2.1.

System Setup

Elastic waves are induced in the sample using a home-built air-pulse delivery system that produces a focused air stream with a duration of $\le 1\mathrm{ms}$. The spatial-temporal profile of the air pulse is characterized as a Gaussian shape. Briefly, the system employs an air gate and a control unit to provide the short-duration air puff. An extra channel for signal output from the control unit allows proper synchronization with the PhS-SSOCT measurement system. The air source pressure can be obtained from a pressure gauge, and the output of the air-pulse system is through a cannula port with a flat edge and the diameter of $\sim 150\mu \text{m}$. The localized air-pulse excitation can be precisely positioned through a 3-D linear micrometer stage. This excitation system can be treated as a noncontact stimulation method.

A PhS-SSOCT imaging system is combined with this air-pulse system to detect elastic waves in the sample. The schematic of the experimental setup for the in vivo study of mouse cornea is shown in Fig. 1. Briefly, the PhS-SSOCT system is composed of a broadband swept laser source (HSL2000, Santec, Inc., Torrance, California) with the central wavelength of 1310 nm, the bandwidth of $\sim 150\mathrm{nm}$, the scan rate of 30 kHz, and the output power of $\sim 36\mathrm{mW}$. Interference is produced by the light coming from the sample and reference paths using a Mach–Zehnder interferometer and the fringes are detected by a balanced photodetector. A fiber Bragg grating is used for triggering the A-scan acquisition. The details of the system description can be found in our previous work.^29,35,36 The axial resolution of the system is $\sim 11\mu \text{m}$, and the phase stability of the system is experimentally measured to be $\sim 16\mathrm{mrad}$ (corresponding to $\sim 3.3\mathrm{nm}$ displacement in air). The air-pulse system generates a transistor–transistor logic signal which is recorded by the analog-to-digital converter for synchronization.

Fig. 1

Schematic of the system setup used in the in vivo study of the mouse cornea.

2.2.

Experimental Materials

In order to simulate soft tissue samples of controlled stiffness, gelatin phantoms of five different concentrations (8%, 10%, 12%, 14% and 16% w/w) were prepared. Gelatin powder (PB Leiner, 250 Bloom/8 Mesh) was mixed with distilled water at 60°C until all granules were dissolved. Special care was taken while stirring the mixture to avoid the formation of air bubbles. The mixture was poured into a round mold to create a disk of $\sim 11\text{-}\mathrm{mm}$-thick and $\sim 33.5\mathrm{mm}$ in diameter [Fig. 2(a)] and cooled down in a refrigerator for 30 min ($\sim 10°\mathrm{C}$).³⁷ The solidified gel formed a solid slab that served as a tissue-mimicking sample.

Fig. 2

Phantom sample is shown as (a). Excitation and measurement locations on (b) gelatin phantom and (c) mouse cornea in vivo. (d) shows the port and the mouse cornea. In (c) and (d), the scale along the long-axis is 4.8 mm, and for the short-axis, the scale is 4.4 mm, and for $z$, the scale is 2.2 mm.

The contact lens used was a commercially available lens (Bausch & Lomb, Slisoft + 12.00D, 100% Silicone) that has a convex-concave shape similar to the cornea and has homogeneous optical and mechanical properties. During the experiments, the contact lens was fixed on a flat plate, and the space between the contact lens and the plate was filled with $1\times$ phosphate-buffered saline simulating the aqueous humor in a second experiment.

A custom-made silicone model of an eye was also used in our study. This model provides an anterior surface scaled to match the curvature and size of the human eye. However, it has homogeneous optical and mechanical properties. The eye-mimicking model’s anterior surface had a radius of curvature of 7.8 mm.

In vivo studies were performed on the corneas of three mice (15 to 22 months old). The cornea was kept hydrated by the periodical application of 0.9% saline solution during experiments. All animal manipulation procedures were approved by the Animal Care and Use Committee of the University of Houston.

Surface waves were excited with the air pressure set as $\sim 10\mathrm{Pa}$ for the gelatin phantoms and silicone eye model, $\sim 2.2\mathrm{Pa}$ for the contact lens, and $\sim 5.9\mathrm{Pa}$ for mouse cornea in vivo. During all experiments, the distances between the tip of the air-pulse system port and the sample surface were kept within 0.3 mm, and time-dependent phase response was recoded from the surface of samples. Our investigation has shown that the air pressure of the system output remains relatively stable with the distance change within 10 mm between the port tip and the sample surface.³⁸ M-mode imaging over time at different positions (M-B scan mode) was utilized for OCT measurement. The spatial distributions of the excitation points and measurement points on the samples are shown in Fig. 2. The distance between the excitation point and the first measurement point was kept at more than 1 mm. The distance between two recording positions was 1 mm during the gelatin phantom, contact lens, and silicone eye model studies and 0.3 mm during in vivo studies.

2.3.

Quantification Methods

To calculate amplitude of the surface waves from phase measurements, the following equation was used:³⁰

The velocity of the elastic wave $c$ was calculated as

Assuming that the phantoms are isotropic homogeneous elastic materials, the Young’s modulus $E$ of the sample can be calculated based on the wave velocity $c$ as follows:³⁹

For the studies on contact lens, silicone eye model, and in vivo mouse cornea, the time delay was calculated relative to the position that is the nearest to the estimated excitation point and two-dimensional (2-D) rendered maps of time delay were generated.

3.1.

