Ultrafast line-field holographic elastography with single excitation for corneal biomechanical characterization

Abstract

Elastography has become an essential tool for assessing tissue biomechanics, in particular for the diagnosis and treatment of keratoconus. For in vivo measurements, high-speed imaging and reduced stimulation are crucial. In this study, we introduce a line-field holographic elastography (LF-HE), which employs line-focus illumination and parallel acquisition to achieve ultra-fast measurement in 14 ms with single excitation. A novel data processing method combining the short time Fourier transform, the phase-resolved color Doppler and full width at half maximum algorithms is proposed to extract the local biomechanical property. Agar phantoms with various concentrations were measured to valid the LF-HE system. The changes of stiffness of in situ porcine corneas treated by riboflavin/UV-A collagen cross-linking (UV-CXL) were also detected in a lateral range of 4.4 mm by modifying the light path of sample arm. This research demonstrated the significant potential of LF-HE for application in ophthalmology clinics.

1. Introduction

The biomechanical characteristics of the cornea play a crucial role in the evaluation and treatment of conditions such as keratoconus [1,2], glaucoma [3,4], and refractive surgery [5,6]. Keratoconus [7] is a kind of ectatic disease, which marked by bilateral, asymmetric, non-inflammatory degeneration leading to central and paracentral thinning and protrusion of the cornea. Some researchers [8–10] have proposed that biomechanical changes occur prior to corneal deformation, and these changes are primarily localized and confined to the cone region, rather than a uniform reduction across the global region. Riboflavin/UV-A collagen cross-linking (UV-CXL) is a clinical intervention for keratoconus that forms chemical bonds between collagen fibers within the corneal stroma, bolstering its overall strength and rigidity. Compared to standard UV-CXL, customized UV-CXL targeted at the weakest areas of the cornea results in fewer epithelial defects and a more regular corneal shape, as well as reducing higher order aberrations (HOAs), and has showed a significant advantage in reducing complications at 1-year postoperative follow-up [10–12]. Consequently, the measurement of corneal biomechanical property distribution of paramount importance for early diagnosis and personalized treatment of keratoconus.

Various elastography techniques are used to characterize tissue biomechanics by assessing the tissue response to loading forces [13]. While ultrasound elastography (UE) and magnetic resonance elastography (MRE) are valuable clinical tools for detecting conditions such as liver fibrosis and breast cancer, they are limited in their ability to delineate corneal lesions due to insufficient spatial resolution and long acquisition times [14,15]. Brillouin microscopy offers a non-invasive means of locally assessing the longitudinal modulus of the cornea without the need for mechanical stimulation or deformation. However, challenges remain in terms of prolonged acquisition time and conversion of longitudinal modulus values to Young's modulus [16].

Optical coherence elastography (OCE) is a promising elastography technique based on optical coherence tomography (OCT) with high spatial resolution and sensitivity. Wave-based OCE has been used to investigate the biomechanical characteristics of the cornea [17,18], iris [19], lens [20], retina [21,22] and other ocular tissues [23]. However, due to the point-by-point scanning mode of a typical OCT system, the frame rate for B-scan is not high enough (approximately several hundred Hertz) to track the propagation of elastic wave from single excitation [24]. Therefore, excitation and M-scan was required at each spatial location of the sample to form M-B scan to visualize the propagating shear waves in one direction. In the previous work [25], our group reported a OCE system with a total acquisition time of 1 s. However, repeated stimulation for several seconds during the OCE measurement may trigger the blink reflex and cause eye motion in patient, which produce unacceptable motion artifacts, even failure in imaging [26–29]. It’s a significant challenge of OCE for clinical applications.

