Evaluation of Residual Corneal Stromal Bed Elasticity by Optical Coherence Elastography Based on Acoustic Radiation Force

Abstract

Despite the rapidly growing popularity of laser vision correction (LVC) in the correction of myopia, its quantitative evaluation has not been thoroughly investigated. In this paper, an acoustic radiation force–optical coherence elastography (ARF-OCE) system was proposed to evaluate LVC by measuring the residual stromal bed (RSB) elasticity, because it is directly relevant to the RSB thickness that is critical to maintaining normal corneal function. As expected, the Young’s modulus of the RSB was calculated, then its relationship with the RSB thickness was determined. More significantly, a specific thickness was revealed in which the Young’s modulus changed dramatically, which may imply that there is a high risk of complication caused by over-cutting of the cornea. To the best of our knowledge, this is the first ARF-OCE imaging of the RSB, which may help to determine the safe RSB thickness and thus may help us to quantitatively assess LVC surgery.

1. Introduction

In recent years, laser vision correction (LVC) surgery has become an efficient method for treating corneal diseases due to its advantages of rapid recovery of vision, less pain, and inexistence of corneal opacity [1]. However, this procedure will inevitably result in a breakdown in the integrity of the cornea and a risk of postoperative complications. Therefore, evaluation of the safety and efficacy is becoming more and more important [2,3]. Currently, of the existing methods for evaluating the effectiveness of refractive surgery, corneal imaging is the most widely used in clinical practice. Examples include corneal topography to characterize cornea morphology, pentacam to measure corneal thickness data, and high-frequency ultrasound to successfully map the corneal epithelial layer and flap thickness [4,5]. In addition, the application of wavefront sensing techniques in ophthalmology may enable noninvasive in vivo observation of the retinal cones [6]. While these evaluation methods can provide parameters of the structural state of the cornea, they cannot provide parameters of the elasticity or viscosity of the cornea, which are directly related to the safety and stability of the surgery. Furthermore, the safety evaluation of LVC is mostly based on the shapes of the cornea revealed at postoperative follow-up [7,8] rather than quantitative approaches, which may influence the accuracy and reliability of the evaluation. According to the principles of LVC, the thickness of the residual stromal bed (RSB) is directly related to the surgery’s safety and efficacy [9,10]. Meanwhile, the difference in thickness means the RSB possesses quite different biomechanical properties. Therefore, calculation of the RSB elasticity may provide an opportunity to determine the RSB thickness and thus offer a quantitative method for assessing LVC.

Currently, clinically approved devices (Ocular Response Analyzer (ORA) [11] and Corneal visualization scheimpflug technology (Covist) [12]) have been designed to detect the mechanical response of the cornea to external excitation and thus to determine the corneal stiffness. However, ORA is unable to resolve this inverse problem of shear wave propagation and recover direct estimates of physical biomechanical parameters such as corneal elasticity or viscosity, which are directly related to the safety and stability of surgery [13]. In addition, the resulting large vibration in ocular tissues will confound the elasticity imaging and preclude the possibility of spatial-resolved measurement. The corneal indentation device (CID) [14] has been employed to analyze the in vivo measurement of regional corneal tangent modulus, while direct comparison of the results is difficult due to the difference inherent in each applied loading. In addition, various other methods have been used for corneal elasticity detection, such as tensile tests [15] and hydraulic bulge tests [16]. Tensile testing is implemented by stretching the corneal strips, while hydraulic bulge testing is carried out by applying intraocular pressure (IOP) to the cornea and then monitoring the function of corneal excursion and pressure. Peak-resolved atomic force microscopy [17] is another method used to characterize corneal elasticity by detecting the corneal force curve in combination with the indentation method. Since the cornea plays an important role in eye protection and refraction, its nondestructive measurement is a fundamental requirement for clinical needs. Therefore, the invasive and destructive nature of these methods limits their application.

Accordingly, some elastic measurement techniques have arisen, such as Brillouin elastic measurement [18], magnetic resonance imaging (MRI) [19], ultrasound elastography [20], and optical coherence elastography (OCE) [21]. Brillouin elastic measurement has potential for wide application due to its extra-high resolution; unfortunately, this has been limited by the unclear relationship between the elastic modulus and the Brillouin frequency shift. MRI has received great attention due to advantages such as deep imaging depth and wide availability; however, these advantages are restricted by the relatively low resolution and the long time required for imaging. Ultrasound elastography is widely used in the study of tumors and diffuse diseases that cannot be detected by traditional ultrasound. Due to the limited spatial resolution of 100 μm, ultrasound elastography requires a high amplitude basis and cannot be applied to monitor subtle changes in the early stages of diseases.

