Measuring the motion of the eardrum using Digital Image Correlation

The human eardrum is a translucent curved membrane and is in direct contact with the middle ear bones. Studying this complicated biomechanical system remains challenging. Digital image correlation (DIC) is an optical technique that allows measuring the shape and displacement of curved surfaces in 3D. In this work, we discuss the advantages and disadvantages of using DIC to study the eardrum at frequencies around 1 kHz. Special attention is given to the application of speckle patterns required to perform DIC on the translucent eardrum. Additionally, we detail an alternative approach to high-speed cameras: phase-locked light pulses. Using light pulses synced to the phase of the sound, regular DIC cameras can be used at their full resolution. This enables a high spatial resolution to thoroughly investigate the motion of the eardrum at the relevant frequencies.


Introduction
The eardrum or tympanic membrane (TM) is a thin multilayer membrane located at the end of the ear canal (Volandri et al., 2011).Its function is to capture sound waves and convert these into mechanical vibrations.The TM is connected to the hearing bones, called ossicles, both of which are part of the middle ear (ME).Studying such a complicated biomechanical system as the TM is not trivial.The ideal measurement technique needs to measure the curved shape of the eardrum, and needs to track TM motion in 3D space.
Over the years, many optical measurement techniques have emerged and found their way into biomechanical research.Laser Doppler vibrometry (LDV) is a well-established method to measure velocities at specific points on a structure (Rothberg et al., 2017).Scanning over the surface can determine the motion at different positionss.However, LDV relies on the Doppler shift and only provides information in the direction of the beam.By using beams positioned under different incident angles, the so-called in-plane component of the motion can be determined (Rosowski et al., 2013).Beam positioning and synchronization are crucial to measure the 3D motion, and a scanning procedure over the surface is still required.Methods such as interferometry are based on light interference to determine displacements with sub-wavelength resolution.Since the light can strike the entire surface, the full-field motion is captured without a scanning procedure.However, the same drawback as LDV exists, namely that in-plane motion can only be recovered by measuring under different viewing angles (Decraemer et al., 1994).Note that both techniques cannot measure the shape of an object without elaborate modification of the imaging procedure (Yamaguchi et al., 2006), since they intrinsically depend on data in the direction of the light.
An alternative technique, digital image correlation (DIC), provides advantages over these interferometric approaches (Muyshondt et al., 2021;Pan, 2018).DIC uses a correlation algorithm to track the motion of an object based on the gray value distributions of pixels in-between imaging frames.By using multiple synchronized cameras, the 3D shape of an object can be readily measured, since the relative viewing angles provide a stereoscopic view of the object.Since it relies on groups of pixels, DIC has an intrinsic resolution along the camera's sensor, i.e., it captures the in-plane behaviour of the motion.By using multiple cameras, the out-of-plane motion can also be determined.Evidently, DIC also has some drawbacks that limit the technique's usefulness in specific applications, such as a lower resolution compared to interferometric approaches.In this paper, we will illustrate our current approach to study the dynamic motion of a human eardrum using DIC.We will highlight the advantages and disadvantages of DIC and discuss why it allows novel insight into the mechanics of the human eardrum.

Sample preparation
Since DIC is an optical technique, visual access is required to the TM surface.Temporal bone samples stored in 14% formaldehyde solution were used for dissections and subsequent measurements.The ear canal was removed to open as much view as possible of the TM surface.One of the key contributors to good DIC results is the optical texture on the surface.DIC does not track individual pixels, but groups of pixels (called facets) and maps these between different cameras to compute the 3D shape.No optical information is present if the surface has a homogeneous gray scale distribution.In Fig 1, a comparison is made between visualization possibilities.Fig. 1A shows a regular TM as seen through a surgical microscope.Since most of the TM is homogenous in color, it is difficult for DIC to map information between different measurements.Moreover, the moisture on the TM surface causes specular reflections, hindering good DIC results.These are the saturated pixels, in white, in Fig. 1A.In contrast, Fig. 1B shows many local grayscale variations, uniquely identifying the image's different parts.In Fig. 1B, a fluorescent dye was applied on the TM using an airbrush.A 532 nm green laser was used to illuminate the TM and, using optical filters, only the longer wavelength of the fluorescent light was allowed to reach the camera's sensor.This approach also removes specular reflections, as is seen by comparing Figs.1A and 1B.

