The sound-driven vibration of the tympanic membrane and ossicular chain of middle-ear bones is fundamental to hearing. Here we show that optical coherence tomography in phase synchrony with a sound stimulus is well suited for volumetric, vibrational imaging of the ossicles and tympanic membrane. This imaging tool — OCT vibrography — provides intuitive motion pictures of the ossicular chain and how they vary with frequency. Using the chinchilla ear as a model, we investigated the vibrational snapshots and phase delays of the manubrium, incus, and stapes over 100 Hz to 15 kHz. The vibrography images reveal a previously undescribed mode of motion of the chinchilla ossicles at high frequencies.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
The tympanic membrane (TM) and ossicular chain play a central role in hearing by providing acoustic impedance matching between the air-filled ear canal and the fluid-filled inner ear. The incoming sound energy is collected by the TM, transmitted through the ossicles to the cochlear fluid, and detected and transformed to neural signals in the inner ear. A dysfunction or damage in the middle ear results in hearing impairment.
Vibrometric measurement of the ossicles and TM has been critical for advancing our understanding of the hearing mechanics and improving treatments such as middle-ear prosthetics. Vibro-acoustic analysis of the middle ear and TM has also been proposed for diagnosis of ossicular disorders and planning surgical interventions [1–3]. In the past, stroboscopic microscopy, capacitive probes, and the Mössbauer effect were used to measure the sound-induced vibrations at specific locations in the middle ear [4,5]. Modern investigations are generally conducted using more sensitive optical interferometric techniques, particularly laser Doppler vibrometry (LDV) and holography [6–8]. LDV and holography are surface measurement techniques and, therefore, require surgical preparation to access structures beyond the TM . They are also subject to artefacts caused by other vibrating structures located behind the tissue of interest if those structures are sufficiently reflective .
Optical coherence tomography (OCT) is a cross-sectional imaging modality and its potential for structural imaging of the middle ear has been previously explored , primarily for assessing pathologies, such as otitis media , middle ear effusions , and cholesteatoma , in diagnostic and intraoperative settings [15,16]. Beyond anatomical imaging, phase-sensitive OCT has shown a promising potential for vibration measurements in hearing research [17–23]. Subhash et al. made one of the first demonstrations of depth-resolved OCT vibrometry at a sound frequency of 500 Hz using a spectrometer-based OCT system . Several groups demonstrated OCT vibrometry of the TM [25–28] and ossicles [29,30] with improved imaging and processing speeds, as well as interfaces suitable for live patient imaging. Up to now, the demonstrations of OCT-based middle ear vibrometry have been largely focused on vibration magnitude, and vibration phase has been generally overlooked. Measuring the phase of vibration with respect to sound stimuli allows the acoustic phase and group delays to be determined along different middle ear components. Accurate measurements of the relative phase of motion along the ossicular chain can help determine modes of motion and identify differences between normal and pathologic states. We have previously developed a technique, called OCT vibrography, to acquire the magnitude and phase of vibration at each location through successive vibrational cycles and reconstruct effective snapshot images of the TM and ossicular motion. However, the system had a limited frequency range below 3 kHz and suffered from random phase noise drift with respect to the sound source, making it difficult to measure phase delays through the ossicular chain reliably and accurately .
In this article, we present an improved OCT system that has overcome these two limitations and demonstrates considerably more precise measurement of the phase delay along the ossicular chain. In chinchilla ears, our results revealed a new mode of vibration, involving twist and bending of the ossicular structure, for acoustic transduction at frequencies above 10 kHz.
