Hearing-impaired sound perception: What can we learn from a biophysicalmodel of the human auditory periphery?
Alejandro OSSES VECCHI(1) , Frauke ERNST(2) , Sarah VERHULST(1)(1) Department of Information Technology, Ghent University, Belgium, alejandro.osses@ugent.be, s.verhulst@ugent.be(2) Department of Otorhinolaryngology, Head and Neck Surgery, University of Giessen, Germany,

frauke.ernst@hno.med.uni-giessen.de,

ABSTRACT
Auditory modelling provides a powerful quantitative framework to study performance in psychoacoustic listening tasks such as signal or modulation detection, and speech perception. Biophysically-inspired auditory models
provide the straightforward possibility to account for different aspects of sensorineural hearing loss (e.g., haircell loss or synaptopathy) and are well suited to study the origin of individual performance differences on
behavioural tasks. Here, we simulated how detection thresholds to low- and high-frequency supra-thresholdstimuli changed for various profiles of sensorineural hearing loss: (1) normal or high-frequency sloping audiograms (> 1 kHz, 30 dB HL at 8 kHz), and (2) normal or gradual loss of auditory-nerve synapses. The tasks
included the detection of amplitude-modulated tones at carrier frequencies of 500 Hz (fmod =5 Hz) and 4 kHz(fmod =100 Hz) presented with or without background noise. The simulations were compared with experimental
data collected from listeners with normal or high-frequency sloping audiograms. The simulations accounted for
up to 8.6 dB of the experimental variability, where the simulated variability was derived from the maximum
shift between simulated thresholds in each condition.
Keywords: Auditory modelling, hearing impairment, psychoacoustics

1

INTRODUCTION

Historically, simulations of signal processing along the auditory pathway have been used as a tool to study
specific aspects of the auditory physiology or to explain experimental results obtained in psychoacoustic experiments [e.g., 2, 5]. In both cases, artificial sounds with controlled properties can be simulated to determine theexpected outcomes of a given experimental task that will be conducted with human listeners, either using an
objective or behavioural experimental approach.
The set of processing stages accounted for by such auditory models mimic with greater or lesser accuracy
constitutive parts of the human ear including: Outer and middle ear, which are often simulated as a combined
bandpass filter; Inner ear, simulated as a set of bandpass filters covering the audible range (cochlear filtering),
followed by some type of transformation that resembles the transduction from mechanical waves into neural
responses, and; Central processing stage that approximates the way in which higher-level neural representations
are further processed and compared to other representations, as it is done in a psychoacoustic detection task.
Following the model classification proposed by Saremi et al. [11], existing auditory models can be classified
into perceptually- or mechanically-inspired models. We refer here to this latter type as biophysical models.
One benefit of using a biophysical model is that aspects of hearing impairment, such as cochlear gain loss
(that leads to elevated hearing thresholds) or synaptopathy (hypothesised to decrease supra-threshold hearing
performance), can be directly accounted for by setting the mechanical model parameters that affect the basilar membrane motion (sensitivity and tuning of cochlear filtering) or by disconnecting auditory nerve fibres
systematically, to account for cochlear gain loss and synaptopathy, respectively.
In this study, we adopt the biophysical model described by Verhulst et al. [13, 14] to study individual differencesin psychoacoustic performance1 . This model was earlier adopted to simulate a tone-in-noise and amplitudemodulation (AM) detection thresholds for high carrier frequencies ( fc =4 kHz) [16]. We extend this work here
to explore how much of the performance variability in a range of detection conditions collected from the same
listeners can be explained by (i) adopting different profiles of cochlear gain loss and synaptopathy, and by(ii) stimulus changes across conditions.
1 Examples of published perceptual models can be found in [2, 6, 17] and of biophysically-inspired models in [7, 18].

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Figure 1. Block diagram of the auditory model. Two stages were added or modified from the original description [13, 14]: “Outer ear model” and “central processor”.