OCE has been proven to be a useful technique for imaging and characterization of soft biological tissue. It has the characteristics of noninvasive detection, high resolution, high sensitivity, and high speed, resulting from employing optical coherence tomography (OCT) [22] as the detection unit to capture tissue deformation.

There are two modes of excitation in OCE elastic imaging of external excitations [23]: quasi-static compression based on stress–strain response and dynamic excitation based on elastic wave measurements. Compression OCE has been widely used for tumor, skin, and cornea studies with its detailed quantitative strain and stiffness maps and nonlinear stress–strain curves, but noncontact applications have hindered its further development [24]. Wave-based OCE, which utilizes mechanical wave propagation to image mechanical contrast in soft tissues, has proven to be a useful technique for a wide range of noncontact elastography applications in the eye.

Currently, OCE is widely used to detect biomechanical properties of ocular tissues such as the cornea [25,26], lens [27], and trabecular meshwork [28], especially the cornea. The corresponding findings indicate the clinical significance of the biomechanical properties of the cornea for studying pathology and evaluating treatment efficacy for diseases that are correlated with the cornea. However, there is still no comprehensive analysis of the biomechanical properties of the RSB, which is not conducive to the further advancement of LVC.

In this work, we designed an ARF-OCE system for measuring the biomechanical properties of the RSB. A swept-source (SS) OCT technique was employed to detect the elastic wave propagations that were induced by ARF, since it can offer noncontact, local, remote, and dynamic excitation, which is more suitable and practical than other methods. Our system was verified by a heterogeneous phantom and was then used on the postoperative porcine cornea, in which the region of interest is located in the center of the cornea, where the association between elasticity and thickness is more representative and typical. In addition, it has been found that RSB elasticity is not only related to its thickness but also to the IOP, and thus the IOP was controlled at 15 mmHg to achieve a reliable elasticity–thickness relationship. As expected, the Young’s modulus of the RSB was calculated, then the relationship with its thickness was determined. More importantly, a specific thickness that could maintain the intrinsic biomechanical properties of the RSB was also obtained, which is the key to assessing LVC.

2. Measurement System

The schematic diagram of the ARF-OCE system is shown in Figure 1, which includes the ultrasonic transducer excitation unit and custom-designed swept-source OCT imaging unit. When compared with the spectral-domain OCT system, the SS-OCT system can provide deeper penetration depth, less phase washout, and increase the imaging speed. The imaging unit includes a swept-source laser (Axsun) with a central wavelength of 1310 nm, a half-height full-width (FWHM) (-10 dB) of 110 nm, a maximum output power of the light source of 20 mw, and a repetition rate of 50 kHz. The axial spatial resolution of the OCT system is 7 μm, the corresponding lateral spatial resolution is 20 μm, and the minimum phase difference of our system is 161 mrad. A custom-built focused ultrasound transducer with a center frequency of 4.5 MHz, a focal spot diameter of 0.7 mm, and a focal length of 35 mm was positioned orthogonally to the OCT beam. In addition, the lateral scan range of our ARF-OCE system was set to be 3.30 mm.

Before the beam enters the sample and reference arms, the light emitted from the laser is separated by an optical fiber coupler. Ninety percent of the output light is transmitted to the sample through a collimator, a two-dimensional galvanometer system, and a scanning lens. Ten percent of the output light travels through a collimator and a slit and is then reflected by a reflecting mirror. The lights returned from the sample and reference arms interfere in a 50:50 fiber coupler, and then a balanced photodetector is employed to detect the interference signals from the coupler. Finally, the data is collected using a data acquisition card (Alazar Technologies, Inc., QC, Canada ATS9350).

As shown in Figure 2, the M-B scanning protocol was used to detect elastic wave propagations, in which the A-line rate is decided by the laser scanning speed (50 kHz). In the sample arm, a 2D galvo was employed to perform fast 2D scanning by sequentially moving the OCT beam from one position to the next position after one M-scan was completed. Therefore, the OCT B-scan images could be achieved when the same M-scans at 1000 lateral positions were finished. It should be noted that each M-scan included 500 A-lines. In addition, the lateral scanning range of our ARF-OCE system was set to be 3.30 mm. The scanning protocol is shown in Figure 2.

