To evaluate the feasibility of using MR elastography (MRE) to assess the mechanical properties of the eye.
To evaluate the feasibility of using MR elastography (MRE) to assess the mechanical properties of the eye.
The elastic properties of the corneoscleral shell of an intact, enucleated bovine globe specimen were estimated using MRE and finite element modeling (FEM), assuming linear, isotropic behavior. The two-dimensional (2D), axisymetric model geometry was derived from a segmented 2D MR image, and estimations of the Young's modulus in both the cornea and sclera were made at various intraocular pressures using an iterative flexural wave speed matching algorithm.
Estimated values of the Young's moduli of the cornea and sclera varied from 40 to 185 kPa and 1 to 7 MPa, respectively, over an intraocular pressure range of 0.85 to 9.05 mmHg (1.2 to 12.3 cmH2O). They also varied exponentially as functions of both wave speed and intraocular dP/dV, an empirical measure of “ocular rigidity.”
These results show that it is possible to estimate the intrinsic elastic properties of the corneoscleral shell in an ex vivo bovine globe, suggesting that MRE may provide a useful means to assess the mechanical properties of the eye and its anatomy. Further development of the technique and modeling process will enhance its potential, and further investigations are needed to determine its clinical potential. J. Magn. Reson. Imaging 2010;32:44–51. © 2010 Wiley-Liss, Inc.
THE MECHANICAL PROPERTIES of the eye and its anatomical components are believed to be of central importance in many pathologic conditions of the eye such as age-related macular degeneration (AMD), glaucoma, Graves' disease, and myopia. For example, it is hypothesized that AMD, a leading cause of blindness in the elderly, may be caused by stiffening of the sclera (1). Glaucoma, another leading cause of blindness, is a condition of retinal or optic neuropathy resulting from elevated intraocular pressures (2). A specific type of hyperthyroidism known as Graves' ophthalmopathy can lead to protrusion of the globe and compression of the optic nerve (3). Likewise, myopia (4) is known to involve the mechanics of the corneoscleral shell, and retinal detachment (5), the mechanics of the vitreous body. In addition, the recent popularity of corneal refractive correction surgeries has also led to renewed interest in the mechanical behavior of the cornea (6). Thus, improving our ability to accurately quantify the mechanical properties of the eye has the potential to improve our basic understanding of eye mechanics and to enhance patient care through improved diagnosis and management of disease.
Historically, the mechanical properties of the eye have been a challenge to assess and difficult to quantify, especially noninvasively. Ocular elasticity has been called “one of the most confused areas of ophthalmology” (7, 8), which is not surprising, because the eye is anatomically and mechanically complex. It is comprised of multiple tissue types and various anatomical structures that exhibit characteristics of heterogeneity, nonlinearity, anisotropy, viscoelasticity, physiological accommodation, and extreme sensitivity to hydration (9–14), mechanical characteristics that are difficult to account for with a single measurement technique.
Conventional mechanical testing methods, including axial strip testing and dynamic mechanical analysis (DMA), have been applied to various tissues of the eye, although these techniques are generally limited in their accuracy because testing requires dissection and flattening of doubly curved tissue samples (15). In addition, these methods are restricted to research applications due to their invasive nature.
Most mechanical assessments of the intact eye have been derived from pressure–volume measurements based on empirical formulations of “ocular rigidity,” which is an expression of the relationship between intraocular volume and intraocular pressure (8, 16, 17). This approach was first introduced in 1937 to standardize the practice of applanation tonometry (16), and is given as follows:
where K is the coefficient of ocular rigidity, P is the intraocular pressure (IOP), and V is the intraocular volume (IOV). The value of K, however, is not always constant or well-behaved, and has been shown by subsequent research to vary considerably from species to species, giving rise to numerous other empirical expressions of ocular rigidity (7). Although ocular rigidity is influenced by the viscoelastic properties of the corneoscleral tissues, no clear relation exists between ocular rigidity and the intrinsic material properties of the tissues involved (8, 17, 18).
An attempt to determine the average elasticity of the whole eye by eliminating the confounding influence of geometry on pressure–volume data (7) represents a worthy advance, but one that continues to suffer from the limited ability of pressure–volume data to provide information about the specific tissues of the eye. Despite this fundamental limitation, pressure–volume analysis by tonometry and inflation (19, 20) is still common practice in ophthalmology and eye-related research, and measures of ocular rigidity continue to form the basis for tonometric determinations of IOP.
