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Cornea  |   November 2014
In Vivo Evidence of Porcine Cornea Anisotropy Using Supersonic Shear Wave Imaging
Author Affiliations & Notes
  • Thu-Mai Nguyen
    Ecole Supérieure de Physique et Chimie Industrielles (ESPCI ParisTech), Paris-Sciences-Lettres Research University (PSL), Institut Langevin, Paris, France
  • Jean-Francois Aubry
    Ecole Supérieure de Physique et Chimie Industrielles (ESPCI ParisTech), Paris-Sciences-Lettres Research University (PSL), Institut Langevin, Paris, France
  • Mathias Fink
    Ecole Supérieure de Physique et Chimie Industrielles (ESPCI ParisTech), Paris-Sciences-Lettres Research University (PSL), Institut Langevin, Paris, France
  • Jeremy Bercoff
    Supersonic Imagine, Aix-en-Provence, France
  • Mickael Tanter
    Ecole Supérieure de Physique et Chimie Industrielles (ESPCI ParisTech), Paris-Sciences-Lettres Research University (PSL), Institut Langevin, Paris, France
Investigative Ophthalmology & Visual Science November 2014, Vol.55, 7545-7552. doi:10.1167/iovs.14-15127
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      Thu-Mai Nguyen, Jean-Francois Aubry, Mathias Fink, Jeremy Bercoff, Mickael Tanter; In Vivo Evidence of Porcine Cornea Anisotropy Using Supersonic Shear Wave Imaging. Invest. Ophthalmol. Vis. Sci. 2014;55(11):7545-7552. doi: 10.1167/iovs.14-15127.

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      © ARVO (1962-2015); The Authors (2016-present)

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Abstract

Purpose.: This work proposes shear wave elastography to quantify the elastic anisotropy of the cornea.

Methods.: Experiments were conducted on enucleated porcine eyeballs and anesthetized swine. We used the supersonic shear wave imaging (SSI) method implemented on a dedicated 15-MHz rotating linear ultrasound array. This setup allows determining the shear wave speed variations for a set of radial propagation directions.

Results.: All the results showed a local anisotropy with one main direction of maximal stiffness. The influence of pulsatility was observed in vivo, and electrocardiogram (ECG) gating was consequently performed for all anesthetized swine. On ex vivo corneas, n = 27 acquisitions were performed in the limbus region, where the collagen fibrils are reported to run tangentially to the sclera. A good match was shown between the direction of maximal stiffness and the expected direction of the collagen fibrils.

Conclusions.: This preliminary study demonstrates the potential of SSI for the assessment of corneal anisotropy in both ex vivo and in vivo conditions.

Introduction
Transmitting and refracting light are the two main functions of the cornea. Both are ensured by a unique collagen structure that provides transparency and appropriate curvature. As illustrated in Figure 1, the cornea is divided into three layers (epithelium, stroma, and endothelium) separated by two membranes. The stroma, accounting for 90% of the whole cornea thickness, plays the major part in the corneal biomechanical behavior. It consists of collagen fibrils that are packed into lamellae. Within one lamella, the collagen fibers run parallel to each other, but the alignment direction can vary from one lamella to another. This arrangement can be observed using various techniques such as x-ray diffraction1,2 or multiphoton microscopy.3,4 X-ray diffraction is an ex vivo method mapping the orientation of the collagen lamellae along the cornea. Multiphoton microscopy provides three-dimensional (3D) images of the collagen lamellae with a micrometric resolution in the corneal thickness and has been proven to be applicable in vivo. Many groups focus their efforts on understanding the biomechanical properties resulting from that complex anisotropic structure. Uniaxial stress–strain measurements have been performed on porcine cornea strips cut along different directions5,6 and have shown differences in the elastic response depending on the cutting direction. More sophisticated experiments were designed to investigate the global behavior of the entire cornea. For instance, inflation tests were performed on bovine corneas. The recorded deformation field was fitted with an anisotropic finite-differences model, describing different collagen fiber alignments in the peripheral and the central region of the cornea.7 
Figure 1
 
(a) Anatomy of the anterior segment of the eye. (b) Microstructure of the cornea. The cornea is divided into three layers (the epithelium, the stroma, and the endothelium) and two membranes. The stroma mainly consists of collagen bundles that are organized in lamellae.
Figure 1
 