A function generator (Tektronix AFG31102) was utilized to generate a 4.5 MHz sine wave signal [29]. Then, the sine wave signal was amplified by approximately 42 dB by the power amplifier (SPANAWAVE PAS-00023-25) to drive the ultrasound transducer to produce the ARF. In order to extract vibrational information from the OCT data using the Doppler heterodyne method, which is sensitive to transverse vibrations, the ultrasonic transducer was placed perpendicular to the OCT beam, while the ARF excitation was initiated at the 101st A-line. The amplitude of the modulated sinusoidal signal generated by the functional generator was set to be around 60 mV in our study. The resulting MI for ARF was approximately 0.19, which is below the FDA standard for ophthalmic MI [30].

2.1. Subjects

In this work, 0.8% and 0.5% homogeneous phantoms were utilized to verify the ARF-OCE system, and they were synthesized using the method reported in previous research [31]. The steps are as follows: (1) adding 0.8 g or 0.5 g of agar powder to 100 mL of distilled water, (2) entrapping 0.6% (v/v) intralipid in the mixture to increase backscattered signals, (3) heating the solution to 96 ℃ while stirring, (4) removing excess air bubbles by transferring the solution to a vacuum chamber for 5 s, and (5) solidifying the solution by placing it in a refrigerator.

Six porcine eyes were obtained from a slaughterhouse and stored at 4 °C in 0.9% saline during transport. Subsequently, they were stored in 15% lanced salt solution (BSS) before thickness ablation surgery was performed. To simulate the changes in corneal stromal bed thickness induced by LVC, the corneal epithelium was removed under a microscope (Shanghai Tolun Optical Instrument Co., LtD-XTL-207A) using a disposable ophthalmic scalpel (Shapt-YD A50 × 3.0) to expose the anterior corneal elastic membrane. The cornea was cut lengthwise from the central front with a 4 mm drill, and the corneal stroma was removed with a surgical blade at a corresponding depth for a total cut depth of no more than the corneal thickness. The thickness cutting depth was monitored and measured synchronously by OCT with an accuracy of 7 μm for a total of 30 min during the whole cutting process. The OCE experiments were carried out within six hours after death. In addition, to avoid the influence of intraocular pressure [32], it was controlled at 15 mmHg by a custom-made IOP controller. The IOP controller consisted of a micro pump, a differential pressure transducer, and a designed duct, where the output value of the pressure sensor showed the injection flow rate of the eyeball in the set value of the micro pump—that is, the IOP state of the cornea.

2.2. Methods

The raw data were obtained from the ARF-OCE system, and the phase-resolved Doppler algorithm was used to reconstruct the elastic wave propagation in the sample [33].

Based on the Doppler phase shift (Δφ) between two adjacent A-lines, the axial displacement change Δd can be calculated by the following equation:

$$\Delta d={\displaystyle {\int }_{{{\displaystyle t}}_1}^{{{\displaystyle t}}_2}\frac{{\lambda }_0\Delta \phi }{4\pi n\tau }}dt$$

(1)

where λ₀ is the center wavelength of the laser source, τ is the time interval between the adjacent A-lines, and n is the refractive index.

To highlight vibration information, it is necessary to remove background noise in the Doppler phase shift image, which could be realized by plotting the time boundary line after the phantoms start to vibrate. Accordingly, the spatial–temporal displacement map along the elastic wave propagation was obtained (Figure 3c). The high-pass filter was processed on the spatial–temporal displacement map, and then a 2D Fourier transform was performed to obtain the wavenumber–frequency domain map (Figure 4a). The vibration curve of some locations was taken from the spatial–temporal displacement image, which was then processed by one-dimensional fast Fourier transform (FFT). Subsequently, the frequency of vibrational curves was used to estimate half-cycle time, which was then compared with center frequency to verify the reliability of the wavenumber–frequency domain map. As shown in Figure 4b, the center frequency was close to the frequency estimated by vibrational curves, which indicates that the high-pass filter can effectively reduce the low-frequency noise while keeping the target frequency undisturbed.

The phase velocity C_p of the detected elastic wave can be expressed as follows [34]:

$$C_p=\frac{2\pi f}{k}$$

(2)

Based on the wavenumber–frequency domain map, the phase velocity of Lamb waves can be derived using Equation (2). The phase velocity corresponding to the maximum strength of the frequency was selected, and then the dispersion curve was obtained (Figure 4c).

A Rayleigh wave is an elastic wave that propagates along a wavelength depth on the surface of a sample. According to the boundary conditions, when the excitation is focused on the tissue surface, the detected elastic waves are assumed to be Rayleigh waves [35,36], which can be used to calculate the Young’s modulus for the phantom model. The elastic modulus E is expressed by Rayleigh wave velocity $C_R$ in the following equation [13]:

$$E=\frac{2\rho {(1+\nu )}^3}{{(0.87+1.12\nu )}^2}{C}_R^2$$

(3)

Here, ρ is the corneal density and v is the Poisson’s ratio.

