Review Article A Clinically Oriented Introduction and...

Review ArticleA Clinically Oriented Introduction and Review onFinite Element Models of the Human Cochlea

Dimitrios Kikidis1 and Athanasios Bibas1,2

1 1st Department of Otorhinolaryngology, Head and Neck Surgery, National and Kapodistrian University of Athens,Hippocrateion General Hospital, 114 Vas. Sophias Avenue, 11527 Athens, Greece

2 UCL Ear Institute, 332 Grays Inn Road, London WC1X 8EE, UK

Correspondence should be addressed to Athanasios Bibas; [email protected]

Received 9 May 2014; Revised 29 August 2014; Accepted 3 September 2014; Published 4 November 2014

Academic Editor: Fan Yang

Copyright © 2014 D. Kikidis and A. Bibas. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited.

Due to the inaccessibility of the inner ear, direct in vivo information on cochlear mechanics is difficult to obtain. Mathematicalmodelling is a promising way to provide insight into the physiology and pathology of the cochlea. Finite element method (FEM) isone of the most popular discrete mathematical modelling techniques, mainly used in engineering that has been increasingly usedto model the cochlea and its elements. The aim of this overview is to provide a brief introduction to the use of FEM in modellingand predicting the behavior of the cochlea in normal and pathological conditions. It will focus onmethodological issues, modellingassumptions, simulation of clinical scenarios, and pathologies.

1. Background

Management of hearing loss requires a thorough under-standing of the pathophysiological mechanisms throughwhich diverse pathologies give rise to hearing impairmentin humans. Furthermore when surgical interventions arerequired, planning and predicting of the surgical outcomerequire a thorough understanding of the ear mechanics.Despite significant progress in surgical techniques and audi-tory implant technologies, more work is needed to developnovel approaches to restore hearing that would take intoaccount patient-specific anatomical and clinical data thatcould predict and maximise the final outcome.

Research into human inner ear physiology and pathologyis usually clinical, with standard audiological and/or imagingstudies. Noninvasive diagnostic tools are often unsatisfactoryin either providing sufficient information on the physiologyof hearing of individual patients or predicting the outcomeof rehabilitation. Inability for in vivo measurements in thehuman cochlea greatly restricts the study of special aspects ofcochlea physiology and pathophysiology. The only potential

sources of raw data regarding cochlear mechanics in humansare temporal bone cadaveric experiments. Von Bekesy exper-iments on the travelling wave in human cadavers [1] arestill highly influential, while more recently in vitro laserDoppler vibrometry (LDV) experiments in human temporalbones have provided more raw data on the vibrationalcharacteristics of the basilar membrane (BM) as well as thespiral lamina [2].

Mathematical models of the cochlea can therefore playa key role in understanding the biomechanical processesinvolved in hearing. A series of suchmodels have been devel-oped during the past decades, towards a better understandingof ear physiology, including travellingwave production, outerhair cell motility, fluid dynamics, and micromechanics of thecochlea. The power of such a model is not only its abilityto explain current physiological concepts and account forempirical (experimental and clinical) observations, but alsoits ability to incorporate future data, as they become availablein the literature. By adjusting key parameters, cochlearmodels may also be used to simulate a variety of pathologicalconditions that lead to hearing loss as well as predict the

Hindawi Publishing CorporationBioMed Research InternationalVolume 2014, Article ID 975070, 8 pageshttp://dx.doi.org/10.1155/2014/975070

2 BioMed Research International

cochlea’s response when stimulated by auditory implants. Itis safe to say that a complete computational model of thecochlea has yet to be attained.

The finite element method (FEM) is one of the mostpopular modelling techniques in structural mechanics. Thebasic concept is the subdivision of the domain of interestinto components of simpler geometry called finite elements(discretization). These elements are interconnected at pointscommon to two or more elements (nodes or nodal points)and/or boundary lines and/or surfaces. FEM encompassesall the methods for connecting many simple equations overthose elements, to approximate a more complex equationover the domain of interest.The response of themathematicalmodel is then considered to be approximated by that of thediscrete model obtained by connecting or assembling thecollection of all elements. Apart from the governing equationsof the system, boundary conditions should also be describedin FE modelling, in which restrictions in the behaviour ofthe system (often in the form of a series of equations) at itsphysical border are considered. Although other modellingmethodologies (i.e., the WKB-numeric method) have beensuccessfully employed in modelling the cochlea, this paperwill focus on FEM, as it is more intuitive to clinicians [3, 4].