In recent decades, experimental image-based approaches for studying eye mechanics have been used with some limited success by directly measuring displacements (strain) in the eye under inflation conditions, and include techniques such as two-point spot-scanning (10), holographic interferometry (21, 22), optical imaging of treated corneal surfaces (23) and wave speed analysis using ultrasound (6, 24, 25). Of the techniques listed here, ultrasound is the only viable method for in vivo application. Despite these developments, and continued incremental improvements to conventional inflation approaches, the need persists for a clinically relevant mechanical test of the eye that is quantitative and noninvasive (26).
One imaging technique with the potential to provide a quantitative, noninvasive assessment of eye mechanics is MR elastography (MRE), a highly sensitive phase-contrast MRI technique capable of imaging microscopic displacements and determining intrinsic mechanical properties (27–29). MRE is performed by introducing mechanical vibrations of a known frequency, and encoding the resulting tissue motion into the phase of the MR images with a synchronous gradient field applied at the same frequency. The acquired images can then be used to determine the mechanical properties of the tissue, typically achieved by making several simplifying mathematical assumptions (29), such as local homogeneity and the absence of boundary effects. These assumptions do not necessarily hold in the presence of the constrained geometry and heterogeneous anatomy of the eye, however, and the application of MRE to the eye requires a more general approach to analysis. Therefore, the purpose of this work was to evaluate the hypothesis that MRE can be used to assess the elastic properties of the intact globe. Because most prior work on eye mechanics has involved the behavior of the corneoscleral shell, we chose to test our hypothesis by estimating the elastic properties of the corneoscleral shell in an intact, ex vivo bovine globe using MRE and a finite-element based wave-data analysis.
A fresh, intact, enucleated bovine globe was cleaned of extraneous tissue and muscle attachments and loosely suspended by rectus muscle sutures in a cylindrical chamber made of 6.35-cm outer-diameter acrylic tube (Fig. 1). As pictured, the globe was mounted with the cornea upright (facing anteriorly) and the optic nerve pointing away from the applied source of motion.
Ex vivo imaging was performed with a 1.5 Tesla (T) whole-body MRI scanner (GE Medical Systems, Waukesha, WI) and a single circular, receive-only radiofrequency coil (7.5-cm diameter). For anatomical MR imaging of the bovine globe, the cylindrical chamber was filled with normal saline solution (9 g/L NaCl) to allow visualization of the boundary between the humor and saline, and the signal-poor corneoscleral shell. A two-dimensional (2D) anatomical image was acquired in the sagittal plane using a T2-weighted (T2W) fast-spin-echo (FSE) sequence with the following imaging parameters: 3200/102-ms repetition time/echo time (TR/TE), 8 ETL, 8-cm field of view (FOV), 3-mm slice thickness, 256 × 256 acquisition matrix, and 2 NEX (signal averages).
Following anatomical imaging, the chamber was drained of the saline solution and a 24-gauge intravenous (IV) catheter was inserted into the posterior chamber, with care being taken to ensure that the needle passed through both the retina and choroid (Fig. 1). The catheter was connected by means of IV pressure tubing to a pair of 1-cc saline-filled syringes, and a pressure sensor (Omega PX26-030GV, Stamford, CT) that allowed the IOP to be measured throughout the course of the experiment. The IOP was increased in a controlled manner by administering a series of 100-μL saline infusions at a rate of approximately 20 μL/s. Saline mist was used to keep the specimen hydrated for the duration of the experiment.
Following each infusion of saline, 2D MRE data was collected using a gradient-recalled echo (GRE) MRE sequence with the following imaging parameters: 40/20-ms TR/TE, 30° flip angle, 8-cm FOV, 5-mm slice thickness, 128 × 128 acquisition matrix, 1 excitation, and 0.75 FOV in the phase-encoding (A/P) direction. Motion in the A/P direction was encoded into the phase of the MR images with six 32 mT/m trapezoidal motion-encoding gradient pairs (MEG) each 3.33 ms long. The total imaging time for four motion phase offsets was 30 s. Continuous cyclical motion at 300 Hz was applied orthogonally to the surface of the limbus with the tip of a thin nylon rod fixed to the center of a piezoelectric disc (3.175 cm diameter). It was determined that this driving location was ideal for simultaneously introducing flexural waves into both the cornea and the sclera. IOP measurements were recorded at the beginning and end of each image acquisition, and approximately 10 s were allowed to elapse between the time of infusion and the data acquisition. The time between MRE acquisitions was approximately 1 minute, and the experiment was continued until the IOP reached 15 mmHg (20.4 cmH2O).