2

MATERIALS AND METHODS

2.1 MODEL DESCRIPTION
2.1.1 Peripheral processing stages
The adopted model offers a quantitative description of the different functional components of the hearing systemand provides simulated neural representations along the ascending (human) auditory pathway up to the inferior
colliculus (auditory brainstem) [13, 14]. The block diagram is depicted in Fig. 1 and illustrates that sounds are
fed into either the outer-ear model [10] (as implemented in the AMT toolbox for MATLAB [12]), to accountfor the transfer function from circumaural headphones to the tympanic membrane, or directly passed througha middle-ear filter, if the sounds are presented over in-ear earphones (Stage 1). The signal is then fed into atransmission-line cochlear filter bank (Stage 2) where basilar membrane vibrations of 401 equidistant locations
along the cochlea are simulated according to the human cochlear place-frequency map. Each partition is a
bandpass filter matching human otoacoustic emission tuning. A non-linear compression is applied to the cochlear
vibrations to simulate the level dependence of cochlear filter tuning. The filter outputs are then converted
into inner hair cell receptor potentials (Stage 3) which are used to generate spike-rate patterns at the levelof the auditory nerve (Stage 4). These patterns are related to three types of fibres that have high- (HSR,
70 spikes/s), medium- (MSR, 10 spikes/s), and low-spontaneous rates (LSR, 1 spikes/s). These patterns are
eventually added up (13 HSR, 3 MSR, and 3 LSR fibres, i.e., 13-3-3) to form the input to a functional modelof the spherical bushy cell in the cochlear nucleus (Stage 5) and inferior colliculus (Stage 6). These stages
capture the modulation and onset sensitivity of bushy cells in the auditory brainstem [8]. The information acrossthe simulated characteristic frequencies available at the outputs of Stages 4, 5, and 6 offer a correlate of humanbrainstem responses recorded from scalp electrodes. In this paper we only use simulated neural responses atthe output of Stage 6 to assess the detection information that human listeners have available when conducting
a psychoacoustic experiment. This process is described further in Section 2.3.2.
2.1.2 Hearing loss
As highlighted in Fig. 1 the auditory model can account for two types of inner-ear dysfunction: cochlear gain
loss and synaptopathy. Cochlear gain loss is caused by damaged outer hair cells and leads to elevated hearing
thresholds and reduced frequency selectivity. In the model (Stage 2), individual audiograms can be simulated bychanging the gain parameters at each frequency partition [15]. In this study we adopted two cochlear gain loss
profiles that reflect: (i) a normal audiogram, and (ii) a high-frequency sloping audiogram above 1 kHz, witha hearing threshold of 30 dB HL at 8 kHz. In the model, synaptopathy can be introduced by disconnecting
auditory nerve fibres (Stage 4). In this study we adopted three synaptopathy profiles: 13-3-3, 13-0-0, and 6-0-0.
2.2 EXPERIMENTAL PROCEDURES
The experiments were conducted in a double-walled sound-proof booth. The stimuli had a sampling frequencyof 44.1 kHz and were presented monaurally either in quiet or using a background noise via Sennheiser HD200
circumaural headphones. The participants’ responses were collected using the AFC toolbox for MATLAB [3].
The experimental procedures complied with the ethical procedures of the University of Oldenburg.
2.2.1 Protocol
The stimuli were presented using three-alternative forced-choice (3-AFC) trials where the adjustable variable,
the modulation depth m, was changed using an adaptive tracking rule (two-down, one-up). The starting m value
was set to −12 dB and the step size was adapted every two reversals (10, 5, 3, 1 dB). Modulation-detection
thresholds were calculated as the mean of the last 6 reversals with a 1-dB step size. Each experimental condition
was measured three times for each participant, and their median was used for further analysis.

