Quantitative confocal optical coherence elastography for evaluating biomechanics of optic nerve head using Lamb wave model

Abstract. The mechanosensitivity of the optic nerve head (ONH) plays a pivotal role in the pathogenesis of glaucoma. Characterizing elasticity of the ONH over changing physiological pressure may provide a better understanding of how changes in intraocular pressure (IOP) lead to changes in the mechanical environment of the ONH. Optical coherence elastography (OCE) is an emerging technique that can detect tissue biomechanics noninvasively with both high temporal and spatial resolution compared with conventional ultrasonic elastography. We describe a confocal OCE system in measuring ONH elasticity in vitro, utilizing a pressure inflation setup in which IOP is controlled precisely. We further utilize the Lamb wave model to fit the phase dispersion curve during data postprocessing. We present a reconstruction of Young’s modulus of the ONH by combining our OCE system with a Lamb wave model for the first time. This approach enables the quantification of Young’s modulus of the ONH, which can be fit using a piecewise polynomial to the corresponding IOP.

Quantitative confocal optical coherence elastography for evaluating biomechanics of optic nerve head using Lamb wave model Zhaodong

Introduction
As an optic neuropathy, glaucoma is one of the leading causes of blindness worldwide. 1,2 Glaucomatous damage to the visual system likely includes important pathophysiologies within the photoreceptors, retinal ganglion cell (RGC), lateral geniculate body, and visual cortex. Evidence has shown that damage to the RGC axons within the lamina cribrosa (LC) of the optic nerve head (ONH) is a central pathophysiology. 3 The ONH is a region of special biomechanical interest because it is a discontinuity in the cornea-scleral shell, and this type of discontinuity typically gives rise to stress or strain concentrations in mechanical systems. 4,5 The mechanical properties of the ONH are dependent on the interaction of its individual components. At low stress, it is likely that the elastin component allows for an initially large volume change formed by the distending ONH and, as pressure increases and the extended collagen fibers limit further deformation, the ONH becomes progressively stiffer. 6 Elevated intraocular pressure (IOP) is the most important risk factor for glaucoma progression, 7 which distorts the tissues of the ONH, and LC within, triggering events, such as compromised axoplasmic flow, vascular perfusion, and astrocyte activation that eventually lead to optic nerve axon degeneration and RGC death. 7,8 An improved understanding of the ONH biomechanical environment and of the dependence of this environment on the biomechanical properties of the ONH tissues is necessary to understand better how biomechanical effects may play a role in glaucomatous optic neuropathy. 9 There are several experimental techniques currently being used to investigate changes in the mechanical compliance of the ONH and posterior scleral surface. 10,11 Most of these identify the pressure-induced deformation at the level of the LC and use this information to determine the biomechanical properties of the tissue. 10 However, it is known that the ONH and anterior laminar surfaces are not only displaced posteriorly but also anteriorly (with reference to Bruch's membrane opening) in a significant portion of glaucoma patients. 12 Characterizing elasticity of the ONH over physiological pressures may provide a better understanding of how changes in IOP lead to changes in the mechanical environment of the ONH. [13][14][15] Optical coherence elastography (OCE) is an emerging technique, which can detect tissue biomechanics noninvasively with both high temporal and spatial resolution compared with conventional ultrasonic elastography. 16 The axial displacement range is typically in the micrometer to nanometer level. Recent work on advanced ultrasonic elastography demonstrated excellent spatial resolution with micrometer axial displacement detection. 17,18 OCE shows great potential to assess the biomechanics of the posterior segment of the eye. In ophthalmology, however, this technique is mainly focused on the anterior segment of the eye, such as the cornea and the lens. [19][20][21][22][23] Some OCE systems utilize oblique incidence air pulses 20,24 or an obliquely oriented transducer 25,26 to induce tissue vibration, which may generate complex waves instead of pure waves and can lead to errors in the estimation of biomechanical parameters. 27 We recently reported a confocal acoustic radiation force (ARF) OCE method that can map out the elasticity of retinal layers with high resolution. 28 This confocal setup avoids generating complex waves, moreover, it allows for easy access to the retinal layers. However, due to the complexity of the retina, only group velocity was used to estimate the biomechanics of normal retina and age-related macular degeneration-induced retina.
One of the challenges in elastography is to reconstruct the biomechanics accurately. 29 Group velocity has long been used to reconstruct the biomechanics, however, this method assumes that the elastic wave propagates in a homogeneous, isotropic, bulk, and purely elastic medium. 30 In most tissues, elasticity and viscosity exist at the same time. Moreover, some tissues such as the ONH exhibit a thin plate morphology, which leads to a failure of biomechanics estimation using group velocity.
In our previous work, we demonstrated the feasibility of a Lamb wave model to quantify the viscoelasticity of imaging phantoms, porcine corneas as well as rabbit arteries. 31 In this study, we investigate the ability of OCE for measurement of the ONH elasticity in pig eyes, utilizing a pressure inflation setup in which IOP is controlled precisely. We further utilize the Lamb wave model to fit the phase dispersion curve during our data postprocessing procedure. To our knowledge, this is the first time that a Lamb wave model has been used in evaluating the biomechanics of the ONH. Our aim was to quantify the mechanical behavior of the ONH in response to elevated IOP.

