Static analysis of tympanic membrane in aero-otitis media by three-dimensional model of the middle ear

Kili Sun , , Xu Bie , , Zhixing Feng , Shen Yu , Xiuzhen Sun , Jizhe Wng , Yingxi Liu , Lin Peng , Zhoxu Yo

aDepartment of Otolaryngology-Head and Neck Surgery, The 2nd Affiliated Hospital of Dalian Medical University, Dalian 116027, China

bDepartment of Otolaryngology-Head and Neck Surgery, Handan Central Hospital, Handan 056001, China

cDepartment of Engineering Mechanics, Dalian University of Technology, Dalian 116024, China

Keywords:Aero-otitis media The middle ear Numerical simulation Statics calculation Tympanostomy tube placement

ABSTRACT The three-dimensional (3D) model of the middle ear is of great significance to the research of middle ear related diseases.The particular focus of this work is to simulate the impact of aircraft altitude and speed changes on the tympanic membrane (TM) during the descent phase, so as to analyze the patho- genesis of aero-otitis media and the mechanical response characteristics of TM under static pressure.The simulations showed that the stress and strain of TM increase as the altitude difference and speed of the aircraft increase, and the maximum stress and strain areas are consistent with the clinical observation of TM hyperemia.Therefore, among many prevention and treatment measures of aero-otitis media, it is a therapeutic method to directly balance the pressure difference between the inner and outer TM.

Aero-otitis media is the result that the ability of middle ear to balance air pressure inadaptable to the changes of ambient air pressure, which is a kind of barotraumatic otitis media, which has attracted much attention in aviation flight and aerospace medicine.Aero-otitis media is one of the important causes of aircraft inflight incapacitation and non-combat loss of combatants.According to statistics, the incidence of aero-otitis media is 2%-17% [1] and in professional pilots is 2.4% [2] .Although the aerospace medicine is developing and progresses, the incidence rate of aero-otitis media is reduced, but it cannot be avoided completely.Abnormal function of the eustachian tube, rapid changes in aircraft altitude and speed, high concentration during flight and other reasons will lead to pas- sengers and flight personnel unable to passively or actively open eustachian tube.Especially during the aircraft descent phase, the cabin pressure increases, and the increased pressure will squeeze the pharyngeal tube pharynx, resulting in aero-otitis media.

Previous studies on aero-otitis media mainly focused on clin- ical cases, but the scale of clinical case studies is small, and the studies are not comprehensive, and it does not involve the study of small changes of the tympanic membrane (TM) morphology.With the advancing of imaging technology and three-dimensional (3D) numerical simulation technology, more and more researchers apply biomechanics to the study of middle ear diseases.The os- sicular chain system in the middle ear contains the smallest set of bones in the human body and the TM, which is just 0.1 mm thick.The structure of ossicular chain system is too small to be observed carefully in clinical imaging, but the numerical simula- tion can make it visualized.Hüttenbrink [3] introduced statics into the middle ear biomechanics by observing the mechanical behavior of the ossicular chain under static pressure variation.Since then, many researchers have applied different experiments [4] and imag- ing techniques [5] to study the static characteristics of TM.Wang et al.[6] used the numerical model of middle ear to research the static displacement of TM under positive and negative pressure.With the further study of biomechanics, the material properties and boundary conditions of the middle ear are constantly opti- mized, and the numerical model of the middle ear is more ac- curate, such as the finite element (FE) model of the middle ear was used to research the response characteristics of the TM under pressure changes and the influence of different material properties on sound transmission [7] .The FE model of the middle ear was used to investigate the difference of average resonance frequency between air conduction and bone conduction [8] and used to re- search the broadband admittance response of the middle ear of neonates [9] .These researchers are based on the numerical model of the middle ear to study the dynamic behavior of the sound transmission characteristics of the middle ear, but there are few studies on the static behavior characteristics, which are equally im- portant, especially combined with aero-otitis media.

In this work, we analyze the clinical cases of aero-otitis me- dia and use scan images of temporal bone specimen to reconstruct the ossicular chain system of the middle ear and obtain a 3D nu- merical model of the ossicular chain system including the TM.In this model, the static behavior of TM under different aircraft alti- tude difference and speed is quantitatively analyzed, and the clin- ical characteristics and static mechanical response characteristics of TM are obtained, that is, the stress and strain of TM increase as the aircraft descending altitude difference and speed increase.This work researches the pathogenesis and prevention measures and treatment measures of aero-otitis media from the perspective of biomechanics and provides new ideas for the prevention and treatment of aero-otitis media.