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Table 1. List of conditions and information about the background noises used in the AM detection tasks.
Noise
type
Q
N2/3-Oct.
N8-Hz
Q
N2/3-Oct.
N160-Hzfc , f mod[Hz]500, 5500, 5500, 5
4000, 100
4000, 100
4000, 100Bandwidth BW( f lower , f upper ) [Hz]233 (397, 630)
8 (496, 504)
1865 (3175, 5040)
160 (3920, 4080)

BW1-ERB
[Hz]
79
79
79
456
456
456

SpecL
[dB]
41.0
50.0
25.0
45.0

BLERB
[dB]
60.0
59.0
51.6
67.0

Ltot
[dB]
64.7
59.0
57.7
67.0

Stimulus
duration [s]
1.0
1.0
1.0
0.5
0.5
0.5

2.2.2 Stimuli
The reference sound (presented twice) was a pure-tone centred at either fc = 500 Hz (duration of 1 s) or
fc = 4 kHz (duration of 0.5 s) and included 25-ms and 12.5-ms raised cosine ramps, respectively. The target
sound (presented once) was an AM tone of the same fc , modulation depth m, modulated at rates of 5 and 100
Hz, respectively. All sounds were set to have an RMS level of 70 dB. AM detection thresholds were collectedin three conditions: (i) in quiet (Q), (ii) in a background noise which had a bandwidth (BW) of 80% the
sideband-to-sideband width of the modulation tone (condition labelled as N8-Hz for 500-Hz tones and N160-Hz
for 4-kHz tones), and (iii) in a 2/3 octave-band wide noise around fc (N2/3-Oct. ). The noises had a spectrum
level (SpecL) equal to 50 and 45 dB, respectively (Table 1). The N2/3-Oct. noise level was set to resemble
relative SpecLs found in speech, resulting in SpecLs of 41 dB at 500 Hz and 25 dB at 4 kHz. It is important
to note that this choice of parameters does not allow us to draw conclusions about the masking power of the
background noises across conditions. Therefore our focus is on evaluating the power of the auditory model topredict the individual performance on the different conditions.
2.2.3 Participants
Thirty-four participants took part in this experiment. Based on their age and audiometric hearing thresholds,
each participant was classified into one of three groups: young normal hearing (yNH), older normal hearing(oNH), or older hearing impaired (oHI). The yNH group had 14 participants (6 females, 8 males) who were
between 18 and 29 years old (avg=24.6, std=3.1). The oNH group had 10 participants (9 females, 1 male) who
were between 56 and 77 y. (avg=66.1, std=7.7). In both groups, the participants had hearing thresholds better
than 20 dB HL for frequencies between 125 Hz and 4 kHz. The oHI group had 10 participants (4 females,
6 males) who were between 61 and 78 y. (avg=70.6, std=6.3), and had hearing thresholds with a high-frequency
slope up to 45 dB HL at 4 kHz.
2.3 SIMULATIONS
2.3.1 Protocol
The AM detection task was implemented as previously described, with the exception that a constant stimulus instead of an adaptive procedure was adopted. The stimuli were generated within the AFC toolbox [3],resampled to a 100-kHz rate, and then fed into the auditory model using (i) two cochlear gain profiles thatapproximate a normal audiogram (‘Flat00’) and a high-frequency sloping audiogram (for f > 1 kHz, 30 dB HL
at 8 kHz, ‘Slope30’), and (ii) three synaptopathy profiles: 13-3-3, 13-0-0, and 6-0-0. The simulations were run
based on 20 stored trials for each condition (Table 1) at four modulation depths m (−28, −20, −12, −4 dB).
The same trials were used in combination with each simulated hearing profile (Flat00+13-3-3, 13-0-0, 6-0-0;
Slope30+13-3-3, 13-0-0, 6-0-0).
2.3.2 Central processor: RMS difference detector
The simulated neural representation of the intervals in the 3-AFC trial were designated as r1 , r2 , and r3 , withinterval 1 containing the target sound (AM tone) and intervals 2 and 3 containing the reference sounds. The
neural representations r1 , r2 , and r3 can be compared by computing RMS differences as follows:
s
s
s
N
1 N
1
1 N
(r1 [n] − r2 [n])2 , ∆r13 =(r1 [n] − r3 [n])2 , ∆r23 =(1)∆r12 =∑∑∑ (r2 [n] − r3 [n])2
N n=1
N n=1
N n=1
where n indicates that r1 , r2 , and r3 are digital signals with a total of N samples. The RMS differences wereassessed from the corresponding neural representations at each characteristic frequency. Based on our definitions,the larger the difference ∆r, the larger the probability that the target sound is correctly detected by a (human)listener. With this rationale, the simulated detection cue (detcue ) can be formulated as:
detcue = min (20 · log10 ∆r12 , 20 · log10 ∆r13 ) − 20 · log10 ∆r23

