Lumped element models facilitate investigating the fundamental mechanisms of human ear sound conduction. This systematic review aims to guide researchers to the optimal model for the investigated parameters. For this purpose, the literature was reviewed up to 12 July 2023, according to the PRISMA guidelines. Seven models are included via database searching, and another 19 via cross-referencing. The quality of the models is assessed by comparing the predicted middle ear transfer function, the tympanic membrane impedance, the energy reflectance, and the intracochlear pressures (ICPs) (scala vestibuli, scala tympani, and differential) with experimental data. Regarding air conduction (AC), the models characterize the pathway from the outer to the inner ear and accurately predict all six aforementioned parameters. This contrasts with the few existing bone conduction (BC) models that simulate only a part of the ear. In addition, these models excel at predicting one observable parameter, namely, ICP. Thus, a model that simulates BC from the coupling site to the inner ear is still lacking and would increase insights into the human ear sound conduction. Last, this review provides insights and recommendations to determine the appropriate model for AC and BC implants, which is highly relevant for future clinical applications.
I. INTRODUCTION
Sound conduction in the human ear occurs via multiple modes, including air conduction (AC), where air vibrations in the ear canal induce hearing sensation, and bone conduction (BC), where skull vibrations induce hearing sensation. One principal pathway transfers AC vibrations to the basilar membrane. In contrast, five main pathways transfer BC vibrations to the basilar membrane: (1) compression of the ear canal, (2) relative motion of the middle ear ossicles due to inertia, (3) compression of the cochlear space, (4) inertia of the cochlear fluid, and (5) secondary fluid paths between the inner ear and cranial cavity (Stenfelt, 2016). Hearing implants that stimulate the inner ear via these BC pathways are frequently used in hearing rehabilitation. The main indication for these devices is conductive hearing loss, as they bypass the dysfunctional AC pathway and transmit sound directly through the skull to the functional inner ear (Reinfeldt , 2015). Typically, these hearing implants deliver vibrational energy to the skull using an actuator. However, other hearing implants may also be coupled to specific parts of the ossicular chain or close to the cochlea (Verhaert , 2013).
Multiple objective measures can quantify hearing sensation and the performance of implantable and conventional hearing aids. One of them is the middle ear transfer function (METF), the ratio of the stapes velocity to the ear canal pressure, which describes sound transmission through the middle ear. Another possible measure is the tympanic membrane impedance (ZTM) or the pressure to volume velocity ratio at the tympanic membrane (Xue , 2020). In addition, energy reflectance (ER), the ratio of reflected to incident energy (Voss and Allen, 1994), can be measured. Last, intracochlear pressures (ICPs)—pressure in the scala vestibuli (PSV), pressure in the scala tympani (PST), and the difference between them (Pdiff)—can be used to quantify the performance of hearing aids as they correlate with the cochlear drive (Borgers , 2018; Dancer and Franke, 1980; Guan , 2020; Niesten , 2015; Stieger , 2018).
Lumped element models (LEMs) are a possible alternative for these measurements. A benefit of such a model is that it does not require cadaveric specimens, and thus circumvents practical and ethical issues (Chang , 2016). Furthermore, in contrast to experiments in cadaveric specimens, LEMs allow testing multiple implants in the same specimen or model; adapting features of the implant; estimating velocities and pressures at anatomical locations that are hardly accessible in a specimen; changing the design features of an implant continuously; studying the influence of one specific feature, and investigating the ear without damaging it (Chang and Stenfelt, 2019; Pascal , 1998). In addition, it illuminates the fundamental mechanisms of sound transmission (Frear , 2018). There already exist multiple LEMs that characterize sound conduction in the human ear. However, they differ in the type of model elements, the parts of the ear that they model, the type of conduction they simulate, and their choice of elements. Therefore, this systematic review aims to assess existing LEMs that simulate sound conduction in the human ear. It provides the model predictions, evaluates the quality of the models by comparing the predictions with experimental data, assesses the approaches to create a model, and provides a recommendation on how to create or choose the appropriate model for a specific application.
II. MATERIALS AND METHODS
A. Systematic review
The systematic review was performed according to the PRISMA guidelines (Page , 2021) using two identification strategies: databases and citation searching. For the latter, the references of the records obtained with the first strategy were screened. Regarding database identification, Scopus, PubMed, and Embase were searched on 12 July 2023, to identify studies that present a LEM of sound conduction in the human ear. The search strategy included terms related to LEMs, sound conduction, and the human ear. It resulted in a total of 104 records, and the supplementary material1 provide a detailed search strategy for each database. Figure 1 shows the flow diagram for selecting the relevant records according to the PRISMA guidelines (Page , 2021).
(Color online) Overview of the selection of different articles using the PRISMA flow diagram (Page , 2021).
(Color online) Overview of the selection of different articles using the PRISMA flow diagram (Page , 2021).
After removing duplicates, the authors I.W. and A.G. screened the 51 unique records on title, abstract, and figures using Rayyan (Rayyan Systems Inc., Cambridge, MA), a software that allows simultaneous independent screening (Ouzzani , 2016). Records were excluded due to the following reasons: the record does not report a LEM (N = 12); describes an animal ear (N = 8); does not model sound but electrical conduction in the auditory nerves (N = 4); reports a model of which an updated version is published (N = 3); or does not model the ear, but the vocal cords, a microphone or an ear simulator (N = 3). Disagreements were resolved by consensus-based discussion. If, based on the title, abstract, and figures, it was unclear if a record met the inclusion criteria, the full text was obtained. For three reports, the full texts were not retrieved. For the other 18 records, the full texts were assessed for eligibility by author IW. Records were excluded if the record reports a LEM that does not predict any of the studied parameters (n = 4), if it uses an existing LEM (n = 3), if it reports a model of which an updated version is published (n = 3), or if the record does not report a LEM (n = 1). Hence, seven studies were included via the database search.