(a) Anatomy of the anterior segment of the eye. (b) Microstructure of the cornea. The cornea is divided into three layers (the epithelium, the stroma, and the endothelium) and two membranes. The stroma mainly consists of collagen bundles that are organized in lamellae.
All these approaches provide valuable biomechanical data but cannot be implemented in vivo. Other elastography systems, based on deformation imaging, have been designed for clinical translation (Roy AS, et al. IOVS 2014:55:ARVO E-Abstract 3701).8,9 These systems provide an indirect estimation of the corneal elastic properties but have not been used yet to investigate the anisotropic behavior of the cornea. In this paper, we propose shear wave elastography as a potentially in vivo-applicable method to investigate experimentally the elastic anisotropy of corneas. For that purpose, the supersonic shear wave imaging (SSI) technique was implemented with house-made rotating arrays connected to a custom high-frequency version of the Aixplorer ultrasound scanner. As a proof of concept, shear wave speed dependence with the propagation direction was measured on ex vivo porcine corneas in both central and peripheral regions. Preliminary in vivo experiments were also performed on a swine model. 
Materials and Methods
Supersonic Shear Wave Imaging
Soft tissues are usually considered incompressible media.10 In that case, the Young's modulus E is proportional to the shear modulus μ:    
In an incompressible, homogeneous, and isotropic medium, the shear modulus is linked to the speed vT of a shear wave propagating in this medium11:  where ρ is the medium density. Thus, the elastic properties of soft tissues can be retrieved by creating a shear wave in the tissue and measuring its propagation speed, as proposed in shear wave elasticity imaging.10  
Supersonic shear wave imaging is an implementation of this principle using the ultrasound radiation force as a shear source and an ultrasound ultrafast imaging mode to follow the propagation of the resulting shear wave. All details about this technique can be found in earlier publications.1214 Our group recently implemented the SSI method with high-frequency linear ultrasonic probes (15 MHz, 128 elements; Vermon, Tours, France) for imaging of the cornea biomechanical properties, as detailed in previous works.15,16 A conventional ultrasound probe is driven using a programmable ultrasound scanner (Aixplorer; Supersonic Imagine, Aix-en-Provence, France). The first step consists in applying a “pushing beam” by focusing an ultrasound beam in the tissue for a few tens of microseconds in order to induce a transient axial displacement of a few micrometers amplitude (Fig. 2a). The tissue relaxation generates a shear wave that is polarized axially, that is, along the beam axis, and propagates transversally. In the second step, the probe is switched to an ultrafast imaging mode: Ultrasound plane waves are emitted, and the backscattered signals are beamformed to obtain images of the tissue during the shear wave propagation (Fig. 2b) at very high frame rates (up to 30 kHz for a 1-cm imaging depth). As illustrated in Figure 2c, several pushing beams are applied at different locations along the cornea to map the whole tissue. They are interleaved with ultrafast imaging acquisitions. A complete acquisition sequence typically lasts a few tens of microseconds. The phase differences between consecutive images are computed to retrieve the axial displacement field over time. The propagation speed of the shear wave is then determined using a time-of-flight algorithm applied independently for each depth of the imaging plane. It consists of cross-correlating the displacements from neighboring pixels to compute the travel time of the shear wave between these pixels. Cross-sectional elasticity maps of the anterior segment of the eye were reconstructed from the estimation of the shear wave speed at each point of the imaging plane with a typical lateral resolution of 400 μm.15 The pixel size of the elasticity maps is 100 × 100 μm (axial × lateral). 
Figure 2
 
Principle of the SSI elastography technique applied to the cornea. (a) An ultrasonic “pushing beam” is focused in the cornea for a few tens of microseconds. (b) The propagation of the resulting shear wave is imaged at a high frame rate (up to 30,000 frames/s) by emitting ultrasound plane waves. (c) A complete acquisition sequence consists of several pushing beams, applied at different positions along the corneal curvature, interleaved with ultrafast imaging series. Such an acquisition typically lasts a few tens of microseconds.
Figure 2
 
Principle of the SSI elastography technique applied to the cornea. (a) An ultrasonic “pushing beam” is focused in the cornea for a few tens of microseconds. (b) The propagation of the resulting shear wave is imaged at a high frame rate (up to 30,000 frames/s) by emitting ultrasound plane waves. (c) A complete acquisition sequence consists of several pushing beams, applied at different positions along the corneal curvature, interleaved with ultrafast imaging series. Such an acquisition typically lasts a few tens of microseconds.
Assessment of the Shear Anisotropy Using SSI With Rotating Arrays
In an isotropic medium, the shear wave speed is independent from the shear wave propagation direction. However, some tissues exhibit anisotropic biomechanical properties that are related to their microstructure. For instance, in a tissue constituted with fibers running parallel to each other (Fig. 3), the shear wave speed depends on the propagation direction relative to the fibers' orientation according to the following equation17:  where ρ is the medium density, θ is the angle between the shear wave propagation direction and the fiber orientation direction, and c44 and c66 are the elastic constants of the medium.17 Display FormulaImage not available and Display FormulaImage not available are particular values of the speed corresponding to the case of a propagation direction, respectively, parallel (θ = 0°) or perpendicular to the fibers (θ = 90°).  
Figure 3
 
Supersonic shear wave imaging elastography in a transverse isotropic medium. The ultrasound radiation force induces a shear wave that is polarized along x1 and propagates in the (x2,x3) plane. The imaging plane forms an angle θ with the fibers' direction.
Figure 3
 
Supersonic shear wave imaging elastography in a transverse isotropic medium. The ultrasound radiation force induces a shear wave that is polarized along x1 and propagates in the (x2,x3) plane. The imaging plane forms an angle θ with the fibers' direction.
As illustrated in Figure 3, performing 3D SSI acquisitions by rotating the ultrasound probe provides measurements of the shear wave speed along different propagation directions, yielding an assessment of the local anisotropic properties of the medium. In strict logic, the anisotropy is assessed only around the center of rotation of the probe. This method has been used in previous works with a different setup to assess the anisotropic properties of the brachial biceps18 and the myocardium.19,20 The following sections describe the application of 3D SSI for investigation of the corneal shear anisotropy. 
Ex Vivo Experimental Setup
Thirty-four 3D SSI acquisitions were performed at different locations of 12 enucleated porcine corneas. Fresh enucleated porcine eyeballs were obtained a few hours post mortem from a slaughterhouse (Etablissements Guy Harang, Houdan, France). The eyeballs were kept refrigerated and experiments were performed within 24 hours after enucleation. 
The experimental setup is shown in Figure 4. The eyeball is immersed in water. The ultrasound probe is mounted on a rotary stage and placed a few millimeters above the cornea (Fig. 4a). As illustrated in Figure 4b, different imaging planes are acquired by rotating the probe (with a sweep angle θ ranging from 0° to 360° with a 10° step). A 180° rotation is enough to perform a complete scan. However, a 360° rotation was chosen to allow averaging data corresponding to the same angle (θ and θ + 180°). 
Figure 4
 
