1.

Introduction

The mammalian cochlea is a remarkably sensitive hearing organ that can detect displacements at angstrom level (e.g., Ref. 1). When the ear drum receives a sound pressure wave, it passes the sound to the middle ear, causing vibration of the ossicular chain that travels, via the oval window, to the fluid-filled cochlea, where fluid waves in the perilymph are generated. The fluid pressure of the perilymph causes a wavelike displacement of the organ of Corti (OC) and its basilar membrane (BM). These displacement traveling waves of motion that propagate along the BM and OC are responsible for the acoustic frequency tuning and the extraordinary sensitivity of the hearing organ that ultimately stimulates the mechanosensory receptor cells. The formidable functions of the cochlea are realized by a so-called “cochlear amplifier,” an entity whose mode of operation somehow depends on the sound-induced motile responses of specialized cells, called outer hair cells (OHCs). The cochlear amplifier must involve a complex biophysical interplay between molecular, cellular, and hydrodynamic processes. In spite of remarkably rapid progress in hearing research, the amplification process is still not understood.

There is significant controversy in the field of cochlear mechanical measurements over the spatial motion pattern of the BM and of the cellular components of the OC in response to sound, particularly at low levels. The cochlear amplifier has been proposed as the mechanism responsible for increasing BM motion when low-level sounds stimulate the ear. The hypothesis is that the cochlear amplifier uses biologically produced force or dynamic system stiffness changes at acoustic frequencies. The most popular and widely accepted model for the cochlear amplifier posits force generation from voltage-sensitive (electromotile) proteins inserted² in the basolateral wall of the OHCs, but an alternative possibility is force production from the stereocilia located at the apical end of each outer hair cell.^{3, 4} In the mammalian cochlea, the hypothesized positive feedback of force from OHCs to BM motion has been of great interest for more than $20\mathrm{yr}$ . Kim ⁵ were the first to suggest a local active process. This was followed $5\mathrm{yr}$ later by the discovery of OHC electromotility.⁶ OHCs possess a piezoelectric-like force production system, as well as a calcium-binding force production system. Just how the OC amplification and sharp tuning are achieved is not yet known. This is largely because there is currently no appropriate means available to access this delicate organ for accurate measurements of magnitude and phase of its cellular elements’ motion. Therefore, an imaging means capable of characterizing the 3-D, minute motion of the hearing organ when stimulated by sound would represent a significant advance in hearing research.

Laser interferometry and its variations are probably the only techniques currently available in the hearing research community to nondestructively measure the motion/displacement of the OC, usually on the BM. There are two unique problems when using optical techniques to measure inner-ear tissue vibration. First, the OC has a low level of reflectance, because the refractive index of the tissue is very close to that of inner-ear fluids surrounding the tissue. Khanna ⁷ found BM reflectance levels at a $633\text{-}\mathrm{nm}$ wavelength of approximately $3\times {10}^{-4}$ to $3\times {10}^{-5}$ . The second problem is the magnitude of motion of the living OC. The motion magnitudes of interest in the OC range from a fraction of a nanometer to about one micrometer. However, the most interesting biology occurs between 0.1 and $10\mathrm{nm}$ . These problems impose the requirements for the measuring techniques to be sensitive to low-level light reflectance (i.e., $>100\text{-}\mathrm{dB}$ sensitivity) and to the displacement at a subnanometer scale. In addition, the cochlear amplifier hypothesis demands that the measuring technique be able to image the 3-D motion of the OC with a resolution at a cellular level.

To cope with the low-level reflectance from the OC, optical interferometry often requires that reflecting beads be applied onto the surface of the BM to enhance the optical reflectance from the tissue surface, so they can be detected. Such an approach is not desirable for the living OC, because the applied beads may alter the functions of the OC. While the confocal slit-scanning interferometer system is capable of direct measurements from tissue⁸ (no reflective objects, such as beads, need be placed on the tissue), its carrier-to-noise ratio (SNR) is generally so low that it limits its use to high-vibration levels (sounds above a $50\text{-}\mathrm{dB}$ sound pressure level⁸). There are also some “beadless” optical measurements suggested by Gummer, but only from the reticular lamina (RL) surface in the apical turn.⁹ The most successful development for BM motion studies without reflective beads has been laser self-mixing interferometry.^{9, 10, 11} Although the results from these techniques are sometimes encouraging, these techniques for in vivo use are limited to the single-point measurements, thus they do not offer the motion scenario among the different cellular compartments in two and three dimensions, which is required to address the hypothesis of the cochlear amplifier.

