Eardrum or tympanic membrane (TM) is a multilayer soft tissue membrane located at the end of the ear canal to receive sound pressure and transport the sound into the middle ear and cochlea. Recent studies reported that the TM microstructure and mechanical properties varied after the ear was exposed to blast overpressure. However, the impact of such biomechanical changes of the TM on its movement for sound transmission has not been investigated. This paper reports the full-field surface motion of the human TM using the scanning laser Doppler vibrometry in human temporal bones under normal and postblast conditions. An increase of the TM displacement after blast exposure was observed in the posterior region of the TM in four temporal bone samples at the frequencies between 3 and 4 kHz. A finite element model of human TM with multilayer microstructure and orthogonal fiber network was created to simulate the TM damaged by blast waves. The consistency between the experimental data and the model-derived TM surface motion suggests that the tissue injuries were resulted from a combination of mechanical property change and regional discontinuity of collagen fibers. This study provides the evidences of surface motion changes of the TM damaged by blast waves and possible fiber damage locations.

## Introduction

Eardrum or tympanic membrane is a multilayer soft tissue membrane separating the ear canal from the middle ear. The tympanic membrane (TM) plays an important role in the transmission of sound pressure from the environment into mechanical vibration of the ossicular chain in the middle ear, which is transported into the inner ear or cochlea and then to the brain for hearing. Exposure to high intensity sound or blast overpressure waves causes injuries to auditory system and results in acute hearing loss in military service members and the long-term hearing disabilities in veterans [1,2]. The primary blast injury to the ear is induced by the direct effect of blast waves upon the TM and middle ear ossicular chain. Rupture of the TM is one of the most frequent injuries of the ear and has been investigated in animals and humans with wide variability [35].

The human TM is composed of three distinct layers. The lateral side is an epidermal layer and the medial side is a mucosal layer. The middle layer is composed of collagen fibers which are embedded in a matrix of ground substance, aligning primarily along the radial and circumferential directions [6]. A major part of the TM is the pars tensa, which is within the tympanic annulus ring located at the boundary; the malleus manubrium bone is attached in the central portion at the medial side [68].

Recent studies reported that the TM microstructure and mechanical properties varied after the ear was exposed to blast waves [9,10]. The postblast TM tears were oriented in the radial direction observed under the scanning electron microscope by Engles et al. [10]. They also measured the complex modulus of the human TM samples by using acoustic loading and laser Doppler vibrometry and found that the storage and loss modulus of the TM decreased significantly after the blast over a frequency range of 200–8000 Hz. In a study performed by Luo et al. [8], the results indicated that Young's modulus is higher in the radial direction than in the circumferential direction, and the fracture strength in the radial direction is also higher than that in the circumferential direction under the condition of the same strain rate. Moreover, the recent study by Luo et al. [9] showed that blast waves cause significant changes on mechanical properties of the TM mainly due to the damage induced in the circumferential fibers and the stiffening in the radial fibers. However, the impact of such biomechanical changes of the TM on its movement for sound transmission has not been investigated.

Full-field motion measurement of the TM can provide simultaneous vibration data from a large number of points on the membrane surface, which has the benefit of showing both the spatial and temporal behaviors of the TM vibration in response to sound stimuli. The term “full-field” herein means that the measurement is performed over the entire visible area of the TM. Measurement of the entire TM surface motion has been used to explore the relationships between the structure and the acoustic function of the middle ear in animals and human cadaveric temporal bones [1114]. To analyze middle ear mechanics in diseased and reconstructed ears, Zhang et al. [15] investigated the effects of middle ear fluid on TM surface motion in human cadaver ears by using scanning laser Doppler vibrometry (SLDV). Recently, the TM surface motion was determined using SLDV in a chinchilla model of acute otitis media by Wang and Gan [16].

This paper reports the full-field surface motion of human TM measured by SLDV over a frequency range of 1–8 kHz in human temporal bones before (or normal) and after blast exposure. In addition to experimental measurement, a three-dimensional (3D) multilayer finite element (FE) model to mimic the fibrous microstructure of the human TM was developed to replace the TM in our previously published FE model of the entire ear [17]. The new TM model was composed of multilayer matrix embedded with radial and circumferential fibers, which was used to simulate the damaged TM by altering the mechanical properties and microstructure of the fiber network after blast exposure. The purpose of this study is to investigate how the TM motion is altered after blast exposure and what is the possible relation between the TM movement variation and its microstructure damage induced by blast waves.

