Assessing corneal biomechanics with Brillouin spectro-microscopy

A new Brillouin spectro-microscope was designed and built to investigate the mechanical properties of bovine and human corneas. This instrument integrates a single-stage virtually imaged phased array spectrometer with a novel adaptive-optics interferometric ﬁ lter to achieve unprecedented rejection of the elastic background signal. As a result, highly-resolved, reproducible data from both thin and thick collagen-based materials were obtained. In particular, this technique is capable of rigorously measuring the relative sti ﬀ ness of di ﬀ erent areas of human corneas, thus providing a true non-contact method to characterise the fundamental mechanical features of both live and ﬁ xed biological tissue samples.

realisation that the geometric broadening of the Brillouin spectra arising from focused illumination does not preclude high-NA Brillouin microscopy. 7 The invention and widespread adoption of VIPAs in recent years has triggered something of a renaissance for Brillouin scattering by cutting the acquisition times to seconds or less and enabling Brillouin imaging. 5 Compared with mechanical methods such as atomic force microscopy (AFM), where measurements require direct interactions between the sample and a probe, Brillouin imaging offers the advantage of a truly local non-contact analysis at microscopic resolution. For example, several recent studies have used Brillouin scattering to characterise the mechanical properties of biological tissues, including live cells, 8 components of the extracellular matrix, 9 and other natural or synthetic biomaterials. 10 Although these developments have yet to be translated to a clinical settings, they show great promise for the diagnosis and treatment of arteriosclerosis plaque 11 and keratoconus. 12 In the present work we review the fundamentals of Brillouin scattering and introduce a new Brillouin spectro-microscope, dedicated to so biomaterials, that enables signicant advances in suppressing parasitic elastic scattering in aqueous media. This instrument was used to evaluate the mechanical properties of dense collagen type-I gels produced aer plastic compression, as well as of corneal tissue of bovine and human origin. The results reported here provide important information about the structure and organisation of the biomaterials analysed. We also address the challenges inherent to this method, notably in relating the measured Brillouin shi to the biomechanical properties evaluated using standard rheological and nano-indentation techniques.
1 Principles and apparatus for Brillouin spectromicroscopy

Brillouin scattering
In Brillouin scattering, an incoming photon (angular frequency u i , wave vectork i ) is inelastically scattered off a travelling thermal phonon (angular frequency u p , wave vectork p ) at an angle q, with a new frequency u s and wave vectork s , as depicted in Fig. 1. In a quantum description, the photon will have either gained or lost a phonon quantum of energy through annihilation or creation of a phonon, respectively referred to as Stokes and anti-Stokes processes. The scattering angle q is set by the experiment's illumination/collection geometry, which also constrains the phonon wavelength via the conservation of energy and momentum: The phonon wavelength is comparable to that of the photons, while the frequency is in general of the order of 10 GHz. In the classical description, the phonon is an acoustic wave, a periodic modulation of density and therefore of refractive index, which can be regarded as a reective Bragg mirror moving at the speed of sound. Then the above equation is just the Bragg condition; the Stokes/ anti-Stokes processes correspond to waves travelling in opposite directions, with the Brillouin shi corresponding to a Doppler shi. The phase velocity v p of the acoustic wave is where Dv B ¼ (u s AE u i )/2p is the experimentally measured Brillouin shi. In general, transverse and longitudinal acoustic waves propagate at different velocity, and will give rise to separate peaks in the Brillouin spectrum. However in the back-scattering geometry (q ¼ 180 ) used in this work only longitudinal waves participate in the scattering processes, 13 and the spectrum consists of a single Stokes/anti-Stokes doublet.

