**Purpose.**:
To examine the correlation between corneal acoustic impedance and Young's modulus in a canine eye model.

**Methods.**:
Twenty canine globes were recovered from healthy animals. Corneal acoustic impedance was measured in the intact globes using two methods: a quantitative ultrasound spectroscopy method and the reflection amplitude method. The intraocular pressure was maintained at 10 mm Hg during the ultrasound measurements. Corneal strips were then prepared for standard uniaxial tensile tests. Young's moduli at various strain levels and those at a loading level equivalent to that for ultrasound measurements were compared with the acoustic impedance of the same cornea.

**Results.**:
The mean acoustic impedance of the canine corneas was 1.72 ± 0.05 MPa · s/m using the quantitative ultrasound spectroscopy method and 1.71 ± 0.04 MPa · s/m using the reflection amplitude method. Young's secant modulus was 1.07 ± 0.48 MPa at 1% strain and 2.01 ± 0.98 MPa at 5% strain, and the tangent modulus was 1.28 ± 0.69 and 3.16 ± 0.71 MPa, respectively. Significant linear correlations between acoustic impedance and Young's modulus (at 1%–5% strains) were found in the measured canine corneas. The correlation remained strong when comparing the two parameters measured under equivalent loading.

**Conclusions.**:
This study suggests a potentially strong correlation between corneal acoustic impedance and Young's modulus at low strain levels. If such correlation also exists in the human eye, it may allow the noninvasively determined acoustic impedance to be used as a surrogate for Young's modulus, which is difficult to obtain in vivo.

^{ 1,2 }Ablative refractive surgery may induce significant changes in corneal biomechanical properties, leading to complications.

^{ 3 }Corneal stiffness also may be confounded in the tonometric measurement of intraocular pressure (IOP), in that stiffer corneas may lead to overestimation, while more compliant corneas lead to underestimation of IOP.

^{ 4,5 }Recent studies have also indicated that corneal stiffness may affect the eye's ability to dampen IOP spikes.

^{ 6,7 }Determination and monitoring of corneal biomechanical properties will thus enable us to better study the mechanisms of these ocular conditions, and facilitate the development of new technologies for their detection and diagnosis.

^{ 8 –11 }It is still desirable to characterize corneal biomechanical properties noninvasively. In vivo biomechanical characterization has also been explored by examining corneal deformation under the force of a rapid air puff (Ocular Response Analyzer [ORA]; Reichert, Inc., Depew, NY).

^{ 12,13 }Corneal hysteresis and the resistance factor measured by ORA may provide new diagnostic information, but it is generally believed that these parameters do not always represent the elastic properties of the cornea.

^{ 14,15 }Ultrasound is mechanical energy, and its propagation causes microscopic deformations within the supporting medium. Acoustic parameters, including acoustic impedance, speed of sound, and attenuation are affected by the microstructure, density, and elasticity of the material in which the sound waves propagate.

^{ 16 }For example, the characteristic acoustic impedance of a lossless medium is a function of aggregate modulus and density: where

*Z*is the acoustic impedance,

*M*is the aggregate modulus, and ρ is the density.

^{ 17 }To our best knowledge, the relationship between corneal acoustic properties and Young's modulus has not been studied before. The goal of this study was to investigate whether there is a correlation between corneal acoustic impedance (determined by ultrasonic measurements) and corneal Young's modulus (determined by tensile tests) in a canine eye model. The acoustic impedance of the cornea can be determined from the amplitude of the reflected ultrasound signals calibrated to that from a material with known properties.

^{ 18 –20 }It can also be calculated from aggregate modulus and density by applying equation 1. A secondary goal of this study is to compare the two methods of measuring corneal acoustic impedance: (1) the reflection amplitude method, and (2) the quantitative ultrasound spectroscopy method that provides an estimation of corneal aggregate modulus and density.

^{ 9 }Third, the variance in the tissue properties of the natural-born animals are likely to be more representative of‘ the general population than laboratory animals or those raised for slaughter whose age and genetic background could be narrow within a short sampling period.

^{ 14,15 }Briefly, the ultrasonic measurement system is composed of a transducer, a pulser-receiver, a digitizer, and a computer (Fig. 1a). During the ultrasonic measurements, the globes were immersed in a saline bath, which served as the coupling medium for the ultrasound pulses to transfer from the transducer to the cornea and vice versa. Short-duration ultrasonic pulses at an intensity level (<3 mW/cm

^{2}) that was lower than the safety threshold for human use were propagated along the axial direction of the eye. The ultrasonic reflections from the cornea were displayed in real time on a computer, and the signals were sampled at 500 MHz by the digitizer and recorded on the hard disk of the computer.

*R*) can be calculated

^{ 21 }: where

*A*

_{s}is the amplitude of the reflection from the sample/water interface,

*A*

_{0}is the amplitude of the incident acoustic waves,

*Z*

_{s}is the acoustic impedance of the sample, and

*Z*

_{w}is the acoustic impedance of water.