Preparation of Specimens
Twenty porcine eyes were obtained from a U.S. Department of Agriculture-approved slaughterhouse. The mixed-breed pigs were all healthy and between 5 and 7 months old before they were killed. The eyes were immersed in saline and kept cold during shipping, and all eyes were tested within 48 h postmortem. The extraocular tissues were removed, and the optic nerve was cut to be flush with the outer surface of the peripapillary sclera by using a surgical blade. At the ONH, the axons converge into bundles to pass through the LC, which spans the scleral canal and is continuous with the adjacent peripapillary sclera. Viewed from the back of eyeball, the ONH was surrounded by peripapillary sclera at the same level after the optic nerve was removed. Then, the entire eyeball was physically stabilized in a custom holder with the ONH facing upward. Two ports were created in the pars plana using 23 G trocars (BL5523WVX, Bausch & Lomb, Inc., Rochester, New York). One connected to a pressure column containing phosphatebuffered saline (PBS) to control IOP, and the other connected with an IOP sensor (Model SPR-524, Millar, Inc., Texas). Realtime readout of the IOP was performed using a custom-build LabView program, which provided feedback on the instantaneous IOP. The height of the infusion line was adjusted accordingly. The sample was then put in a PBS bath, which served as a medium for ultrasound propagation and a preservative for ocular tissue. The IOP was increased by manually raising the height of the PBS column from 10 to 30 mmHg. We used a pressure increment of 5 mmHg for each step, and the IOP was held constant at each level for 1 min before the data were acquired.

System Setup
To assess the biomechanical properties of the ONH, a customized OCE system combining an ultrasonic transducer and a spectral-domain optical coherence tomography (SD-OCT) system was developed, as shown schematically in Fig. 1(a). In the SD-OCT system, a light beam was emitted from a superluminescent diode (SLD, M-D-890-HP1, Superlum Diodes Ltd, Carrigtwohill, Ireland) with a central wavelength of 890 nm and a bandwidth of 144 nm to detect tissue structural information as well as response to ultrasonic ARF. The light beam was filtered through an optical isolator (IO-F-SLD150-895, Thorlabs, Inc., Newton, New Jersey) to prohibit backprojection of light into the SLD and then split by an 80/20 optical coupler for efficient and safe data collection. In the reference arm, the light beam was collimated, attenuated, and reflected. In the sample arm, light was collimated, scanned through a galvanometer (GVS002, Thorlabs Inc.), and then focused via a 54-mm scan lens (LSM04-BB, Thorlabs Inc.) through the hollow part of the ring transducer to the tissue. The backscattering signal from the sample arm was interfered with the reflected signal from the reference arm and transmitted to the detecting arm. This interference signal was split by wavelength via a diffraction grating and finally detected by a line scan CCD camera (spL4096-140 km, Basler AG, An der Strusbek 60-62, Germany) at a 50-KHz A-line rate. The signal was further processed to OCT intensity images and phase-resolved displacement maps. The axial resolution of this SD-OCT is around 3 μm in air. A custom-built 5 MHz modified PZT material ring transducer was used to generate tissue motion. The aperture size is 23 mm with a f-number of 1. The peripapillary sclera was selected as the ultrasonic excitation area, where uniform distribution of acoustic output initiated the propagation of elastic waves in the tissue. The detected displacement of the ONH was attributed to the response of this generated ARF. The excitation pulse was limited to 2 ms to allow the tissue to respond to the ARF naturally and recover to its original position before the next ultrasonic excitation. Confocal alignment of the ultrasound transducer and the SD-OCT system was achieved by using hydrophone (HGL-0085, ONDA Co, Sunnyvale, California) guidance before the experiment.
To acquire the OCT intensity images and phase-resolved displacement maps, a global clock was used to synchronize all subunits of the overall imaging system, including the ultrasound transducer, the CCD imager, and the SD-OCT, as shown in Fig. 2. ARF was generated with the galvanometer set to the P0 location and then, the elastic wave was free to propagate along with the imaged object. M-mode raw data were acquired at each of the galvanometer locations (e.g., P0, P1, P2, etc.) for 400 A-lines resulting in a total location interval of 8.8 ms (0.02 ms delay in every A-line for data storage). The step size for consecutive lateral positions was 4 μm with 1000 lateral points in total. Then, the raw data were saved to disk for offline processing.