Measurement procedure
The setup used in this work is similar to previous work done in our group (Livens et al., 2021b;Pires et al., 2021).We will describe the main procedure in brief.
Calibration, recording, and DIC computations were performed using commercial software (Dantec Dynamics, ISTRA 4D 4.7, Denmark).Three synchronized cameras (Manta G507B, Allied Vision, Germany) were used to measure the TM.A notch filter (NF533-17, Thorlabs, Germany) was placed in front of each camera sensor to filter out the original green laser light, so images like Fig. 1B are captured.
The temporal bone is mounted to a sealed cavity connected to a speaker and microphone.A glass window is present on one side of the cavity to allow for visual access.To measure the resulting motion of the TM, phase-locked light pulses are used.The sound is defined as a periodic pure tone signal, and the light pulses are synchronized with the sound signal.Subsequent time steps of the motion are illuminated by shifting the light with respect to the sound period.This stroboscopic approach allows to measure high-frequency motion without the need for high-speed cameras.A Q-switched pulsed laser (CNI, DPS-532-B, Changchun, China) was used as a light source, so for each frame during the measurement sequence, one very short but very bright pulse illuminates the TM.A sound pressure level of 140 dB (i.e., 200 Pa) was used to allow for a good signal to noise ratio of the resulting displacement.

Data processing
DIC results depend on the settings used to correlate the different frames of the measurement.For conciseness, we refer to previous work for the reader interested in the effect of different DIC parameters (Livens et al., 2021b;Pires et al., 2021).Of importance is that a facet size of 29 pixels, and a step size of 9 pixels are used.The resulting displacement fields are smoothed using the built-in cubic spline smoothing option of ISTRA 4D.

Results
In Figs.2-3, some typical DIC results highlight the technique's usefulness.Figs 2A-B show that DIC allows accurate measurements of the 3D surface's shape.For further computations, the surface points computed by DIC are converted to a quadratic mesh (Pires et al., 2021).In Figs.2A-2B, the black dots are the nodal coordinates of the finite element mesh.Figs.2A-B also highlight that the results are directly tied to the object itself in DIC.The eardrum was slanted slightly with respect to the DIC cameras.However, if visual access is sufficient, the 3D shape of the object can be measured.
Fig. 3 shows the displacement components of the eardrum.For comparison with literature data in the discussion, the amplitude is normalized with respect to the input pressure.The horizontal (U), vertical (V) and out-of-plane component (W) of the motion are given in Figs.3A, 3B, and 3C respectively.In Fig. 3D, the magnitude of these three components are given for location X=1 mm, Y=1 mm on the eardrum surface.Note that DIC captures the entire surface at once and does not require a scanning procedure of the surface to achieve Figs.3A-C.The light pulses are phase-locked with a sound of 1500 Hz (period of 0.67 ms).Between each frame, the light is shifted by 0.67/50 = 0.013 ms to illuminate a different part of the motion cycle.After 50 frames, one full cycle is measured, so the amplitude and phase of the motion can be determined.Despite the relatively high sound amplitudes, the motion is still linear and symmetric around  = 0 mm, as seen in Fig. 3D.