Optical coherence tomography^{12, 13} (OCT), especially¹⁴ after its advent of Fourier domain OCT (FDOCT), is a very promising and noninvasive tool capable of providing high-speed and high-sensitivity $(>100\text{-}\mathrm{dB})$ 3-D imaging of biological tissues. By utilizing low-coherence interferometry, OCT performs optical ranging within a sample that enables the visualization of microstructures in biological tissue based on local optical scattering properties, with imaging resolutions approaching that for conventional histology. OCT is becoming the most successful optical technology to date in disease diagnostics. It was initially validated as an imaging technique to study healthy and diseased retinas^{15, 16} and then quickly evolved into a diagnostic tool for use in clinics for other organs (e.g., Refs. 17, 18). Recently, OCT has been used for the inner-ear imaging studies in animal models, which demonstrated the OCT capability for distinguishing different structural and morphological features of the cochlea in situ and ex vivo,^{19, 20} as well as in vivo.²¹ By using a time-domain OCT (TDOCT) system with its inherent low system sensitivity $(<100\mathrm{dB})$ and low imaging speed, these previous studies were only able to provide cross-sectional (2-D) images of the cochlea under study, which is not ideal for hearing research. Most recently, there were reports of using an ultrafast, spectral domain OCT system for 3-D morphological imaging of the cochlea in mice in vivo, with an imaging rate²² of $2\text{volumes}∕\mathrm{s}$ .

Hong and Freeman²³ were the first to use OCT to study cochlear mechanics, where they employed an extension of the OCT technique,²⁴ i.e., Doppler OCT (DOCT), that relied on the Doppler effect induced by tissue motion to measure tissue displacement.^{25, 26} However, it was quickly realized that the reported DOCT was not capable of measuring the minute tissue motion in the OC at the nanometer scale. Later, Chen ²⁷ reported a novel use of the TDOCT to measure tissue vibration of the OC, in which the low-coherence properties of the light source and a lock-in amplifier were used to realize a localized spectrum analyzer for measuring tissue vibration at a nanometer scale. Although the results were encouraging, such implementation of TDOCT faced several challenges that must be addressed to investigate the 3-D mechanical properties of the OC in response to a wide frequency and intensity range of acoustic pressures. These challenges were first, the system provided only a single-point measurement at any one time, which limits the quality of the measurement procedure for the many points of interest within the OC. Second, to improve the system SNR and give absolute calibration, a vibrating piezo mirror with a known frequency of vibration had to be used in the reference arm, so the system could be tuned, usually manually, to the most sensitive region of a cosine function. This tuning to the sensitive region was often difficult to achieve in practice. These problems make the current TDOCT system extremely difficult, if not impossible, to apply and address the critical issues that require us to measure the motion of the OC in two and three dimensions.

To meet the aforementioned challenges of using the TDOCT system, in this paper, we report a novel use of phase-sensitive OCT (PSOCT) to measure the nanomotions of the OC. The method is based on spectral domain implementation of the OCT system recently developed in the OCT research community^{14, 28} and analyzes the phase information contained in the OCT signals. Followed by a Fourier transform (FT) analysis of the measured phase changes in the spectral interferograms induced by the nanomotion of the OC, we demonstrate that PSOCT is able to characterize and image the vibration of cellular compartments in the OC with an unprecedented sensitivity down to $\sim 0.5\mathrm{\AA }$ .

Note that the concept of using the phase information of the OCT signals has been explored previously to detect the sample displacement at a sensitivity of tens of picometers.^{29, 30, 31, 32, 33} These prior methods are mostly based on common-path optical coherence tomography, so the system is stable enough to measure the slow dynamic changes of cells.^{29, 30, 31, 32, 33} Recent development has seen the use of PSOCT, still based on the common-path configuration, to detect the photothermal effect of nanoparticles embedded within the gel phantoms.^{34, 35} However, we realized that the common-path configuration does not offer flexibility for the user, since the reference reflector must always be close to the sample structure. This was particularly problematic for the current study of imaging the responses of the OC to the sound stimulation. In this paper, we apply PSOCT by using conventional system setup to achieve our goal of measuring tissue motion in the OC. Because we were interested in the frequency response of the OC at the base turn, whose range is between 12 and $20\mathrm{KHz}$ , the system noise and slow sample motion would have a minimal effect on our ability to measure the tissue vibration of the OC.

2.

Methods and Material

2.1.