The Lamb wave model was used to evaluate the elasticity of the cornea, since the thickness of the cornea is smaller than the wavelength of the induced elastic wave. The link between the phase velocity of Lamb wave $V_L$ and shear wave velocity may be calculated at low frequencies using the following formula [37]:

$$V_L=\sqrt{\frac{2\pi \times f\times h\times V_s}{\sqrt{3}}}$$

(4)

where f and h are the frequency and corneal thickness, respectively.

Because the cornea is submerged by the liquid, the corresponding Lamb wave velocity can be corrected by multiplying a factor of $1/\sqrt{2}$ due to a total leakage of the compressional wave and total reflection of the shear wave at both boundaries [13,37]. Therefore, $V_L$ can be calculated by the following corrected equation:

$$V_L=\sqrt{\frac{\pi fh{V}_s}{\sqrt{3}}}$$

(5)

The correlation between elastic modulus and shear wave velocity (Vs) is: $E=3\times \rho \times V_s^2$. The corresponding Young’s modulus can be calculated based on the Lamb wave velocity using the following equation:

$$E=\frac{9\rho \times V_L{}^4}{{(\pi \times f\times h)}^2}$$

(6)

where ρ and h are the corneal density and thickness, respectively, and $V_L$ and f are the phase velocity and frequency. The density of the homogeneous phantom is 1000 kg/m³ and the density of the cornea is 1064 kg/m³ [38], respectively.

3. Results

The B-scan OCT image of the 0.8% homogeneous phantom is shown in Figure 3a. The corresponding Young’s modulus can be calculated based on Equation (5). The values of Young’s modulus at 0.8% and 0.5% phantoms are 44.86 ± 2.66 KPa and 18.36 ± 0.42 KPa, respectively, which is consistent with previous reports [39,40]. To further validate the veracity of the results, a compression test was performed using MTS Synergie 100 on the agar phantoms. The resulting values of Young’s modulus at 0.8% and 0.5% phantoms are 50.0 ± 6.5 KPa and 22.0 ± 3.8 KPa, respectively; which is in close agreement with our experimental values, indicating the feasibility and reliability of our system for elasticity imaging.

After verification, OCE detection was carried out on the ex vivo porcine models. Figure 5 shows shear wave propagations at five different times, which is used as an example for interpreting shear wave propagation in the cornea. It was found that the shear wave travels from the left to the right side of the cornea after it is produced. Furthermore, the shear wave is produced at the focus of the ultrasonic transducer, which is marked by a white arrow in Figure 5b.

To study the relationship of the RSB elasticity to its thickness, multiple surgeries were performed on one porcine eye to achieve different thicknesses, as shown in Figure 6. The corresponding structure and elasticity information is shown in

Table 1. Physical parameters of the RSB.

Thickness (μm)	Proportion of the Thickness (%)	Young’s Modulus (kPa)
1040.65	100%	11.61
753.34	72%	33.78
630.02	60%	31.06
497.98	47%	52.36
308.71	29%	126.38
168.05	16%	315.74

. According to the results, the Young’s modulus value increases by 167.52% compared to the intact cornea as the thickness is reduced to 630.02 μm. The corresponding value increases by 67.74% when the thickness is further reduced to 497.98 μm. After reaching the critical point, the value of Young’s modulus growth rate settles around the range of 140.64–149.83%.

The same surgery and OCE measurements were performed on the other five samples to obtain a comparative and comprehensive analysis. As shown in Figure 7, there was almost no difference among these six samples in terms of their intact corneal stiffness, which ranged from 12.79 kPa to 32.35 kPa. It was also found that the Young’s modulus for all the samples increased with decreasing RSB thickness, which created a dramatic elasticity change (varies from 12.79 kPa to 445.12 kPa and the main frequency ranges from 730.01 Hz–1345.50 Hz). Furthermore, each sample had its own critical point at which the elasticity changed significantly. The specific thicknesses of each of the six samples were calculated to be 534.21 μm, 446.1 μm, 358.67 μm, 399.76 μm, 176.32 μm, and 630.02 μm, respectively.

Subsequently, data from multiple groups were fitted with a third-order fitting function to further explore the critical thickness of the RSB and estimate more about the thicknesses. The results are shown in Figure 8, where the abscissa represents the thickness of RSB and the ordinate represents the corresponding Young’s modulus. In general, the Young’s modulus is inversely proportional to the thickness. Specifically, the Young’s modulus increases smoothly at first, then dramatically increases when the proportion is below 57.08%. These significant changes reflect that the existence of the thickness threshold can break the balance between elasticity and thickness, which may lead to a high risk of biomechanical failure [41].