680

(2)

Simulations

yNH
oNH
oHI

B
fc=4000 Hz
fmod=100 Hz

N 2 / 3 -Oc t . N 8 -H z

QCondition

Mod. depth at threshold [dB]Mod. depth at threshold [dB]Experiments
0 A-2 fc=500 Hz-4 fmod=5 Hz
-6
-8
-10
-12
-14
-16
-18
-20
-22
-24
-26
-28
-30
Q

N 2 / 3 -Oc t . N 1 6 0 -H z

0 C
-2
-4
-6
-8
-10
-12
-14
-16
-18
-20
-22
-24
-26
-28
-30

D
fc=500 Hz
fmod=5 Hz

fc=4000 Hz
fmod=100 Hz

Flat00, 13-3-3
Flat00, 13-0-0
Flat00, 6-0-0
Slope30, 13-3-3Slope30, 13-0-0
Slope30, 6-0-0

Q

N 2 / 3 -Oc t . N 8 -H z

Q

N 2 / 3 -Oc t .N 1 6 0 -H z

Condition

Figure 2. A,B: Experimental AM detection thresholds for fc s at 500 Hz and 4 kHz, respectively. The results
are shown as medians (filled markers) with their corresponding interquartile ranges (IQR). The data for theyNH, oNH, and oHI groups are indicated in blue, magenta, and red, respectively. Open markers indicate individual data. C,D Simulated AM thresholds for the same tasks, derived as the median detection cues across
20 repetitions for each condition. The simulation results are shown here to facilitate their comparison with theexperimental thresholds and are explained more comprehensively in the text.
To determine whether a given detcue value is actually detectable, a threshold detthres has to be determinedsuch that a correct (simulated) detection is obtained when detcue >detthres . For this study we chose to use a
different detthres value for each experiment and we made assumptions to motivate this calibration procedure:(i) the simulated representations should have a (neural) floor level, below which participants are not able tointegrate any information, and (ii) detthres can be estimated from the experimental data, more specifically fromthe detcue value derived from the model at a better-than-average experimental performance. This is in line withthe classical view that the information available in simulations can be optimally integrated and should therefore
compare to the results of best performance participants [see, e.g., 5, Chapter 6]. We used the yNH thresholdat the lower limit of the interquartile range (IQR) in the easiest noise condition (−14.8 dB in N8-Hz , Fig. 2A;−14 dB in N2/3-Oct. , Fig. 2B). The floor level used in the model was set to −98 dB re. 1µV and corresponded
to the lowest difference value (min (∆r12 , ∆r13 )) obtained across all conditions at m = −28 dB, which was found
for the Q condition at fc = 500 Hz (not shown).

3

RESULTS

3.1 EXPERIMENTS
The experimental results for the six conditions of the AM detection task are shown in Fig. 2 for carrier frequencies fc of 500 Hz (panel A) and 4 kHz (panel B), where higher detection thresholds indicate poorer performance.
The filled markers indicate median thresholds and the error bars indicate their corresponding interquartile ranges(IQRs). The open markers indicate individual thresholds averaged (median) across 3 repetitions.
At fc = 500 Hz, fmod = 5 Hz, the Q performance was better than that of the N8-Hz , and N2/3-Oct. conditions.
Although the IQRs had similar values in all three groups, the spread of the data (Fig. 2A) was larger for theyNH group, smaller for oNH and in between for the oHI group. Furthermore the Q performance was overall
3 dB worse for the oNH group compared to both yNH and oHI, while the overall performance in the otherconditions (N2/3-Oct. , N8-Hz ) was similar across groups.
At fc = 4 kHz, fmod = 100 Hz, the experimental conditions sorted from better to worse performance were: Q,
N2/3-Oct. , and N160-Hz . The IQRs were consistent within each participant group, with an approximate length of
3 dB for yNH participants, 6 dB for oNH participants (but 2 dB at N160-Hz ), and about 4 dB in N2/3-Oct. . The
individual data points (open markers in Fig. 2B) had a similar spread across conditions in the yNH and oHIgroups, while it was larger for the oNH group, especially in the Q and N2/3-Oct. conditions. In the Q condition,yNH and oHI had a similar overall performance, with a 6-dB poorer performance for oNH participants. The best
performance in the N2/3-Oct. condition was obtained for the oHI group (threshold at m = −15.25 dB) followedby the yNH and oNH groups with thresholds 3 and 6 dB poorer, respectively. A similar overall performance
was obtained for all groups in the N160-Hz condition.
In the most difficult conditions (N2/3-Oct. at fc = 500 Hz, N160-Hz at fc = 4 kHz) there were a number of participants who were not able to perform the AM task. Their results are shown as data points at m = 0 dB (Fig.2A,
2 data points from each participant group; Fig.2B, 2 data points from oNH and 2 from oHI).