## Methods

### Sample Preparation.

Two pairs of fresh human temporal bones (TBs) from two donors of age 67 and 71 yr old were involved in this study. TB samples were packed in dry ice and shipped from LifeLegacy Foundation, a certified human tissue supplier for military-related research. The study protocol was approved by the U.S. Army Medical Research and Material Command (USAMRMC), Office of Research Protections (ORP). The experiments were conducted within one week after the temporal bones arrived. The samples were processed with a solution of 0.9% saline and 15% povidone at 5 °C to maintain the physiological condition before the experiment. Each sample was examined under an operating microscope (OPMI-1, Zeiss, Thornwood, NY) to confirm a normal ear canal and an intact TM.

The surgery to expose the TM was conducted under the microscope by separating the pinna and soft tissues from the lateral bony wall of the TB with a #10 scalpel and removing the bony part of the ear canal for the SLDV measurement. After the test in a normal TB sample was completed, the removed pinna and soft tissues were reattached to the TB by suture and the TB sample was exposed to blast tests. The pinna and soft tissues were then removed again to expose TM for the SLDV measurement after blast tests.

### Experimental Protocol

#### Surface Motion of the Tympanic Membrane Measured With Scanning Laser Doppler Vibrometry.

The schematic diagram of the experimental setup with SLDV to measure the motion of the TM surface is shown in Fig. 1. The TB was fixed in a temporal bone holder and placed on a vibration isolation table. The experiment was conducted following the protocol reported by Zhang et al. [15]. Briefly, a chirp stimulus at 80 dB sound pressure level with a frequency range of 1–8 kHz was produced by a function generator (Polytec Ethernet Generator, Polytec, Inc., Irvine, CA), an amplifier (RCA SA-155, Radio Shack, Fort Worth, TX), and a speaker (CF1, Tucker-Davis Technologies, Alachua, FL). The sound was delivered through a tube with an inner diameter of 1 mm. A probe microphone (Model ER-7, Etymotic Research) used for monitoring the input sound pressure level was secured parallel to the sound delivery tube and placed about 2 mm away from the TM.

A SLDV (PSV-500, Polytec, Inc., Irvine, CA) with a software package (PSV 9.2, Polytec, Inc., Irvine, CA) was used to measure the full-field vibration of the TM. The orientation of the plane of the tympanic annulus was set perpendicular to the laser beam. Figure 2(a) shows a typical view of a TM sample captured by the SLDV. Scanning grids of 400–500 measurement points were distributed evenly over the entire surface of the TM and aligned by drawing them onto the TM live video image using the PSV 9.2 software (see Fig. 2(b)). The vibration velocity of each measurement point along with the sound pressure was recorded simultaneously by PSV 9.2 over the frequency range from 1 to 8 kHz. The displacement amplitudes at different frequencies were simply calculated from the velocity and normalized by the input sound pressure.

#### Exposure of Temporal Bone Samples to Blast Waves.

Upon completing the surface motion measurement of a normal TM, the previously removed pinna and soft tissue around the ear canal were reattached to the TB by suture. The TB was then mounted to a “head block” inside an anechoic test chamber in our lab at the University of Oklahoma as shown in Fig. 3. Following the previously established methodologies, a compressed nitrogen-driven blast apparatus was utilized to produce blast overpressure by rupturing a polycarbonate film (McMaster-Carr, Atlanta, GA) [9,10,18]. Blast overpressure level was controlled by changing the thickness of the film or the distance from the blast reference plane. The blast pressure at the entrance of the ear canal was monitored by a pressure sensor (Model 102B16, PCB Piezotronics, Depew, NY) mounted on a column approximately 1 cm away from the head block (Fig. 3). The data acquisition system consisted of the cDAQ 7194, A/D converter 9215 (National Instruments, Inc., Austin, TX), and a software package LabVIEW (National Instruments, Inc., Austin, TX). The sampling rate of the acquisition system was 100 k/s, which was proved to be appropriate in the previous studies [4,9,10,18].