Relation of the Brillouin shi to mechanical moduli
The acoustic velocity is correlated to the mechanical moduli of the material. Since we are probing longitudinal waves only, and because the phonon wavelength is much smaller then the material's extent, the relevant moduli is the socalled p-wave or longitudinal modulus M, which is related to the velocity by v p ¼ ffiffiffiffiffiffiffiffiffi ffi M=r p (r is the density of the medium). Rheological or nano-indentation techniques measure Young's modulus E, and it would therefore be desirable to be able to relate these two quantities. For a number of reasons this is not straightforward; indeed preliminary comparative experiments 14 have shown that the Brillouin modulus is two or three orders of magnitude larger than Young's modulus. First, the acoustic isotropy of highly ordered tissues such as corneal collagen is questionable. Second, M is measured at GHz acoustic frequencies whereas E is a quasi-static measurement. Acoustic dispersion could therefore   signicantly increase the moduli in the hypersonic regime. 15 Thirdly, one may be tempted to use the usual relation 3 where n is the Poisson ratio. For biomaterials of interest, rich in water and therefore nearly incompressible, the Poisson ratio is close to 0.5. Examination of eqn (3) shows that it diverges at that point, and the conversion is therefore prone to very large errors. Finally, in heterogenous materials acoustic connement effects (due to the presence of various acoustically reective structures and interfaces) may alter the phonon density of states, causing a distortion of the Brillouin lineshape and affecting the extraction of the Brillouin shi. Such effects have been reported on the Brillouin spectrum of water in the presence of planar and cylindrical acoustic resonators. 16 At present, none of these issues have been properly investigated, much less resolved. In what follows we shall therefore not attempt to convert the measured Brillouin shis into mechanical moduli and use the Brillouin shi Dv B as the metric.

Epiuorescence confocal microscope set-up
The Brillouin spectro-microscope is schematically depicted in Fig. 2. A frequencydoubled Nd:YVO 4 diode-pumped solid-state laser (CNI, MSL-FN-671) operating at l ex ¼ 671 nm, coupled into a single-mode polarisation-maintaining bre (Corning SM600), provided single mode illumination (transverse and longitudinal) with a spectral linewidth smaller than 1 MHz. The bre output was collimated to a 3 mm diameter beam, reected off a pair of scanning mirrors (Thorlabs GVS002), and expanded to an 8 mm diameter by two achromatic doublets (focal lengths 75 and 180 mm) to ll the back focal plane of a 20Â water dipping microscope objective (Olympus XLUMPLFLN20xW, numerical aperture 0.5). The doublets served as the scan relay optics by imaging the mirrors onto the objective's back focal plane. In addition, a quarter-wave plate inserted just before the objective was used to transform the laser linear polarisation into a circular polarisation. Scattered light was collected by the same objective, descanned by the same mirrors, separated from the excitation light by a polarising beam-splitter, and coupled into a single-mode bre which also acted as the confocal pinhole. The nal imaging resolution was calculated to be 1 Â 1 Â 5 mm. For depth sectioning, the sample was mounted on a vertical translation stage (Newport MFA-CC).

Suppression of elastic scattering
The elastically-scattered light usually represents a much stronger signal compared to the Brillouin scattering itself. In order to suppress the former, an original wavefront division interferometer was introduced in the system. Light exiting the microscope output bre was collimated to a 4 mm diameter beam and intersected by a parallelepipedic glass prism such that exactly half of the beam travels above the prism, and half inside. The path difference d between the two halves depends on the angle q i between the prism and the incident beam. It was calculated as This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.
and then adjusted by tuning the prism angle to achieve destructive interference at the laser wavelength when recoupling the beam into a single-mode bre, while allowing the passage of inelastically scattered (Brillouin) light. The lter transmission is a periodic function of the prism angle and of the frequency, with a free spectral range (FSR) c/d (c is the speed of light in a vacuum). Using a 30 mm long BK7 prism of refractive index n ¼ 1.51, the FSR is about 20 GHz. Assuming the amplitude of the two paths is exactly matched (through translation of the prism), the maximum extinction S max is limited only by the laser linewidth s and calculated as:

VIPA spectrometer
The VIPA (LightMachinery) has a free spectral range of 30 GHz. Light exiting the lter output bre was collimated to a 0.8 mm diameter and focused on the VIPA entrance window by a 100 mm cylindrical lens. A 400 mm cylindrical lens imaged the VIPA's angular spectrum onto a CCD camera (Andor iXon DU888, operated in non-electron-multiplying mode) with the help of a 50 mm cylindrical lens, orientated orthogonal to the others, to provide focussing along the non-dispersed axis.