System Setup

The PSOCT system setup we used in this study is shown schematically in Fig. 1 , similar to our previous studies.^{36, 37} The system employed conventional spectral domain OCT (SDOCT) to achieve ultra-high-sensitive measurement of the phase changes within the spectral interferograms induced by the nanomotion of the cellular components within the OC. We used a superluminecent diode (SLD, Denselight Ltd., Singapore) with a central wavelength of $1310\mathrm{nm}$ and a spectral bandwidth of $56\mathrm{nm}$ as the light source, which provided an axial imaging resolution of $\sim 13\mu \mathrm{m}$ in air ( $\sim 9\mu \mathrm{m}$ within the OC, assuming the refractive index is 1.42). We coupled the light from the SLD into a fiber-based Michelson interferometer, via an optical circulator. In the reference arm, we delivered the light onto a stationary mirror. In the sample arm, we focused the light into a sample via an objective lens.

Fig. 1

Schematic of the PSOCT system used in this study to measure the nanomotion within OC, where PC represents the polarization controller, and CCD, the charged coupled device. A laser diode emitting light at $633\mathrm{nm}$ was used for aiming purposes during imaging.

With a $50\text{-}\mathrm{mm}$ -focal-length objective lens in the sample arm, the size of the focus spot on the sample was $\sim 16\mu \mathrm{m}$ , i.e., the lateral resolution of the system was $\sim 16\mu \mathrm{m}$ . The zero-delay line of the system was set at $\sim 0.5\mathrm{mm}$ above the focus spot of the sample beam, at which position we carefully placed the OC. A $2\times 2$ optical fiber coupler recombined the light backscattered from the sample and reflected from the reference mirror. Then, we routed this combined beam to a home-built, high-speed spectrometer via the optical circulator. The spectrometer consisted of a $30\text{-}\mathrm{mm}$ -focal-length collimator, a $1200\text{-lines}∕\mathrm{mm}$ transmitting grating, an achromatic lens with a $100\text{-}\mathrm{mm}$ focal length, and a $14\text{-bit}$ , $1024\text{-pixels}$ InGaAs line scan camera (Goodrich Ltd., United States). This spectrometer setup had a designed spectral resolution of $0.141\mathrm{nm}$ , which gave a measured imaging depth of $\sim 3.0\mathrm{mm}$ on the each side of the zero-delay line. The line-scan rate of the camera was $\sim 47\mathrm{KHz}$ . With this line-scan rate, we measured the SNR at $0.5\mathrm{mm}$ axial depth position at $\sim 100\mathrm{dB}$ and the phase noise at $\sim 3.0\mathrm{mrad}$ .

In the sample arm, the probing beam can be scanned by an $x\text{-}y$ galvoscanner in a raster fashion. In most of the experiments we report in this paper, the galvoscanner was disabled, so we acquired the time-varying spectral interferograms ( $M$ -mode scanning) to perform the quantitative analysis of the nanometer-scale vibration within sample (see in the following). In other experiments, to provide the vibration distribution over cross section of the sample ( $B$ scan), we performed $M\text{-}B$ mode scanning.

3.

Results and Discussion

In the preliminary studies, to validate the proposed method using the PSOCT to measure the subnanometer tissue motion in the OC, we performed a series of experiments using the PSOCT system described in Fig. 1. We first tested the method by using a vibrating piezostack as the sample. The piezostack was driven by a sinusoidal signal generated by a signal generator. We used the PSOCT system to measure the optical signals reflecting back from the surface of the piezostack for a time duration of $50\mathrm{ms}$ (i.e., $M$ -mode scanning), and then we employed the method described in Sec. 2.2 to characterize the known vibration source. To simulate the weak back-scattering light intensity from a biological tissue, e.g., the OC, we attenuated the light impinging onto the sample by $60\mathrm{dB}$ by placing a 3-optical density neutral density filter into the path of the sample beam.

In the experiments, we measured the piezostack first without applying the vibration to it, and then with the application of vibration at an oscillating frequency of $17\mathrm{KHz}$ at magnitudes of 0.2 and $2\mathrm{nm}$ , respectively, comparable to the motion characteristics of the OC. Figure 2 shows the results. The phase difference of the OCT signals from a static piezostack [Fig. 2] represents the phase noise of the system that measures at root mean square $\left(\mathrm{rms}\right)=3\mathrm{mrad}$ , typical of a SDOCT system of $100\text{-}\mathrm{dB}$ SNR. The FT of Fig. 2 shows no useful signal, as expected [see Fig. 2]. Note that the frequency at $\sim 10\mathrm{KHz}$ is an artifact due to the jitter noise from the scanning mirror that steers the light onto the sample. This can be eliminated by careful system design and the proper choice of scanners that are of high stability and reliability. For example, one can design an optimized driving circuit to drive the galvoscanner that suppresses the jitter noise at $\sim 10\mathrm{kHz}$ . At the vibration amplitude of $0.2\mathrm{nm}$ , the phase differences of OCT signals still looked like a noise [Fig. 2]. However, in the Fourier domain, the applied $17\text{-}\mathrm{KHz}$ vibration was clearly contrasted with a measured $\mathrm{SNR}=\sim 56$ [Fig. 2], demonstrating high sensitivity of the proposed PSOCT system. Last, with a vibrating amplitude of $2\mathrm{nm}$ , roughly at the noise level of a TDOCT system of $80\text{-}\mathrm{dB}$ sensitivity, the SNR of the applied $17\mathrm{KHZ}$ vibrating signal was $\sim 365$ using our proposed method.