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Amplitude difference[dB re. 1 µV]

−78

−76

r12

A Q

−77

B N
2/3−Oct.

−78

−90

−74

r

12

C N
160−Hz
r

−79
−102

Floor

r23

r23

−82

r23

−126
Detection cue [dB]

−75

−81

−114

20

12

−80

−76

−83

D

Modulationdet
depth[dB]curve
cue,13−3−3

10

16

8

12

6

8

detcue,6−0−0 curve

40E

Modulation depth [dB]10−28 −24 −20 −16 −12 −8Modulation depth [dB]−4

Modulation depth [dB]8detcue,13−3−3

curve

6

4

4

2

2

0

−4

F

detcue,13−3−3 curve0−28 −24 −20 −16 −12 −8Modulation depth [dB]−4−28 −24 −20 −16 −12 −8 −4Modulation depth [dB]0

Figure 3. Simulation amplitude differences (top) and detection cues (bottom) for AM detection at fc = 4 kHz forthe normal hearing model (Flat00, 13-3-3) for the conditions in quiet (A,D), N2/3-Oct. (B,E), and N160-Hz (C,F).
Panels A–C: Differences ∆r12 (filled markers) and ∆r23 (open markers). Panels D–F: Detection curves derived
using Eq. 1. The simulated thresholds (magenta diamonds) were −26.4, −14.1, and > 0 dB (no estimation),
respectively. The detthres was set to 2.2 dB (magenta dashed line) and detfloor was set to −98 dB re. 1µV (greyline in A). Each of the curves was derived from 20 difference values and the error bars indicate the IQRs of
those values. For the curves in panels D–F, the average IQRs across modulation depths are 0 (no variability),
0.4 dB, and 1.1 dB, respectively (clearly visible in panel F only). In panels D–E, the square markers indicate
the detection curves for one synaptopathy profile (Flat00,6-0-0). The 6-0-0 thresholds (open magenta markers)
were −18.1, −13.7 (shifts of 8.3 dB and 0.4 dB with respect to Flat00, 13-3-3). Note that the ordinate axes inpanels D–F are not to scale and that simulations at m = 0 dB were added to the N160-Hz conditions.