4. Discussion

In recent years, high incidence of various ocular diseases has promoted the continuous progress of LVC; however, complications such as corneal hyperplasia and iatrogenic keratectasia are still unavoidable [41,42]. Studies have shown that the thickness of the RSB is not only closely related to the safety and efficacy of the surgery, but also to its elasticity, suggesting that quantification of elasticity may be an accurate way to evaluate the surgery [43,44]. Although the elasticity of the corneal stroma has been studied in previous reports [45,46], excised corneal slices were used as the sample; thus, the normal corneal morphology and IOP level could not be maintained. Existing laser-assisted in situ keratomileusis (LASIK) uses an excimer laser to cut the cornea to create a flap [47,48]. Moreover, it has been proposed that the flap does not act as a barrier to mechanical stress; thus, iatrogenic keratectasia can easily occur when the RSB is extremely thin, which is a common problem in the surgery of high myopes [49]. Even though the rate of complications has decreased with technological progress, keratectasia remains the most vision-threatening side effect [10,50,51,52]. Therefore, the biomechanical properties of RSB should be further studied to provide some reference for related surgery.

In this study, an ARF-OCE system—which combines advantages of noninvasive detection, high resolution, high sensitivity, high acquisition speed, and high-speed imaging—was proposed for measuring the RSB elasticity of intact eyeballs. This may provide more accurate and valuable information for surgery assessment. After verification by the phantom experiment, OCE imaging was carried out on porcine eyes under constant IOP, in which the relationship between the RSB elasticity and its thickness was carefully studied.

It was found that the Young’s modulus of the intact cornea is in the range of 12 kPa to 33 kPa, which is highly consistent with previous studies [53,54,55]. After the surgery, the biomechanical properties of the RSB change and the corresponding Young’s modulus increased with decreasing thickness. More precisely, the Young’s modulus increased steeply and remained in a high-modulus regime with thicknesses below a specific thickness, which is close to 38 times higher than that of the intact cornea. Our findings imply that the RSB must have enough thickness, otherwise biomechanical failure may occur [30]. This ratio of thicknesses ensures that the RSB can achieve stable elasticity. Therefore, the specific thickness of the individual difference is determined by the ratio of the RSB to the original cornea. Subsequently, the fitted curve of the data was depicted, in which a clear inflection point of the growth rate of the Young’s modulus was determined to be 57.08% (proportion of RSB in intact corneal thickness). It is worth noting that this specific thickness is close to the minimum thickness limit for the RSB in current LVC surgery, which was achieved by using the qualitative method as mentioned in the introduction [56], suggesting that our method could provide accurate and quantitative assessment for LVC surgery.

In this preliminary work, a new method for LVC evaluation was proposed, which may have many future applications. The advantage of ARF as an exciter for OCE systems is that it enables remote excitation of the surface and the interior of the sample on a noncontact and nonintrusive basis. Thus, it is possible to measure the elasticity of internal tissues (such as the retina and lens) and surface tissues (such as the cornea, blood vessel walls, and skin). Based on our findings, the feasibility and reliability of our approach have been verified, but there are still real challenges in applying existing ARF-OCE systems to practice. Firstly, to meet clinical needs, imaging speed should be further enhanced, which can be effectively achieved by applying a high-repetition-rate laser source and the optimized data processing streams. Secondly, the spatial resolution should be further improved to obtain more detailed information, which means that a swept laser with a longer wavelength and a wider bandwidth needs to be introduced into our system. Thirdly, the imaging range is limited by the eyepiece; combining a full-field optical coherence tomography (FF-OCT) would extend the imaging range. Finally, to obtain a higher resolution OCE and the map of elasticity, the ultrasonic transducer should be further optimized to generate a smaller excitation area and higher tissue frequency content, thus improving system resolution. In addition, since the cornea is a viscoelastic tissue, viscosity needs to be taken into account when evaluating its biomechanical properties.

5. Conclusions

In this study, an ARF-OCE system was developed to evaluate RSB elasticity. After the feasibility and practicability were verified using phantom models with different concentrations, the postoperative porcine corneas were carefully studied, and the Young’s modulus of the RSB and the corresponding elasticity–thickness relationship were obtained. More importantly, a specific thickness of the RSB was determined, which could guarantee its biomechanical properties in a normal range, and thus the risk of postoperative complications may be effectively reduced. With the advantages of noninvasive detection, high resolution, high sensitivity, and high-speed imaging, ARF-OCE can provide not only information on the Young’s modulus and thickness of the RSB, but also the possibility of quantitative evaluation of LVC surgery.