Experimental setup for 3D SSI acquisitions on enucleated porcine eyeballs. (a) The eyeball is immersed in water. The probe is mounted on a rotary stage and placed a few millimeters above the cornea. (b) Acquisitions are performed in different imaging planes (θ ranges from 0° to 360°). (c) The intraocular pressure is monitored during the entire experiment. Two needles are inserted in the anterior chamber of the eye. The first one is connected to an elevated water tank; the other one is connected to a digital manometer. A computer collects the manometer measurements and subsequently adapts the height of the water tank.
Figure 4
 
Experimental setup for 3D SSI acquisitions on enucleated porcine eyeballs. (a) The eyeball is immersed in water. The probe is mounted on a rotary stage and placed a few millimeters above the cornea. (b) Acquisitions are performed in different imaging planes (θ ranges from 0° to 360°). (c) The intraocular pressure is monitored during the entire experiment. Two needles are inserted in the anterior chamber of the eye. The first one is connected to an elevated water tank; the other one is connected to a digital manometer. A computer collects the manometer measurements and subsequently adapts the height of the water tank.
In order to obtain repeatable measurements, it is crucial to control the intraocular pressure (IOP). Indeed, previous inflation experiments21 have shown that the overall corneal elasticity increases significantly as the IOP increases. Thus, IOP monitoring with automated feedback correction was set as shown in Figure 4c. Two needles are inserted into the anterior chamber of the eyeball. The first one is connected to an elevated water tank that produces a hydrostatic pressure. The second one is connected to a digital manometer (AZ 8215; Bioseb, Vitrolles, France), and the resulting IOP measurements are sent to a computer. The computer subsequently adapts the height of the water tank to maintain the IOP at 20 ± 2 mm Hg. 
Among the 34 acquisitions, 7 acquisitions were performed in the central part of the cornea and 27 acquisitions were performed in the peripheral part of the cornea (at a maximal distance of 1.3 mm from the limbus). Attention was focused on this region in order to investigate the potential link between the collagen fiber orientation and the shear anisotropy. Indeed, x-ray diffraction studies performed on excised porcine corneas2 reported that collagen fibers have a circumferential arrangement with a well-defined orientation in the peripheral region (within a 2-mm distance from the limbus, fibers are tangential to the limbus), whereas the central part exhibits a higher variability. 
In Vivo Experimental Setup
Four in vivo acquisitions were on anesthetized swine (n = 4 eyes). The experiments were conducted at the research unit of Institut Mutualiste Montsouris (IMM Recherche, Paris, France). Animal preparation and imaging procedure were approved by the institutional ethics committee of the IMM research group. The study was conducted in compliance with the Guide for the Care and Use of Laboratory Animals and in accordance with European Community recommendations. All the animals were treated in accordance with the ARVO Statement for the Use of Animals in Ophthalmic and Vision Research. The swine were under general anesthetic and mechanical ventilation. 
Figure 5a shows the experimental setup. The eyelids are maintained open using a palpebral speculum. A rubber ring is strapped around the ocular orbit to immerse the eye in water during the acquisitions. The ultrasound probe is mounted on a rotary stage and placed a few millimeters above the cornea. 
Figure 5
 
(a) Experimental setup for 3D SSI in vivo experiments on porcine corneas. The animal is anesthetized. The eyelids are maintained open using a palpebral speculum. A rubber ring is strapped around the orbit to enable the immersion of the eye in water. The probe is mounted on a rotary stage and placed a few millimeters above the cornea. (b) For each imaging plane, the acquisitions are triggered with the cardiac cycle in order to avoid pulsatility-induced IOP variations.
Figure 5
 