Data acquisition and processing
The spectra imaged on the CCD camera were acquired with a typical exposure time of 100 to 1000 ms, increasing with the penetration depth in the sample. Vertical binning was used on the sensor so that one-dimensional spectra were produced without further processing. The beam scanning, sample vertical motion, and interferometer feedback were controlled using a Python-based, custom-made soware specically developed for this purpose (MicroscoPy, pypi.python.org/pypi/MicroscoPy). Raw spectra were stored as a multidimensional array in HDF5 les, alongside position information and other metadata. Data processing was performed using Mathematica. Briey, the spectral axis was calibrated against reference spectra of water or solid polystyrene, with frequency expressed as a quadratic function of pixel coordinates, and a linear least-square t to the positions of 3 to 4 Rayleigh peaks and their associated Brillouin peaks. Both the Stokes and anti-Stokes peaks of the brightest interference order were then tted with a Lorentzian function, and the Brillouin shi was calculated as the average of both the Stokes and anti-Stokes frequencies, making measurements insensitive to laser dri and temperature uctuations (which can cause a global spectral dri of the order of 1 GHz h À1 ).

Filter feedback
Unlike the measurement of Brillouin frequency, the interferometric lter is sensitive to frequency dris (on a timescale of minutes) and requires continuous adjustments to maintain its extinction to the required level. For this purpose, a simple feedback mechanism was incorporated by the addition of a piezoelectric actuator to periodically modulate the interferometer angle to produce a $10% modulation in the (post-ltering) elastic amplitude. The latter is measured directly on the acquired spectrum by integrating the pixel intensities around the elastic peak. A digital PID (proportional-integral-differential) control loop was used to keep the prism angle close to its optimum position (corresponding to a minimum in the elastic amplitude), with a time constant of the order of minutes to average out the large uctuations in the amplitude of the elastic scattering while scanning through the sample.

Preparation of compressed collagen gels
Compressed collagen gels were prepared as described elsewhere. 17 Briey, icecold rat tail collagen type-I (2 g L À1 in 0.6% acetic acid; First Link Ltd, UK) was mixed with 10Â Modied Essential Medium (MEM; Life Technologies, CA, USA) and neutralised with 1 M NaOH in an 8 : 1 : 1 volume ratio, respectively, and allowed to gel at 37 C for 30 min. Polymerised gels were subjected to plastic compression under a 134 g load for 5 min at room temperature by placing the gels between layers of gauze and on top of 10 sheets of lter paper. Plasticallycompressed collagen gels were then transferred to a Petri dish onto 3-or 4-gel stacks and washed at room temperature for at least 30 min in distilled water before being analysed by Brillouin microscopy. Chemically-stiffened collagen gels were analysed aer xing the compressed collagen gels in 4% (w/v) paraformaldehyde, with extensive washing in distilled water before imaging. Experiments were performed in triplicate.