2. OCT vibrography system
2.1 Optical system, sound stimulus, and time synchronization
The imaging system (Fig. 1) uses a wavelength-swept laser based on a rotating polygon mirror [32–34]. The laser output has a center wavelength of 1280 nm and a 3-dB bandwidth of 80 nm at a sweep rate of 45 kHz. The corresponding axial resolution is 15 μm. A fiber-based Mach-Zehnder interferometer (MZI) (Thorlabs INT-MZI-1300) is employed to provide reference interference fringes for clock jitter compensation. In the sample arm, the laser beam is scanned by a pair of galvanometer mirror scanners (Cambridge Technology, 6210H), expanded by lenses L1 (50 mm) and L2 (75 mm) and focused by an objective lens L3 (100 mm) to a spot size (lateral resolution) of 30 µm (full width at half maxima) at the focus. The total optical power incident on the sample is 10 mW. Additionally, a long-pass dichroic mirror with a cutoff wavelength of 950 nm is employed and directs room light reflected from the sample to a CCD camera (Allied Vision, Mako G) to provide an otoscopic view of the sample, facilitating sample alignment.
An all-purpose input/output (I/O) board (National Instrument, USB-6353) is used to generate electrical waveforms to drive a compression speaker (Peavey RX22) via a 300W power amplifier (Crown Audio, XLI). The output face of the speaker is directly coupled to a latex tube connected to a custom-built sound coupling tube made of brass. One side of the brass tube has a transparent, tilted glass window to transmit the optical imaging beam. The other side of the tube is coupled to the auditory canal of the specimen. A low-noise microphone (Etymotic ER-7C) in the coupler records the stimulus sound pressure in situ within 5 mm of the center of the TM.
A fiber Bragg grating (FBG) and photodiode (PD) provide a pulse signal synched to each wavelength sweep of the laser output (“FBG optical clock”). This signal triggers a high-speed data acquisition (DAQ) card for digitizing interferometric signals from dual balanced photodetectors (BPD) in the OCT interferometer and the reference MZI. The output trigger of the DAQ card is then used as the clock “Sync” signal for the I/O board that generates the sound stimulus, controls the galvanometer scanners, and acquires the microphone signal. This arrangement ensures time synchronization for the measurement of OCT interference signals, beam scanning, and the generation and recording of sound waves. The timing jitter measured using a digital oscilloscope (Keysight DSO1024A, 200 MHz, 2 GS/s) between the I/O board output and the FBG clock was 5.7 ns, which provides a phase uncertainty of less than 9x10−5 cycles with stimuli of 15000 Hz.
2.2 Data acquisition in synchrony with sound frequency
Each complete wavelength (λ) sweep of the laser yields an individual axial scan (A-line) along the depth (z) axis. The optical beam is scanned in the transverse directions (x and y) to form a complete volume image. The A-line rate (fA) is the same as the wavelength-sweep repetition rate. The digitization rate of the DAQ is set to 99 MHz so that 2,048 samples of the dual-balanced detector signal are acquired during each A-line. For phase synchrony, the acoustic frequency fs is restricted to be an integer fraction of the A-line rate; that is, fs = fA n/m, where n and m are integers. The data acquisition and beam scanning are arranged such that m A-lines are acquired at every transverse location (an M-scan) during n cycles of the sound wave (Fig. 2). Typically, we set m to be a rather large, even number in a range of 180 to 250, and n is variable from the minimum of 1 for low sound frequencies, up to 100 for high frequencies within the Nyquist criterion. With m = 200, for example, for a wavelength sweep rate of 45 kHz, the allowed fs ranges from 225 Hz (n = 1) to 22.5 kHz (n = 100) at an interval of 225 Hz. A different m value yields a different set of fs. This allows a wide range of sound frequencies to be tested. For fA = 45 kHz and m = 200, the acquisition of a single M-scan at each transverse location takes 4.44 ms, regardless of the sound frequency. Data acquisition over an entire frame (128 M-scans) or volume (128 × 128 M-Scans) takes 0.57 s and 72.7 s, respectively. Such sampling produces a 3D data set of vibrography images at one sound frequency of 1024 (z) × 128 (x) × 128 (y) voxels. Such a measurement set is repeated for each sound stimulus frequency.