Lamb Wave Model
Young's modulus can be estimated simply in free space using the following set of equations: 17 E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 1 ; 6 3 ; 3 4 8 μ ¼ ρc 2 g ; E ≈ 3 μ: The shear modulus (μ) can be obtained using the density (ρ) and constant group velocity (c g ). Young's modulus (E) is approximately three times the shear modulus. One of the assumptions above also includes a pure elastic medium for guided wave propagation. However, the ONH exhibits a thin-layer structure and is small compared with the shear wavelength. Given that Lamb waves typically travel in thin plates with a fluid boundary interface and ARF is applied orthogonally, a Lamb wave is identified as the guided wave propagated in the ONH. The speed of Lamb waves is dispersive and they can only propagate in the low-frequency range due to the viscosity in soft tissue. Since ARF was generated vertically from top to bottom through the thickness of the fluid column, with particles oscillating in the same direction, antisymmetric Lamb waves are mainly induced. Moreover, the zeroth order mode can travel at any frequency and is most commonly detected in the low-frequency range as compared with nonzeroth order mode Lamb waves. For a thin plate submerged in an incompressible fluid, the dispersion equation based on the zeroth order antisymmetric Lamb wave mode is as follows: 31 E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 2 ; 3 2 6 ; 5 3 2 is the shear wavenumber, U ¼ μ þ iωη is the shear modulus, μ and η are shear elasticity and shear viscosity, respectively, and h is the half thickness of the ONH.

Postprocessing
The OCT intensity and Doppler phase raw data were first obtained, the spatial-temporal map along with lateral positions and time was then acquired by averaging the axial displacements through the entire thickness of the ONH. The ultrasonic excitation regions in the field-of-view were all within the full width at half maximum axial intensity of acoustic field. The group velocity was obtained by applying linear regression to the wave crest at different lateral positions. The spatial-temporal map was then transformed to frequency/wavenumber domain (kspace map) by using the two-dimensional (2-D) fast Fourier transform (FFT). The k-space map below 5 Hz was masked to avoid low-frequency noise. The phase velocity was acquired by dividing the frequency by the corresponding maximum wavenumber as follows: E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 3 ; 6 3 ; 6 3 1 c L ¼ 2πf∕k L : The phase velocity was sampled up to 1200 Hz in 125-Hz increment. Then, the shear modulus and viscosity-related fitted phase velocity were selected to minimize the error in every sampled phase velocity R 2 using the following cost function: 31 where c f is the curve fitted phase velocity, f 1 ; : : : ; f n are sampling frequencies with 125-Hz interval. The error rate was also calculated to evaluate the precision of the fitting procedure by using experimental data and fitted data at every sampled frequency: 31 3 Results

Calibration of the Imaging System
The acoustic field of the 5-MHz ultrasonic transducer was measured using a needle hydrophone aligned to the focal point of the transducer. The measured −6 dB lateral beamwidth was 384 μm and the −6 dB axial focal distance was 3.84 mm, which can cover the OCT imaging depth in the ONH (∼0.4 mm) and enable an even distribution of acoustic intensity during data acquisition. In a previous study, the reconstructed Young's modulus of an agar imaging phantom using group velocity was found to be comparable with mechanical testing. 32 We also previously demonstrated the feasibility of reconstructing Young's modulus of rabbit cornea and the posterior segment of the eye in vivo. 28,[33][34][35] With respect to the Lamb wave model, we previously showed the accuracy of this model in calculating Young's modulus in a thin and viscoelastic gelatin phantom as well as for corneal and arterial tissues. 31

ONH Response to Elevated IOP
The biomechanical response of the ONH to elevated IOP was investigated with our Lamb wave model. After each data acquisition, OCT intensity and phase-resolved Doppler OCT data were acquired. Figure 3 show the sampled phase velocity and curve fitting results, as described above for a range of IOP levels, where IOP ¼ 10, 20, and 30 mmHg, respectively. The experimental data match the curve-fit result with good agreement, and the average error rates (ERs) are from 5.4% to 11.09% when the IOP is below 30 mmHg. Young's modulus can be obtained by this curve-fitting procedure and is shown in Fig. 6