(a) Experimental setup for 3D SSI in vivo experiments on porcine corneas. The animal is anesthetized. The eyelids are maintained open using a palpebral speculum. A rubber ring is strapped around the orbit to enable the immersion of the eye in water. The probe is mounted on a rotary stage and placed a few millimeters above the cornea. (b) For each imaging plane, the acquisitions are triggered with the cardiac cycle in order to avoid pulsatility-induced IOP variations.
In in vivo conditions, the IOP is known to increase (approximately 2–3 mm Hg) during the cardiac cycle because of pulsatility.22 Thus, the electrocardiogram (ECG) of the animal was recorded and used to trigger the SSI acquisitions with the heartbeat. Nine dynamic images spanning the length of the cardiac cycle were acquired at equal intervals during an ECG-gated acquisition for the first pig to investigate the influence of pulsatility on the corneal elasticity measurements. For all other pigs, elasticity mapping was triggered at a ~400-ms delay after the QRS complex. This procedure is illustrated in Figure 5b: One imaging plane is acquired at each cardiac cycle at a fixed moment of the cycle. 
Data Analysis
Two-dimensional elasticity “top view maps” of the cornea were reconstructed from the different imaging planes by averaging the shear wave speed over the entire corneal thickness for each imaging plane. Polar diagrams were also generated to represent the amplitude of the shear wave speed variations with the propagation direction θ. A dominant direction θmax was then computed by solving  where vg(θi) is the shear wave speed along the direction θi, vgmin is the minimum speed, i indexes the imaging planes, and ∑ denotes the sum. This equation can be interpreted as follows:  
  •  
    vg(θi) − vgmin is the magnitude of the speed variation relatively to the minimal speed.
  •  
    (vg(θi) − vgmin).cos(θiθ) is the sum of the projections of the speed variations along the direction θ.
  •  
    θmax is the direction along which the sum of the projections is maximal. In the following sections, θmax is referred as the “main direction of shear anisotropy.”
The degree of anisotropy can be estimated by the fractional anisotropy (FA) as19:    
where vmax, vmin, and v are, respectively, the maximal, minimal, and mean value of the shear wave speed. FA expresses the quadratic norm of the deviation of the speed compared to the mean value v. In other words, the higher the speed variation with the propagation direction, the higher the degree of anisotropy. A fractional anisotropy equal to 0 denotes an isotropic medium, whereas a value close to 1 denotes a highly anisotropic medium. 
Results
Ex Vivo Experimental Evidence of the Corneal Shear Anisotropy
Influence of the Intraocular Pressure.
The elasticity maps obtained on a typical ex vivo porcine cornea are shown in Figure 6. For this example, the acquisition was localized in the central region of the cornea. Two IOP values were investigated. For a low IOP (10 mm Hg), the shear wave speed map appears homogeneous. In contrast, for IOP = 20 mm Hg (close to physiological conditions), the shear wave speed depends on the propagation direction. 
Figure 6
 
Top view elasticity maps (in m/s) of an ex vivo porcine cornea for two different IOP values. Each sector corresponds to one imaging plane, that is, to one propagation direction. The 0° direction was arbitrarily chosen parallel to the long axis of the cornea.
Figure 6
 
Top view elasticity maps (in m/s) of an ex vivo porcine cornea for two different IOP values. Each sector corresponds to one imaging plane, that is, to one propagation direction. The 0° direction was arbitrarily chosen parallel to the long axis of the cornea.
This result is underlined in Figure 7, which shows the shear wave speed variations as a function of the propagation direction and the IOP. The plots of Figure 7a were generated by averaging the data of Figure 6 over a 1-mm-diameter disk around the center of the elasticity map. Figure 7b shows a polar diagram of the amplitude of the shear wave speed variations. Both representations show that no shear wave speed angular dependence is observed for a low IOP (10 mm Hg), whereas a significant anisotropy is seen for an IOP value that is close to physiological conditions. The fractional anisotropy values are, respectively, 0.09 ± 0.02 for IOP = 10 mm Hg and 0.14 ± 0.01 for IOP = 20 mm Hg. The polar diagram for the 20 mm Hg IOP has a dipolar shape that emphasizes the existence of one direction of maximal shear wave speed. For this example, the main direction of shear anisotropy is 140° ± 10° (determined using Equation 4). Similar anisotropic behavior was observed for the seven corneas that were investigated in the central region with an IOP of 20 mm Hg. A fractional anisotropy of 0.17 ± 0.06 was obtained for these corneas (mean value ± interexperiment variance). 
Figure 7
 
(a) Shear wave speed variations as a function of the propagation direction for two different IOP values. For each angle, the shear wave speed is averaged axially over the entire corneal thickness and laterally over a 1-mm-diameter disk around the center of the imaging plane. The error bars correspond to the spatial heterogeneity. (b) Polar representation of the amplitude of the shear wave speed variations (in m/s) for two different IOP values. For IOP = 20 mm Hg, the red line indicates the main direction of shear anisotropy (140°).
Figure 7
 
(a) Shear wave speed variations as a function of the propagation direction for two different IOP values. For each angle, the shear wave speed is averaged axially over the entire corneal thickness and laterally over a 1-mm-diameter disk around the center of the imaging plane. The error bars correspond to the spatial heterogeneity. (b) Polar representation of the amplitude of the shear wave speed variations (in m/s) for two different IOP values. For IOP = 20 mm Hg, the red line indicates the main direction of shear anisotropy (140°).
Assessment of the Shear Anisotropy in the Peripheral Region.
In order to investigate the possible link between the shear anisotropy main direction and the orientation of the collagen fibers, we performed acquisitions in the peripheral part of porcine corneas. 
Figure 8 presents two examples of the results obtained in the peripheral part of ex vivo swine corneas. The marker reported on the pictures of the eyeball (Figs. 8a, 8d) indicates the location of the measurements and corresponds to the center of the elastic maps shown in Figures 8b and 8e. The location of the limbus was determined on B-mode echographic images. These results show that the main direction of shear anisotropy is close to the tangent to the limbus. 
Figure 8
 