2.3 Data processing to determine the amplitude and phase of vibration
For each A-line, the wavelength-domain interferogram is corrected for a background offset and resampled linearly in wavenumber (k) based on the MZI reference data . This step also reduces timing jitter between the data acquisition clock and wavelength sweep . The resampled interferogram is multiplied by an apodization window function and further corrected for chromatic dispersion in the interferometer. The corrected interference fringes a(k,t,x,y) are Fourier transformed (k to z) to produce an A-line profile, A(z,t,x,y). The magnitude of the complex A-line represents optical reflectance and is displayed (in log scale) to show the structure of the sample. The phase ϕ(z,t,x,y) of the A-line contains the z-axis coordinates of the structure within a sub-wavelength range. It should be noted that the phase ϕ represents the phase of the optical interference signal and should not be confused with a “vibration phase” denoted φ, which refers to the phase of the mechanical motion of the structure. The sinusoidal displacement of each voxel at (z, x, y) at time t, , is linked to the interference phase OCT via:37]:
The time series of displacement functions uz(t,ROI) contains all the information about the axial component of the sound-driven vibration. The magnitude and phase of the mechanical vibration at the sound frequency can be readily obtained by a Fourier transform of the displacement with respect to the time coordinate:
The amplitude and phase of Uz(fs,x,y,z) at the applied sound frequency fs gives the magnitude and phase of vibration in response to the stimulus. The acoustic transfer function is obtained by normalizing the measured signal with respect to the input sound stimulus recorded with the microphone. Axial velocity vz (≡ duz/dt) is computed from (i2πfs)Uz(fs).
The smallest vibration that can be measured is ultimately limited by the optical signal-to-noise ratio (SNR), defined as the power ratio of the amplitude (reflectivity) to the noise floor of |A(z,x,y)|. To a first-order approximation, the theoretical limit of vibration sensitivity σu is given by [36,38,39]:
Upon taking the Fourier transform (t to f), the M-scan is effectively averaged m times, such that the frequency-domain amplitude sensitivity is. The theoretical sensitivity can be further improved with ROI averaging (described above) by a factor of when the ROI consists of N samples with an equal SNR.
The SNR-limited vibration phase noise is linked to the amplitude noise and given by:
At stimulus levels above ~100 dB SPL, the TM can move more than λ0/2 between two consecutive A-line scans, making |Δϕ| > π. This can cause a phase wrapping artifact in the phase-sensitive measurement because the phase difference Δϕ has 2π ambiguity. In addition, the TM motion can generate erroneous optical phase readings when the amplitude of motion becomes larger than the axial resolution of the OCT system. To avoid these artifacts, we limited the stimulus to levels where these artifacts did not occur. When we concentrate on ossicular motion, the SPL level is varied to produce a full-range of ossicular motion, and care is taken to segment out the TM region causing artifacts.
2.4 System performance measurement: phase sensitivity and stability
To characterize the sensitivity of our OCT vibrography system, we measured the vibration signal from a stationary object (2.8-kg block of aluminum) while varying the SNR by adjusting the optical power in the sample arm using a variable attenuator. First, the galvanometer scanner was turned off, and a 1 s M-scan was acquired for each level of attenuation. Then, another set of M-scans was acquired while the galvanometer scanner was turned on and a constant voltage was applied so that the probe beam was held at a fixed location on the object. The optical SNR, motion amplitude sensitivity, and noise spectra were computed from the data set.
The sensitivity measured with the scanner off was in good agreement with the theoretical limitation (Fig. 3(a)). However, when the scanner was on, we found an excess amplitude noise with an amplitude of 4 nm, which is presumably due to mechanical jitter of the galvanometer mirror coupled with the feedback control of the driver. At relatively high SNR levels above 30 dB, the system’s sensitivity was limited by this scanner noise. In most parts of the middle ear structure, the optical SNR tends to be below 30 dB, in which the measurement is SNR-limited. The noise floor without the scanner noise was flat in the frequency domain (Fig. 3(b)) as expected from a purely SNR-limited case. When the scanner was on and the SNR was >35 dB, the mechanical scanner noise described a broad envelope centered around 8 kHz. The noise spectrum without the scanner noise revealed sharp noise peaks with an equal spacing of 625 Hz, which correspond to the 72 facets of the rotating polygon filter in the wavelength-swept laser source. We avoided these fixed noise frequencies when setting the sound stimulus frequency.