In order to avoid the M-B scan mode in OCE, Larin’s group proposed a phase-sensitive OCE that utilizes a Fourier-domain mode-locked (FDML) scanning laser source with an A-scan frequency of 1.5 MHz [30]. Because of the ultra-fast swept light source, this method captures consecutive B-scans via a single air-pulse stimulus (B-M mode) with a total acquisition time of 30 ms. An alternative approach involves illuminating the sample in parallel with a line focusing, which facilitates parallel elastography. Recently, they proposed an ultrafast line-field OCE (LF-OCE) system to detect changes in corneal stiffness in the rabbit eye under various physiological conditions [31]. However, the above two OCE technologies have high costs and complex systems due to the use of high-speed light source or area array cameras. In a separate study, Larin’s group introduced a non-contact line-field low coherence holography system to evaluate the biomechanical properties of the porcine corneas [32,33]. Based on line illumination, it used a linear array camera to collect holographic interference signals in parallel. To reduce the speckle noise in the interferogram induced by light coherence, this system utilized a superluminescent diode (SLD) as the light source, characterized by its broad spectrum and short coherence length. Inevitably, this configuration limits the interferometric range for curved sample up to only roughly 1 mm in lateral, which may hinder the detection of corneal biomechanics in moderate range [34,35]. Additionally, the capability of high-speed elastography to detect localized biomechanical changes in the cornea has yet to be confirmed.

In this work, we introduce a line-field holographic elastography (LF-HE) system that employs a narrow-spectrum laser diode (LD) as the light source and specially designed sample arm to expand the longitudinal imaging range, extending the measurement range on the cornea to 4.4 mm. The system utilizes a piezoelectric probe to induce elastic waves, and a novel data processing method combining the short time Fourier transform (STFT), the phase-resolved color Doppler (PRCD) is proposed to obtain the phase information, which improves the signal-to-noise ratio (SNR) and enhances imaging robustness. In addition, STFT and FWHM (full width at half maxima) algorithms are combined to calculated the local velocity, and the Young’s modulus distribution can be extracted by holographic elastography for the first time. The system was validated by both homogeneous and heterogeneous tissue mimicking phantoms. By conducting elastography measurements on UV-CXL treated porcine corneas in situ, the LF-HE system demonstrated of great potential for assessing the distribution of corneal elasticity.

2. Methods

2.1. Experimental setup

The LF-HE system is shown in Fig. 1(a). An 853 nm LD serves as the light source with a bandwidth of 1.6 nm was used to increase the coherence gate to 0.227 mm. The collimated beam subsequently passed through a cylindrical lens (CL, LJ1878L1-B, Thorlabs, Inc.) with a focal length of 10 mm, creating a line focus. Specifically, it is parallel horizontally and converging vertically. Through a 50:50 cube beam splitter, two 30 mm focus achromatic lens (L1 and L2, MAD305-B, LBTEK, China) were used to deliver the line beam to the sample surface and reference mirror. A tilted neutral density filter is placed before the reference mirror to reduce the reflective intensity. The reflected light was interfered and transmitted through an 80 mm focus achromatic lens (L3, AC508-080-AB, Thorlabs, Inc) to the line array camera (Teledyne e2 v EV71Y01CUB2210-BB2, Octoplus, Inc.), which worked at a line rate of 100 kHz. The line-focused light illuminated 2048 pixels on the sensor, corresponding to a lateral imaging length of 7.6 mm on the sample. The excitation device comprised a piezoelectric transducer (PZT) (PDS210, Shanghai Nano Motions Technology Co., Ltd) and a spherical tip with a diameter of 1.2 mm. A 1 kHz single-cycle sinusoidal waveform is emitted from the function generator to excite the elastic wave with a duration of 1 ms. For the measurements on porcine corneas, L1 and L2 were replaced with 50 mm achromatic lenses to extend the length of the light beam. To improve the signal intensity of the holography for curved corneal surface, a 32 mm focus condenser lens (L4, ACL4532U-B, Thorlabs, Inc.) was added following L2 to create a convergent line beam on the cornea. This configuration also forms a curved coherence gate, which ensure a consistent optical path difference between the anterior surface of cornea and the reference arm in this interferometric system, as illustrated in Fig. 1(b). The intraocular pressure (IOP) of the whole porcine eye was controlled by adjusting the liquid volume of the infusion bottle or the height of the infusion bottle.

Fig. 1.

Schematic diagram of LF-HE system. (a) CL: cylindrical lens. BS: cube beam splitter. L1-L3: lenses. PZT: piezoelectric transducer. (b)The replaced sample arm designed for the porcine eye. L4: condenser lens. (c)The vertical optical path changes before and after the improvement of the sample arm.