Using conventional MRE inversion algorithms to calculate the mechanical properties of the eye is not feasible (29), because the anatomy of the eye does not meet conventional assumptions of local homogeneity and the absence of boundary effects. Therefore, the mechanical properties of the corneoscleral shell were estimated with finite element modeling (FEM) using commercially available software (COMSOL Multiphysics v3.4, Stockholm, Sweden). A 2D, axisymmetric frequency-response analysis was performed at 300 Hz on a model geometry derived from the segmented anatomical image of the bovine globe anatomy. In this initial work, the lens and the corneoscleral shell were the only structural components incorporated into the FE model. The iris and cilliary components were ignored for simplicity, creating a single, connected intraocular space. Both the aqueous and vitreous humor were modeled as a continuous viscous fluid, a reasonable assumption for the extremely soft vitreous body (30), which strongly attenuates high-frequency shear waves. The corneoscleral shell was subdivided (by visual inspection) into three subdomains consisting of the cornea, limbus, and sclera, each section with distinct, but uniform material properties. The lens was treated as a single, soft, homogeneous subdomain, with a Young's modulus of 1 kPa, in accordance with values reported in the literature (31).
Because the waves imaged with MRE represent the interaction between the intraocular fluid and the corneoscleral shell, a so-called “leaky Lamb wave” (32, 33), a multiphysics FE model consisting of two domains was constructed, including a structural stress-strain (solid) domain for modeling the corneoscleral shell and lens, and a pressure acoustics (fluid) domain for modeling the intraocular fluid space. The solid domain was modeled using the following time-harmonic equation, which assumes a linear, isotropic medium:
where c is the stiffness tensor, η is the loss factor, ω is the angular frequency, ρ is the density, u is displacement, and F is the forcing function (34). Likewise, the fluid domain was modeled with the following time-harmonic equation:
where p is the acoustic pressure, ωis the frequency, and q and Q are dipole and monopole sources, respectively. Variables ρc and cc are complex functions of the density and wave speed, respectively, that contain frequency-dependent terms to account for mechanical damping (35).
In the solid domain, tissues were assumed to be nearly incompressible, with a Poisson's ratio of 0.49 (36). A constant loss factor of 0.05 was empirically determined to account for attenuation in the corneoscleral shell. Viscoelastic and other effects due to anisotropy and nonlinearity were not incorporated in this preliminary work. In the fluid domain, the speed of sound was assumed to be 1500 m/s, and a bulk viscosity several times that of water (0.003 Pa·s) was prescribed to account for mechanical damping. Preliminary sensitivity analysis showed realistic values of the fluid viscosity and loss factor to have negligible effects on the wave speed. Finally, the structural and acoustic modeling domains in this multiphysics model were coupled by allowing the intraocular fluid pressure to load the corneoscleral shell, and by allowing the shell to accelerate the fluid. An oscillating point source was placed at the apex of the cornea to simulate the source of cyclic motion.
For each experimental IOP, the Young's moduli of the cornea and sclera were varied independently, and the model was solved iteratively until it produced a wavefield that was comparable to the wave images produced by the MRE experiment. The Young's modulus of the limbus was determined by taking the average of the corneal and scleral moduli, in accordance with other experimental findings (37). Each FEM iteration was evaluated by placing identical, curved 1D profiles in both the MRE and FE data sets in the intraocular humor along the interior border of the cornea and sclera (see Fig. 6), where displacements in the humor were assumed to match the flexural waves in the corneoscleral shell. To reduce the presence of noise and low spatial frequency bulk motion, the MRE data was initially bandpass filtered in 2D (using a 4th-order Butterworth filter with cut-off frequencies of 4 and 40 cycles per FOV). The 1D wave profiles were also bandpass filtered (1.28 to 25.6, and 1.28 to 10.67 cycles per FOV for the cornea and sclera, respectively), and directionally filtered to reduce the effects of wave interference (38).