Shear anisotropy observed in the peripheral part of ex vivo porcine corneas. (a, d) The cross (+) indicates the location of the measurement. (b, e) Top view elasticity maps of the cornea. The color scale represents the group velocity. The dashed line represents the location of the limbus. (c, f) Polar representation of the shear wave speed variations (in m/s) as a function of the propagation direction. The shear wave speed is averaged over a 1-mm diameter disk around the center of the elasticity map. The solid red line represents the main direction of shear anisotropy.
Figure 8
 
Shear anisotropy observed in the peripheral part of ex vivo porcine corneas. (a, d) The cross (+) indicates the location of the measurement. (b, e) Top view elasticity maps of the cornea. The color scale represents the group velocity. The dashed line represents the location of the limbus. (c, f) Polar representation of the shear wave speed variations (in m/s) as a function of the propagation direction. The shear wave speed is averaged over a 1-mm diameter disk around the center of the elasticity map. The solid red line represents the main direction of shear anisotropy.
Experiments were conducted on five swine eyes with a total of n = 27 acquisitions at different locations. The distance from the limbus ranged from 0.7 to 1.3 mm. For each acquisition, the direction of the tangent to the limbus was determined from the B-mode echographic images and the main direction of shear anisotropy from the elasticity measurements. Both directions were determined with a 10° resolution. The median deviation between the two directions was 20° ± 22°, and the fractional anisotropy was 0.28 ± 0.1 for all 27 experiments (mean value ± interexperiment variance). 
In Vivo Feasibility Study
Repeatability With ECG Synchronization.
Variation of the mean group velocity in the cornea during one cardiac cycle in an anesthetized pig is displayed in Figure 9. For this case, the cardiac period was 680 ms. The group velocity rises significantly 200 ms after the QRS complex and returns to the baseline after 350 ms (corresponding to a fraction of heartbeat of 0.5 in Fig. 9) in this example. Further measurements were thus triggered at a 0.6 heartbeat delay after the QRS complex. 
Figure 9
 
Variations of the shear wave speed during a cardiac cycle observed on an anesthetized pig (blue curve). The shear wave speed was averaged over the 2 central millimeters of the cornea. The error bars correspond to the spatial heterogeneity. Time is normalized by the heart rate, with 0 corresponding to the QRS complex. The shape of the ECG signal (green dashed line) is only indicative.
Figure 9
 
Variations of the shear wave speed during a cardiac cycle observed on an anesthetized pig (blue curve). The shear wave speed was averaged over the 2 central millimeters of the cornea. The error bars correspond to the spatial heterogeneity. Time is normalized by the heart rate, with 0 corresponding to the QRS complex. The shape of the ECG signal (green dashed line) is only indicative.
Figure 10 shows the results of multiple measurements at three different locations in a porcine eye with cardiac cycle synchronization. The standard deviation over multiple measurements is less than 0.5% of the shear wave speed for this example. This demonstrates the repeatability of the elasticity measurements. 
Figure 10
 
In vivo repeatability of the shear wave speed measurements when synchronizing the acquisitions with the cardiac cycle. (a) Elastic cross-sectional map of a porcine cornea acquired in vivo (co, cornea; le, lens; ir, iris). (b) Results of multiple measurements of the shear wave speed. The markers (+, o, x) are reported on (a) and represent the different locations of the measurements. The average and standard deviation over these multiple measurements are indicated for each location.
Figure 10
 
In vivo repeatability of the shear wave speed measurements when synchronizing the acquisitions with the cardiac cycle. (a) Elastic cross-sectional map of a porcine cornea acquired in vivo (co, cornea; le, lens; ir, iris). (b) Results of multiple measurements of the shear wave speed. The markers (+, o, x) are reported on (a) and represent the different locations of the measurements. The average and standard deviation over these multiple measurements are indicated for each location.
In Vivo Results.
An example of the results obtained in the central region of an in vivo swine cornea is presented in Figure 11. Figures 11b and 11c were obtained after averaging the shear wave speed over a 2-mm-diameter disk around the center of the elasticity map. These results show a significant anisotropy with one main direction of shear anisotropy (at 50° ± 10° of the nasal–temporal meridian for this example). 
Figure 11
 
(a) Top view elasticity map of an in vivo porcine cornea. The color scale represents the shear wave speed (in m/s). The 0° axis was arbitrarily chosen parallel to the nasal–temporal meridian of the eye. (b) Shear wave speed variations as a function of the propagation direction. (c) Polar representation of the amplitude of the shear wave speed variations (in m/s). The solid red line represents the main direction of shear anisotropy.
Figure 11
 