2.2. Tissue mimicking phantoms

The feasibility of LF-HE system was evaluated in preliminary experiments utilizing tissue mimicking agar phantoms in various concentrations (1.0%, 1.2%, 1.4%, 1.6%, 1.8% and 2.0%, N = 3 for each concentration). The agar phantoms were mechanically tested immediately after LF-HE measurements, using a uniaxial mechanical testing machine (TH-8203A, Suzhou Tophung Machine Equipment Co., Ltd., China) to verify the accuracy of the LF-HE technique. Additionally, the heterogeneous agar phantom was created with concentrations of 1.0% and 2.0% to evaluate the system's sensitivity of spatial stiffness variations.

2.3. Porcine cornea samples

Following preliminary agar phantoms experiments, the changes of stiffness of in situ porcine corneas before and after UV-CXL were assessed using the LF-HE system. A total of ten porcine eyes were obtained from a local slaughterhouse and transported to the laboratory for LF-HE measurements within 12 hours of procurement. Fresh porcine eyes were then temporarily stored in 1× phosphate-buffered saline (PBS) solution. Throughout the measurements, the IOP of the porcine eyes was maintained at 15 mmHg. Ten porcine eyes were randomly divided into full-treated (FT) group and half-treated (HT) group on average. The corneal epithelium was then excised using a blunt-tipped surgical instrument, after which two drops of a solution 0.1% riboflavin dissolved in 20% dextran were placed into a 11 mm diameter corneal ring drill for 30 minutes. The cornea was then irradiated by a UV light source (365 nm, 3 mW/cm²) for 30 minutes. The whole cornea was irradiated for the FT group, while HT group underwent UV-CXL exclusively in the half lower region, and the upper region was masked during UV irradiation. The LF-HE measurements were implemented before (untreated, UT) and after the UV-CXL treatment respectively for each eye.

2.4. Data processing and velocity calculations

After the induction of elastic waves on the sample by the piezoelectric probe, the LF-HE system acquires 1400 frames of interferometric signals consecutively. The 2048 points of each frame represent the positions on the sample, while the frame number represents the time dimension. One measurement can be completed in 14 ms, given the line rate of the camera is 100 kHz. The data process framework is illustrated in Fig. 2: (1) The DC components is removed from each frame. (2) A sliding window with a width of 128 pixels and a step size of 10 pixels is set on each frame to divide it into 193 segments in spatial dimensions, and the STFT is then applied to each window. (3) The same segments in all frames form a 2D complex subset of 64 × 1400 pixels, and the PRCD algorithm is employed to the subset to calculate the phase variation between adjacent signals as follows [36]:

$$\mathrm{\Delta }\phi =\frac{1}{T}\text{ta}{\mathrm{n}}^{-1}\left[\frac{\text{Im}(A_{j+1,z})\text{Re}(A_{j,z})-\text{Im}(A_{j,z})\text{Re}(A_{j+1,z})}{\text{Re}(A_{j,z})\text{Re}(A_{j+1,z})-\text{Im}(A_{j+1,z})\text{Im}(A_{j,z})}\right]$$

where $\text{Re}(A_{j,z})$ and $\text{Im}(A_{j,z})$ represent the real and imaginary parts of the complex data after the Fourier transform, respectively. The subscript j and z indicate the frame number (1 ∼1400) and pixel number (1∼64) in each subset. (4) After the unwrapping, the phase signals are averaged in z direction, resulting a spatial-temporal phase map with 193 × 1400 pixels. (5) The region of interest which contains the main perturbation signal is selected on the median filtered spatial-temporal phase map. (6) The local group velocity of wave propagation is finally calculated based on FWHM algorithm. For a targeted position, the spatial distribution $S(x)$ and temporal distribution $T(t)$ (the red and blue boxes in Fig. 2, respectively) are extracted from the spatial-temporal phase map. Gaussian fits to the curves are performed and the FWHM are calculated. The rate of the FWHM is the local velocity at this position [37].

$$c_g=\frac{\text{FWHM}(S(x))}{\text{FWHM}(T(t))}$$

Fig. 2.