The pressure waveform of each blast had a single positive overpressure peak, and the peak pressure was used to assess the pressure level of blast. Each TB specimen experienced four repeated blasts at a level of 38–54 kPa (or 5.5–7.5 psi). Note that the rupture threshold of human TM was 52.4–62.1 kPa [10,19], and thus, the repeated blasts in this study can induce discernable tissue damage in the TM without rupturing it. After the completion of blast exposure, a microscopic examination was applied to each TM to ensure the nonexistence of the rupture. The surface motion measurement was conducted again immediately after the completion of blast tests, following the same protocol described in Sec. 2.2.1 and the results were compared with the preblast data obtained in each TB.

### Finite Element Modeling Normal andDamaged Human Tympanic Membrane

#### Multilayer Finite Element Model of Normal Tympanic Membrane—Structure.

A multilayer FE model of the human TM with fibers was created in ansys (ANSYS, Inc., Canonsburg, PA) based on the entire ear model published by Gan et al. [20] and Zhang et al. [15]. Figure 4(a) shows the ear model which consists of the ear canal, TM, middle ear ossicles, middle ear suspensory ligaments and muscle tendons, middle ear cavity, and the spiral cochlea with two and half turns. The TM in this published human ear model is a single layer of membrane with thickness of 75 μm. In this study, the pars tensa part of the TM was modeled as a membrane consisting of five layers: epidermal layer, radial layer, middle layer, circumferential layer, and the mucosal layer from the lateral to the medial side as shown in Fig. 4(b) schematically. The thickness of each layer was assumed to be 10, 30, 5, 20, and 10 μm, respectively [21]. The total thickness was 75 μm, the same value as that used in the published ear model [15,20,22]. Note that the middle layer was a virtual layer designed to allow the relative motion between the circumferential and radial layers. Figure 4(b) is a diagram showing the cross section of the TM along the circumferential direction. The radial fibers were embedded between the radial and middle layers, while the circumferential fibers were between the circumferential and mucosal layers [23].

The fiber orientations in the radial and middle layers were following the directions of two major types of collagen fibers observed from experiments: the radial fibers originated from the manubrium and ended at the annulus; the circumferential fibers started and ended at the manubrium, parallel to the TM annulus and orthogonal to the radial fibers [7,8,21,24]. The fibers in the radial and circumferential layers simulated in the TM model are shown in Fig. 4(c). The pars flaccida was modeled as a nonfiber matrix. Note that this method of multiscale modeling of fiber-embedded tissues was reported by Shirazi and Shirazi-Adl [25] and Tiburtius et al. [26].

#### Multilayer Finite Element Model of Normal Tympanic Membrane—Materials.

The matrix of five layers of pars tensa was assumed as solid elements in ansys (Solid 185) and the pars flaccida of the TM was modeled as the matrix of solid elements (Solid 185) without fibers. The radial and circumferential fibers were modeled using beam elements (Beam 188) with a rectangular cross section. The fibers, matrix, pars flaccida, and tissues attached to the TM including the TM annulus and manubrium were all modeled as linear elastic materials. The elastic modulus of the TM annulus, manubrium, and pars flaccida was 0.6 MPa, 4.7 GPa, and 10 MPa, respectively [22]. The elastic modulus for matrix of the pars tensa or five layers was the same as that used for pars flaccida (10 MPa).

In TM model, the length of the radial fiber and the radial side length of the matrix element were equal, as well as the equal length of circumferential fiber and the circumferential side matrix. The thickness of the fiber element equaled to its layer so that the volume fraction of fibers was controlled by fiber's width. The volume fraction of fibers in a certain direction at a node of the TM was assumed to be the ratio of the fiber volume to the matrix which could be simplified as the width of the fiber at the node divided by the distance between the current and next adjacent nodes in the given direction within the layer of the fiber [25,26]. For the volume fraction of fibers in human TM, Fay et al. [21] suggested a value around 30–50%, and thus, the width of the radial or circumferential fiber elements was selected at 90 μm in this study which resulted in an approximately volume fraction of 20–40% in either radial or circumferential direction in the boundary area of the TM. Note that the volume fraction would increase from the edge to center because of the width of the fiber element remaining constant, while the size of the matrix element gradually decreased from the edge to center.

