084/m9 figshare.30614852.

## ACKNOWLEDGMENTS

The authors thank Afagh Farhadi, Laurel Carney, and Torsten Dau for the discussion related to the results of this paper. The authors also thank the two reviewers who provided very important feedback that helped improve the quality of the manuscript. DeepSeek (DeepSeek AI) was used to perform grammar and clarity checks on fully written sections of the manuscript. The model was used to suggest improvements in punctuation, sentence structure, and readability, although not all suggestions were incorporated. The tool was used in a manner that does not conflict with APS ethical policies and the authors have reviewed and edited all content and take full responsibility for the final version of the manuscript, including its integrity, accuracy, and scientific rigor.

## GRANTS

This work has received financial support from the Agence Nationale de la Recherche (ANR) (Grant No. ANR-22-CE28-0010 to E.P., InspectSyn) and the CNRS through the Mission pour les Initiatives Transverses et Interdisciplinaires (MITI) interdisciplinary programs (HearDevComp, to E.P. and L.C.).

## DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the authors.

## AUTHOR CONTRIBUTIONS

E.P. and L.C. conceived and designed research; N.G. and C.B. performed experiments; E.P. and V.B. analyzed data; E.P. interpreted results of experiments; E.P. prepared figures; E.P. drafted manuscript; E.P. and L.C. edited and revised manuscript; E.P., V.B., N.G., C.B., and L.C. approved final version of manuscript.

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