Data processing framework. The red and blue boxes show the FWHM of the Gaussian fitting to the distribution curves at the targeted position, respectively. STFT: short time Fourier transform, PRCD: phase-resolved color Doppler, FWHM: full width at half maximum.

The global velocity in the line field can be averaged from the velocity distribution on the sample. Finally, The Young’s modulus can be calculated using the Rayleigh wave equation:

$$E=\frac{2\rho {(1+v)}^3}{{(0.87+1.12v)}^2}{c}_g^2$$

Where $v=0.49$ is the Poisson's ratio. The density $\rho$ of the agar plate and porcine cornea are assumed to be 1000 kg/m3.

3. Results

3.1. Agar phantom

For the agar phantoms, biomechanical distribution measurements were obtained over a length range of 7.6 mm. Figure 3 shows the results of homogeneous agar phantoms with various concentrations measured by LF-HE and mechanical testing. For 1.0%, 1.2%, 1.4%, 1.6%, 1.8% and 2.0% agar phantoms, the Young's modulus measured by LF-HE were 60.89 ± 1.64 kPa, 87.45 ± 2.49 kPa, 114.84 ± 5.70 kPa, 154.93 ± 6.00 kPa, 203.32 ± 8.28 kPa, and 284.44 ± 11.03 kPa, respectively. The corresponding results of the mechanical testing were 74.23 ± 3.6 kPa, 100.28 ± 3.12 kPa, 122.36 ± 3.52 kPa, 176.30 ± 2.25 kPa, 225.47 ± 2.18 kPa and 297.26 ± 5.06 kPa, respectively. The agreement of two sets of data with those of the mechanical testing demonstrators the accuracy of the LF-HE. For the heterogeneous agar phantoms consisting of 1.0% and 2.0%, the local velocity distributions are shown in Fig. 4(c). The sigmoid function [38] was applied to fit the velocity data, to calculate the FWHM of the fitted curve derivative, and yielded spatial resolution of 0.31 mm. Moreover, the local velocities were averaged respectively in portions of 1.0% and 2.0%, and were compared to corresponding homogeneous agar with the same concentrations to verify ability of the system to detect local stiffness changes, as shown in Fig. 4(d).

Fig. 3.

Young's modulus of homogeneous agar with various concentrations measured by LF-HE and mechanical testing.

Fig. 4.

Results of heterogeneous phantoms. (a) Photo of the heterogeneous phantom composed of 2.0% and 1.0% agar, where the red asterisk key represents the position of the excitation point, and the red line represents the position of the light spot. (b) Spatial-temporal displacement map of the heterogeneous phantoms, where the black dotted line is the boundary between the two concentrations. (c) Local velocity distributions of heterogeneous agar phantoms, along with sigmoid fitting and its derivatives derived from the velocities. The arrow length represents the FWHM of the sigmoid derivative, which is the spatial resolution (d) Comparison of Young's modulus of the heterogeneous agar phantoms with the homogeneous agar phantoms. FWHM: full width at half maximum.

3.2. Porcine cornea

For porcine corneas, the LF-HE successfully achieved biomechanical distribution measurements in the 4.4 mm range. Figure 5(b) shows the results of the FT group before and after UV-CXL treatment. The group velocity significantly increased by a mean value of 70.0% for all samples after UV-CXL (p < 0.001, paired t-test). For the HT group, as shown in Fig. 5(e), there are no significant differences between the untreated upper portion after HT and the same cornea before UV-CXL (p = 0.404). Conversely, a significant difference was observed between the treated lower and untreated upper portions of the corneas (p < 0.001), with a mean increase of 80.0% on the lower portions for the five corneas. Figure 5(c) and (f) display the velocity distributions of cornea1 in FT and HT groups, respectively. All the results from the porcine corneas in are further summarized and shown in Fig. 6. It was evident that LF-HE can effectively differentiate between untreated and UV-CXL treated samples, making it a viable tool for assessing localized corneal biomechanics.

Fig. 5.