Fig. 2

Phase-sensitive measurements from a piezostack vibrating at $17\mathrm{KHz}$ : (A), (B), and (C) phase changes due to the varying optical path length induced by the piezo at a vibrating magnitude of 0 (static), 0.2, and $2\mathrm{nm}$ , respectively, and (D), (E), and (F) the corresponding frequency spectra of the phase changes in the OCT signals.

To test the accuracy of measured magnitude using PSOCT, we applied varying levels of vibration amplitude to the piezostack. The results are shown in Fig. 3 , along with the measurements obtained independently from a standard laser vibrometer for comparison. The correlation between the measurements from PSOCT and the laser vibrometer was excellent. Note that the reliable measurement of minimal vibrating magnitude for PSOCT was $\sim 0.05\mathrm{nm}$ , where the noise level was at $\sim 0.03\mathrm{nm}$ , which was not achievable by the laser vibrometer or by our previous TDOCT system.²⁷ These measurements demonstrate the accuracy of the proposed method to measure the vibration at a subnanometer scale.

Fig. 3

Measured magnitude of vibration of a piezostack at $17\mathrm{KHz}$ by applying varying driven voltages obtained from PSOCT system (circles) and a standard laser vibrometer (squares), respectively. The lines represent the least-squares fitted curves of the corresponding measured data.

Next, we tested the proposed PSOCT system on the prepared OC from guinea pigs (see Sec. 2.3). We chose the vibration frequencies $>10\mathrm{kHz}$ in the experiment, because they were meaningful to the response characteristics of the OC at the position near the cochlear basal turn. Figure 4 shows the results from one cochlea that we vibrated at $17\mathrm{KHz}$ with a magnitude of $0.2\mathrm{nm}$ . The top left corner of Fig. 4 shows a typical cross-sectional image of the OC our system obtained operating at the imaging mode, where the important physiological features of the OC are clearly demarcated, including BM, RL, tectorial membrane (TM), and Reissner’s membrane (RM). In addition, the region of hair cells is also visible in the OCT images. We present a histological drawing of the OC alongside for comparison, demonstrating the feasibility of the proposed system in imaging the cellular morphology of the OC. Figures 4, 4, 4 show, respectively, the proposed PSOCT system measures of the frequency responses at different positions, where we can see that the vibration magnitude of the BM is comparable to that of the bone; however, the vibration of RL is $\sim 8$ times higher than those of the bone and BM. This is consistent with the mass and elastic properties of the OC, where the cellular structure may vibrate differently than the BM.

Fig. 4

PSOCT measures the frequency response from an OC vibrating at $17\mathrm{KHz}$ with magnitude of $0.2\mathrm{nm}$ , obtained from (A) bone, (B) basilar membrane, and (C) reticular lamina, respectively. The top left corner shows a typical cross sectional OCT image obtained from the PSOCT system, along with a histological drawing of the organ for comparison.

To demonstrate the capability of the proposed PSOCT to measure the entire depth of the OC in parallel, we analyzed the acquired data set to quantify magnitudes of vibration within the OC at the position marked in Fig. 4 (dashed line), as well as in the bone. The results are shown in Fig. 5 . In the experiments, we purposely secured a coverslip on the top of the cochlea but within the imaging range of the system. We also analyzed the signals acquired from the coverslip to obtain its vibration magnitude. The vibration at the BM is first comparable to that of the coverslip, and then becomes gradually amplified when it gets farther into the depth and reaches a maximum at the RM [Fig. 5]. There are no significant measurable changes along the depth in the bone [Fig. 5], which vibrates at a strength approximately equal to the coverslip, demonstrating the feasibility of PSOCT to measure the meaningful frequency responses within the OC in parallel. With reference to the coverslip, the system detected a phase difference between the BM and the RL [Fig. 5], while there is no phase difference seen along the depth of bone, indicating that the proposed system is also capable of measuring the phase lags that likely occur within the OC when it senses the acoustic sound pressure.