Next, to measure vibration phase noise we placed a piezoelectric transducer (PZT) in the sample stage. The transducer was driven to oscillate with an amplitude of ~5 nm at a constant frequency of 9 kHz. Figure 3(c) shows the variation of measured vibration phase relative to the phase of the stimulus over a duration of 1 s, measured synchronized to the stimulus generation as described above (“Sync”). Each data point represents an average of 225 A-lines, a simulation of ROI averaging with = 225 that was used in some middle-ear imaging experiments described later. Apart from some random fluctuation, the measured phase was stable over time. However, when the PZT was driven by a function generator with an independent clock (“Sync Off”), we measured large, random phase drift, confirming the benefit to phase stability of timing synchronization.
To characterize the phase noise, we varied the optical SNR using a variable attenuator in the sample arm of the OCT interferometer. The scanner was turned off to remove the effect of the mechanical noise. The result agreed well with the theoretical line for a SNR-limited case with N = 225 (Fig. 3d).
3. Results of chinchilla ear measurements
3.1 Vibrography imaging of the chinchilla middle ear
Vibrography experiments were performed on two cadaver chinchilla heads less than 2 weeks after sacrifice of animals. The specimens were kept frozen, and thawed a day before experiments. The head was mounted on a brass rod held in a multi-axis micro-positioner. The pinna, cartilaginous ear canal and much of the boney ear canal were removed to expose the central and superior areas of the TM. The thin dermal outer layer of the TM was removed to increase the transparency of the TM, and because the freeze thaw cycle had already loosened this layer over part of the TM surface. Laser-Doppler measurements have demonstrated that removing this layer has little effect on TM or ossicular motion. The specimen was positioned with a slight tilt around the long axis of the head to better view the incus and stapes. During each experiment, the remnant auditory canal was sealed to the sound coupling chamber using silicone molding material .
Prior to vibrography measurements, we scanned the OCT probe beam over the entire TM to acquire a 3D anatomical image of the middle ear. A representative cross-section and 3D rendered image are shown in Figs. 4(a) and 4(b). A large part of the ossicular chain could be observed, including the manubrium of the malleus underneath the TM, the long process of the incus, the anterior crus of the stapes, and the anterior stapes footplate. The head of the malleus and body of the incus are not visible because they are located behind the thick ear canal bone. Figure 4(c)-(e) show the reflectivity and axial velocity magnitude and phase (φ) maps of the cross-sectional plane, and clearly show all 3 ossicles: malleus, incus, and stapes. A 3 × 3 × 3 Gaussian filter was applied to the reflectivity and vibrometry maps to reduce speckle noise (Fig. 4(c)-(e)). The velocity and phase data were encoded in the structural image with color in a Hue-Saturation-Value (HSV) scheme using hue corresponding to the velocity or phase and color value being proportional to the reflectivity in log scale. The velocity was normalized to the sound pressure near the TM (in Pa) measured in real time using the microphone. The illustrated vibration phase is relative to the vibration of the umbo (rather than the speaker) so the phase at the umbo is always 0. The in-phase movement of much of the TM and three ossicles is clearly seen, whereas the vibration of the parts of the auditory canal and the wall and floor of the middle-ear cavity are of varied phase and of much smaller amplitude.