Results of porcine corneas. (a) Full-treated porcine cornea. (b) Group velocity before and after UV-CXL of FT group (N = 5). (c) Group velocity distributions of cornea 1 before and after UV- CXL in FT group. (d) Half-treated porcine cornea where the upper half is masked during the UV-CXL treatment. (e) Group velocity before and after UV-CXL of FT group (N = 5). (f) Group velocity distributions of cornea 1 before and after UV- CXL in HT group. UT: untreated, FT: full-treated, HT: half-treated.

Fig. 6.

Young's modulus of UT, FT and HT corneal. UT: untreated, FT: full-treated, HT: half-treated.

4. Discussion

In this study, we demonstrated the feasibility of the ultrafast line-field holographic elastography system and algorithms by homogeneous and heterogeneous agar phantoms. We also evaluated the change in Young's modulus of porcine corneas in situ before and after UV-CXL treatment. While OCE measurement of corneal elastography [39–41] have suffered from long acquisition time and repeated excitations, the LF-HE in this study achieves corneal biomechanical measurements within 14 ms with a single excitation. This ultra-fast measurement method effectively reduces corneal irritation and motion artefacts, which are crucial for clinical measurements of corneal biomechanics.

As illustrated in Fig. 3, The Young's modulus measured from the homogeneous concentration agar phantoms using mechanical testing is greater than that obtained from the LF-HE, this discrepancy may arise from the nonlinear nature of the stress-strain curve of agar [42]. Compared to mechanical testing, LF-HE uses a much milder and rapidly localized stimulus to induce an elastic wave. The distributions of group velocity before and after UV-CXL treatment of porcine cornea (Fig. 5(c)) shows that the surface biomechanics are not uniform. It indicates that the real corneal biomechanics distribution, where it’s stiffer in the central zone [13,43,44]. In Fig. 5(f), it’s found that the boundary of group velocities between the UV-CXL treated and untreated regions of the HT cornea is not clear. It may be caused by the dispersion of UV light at the edge of the masker during the UV-CXL.

Conventional holography typically employs low-coherence light emitting diode [45] or superluminescent diode light sources [33,46]. However, a short coherence length results in a limited longitudinal interference range during holographic elastography measurements. Consequently, the application of low-coherence holography is primarily restricted to planar samples. In the case of curved samples, such as the cornea, the measurement range reported in the literature is less than 1 mm [33], which is inadequate for assessing the biomechanics associated with keratoconus. It is because the limited coherence gate can’t cover the significant height difference between the curved corneal center and periphery, making failure to interfere in a wide lateral range [35]. Therefore, we employed a narrow-spectrum LD as the light source in our experiments, which has stronger spatiotemporal coherence and produces a relatively long interference range. Our coherence length can be increased to 0.227 mm, compared to the previous 0.031 mm [32,33]. As the measurement range increasing for cornea, the interferometric signal is found degraded especial in the corneal periphery, because of the increased incidence angle of the parallel light beam at the corneal periphery, compared to the near-normal incidence in the central region. To address this issue, a condenser lens is added after the objective lens in the sample arm, thereby generating a converging light beam and ensures near-normal incidence throughout the entire line-focus. Meanwhile, a coherence gate with curved shape, rather than a planar shape, is generated and fit the corneal curvature by the condenser lens. This modification in the sample arm substantially improves the absolute intensity across a relative longer line field. As a result of the hardware improvement mentioned above, our system achieved lateral range measurement of 4.4 mm for the cornea, with a measured sagittal height (the axial height difference between the highest and lowest corneal points) of nearly 0.3 mm.

Nevertheless, the long coherence length brings along a consequent increase in speckle noise. To address this problem, an algorithm combining the STFT and PRCD is proposed. Hilbert transform algorithm has been demonstrated effective to extract the phase information for line-field holographic imaging in literature [33,46]. Figure. 7(a) and (b) shown the spatial-temporal displacement maps from the same acquired signal using the two methods, respectively. We further calculated the SNR distribution of acquired signals over the measured range. As shown in Fig. 7(c), the average SNR of our algorithm is 21.21 ± 0.62 dB, while that of the Hilbert transform is 9.49 ± 0.27 dB. In contrast, based on the STFT and the PRCD algorithm, our innovative data processing method significantly enhances imaging robustness and exhibits less sensitivity to speckle noise.

