Analysis of the effects of curvature and thickness on elastic wave velocity in cornea-like structures by finite element modeling and optical coherence elastography

Abstract

Wave models that have been used to extract the biomechanical properties of the cornea from the propagation of an elastic wave are based on an assumption of thin-plate geometry. However, this assumption does not account for the effects of corneal curvature and thickness. This study conducts finite element (FE) simulations on four types of cornea-like structures as well as optical coherence elastography (OCE) experiments on contact lenses and tissue-mimicking phantoms to investigate the effects of curvature and thickness on the group velocity of an elastic wave. The elastic wave velocity as determined by FE simulations and OCE of a spherical shell section decreased from $2.8 m/s to $2.2 m/s as the radius of curvature increased from 19.1 mm to 47.7 mm and increased from $3.0 m/s to $4.1 m/s as the thickness of the agar phantom increased from 1.9 mm to 5.6 mm. Both the FE simulation and OCE results confirm that the group velocity of the elastic wave decreases with radius of curvature but increases with thickness. These results demonstrate that the effects of the curvature and thickness must be considered in the further development of accurate wave models for reconstructing biomechanical properties of the cornea. Assessing the biomechanical properties of the cornea is of great importance for detecting and monitoring the progression of ocular diseases, such as keratoconus, as well as evaluating the effectiveness of therapies, such as UVinduced collagen cross-linking. 1 In recent years, a number of noninvasive techniques have been proposed to characterize corneal biomechanical properties. For instance, the CorVis can image corneal dynamic responses from a strong air-puff stimulation, 2 and Brillouin microscopy is able to show the depth-resolved Brillouin frequency shift distribution of the cornea.3 Although these methods can provide important measurements that reflect the biomechanical characteristics of the cornea, directly quantifying the viscoelasticity of the cornea by these techniques is still a challenge.Optical coherence elastography (OCE) is a rapidly emerging method that can noninvasively measure the local biomechanical properties of tissues.4 OCE is similar to other elastographic techniques such as ultrasound elastography (USE), 5 magnetic resonance elastography (MRE), 6 and supersonic shear wave imaging (SSI) 7-9 where an externally induced deformation is measured by the respective imaging modality. OCE has micrometer scale spatial resolution 10 and millisecond temporal resolution but has a limited penetration depth of a few millimeters in scattering media such as tissue. However, penetration depth is not an issue for corneal imaging, and thus, OCE is specifically suitable for obtaining the biomechanical properties of the cornea. In our previous work, an OCE system comprised of an external noncontact loading device and an optical coherence tomography (OCT) system was utilized for tumor detection, 11 lens, 12 cornea, 13 cartilage, 14 and cardiac muscle 15 elasticity estimations. Although we have utilized a fo...

Observation of sound-induced corneal vibrational modes by optical coherence tomography

“…The speed depends on in-plane tension and Young's modulus, as well as geometrical factors such as the size, curvature and thickness [21]. The measured resonance peaks seem to fit well with the circular membrane theory [22] Fig.…”

Noncontact Elastic Wave Imaging Optical Coherence Elastography for Evaluating Changes in Corneal Elasticity Due to Crosslinking

“…$$E=\frac{2\rho {false(1+\upsilon false)}^3}{{(0.87+1.12\upsilon )}^2}{c}_g^2,$$ where ρ was the density of the material ( ρ =1000 kg/m 3 for the agar phantoms and ρ =1062 kg/m 3 for the cornea [65]), ν =0.49 was the Poisson’s ratio to account for the nearly incompressible nature of the phantoms and corneas [66], and c g was the elastic wave group velocity. Spectral analysis was utilized to provide depth-resolved elasticity mapping [51].…”

Optical coherence elastography – OCT at work in tissue biomechanics [Invited]

“…For example, finite-element modelling (FEM) supported by experimental data showed that taking account of the stress at the tissue surface, e.g., imparted by a fluid, significantly reduced the group velocity of the elastic wave and, thus, could produce errors in quantification of elastic properties [109,111]. Geometrical factors, such as tissue curvature and thickness, also have profound effects on the measured elastic wave speed [105]. Han et al performed a systematic analysis of the accuracy of four analytical models and FEM for extracting the elastic modulus of soft samples [45].…”

“…Point dynamic loading is attractive as a source of shear waves, and an attractive noncontact localized method is the micro-air puff developed and applied extensively by the Larin group [45, 57, 63, 81, [97][98][99][100][101][102][103][104][105][106][107][108][109][110][111][112][113][114][115][116], mainly to the cornea, but also to skin [108,116], cardiac and skeletal muscles [104], cartilage [101,106], fat and soft tissue tumors [97], and kidneys [112]. Similar to ARF-based excitation, an air puff can deliver a localized and well-controlled impulse stimulus, which can be accompanied by measurement of the tissue displacement or measurement of the air puff-induced elastic wave.…”