Sixteen cases clinically diagnosed with aero-otitis media were collected for history-taking (pathogeny, onset time, clinical symp- toms), specialist examination (endoscopy, acoustic immittance measurement), clinical treatment (conservative treatment and op- erative treatment) and prognosis analysis.They had provided writ- ten consent to participate in the study.

The geometrical model was constructed based on the right temporal bone specimen of a man without a history of otologi- cal diseases.The specimen was fixed with formalin and obtained 10 cm × 8 cm × 5 cm.A set of high-precision images were ac- quired from micro- computed tomography (micro-CT).A total of 200 images (including middle ear contents and TM) were used for 3D reconstruction with the Mimics 20.0 software.The threshold range was 674-2920 according to the middle ear tissue density.The obtained 3D model was input into Geomagic Studio software for surface optimization (Fig.1).

Fig. 1. (a) Mask of ossicular chain system in Mimics 20.0 software; (b) Surface optimization in Geomagic Studio software.

The optimized 3D model was input into Hypermesh software for mesh division, material property assignment, boundary con- dition constraint and load surface creation.Since the triangularmesh could better represent the complex geometric characteris- tics of the middle ear [10] , all surface meshes in this work were triangular meshes.The TM is a double-sided solid model, whose surface curvature changes greatly.The inner surface of TM was re- tained by geometric cleaning and the SHELL63 elastic shell element was selected.The ossicular bone, joints, ligaments, tensor tympani muscle and stapedius muscle were all tetrahedral meshes, and the SOLID45 solid model was selected (Fig.2 a and 2 b).

The TM was divided into 5 parts according to different material properties: attachment of malleus handle, umbo, pars tensa, pars flaccida, tympanic annulus.The elastic modulus and density were taken as shown in Table 1 , and the Poisson ratio of the ossicular chain system was taken as 0.3.

Table 1 Material properties of FE model of the ossicular chain system.

Table 2 Clinical symptoms and specialist examination results of patients with aero-otitis media.

Table 3 Pressure difference (mmHg) between the inner and outer TM and ear symptoms [21] .

According to the anatomical characteristics of the middle ear, the tympanic annulus and the ends of the muscles and ligaments associated with ossicles were set as fixed constraints (Fig.2 c).Because the inner ear was not involved in this work, the location of the stapedial ligament was set as a fixed constraint.Considering the difference between the inner and outer load surfaces of TM, the load surface was created as shown in Fig.2 d.

Fig. 2. Mesh division (a) , model partition (b) , boundary condition constraint (c) and load surface creation (d) were performed in Hypermesh software.

Fig. 3. (a) TM retraction (Ⅰ °), (b) Hyperemia of the pars flaccida and the malleus handle (Ⅱ °), (c) Hyperemia of full TM (Ⅲ °), (d) Eardrum effusion (Ⅲ °).

The final FE model was input into ANSYS software for TM static calculations, in which the TM is a homogeneous isotropic, linear elastic, small deformation model and conforms to Hooke’s law.In this work, the calculation results were input into the Hy- perView post-processing software to obtain the stress and strain nephograms of the TM, and then the maximum stress and strain data were input into the Origin 8 software for graphics drawing.

Among the 16 cases with aero-otitis media, 68.75% were in- duced by upper respiratory infection, 75% by nasal disease, and 81.25% occurred during the aircraft descent phase.Ear endoscopy showed that 96.88% of TM was retracted, 37.5% of TM was hyper- emic, and 31.25% was eardrum effusion.According to the Diagnos- tic criteria of occupational aeropathy [18] , TM hyperemia in this work was divided into three degrees, as shown in Table 2 .The av- erage course of the disease was 7.53 days, and 93.75% of the pa- tients improved after non-operative treatment.In this work, we observed a case of recurrent otitis media for 2 years, which was related to flying.We gave the patient conservative treatment for 3 months, but the eardrum effusion did not improve.Then, the patient was treated with tympanostomy tube placement and fol- lowed up for 3 months.The patient did not experience an aero- otitis media after repeated flights.After 3 months, the tympanos- tomy tube was taken out.Pure-tone audiometry showed that the low-frequency hearing of both ears recovered to normal range and ear endoscopy showed that the eardrum effusion of both ears dis- appeared.

To validate the present FE model of the middle ear, harmonic response analysis is applied to the TM (Fig.4).The compari- son indicates that the FE results are in reasonable with the pub- lished data across the frequency range of 20 0-80 0 0 Hz, and the model derived amplitude curves have the same variation trend.This shows that the present FE model is acceptable and can meet our research requirements for the acoustic properties of the mid- dle ear.In addition, several numerical simulations are performed to implies the reproducibility of the 3D model.

Fig. 4. The displacement responses of the TM from the present FE model of the middle ear in comparison with the steady-state experimental data and the FE results [19] .