Discussion
In this paper, we have presented reconstruction of the Young's modulus of the ONH by combining our OCE system with a Lamb wave model for the first time. The high spatial and temporal resolution of our OCE system enables the acquisition of a highly sensitive spatial-temporal map, which enables high accuracy for subsequent postprocessing. The confocal configuration of the transducer with OCT allows the ARF to be applied to the imaging object orthogonally, which avoids generation of complex elastic waves, such as Love waves, which increases the accuracy of biomechanical estimation. The confocal configuration also allows the OCT beam to penetrate through the center hole in the ultrasonic transducer without incurring significant attenuation, which should enable us to assess the biomechanics of the ONH in vivo for future studies. We further introduced a Lamb wave model in this study. By fitting the experimental phase velocity to the Lamb wave model with low ER, the biomechanics of the ONH can be reconstructed with elevated IOP. Previous work by other groups studied the Young's modulus of the LC and parapapillary sclera as a measure of ONH stiffness. [36][37][38] A common approach for the determination of Young's modulus is tensile testing of tissue strips. 36,37 However, different techniques of measuring stiffness give different stiffness values, making a direct comparison of these values difficult. For instance, a stress-strain measurement showed Young's modulus of the LC was in the range of E ¼ 11.8 to 15.6 MPa and E ¼ 28.5 to 36.0 MPa of the parapapillary sclera, 36 whereas a Young's modulus of 17.2 (AE2.7) kPa was measured for the normal human LC using atomic force microscopy nanoindentation. 38 To the best of our knowledge, this study  is the first to apply OCE to analyze Young's modulus as a measure of stiffness in the ONH. As expected, Young's modulus measured reflects the more real values representative of whole eyes.
Although the quantification of the ONH biomechanical properties with elevated IOP has been demonstrated, there are still some challenges that need to be addressed for future applications. First, a faster imaging speed is required, especially for stiffer imaging objects. For this study, the imaging speed is sufficient to track the elastic wave propagation in the ONH. But for the peripheral sclera, which is stiffer than the ONH, our imaging system may not be fast enough to track wave propagation. A highspeed camera could help solve this issue. Second, the measured mechanical index of the current system is around 1.5, which exceeds U.S. Food and Drug Administration (FDA) regulations (0.23 in ophthalmology). Since, in this study, we acquired only a few hundred nanometers of axial displacement, 32,39 the ultrasonic output can be reduced to meet the FDA regulations and maintain the ability to track elastic wave propagation. Third, ER is increased with elevated IOP. Since ultrasonic output remains unchanged in this study, the ONH became stiffer with elevated IOP, thus, the axial displacement decreased correspondingly. The signal-to-noise ratio may be decreased with a lower detected axial displacement, which leads to a high ER. 40 However, the estimated elasticity is still in a reasonable range. Finally, we showed that it is feasible to reconstruct Young's modulus more accurately using ONH as the subject, however, the viscosity of the ONH with elevated IOP is not provided here. Tissue is predominantly elastic, with viscosity being typically much smaller as compared with elasticity. According to Eq. (2), when μ ≫ ωη, the contribution of viscosity to overall viscoelasticity decreases as elasticity increases, curve fitting is unaffected by changes in viscosity. Moreover, the viscosity of the ONH is not important in this study, and to the best of our knowledge, there is currently no disease related to abnormal viscosity or alteration of viscosity.

Conclusion
In summary, we have demonstrated a method to quantify the biomechanics of the ONH with elevated IOP. The new method uses a confocal OCE system and realizes both high temporal and spatial resolution. We explored the feasibility of applying the Lamb wave model to reconstruct the biomechanics of thin-layered and viscoelastic ONH. By fitting the phase dispersion curve with minimized R 2 , the biomechanics of the ONH can be accurately determined. The study suggests that it should be feasible to evaluate biomechanics in vivo using the confocal configuration, which could lead to assessment of the biomechanics of the ONH in the clinic, allowing us to study the progression of glaucoma over time. Due to this advance, we believe that our confocal OCE system and methodology holds great potential for the detection of biomechanical properties in the posterior segment of the eye in clinical diagnosis.

Disclosures
No conflicts of interest, financial or otherwise, are declared by the authors. Zhongping Chen received his BS degree in applied physics from Shanghai Jiao Tong University, Shanghai, China, in 1982. He received his MS degree in electrical engineering and PhD in applied physics, both from Cornell University, Ithaca, New York, United States, in 1987 and 1993, respectively. He is currently working as a professor of biomedical engineering and the director of the F-OCT Laboratory at the University of California, Irvine, California, United States. He is a cofounder and board chairman of OCT Medical Imaging, Inc., Irvine, California. His research interests include the areas of biomedical photonics, microfabrication, biomaterials, and biosensors. His research group has pioneered the development of functional optical coherence tomography, which simultaneously provides high-resolution three-dimensional images of tissue structure, blood flow, and birefringence. He has published more than 220 peer-reviewed papers and review articles and holds a number of patents in the fields of biomaterials, biosensors, and biomedical imaging. He is a fellow of the American Institute of Medical and Biological Engineering, a fellow of SPIE, and a fellow of the Optical Society of America.