To compare the experimental and simulated profiles, the phase of the first temporal harmonic of the profiles was used to calculate the flexural wave speed at each position along the profile by calculating the nearest-neighbors derivative of the first-harmonic profile. The goodness of fit between the experimental and simulated profiles was evaluated by calculating the average least squares difference between linear portions of the wave speed profiles. When the least squares difference in the profiles was minimized, and the experimental and simulated wave speeds matched to 1%, the simulated elastic moduli were considered to be an accurate representation of the experimental elastic moduli of the respective tissue.
As depicted in Figure 2a, the 2D T2W FSE sequence provided significant contrast between the solid and fluid anatomical components of the bovine globe specimen, allowing the geometry of the corneoscleral shell and lens to be adequately resolved. The 2D GRE magnitude image from a typical 300-Hz MRE acquisition is presented in Figure 2b, depicting the quality of the image signal and indicating the orientation of the motion source. In the corresponding 2D bandpass-filtered wave data (Fig. 2c), fluid displacements were clearly visualized in the anterior and posterior compartments with wavelengths assumed to be equivalent to those in the adjacent corneoscleral shell (owing to the “no-slip” boundary condition in fluid dynamics) (33). Single phase offset images from a total of 12 MRE acquisitions at increasing IOPs are presented in Figure 3, in conjunction with the corresponding PV data, illustrating an exponential increase in IOP with respect to changes in intraocular volume and a corresponding increase in flexural wavelengths in both the anterior and posterior compartments.
A binary image of the bovine globe is presented next to the anatomical MR image in Figure 4, demonstrating that it was possible to accurately segment the anatomy of the corneoscleral shell and lens for FE modeling. Figure 5 depicts three steps from the 2D axisymmetric FE model, including the MRI-based model geometry with labeled subdomains (Fig. 5a), solution mesh (Fig. 5b), and a typical solution for the vertical component of the fluid velocity (equivalent to displacement as a measure of wave speed) in the intraocular space (Fig. 5c), which strongly resembles the MRE wave data. Figure 6 shows the locations of the 1D profiles used to compare the experimental MRE data and the simulated FEM data, and that the profile curvature closely matches that of the adjacent corneoscleral shell.
The results obtained from the iterative wave speed matching technique used to estimate the elastic properties of the corneoscleral shell are summarized in Table 1, which contains a listing of the PV data, wave speed data, and estimated elasticities of the cornea and sclera. At IOPs above 9 mmHg, the 300-Hz flexural wavelengths in the sclera began to approach the scale of the globe, making it difficult to accurately characterize the wavespeed. The simulated wave speeds for the lower IOPs, were generated by adjusting the Young's modulus in the FEM model, matched (if possible) to within 1% of those measured with MRE. Estimated values of the Young's moduli in the cornea and sclera varied from 40 to 185 kPa and 1 to 7 MPa, respectively, over an IOP range of 0.85 to 9.05 mmHg (1.2 to 12.3 cmH2O). These estimates are plotted as a function of flexural wave speed in Figure 7, demonstrating that there is a strong, tissue-dependent correlation between these two properties. The data are fit well by an exponential model with correlation coefficients exceeding 0.9 for both tissues. Figure 8 shows plots of the FEM-derived estimates of Young's modulus for the cornea and sclera as functions of dP/dV for each acquisition, an empirical measure of ocular rigidity, illustrating a distinct but strongly correlated and nonlinear relationship for both tissue types.