Fig. 5. The strain (a) and stress (b) nephogram of TM at different altitudes during aircraft descent phase; Maximum strain (c) and maximum stress (d) curves of TM at different altitudes.

Fig. 6. The strain (a) and stress (b) nephogram of TM in 1 s and 10 s during airliner descent phase; The strain (c) and stress (d) nephogram of TM in 1 s and 10 s during fighter descent phase; Maximum strain (e) and maximum stress (f) curves of TM at different flight time.

Aero-otitis media mostly occurs in the aircraft descent phase, which is determined by its pathogenesis.Therefore, this work fo- cused on the TM mechanical behavior characteristics of patients with aero-otitis media during the phase of aircraft descent.

The cabin pressure regulator of airliner can automatically con- trol the cabin pressure according to the change of atmospheric pressure, so that passengers are in the tolerable pressure range.

International standard atmospheric pressure calculation for- mula: when 0＜h≤11 km, the atmospheric pressurePhchanges with altitude:

when 11 km＜h≤20 km, the atmospheric pressurePhchanges with altitude:

wherehis the altitude,Phis the atmospheric pressure ath,P0 is the sea level pressure andP0 = 101325 Pa,Ris the gas constant andR= 287 J/(kg ·K),αis the mean annual temperature decline rate andα= 0.0065 °C/m 1 ,g= 9.81 m/s2.

The cabin pressurePcchanges with altitude:

wheremis pressurization rate (m＞0), which related to the max- imum residual pressure of cruise phase, andCis the flow resis- tance.When the aircraft is flying near the ground, the flow resis- tance is 3300 Pa.When the aircraft altitude is 12 km, the pressure difference between inside and outside of the cabin is 55,960 Pa, so it can be concluded thatm= 1.5583,C= 3300 Pa.

In this work, we simulated that the eustachian tube was com- pletely closed without considering the gas exchange of the middle ear mucosa.With the change of airliner altitude (at 1 km interval), the pressure difference on the surface of the TM also changed, and the stress-strain of the TM also changed accordingly.

During the descent phase of the airliner, the pressure inside the tympanic cavity is the pressure of the cruise phase, and the pres- sure outside the tympanic cavity is the pressure inside the cabin.Due to the increasing pressure in the cabin, the pressure inside the tympanic cavity is less than that outside, resulting in TM re- traction.In Fig.5 a, the maximum strain of TM occurred in the an- terior inferior quadrant of pars tensa, followed by the posterior in- ferior quadrant, and the strain of pars flaccida near the attachment of malleus handle was also larger.In Fig.5 b and d, the maximum stress of TM increased along with aircraft altitude difference in- creasing, which was mainly concentrated on inferior of pars tensa, near tympanic annulus and umbo, and the stress around malleus handle was also larger.

Fig. 7. The strain (a) and stress (b) nephogram of TM under different pressure difference.The curve (c) showed the relationship between clinical symptoms and stress-strain of TM in patients with aero-otitis media.

According to the physiological requirements of China’s mili- tary standard cabin pressure schedule, the optimum value of cabin pressurization rate less than 1.44 kPa/min is suitable for airliner, and the ceiling value less than 0.66 kPa/s is suitable for fighter and bomber.During aircraft descent phase, the aircraft altitude per unit time increased along with aircraft speed increases, which resulted in the increase of pressure difference between the inner and outer TM, and the maximum stress and strain of TM increased accord- ingly.

In the same flight time, the maximum stress and strain of fighter was far larger than that of airliner.In Fig.6 a and c, the maximum strain of TM occurred in the anterior inferior quadrant of pars tensa, followed by the posterior inferior quadrant, and the strain of pars flaccida near the attachment of malleus handle was also larger.In Fig.6 b and d, the maximum stress of TM occurred in the umbo and the inferior of pars tensa, near tympanic annulus, and the stress around malleus handle was also larger.

Jensen and Bonding [20] found that the rupture pressure (RP) of the TM was related to age, and RP had individual differences, ranged from 0.128 ATM to 2 ATM.Therefore, the rupture of TM was not involved in this work.During the aircraft descent phase, when otalgia occurred (Table 3), the maximum stress and strain of TM were 4.731 MPa and 0.5023 mm, respectively (Fig.7), when middle ear effusion occurred, the maximum stress and strain of TM were 7.885 MPa and 0.8370 mm, respectively.