(a) Top view elasticity map of an in vivo porcine cornea. The color scale represents the shear wave speed (in m/s). The 0° axis was arbitrarily chosen parallel to the nasal–temporal meridian of the eye. (b) Shear wave speed variations as a function of the propagation direction. (c) Polar representation of the amplitude of the shear wave speed variations (in m/s). The solid red line represents the main direction of shear anisotropy.
Each of the four experiments conducted on the central part of in vivo porcine corneas resulted in a similar anisotropic pattern with one main direction of shear anisotropy. The fractional anisotropy was 0.25 ± 0.1 for the four in vivo experiments (mean value ± interexperiment variance). 
Discussion
We have used the SSI elastography method to investigate the local shear anisotropy of the cornea. For that purpose, elastography rotating scans of porcine corneas were performed in both ex vivo and in vivo conditions. The corresponding sets of data were used to study the dependence of the shear wave speed with the propagation direction. It should be underlined that only local anisotropy, within ~2-mm-diameter regions of interest, was assessed with this method. 
Local shear anisotropy was observed on ex vivo porcine corneas. It turns out that a minimal IOP is required in order to detect such a significant anisotropy. One possible explanation could be the need for the collagen fibers to be sufficiently stretched to induce a detectable elastic anisotropy. Thus, all the ex vivo experiments were conducted at IOP = 20 mm Hg, which is close to the physiological level. Further studies could aim at investigating more specifically the influence of IOP on anisotropy with a systematic incrementation of the IOP over a larger range. All the examined corneas exhibited a similar local anisotropic pattern with one main direction of maximal shear wave speed. Such a bipolar pattern is in agreement with x-ray diffraction studies2 reporting that collagen fibrils of porcine corneas have locally one preferred alignment direction. The direction we obtained, however, varied between the different experiments performed on the central part of the corneas. 
In order to improve our understanding of this anisotropic behavior, additional acquisitions were performed at the peripheral region of porcine corneas, where the collagen fibers are expected to be aligned tangentially to the limbus with a stronger level of organization than in the central region.2 A good match between the main direction of anisotropy and the expected orientation of the fibers was obtained (deviation < 20° ± 22° for n = 27 acquisitions). Nevertheless, a wide range of fractional anisotropy values was observed as summarized in the Table. It would thus be helpful to further investigate how fractional anisotropy is related to the fibril organization and to compare the SSI results with measurements of the actual collagen fiber orientation on the same sample. Possible methods to evaluate the collagen fiber orientation include x-ray diffraction or multiphoton microscopy. The possibility of imaging intact eyeballs both ex vivo and in vivo makes SSI an appealing novel method to investigate biomechanical properties of the cornea. Further validation and cross-comparison with gold standard techniques would thus provide new information on biomechanical properties for ophthalmic applications. 
Table. 
 
Summary of the Fractional Anisotropy Obtained at Different Locations of Porcine Corneas in Both Ex Vivo and In Vivo Conditions
Table. 
 
Summary of the Fractional Anisotropy Obtained at Different Locations of Porcine Corneas in Both Ex Vivo and In Vivo Conditions
Fractional Anisotropy, Median ± Interexperiment Deviation
Ex vivo
 Central, n = 7 0.17 ± 0.06
 Periphery, n = 27 0.28 ± 0.10
In vivo
 Central, n = 34 0.25 ± 0.10
Finally, the in vivo feasibility of the method was demonstrated by obtaining local shear anisotropy measurements of porcine corneas in in vivo conditions. The necessity of synchronizing the SSI acquisitions with the cardiac cycle (to avoid pulsatile variations of the corneal elasticity) was underlined. In the current configuration, a complete 360° SSI scan consisting of 37 imaging planes typically lasts up to 10 minutes. For the four in vivo experiments, one main direction of maximal shear wave speed was observed, consistent with the ex vivo experiments. For practical reasons, the in vivo experiments were limited to the central part of the cornea. A further study could involve mapping of corneal anisotropy by performing multiple measurements at different locations of the cornea. In that case, the acquisition time would need to be decreased. The time needed for the different instruments to communicate (ECG, ultrasound scanner, and rotating motor) is currently such that acquisitions are not triggered at each heartbeat. With faster communication, a complete 360° SSI scan could be performed in less than 1 minute by acquiring one imaging plane at each heartbeat. 
In this study, we did not investigate the depth dependence of the anisotropy. The axial resolution of SSI is limited because the shear wave front must be continuous. Hence, depthwise heterogeneity can be detected only if the stiffness contrast is high enough or if the heterogeneity is thick enough. Such a case was observed in previous studies on the effect of corneal cross-linking,15 where we reported through-thickness variations of the corneal stiffening induced by cross-linking. However, in the present study, we did not observe any significant through-thickness variation of the shear wave speed or the anisotropy. For instance, Figure 10a shows a cross-sectional elasticity map of the cornea that exhibits a uniform shear wave speed across the corneal depth. Therefore, we chose to display anisotropy results by averaging the data over the entire corneal depth. It could be interesting to assess the depth dependence of the anisotropy before and after a cross-linking treatment, as other studies have underlined that riboflavin/UV-A–induced cross-linking changes the collagen organization23 and mainly affects the anterior part of the stroma.15,24 
The in vivo experiments additionally showed the ability of the SSI technique to measure the elasticity of the intraocular lens: In the preliminary result shown in Figure 10, the lens capsule appears much softer than the cornea. This is in good agreement with previous observations: The intraocular lens is known to be easily deformable to enable accommodation.25 This is an unexpected but interesting result. Although the “pushing” beam is focused in the cornea, it propagates all the way to the lens. The beam diverges after the focus location but remains collimated and creates a radiation force in the lens. This force is less intense than in the cornea. Nevertheless, as the lens is softer than the cornea, the amplitude of the displacements induced in the lens is high enough to be detected. Thus, the elasticity of both cornea and intraocular lens capsule can be mapped using the same acquisition. Assessment of intraocular lens elasticity could be clinically valuable for the management of presbyopia, which is considered to be caused by lens stiffening with age. Therapeutic approaches have been proposed to recover presbyopic lens elasticity26 and could benefit from SSI monitoring. 
In conclusion, local shear anisotropy has been measured on ex vivo porcine corneas and in vivo swine with SSI. The main direction of anisotropy correlated with expected fiber alignments at the periphery of the cornea. These results remain to be compared with x-ray diffraction or multiphoton imaging of the same samples, but are particularly promising as they could be more easily translated to the clinic than the latter techniques. Moreover, the elasticity of the intraocular lens was additionally measured in vivo. This paves the way to noninvasive assessment of the biomechanical properties in the full anterior eye segment. 
Acknowledgments
We thank the Institut Mutualiste Montsouris research unit (Paris, France) for their support on animal experimentations, and the slaughterhouse Etablissements Guy Harang (Houdan, France) for providing enucleated porcine eyeballs. We also thank Gael Latour and Marie-Claire Schanne-Klein for fruitful discussions. 
Supported by the French National Research Agency (ANR MicroElasto) and by LABEX WIFI (Laboratory of Excellence ANR-10-LABX-24) within the French program Investments for the Future under reference ANR-10-IDEX-0001-02 PSL*. 
Disclosure: T.-M. Nguyen, None; J.-F. Aubry, None; M. Fink, None; J. Bercoff, Supersonic Imagine (E); M. Tanter, Supersonic Imagine (C) 
References
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Figure 1
 
