Mapping the phase and amplitude of ossicular chain motion using sound-synchronous optical coherence vibrography

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


Introduction
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][2][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][7][8].LDV and holography are surface measurement techniques and, therefore, require surgical preparation to access structures beyond the TM [9].They are also subject to artefacts caused by other vibrating structures located behind the tissue of interest if those structures are sufficiently reflective [10].
Optical coherence tomography (OCT) is a cross-sectional imaging modality and its potential for structural imaging of the middle ear has been previously explored [11], primarily for assessing pathologies, such as otitis media [12], middle ear effusions [13], and cholesteatoma [14], 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][18][19][20][21][22][23].Subhash et al. made one of the first demonstrations of depthresolved OCT vibrometry at a sound frequency of 500 Hz using a spectrometer-based OCT system [24].Several groups demonstrated OCT vibrometry of the TM [25][26][27][28] and ossicles [29,30] with improved imaging and processing speeds, as well as interfaces suitable for live patient imagin been largely overlooked.M acoustic phas Accurate mea determine mo We have pr magnitude an reconstruct ef had a limited respect to the chain reliably In this ar limitations an along the oss involving twi above 10 kHz

Optical s
The imaging mirror [32][33][34] of 80 nm at a based Mach-Z reference inte is scanned by expanded by mm) to a spot total optical p mirror with a the sample to sample, facilit

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 [35].This step also reduces timing jitter between the data acquisition clock and wavelength sweep [36].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: where λ 0 is the center wavelength of the swept source in vacuum, and n 0 is the refractive index of the medium.The optical phase difference Δφ between adjacent A-lines at each spatial location is computed with [37]: where A* denotes the complex conjugate of A(z,t,x,y), and the summation is carried over a region of interest (ROI) for averaging motion within the region.The ROI may be a short axial segment or small volume.The averaging enhances the effective sensitivity of phase measurement without affecting spatial resolution because phase does not change significantly over multiple imaging voxels.The ROI-averaged displacement function is given by: ( ) ( ) , , , where the summation integrates the phase differences to obtain accumulated absolute phase from t 0 , the beginning of each sound wave cycle.
The time series of displacement functions u z (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 U z (f s ,x,y,z) at the applied sound frequency f s 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 The smallest vibration that can be measured is ultimately limited by the optical signal-tonoise 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 σ u 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 N 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: The phase noise is also reduced by a factor of N when the data are averaged over N samples.
At stimulus levels above ~100 dB SPL, the TM can move more than λ 0 /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.

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 N = 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 c benefit to pha To charac the sample arm the mechanica with N = 225    n can be ether with mbo with nce arises observed nce of ~5 ); the rest o the TM, and phase the stapes (green square 75%) than the incus and stap additional del than ~8 kHz, delay of the m difference be increase can measurements consistent wit [5,9].

Discussion
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 [44].This additional rotational mode of the ossicular chain can function to increase the motion of the incus and stapes at frequencies and may contribute critically to the efficient acoustic conduction of the ossicular chain over 10 octaves of sound frequency [45].
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 [31].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) [46].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 [29], 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 [49]) 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.

1 .
Fig. 1 used: acquis mirror Fig. 3 functi OFF Power or on.phase standa well interv3.Results o 3.1 Vibrogra Vibrography after sacrifice experiments.pinna, cartilag central and su increase the tr this layer ove removing this with a slight t each experim silicone mold Fig. 4 plane recons measu standa maps.footpl3.2AcousticTo measure th First, we fixe Fig. 5 phase obtain The d (c) Th From the obtained.Figu the data from respect to the simply from linear slope (d mm between of the delay m and from the of incus and s

Figure 6
Figure 6 show frequencies: 3 with the stim vibration patt phase maps indicating stan presence of measurements

Fig. 8 .
Fig. 8. Reconstructed ossicular motion at 500 Hz and 15.0 kHz.(a) Motion-exaggerated animations and representative snapshots at φ = 0 and π.See Supplementary Visualization 1 for 500 Hz and Supplementary Visualization 2 for 15 kHz.(b) Schematics of the two rotational modes of ossicular motion.The fundamental mode is predominant at frequencies below 5 kHz.Above 9 kHz, the secondary rotational motion becomes evident.