2. Finite Element Modelling ofthe Normal Human Cochlea

2.1. Basilar Membrane. With a few exceptions, the majorityof human cochlea modelling focuses on efforts to accuratelysimulate BM vibratory characteristics and travelling wavedevelopment, and thus this overview will largely concentrateon these modelling attempts. The usual approach is theuse of 2-chamber (scala media included in scala vestibule),uncoiled, passive mechanical models. Thus, cochlear cur-vature, the micromechanics of the OC, and Reissner’s andtectorialmembrane are not accounted for [5–7].Most of thesemodels are also not coupled to the middle and outer earand stimulation of the perilymph is simulated by applyingthe input pressure directly to the oval window. As thecochlea is universally modeled as a rigid structure, no fluiddisplacement occurs at its wall boundary and the normalcomponent of fluid velocity at that point is zero. It is usuallyassumed that the pressure difference acts as a load on theBM causing it to deflect and the fluid velocity relative to thebasilar membrane is zero at this interface. The perilymphis usually modeled as being incompressible and inviscid.However, inviscid flowmay not be a valid assumption close tofluid boundary where the boundary layer plays a significantrole, as in the space between the tectorial membrane and thereticular lamina.

A large number of parameters in regard to the physicalcharacteristics and mechanical properties of the differentstructural elements are usually required for the constructionof cochlear models (i.e., Young’s modulus, biochemical andelectrical properties, etc.). Not all of the relevant values areavailable in humans, so these either are borrowed from ani-mal studies, are experimentally measured in vitro (usually byhuman temporal bone experiments), or have to be estimated

Scala vestibuli

Scala tympani

Organ of Corti

Reissner’s membrane

Bony spiral lamina

Limbus

Basilar membraneInner pillar

Spiral ligament

Figure 1: Human OC (approximately 12mm from base). Theosseous spiral lamina stops at the level of the insertion of the RM tothe spiral limbus and is not in contact with the inner pillar.Thus, theOC rests entirely on themembranous spiral lamina (inner pilar) andthe BM (specimen no. 280L, 10x, HumanTemporal BoneCollection,UCL Ear Institute).

through the comparison of model results with experimentalstudies. Overfitting may become a problem and thus reducethe predictive power of these models.

The BM is divided into two sections: (a) the arcuatezone, which consists of a single layer of radial fibers, and(b) the pectinate zone, which consists of a double layer ofradial fibers in an amorphous ground substance. These fibersconsist of collagen II without longitudinal cross links [8], soa highly orthotropic structure is assumed with high stiffnessin the radial and low stiffness in the longitudinal direction.It is therefore important to include orthotropicity in BMmodelling.

The BM is usually modeled as attached to the spirallamina and the lateral wall in a simply supported manner.However, the complex microanatomy of the medial insertionto the spiral lamina suggests that the spiral lamina supportshould not be modelled as a simple suspension. As is evidentfrom histological sections (Figures 1 and 2), the main sup-porting bundles of the osseous spiral lamina continue directlyinto the BM fibers, suggesting that a clamped boundarycondition may be more appropriate. It has also been shownthat the osseous spiral lamina is not as rigid as previouslythought and was found to vibrate similar to the BM, wherethe two are attached [2]. So far, cochlear models have notincorporated the flexibility of the osseous spiral lamina. Also,only few models take into account the fact that the lateralend of the BM is attached to the outer wall through thespiral ligament, which may also vibrate in response to sound.The fibers from the basilar membrane also continue directlyinto the spiral ligament, which again probably supports aclumped boundary condition rather than a simply supportedone (Figure 2).