After the database search, the references of the included studies were screened. This screening led to 39 records identified via citation searching, of which 35 were retrieved. A total of 16 records were excluded because the record does not report a LEM (n = 6); the reported LEM does not predict any of the studied parameters (n = 5); it does not model AC or BC (n = 3); it models an animal ear (n = 1); or it reports a model of which an updated version is published (n = 1). Thus, 19 records were included via citation searching, resulting in a total of 26 records included in the review.
B. Risk of bias assessment
To the best of the authors' knowledge, there is no validated tool to assess the risk of bias in LEMs. Therefore, in this review, all included models are evaluated. First, their differences and similarities are summarized. Ultimately, the quality of the LEMs is assessed by comparing the predictions of the LEMs to experimentally obtained data. The following six parameters are evaluated:
-
The METF, which is the ratio of the stapes velocity to the ear canal pressure. It describes sound transmission through the middle ear (Ravicz and Rosowski, 2013) and is used in the American Society for Testing and Materials (ASTM) standard to verify the quality of the AC pathway (ASTM, 2014).
-
The tympanic membrane impedance (ZTM), which is the pressure to volume velocity ratio at the tympanic membrane (Xue , 2020) and thus reflects how resistant the tympanic membrane and the subsequent hearing structures are to applied pressure.
- The ER, which is the ratio of reflected to incident energy (Voss and Allen, 1994) and is calculated as in Eq. (1):
With Zchar, the characteristic impedance of the ear canal, ρ the equilibrium air density, c the velocity of sound, and Se the cross-sectional area of the ear canal. This parameter is of interest as it reflects the efficiency of the ear:
-
The ICP in the scala vestibuli (PSV).
-
The ICP in the scala tympani (PST).
-
The intracochlear differential pressure (Pdiff), which is the complex difference between the ICP in the scala vestibuli and tympani.
The latter three are of interest because they correlate with the cochlear drive and thus can be used to estimate hearing sensation (Borgers , 2018; Dancer and Franke, 1980; Guan , 2020; Niesten , 2015; Stieger , 2018). For AC stimulation, these three parameters are normalized to the pressure in the ear canal, while for BC, they are normalized to the promontory velocity.
Regarding the experimental data, the data of Aibara (2001), Rosowski (2007), and Voss (2000) are used for the METF. The ZTM is compared to the ranges of Hudde (1983), Rabinowitz (1981), and Withnell and Gowdy (2013), while the ER is compared to the ranges of Hudde (1983), Farmer-Fedor and Rabbitt (2002), Feeney (2009), and Margolis (1999). For the ICPs regarding AC, the experimental data are measured by Aibara (2001), Grossöhmichen (2016), Nakajima (2005), and Puria (1997). For BC, the ICP data are measured by Fierens (2022), Mattingly (2020), Putzeys (2022), and Stieger (2018).
The predicted parameters of the LEMs are reproduced in Matlab (MathWorks, Natick, MA) for most records. In contrast, reported parameters were used for the models of Keefe (2015), O'Connor and Puria (2008), Stenfelt (2020), and Xue (2020). Regarding the model of Stenfelt (2020), the model predictions for PSV are provided at two positions, further referred to as A, in the center of the vestibule, and B, at the border between the vestibule and the scala vestibuli. The models of Hudde and Engel (1998), Hudde and Weistenhöfer (1999), Peake (1992), Onchi (1961), Voss (2001), and Withnell and Gowdy (2013) are not included in the comparison because they are not reproducible with the information presented in the paper. In addition, they did not report the predicted METF, ZTM, ER, or ICPs. Neither is the model of Elliott (2016) since it does not model ear canal pressure. Regarding the model of Rosowski (2004), only results for AC are included in the comparison with experimental data as the results of BC are not normalized to promontory velocity.
A grade, expressed as a percentage, is calculated to quantify the fit between the model predictions and the experimental data. This percentage reflects the number of frequencies, on a logarithmic scale between 100 Hz and 10 kHz, for which the model prediction is between the lowest and highest experimentally measured data points. This analysis is performed for both the amplitude and the phase of every parameter.
III. RESULTS
A. Summary of the models
This section provides an overview of the similarities and differences among the models in terms of various aspects, including the number of model elements, the type of model elements, the incorporated parts of the ear, the simulated conduction type, the methodology for selecting model elements, the comparison of model predictions with experimental data, and the inclusion of clinical applications. To illustrate these similarities and differences, Fig. 2 shows a schematic view of three LEMs, namely, the LEM developed by Feng and Gan (2004) (further referred to as model 1), by Stenfelt (2020) (further referred to as model 2), and by O'Connor and Puria (2008) (further referred to as model 3). A schematic view of all models is shown in the supplementary materials.1 Further, the following paragraphs and Table I compare the LEMs of the reviewed records, sorted by the number of elements used in the models.
(Color online) Schematic overview of the LEMs. (1) LEM with mechanical elements of the middle ear for AC. Reproduced from Feng, B., and Gan, R. Z. (2004). “Lumped parametric model of the human ear for sound transmission,” Biomech. Model. Mechanobiol. 3, 33–47, with permission from SNCSC. (2) LEM with electrical elements of the inner ear for AC and BC. Reproduced from Stenfelt (2020). “Investigation of mechanisms in bone conduction hyperacusis with third window pathologies based on model predictions.” Front. Neurol. 11, 966; licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0; https://creativecommons.org/licenses/by/4.0/) license. (3) LEM with electrical elements of the whole ear for AC. Reproduced from Xue, L., Liu, H., Wang, W., Yang, J., Zhao, Y., and Huang, X. (2020). “The role of third windows on human sound transmission of forward and reverse stimulations: A lumped-parameter approach.” J. Acoust. Soc. Am. 147, 1478–1490, with permission of Acoustical Society of America. Copyright 2020, Acoustical Society of America.