Volume fraction and elastic modulus of the fibers are critical parameters affecting the TM stiffness. The equivalent elastic moduli of the TM in the radial and circumferential directions are calculated by the empirical method derived from composite material mechanics as shown in the following equation [27]:
$Eave=EfV+Em(1−V)$
(1)
where Eave is the equivalent elastic modulus of the composite, which is the TM with fibers embedded in the matrix in this study; Ef and Em are elastic modulus of the fiber and matrix, respectively; and V is the volume fraction of the fibers. The fibers in human TM mostly consist of collagen types I and II fibrils whose elastic modulus varied from 1 to 10 GPa [21,28] and the average elastic modulus in the radial direction was about 1.5–2 times of that in the circumferential direction [8,9,22]. After a cross-calibration process to match the model-derived TM surface motion to the experimental data, the elastic modulus of radial fiber was determined to be 10 GPa while 6 GPa for the circumferential fiber.

#### Multilayer Finite Element Model of Damaged Tympanic Membrane.

Mechanical tests on TM samples indicated that the exposure to blast overpressure resulted in changes of mechanical properties of the TM [9,10]. Microstructural variations of the TM were detected by scanning electron microscope images, which provide an insight into the structural aspects of the injury on the surface of the TM [10]. To investigate the relationship between the changes of the microstructure and mechanical properties of the TM and its surface motion, the blast-induced damage was simulated in the FE model of the TM using three approaches.

The first approach was to uniformly reduce the elastic modulus of fibers to simulate the mechanical properties of the fibers that were altered by blast waves. The elastic modulus of the radial and circumferential fibers was set to be 1 and 0.6 MPa, respectively, much lower than the normal fibers. The second approach was to reduce the volume fraction of fibers to simulate the loss of fibers. The width of fibers was reduced to 9 μm which resulted in the volume fraction of fibers to 1/10 of the original value. The third approach was to remove the part of fibers in certain quadrant of the TM to simulate the regional loss of fibers. This simulation of blast-induced damage was conducted following the SLDV measurement in TB samples. We hypothesized that the regions in the TM where the high displacement peak appears during the surface motion measurement may represent more severely damaged fiber network than the other regions. The model-predicted TM surface motion was compared with the experimental data over the frequency range from 1 to 8 kHz.

## Results

### Full-Field Surface Motion of the Tympanic Membrane Measured by Scanning Laser Doppler Vibrometry.

Figure 5 shows the full-field surface motion of specimen TB-60 (right ear) at five frequencies of 1, 2, 3, 4, and 8 kHz before and after four repeated blasts at the level of 53 kPa. The color bars on the right side of images represent the displacement amplitude normalized by the input sound pressure in nm/Pa. The orientation of the right ear TM is shown in the upper left-hand corner of the figure. Note that the scale of the color bar varies from 1 kHz to 8 kHz to provide better illustration of images.

For normal ear at 1 kHz, the deflection shape of the TM motion showed a major vibration peak in the posterior region of the membrane. The maximum displacement amplitude was close to 180 nm/Pa. For the ear after blast exposure, the location of the maximum displacement stayed in the posterior region of the membrane, but the maximum displacement decreased to around 100 nm/Pa. A low-displacement region located around the manubrium separated the membrane into the posterior region with higher displacement and the anterior region with less mobility in both pre- and postblast TMs. The blast exposure did not alter the shape of deflection and the location of the maximum movement at 1 kHz.

The high vibration peak areas were still in the posterior region of the TM before blast at 2 kHz, and multiple peaks emerged around 80 nm/Pa. After blast exposure, a major peak with a maximum displacement of 200 nm/Pa appeared in the posterior region of the TM and a fusion of minor peaks into one major peak was similar to what was observed at 1 kHz, but the significant increase of the displacement amplitude in the posterior region was different. The low-mobility area around the manubrium separated the TM into the high-mobility posterior and low-mobility anterior quadrants unsymmetrically, which was clearer in the TM experienced blasts. The blast exposure induced changes in displacement magnitude instead of the location of the vibration peaks.

Distribution of the deflection shape of the TM motion at 3 kHz of both normal and blasted TMs showed no conspicuous difference compared to the deflection shape at 2 kHz. The displacement amplitude was almost uniformly decreased over the entire surface when the frequency increased from 2 to 3 kHz. The maximum displacement in normal TM before blast exposure was 70 nm/Pa and increased to 180 nm/Pa in blasted TM. The high-mobility area still located in the posterior region which was consistent with the results at 2 kHz.