3.2 Acoustic transfer function of the middle ear
To measure the acoustic transfer function of the middle ear, we used two different methods. First, we fixed the probe beam at the umbo and used a Schroeder frequency comb  to obtain the complete frequency response of the umbo over a frequency range of 100 Hz to 5 kHz. The broadband stimuli did not have sufficient acoustic power to produce sufficient SNR (> 10 dB) at frequencies above 5 kHz, although longer integration time could increase SNR. It was repeated for the probe beam fixed at the incus tip to measure the acoustic transfer function near the head of the stapes. This method is commonly used in conventional LDV measurements. The main difference is that the OCT measurement is performed through the intact TM, whereas LDV require the TM above the incus to be removed. The broadband results are presented as solid lines in Fig. 5(a).
In the second method, we acquired volumetric vibrography data at a specific monotonal sound stimulus and repeated the measurement for different sound frequencies, typically, at 0.36, 0.5, 1.0, 2.0, 3.0, 4.5, 6.4, 9.0, 11.3, and 15.0 kHz. The SPL was set to a range between 80 and 100 dB. The axial velocity and phase of the umbo, incus and stapes were obtained by manually selecting ROI’s in the volumetric data set. The umbo ROI was defined as a 0.5mm diameter circle at the tip of the manubrium, and the incus and stapes ROI’s were the entire visible portion of these ossicles. The data are shown in Fig. 5(a)-(c) as circle, triangle and square markers, respectively. The data obtained with the two distinct stimuli up to 5 kHz are in good agreement with each other. From 5 to 15 kHz, only results from monotonal stimulation are shown.
From the volumetric data set, the acoustic transfer function at any location can be obtained. Figure 5(b) plots the velocity and phase transfer function of the stapes together with the data from the umbo and incus (in linear frequency scale). The phase of the umbo with respect to the sound stimulus varies with the frequency. A linear frequency dependence arises simply from wave propagation delay (∂φ/∂fa = 2π × group delay time) . The observed linear slope (dashed line) corresponds to an average delay time of ~67 µs. The distance of ~5 mm between the microphone and the TM accounts for 15 µs (sound speed: 340 m/s); the rest of the delay may be attributed to the phase delay in the acoustic coupling from air to the TM, and from the TM to the manubrium [42,43]. Figure 5(c) highlights the magnitude and phase of incus and stapes motion relative to that of the umbo. The vibration amplitude of the stapes (green squares) is larger than that of the incus (magenta triangles), but both move less (35-75%) than the umbo over the entire frequency range. As frequency increases, the phase of the incus and stapes deviate from that of the umbo. The negative phase slope in c indicates an additional delay in the motion of the stapes and incus relative to the umbo. At frequencies less than ~8 kHz, the phase follows a nearly linear trend (dashed line), indicating a simple group delay of the mechanical wave. Above that frequency there is a sudden increase in the phase difference between the umbo and the other two ossicles; as will be described later, this increase can be explained by the onset of a new mode of ossicular motion. These measurements of the relative sound-induced motion of the umbo, incus and stapes are consistent with past measurements in the same species performed using Mössbauer and LDV [5,9].
3.3 Projected and volumetric vibrography images of the TM and ossicular chain
Figure 6 show vibrography images of the TM in a top projection view at three different sound frequencies: 360 Hz, 4.5 kHz, and 9.0 kHz. At 360 Hz, the surface of the TM moves in phase with the stimulus. With increasing sound frequencies, the TM exhibits more complex vibration patterns with increasing numbers of maxima and minima in the velocity maps. The phase maps show complex patterns mixed with π phase shifts over a small distance, indicating standing waves, and more gradual phase gradients, indicating traveling waves. The presence of both standing and traveling components are consistent with previous measurements of sound-induced motion of the chinchilla TM using laser holography .