(Color online) Schematic overview of the LEMs. (1) LEM with mechanical elements of the middle ear for AC. Reproduced from Feng, B., and Gan, R. Z. (2004). “Lumped parametric model of the human ear for sound transmission,” Biomech. Model. Mechanobiol. 3, 33–47, with permission from SNCSC. (2) LEM with electrical elements of the inner ear for AC and BC. Reproduced from Stenfelt (2020). “Investigation of mechanisms in bone conduction hyperacusis with third window pathologies based on model predictions.” Front. Neurol. 11, 966; licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0; https://creativecommons.org/licenses/by/4.0/) license. (3) LEM with electrical elements of the whole ear for AC. Reproduced from Xue, L., Liu, H., Wang, W., Yang, J., Zhao, Y., and Huang, X. (2020). “The role of third windows on human sound transmission of forward and reverse stimulations: A lumped-parameter approach.” J. Acoust. Soc. Am. 147, 1478–1490, with permission of Acoustical Society of America. Copyright 2020, Acoustical Society of America.
Comparison of the models. Number of elements: total number of elements used in a model. Type elements: whether the model consists of electrical or mechanical elements. Part ear: whether the LEM simulates the outer, middle, or inner ear. Type conduction: whether the LEM simulates AC or BC. Choice elements: whether elements are reused from previous models, based on anatomical properties, or fit to experimental data. Compared with data: whether the model predictions are compared to experimentally obtained data. ✓: included in the model. Ø: not included in the model. ✓*: Modeled with Thévenin equivalent.
Author (Year) . | Number of elements . | Type Elements . | Part Ear . | Type conduction . | Choice Elements . | Compared with experimental data . | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Electrical . | Mechanical . | Outer . | Middle . | Inner . | AC . | BC . | Previous model(s) . | Anatomy based . | Fit to data . | |||
Liu and Neely (2010) | 7 | Ø | ✓ | ✓ | ✓ | ✓* | ✓ | Ø | ✓ | ✓ | ✓ | Ø |
Voss (2001) | 7 | ✓ | Ø | ✓ | ✓ | ✓* | ✓ | Ø | ✓ | ✓ | ✓ | ✓ |
Hudde and Weistenhöfer (1999) | 8 | ✓ | Ø | ✓ | ✓ | ✓* | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |
Peake (1992) | 9 | ✓ | Ø | ✓ | ✓ | ✓* | ✓ | Ø | ✓ | ✓ | ✓ | ✓ |
Hudde and Engel (1998) | 9 | ✓ | Ø | ✓ | ✓ | ✓* | ✓ | Ø | Ø | ✓ | ✓ | Ø |
Frear (2018) | 10 | ✓ | Ø | ✓* | ✓* | ✓ | ✓ | Ø | Ø | ✓ | ✓ | ✓ |
Guan (2020) | 10 | ✓ | Ø | ✓* | ✓* | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |
Møller (1961) | 10 | ✓ | Ø | ✓* | ✓* | ✓* | ✓ | Ø | Ø | ✓ | ✓ | ✓ |
Rosowski (2004) | 11 | ✓ | Ø | ✓* | ✓* | ✓ | ✓ | ✓ | ✓ | Ø | ✓ | Ø |
Elliott (2016) | 13 | ✓ | Ø | Ø | ✓* | ✓ | ✓ | Ø | ✓ | ✓ | Ø | ✓ |
Marquardt and Hensel (2013) | 13 | ✓ | Ø | ✓* | ✓* | ✓ | ✓ | Ø | ✓ | Ø | ✓ | ✓ |
O'Connor and Puria (2008) | 14 | ✓ | Ø | ✓ | ✓ | ✓ | ✓ | Ø | ✓ | ✓ | ✓ | ✓ |
Zwislocki (1962) | 18 | ✓ | Ø | ✓ | ✓ | ✓* | ✓ | Ø | Ø | Ø | ✓ | ✓ |
Kringlebotn (1988) | 20 | ✓ | Ø | ✓ | ✓ | ✓* | ✓ | Ø | ✓ | ✓ | ✓ | ✓ |
Lutman and Martin (1979) | 20 | ✓ | Ø | ✓ | ✓ | ✓* | ✓ | Ø | ✓ | ✓ | ✓ | ✓ |
Stenfelt (2020) | 20 | ✓ | Ø | ✓* | ✓* | ✓ | ✓ | ✓ | ✓ | ✓ | Ø | ✓ |
Onchi (1961) | 21 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | Ø | ✓ | Ø | ✓ | ✓ |
Feng and Gan (2004) | 22 | Ø | ✓ | ✓ | ✓ | Ø | ✓ | Ø | ✓ | ✓ | ✓ | ✓ |
Rosowski and Merchant (1995) | 22 | ✓ | Ø | ✓ | ✓ | ✓* | ✓ | Ø | ✓ | Ø | ✓ | ✓ |
Han (2023) | 24 | Ø | ✓ | ✓ | ✓ | Ø | ✓ | Ø | ✓ | Ø | ✓ | ✓ |
Xue (2020) | 24 | ✓ | Ø | ✓ | ✓ | ✓ | ✓ | Ø | ✓ | Ø | Ø | ✓ |
Pascal (1998) | 25 | ✓ | Ø | ✓ | ✓ | ✓* | ✓ | Ø | ✓ | ✓ | Ø | ✓ |
Withnell and Gowdy (2013) | 25 | ✓ | Ø | ✓ | ✓ | ✓* | ✓ | Ø | ✓ | ✓ | Ø | ✓ |
Goode (1994) | 27 | ✓ | Ø | ✓ | ✓ | ✓* | ✓ | Ø | ✓ | ✓ | ✓ | ✓ |
Keefe (2015) | 32 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | Ø | ✓ | ✓ | ✓ | ✓ |
Giguère and Woodland (1994) | 560 | ✓ | Ø | ✓ | ✓ | ✓ | ✓ | Ø | ✓ | ✓ | ✓ | Ø |
Author (Year) . | Number of elements . | Type Elements . | Part Ear . | Type conduction . | Choice Elements . | Compared with experimental data . | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Electrical . | Mechanical . | Outer . | Middle . | Inner . | AC . | BC . | Previous model(s) . | Anatomy based . | Fit to data . | |||