Experimental procedure
Crucial for accurate DIC measurements is the presence of a random stochastic image pattern.As shown in Fig. 1B, fluorescent particles sprayed onto the TM using an airbrush allow for a suitable DIC pattern.One caveat is that creating optical access to the eardrum is time-consuming.The bone of the ear canal needs to be removed as much as possible to open up the view to the lateral eardrum surface.While this process is timeconsuming, the speed at which the preparations are performed is less crucial.
Most of the steps used in this work are based on established procedures (Gladiné and Dirckx, 2019;Livens et al., 2021b;Pires et al., 2021).However, we have made one novel change.Namely, we used a pulsed single shot laser, stroboscopic illumination using a Bragg-cell chopped constant wave laser.We found two main advantages using this approach.Firstly, Bragg-cell modulation requires removing the constant zeroth order diffraction during dynamic measurements.In doing so, much light is lost, resulting in poor use of the camera sensor's dynamic range.With the pulsed laser, all the light strikes the sensor at once.For similar shutter times, the latter approach resulted in brighter images.The second advantage is related to the pulsed laser itself: the light pulse is only a few nanoseconds in width.Therefore, only a very short instance of the motion is illuminated.With Bragg-cell modulation, many pulses at the same phase of the motion need to be sent within one DIC frame to achieve adequate light levels.The pulsed laser, therefore, further mitigates the change of motion blurring during each of the DIC frames.
Note that in DIC applications on surfaces such as metal or wood, stroboscopic LEDs are also a possibility and do not require a fluorescent light source.

Results and comparison to literature data
Human temporal bones stored on formaldehyde were used to validate the setup's correctness and resulting data.This allowed for multiple repeatable experiments and subsequent changes to the setup without worrying about sample degradation effects.Evidently, the fixative will influence these data (Thavarajah et al., 2012).Fixation leads to tissue stiffening, which increases the system's resonance frequency.Figs.3A-D are thus representative of an eardrum, but with the frequency response curve shifted.Fig. 3C showed a maximum displacement of 135 nm/Pa, which corresponds well to literature data on non-fixated human temporal bones (Koike et al., 2002;Rosowski et al., 2011).However, Fig. 2C showed that the eardrum displacement is still homogeneous, i.e., no higher-order modes are present.On non-fixated samples, the resonance frequency lies around 1000 Hz.At 1500 Hz, higher-order mode shapes can be seen on non-fixated TM surfaces (Rosowski et al., 2011).These observations indicate that our data is a good proxy for a regular eardrum, but shifted to higher frequencies due to stiffening.
The advantage of DIC is that not only the W-displacement, but also the in-plane U and V components are computed, see Fig. 3.As seen in Fig. 2, the shape of the object's surface is determined in 3D, and all required components of the motion can be determined.One downside of DIC is lower sensitivity compared to other techniques such as LDV.For the field of view seen in Fig. 1B, a resolution of 50 nm for the U and V displacements and 300 nm for the W displacement was achieved, respectively.LDV reaches resolutions of picometers for W, but requires a more complicated scanning procedure and three aligned beams to compute U and V displacements.Holography reaches resolutions in the order of nanometers for W, but also lacks the possibility of easily measuring the U and V displacements.The sound pressure level was set to 140 dB to measure the motion seen in Fig. 3.We found this to be a good optimum between high signal-to-noise and preserving the linearity of the motion.Fig. 3D supports this claim since the curve is symmetric and shows no local fluctuations typically seen at high noise levels.Lower sound levels were also tested, but then Figs. 3A and 3B became noisy, making data interpretation more difficult.

Conclusion
In this work, the usefulness of stroboscopic-DIC was exemplified by studying the motion of the human eardrum under incident sound.The samples were temporal bones stored on formaldehyde.We showed that a pattern suitable for DIC could be applied to the translucent eardrum using a fluorescent dye.Using a pulsed laser, we could precisely time the illumination of each DIC frame, effectively freezing the motion during each DIC frame.By shifting the light pulses along the phase, the entire period of the motion was measured.
The method allows to study motions of the eardrum in 3D at different frequencies.These data are valuable input for future computer simulation studies, from which the effect of eardrum material properties and geometry can be inferred.

Fig 1 .
Fig 1.Effect of different illumination strategies.A) The human eardrum illuminated by white light contains little contrast and many reflections.B) Better grayscale variations can be achieved using fluorescent particles sprayed onto the TM surface.

Fig 2 .
Fig 2. (A-B) Shape of the eardrum measured by DIC.(A) Frontal view.(B) Oblique view.The coordinates determined by the DIC software are represented on a mesh for visualization.