3.2 SIMULATIONS
Simulated difference values ∆r12 and ∆r23 (Eq. 1) are shown in Fig. 32 using a normal hearing model (Flat00,
13-3-3) for the AM task at fc = 4 kHz. The procedure used to derive the simulated thresholds is depicted inFig. 3, where the simulated detection curves (panels D–F) were assessed as the distance between ∆r23 (or floor
level) and ∆r12 (or ∆r13 ), and detcue was obtained as the amount of detection cue that produces a simulated
threshold at m = −14 dB (see Section 2.3.2) yielding a detcue value of 2.2 dB. A similar calibration procedure
was adopted to derive simulated thresholds in the AM task at fc = 500 Hz and fmod = 5 Hz, obtaining a detcue
value of 0.54 dB. The resulting simulated thresholds are shown in Fig. 2C–D and Table 2.
In the high-frequency task, the simulated thresholds worsened from Q, to N2/3-Oct. and N160-Hz , which coincides
with the order of difficulty observed experimentally. For the Flat00 13-3-3 profile and fixed detcue , the assessedvalues were −26.4 dB, −14.1 dB, and > 0 dB (no estimation), respectively. The simulations with cochlear gain
loss (Slope30) improved these thresholds by 1.1 and 2.1 dB in the Q and N2/3-Oct. conditions (see Table 2),
respectively. The different synaptopathy profiles increased the Q thresholds considerably by up to 8.3 dB (square
markers along the detcue,6-0-0 curve, Fig. 2D) and only marginally in the N2/3-Oct. condition (square markers in
Fig. 2E). Although not shown here, a similar shift in the detection curves in the N160-Hz condition was found(but the cues never exceeded detthres = 2.2 dB).
In the low-frequency task, the simulated thresholds ranked from better to worse were found for the N8-Hz , Q,
and N2/3-Oct. conditions, respectively. Although this is not exactly the same difficulty order found experimentally(where Q had lower thresholds), the N8-Hz and Q thresholds differ only by about 1 dB: For normal hearing
model (Flat00, 13-3-3) the assessed values were −15.6 dB, −14.9 dB, and > 0 dB (no estimation), respectively.
Simulations with the Slope30 profile showed an (almost) marginal improvement of up to 0.5 dB in the N8-Hz
condition (see Table 2). Different synaptopathy profiles increased the simulated thresholds in the Q and N8-Hz
conditions considerably by 8.6 dB and 5.7 dB, respectively (see the shift from square to diamond markers in
Fig. 2C and also row “Flat00, 13-3-3–6-0-0” in Table 2). A marginal 0.5-dB shift of the detection curves wasfound in the N2/3-Oct. condition (not shown here).
2 The difference r was omitted for clarity but the obtained values were in a similar range than ∆r .
13
12

682

Table 2. Simulated thresholds thressim using the RMS difference detector for six hearing profiles. The thresholds(also shown in Fig. 2C-D) were assessed using the procedures visualised in Fig. 3. Simulated threshold shifts
when introducing either cochlear gain loss or synaptopathy are shown in the bottom rows of the table.

Hearing profile
Flat00, 13-3-3
Flat00, 13-0-0
Flat00, 6-0-0
Slope30, 13-3-3Slope30, 13-0-0
Slope30, 6-0-0
Compared profiles
Slope30-Flat00, 13-3-3Slope30-Flat00, 13-0-0
Slope30-Flat00, 6-0-0
13-0-0−13-3-3, Flat00
6-0-0−13-3-3, Flat00
13-0-0−13-3-3, Slope30
6-0-0−13-3-3, Slope30

fc =500 Hz, fmod =5 Hz
Threshold thressim [dB]Q
N2/3-Oct. N8-Hz
-14.9
>0
-15.6
-13.2
>0
-14.0
-6.3
>0
-9.9
-15.0
>0
-16.1
-13.4
>0
-14.5
-6.6
>0
-10.3
thresshift [dB]Q
N2/3-Oct. N8-Hz
-0.1
−
-0.4
-0.2
−
-0.5
-0.3
−
-0.4
1.7
−
1.6
8.6
−
5.7
1.4
−
1.6
8.4
−
5.8

fc =4 kHz, fmod =100 Hz
Threshold thressim [dB]Q
N2/3-Oct. N160-Hz
-26.4
-14.1
>0
-24.9
-13.7
>0
-18.0
-13.7
>0
-27.5
-16.2
>0
-26.0
-15.8
>0
-19.2
-15.8
>0
thresshift [dB]Q
N2/3-Oct. N160-Hz
-1.1
-2.1
−
-1.1
-2.1
−
-1.2
-2.1
−
1.5
0.4
−
8.4
0.4
−
1.5
0.4
−
8.3
0.4
−

Summarising, cochlear gain loss caused smaller threshold shifts than synaptopathy, which introduced simulated
threshold shifts between 5.7 and 8.6 dB in three of the six simulated conditions, two of them in the lowfrequency task. In all three cases, the shift was caused by an increase in the neural noise floor.