Liu and Neely (2010) | 7 | Ø | ✓ | ✓ | ✓ | ✓* | ✓ | Ø | ✓ | ✓ | ✓ | Ø |
Voss (2001) | 7 | ✓ | Ø | ✓ | ✓ | ✓* | ✓ | Ø | ✓ | ✓ | ✓ | ✓ |
Hudde and Weistenhöfer (1999) | 8 | ✓ | Ø | ✓ | ✓ | ✓* | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |
Peake (1992) | 9 | ✓ | Ø | ✓ | ✓ | ✓* | ✓ | Ø | ✓ | ✓ | ✓ | ✓ |
Hudde and Engel (1998) | 9 | ✓ | Ø | ✓ | ✓ | ✓* | ✓ | Ø | Ø | ✓ | ✓ | Ø |
Frear (2018) | 10 | ✓ | Ø | ✓* | ✓* | ✓ | ✓ | Ø | Ø | ✓ | ✓ | ✓ |
Guan (2020) | 10 | ✓ | Ø | ✓* | ✓* | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |
Møller (1961) | 10 | ✓ | Ø | ✓* | ✓* | ✓* | ✓ | Ø | Ø | ✓ | ✓ | ✓ |
Rosowski (2004) | 11 | ✓ | Ø | ✓* | ✓* | ✓ | ✓ | ✓ | ✓ | Ø | ✓ | Ø |
Elliott (2016) | 13 | ✓ | Ø | Ø | ✓* | ✓ | ✓ | Ø | ✓ | ✓ | Ø | ✓ |
Marquardt and Hensel (2013) | 13 | ✓ | Ø | ✓* | ✓* | ✓ | ✓ | Ø | ✓ | Ø | ✓ | ✓ |
O'Connor and Puria (2008) | 14 | ✓ | Ø | ✓ | ✓ | ✓ | ✓ | Ø | ✓ | ✓ | ✓ | ✓ |
Zwislocki (1962) | 18 | ✓ | Ø | ✓ | ✓ | ✓* | ✓ | Ø | Ø | Ø | ✓ | ✓ |
Kringlebotn (1988) | 20 | ✓ | Ø | ✓ | ✓ | ✓* | ✓ | Ø | ✓ | ✓ | ✓ | ✓ |
Lutman and Martin (1979) | 20 | ✓ | Ø | ✓ | ✓ | ✓* | ✓ | Ø | ✓ | ✓ | ✓ | ✓ |
Stenfelt (2020) | 20 | ✓ | Ø | ✓* | ✓* | ✓ | ✓ | ✓ | ✓ | ✓ | Ø | ✓ |
Onchi (1961) | 21 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | Ø | ✓ | Ø | ✓ | ✓ |
Feng and Gan (2004) | 22 | Ø | ✓ | ✓ | ✓ | Ø | ✓ | Ø | ✓ | ✓ | ✓ | ✓ |
Rosowski and Merchant (1995) | 22 | ✓ | Ø | ✓ | ✓ | ✓* | ✓ | Ø | ✓ | Ø | ✓ | ✓ |
Han (2023) | 24 | Ø | ✓ | ✓ | ✓ | Ø | ✓ | Ø | ✓ | Ø | ✓ | ✓ |
Xue (2020) | 24 | ✓ | Ø | ✓ | ✓ | ✓ | ✓ | Ø | ✓ | Ø | Ø | ✓ |
Pascal (1998) | 25 | ✓ | Ø | ✓ | ✓ | ✓* | ✓ | Ø | ✓ | ✓ | Ø | ✓ |
Withnell and Gowdy (2013) | 25 | ✓ | Ø | ✓ | ✓ | ✓* | ✓ | Ø | ✓ | ✓ | Ø | ✓ |
Goode (1994) | 27 | ✓ | Ø | ✓ | ✓ | ✓* | ✓ | Ø | ✓ | ✓ | ✓ | ✓ |
Keefe (2015) | 32 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | Ø | ✓ | ✓ | ✓ | ✓ |
Giguère and Woodland (1994) | 560 | ✓ | Ø | ✓ | ✓ | ✓ | ✓ | Ø | ✓ | ✓ | ✓ | Ø |
1. Number of elements
Most models, such as those in Fig. 2, contain between 7 and 32 elements. However, there is one notable exception that comprises 560 elements (Giguère and Woodland, 1994). Additionally, it is worth noting that models with more elements are more likely to simulate more parts of the ear, as visualized in Table I.
2. Type of model elements
Regarding the types of elements, some models use a mechanical representation, such as model 1 in Fig. 2, while others use an electrical representation of elements, such as models 2 and 3. Yet, others use both electrical and mechanical elements. For example, the model of Keefe (2015) uses electrical elements to model the outer and inner ear, while it uses mechanical elements for the middle ear. Also, Onchi (1961) reports a model with mechanical elements and a transformation to a model with electrical elements.
3. Parts of the ear
The LEMs also describe different parts of the ear. For example, model 1 describes the middle ear, model 2 describes the inner ear, and model 3 describes all three parts of the ear. Models that only describe a part of the ear in detail often use a Thévenin equivalent for the other parts, for example, the middle ear impedance (ZME) in model 2.
4. Type of conduction
Every LEM simulates the AC pathway, but only some model BC, and from those, only the one by Stenfelt (2020), model 2 in Fig. 2, models all five main pathways. The models of Guan (2020), Hudde and Weistenhöfer (1999), and Rosowski (2004) simulate, respectively, inertia of the inner ear fluid, inertia of the middle ear ossicles, and compression of the cochlear walls. To the best of the authors' knowledge, there does not exist a LEM that simulates BC from the coupling site of the actuator to the ICP.
5. Choice of elements
The reports used multiple strategies to determine model elements and their values. Except for Frear (2018), Giguère and Woodland (1994), Hudde and Engel (1998), and Zwislocki (1962), all authors reused some elements of one or more previous models. Another strategy to determine elements and their value is to base them on anatomical data. For example, some LEMs use the area of the tympanic membrane or the mass of the stapes. In addition, most researchers also optimized values of some elements such that the predicted pressures and velocities fit experimentally obtained data.