Figure 7 shows constructed vibrography maps of the ossicular chain in a projection view at 500 Hz, 6.4 kHz, and 15.0 kHz. The most prominent structure is the manubrium of the malleus (M), and to its left, the inferior part of the long process of the incus (I) and the stapes (S) are seen. The head of the malleus and the body of the incus are behind the ear canal bone and so are not visible. At 500 Hz, the axial velocity increases along the manubrium from the lateral process (LP) to the umbo (U) (Fig. 7(a)), and the ossicles move all in phase (Fig. 7(d)). This motion is consistent with a lever-like rotation around the malleus-incus joint. At higher frequencies, the velocity gradient along the manubrium is increasingly nonlinear (Fig. 7(b) and 7(c)), and the phase of the upper most portion of the malleus (the lateral process), incus, and stapes lag from that of the umbo (Fig. 7(e) and 7(f)).
Phase gradients along the manubrium can be appreciated more easily with a reduced phase range for the color-coded display, shown in Fig. 7(g)-(i). At 6.4 kHz, the phase gradient along the manubrium indicates a flexural motion of the ossicle (Fig. 7(h)). At 15 kHz, while the axial flex is present, most interestingly, a lateral phase gradient appears (Fig. 7(i)), suggesting a twist motion around the axis.
From the volumetric data set, we constructed 3-dimensional rendering of the ossicular motion with exaggerated vibration amplitude. The movies taken at 500 Hz and 15 kHz clearly show the differences in the ossicular motion, particularly of the manubrium (Fig. 8(a)). At the low frequency, the in-phase rotational motion of the manubrium, incus and stapes around the malleus-incus axis is predominant. At 15 kHz, this fundamental rotational mode is accompanied by the second rotational motion around a new axis parallel to the manubrium. In addition, the twist motion and flexural bending of the manubrium are noticeable. Figure 8b illustrates the two modes of ossicular motion.
The acoustic transfer function, projection phase maps, and reconstructed 3D rendered animations provide comprehensive and quantitative information and clear insights about the sound-driven motion of the ossicular chain. The near-half-cycle difference between the umbo and the incus-stapes at 15 kHz is consistent with the second ossicular rotational axis that is parallel to the manubrium and positioned between the manubrium and the incus. Such rotational modes have been hypothesized for small mammals by Fleischer . This additional rotational mode of the ossicular chain can function to increase the motion of the incus and stapes at higher frequencies and may contribute critically to the efficient acoustic conduction of the ossicular chain over 10 octaves of sound frequency .
OCT shows promise as a tool to aid the diagnosis of middle ear pathology, by allowing visualization of middle-ear structure behind the TM, and quantification of sound-induced ossicular motion that can help distinguish abnormal function and its causes . The maximum sound frequency in the current OCT system is limited to the Nyquist frequency of 22.5 kHz. This frequency range is adequate for hearing research in humans (20 Hz to 20 kHz hearing range), and covers most of the chinchilla hearing range (50 Hz to 33 kHz) . The total duration of a volumetric measurement, on the order of a minute, is a challenge for live patient or animal imaging due to motion artifacts. One possible approach, explored by MacDougall and colleagues , is to use standard anatomic OCT imaging to target a single location at which vibrometry can rapidly be performed. OCT systems with higher A-line rates of up to several MHz have been reported [47,48] and may enable considerable reduction of the total measurement time by allowing data acquisition in the B-M mode (comparing phases between successive B-scans ) instead of the M-B mode (comparing phases between successive A-lines) used in this study.
In conclusion, we have described OCT vibrography for measuring and visualizing the sound-induced motion of the ossicles and TM and demonstrated its usefulness through the measurement of the chinchilla ear. The acoustic transfer functions we recorded are consistent with previous measurements obtained by LDVs and holography measurements. However, the unique ability of OCT vibrography to acquire volumetric data in conjunction with 3D structural images enabled us to appreciate the greater details of the ossicular motion, including the fundamental rotation around the malleus-incus axis and, importantly, to identify a second rotational mode of ossicular motion at high frequencies. Our results demonstrate OCT vibrography as a powerful tool in hearing research.
National Institutes of Health (P41-EB015903, R01-DC000194); Fonds de Recherche du Québec.
We thank Brian Battersby for his help with software development.
The authors declare that there are no conflicts of interest related to this article.
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