Shapes of the TM deflection at 4 kHz started to change. In preblast TM, although the high-displacement area still existed in the posterior, another high-vibration area appeared in the anterior region. In postblast TM, multiple peaks emerged at the posterior, anterior, and inferior regions. The posterior and anterior peaks shared a maximum displacement of 60 nm/Pa. The postblast TM at 4 kHz still illustrated the deflection shape similar to the normal TM, which had high-mobility peaks in the posterior region. The changes induced by blast exposure at 4 kHz include the increased maximum displacement peaks and a new peak appeared in the anterior region.

When frequency increased to 8 kHz, no prominent major peaks were observed on the TM before and after blast exposure due to the complexity of the deflection shape and the decrease of the vibration amplitude. The whole TM surface was vibrating below 20 nm/Pa. The superior quadrant including the manubrium showed that the lowest mobility and multiple minor peaks were observed in the anterior region. Neither displacement magnitude nor the distribution of the contours showed discernable difference before and after the blast exposure. In summary, the results obtained from the TM of TB-60 indicate that at the middle frequencies (2–4 kHz), the areas with high mobility concentrated in the posterior region of the membrane and the blast damage mainly increased the TM movement in that region without changing the peak distribution pattern.

The deflection shapes of four TMs from all TBs at 3 kHz are presented in Fig. 6 to investigate whether this phenomenon exists in all TM samples. The left column of Fig. 6 displays the shapes of TM deflection before blast exposure, and the right column shows the TM deflection shapes after blast exposure. The TM surface motion of four TBs are displayed from top to bottom in Fig. 6. Similar to Fig. 5, the color bars on the right side of images represent the displacement amplitude normalized by the input sound pressure in nm/Pa. The orientation of each TB's TM is shown in the upper left-hand corner of each image (TB-57: left ear, TB-58: right ear, TB-59: left ear, and TB-60: right ear). A major peak of displacement in the posterior region of the TM was observed in all four TM samples. The maximum displacement of the TM increased from 80 to 140 nm/Pa in TB-57, 58, and 59 and from 70 to 180 nm/Pa in TB-60 after blast exposure. The shapes of the TM deflection or displacement contours remained unchanged after the blast exposure. A single major peak of the TM was observed in the central posterior region of TBs 57, 58, and 60, but TB-59 showed a more complicated shape of deflection. However, the maximum displacement still located in the posterior region and the blast-induced damage increased the displacement amplitude at the same level compared to the other three specimens.

Displacement contours of all four TMs before and after blast exposure at 4 kHz are shown in Fig. 7. Like Fig. 6, the TM displacement after blast exposure increased in the posterior region of the membrane at 4 kHz, and the peak distribution pattern was similar to that observed at 3 kHz. However, the displacement amplitude was lower than that at 3 kHz. The maximum TM displacement of TB-57 in the posterior region increased from 40 to 100 nm/Pa after the blast, but in TB-58, the peak vibration area of the TM increased due to the blast. In TB-59, the maximum displacement increased from 50 to 80 nm/Pa, while from 30 to 60 nm/Pa in TB-60. Note that at 4 kHz, high-vibration areas emerged in the anterior region of the TM after the blast exposure. Moreover, the long and narrow high-displacement area appeared in the anterior region of the TM after blast in TB-57. In TB-59 and TB-60, the displacement in the anterior high-vibration area increased after the blast. This phenomenon indicated that the vibration mode of single posterior peak domination changed to a two-peak formation starting at 4 kHz.

### Tympanic Membrane Surface Motion Simulated by Finite Element Model.

Following the three approaches described in Sec. 2.3.3, a damaged TM model to mimic the blast-induced changes in TM microstructure and mechanical properties was created as shown in Fig. 8. In addition to reducing the elastic modulus and the volume fraction of fibers in the model, part of the fibers in the posterior–inferior quadrant of the TM was removed to simulate the local damage or loss of fibers based on observations from the surface motion measurements from experiments (Figs. 57). This was also designed to test the hypothesis that the regions in the TM where the highest displacement peak appears during the surface motion measurement may represent more severely damaged fiber network than the other regions. As shown in Fig. 8, a round-shape nonfiber area with a diameter of approximately 4 mm was created by deleting the fiber elements in the posterior–inferior quadrant. The location, size, and shape of the nonfiber area were simulated based on the high-displacement area of the TM in Fig. 5 at 1, 2, and 3 kHz.