6. Comparison with experimental data
Almost all studies (21 out of 25) compared some of their final LEMs predicted impedances, pressures, or velocities with experimentally obtained data. The supplementary materials1 gives a complete overview of the reported comparisons between predicted and experimental data. In brief, most reports compare with experimental data from the literature, but some reports use data obtained by their research group. In addition, some reports compared only one specific parameter, such as impedance, pressure, or velocity (Elliott , 2016; Hudde and Weistenhöfer, 1999; Lutman and Martin, 1979; Møller, 1961; Onchi, 1961; Peake , 1992; Voss , 2001; Withnell and Gowdy, 2013; Zwislocki, 1962), while others compared up to seven different parameters (Frear , 2018). Furthermore, the sample size of the experimental data varies between 3 (Hudde and Weistenhöfer, 1999; Onchi, 1961) and 68 (Kringlebotn, 1988; Rosowski and Merchant, 1995) specimens or subjects.
7. Clinical applications
LEMs can be used to investigate multiple clinical applications, such as changes in hearing sensitivity caused by clinical pathologies or hearing aids. Table II gives an overview of these applications and the LEMs that simulate them.
Clinical applications and LEMs that simulate them.
Clinical application . | LEMs . |
---|---|
Tympanic membrane perforation | Goode (1994), Voss (2001) |
Otosclerosis | Goode (1994), Zwislocki (1962) |
Round window reinforcement | Elliott (2016) |
Superior canal dehiscence and third window effect | Rosowski (2004), Stenfelt (2020), Xue (2020) |
Round window stimulation | Frear (2018), Xue (2020) |
Ligament and tendon detachment and fixation | Han (2023) |
Clinical application . | LEMs . |
---|---|
Tympanic membrane perforation | Goode (1994), Voss (2001) |
Otosclerosis | Goode (1994), Zwislocki (1962) |
Round window reinforcement | Elliott (2016) |
Superior canal dehiscence and third window effect | Rosowski (2004), Stenfelt (2020), Xue (2020) |
Round window stimulation | Frear (2018), Xue (2020) |
Ligament and tendon detachment and fixation | Han (2023) |
B. Quality assessment
1. METF
Figure 3 shows model predictions and the experimental ranges of the METF, or the ratio between stapes velocity and ear canal pressure. Most predicted METFs lie within the range of the experimentally obtained data. However, the METF of Liu and Neely (2010) lies below the range and lacks the typical configuration. The one by Pascal (1998) lies above the experimental ranges at frequencies below 400 Hz. For both LEMs, the model elements were not optimized to fit the experimental data of the METF. Also, the model of Giguère and Woodland (1994), where the original paper did not compare its predictions with experimental data, lies above the experimental ranges for frequencies between 440 and 1010 and 3760–5280 Hz. Regarding the phase of the METF, most models follow the trend of the experimental data, except the one from Liu and Neely (2010), which neither follows the trend for the amplitude. The best fit for the phase is found in the models of Han (2023), Feng and Gan (2004), Xue (2020), Goode (1994), Kringlebotn (1988), and Keefe (2015). These models have in common that they all simulate the external and middle ear in detail, as opposed to with a Thévenin equivalent, and fitted their model based on experimental data.
(Color online) Model predictions of (1) the METFs (stapes velocity normalized to ear canal pressure) compared with the combined experimental data of Aibara (2001), Rosowski (2007), and Voss (2000). (2) The ZTM (ratio of pressure to volume velocity at the tympanic membrane) compared with the combined experimental data of Hudde (1983), Rabinowitz (1981), and Withnell and Gowdy (2013). (3) the ER (ratio of reflected to incident energy) compared with the combined experimental data of Hudde (1983), Feeney (2009), Farmer-Fedor and Rabbitt (2002), and Margolis (1999).
(Color online) Model predictions of (1) the METFs (stapes velocity normalized to ear canal pressure) compared with the combined experimental data of Aibara (2001), Rosowski (2007), and Voss (2000). (2) The ZTM (ratio of pressure to volume velocity at the tympanic membrane) compared with the combined experimental data of Hudde (1983), Rabinowitz (1981), and Withnell and Gowdy (2013). (3) the ER (ratio of reflected to incident energy) compared with the combined experimental data of Hudde (1983), Feeney (2009), Farmer-Fedor and Rabbitt (2002), and Margolis (1999).
2. Tympanic membrane impedance
Figure 3 also shows ZTM, or the ratio of pressure to volume velocity at the membrane. Some model predictions of this parameter are below the ranges (Giguère and Woodland, 1994; Keefe, 2015), while another lies above the ranges (Goode , 1994), and even others show predictions above and below the ranges depending on the frequency (Feng and Gan, 2004; Han , 2023; Liu and Neely, 2010; Rosowski , 2004). In addition, some models show a resonance peak, which is not observed in the experimental data (Møller, 1961; O'Connor and Puria, 2008; Xue , 2020; Zwislocki, 1962). The best fit is found for the models of Kringlebotn (1988), Lutman and Martin (1979), Rosowski and Merchant (1995), Xue (2020), and Pascal (1998). These models have in common that they have at least 20 elements, and that they model all three parts of the ear.
3. ER
Figure 3 also shows the ER or the ratio of the reflected to incident energy. Most models show a high reflectance at the low and high frequencies, and a low reflectance at the mid frequencies, similar to the experimental data. Nevertheless, the predicted ERs are in general lower than the experimental data. Only the model of Liu and Neely (2010) shows a reflectance that falls within the experimental ranges and aligns with the established trend. Regarding the phase, experimental data are only available for frequencies above 1 kHz. The model of Liu and Neely (2010) also lies in this phase range.
4. ICP for AC
ICPs are a promising measurement tool to evaluate cochlear drive and, thus hearing sensation. Aibara (2001), Grossöhmichen (2016), Nakajima (2009), and Puria (1997) measured these pressures in human cadaveric specimens for AC, and normalized them to ear canal pressure. These normalized pressures, along with the model predictions, are presented in Fig. 4. Amplitudes of the pressures predicted by most models follow the trend of the experimental data. However, the model predictions of the phase do not always follow the trend of the experimental data.