4

DISCUSSION

The supra-threshold AM detection task was conducted for a high- ( fc = 4 kHz) and low-frequency carrier ( fc =500 Hz) where different stimulus characteristics–temporal envelope and temporal fine structure–are believed toinfluence the (measured or simulated) detection cues in auditory neural representations. Our analysis of bothexperimental and simulated results was focused on understanding how the participants’ results in the high- andlow-frequency regions were affected by cochlear gain loss or synaptopathy and, therefore, our analysis could belinked to how temporal fine structure and temporal envelope cues are affected by sensorineural hearing loss.
According to our group classification, oHI participants were expected to suffer from cochlear gain loss whileyNH and oNH were not. There is also a low risk that yNH participants suffered from synaptopathy, while oNH
and oHI participants might have been at risk for synaptopathy given their advanced age [9].
4.1 EXPERIMENTS
When comparing the results of the yNH and oHI groups, we observed that the AM detection task for a highfrequency carrier (fc = 4 kHz, fmod = 100 Hz) is more affected by cochlear gain loss than the low-frequency
task (fc = 500 Hz, fmod = 5 Hz), given that the best performing oHI participants in Fig. 2B had lower thresholds than the yNH participants. This performance improvement is also reflected in one (median) threshold at
m = −15.25 dB in the N2/3-Oct. condition, which was 3 and 6 dB below the performance of yNH and oNH
participants, respectively. The elevated detection thresholds for oNH participants seem to stem from a reduced
high-frequency coding despite their normal hearing audiograms.
In the low-frequency AM detection task, oNH participants had an elevated detection threshold in quiet only (by3 dB, Fig. 2A), while for all other conditions, the three groups had a similar overall performance. Therefore, it
seems that cochlear gain loss alone does not play a prominent role for low-frequency AM detection.
4.2 SIMULATIONS
Threshold accuracy: The simulated thresholds (Fig. 2C-D) did not fully agree with the obtained experimental
thresholds (2A-B) with a larger range of values (overall thressim were between -16.4 dB to > 0 dB, thresexp
values were between −18.8 dB and −6.4 dB). At fc = 500 Hz, fmod = 5 Hz, the thressim values did not decreasein the Q condition with respect to N8-Hz as was expected from the experimental data (expected decrease by
4-6 dB) and increased by 0.7 dB instead. The non-estimated thressim in N2/3-Oct. (m > 0 dB) denotes that lessdetection cues can be extracted using the auditory model in this condition and, therefore, the AM detection isharder than in the N8-Hz and Q conditions. This tendency was also observed in the experimental data, where 6
participants could not finish the task. At fc = 4 kHz, fmod = 100 Hz, the thressim in Q were about 12 dB better683