Fig. 7.

Results of STFT combined with PRCD vs. Hilbert transform algorithm. (a) Spatial-temporal phase map based on STFT combined with PRCD algorithm. (b) Spatial-temporal phase map based on Hilbert transform algorithm. (c) Comparison of the SNR of two algorithms.

In addition, the STFT algorithm divides the line field signal into multiple segments using a sliding window, and then the FWHM algorithm is employed to calculate the local wave velocity at each segment. Based on these data processing, the Young’s modulus distribution in line field is obtained, and a lateral resolution of 0.31 mm on heterogeneous phantom was achieved (Fig. 4(c)). The previous reported holographic elastography [32,33] only calculated the global Young’s moduli by linearly fitting the elastic wave propagation delays to the corresponding propagation distances. So, our work obtains the Young’s modulus distribution with a moderate high spatial resolution by holographic elastography for the first time.

Corneal tissue exhibits frequency-dependent biomechanical behavior, so the frequency range of excitation affects the resolution and accuracy of the measured mechanical properties [28,47]. In our experiment, the PZT actuator operated using a 1 kHz single-cycle sinusoidal waveform. After the Fourier transform, the frequency range of this waveform was 0-2 kHz in frequency domain, with a center frequency of 1 kHz. This was the result of a trade-off between accuracy and range. Lower frequency excitation is susceptible to excite resonance modes of the cornea or the whole eyeball, resulting in a large deviation of phase velocity [48]. As the excitation frequency increases, the wavelength of elastic wave decreases and the spatial resolution increases as well. However, the attenuation of wave propagation increases meanwhile. The main goal of our research is detecting the wave propagation over an extended range, thereby an extra high frequency is not befitted our measurement. In order to verify it, we further conducted the Lamb wave analysis on the measured corneal signals from our experiment, by the method proposed in previous research of our group [25]. As shown in Fig. 8(a), the center frequency in the wavenumber (k) – frequency map was 973.88 ± 23.85 Hz, which was basically consistent with the theoretical value. As a validation work of holographic elastography system proposed in this study, a contact probe was employed to induce elastic waves. Non-contact excitation methods such as air pulse and air-coupled ultrasonic radiation force will be more suit for clinical application. We will further improve our work when measuring the human cornea in the clinical research.

Fig. 8.

Lamb wave analysis result in the porcine cornea. (a) Wavenumber-frequency domain map of porcine cornea. (b) Phase velocity dispersion curve of porcine cornea.

While the Rayleigh-Lamb wave mode is preferred over the Rayleigh mode for tissues with a thin layer structure, such as the cornea [49,50], we only employed the group velocity in this in this research. The reason is that the elastic distribution over the sample can be obtained based on group velocity, which is another primary objective of this research. The group velocity in our experiments indicated the primary phase velocity at the center frequency, which may potentially lead to an overestimation or underestimation of the measured Young's modulus. But it is acceptable because the elastic various is more important than the absolute value for the application.

5. Conclusion

In summary, we have successfully demonstrated the ultrafast holographic elastography technique in line field. Elastic wave propagation in both agar phantoms and porcine corneas in situ treated by UV-CXL were measured with single excitation in 14 ms. Based on the specially designed sample arm, the corneal Young’s modulus was measured with a lateral range of 4.4 mm. The phase information is processed using a combined STFT and PRCD algorithm, which improves the SNR and enhances imaging robustness. More importantly, the localized biomechanical distribution of the sample is obtained by holographic elastography for the first time using the STFT and FWHM algorithm. The advantages of ultrafast imaging and relative long detecting range make this LF-HE have a great potential application in human corneal biomechanics measurement in clinics.

Funding

National Natural Science Foundation of China 10.13039/501100001809 ( 62275201); Natural Science Foundation of Zhejiang Province 10.13039/501100004731 ( LY23F050012).

Disclosures

The authors declare that there are no conflicts of interest related to this article.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but maybe obtained from the authors upon reasonable request.