Preparation of corneal tissue
Bovine corneal tissue (depicted in Fig. 3) was isolated from fresh cow eyes obtained from an abattoir (Linden Food Burradon Ltd, UK). The tissue corresponding to the cornea and the surrounding sclera was excised from whole cow eyes, kept on ice during the isolation, incubated with a penicillin-streptomycin solution (1000 U mL À1 ; Thermo Scientic, MA, USA) for 30 min at room temperature to inhibit bacterial contamination, washed in an excess of phosphate buffered saline (PBS), and kept at 4 C in either PBS supplemented with 0.025% sodium azide preservative or at room temperature in Carry-C tissue preservation medium (Alchimia, Italy) until further analysis was performed. Human corneal tissues were kindly provided by Dr Francisco Figueiredo, FRCOphth (Royal Victoria Inrmary Newcastle, UK). Tissues remaining from corneal transplant procedures were kept up to 30 days aer isolation from cadaveric donors (ages ranging 58-72 years old; male-female donor ratio of 1 : 1; no prior history of corneal diseases or ocular trauma), in accordance with the Newcastle University and Newcastle-upon-Tyne Hospital Trust Research Ethics Committees' guidelines. Isolated tissues were then extensively washed in PBS, dried of excess adsorbed liquid, and then maintained at room temperature in Carry-C tissue preservation medium until further analysis was performed. Tissues were imaged in Petri dishes while completely submerged in PBS or Carry-C medium.

Statistical analysis
The Brillouin shi was measured at eight different z-positions from ve distinct collagen gels (n ¼ 5), with differences between average shis analysed using an unpaired two-tailed Student's t-test, with p ¼ 0.0001 and R 2 ¼ 0.91.

Brillouin spectro-microscope assembly and specications
The new Brillouin spectro-microscope was specically dedicated to study the mechanical properties of so biological tissues. These systems are characterised by low scattering signals, high elastic backgrounds, and the requirement of sub-GHz resolutions. For this particular instrument we used a l ex ¼ 671 nm DPSS laser with high spectral purity and sub-MHz linewidth (Fig. 2). At this wavelength, the Stokes/ Fig. 4 Brillouin spectrum of water, measured with the filter tuned to maximize (blue curve) and minimise (orange) the transmission at the laser frequency. In the first case, the Brillouin peaks are essentially invisible, overwhelmed by the stronger elastic scattering. In the latter, the Brillouin peaks are easily resolved and the elastic peak has been suppressed by nearly 50 dB. The grey line shows the sinusoidal transmission of the filter, whose free spectral range is 20 GHz.

Paper Faraday Discussions
This anti-Stokes components of Brillouin scattering are typically shied by 5-7 GHz in aqueous media. 18 Because such small shis are inaccessible to grating spectrometers, Brillouin spectrometry has traditionally relied on multi-pass scanning Fabry-Pérot interferometers to achieve both the necessary resolution and fringe contrast; the acquisition time for a single spectrum was measured in minutes or even hours. 19 This limitation is overcome by VIPAs, which combine the large dispersive power of the etalon with the spatial dispersion of gratings. They are essentially Fabry-Pérot etalons, dispersing focused light into fringes of equal inclination, with the important difference that the input light is focused by a cylindrical lens in only one direction and enters the etalon through a narrow antireection-coated window. All of the input light is therefore transmitted, forming a one-dimensional spectrum instead of circular fringes, and resulting in a more efficient device. However, VIPAs have limited nesse (100 at most), and therefore poor fringe contrast (<40 dB), insufficient to resolve (anti-)Stokes Brillouin peaks amidst a strong elastic background, such as that inevitably arising from epi-uorescence confocal microscopy. This is commonly addressed by cascading two VIPAs in a cross-axis conguration, 20 at the cost of reduced throughput and considerable complexity. Another approach involves the absorption of the elastic scattering in hot vapour cells, although this oen distorts the Brillouin peaks as well. 21 In the present work, we used an original adaptive-optics wavefront division interferometer, described above, that enables the interferometric ltering of the elastic scattering, as demonstrated in Fig. 3. With the elastic suppression turned off (interferometer detuned), the signal was overwhelmed by a strong elastic background (blue line) as shown in Fig. 4. By tuning the interferometer to minimise the amplitude of the central elastic peak, the Brillouin Stokes and anti-Stokes components became clearly resolved (orange line). The Brillouin shi was detected at 5.86 AE 0.01 GHz (or 0.195 cm À1 ), corresponding to a sound velocity of 1475 AE 10 m s À1 , as expected for distilled water at 20 C. 22 Furthermore, the elastic suppression ratio exceeded 46 dB, a signicantly better outcome compared to other methods currently in use. 20,21,23 Consequently, the strong extinction made possible by the interferometric lter allows the implementation of a single-stage VIPA conguration instead, which constitutes, to the extent of our knowledge, a novel development in Brillouin microscopy.
Furthermore, the use of an immersion objective allows the samples to be observed in physiological conditions, as well as enabling several other important benets for Brillouin imaging. Firstly, it prevents the dehydration of the biological tissues, a parameter that greatly affects their mechanical properties. 24 Secondly, it reduces specular reection at the sample surface, therefore reducing the elastic background. And nally, it limits the loss of resolution normally caused by spherical aberration when focusing deep into thick samples. This issue is particularly relevant in imaging cornea specimens, particularly with bovine origin, where the tissue can be up to 2 mm thick (see below).