(a) Anatomy of the anterior segment of the eye. (b) Microstructure of the cornea. The cornea is divided into three layers (the epithelium, the stroma, and the endothelium) and two membranes. The stroma mainly consists of collagen bundles that are organized in lamellae.
Figure 1
 
(a) Anatomy of the anterior segment of the eye. (b) Microstructure of the cornea. The cornea is divided into three layers (the epithelium, the stroma, and the endothelium) and two membranes. The stroma mainly consists of collagen bundles that are organized in lamellae.
Figure 2
 
Principle of the SSI elastography technique applied to the cornea. (a) An ultrasonic “pushing beam” is focused in the cornea for a few tens of microseconds. (b) The propagation of the resulting shear wave is imaged at a high frame rate (up to 30,000 frames/s) by emitting ultrasound plane waves. (c) A complete acquisition sequence consists of several pushing beams, applied at different positions along the corneal curvature, interleaved with ultrafast imaging series. Such an acquisition typically lasts a few tens of microseconds.
Figure 2
 
Principle of the SSI elastography technique applied to the cornea. (a) An ultrasonic “pushing beam” is focused in the cornea for a few tens of microseconds. (b) The propagation of the resulting shear wave is imaged at a high frame rate (up to 30,000 frames/s) by emitting ultrasound plane waves. (c) A complete acquisition sequence consists of several pushing beams, applied at different positions along the corneal curvature, interleaved with ultrafast imaging series. Such an acquisition typically lasts a few tens of microseconds.
Figure 3
 
Supersonic shear wave imaging elastography in a transverse isotropic medium. The ultrasound radiation force induces a shear wave that is polarized along x1 and propagates in the (x2,x3) plane. The imaging plane forms an angle θ with the fibers' direction.
Figure 3
 
Supersonic shear wave imaging elastography in a transverse isotropic medium. The ultrasound radiation force induces a shear wave that is polarized along x1 and propagates in the (x2,x3) plane. The imaging plane forms an angle θ with the fibers' direction.
Figure 4
 
Experimental setup for 3D SSI acquisitions on enucleated porcine eyeballs. (a) The eyeball is immersed in water. The probe is mounted on a rotary stage and placed a few millimeters above the cornea. (b) Acquisitions are performed in different imaging planes (θ ranges from 0° to 360°). (c) The intraocular pressure is monitored during the entire experiment. Two needles are inserted in the anterior chamber of the eye. The first one is connected to an elevated water tank; the other one is connected to a digital manometer. A computer collects the manometer measurements and subsequently adapts the height of the water tank.
Figure 4
 
Experimental setup for 3D SSI acquisitions on enucleated porcine eyeballs. (a) The eyeball is immersed in water. The probe is mounted on a rotary stage and placed a few millimeters above the cornea. (b) Acquisitions are performed in different imaging planes (θ ranges from 0° to 360°). (c) The intraocular pressure is monitored during the entire experiment. Two needles are inserted in the anterior chamber of the eye. The first one is connected to an elevated water tank; the other one is connected to a digital manometer. A computer collects the manometer measurements and subsequently adapts the height of the water tank.
Figure 5
 
(a) Experimental setup for 3D SSI in vivo experiments on porcine corneas. The animal is anesthetized. The eyelids are maintained open using a palpebral speculum. A rubber ring is strapped around the orbit to enable the immersion of the eye in water. The probe is mounted on a rotary stage and placed a few millimeters above the cornea. (b) For each imaging plane, the acquisitions are triggered with the cardiac cycle in order to avoid pulsatility-induced IOP variations.
Figure 5
 
(a) Experimental setup for 3D SSI in vivo experiments on porcine corneas. The animal is anesthetized. The eyelids are maintained open using a palpebral speculum. A rubber ring is strapped around the orbit to enable the immersion of the eye in water. The probe is mounted on a rotary stage and placed a few millimeters above the cornea. (b) For each imaging plane, the acquisitions are triggered with the cardiac cycle in order to avoid pulsatility-induced IOP variations.
Figure 6
 