One of the first models to accurately simulate BM vibra-tion characteristics was developed by Bohnke and Arnold[9]. It was a 2-chamber 3D finite element passive modelconstructed usingmicrotomography. Notable boundary con-ditions were clamping of the spiral lamina inner boundary,

BioMed Research International 3

Outer pillar Inner pillar

Outer hair cells

Tectorial membrane

Spiral ligament

Deiter’s cellsHensen cells

Pectinate zoneArcuate zone

Figure 2: Human OC (approximately 12mm from base). Thefibers from the pectinate zone of the BM continue into the spiralligament, where they are anchored (specimen no. F174R, 20x,Human Temporal Bone Collection, UCL Ear Institute).

allowing no rotation and displacement, and simple supportat the side of the spiral ligament, allowing for rotation at thelongitudinal (x) axis. Perilymph was considered inviscid.TheBM dimensions were calculated using guinea pig values [10].The input values were pressure loads of 1 Pa (equivalent to 94dBSPL) at 3 frequencies (100Hz, 2000Hz, and 10000Hz).Thepredictions of the BM displacement were in agreement withVonBekesy’s observations [1]. It was noted that themaximumdisplacement of the BM was of the same order of magnitude(0.2 nm) for the three frequencies tested.

Gan et al. [11] developed a passive uncoiled FE modelof the cochlea, coupled to a model of the external canal andthe middle ear. The same team developed later a more com-prehensive model with a coiled cochlea [12]. Although theauthors mention that information for the construction of thegeometric model was obtained from temporal bone histologysections, it is apparent that actual 3D image reconstructionwas not performed from the available sections, at leastregarding the cochlea. The authors were able to compute themiddle ear transfer function and the BM vibration displace-ment normalised by the stapes displacement as a function ofthe distance from base. Although validation for the middleear transfer function was achieved by experimental data fromhuman cadaver ears, it is not clear which data were used forthe validation of the BM response.Themodel was also used tocompute the efficiency of the forward and reversemechanicaldriving with middle ear implant, as well as the passivevibration of the BM when a cochlear implant was placed inthe scala tympani. This is probably the only FE model whereRM is taken into account.The introduction of the scalamediain their model allowed for a more realistic representation ofthe physical properties of the cochlea. Scala media modellingintroduced an asymmetry between the forward and reversedriving of the cochlea.Thus, it was also used to predict how itsmechanical properties affected the vibratory characteristicsof the BM. According to the authors, the model may be

used to predict how changes in the morphology or function(permeability) of the RM can affect cochlear function.

2.2. Organ of Corti. The OC was initially modeled as a rigidstructure, but FE methods were employed later to captureits micromechanical properties in more detail [9, 13, 14].However, these models are either 2D or 3D but of a limitedlength along the x-axis, which limits their ability to accuratelypredict the coupled response of the basilar membrane.

In most models, the osseous spiral lamina is seen toextend to the inner pillar cells, as observed in animals.This isin contrast to themobile outer pillar cell that rests on the BM.In thisway, the base of the inner pillar cell would have a hinge-like action at the point of contact with the bony spiral lamina.However, this relationship does not exist in humans, wherethe bony spiral lamina has no such spread, and it falls shortof reaching the attachment of the RM to the spiral limbus(Figure 1). Thus, in the human cochlea, the entire OC restson the membranous spiral lamina or the BM.

Bohnke and Arnold [9] designed one of the first 3Dmodels of the OC to account for the active function of theOHCs. The ability of the OHCs to elongate and contractwas modeled by heating and cooling according to a thermalexpansion coefficient 𝑎 = 10−4.This feature could be switchedon or off to simulate the active or passive OC, respectively.To achieve an effective gain of 40 dB for the displacement ofthe reticular lamina, OHCs gain of 2 (i.e., the ratio of somaticOHCs length change to stereocilia bundle displacement) waschosen to reflect experimental results [15]. When the activefeature of theOHCswas considered, an additional increase ofthe reticular displacement (40 dB, amplitude = 160 nm) withadditional distortion of the BM was observed.