^{18,19}As shown in Figure 2, the peak-to-peak value of the reflected signals can be used to determine the amplitude of the reflection. In this study, the mean amplitude (

*A*

_{c}, which is the average of the reflection amplitudes from anterior and posterior surfaces of the cornea) was used to calculate corneal acoustic impedance. The reference signal was measured from a material (Soflens-59; Bausch & Lomb, Rochester, NY) with a density of 1.14 g/mL and a speed of sound of 1675 m/s (measured on the bulk material). The acoustic impedance of the reference material was calculated as the product of density and speed of sound. The amplitude of the incident acoustic waves (

*A*

_{0}) can be calculated: where

*A*

_{r}is the amplitude of the reflected signal at the reference/water interface,

*Z*

_{r}is the acoustic impedance of the reference material, and

*Z*

_{w}is the acoustic impedance of water. With the calculated

*A*

_{0}and the measured

*A*

_{c}, the acoustic impedance of the cornea,

*Z*

_{c}, can be calculated:

^{ 22 –24 }

*R*= 0.97,

*P*< 0.001). Figure 3 shows the comparison of the acoustic impedance obtained from these two methods.

Strain | Modulus (MPa) (Mean ± SD) | Correlation Coefficient R Modulus vs. Acoustic Impedance | ||||||
---|---|---|---|---|---|---|---|---|

Secant | Tangent | Secant | Tangent | |||||

Spec | Amp | Spec | Amp | |||||

1% | 1.07 ± 0.48 | 1.28 ± 0.69 | 0.93 | 0.88 | 0.90 | 0.83 | ||

2% | 1.28 ± 0.61 | 1.80 ± 0.90 | 0.91 | 0.85 | 0.84 | 0.79 | ||

3% | 1.54 ± 0.74 | 2.28 ± 1.14 | 0.88 | 0.83 | 0.76 | 0.72 | ||

4% | 1.80 ± 0.88 | 2.74 ± 1.41 | 0.84 | 0.79 | 0.69 | 0.64 | ||

5% | 2.01 ± 0.98 | 3.16 ± 1.71 | 0.80 | 0.74 | 0.62 | 0.56 | ||

Equivalent loading | 1.05 ± 0.40 | 1.28 ± 0.47 | 0.93 | 0.88 | 0.83 | 0.74 |

*P*) can be estimated by Laplace's Law: assuming an average radius of curvature (

*r*) of 8.5 mm for canine corneas (based on reports in the literature for medium to large dogs)

^{ 25 }and using the measured corneal thickness (

*t*; from analysis of the ultrasound data). The modulus was then obtained from the stress–strain relationship at the corresponding stress.

*R*= 0.93,

*P*< 0.001). The linear regression equation is where

*x*is corneal acoustic impedance, and

*y*is corneal secant modulus.

^{ 10 }We have analyzed the potential effect of nonlinearity and found it did not significantly alter the observed correlation at low strains levels, which are typically what the cornea experiences under physiological pressure loadings. At higher strains (>4%), the correlation was still significant but weaker, most likely because of the nonlinear effect and the larger variance of modulus at higher strains. The strong correlation may reflect the rather simple composition of cornea. As a collagenous tissue, corneal collagen content may have similar influence on its density and Young's modulus. For instance, higher collagen content is likely to be associated with a higher density and a higher stiffness. Acoustic impedance represents the resistance to sound passing through the material. A stiffer and denser material usually exerts greater resistance and thus has higher acoustic impedance. Other tissue properties such as collagen cross-linking may also affect the elastic properties and the ultrasound reflectance in similar ways.

^{ 26 }

^{ 1,10 }Third, although in general the value of the modulus for a given cornea is sensitive to strain levels, it was fairly constant at low strain levels (Fig. 4). Thus, the correlation between acoustic impedance and modulus could hold at low strains regardless of the strain levels.

^{ 27,28 }

^{ 9,11 }Thus, the strain rates used in the tensile tests may affect the measured properties. Higher strain rates tended to yield higher modulus for a viscoelastic material. Although the effect is less prominent at low strain levels, such as those used in the present study,

^{ 10 }the effect of strain rate should be investigated in the future. In addition, the acoustic impedance was only measured at one intraocular loading (which corresponded to various strain rates). Future studies are needed to examine whether corneal acoustic impedance is dependent on strain levels. The measurements were performed at room temperature, which differs from the in vivo situation. Temperature (25–40°C) is known to affect both mechanical and acoustical properties. Future studies are needed to compare the properties measured at body temperature, which are more representative of in vivo measurements. Importantly, the studies were performed in canine corneas, which may differ from human corneas. Future studies are needed to confirm the correlation in human eyes. In the present study, the cornea was treated as a single homogeneous layer and the through-thickness average of the acoustic properties was correlated with the mechanical properties obtained from strip testing. The sublayers such as corneal epithelium, Bowman's, Descemet's, and endothelium are not differentiable at the ultrasound frequencies used in the present study. However, it is possible to separately analyze the signals of the anterior and the posterior cornea, which may be of clinical interest, for example in the noninvasive measurement of biomechanical changes in the anterior stroma after cross-linking treatment. Corneas also have a strong anisotropy because the collagen fibers are mainly aligned parallel to the surface. Ultrasonic techniques have been developed in the past to characterize multilayered anisotropic composites.

^{ 29 }These approaches may be adopted for characterizing corneal anisotropy if the unique challenges related to cornea (such as its significant fluid content and curvature) can be successfully addressed.