The middle ear is an irregular air-filled cavity with complicated pressure balance mechanisms [22-24] , including the mucosal gas exchange mechanism in the middle ear, the eustachian tube mech- anism and the buffering mechanism of the TM, among which the eustachian tube mechanism plays a major role in aviation flight.At rest, the eustachian tube is closed and the middle ear cavity con- forms to Boyle’s law, that is, the volume of gas in the middle ear cavity is inversely proportional to the pressure.During the descent phase, the cabin is in boost mode, the pressure of eustachian tube cartilage, nasopharynx and middle ear mucosa increased, while the tympanic cavity is in a relatively low-pressure state.At this time, the tympanic cavity- cabin pressure gradient is negative, and the eustachian tube cannot be opened passively.When yawning and swallowing, it can induce the activity of tensor veli palatini, or Val- sava, Toynbee and other actions to make the nasopharynx pressure far greater than the pressure inside the tympanic cavity, to actively open the eustachian tube and balance the pressure inside and out- side the tympanic cavity.There are many reasons in clinic that the gas of nasopharynx cannot enter the tympanic cavity through eu- stachian tube.During the descent phase, the eustachian tube was “locked” when the relative negative pressure in the tympanic cav- ity reaches about 90 mmHg [21] , that is, the maximum strain of the TM was 0.7536 mm.At this time, even if Valsava, Toynbee and other actions were enforced, the eustachian tube could not be opened.When the organism cannot balance the pressure between the inner and outer TM through eustachian tube, other compensa- tion mechanisms will be triggered.Since the mucosal gas exchange mechanism in the middle ear continuously regulated small pres- sure changes and played a limited role in the short time of aircraft descent phase [23] , so the mucosal gas exchange mechanism in the middle was not considered in this work.According to Boyle’s law, the pressure difference between the inner and outer TM increases during aircraft descent phase, and the volume of gas in the middle ear cavity can be reduced by TM retraction.Due to the large area of pars tensa, the volume replaced by retraction is larger, which is more effective in reducing the volume of middle ear cavity.

The numerical simulation of this work shows that with the increase of aircraft descending altitude difference and speed, the pressure difference between the inner and outer TM increased, and the maximum stress and strain of TM increased.The stress is con- centrated on the tympanic annulus and around malleus handle, es- pecially in the umbo, and the pars flaccida near the attachment of malleus handle is also larger, which is consistent with the clini- cal observation of hyperemia around malleus handle and pars flac- cida.If the pressure difference between the inner and outer TM further increases, the blood vessels on the surface of the TM rup- ture, and the full TM hyperemia will occur.The maximum strain occurs in the anterior inferior quadrant of pars tensa, which is consistent with the clinical observation that the position of pres- sure perforation of TM, and the strain of pars flaccida is also larger, which is consistent with the clinical observation of full TM retrac- tion.With the further increase of the negative pressure in the mid- dle ear cavity, the pressure difference between the middle ear and the middle ear mucosa increases, leading to mucosal edema and serum leakage, resulting in eardrum effusion (as shown in Fig.3 d), and even TM rupture in severe cases.Mucosal edema and eardrum effusion can reduce the volume of middle ear cavity gas and in- crease the pressure, thus buffering the negative pressure of middle ear.

During the descent phase, the eustachian tube can be opened passively or actively for those whose eustachian tube has not been locked.For patients with eustachian tube locking, the first step in treatment is to improve the function of the eustachian tube, such as eustachian tube insufflation, decongestant drugs, anti- inflammatory drugs and so on.When the function of eustachian tube cannot be improved, it is necessary to start from the angle of eliminating the pressure difference between the inner and outer TM, such as tympanostomy tube placement, that is, to establish an “artificial eustachian tube” between the middle ear and the at- mosphere.At this time, the pressure difference between the inner and outer TM disappears, the stress and strain of TM also disap- pear, and the shape of the TM returns to normal.In addition, the eustachian tube pressure difference disappears, the swollen mu- cosa in the tympanic cavity and eustachian tube cavity gradually recovers, and the function of eustachian tube is recovered.This method is cheap, convenient to operate, minimally invasive and effective, the TM can heal within a short time after the tube is removed, with a low incidence of complications [25] .With the de- velopment and widespread application of ear microsurgery, tym- panostomy tube placement will play an important role in the pre- vention and treatment of aero-otitis media.

In this work, we combine the numerical model of the middle ear with the clinical data of aero-otitis media and observe that the maximum stress and strain areas are consistent with the clinical observation of TM hyperemia.For the patients with recurrent aero- otitis media and no improvement after conservative treatment for 3 months, the tympanostomy tube placement is feasible, to directly balance the pressure difference between the inner and outer TM.This work provides new ideas for the prevention and treatment of aero-otitis media from the perspective of biomechanics.

Declaration of Competing Interest

The authors declared that they have no conflict of interest.

Acknowledgments

This work was supported by the National Natural Science Foun- dation of China (Grant Nos.11772087 and 12172082).This work was approved by the Ethics Committee of the 2nd Affiliated Hos- pital to Dalian Medical University.