Nam and Fettiplace [16] presented a three-dimensionalmodel to illustrate deformation of the OC by the two activeprocesses: voltage-driven contractility of the outer hair cellbody and active motion of the hair bundle. The modelwas able to capture isolated local responses with simulatedlongitudinal lengths of 400 and 600𝜇m at the base and apex.In some simulations, lengths of 1200mm were used. This isprobably the only model incorporating such a long lengthin their OC model, providing a limited coupled responsebetween the OHCs and the BM. The radial structural com-ponents were coupled in the longitudinal direction by threecontinuous longitudinal structures and one discrete longitu-dinal structure. Continuous longitudinal coupling includedlongitudinal beams of BM, reticular lamina, and tectorialmembrane, whereas the coupling by the OHCs and Deiter’scell phalangeal processes was discrete. Outer hair cells andDeiter’s cells were tilted in opposite directions, and this isone of the few models that takes into account the phalangealattachments to accurately reflect their microanatomic orien-tation [17]. The radial stiffness of the tectorial membrane wasfound to have an important effect in mechanical feedback.

2.3. Outer Hair Cell Modelling. The mechanisms underlyingcochlear amplification include the prestin-mediated somaticmotility of the OHCs as well as active movements of thehair bundles contributed by themechanotransducer channels


(stereociliary motility) [18]. Spector et al. [19] modeled theOHCs taking into account the angle of their inclinationas well as their length, so that they could simulate theactive process in the cochlea, whereby two cross sectionsalong the cochlea are coupled through the connection ofthe same column of active OHCs. One of the advantagesof this approach was the use of coefficients to representthese active forces. Pathological conditions that may affectthe mechanoelectrical transduction (i.e., presbyacusis) canthus be modelled by this approach, by modifying thesecoefficients.

Stereocilia hair bundles are not usually meshed but areincluded as single elements. Duncan and Grant [20] devel-oped a finite element model taking into account the stiffnessand deflection properties of the hair bundle, but withoutcoupling to the rest of the OC.Themain boundary conditionwas the anchorage of each cilium at its base. Loading of themodel was simulated by a single static force applied to the tipof the tallest cilium. Tips and lateral links were removed inturn from the model to assess their effect on bundle stiffness.When the tip links were removed, the overall bundle stiffnessreduced by 55%.

As mentioned previously, the cochlea is usually uncoiledinmostmodelling approaches, as coilingwas reported to havea negligible effect on cochlear micromechanics. However,recent modelling suggests that, by taking into account thecurvature of the cochlear duct, the shear gain of the cochlearpartition at the apex is increased,which is an indirectmeasureof the bending magnitude of the OHCs stereocilia [16]. Thiseffect is not observed in the basal region of the cochlea, andit seems that it is the radius of curvature that is the mainparameter responsible for the difference in this effect. One ofthe limitations of this study was that calculations were basedonly on the relative motions of the cochlear structures andnot on the absolute amplitude of the BM vibration.

2.4. Tectorial Membrane. Gueta et al. [21] investigated theeffect of the anisotropic properties of the tectorial membraneon the deflection of the stereocilia. By first using forcespectroscopy, it was found that the stiffness of the tectorialmembrane was significantly larger in the vertical than thelateral axis. Consequently, it is more resistant to the verticalmotion of stereocilia and is therefore deflected laterally whenpushed against. This was confirmed by FE simulations ofthe interaction between the stereocilia and the tectorialmembrane, when this anisotropy was incorporated into themodel, thus providing an additional mechanism for thedeflection of outer hair cell stereocilia apart fromviscous fluidforces. It is suggested by the authors that the coexistence ofboth mechanisms may enhance the lateral deflection of theOHCs stereocilia.

Gavara and Chadwick [22] explored the difference inanisotropy between the radial and longitudinal axis of thetectorial membrane based on the anisotropy caused by theorientation of the collagen fibres. It was found that tecto-rial membrane deformations are more pronounced in thedirection parallel to the collagen fibers (radial direction) thanperpendicular to them (longitudinal direction). It is therefore

assumed that there is a strong coupling of the three OHCs inthe same radial direction, while OHCs placed at a differentlongitudinal direction remain uncoupled. However, othermodels stress the importance of longitudinal coupling of thetectorial membrane, which allows for interaction betweencells placed at different places along the BM, and are able toclosely replicate the amplitude of BM traveling wave in vivo[23, 24].

2.5. Reissner’s Membrane. As described above, only Zhangand Gan [12] have included the RM and the scala media intheir model and the way they affect BM vibratory charac-teristics. Apart from its effect on the BM, Reichenbach etal. [25] have recently described travelling waves on RM. Byusing scanning laser Doppler vibrometry on the RM of avariety of animal species, travelling waves were measured,thus supporting a theory on its role in otoacoustic emissions.