Mechanical properties of high-density collagen gels
In order to explore the potential uses and limitations of our instrument, we started by evaluating dense collagen gels produced by a plastic compression method. These thin biomaterials have been extensively used as versatile models of connective tissue such as cornea 17,24 and skin. 25 Furthermore, their mechanical properties (e.g., elastic modulus) have been shown to be highly-dened and dependent on the compression load and duration. 24,26,27 As such, collagen gels are relevant as models for the determination of the biomechanical properties of so materials. The Brillouin shi observed for compressed collagen gels was shown to be very consistent for all gels analysed, both from those in the same stack (4 gels per stack) or between different replicates, with an average shi of 6.06 AE 0.04 GHz (Fig. 5a), and despite the strong elastic background scatter due to the proximity of the interface. In addition, the shis detected at the surface and within the gels were similar, and their variation smaller than that observed between gels (Fig. 5a). This suggested that the mechanical properties of the compressed collagen gels were uniform between gels and throughout their thickness. Moreover, stiffened collagen gels (crosslinked with paraformaldehyde) showed signicantly higher Brillouin shis of 6.35 AE 0.07 GHz (Fig. 5b), a clear indication that alterations in the stiffness of the collagen gels results in signicantly different shis in Brillouin scatter. Interestingly, the Brillouin proles also allowed us to determine gross sample depth, with the stiffened collagen gels showing an approximately 50% reduction in thickness compared to the untreated compressed collagen gels. This shrinkage constitutes a common effect of conventional cross-linking methods, 28 and may partially account for the increased gel stiffness. This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.