(Color online) Model predictions of ICPs (PSV, PST, and Pdiff) for AC normalized to ear canal pressure, compared with the combined experimental data of Aibara (2001), Grossöhmichen (2016), Nakajima (2009), and Puria (1997).
(Color online) Model predictions of ICPs (PSV, PST, and Pdiff) for AC normalized to ear canal pressure, compared with the combined experimental data of Aibara (2001), Grossöhmichen (2016), Nakajima (2009), and Puria (1997).
(Color online) Model predictions of ICPs (PSV, PST, and Pdiff) for BC normalized to promontory velocity, compared with the combined experimental data of Stieger (2018), Mattingly (2020), Fierens (2022), and Putzeys (2022).
(Color online) Model predictions of ICPs (PSV, PST, and Pdiff) for BC normalized to promontory velocity, compared with the combined experimental data of Stieger (2018), Mattingly (2020), Fierens (2022), and Putzeys (2022).
What is also noteworthy is that the amplitudes of the PSV and Pdiff predicted by the LEMs of Guan (2020) and Rosowski (2004), the models that also simulate BC stimulation, are above the experimental ranges. Further, the LEM of Keefe (2015) is the only one that models PSV, PST, and Pdiff, and for which all pressures are between the experimental ranges. In contrast with other LEMs, this LEM simulates all three parts of the ear, has many elements (32), uses a combination of the three fitting strategies, and also includes an impedance for middle ear cavities.
5. ICP for BC
Similar to AC, ICPs are also a promising tool to evaluate cochlear drive and hearing sensation for BC. Here, pressures are normalized to promontory velocity, as shown in Fig. 5. Again, the predicted data fit well within the experimental ranges. Regarding the model from Stenfelt (2020), the fit to Pdiff improves when PSV is predicted at position A, the center of the vestibule, rather than position B, the border between the vestibule and scala vestibuli.
6. Summary of the quality assessment
Table III summarizes the previous findings by evaluating the fit between the model predictions and experimental data for all parameters. Figures 6 and 7 show the frequency ranges for which the predictions lay within the experimental ranges, and the exact cut-off frequencies can be found in the supplementary materials.1 These results show that each model is good at predicting some of the parameters, but none of the models has a good fit for all of them.
Evaluation of the fit between model predictions and experimental data, based on the percentage of the predictions within the experimental data on a logarithmic scale. +++, >90%; ++, >75%; +, >50%; ---, <10%; --, <25%, -, <50%; Ø, the model does not predict the parameter. METF, middle ear transfer function; ZTM, tympanic membrane impedance; ER, energy reflectance; AC, air conduction; BC, bone conduction; PSV, scala vestibuli pressure; PST, scala tympani pressure; Pdiff, differential pressure.
Author (Year) . | | METF | . | ∠METF . | Re (Z TM) . | Im (Z TM) . | | ER | . | ∠ER . | AC : | P SV | . | AC : ∠P SV . | AC : | P ST | . | AC : ∠P ST . | AC : | P diff | . | AC : ∠P diff . | BC : | P SV | . | BC: ∠P SV . | BC : | P ST | . | BC : ∠P ST . | BC : | P diff | . | BC : ∠P diff . |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Liu and Neely (2010) | + | - | - | -- | +++ | - | + | - | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø |
Frear (2018) | +++ | + | Ø | Ø | Ø | Ø | ++ | - | + | -- | +++ | -- | Ø | Ø | Ø | Ø | Ø | Ø |
Guan (2020) | +++ | + | Ø | Ø | Ø | Ø | - | - | + | -- | --- | -- | ++ | + | ++ | + | ++ | + |
Møller (1961) | Ø | Ø | ++ | + | - | --- | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø |
Rosowski (2004) | Ø | Ø | --- | - | +++ | - | - | + | +++ | - | -- | -- | Ø | Ø | Ø | Ø | Ø | Ø |
Marquardt and Hensel (2013) | +++ | + | Ø | Ø | Ø | Ø | +++ | + | +++ | --- | +++ | - | Ø | Ø | Ø | Ø | Ø | Ø |
O'Connor and Puria (2008) | +++ | ++ | ++ | + | - | -- | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø |
Zwislocki (1962) | +++ | + | - | + | -- | --- | + | - | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø |
Kringlebotn (1988) | +++ | +++ | ++ | ++ | --- | -- | +++ | ++ | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø |
Lutman and Martin (1979) | +++ | + | +++ | + | --- | - | + | - | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø |
Stenfelt (2020) A | Ø | Ø | Ø | Ø | Ø | Ø | +++ | Ø | + | Ø | Ø | Ø | ++ | Ø | ++ | Ø | ++ | Ø |
Stenfelt (2020) B | Ø | Ø | Ø | Ø | Ø | Ø | +++ | Ø | + | Ø | Ø | Ø | ++ | Ø | ++ | Ø | + | Ø |
Feng and Gan (2004) | ++ | +++ | +++ | - | + | -- | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø |
Rosowski and Merchant (1995) | +++ | ++ | ++ | ++ | --- | -- | +++ | + | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø |
Han (2023) | +++ | +++ | + | -- | + | - | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø |
Xue (2020) | +++ | +++ | ++ | + | - | - | +++ | +++ | Ø | Ø | +++ | - | Ø | Ø | Ø | Ø | Ø | Ø |
Pascal (1998) | + | + | +++ | + | --- | --- | + | + | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø |
Goode (1994) | ++ | +++ | - | - | + | - | + | + | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø |
Keefe (2015) | +++ | +++ | ++ | + | -- | --- | +++ | +++ | +++ | + | +++ | + | Ø | Ø | Ø | Ø | Ø | Ø |
Giguère and Woodland (1994) | + | - | + | + | --- | --- | Ø | Ø | Ø | Ø | ++ | + | Ø | Ø | Ø | Ø | Ø | Ø |
Author (Year) . | | METF | . | ∠METF . | Re (Z TM) . | Im (Z TM) . | | ER | . | ∠ER . | AC : | P SV | . | AC : ∠P SV . | AC : | P ST | . | AC : ∠P ST . | AC : | P diff | . | AC : ∠P diff . | BC : | P SV | . | BC: ∠P SV . | BC : | P ST | . | BC : ∠P ST . | BC : | P diff | . | BC : ∠P diff . |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Liu and Neely (2010) | + | - | - | -- | +++ | - | + | - | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø |
Frear (2018) | +++ | + | Ø | Ø | Ø | Ø | ++ | - | + | -- | +++ | -- | Ø | Ø | Ø | Ø | Ø | Ø |
Guan (2020) | +++ | + | Ø | Ø | Ø | Ø | - | - | + | -- | --- | -- | ++ | + | ++ | + | ++ | + |
Møller (1961) | Ø | Ø | ++ | + | - | --- | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø |
Rosowski (2004) | Ø | Ø | --- | - | +++ | - | - | + | +++ | - | -- | -- | Ø | Ø | Ø | Ø | Ø | Ø |
Marquardt and Hensel (2013) | +++ | + | Ø | Ø | Ø | Ø | +++ | + | +++ | --- | +++ | - | Ø | Ø | Ø | Ø | Ø | Ø |
O'Connor and Puria (2008) | +++ | ++ | ++ | + | - | -- | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø |
Zwislocki (1962) | +++ | + | - | + | -- | --- | + | - | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø |
Kringlebotn (1988) | +++ | +++ | ++ | ++ | --- | -- | +++ | ++ | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø |
Lutman and Martin (1979) | +++ | + | +++ | + | --- | - | + | - | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø |
Stenfelt (2020) A | Ø | Ø | Ø | Ø | Ø | Ø | +++ | Ø | + | Ø | Ø | Ø | ++ | Ø | ++ | Ø | ++ | Ø |
Stenfelt (2020) B | Ø | Ø | Ø | Ø | Ø | Ø | +++ | Ø | + | Ø | Ø | Ø | ++ | Ø | ++ | Ø | + | Ø |
Feng and Gan (2004) | ++ | +++ | +++ | - | + | -- | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø |
Rosowski and Merchant (1995) | +++ | ++ | ++ | ++ | --- | -- | +++ | + | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø |
Han (2023) | +++ | +++ | + | -- | + | - | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø |
Xue (2020) | +++ | +++ | ++ | + | - | - | +++ | +++ | Ø | Ø | +++ | - | Ø | Ø | Ø | Ø | Ø | Ø |
Pascal (1998) | + | + | +++ | + | --- | --- | + | + | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø |
Goode (1994) | ++ | +++ | - | - | + | - | + | + | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø | Ø |
Keefe (2015) | +++ | +++ | ++ | + | -- | --- | +++ | +++ | +++ | + | +++ | + | Ø | Ø | Ø | Ø | Ø | Ø |
Giguère and Woodland (1994) | + | - | + | + | --- | --- | Ø | Ø | Ø | Ø | ++ | + | Ø | Ø | Ø | Ø | Ø | Ø |
(Color online) Frequency ranges where the model predictions are within the experimental ranges: amplitudes, except for ZTM, where resistance is shown. A full line means that the model prediction is within the experimental data. The absence of a line signifies that either the model could not predict the parameter or that the model's prediction lies outside the established range. METF, middle ear transfer function; ZTM, tympanic membrane impedance; ER, energy reflectance; AC, air conduction; BC, bone conduction; PSV, scala vestibuli pressure; PST, scala tympani pressure; Pdiff, differential pressure.
(Color online) Frequency ranges where the model predictions are within the experimental ranges: amplitudes, except for ZTM, where resistance is shown. A full line means that the model prediction is within the experimental data. The absence of a line signifies that either the model could not predict the parameter or that the model's prediction lies outside the established range. METF, middle ear transfer function; ZTM, tympanic membrane impedance; ER, energy reflectance; AC, air conduction; BC, bone conduction; PSV, scala vestibuli pressure; PST, scala tympani pressure; Pdiff, differential pressure.
(Color online) Frequency ranges where the model predictions are within the experimental ranges: amplitudes, except for ZTM, where reactance is shown. A full line means that the model prediction is within the experimental data. The absence of a line signifies that either the model could not predict the parameter or that the model's prediction lies outside the established range. METF, middle ear transfer function; ZTM, tympanic membrane impedance; ER, energy reflectance; AC, air conduction; BC, bone conduction; PSV, scala vestibuli pressure; PST, scala tympani pressure; Pdiff, differential pressure.
(Color online) Frequency ranges where the model predictions are within the experimental ranges: amplitudes, except for ZTM, where reactance is shown. A full line means that the model prediction is within the experimental data. The absence of a line signifies that either the model could not predict the parameter or that the model's prediction lies outside the established range. METF, middle ear transfer function; ZTM, tympanic membrane impedance; ER, energy reflectance; AC, air conduction; BC, bone conduction; PSV, scala vestibuli pressure; PST, scala tympani pressure; Pdiff, differential pressure.
IV. DISCUSSION
LEMs enhance our comprehension of sound conduction in both healthy auditory systems and those affected by specific pathologies. Moreover, these models offer valuable insights into simulating various auditory devices such as earphones and headphones (Fujise, 2018; Kulkarni and Colburn, 2000; Voss and Herrmann, 2005), but also hearing aids and implants (Denk , 2017; Frear , 2018; Rusinek and Weremczuk, 2020; Sankowsky-Rothe , 2015; Xue , 2020) and hearing protection (Kalb, 2010; Schroeter and Poesselt, 1986; Zhong and Zhang, 2021). Therefore, this section discusses considerations when developing or selecting a LEM. Subsequently, the limitations associated with this systematic review are also thoroughly examined.
A. Considerations when creating a new model or determining the appropriate existing model for a specific application
Depending on the model's purpose, some characteristics can be beneficial or unfavorable. Regarding the type of model elements, electrical or mechanical, neither is better as it is possible to transform mechanical elements into electrical ones and vice versa. However, it is more intuitive to model pressures and volume velocities in the outer and inner ear with electrical elements, and to model forces and linear velocities in the middle ear with mechanical elements.