2.6. Round Window. Modelling the round window mem-brane is of particular importance as middle ear implantshave been used for directly exciting the cochlea in casesof mixed and severe conductive hearing loss. It has beenrecently shown that mechanical stimulation of the roundwindow membrane with an active middle ear prosthesisproduces cochlear microphonics and stapes velocities thatare functionally equivalent to acoustic stimulation [26].Zhang and Gan [12] examined the mechanical properties ofthe human round window membrane using both acousticstimulation and laser Doppler vibrometry measurementsin human temporal bones. A FEM was subsequently usedto determine the complex and relaxation moduli, by usingan inverse problem solving method. It was shown that theaverage storage modulus changes from 2.32 to 3.83MPaand the average loss modulus from 0.085 to 0.925MPa forfrequencies between 200 and 8000Hz.

2.7. Input to the Cochlea and Middle Ear Coupling. Thephysiological motion of the stapes footplate is piston-like atlow frequencies but shifts to a rocking movement around itsshort and long axes at higher frequencies. However, mostcurrent human cochlear models do not consider the effectsof this rockingmotion because it is believed not to contributeto considerable fluid volume displacement so as to have aneffect on cochlear mechanics.

Models developed by Kim et al. [27, 28] and Zhang andGan [12] have coupled FE models of the external and middleears to the cochlea. Modelling the stapedial annular ligamentis important as the oval window is input site for the excitationsignal. Gan et al. [29] constructed an FE model of the stape-dial annular ligament that they used together with experi-mental setup in temporal bones to calculate its mechanicalproperties.Using amicromechanical testing system, the shearmodulus of the annular ligament was calculated to changefrom 3.6 to 220 kPa when the shear stress increases from 2 to140 kPa. A 3D finite element model of the experimental setupwith the stapedial annular ligament was created for assessingthe effects of loading variation and measurement errorson results. A fixed boundary condition was applied at the


periphery of the annular ligament to simulate its attachmentto the oval window, and the stimulating force was appliedat the center of stapes head perpendicular to the stapesfootplate. The FE modeling results confirmed that simpleshear dominated the deformation of the annular ligament.

2.8. Validation Methodology of Existing Models. Clinical val-idation of cochlear models is not straightforward, since thereare no direct noninvasive techniques to measure the BMresponses of the human cochlea in vivo. To the best ofour knowledge, no cochlear models have used true clinicalvalidation. The most commonly used validation approachin cochlear modelling is the comparison with Von Bekesy’sexperimental data BM displacement and the distribution ofthe characteristic frequency as described by Greenwood [30].Experimentally determined amplitude-frequency curves byStenfelt et al. [2] and Gundersen et al. [31] have also beenused. However, all these measurements involve the passivecochlea, so the active cochlear processes cannot be validated.BM velocity and amplitude measurements from differentspecies have also been used for validation using laser Dopplervibrometry.

Novel validation approaches could include the useof cochlear impedance and psychophysical masking data,which, to the best of our knowledge, have not been cur-rently described in the literature. Cochlear impedance andintracochlear sound pressure measurement data provide ameans to validate cochlear models acoustically as a wholesystem. To the best of our knowledge, no FEMmodel has yetbeen verified against these important acoustical properties.For a quantitative model validation, intracochlear pressuredata exist from human cadaver cochleae. Nakajima et al.performed simultaneous sound pressure measurements inscala vestibuli and scala tympani of the cochlea in humancadaveric temporal bones and measured the transfer func-tions of scala vestibuli and scala tympani pressures relativeto the ear canal pressure [32]. The pressure in scala vestibuliwas generally 10–20 dB larger than in scala tympani overa wide range of frequencies. For frequencies below 500Hz,the phase of the scala tympani pressure relative to ear canalpressure was slightly less than zero, while the phase of thescala vestibuli pressure had almost a 𝜋/4 lead. Above 500Hz,the phases of the pressures were similar. Nakajima et al. werealso able to measure the differential impedance across thecochlear impedance. This has the advantage that, in contrastto standard cochlear impedance measurements, the roundwindow impedance is not taken into account, and hence thesedata can be used for validation in models where the cochleais not coupled to the middle ear.