The deflection shapes of the TM along the direction perpendicular to the plane of the tympanic annulus were calculated from the FE model of the entire ear shown in Fig. 4 (left ear) with the normal TM or damaged TM at five selected frequencies (1, 2, 3, 4, and 8 kHz) and plotted in Fig. 9. The orientation of the left ear is shown in the upper left-hand corner of the figure. Scale bars in unit nm/Pa are shown in the right column for each group of images obtained at the same frequency. From the left to right, the images in the first column show the deflection or displacement shapes of normal TM derived from the FE model of the ear over the frequencies of 1–8 kHz from the top to bottom. The images in the second column show the deflection shapes of damaged TM simulated by reducing elastic modulus of the fibers. Images in columns 3 and 4 represent the deflection shapes of damaged TM simulated by reducing fiber volume fraction and partially removing local fibers, respectively.

In normal TM, a prominent major peak was observed in the posterior–inferior region at all frequencies and the dominance of a single peak decreased with the frequency increasing. A secondary peak emerged in the anterior region at 3 kHz or higher frequencies and the multiple minor peaks formed a complicated shape of deflection at 8 kHz. The maximum displacement gradually decreased as frequency increasing from 118 nm/Pa at 1 kHz to 4.5 nm/Pa at 8 kHz. The normal TM showed the lowest surface mobility over the frequencies.

For damaged TM simulated in the model, the major peak in the posterior region was discernable at the frequencies below 3 kHz. The location of the major peak was consistent with what was observed in the normal TM and the maximum displacement value was greater in the damaged TMs. At 1 kHz, there was only one major displacement peak in all TMs, and the TM with reduced elastic modulus showed the highest maximum displacement of 632.7 nm/Pa among three damaged TM models. At 2 kHz, the second peak in the anterior region emerged in the TM with a reduced elastic modulus, but the other two damaged TMs kept the similar deflection shape as the normal TM. The highest displacement at a value of 149.5 nm/Pa emerged in the TM of partially removed fibers. At 3 kHz, multiple peaks appeared to form a half-ring-shaped high displacement area in the TM with reduced elastic modulus. The TMs with reduced volume fraction and removed fibers showed deflection shape close to the normal TM, but with increased mobility. The highest maximum displacement decreased to 49.1 nm/Pa in the removed fibers. At 4 and 8 kHz, the trend continued in all four TMs. A ring-shaped high-displacement area emerged on the surface of the TM with reduced elastic modulus. The behavior of the TM with reduced volume fraction at high frequencies was similar to what was observed in the reduced modulus TM. The TM of partially removed fibers was unique, whose deflection shape remained unchanged over the entire frequency range. The high-displacement area remained at the same location, but the maximum displacement gradually decreased from 400 nm/Pa at 1 kHz to 5.9 nm/Pa at 8 kHz. The FE model-derived TM surface motion was generally consistent with those observed from the experimental results measured by SLDV (Figs. 57).

## Discussion

### Comparison of Scanning Laser Doppler Vibrometry Measured Tympanic Membrane Surface Motion With Published Data—Normal Tympanic Membrane.

In this study, the full-field surface motion of human TM under a chirp stimulus of 1–8 kHz was measured by SLDV before and after blast exposures. As an important indicator to evaluate the sound transmission function of the TM and middle ear, the surface motion of the TM has been measured on human and animal ears using SLDV [15,16,29] and stroboscopic holography [3032]. The maximum displacements on the human TM surface were 400, 80, and 16 nm/Pa at 1, 4, and 8 kHz, respectively, reported by Zhang et al. [15]. The values measured by stroboscopic holography in two different human cadaveric TMs reported by Cheng et al. [31] were 200/200, 30/35, and 16/8 nm/Pa at 1, 4, and 10 kHz, respectively. In this study, the maximum displacements on the TM surface of TB 60 before blast exposures (normal ear) were 180, 30, and 20 nm/Pa at 1, 4, and 8 kHz, respectively. Although there were some variations, the values of the TM maximum displacement measured in this study were generally consistent with the published data over the frequency range of 1–8 kHz.