Top view elasticity maps (in m/s) of an ex vivo porcine cornea for two different IOP values. Each sector corresponds to one imaging plane, that is, to one propagation direction. The 0° direction was arbitrarily chosen parallel to the long axis of the cornea.
Figure 6
 
Top view elasticity maps (in m/s) of an ex vivo porcine cornea for two different IOP values. Each sector corresponds to one imaging plane, that is, to one propagation direction. The 0° direction was arbitrarily chosen parallel to the long axis of the cornea.
Figure 7
 
(a) Shear wave speed variations as a function of the propagation direction for two different IOP values. For each angle, the shear wave speed is averaged axially over the entire corneal thickness and laterally over a 1-mm-diameter disk around the center of the imaging plane. The error bars correspond to the spatial heterogeneity. (b) Polar representation of the amplitude of the shear wave speed variations (in m/s) for two different IOP values. For IOP = 20 mm Hg, the red line indicates the main direction of shear anisotropy (140°).
Figure 7
 
(a) Shear wave speed variations as a function of the propagation direction for two different IOP values. For each angle, the shear wave speed is averaged axially over the entire corneal thickness and laterally over a 1-mm-diameter disk around the center of the imaging plane. The error bars correspond to the spatial heterogeneity. (b) Polar representation of the amplitude of the shear wave speed variations (in m/s) for two different IOP values. For IOP = 20 mm Hg, the red line indicates the main direction of shear anisotropy (140°).
Figure 8
 
Shear anisotropy observed in the peripheral part of ex vivo porcine corneas. (a, d) The cross (+) indicates the location of the measurement. (b, e) Top view elasticity maps of the cornea. The color scale represents the group velocity. The dashed line represents the location of the limbus. (c, f) Polar representation of the shear wave speed variations (in m/s) as a function of the propagation direction. The shear wave speed is averaged over a 1-mm diameter disk around the center of the elasticity map. The solid red line represents the main direction of shear anisotropy.
Figure 8
 
Shear anisotropy observed in the peripheral part of ex vivo porcine corneas. (a, d) The cross (+) indicates the location of the measurement. (b, e) Top view elasticity maps of the cornea. The color scale represents the group velocity. The dashed line represents the location of the limbus. (c, f) Polar representation of the shear wave speed variations (in m/s) as a function of the propagation direction. The shear wave speed is averaged over a 1-mm diameter disk around the center of the elasticity map. The solid red line represents the main direction of shear anisotropy.
Figure 9
 
Variations of the shear wave speed during a cardiac cycle observed on an anesthetized pig (blue curve). The shear wave speed was averaged over the 2 central millimeters of the cornea. The error bars correspond to the spatial heterogeneity. Time is normalized by the heart rate, with 0 corresponding to the QRS complex. The shape of the ECG signal (green dashed line) is only indicative.
Figure 9
 
Variations of the shear wave speed during a cardiac cycle observed on an anesthetized pig (blue curve). The shear wave speed was averaged over the 2 central millimeters of the cornea. The error bars correspond to the spatial heterogeneity. Time is normalized by the heart rate, with 0 corresponding to the QRS complex. The shape of the ECG signal (green dashed line) is only indicative.
Figure 10
 
In vivo repeatability of the shear wave speed measurements when synchronizing the acquisitions with the cardiac cycle. (a) Elastic cross-sectional map of a porcine cornea acquired in vivo (co, cornea; le, lens; ir, iris). (b) Results of multiple measurements of the shear wave speed. The markers (+, o, x) are reported on (a) and represent the different locations of the measurements. The average and standard deviation over these multiple measurements are indicated for each location.
Figure 10
 
In vivo repeatability of the shear wave speed measurements when synchronizing the acquisitions with the cardiac cycle. (a) Elastic cross-sectional map of a porcine cornea acquired in vivo (co, cornea; le, lens; ir, iris). (b) Results of multiple measurements of the shear wave speed. The markers (+, o, x) are reported on (a) and represent the different locations of the measurements. The average and standard deviation over these multiple measurements are indicated for each location.
Figure 11
 
(a) Top view elasticity map of an in vivo porcine cornea. The color scale represents the shear wave speed (in m/s). The 0° axis was arbitrarily chosen parallel to the nasal–temporal meridian of the eye. (b) Shear wave speed variations as a function of the propagation direction. (c) Polar representation of the amplitude of the shear wave speed variations (in m/s). The solid red line represents the main direction of shear anisotropy.
Figure 11
 
(a) Top view elasticity map of an in vivo porcine cornea. The color scale represents the shear wave speed (in m/s). The 0° axis was arbitrarily chosen parallel to the nasal–temporal meridian of the eye. (b) Shear wave speed variations as a function of the propagation direction. (c) Polar representation of the amplitude of the shear wave speed variations (in m/s). The solid red line represents the main direction of shear anisotropy.
Table. 
 
Summary of the Fractional Anisotropy Obtained at Different Locations of Porcine Corneas in Both Ex Vivo and In Vivo Conditions
Table. 
 
Summary of the Fractional Anisotropy Obtained at Different Locations of Porcine Corneas in Both Ex Vivo and In Vivo Conditions
Fractional Anisotropy, Median ± Interexperiment Deviation
Ex vivo
 Central, n = 7 0.17 ± 0.06
 Periphery, n = 27 0.28 ± 0.10
In vivo
 Central, n = 34 0.25 ± 0.10
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