Psychoacoustic masking methods are widely used toestimate some response properties of the human BM [33–36]. The resulting psychoacoustic tuning curves (PTCs) arethought of as isoresponse curves and are assumed to corre-spond to BM tuning (or isoresponse) curves. Consequently,it is assumed that the tip frequency of any given PTCmatchesapproximately that of a corresponding BM tuning curve andthus could be used for the validation of the human cochlearmodels.

3. Finite Element Modelling in ClinicalScenarios and Applications

Apart from simulating normal physiology, one of the mostpowerful uses ofmodels is their ability to predict pathologicalconditions and to simulate surgical management. Whatfollows is a brief review of some of the papers that haveused FE cochlear models to simulate clinical pathologies andsurgical applications.

3.1. Basilar Membrane Pathology. Skrodzka [37] used acochlear FEM to predict travelling wave patterns and char-acteristic frequencies by simulating BM structural damage.Mechanical damage to the BM (rupture)may result followingacoustic trauma (leading to permanent sensorineural hearingloss) or cochlear implant insertion (leading to decreasedperformance in cases of combined electrical-acoustic stim-ulation strategies). The BM rupture was modeled as a holecentered at a point 7mm from the basal end. An additionalmass was added in the same place, increasing the BMthickness by a factor of 10. The main excitation frequencyused in modified BM models testing was 5 kHz. The modelpredicted that the structural alterations of the BM affectedvelocity values and location of the maximum displacement.Interestingly, some BM locations were predicted to resonatein more than one frequency.These predictions have not beenvalidated clinically.

3.2. Semicircular Canal Dehiscence. Kim et al. [38] modeledsuperior semicircular canal dehiscences (SSCD) in a passivecoiled 3D FE model, by removing a section of the outer bonywall of the canal. The geometric reconstruction was obtainedby using mCT and the cochlea was coupled to the middleear. The following modelling assumptions were taken intoaccount: (1) perilymph was considered inviscid, (2) the BMhad orthotropic elasticity, and (3) damping was accountedfor by a complex Young’smodulus. A zero-pressure boundarycondition was applied to the area exposed by the dehiscence,since at this point the perilymph is in contact with the cere-brospinal fluid, which ismuch larger in volume. BMvelocitieswere calculated in different frequencies, for both AC and BCstimulation, and hearing loss was calculated as the differencein the maximum amplitude of BM velocity between thepre- and postdehiscence simulations. BC stimulation wassimulated by applying rigid-body vibrations along arbitrarydirections in the three-dimensional plane. The model pre-dictions were consistent with the audiometric thresholds ofpatients with a SSCD, showing an improvement in boneconduction and elevation of air conduction thresholds atfrequencies below 1 kHz, although the variation in clinicalpresentation is high.Additional information derived from themodel was the importance of the width of the dehiscenceclosest to the oval window.

3.3. Stapedotomy. Kwacz et al. [39] used an FE model ofthe uncoiled cochlea to study the influence of stapedotomyon round window membrane vibration and to estimate thepostoperative outcome. The model was validated against


experimental measurements from cadaver temporal bonesusing laser Doppler vibrometry. The reduction in the RWmembrane vibration amplitude was related to the pistondiameter, and the maximum reduction was achieved at thehighest frequencies (>3 kHz). This reduction corresponds toan incomplete closure of the air-bone gap resulting in residualconductive hearing loss after stapedotomy. The authors alsoused the FE model to test a new prosthesis that theydeveloped in their laboratory.

3.4. Middle Ear and Cochlear Implantation. Finite elementmodels of the cochlea are very useful to surgeons forenhancing their understanding of the mechanics and stressesinvolved when placing different auditory implants. Simula-tions are also important for manufactory designers to selectappropriate mechanical profiles for future implants.

Zhang and Gan [12] simulated the efficiency of middleear transducer (MET) on different coupling conditions. It wasthus shown that coupling of the MET to the round windowmembrane (reverse driving) wasmore efficient than couplingto the ossicles (forward driving), as far as BM vibrationamplitude was concerned. This was attributed to the smallerdistance to the BM, through the RW stimulation.