Including all ear parts makes a model more complete but also necessitates more model elements. As seen in the quality assessment, more model elements will generally improve the fit of the model predictions to the experimental data. However, the trade-off is that certain model elements can lack physical meaning, and needlessly increase the complexity of the model. In addition, it increases the computational time to converge to a good fit. The significance of this cost primarily arises when fitting a new model rather than when using an existing model. Thus, excluding the other parts or replacing them with a Thévenin equivalent is useful when investigating only a part of the ear, as this reduces the number of elements.
There are multiple strategies to determine the values of the model elements. They can be reused from previous models or derived from anatomical properties. Nevertheless, the ultimate objective is to fit them into experimental data to obtain optimal values. When optimizing a model to achieve the best fit for one parameter, the fit with other parameters becomes uncertain. However, when optimizing a model for multiple parameters, careful selection of model elements is required to strike a compromise that ensures satisfactory fits for each of them. This approach may result in a less precise fit for individual parameters, but it will yield a more comprehensive and physically meaningful representation of the hearing organ as a whole. The same principle applies when considering fitting solely to amplitude or both amplitude and phase. In addition, certain models are based on the data available at the time. These models have not been updated for this review, though new data could enhance their accuracy and validity.
Moreover, adding another stimulation type, such as BC, to a model increases the number of parameters to fit. This increased number of parameters explains why those models tend to have a worse fit to the experimental AC data than models that solely focus on AC stimulation. Both models that incorporate BC stimulation simulate the segment from the velocity at the promontory to the pressures within the cochlea. However, with BC, sound travels from the coupling site through the skin and skull before it reaches the cochlea. It does not travel primarily through the promontory, indicating the lack of a model that accurately simulates sound conduction from the coupling site to the promontory. A model that simulates sound conduction from the coupling site to the promontory velocity could be fitted to data that provides the mechanical point impedance or the force divided by the velocity at the stimulation location (Håkansson , 1986; Stenfelt and Goode, 2005).
Furthermore, BC sound travels to the inner ear fluid via five pathways, but the model of Guan (2020) only simulates one of them. In contrast, the one from Stenfelt (2020) simulates the five main pathways. However, it is crucial to consider that the combination of the five pathways is determined by the root of the summed squares, thereby eliminating the phase information. Moreover, depending on the position of the coupling site, the sound stimulus may generate another promontory velocity and ICP (Fierens , 2022), and none of the current models are able to simulate different coupling sites.
If a model incorporates a clinical application, it offers significant advantages for examining the specific impact of the pathology in question or the effectiveness of the hearing aid on auditory perception. When only minor modifications are required to integrate the clinical application into the model, it validates the physical significance of the model elements. However, including a clinical application necessitates fitting the model for both normal hearing and the pathology under investigation. As previously mentioned, fitting to multiple parameters results in a compromise of the fit for individual parameters.
The appropriate model should, first of all, be able to predict the parameters under investigation. This ability can be verified in Table III or the supplementary materials,1 which gives the exact values of the frequency ranges. Furthermore, if two models predict the parameters equally well, choosing the model with the least elements is recommended to reduce the computational cost. Hence, the models in the figures are sorted by the number of elements. Last, if the application includes a pathology, choosing a model that includes this pathology is recommended.
B. Limitations
This review compared the METF, ZTM, ER, and ICPs—values often used to evaluate hearing sensation—of the LEMs with experimentally obtained data. However, the models can also predict other characteristics, which are not discussed in this review. Examples of these characteristics are cochlear impedance (ratio of pressure to volume velocity in the scala vestibuli) (Keefe, 2015), ICP relative to stapes velocity, and mechanical impedance of the mastoid (ratio of output force from a BC actuator to velocity at the mastoid) (Nie , 2022). Therefore, when a LEM cannot accurately predict the METF, ZTM, ER, or ICPs, it possibly predicts these other characteristics accurately and vice versa.
Another limitation of the quality assessment is that it only considered the fit of the model predictions with the experimental data for the reported model element values. However, it does not consider the possibility of optimizing the free element values to achieve a more accurate fit, particularly in cases where models were published prior to the availability of experimental data. In addition, other metrics that are not suitable for quantization, such as the consistency of the physical schematization, the simplicity, the physical meaning of the free model elements, and the ease of reproducing a model, were not considered during the quality assessment.
Further, this review evaluated LEMs based on the results for non-pathologic ears, while some models also simulate pathologic ears (Elliott , 2016; Goode , 1994; Guan , 2020; Han , 2023; Rosowski , 2004; Stenfelt, 2020; Voss , 2001; Xue , 2020; Zwislocki, 1962). In addition, this review only evaluates AC and BC, even though other stimulation types, such as round window stimulation (Frear , 2018; Xue , 2020) and mechanical stimulation of the middle ear (Rusinek and Weremczuk, 2020), exist too. Last, this review did not include animal models, although they resemble human models (Dallos, 1970; Dancer and Franke, 1980; Lemons and Meaud, 2016; Puria and Allen, 1998).
V. CONCLUSION
For AC, some LEMs simulate the ear from the outer to the inner ear and can accurately predict the METF, ZTM, ER, and ICPs. Regarding BC, however, LEMs only model a part of the ear, and most only model one of the five main pathways. Thus, a LEM that models BC from the coupling site of the actuator to ICP in the inner ear is still lacking and would help investigate more clinically relevant aspects of human ear sound conduction pathways and the functioning of BC implants.
ACKNOWLEDGMENTS
The authors are grateful to Professor Dr. N. Green and Dr. C. Stieger for sharing their experimental data, Professor Dr. S. Stenfelt for discussing and sharing data from his LEM, and Professor Dr. J. Rosowski for the critical review. This work was supported by Flanders Innovation and Entrepreneurship (HBC.2020.2201), Research Foundation—Flanders (FWO1SD3322N, FWO1804816N), and Cochlear Ltd.
See supplementary material at https://doi.org/10.1121/10.0020841 for an overview of the search strategy, the schematic views of the included LEMs, a summary of the reported comparison between predicted and experimental data, and the frequency ranges for which the model predictions are within the experimental data ranges.