|ΔV (mL)||IOP (mmHg)||Cornea||Sclera|
|cm (m/s)||cs (m/s)||Ec (kPa)||cm (m/s)||cs (m/s)||Es (MPa)|
These results show that it is possible to estimate the intrinsic elastic properties of specific tissues in the corneoscleral shell of an ex vivo bovine globe using MRE. Fluid displacements in the intraocular space due to flexural waves propagating in the corneoscleral shell of the bovine glove were adequately resolved using a conventional GRE-based MRE acquisition performed at 300 Hz. Wavelengths in the fluid adjacent to the cornea were observed to be considerably shorter than those adjacent to the sclera, supporting the common observation that corneal tissue is considerably softer than the sclera. In addition, wavelengths in the cornea and sclera were seen to increase with an increase in IOP, reinforcing the conventional understanding of the relationship between stiffness (ocular rigidity) and IOP. Simulated wave speeds produced by the 2D axisymmetric FE model derived from anatomical image data were successfully matched to the experimental wave speeds by independently manipulating the simulated elastic properties of the cornea and sclera. The strong but distinct correlation between Young's modulus and dP/dV (Fig. 8) emphasizes the fact that ocular rigidity is only an indirect reflection of the underlying mechanical properties, and that despite the strong correlation, the PV data provides no direct insight into the intrinsic mechanical properties of the individual tissue types. Unlike the PV data, however, the MRE data can be used to estimate the true elasticity of specific tissues in the corneoscleral shell. Overall, these results support the hypothesis that MRE can be used to estimate the mechanical properties of tissues in the eye.
The FE based estimation technique used in this preliminary work makes several simplifying assumptions. Some anatomical features were not included in the FE model, such as the iris, cilliary components, intravitreal membranes, and various layers of the corneoscleral shell. In addition, tissues were assumed to be uniform, linear, isotropic and purely elastic. Although viscoelastic and nonlinear effects were not thoroughly considered, they have been shown to be relevant for the eye, which can behave quite differently under varying inflation and loading conditions (10, 39). This experiment also includes static (PV) and dynamic (MRE) loading of the corneoscleral shell, and viscoelastic effects are known to vary as a function of mechanical frequency, which can be significant at 300 Hz (40). Other influential modeling parameters include Poisson's ratio (a measure of compressibility), density, and the properties of the intraocular fluid, which were assigned by making reference to relevant literature. Given the exponential relationship between Young's moduli and the wave speeds (Fig. 7), it is reasonable to assume that the accuracy of this estimation technique is sensitive to errors in both measured and simulated wave speeds. Flexural wave speed is influenced by several parameters, including the geometrical thickness of the corneoscleral shell, assumed to be accurately represented in the FE model of this work, given the high resolution of the anatomical MR image acquired (Fig. 4). The importance of accurate wave speed measurements underscores the need for high MRE phase-to-noise ratio (PNR) and the benefit of high-frequency and “high-resolution” wave data. Therefore, the comparatively higher motion amplitude (i.e., PNR) and shorter wavelength (i.e., high-resolution) in the anterior compartment adjacent to the cornea may help to explain why the correlation coefficients reported in the results section are generally higher for the cornea than the sclera. Lastly, the FE model used in this work was based on 2D axisymmetric geometry, a reasonable simplifying assumption, given the axial symmetry of the eye and previous work (10, 41, 42), but it stands to reason that a full 3D model and a 3D three-axis MRE dataset could allow for a more complete simulation.
Despite the simplifying assumptions used in this preliminary investigation, however, good correlation was observed between the Young's moduli obtained with this technique and the range of elasticity values reported in the literature, on the order of 100 kPa for corneal tissue (25, 26) and 1 MPa for scleral tissue across species (10, 41, 42). The development of a more complete FE model would make it possible to account for more complex mechanical behavior, such as viscoelasticity and the intrinsically nonlinear stress–strain behavior of the corneoscleral shell (10), and to make morphological assessments for the purpose of validating inflation data. Despite this great potential for development, the general nature of FE modeling even in the form of this initial implementation permits the direct treatment of confounding waveguide effects (due to the heterogeneous nature of the eye), and the subsequent determination of intrinsic material properties, representing a significant improvement over conventional techniques.
In conclusion, this work presents the first application of MRE to the eye, demonstrating the feasibility of acquiring and analyzing dynamic displacement data in an intact globe, and supporting the hypothesis that MRE-based estimation of the intrinsic mechanical properties of the eye and its underlying anatomy is possible. Unlike conventional mechanical testing and PV-based assessments of eye mechanics, MRE has the potential to image microscopic displacements in an intact eye without segmenting or sectioning the anatomy, representing a significant advance that could provide a useful tool for further characterizing the biomechanics of the eye and its anatomic structures. Further development of this technique will make it a more powerful tool, and future work will help to determine its potential for in vivo and clinical application.