FE simulations of cochlea implantation have been usedto predict BM vibration patterns after electrode insertionas well as predict trauma to the cochlea by using differentelectrodemechanical properties. Zhang andGan [12] showedthat cochlear implant insertion resulted in a change in thefrequency response of the BM, by shifting the peak responsetowards the apex. Passive vibration of the BM above theimplant was also greatly diminished. The BM vibration waseliminated at high frequencies and remained at certain levelat low frequencies (below 1 KHz). The results show that thepassive vibration of BMwas preserved at low frequency. Chenet al. [40] used a FEmodel of the cochlea to predict the inser-tion trajectory and contact pressures of a straight cochlearimplant electrode array from nucleus. It was predicted thatan electrode with a uniform stiffness would produce highercontact pressures at the tip (and hence significant moredamage at insertion) than a graded stiffness electrode. Khaand Chen [41] used a FE model to predict the damage to theBM caused by the proximal end of the cochlear implant array.It was predicted that the contour array design is most likelyto impinge on the BM, compared with the straight array andthe single wire electrode, by exerting higher stresses on thescala tympani’s upper surface. In another study by Lim et al.[42], a 3D FE model of the cochlea was used to evaluate sixelectrodes with different stiffness properties due to differentwire arrangements. It was found that the contact pressure atthe tip and the insertion force were highest when the wireswere arranged horizontally. The cochlear implant insertiontechnique was simulated in a FE analysis of the cochlea byKha et al. [43]. It was predicted that anticlockwise rotationsbetween 251∘ and 901∘ applied at the basal end of the array (onthe right side) significantly reduce stress trauma on the BMwhich support the practice of applying small rotation partwaythrough insertion of electrode array to minimize damage tothe BM.

4. Identification of Beyond the State of the ArtCharacteristics for Future Modelling

4.1.MultiscaleModelling. Multiscalemodelling involves solv-ing physical or mechanical problems, which have distinctfeatures atmultiple (spatial or temporal) scales.Themain aimof multiscale modelling is the calculation or computation ofmechanical properties or system behavior at one level usinginformation or models from higher or lower levels. Althoughcombining models at different scales may help to modelcomplex structures, the combination of models will only beas accurate as the least accurate model in the combination.Multilevel modelling has already been employed in otherphysiological systems, mainly in the cardiovascular domain[44–49]. Multiscale modelling can also extend and includepathological processes. To the best of our knowledge, thereis currently no multiscale FE model of the entire cochlea.Steele et al. [50] have published amultiscale model of the OC.However the article focuses on the multiscale differences inthe mechanical properties (mainly stiffness related) at scalesin the OC (vibrating cochlear partition, the hair cells, andstereocilia).

4.2. Patient-Specific Modelling. Patient-specific modellingmay be proved useful in predicting outcome following med-ical or surgical intervention and it has been employed invarious medical and biological domains. In orthopedics, forexample, it may provide surgeons with data regarding bonestress distribution or implantmicrodisplacements [51]. Itmayalso be used to provide enhanced information from imagingdata regarding risk fracture prediction. In interventionalcardiology, it has been recently used to investigate the useof FE analysis on the impact of carotid stent placement byusing data from individual patients [52]. To date, there are nopatient-specific models of the cochlea or the ear.

5. Conclusions

Finite element method is a powerful modelling approachfor structural mechanics, and as such it has been proveduseful in the study of cochlear mechanics, in both health anddisease. As far as clinical applications are concerned, there is agood agreement betweenmodel predictions and clinical data,especially regarding superior semicircular canal dehiscence,stapedotomy, and auditory implantation. One of the mainrestrictions of the current FEM models is the arbitrary orapproximate use of parameter values, as well as the difficultyin proper clinical validation. Although model parametervalues can be fine-tuned so that model behavior matchesclinical data, it may not be possible to demonstrate that themodels are physiologically realistic. On the other hand, invivomeasurement of basilar membrane vibration is currentlynot feasible, and hence validation methodology is restrictedto in vitro measurements in temporal bones. Future attemptsshould focus on multiscale and patient-specific modelling aswell as the ability to couple cochlear models with models ofthe central auditory pathway.


Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper.

Acknowledgment

Thisworkwas supported by the EuropeanUnion underGrantno. 600933 for the SIFEM project (http://www.sifem-project.eu/).

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