The shape of the TM deflection is another parameter to evaluate the mobility of the TM. At 1 kHz, a single prominent peak was observed in the posterior–superior area of the TM (Fig. 5), which was close to what was reported by Cheng et al. [31] and to that the peak displacement emerged in the posterior–inferior region of the TM by Zhang et al. [15]. The peak area appearing in the posterior region in the previous and current studies was also observed in the surface motion of animals at the low frequencies [11,29,33]. At 4 kHz, a half-ring-shaped or ring-shaped high displacement area covered most of the TM surface except the superior region observed in this study and previous studies. At 8 kHz, multiple high displacement areas were in shape of concentric circles centered at the umbo and spread out to the TM annulus, which was also observed in Cheng et al. [31] and Zhang et al. [15]. Overall, the full-field surface motion of the normal human TM measured in this study agreed with the published data, which confirmed that the experimental setup is reliable.

### Comparison of Finite Element Model-Predicted Tympanic Membrane Surface Motion With the Experimental Data—Normal and Blast-Damaged Tympanic Membrane.

The full-field TM motion was measured experimentally (Figs. 57) and simulated by the FE model (Fig. 9). The maximum displacement in the posterior–inferior region of the normal TM predicted by the FE model was 118, 16.3, and 4.5 nm/Pa at 1, 4, and 8 kHz, respectively, which is consistent with the experimental data of 105, 25, and 10 nm/Pa in TB 60 at 1, 4, and 8 kHz, respectively. The major peak in the posterior–inferior region of the TM was observed in the normal TM at frequencies below 4 kHz in Figs. 5 and 9. Multiple peaks emerged on the TM surface including the superior were observed at 8 kHz in both experimental and model-derived results. Therefore, the multilayer fibrous model of TM was capable to simulate the behavior of normal TM over the frequency range.

The key application of the FE model for damaged TM was to investigate how the TM motion is altered after blast exposure and what is the possible relation between the TM movement variation and its microstructure damage induced by blast waves. Figures 6 and 7 demonstrated a typical feature of the change in full-field surface motion of the TM after blast exposures: an increase of the maximum displacement with a major peak in the posterior region at the frequencies between 3 and 4 kHz. As shown in Figs. 6 and 7, the increased displacement of the major peak was observed in all four samples at 3 and 4 kHz. The deflection shapes of damaged TMs derived from FE model with reduced elastic modulus of the fibers, reduced fiber volume fraction, and partially removed local fibers generally followed the same trend of the experimental data with some minor discrepancies in Fig. 9.

The damage simulation with reduced elastic modulus captured the increased magnitude of the major displacement peak at low frequencies but shared the least similarity with the experimental results among three damage models. The expansion of the major peak area and the increase of the magnitude were minimum at frequencies above 2 kHz. In contrast, the TM with reduced fiber volume fraction followed the trend of the experimental data better than that of reduced elastic modulus over the frequency range. The typical feature of the major displacement peak was observed at frequencies below 4 kHz, but the multiple peaks or the expansion of the high-displacement area over the entire surface of TM were only observed at 8 kHz in both normal and damaged TMs. The increase of the peak displacement from the normal to the reduced volume fraction TM was significant as shown from the scale bars. In the TM with partially removed fibers, the deflection shape of a major peak in the nonfiber area stayed unchanged but the amplitude decreased with the frequency. In summary, the FE simulation indicated that the pattern of the TM surface motion was significantly affected by the microstructure or fiber damage of the tissue. The consistency between the simulation and the experimental data revealed that the postblast TM motion change could be resulted by the alteration of the fiber mechanical properties or the loss of fibers.

### Contribution and Limitation of This Study.

Rupture of the TM is a typical injury caused by blast exposure which can result in severe hearing loss and pain [1,4,34]. However, recent biomechanical measurement on the TM after blast indicated the microstructural damage and mechanical property changes of the TM even there was no discernable existence of the rupture [9,10,35]. These permanent alterations in TM tissues would affect the progressive hearing loss after blast exposure [36,37], but the role of the TM damage in the progressive hearing loss or recovery process remains unclear. This study on measurement of the full-field surface motion of the TM damaged by blast waves may provide needed information for characterization of the postblast sound transmission function of the middle ear.