Gelatin Phantom Studies

Figure 3(a) shows typical amplitude of the surface waves propagating in the 14% gelatin phantom recorded at various measurement locations away from the excitation position. These data clearly demonstrate that the amplitude decreases and the time delay increases with the increasing distance. Although the spatial-temporal profile of the air pulse is well characterized as a Gaussian pulse, it was not delivered perfectly normal to the specimen surface (mostly due to the geometrical coupling with the OCT imaging lens). It is possible that the angular separation of the air pulse and the measurement axis ($\sim 30\mathrm{deg}$ in this experiment) may influence the shape and force of the stimulus, thereby producing additional frequencies [the small amplitude vibration before the major deformation, as seen in Fig 3(a)]. Figure 3(b) shows the velocity of the surface waves measured in gelatin phantoms of different concentrations. The data indicate that the wave velocity increases with increasing concentration of gelatin, corresponding to the increase in the sample stiffness, which is consistent with our previous study.³⁰ The typical delay map of the 12% gelatin phantom is shown in Fig. 4, which also indicates that the time delay increased with the increasing of the distance.

Fig. 3

(a) Phase responses recorded at various measurement points away from the source of excitation in 14% gelatin phantom. (b) The wave velocity as a function of the concentration of gelatin ($n=9$).

Fig. 4

Typical delay map measured in 12% gelatin phantom.

The obtained Young’s moduli of the gelatin phantoms are presented in Fig. 5. For the quantification, the density ($\rho$) of gelatin phantoms was assumed to be $1000\mathrm{kg}/{\mathrm{m}}^3$ and the Poisson’s ratio ($v$) of 0.5 was used to obtain $E$ from Eq. (3).⁴⁰ The calculated Young’s moduli of 8%, 10%, 12%, 14% and 16% gelatin phantoms are $12.2\pm 0.6\mathrm{kPa}$, $17.5\pm 1.6\mathrm{kPa}$, $25.1\pm 3.8\mathrm{kPa}$, $36.1\pm 4.0\mathrm{kPa}$, and $48.8\pm 8.2\mathrm{kPa}$, respectively. Additionally, a uniaxial testing system (In-Spec 2200, Instron, Inc., Northwood, Massachusetts) was used to measure the Young’s moduli of gelatin phantoms with the same concentrations (Fig. 5). It can be easily seen that the estimated Young’s moduli obtained from the wave velocity using OCT are reasonably close to those obtained using the uniaxial testing system. The small differences may be attributed to the fact that different samples were used in these two measurement methodologies (OCT measurements versus uniaxial testing).

Fig. 5

Young’s moduli of gelatin phantoms calculated from wave velocity and measured by the uniaxial testing system.

3.2.

Contact Lens Study

The experiment with a contact lens was performed with 0.9% saline solution placed between the contact lens and the supporting plate. Figure 6 shows the 2-D rendered map of time delay of the elastic waves in the contact lens. The result in Fig. 6 shows that the delay increases within greater distance in the contact lens and then decreases with the further increase in the distance.

Fig. 6

2-D rendered map showing the time delay distribution on the surface of contact lens with 0.9% saline beneath the lens.

There are several possible explanations for the observed difference in the delay distribution in phantoms and in the contact lens. One possibility is that the presence of the liquid on the lens posterior surface and the geometry of the lens produce a difference in how the energy propagates within the medium. For instance, the pressure pulse generates P-waves or compression waves that propagate much faster in the saline solution with low attenuation than the elastic waves in the cornea or lens material. As a result, these waves could produce additional sources of mechanical excitation in the lens after reflection from the hard surface. Therefore, the complex time delay distribution in the contact lens could be explained by the interaction of the different types of the waves. It is clear, however, that the presence of the liquid on the lens posterior surface complicates the wave pattern similar to what we observed in in vivo studies (see Fig. 7).

Fig. 7

(a) The measured time delay of elastic waves on (a) silicone phantom eye model and (b) 18-month-old mouse cornea in vivo.

3.3.

Silicone Eye Model and In Vivo Study of 18-Month-Old Mouse Cornea

Figures 7(a) and 7(b) show the OCT structural images and 2-D rendered maps for the time delay of the elastic waves measured in the silicone eye model and the mouse cornea in vivo, respectively. In Fig. 7(a), the time delay of the elastic wave increases as distance increases across the thick and homogeneous silicon layer that is different from what is observed in the real mouse eye. In Fig. 7(b), similar results as in Fig. 6 can be observed: the time delay of elastic waves increases with the increasing distance before reaching the corneal apex but decreases with greater distance after crossing the apex.

The distribution of time delay before the elastic waves that reach the apex can be used to quantify the wave velocity. For the 18-month-old mouse cornea, the velocity of the elastic wave is calculated as 0.92 to $7.42\mathrm{m}/\mathrm{s}$ at different lateral positions due to heterogeneity of the tissue, which are potentially useful for the estimation of cornea elasticity. Additional work is required to develop a quantitative model to estimate corneal elasticity and to obtain corneal elastography because corneal tissue is inhomogeneous in both structure and composition. Equation 3, used here for isotropic homogenous materials, may not be proper to be used for the tissues like the cornea, which are composed of multiple layers and have curved surfaces.

This method does not involve tools that disrupt tissue or physically contact the eye. The displacement caused by air-pulse excitation on the cornea in these experiments is on the order of micrometers, which is much smaller than the indentation produced by the air puff used in clinical measurement of intraocular pressure (tonometry). Therefore, this approach is less invasive than current clinical procedures and suitable for delicate tissues or other sensitive materials. The high sensitivity of the PhS-SSOCT system enables accurate detection of the displacement of the cornea. These advantages allow the dynamic assessment of elastic waves propagating in ocular tissues and make it possible to estimate their biomechanical properties in vivo.