than for N2/3-Oct. while the experimental thresholds denoted an overall shift of 6 dB. No estimation was possible
in the N160-Hz condition, indicating that in this frequency range this is the most difficult condition. This trend
was also observed in the experimental data. The deviations between thressim and thresexp may be caused bya reduced sensitivity of the model to inherent modulations of the N2/3-Oct. and N160-Hz noises for 500-Hz and
4-kHz tones, respectively, when superimposed with the corresponding modulation frequencies of 5 and 100 Hz.
Threshold variability: As summarised in Table 2, cochlear gain loss (Slope30 profile) introduces a small threshold improvement of up to 2.1 dB in the N2/3-Oct. condition for 4-kHz AM tones. In this condition, the experimental data showed a threshold shift of 3 dB (between yNH and oHI). The simulated threshold shift became(almost) marginal in the 500-Hz AM task where an average improvement of 0.4 dB or less was observed.
Simulations for different synaptopathy profiles did show a threshold shift between 5.7 and 8.6 dB for 500-Hz
AM-tones (from 13-3-3 to 6-0-0 in the Q and N2/3-Oct. conditions), while for 4-kHz tones, a significant effect was only found in the Q condition (maximum threshold shift of 8.4 dB). These observations support thatcochlear gain loss introduces a smaller detection threshold shift (2 dB in our simulations) than synaptopathy (upto 8.6 dB). The increment of experimental thresholds in Q for 500-Hz (3-dB shift) and 4-kHz tones (6-dB shift)for oNH participants with respect to yNH, could be explained by the simulated threshold shift (thresshift ) due tosynaptopathy, given that in both conditions thresshift was about 8 dB (more than the average experimental shift).
Noisy conditions (N8-Hz , N160-Hz , and both N2/3-Oct. ) contain representations r1,2,3 that are stochastic, introducing
variability in the assessed detection cues due to the statistical properties of the background noises. For the AM
detection of 4-kHz tones in N160-Hz (Fig. 3F), this external variability would affect the detection sensitivity by±1.5 dB (“vertical shift” of the detection curve). For the N2/3-Oct. condition (Fig.3E), the external variability(IQR of 0.4 dB) can shift the estimated threshold by 1 dB (i.e., ±0.5 dB). Comparable threshold shifts wereassessed for the AM task at 500 Hz (not shown here).
4.2.1 Limitations of the model
Based on the obtained results (Fig. 2C-D), it is possible to infer that the auditory model is not sensitive enoughin the most difficult AM conditions and that the model is more sensitive to the 4-kHz task at fmod =100 Hz
than to the 500-Hz task at fmod = 5 Hz. This is also evidenced by the detthres values of 0.54 dB and 2.2 dB(1.46 dB difference) obtained during the model calibration, where a more balanced sensitivity to low- and highfrequencies should have lead to values that are closer to each other (difference close to zero). This sensitivity
variation might be related to the evaluated modulation frequency range. Stages 5 and 6 of the model act as amodulation filter with a passband centred at fmod = 100 Hz, while other models in the literature claim that more
modulation filters are needed primarily for frequencies below fmod < 250 Hz [1, 2, 17]. If the auditory model ismade more sensitive in a given modulation frequency region, the simulated thresholds in that range may spread
more than reported here. In our low-frequency experiment this could lead to a higher effect of synaptopathy
than the (up to) 8.6 and 5.8 dB in the Q and N8-Hz conditions.
4.2.2 Limitations of the central processor
In this paper we adopted a central processor that compares within-trial intervals to derive simulated detection
cues. Our detector corresponds to an extension of the cue extraction procedure used in a previous study [16],and is compatible with AM detection tasks with target and reference intervals affected by the stimulus externalvariability. Despite the moderate success of our simulations, where we could derive simulation thresholds for
only four of the six test conditions, a careful interpretation of simulation and experimental data can provide
interesting insights about the underlying auditory decision processes. Other approaches to derive detection cues
include the use of a memory component (template) within the model, which has been found relevant to accountfor a number of AM detection tasks [see, e.g., 4].
Our simulation results where synaptopathy played a relevant role rely on the assumption that a neural floor level
exists. This assumption is similar to the use of an internal noise to limit the model performance [e.g., 2]. It
could be tested whether a more elaborate neural noise model would improve the simulations across conditions.

5

CONCLUSION

In this paper the auditory model described by Verhulst et al. [13] was used to simulate AM detection performance at two carrier and modulation frequencies fc = 500 Hz modulated at fmod =5 Hz and fc = 4 kHz
modulated at fmod =100 Hz. AM detection thresholds were derived using a within-trial comparison of simulated
neural representations (model output of Stage 6, Fig. 1). The simulation results shown in Fig. 2C–D revealthat synaptopathy importantly reduces AM performance in 3 of the 6 conditions tested with threshold shifts
between 5.7 and 8.6 dB for those conditions. In turn, cochlear gain loss (high-frequency sloping audiogram,684

hearing threshold of 30 dB HL at 8 kHz) introduces a slight increment in performance (less than 2.1 dB), inline with the findings published in [16]. We found, however, that our auditory model seems to have a reduced
sensitivity in some of the conditions we tested, especially in the low-frequency task and this reduced sensitivity
may be related to the adopted modulation rate fmod =5 Hz. If the model is made more sensitive, then the actual
variability attributed to cochlear gain loss or synaptopathy may be larger than reported here.

ACKNOWLEDGEMENTS
We would like to thank Sabrina Pieper for collecting the experimental data. This study received support fromthe European Research Council (ERC) (RobSpear, grant agreement Nr. 678120: AO, SV) and was further
supported by the DFG Cluster of Excellence EXC 1077/1 “Hearing4all” (FE).

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