The experimental data obtained in this study demonstrate that the major peak of the TM motion located in the posterior region of the TM and an increase in maximum displacement at 3–4 kHz in that region were discovered in all TBs after the blast exposure. For a more detailed analysis of the maximum displacement on TM, Fig. 10(b) shows the displacement–frequency curves of a point selected at the center of the major peak at 3 kHz in TB 60 (see Fig. 10(a)) before and after the blast exposure. The frequencies of reaching maximum displacement for normal and postblast ears were almost the same, while the peak value of the curve after blast was approximately 50 nm/Pa higher than the normal curve or the curve before blast to reach a value of 180 nm/Pa. At frequencies from 1 to 4 kHz, the displacement at this selected point increased significantly after the blast exposure. These results together with those shown in Figs. 57 suggest that the increase of the TM mobility in postblast human ears is both frequency and location dependent.

In this study, the multilayer model of the TM including the radial and circumferential fiber network was successfully constructed. The consistency between the model-derived and the experimental data indicates that the model is capable to characterize the structure–function relationship of the normal and damaged TMs over the frequency range. The multilayer TM model generates a connection between the microstructure and mechanical properties of the TM with the TM surface motion which improves biomechanical analysis on the TM with higher complexity. For example, using this model, we will predict the stress distribution in the TM to understand the mechanism of TM rupturing process in future studies. The evaluation on the TM graft of fibrous structure [36] and the simulation of interlayer edema in TM resulted by otitis media [38] are also clinical-relevant applications of this model in future studies.

There are some limitations in this study. In Fig. 5, the results at 1 kHz show a higher displacement in the TM before blast exposure. The reason behind this could be the surgical process to expose the TM in this TB. At the superior edge of the TB sample, the epidermal layer of the TM might be connected to the ear canal tissue which affected the TM motion at the low-frequencies. The mechanical properties of the TM model may require further adjustment. To simulate the damage and emphasize the effect of fibers, the average stiffness of the TM model was relatively high which resulted in a smaller displacement than the experimental data. The viscoelastic behavior of the collagen fibers will also need to be considered to improve the accuracy of the model, especially at high frequencies.

## Conclusion

In this study, the full-field surface motion of human TM before and after blast exposures was measured by SLDV over a frequency range from 1 to 8 kHz. An FE model of human TM with multilayer fiber network was created to simulate the normal and blast-damaged TMs. The major displacement peaks whose magnitude increased after the blast exposure emerged in the posterior region of the TM were observed in all TBs at the frequencies of 3–4 kHz. The model-derived data successfully characterized the features of the TM surface motion measured from the normal and damaged ears. The results suggested that the blast-induced TM damage might be a combination of global and regional loss or mechanical property changes of the fibers. The technology developed in this study can detect and simulate the blast-induced microstructural damage in the TM and improve our understanding of postblast injuries in the auditory system. The multilayer TM model created in this study provides a practical tool for microstructural biomechanical analysis of TM damage.

## Acknowledgment

The authors would like to express their deep appreciation for the guidance and vision offered by Professor Y. C. Fung to biomechanical measurement and modeling of human ear for sound transmission. For the first author (Rong Z. Gan), Professor Fung has personally mentored her research and career development in biomedical engineering for 40 years. Professor Fung introduced her to the biomechanics field in 1979. Following several milestones guided by Professor Fung, her major research direction shifted from lung biomechanics to hearing and ear biomechanics at the University of Oklahoma in 1999. Since then, a new research area, “Biomechanics for Restoration of Hearing,” has been established with the great impacts on hearing research across the World in both measurement technologies and computational modeling. Professor Fung's influences on Rong Gan's research in hearing biomechanics will continue to be demonstrated through the past, present, and future research projects.

For the second author (Shangyuan Jiang), Professor Fung's Biomechanics textbooks have guided his studies for completing the Ph.D. research in mechanical properties of ear tissues. The quality and breath of Professor Fung's contributions to the field of biomechanics are motivating all younger generations of students and researchers.

We dedicate this innovative work with scanning laser Doppler vibrometry measurement and 3D multilayer modeling of damaged eardrum (tympanic membrane) induced by blast waves to honor Professor Fung's 100th birthday. This research was supported by grants from the U.S. Department of Defense (W81XWH-14-1-0228).

## Funding Data

• U.S. Department of Defense (Grant No. W81XWH-14-1-0228, Funder ID: 10.13039/100000005).

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