Mechanical properties of corneal tissue
Having determined the Brillouin shi of thin collagen samples, we then evaluated the limitations of the technique for the analysis of thick biological samples. Bovine corneas were used for these experiments, as these tissues are relatively transparent despite the 1.2-1.5 mm thickness of their centre region (Fig. 3). In addition, as the correct evaluation of mechanical properties in biological tissues requires a constant and physiologically-relevant level of tissue hydration, Brillouin spectro-microscopy measurements should be performed in such conditions. Corneas are naturally hyperosmotic, slightly dehydrated tissues in vivo. 29 To replicate a dehydration state, whole bovine corneas were immersed in glycerol immediately aer isolation, and then washed and kept in PBS to remove the glycerol and evaluate the effects of re-hydration through time on tissue stiffness and thickness (Fig. 6a). The scan series performed throughout the entire depth of the tissues showed that corneas swell progressively, with their thickness almost doubling aer 26 h in PBS. This constituted a clear indication of increased hydration well beyond normal in vivo levels. 30 Concomitantly, the Brillouin shi measured at all depths of the corneal tissue decreased with time, indicating that the swollen corneas became soer. Specically, at t ¼ 0.5 h, the corneas showed shis of 6.3-6.5 GHz at their anterior and 6.5-6.2 GHz at their posterior regions, respectively, whereas at t ¼ 26 h, shis varied between 6.0 and 6.3 GHz. Furthermore, the pattern of the shis measured in the swollen corneas indicated a loss of structural integrity within the tissue (Fig. 6a), a common consequence of excessive corneal hydration and oedema. 31,32 Overall, these results highlighted the importance of performing the measurements in appropriate conditions (i.e., physiological-like) for a given tissue or organ. When measuring the in-depth Brillouin scattering of bovine corneas maintained in Carry-C, a medium specically developed to preserve corneas in their physiological hydration state, the proles were remarkably similar to those previously reported for the central regions of human corneas (Fig. 6b). 33 In particular, these proles were divided into four regions (Fig. 6b): an anterior-most peak with 6.5-6.6 GHz shis corresponding to the corneal epithelium (I), a slope ranging between 6.55 and 6.5 GHz corresponding to the anterior stroma (II), a plateau of shis of approximately 6.5 GHz corresponding to the posterior stroma (III), and a steep slope corresponding to the posterior-most region of the cornea (IV). 34 Furthermore, this pattern was maintained unaltered, along with the natural thickness of the bovine corneal tissue, even aer keeping it for more than a week in Carry-C medium. The Brillouin images were also capable of distinguishing differences in stiffness from normal and stiffened-treated corneal tissue. The anterior-most region of the whole bovine corneas xed with paraformaldehyde showed signicantly higher shis compared to the same region from the untreated tissues (Fig. 7). Moreover, this increase in shi was observed not only at the surface, where the tissue was treated, but also in-depth (Fig. 7, insets), providing information about the range of penetration for such treatment.
These results also highlight the non-contact nature of Brillouin spectromicroscopy for investigating the mechanical properties in the interior of biological tissues. However, this ability was shown to be limited by the transparency of the material. For example, imaging more opaque areas of the bovine cornea (such as the limbus, Fig. 3) resulted in a considerable reduction in the signal-to-noise ratio at deeper levels of the tissue (data not shown). In contrast, this limitation was not evident in the human cornea, where the (species specic) improved  transparency of the limbus (Fig. 8a) still allowed highly-resolved spectra to be obtained. In particular, human corneal tissues maintained in the Carry-C medium were able to be imaged in a sequence of in-depth measurements, thus allowing the assembly of z-scans into 2D heat maps (Fig. 8c). Remarkably, these sequences not only provided a notion of the tissue's morphology, but also the ner differences in stiffness between different regions of the tissue (Fig. 8c: anterior (upper) vs. posterior (lower region); limbus (le) vs. central cornea (right)). Specically, the values for the Brillouin shi observed in the limbus were lower than those in the central cornea, particularly in the anterior-most region of the tissue. This data was supported by previous, although much less detailed, studies using AFM 35 or stress-strain analysis of the cornea. 36 Taken together, these results represent a more complete overall view of the stiffness of biological tissues, providing information about the mechanical properties of human corneas of unparalleled accuracy and resolution.

Conclusions
In summary, we have introduced a new Brillouin microscope consisting of a brecoupled confocal scanning microscope, an interferometric lter to suppress elastic scattering, and a single-stage VIPA spectrometer. The microscope's ability to acquire depth-resolved Brillouin spectra in very thin as well as very thick samples (e.g. in 50mm-thick collagen gels or in bovine corneas up to 2 mm) has been demonstrated, thanks to the interferometric lter that allows sufficient rejection of specular reections at the sample surfaces. This technique was used to monitor the response of compressed collagen gels and corneal tissue to stiffening (cross-linking) treatments. Brillouin imaging of the limbus in human corneal rings also revealed a clear contrast between the stiffer inner stroma of the centre and the soer limbus. These results validate Brillouin spectro-microscopy as a potent tool for assessing the mechanical properties of so biomaterials, particularly transparent ones. We thus envisage many possible applications for this technique, including fundamental characterisation studies and as a tool to diagnose the rigidity of many tissues, namely the cornea.
However, the quantication of the absolute stiffness of so tissues by Brillouin spectroscopy (i.e., using Brillouin shi values to calculate the elastic modulus) constitutes a challenge that remains unresolved.