Fig. 5

Capability of PSOCT to measure the motion of the OC along the depth in parallel. The vibrating magnitudes along a depth of (A) the OC, and (C) the bone, respectively, are quantified by the PSOCT method. (B) and (D) are the corresponding phase differences of vibration with reference to the coverslip. The red line shows the measured level of vibrating magnitude from the coverslip. (Color online only.)

Finally, we demonstrated the capability of the proposed PSOCT to obtain the vibrating map over the entire cross section of the imaged OC. In this experiment, we enabled the $x$ scanner in the sample arm (Fig. 1), and we used it to step the probe beam across the OC, so we were able to acquire the data set representing a cross section (i.e., $M\text{-}B$ mode scanning). Within each step, the data acquisition time ( $M$ -mode scan) was $50\mathrm{ms}$ . There were 64 steps across the OC, requiring $\sim 3\mathrm{s}$ to acquire the data set. We then employed the proposed data-analyzing approach to quantify the vibrating characteristics of the OC. The results are shown in Fig. 6 for two frequencies applied: 14 [Fig. 6] and $20\mathrm{KHZ}$ [Fig. 6], respectively. For $14\mathrm{KHz}$ , the magnitude of source vibration was $0.4\mathrm{nm}$ , while for $20\mathrm{KHz}$ , it was $0.1\mathrm{nm}$ . The results demonstrate the feasibility of PSOCT to measure the vibration characteristics of cellular tissue elements within the OC. As mentioned, we did not attempt to interpret these images, as the OC was more than $1\mathrm{h}$ postmortem, and the vibration energy was delivered as a vibration of the whole cochlea. Nevertheless, these pseudocolor intensity maps of vibration show a complexity of motion that is quite striking. They are reminiscent of the complex motion observed in phase-synchronized confocal image maps of the apical OC motion with acoustic stimulation.³⁹ Note here that the BM shows the greatest amount of motion consistent with the center of the membrane having a maximum and perhaps with a resonance related to the tonotopic spatial location. In Fig. 6, another location of maximum motion appears in the area of the inner hair cells. This brings to mind the rocking of the RL about the head plates of the pillar cells proposed by Lukashkin and Russell.⁴⁰ However, this is just conjecture at the time of these preliminary studies, and these experiments simply emphasize that the PSOCT is feasible to provide the type of spatial vibration measurement required for the next generation of cochlear mechanics study.

Fig. 6

(A) Cross-sectional image of the OC as imaged by PSOCT system; (B) the corresponding quantitative map of vibrating magnitude for the cross section as marked by the dashed square in (A), with the vibrating source at frequency of $14\mathrm{KHZ}$ and a magnitude of $0.4\mathrm{nm}$ ; and (C) the same as in (B), but with a frequency of $20\mathrm{KHZ}$ and a magnitude of $0.1\mathrm{nm}$ . The color bar at the left of (B) and (C) has a unit of nanometers. The star in the color bar indicates the measured vibrating magnitude from the coverslip. (Color online only.)

Currently, there are no imaging modalities other than the proposed PSOCT that can provide such highly sensitive imaging of subnanometer-scale motion of the cellular compartments within the OC. The ability of PSOCT to visualize the complex motion pattern of the entire hearing organ in response to sound stimulation could change/revolutionize our current understanding of cochlear biomechanics. However, our current system resolution $(\sim 16\mu \mathrm{m})$ is still not high enough to image the cellular morphologies within the OC. An ultra-high-resolution OCT system that uses state-of-the art, broad-bandwidth optical sources, such as a femtosecond laser or a supercontinuum laser, in conjunction with a high-numerical-aperture microscopic objective may, in future development, provide sufficient cellular-level resolution to image the hair cells in the OC.

4.

Conclusion

The lack of a high-resolution, highly sensitive, and noninvasive method for imaging the subnanometric tissue motion of the cellular structures within the OC limits our understanding of cochlear biomechanics on how a sound wave propagates through the ribbon-shaped BM, and how the movement of the membrane imparts movement to the cellular and acellular components of the OC, which are attached to the BM. We proposed to use PSOCT to measure the cellular structure motions within the OC at a subnanometer scale and demonstrated its feasibility. We achieved this by measuring the phase changes within the spectral interferograms, imparted by localized tissue motion, and subsequently followed by the FT analyzes. We showed that the conventional SDOCT setup has sufficient sensitivity to measure the depth-resolved vibration with a magnitude as small as $0.05\mathrm{nm}$ .