Possible depth-resolved reconstruction of shear moduli in the cornea following collagen crosslinking (CXL) with optical coherence tomography and elastography.

Corneal collagen crosslinking (CXL) is commonly used to prevent or treat keratoconus. Although changes in corneal stiffness induced by CXL surgery can be monitored with non-contact dynamic optical coherence elastography (OCE) by tracking mechanical wave propagation, depth dependent changes are still unclear if the cornea is not crosslinked through the whole depth. Here, phase-decorrelation measurements on optical coherence tomography (OCT) structural images are combined with acoustic micro-tapping (AµT) OCE to explore possible reconstruction of depth-dependent stiffness within crosslinked corneas in an ex vivo human cornea sample. Experimental OCT images are analyzed to define the penetration depth of CXL into the cornea. In a representative ex vivo human cornea sample, crosslinking depth varied from ∼100 µm in the periphery to ∼150 µm in the cornea center and exhibited a sharp in-depth transition between crosslinked and untreated areas. This information was used in an analytical two-layer guided wave propagation model to quantify the stiffness of the treated layer. We also discuss how the elastic moduli of partially CXL-treated cornea layers reflect the effective engineering stiffness of the entire cornea to properly quantify corneal deformation.

Possible depth-resolved reconstruction of shear moduli in the cornea following collagen crosslinking (CXL) with optical coherence tomography and elastography.

Corneal collagen crosslinking (CXL) is commonly used to prevent or treat keratoconus. Although changes in corneal stiffness induced by CXL surgery can be monitored with non-contact dynamic optical coherence elastography (OCE) by tracking mechanical wave propagation, depth dependent changes are still unclear if the cornea is not crosslinked through the whole depth. Here, phase-decorrelation measurements on optical coherence tomography (OCT) structural images are combined with acoustic micro-tapping (A$\mu$T) OCE to explore possible reconstruction of depth-dependent stiffness within crosslinked corneas in an ex vivo human cornea sample. Experimental OCT images are analyzed to define the penetration depth of CXL into the cornea. In a representative ex vivo human cornea sample, crosslinking depth varied from $\sim 100\mu m$ in the periphery to $\sim 150\mu m$ in the cornea center and exhibited a sharp in-depth transition between crosslinked and untreated areas. This information was used in an analytical two-layer guided wave propagation model to quantify the stiffness of the treated layer. We also discuss how the elastic moduli of partially CXL-treated cornea layers reflect the effective engineering stiffness of the entire cornea to properly quantify corneal deformation.

Noncontact Acoustic Micro-Tapping Optical Coherence Elastography for Quantification of Corneal Anisotropic Elasticity: In Vivo Rabbit Study.

Purpose: The purpose of this study was to demonstrate accurate measurement of corneal elastic moduli in vivo with noncontact and noninvasive optical coherence elastography. Methods: Elastic properties (in-plane Young's modulus, E, and both in-plane, µ, and out-of-plane, G, shear moduli) of rabbit cornea were quantified in vivo using noncontact dynamic acoustic micro-tapping optical coherence elastography (AµT-OCE). The intraocular pressure (IOP)-dependence of measured mechanical properties was explored in extracted whole globes following in vivo measurement. A nearly incompressible transverse isotropic (NITI) model was used to reconstruct moduli from AµT-OCE data. Independently, cornea elastic moduli were also measured ex vivo with traditional, destructive mechanical tests (tensile extensometry and shear rheometry). Results: Our study demonstrates strong anisotropy of corneal elasticity in rabbits. The in-plane Young's modulus, computed as E = 3µ, was in the range of 20 MPa to 44 MPa, whereas the out-of-plane shear modulus was in the range of 34 kPa to 261 kPa. Both pressure-dependent ex vivo OCE and destructive mechanical tests performed on the same samples within an hour of euthanasia strongly support the results of AµT-OCE measurements. Conclusions: Noncontact AµT-OCE can noninvasively quantify cornea anisotropic elastic properties in vivo. Translational Relevance: As optical coherence tomography (OCT) is broadly accepted in ophthalmology, these results suggest the potential for rapid translation of AµT-OCE into clinical practice. In addition, AµT-OCE can likely improve diagnostic criteria of ectatic corneal diseases, leading to early diagnosis, reduced complications, customized surgical treatment, and personalized biomechanical models of the eye.

Non-contact acoustic micro-tapping optical coherence elastography for quantification of corneal anisotropic elasticity: in vivo rabbit study.

PURPOSE: To demonstrate accurate measurement of corneal elastic moduli in vivo with non-contact and non-invasive optical coherence elastography. METHODS: Elastic properties (in-plane Young's modulus E and both in-plane, u, and out-of-plane, G, shear moduli) of rabbit cornea were quantified in vivo using non-contact dynamic Acoustic micro-Tapping Optical Coherence Elastography (AuT-OCE). The IOP-dependence of measured mechanical properties was explored in extracted whole globes following in vivo measurement. A nearly-incompressible transverse isotropic (NITI) model was used to reconstruct moduli from AuT-OCE data. Independently, cornea elastic moduli were also measured ex vivo with traditional, destructive mechanical tests (tensile extensometry and shear rheometry). RESULTS: Our study demonstrates strong anisotropy of corneal elasticity in rabbits. The in-plane Young's modulus, computer as E=3u, was in the range of 20-44 MPa, whereas the out-of-plane shear modulus was in the range of 34-261 kPa. Both pressure-dependent ex vivo OCE and destructive mechanical tests performed on the same samples within an hour of euthanasia strongly support the results of AuT-OCE measurements. CONCLUSIONS: Non-contact AuT-OCE can non-invasively quantify cornea anisotropic elastic properties in vivo. TRANSLATIONAL RELEVANCE: As OCT is broadly accepted in Ophthalmology, these results suggest the potential for rapid translation of AuT-OCE into clinical practice. In addition, AuT-OCE can likely improve diagnostic criteria of ectatic corneal diseases, leading to early diagnosis, reduced complications, customized surgical treatment, and personalized biomechanical models of the eye.

Acoustic Micro-Tapping Optical Coherence Elastography to Quantify Corneal Collagen Cross-Linking: An Ex Vivo Human Study.

Purpose: To evaluate changes in the anisotropic elastic properties of ex vivo human cornea treated with ultraviolet cross-linking (CXL) using noncontact acoustic micro-tapping optical coherence elastography (AµT-OCE). Design: Acoustic micro-tapping OCE was performed on normal and CXL human donor cornea in an ex vivo laboratory study. Subjects: Normal human donor cornea (n = 22) divided into 4 subgroups. All samples were stored in optisol. Methods: Elastic properties (in-plane Young's, E, and out-of-plane, G, shear modulus) of normal and ultraviolet CXL-treated human corneas were quantified using noncontact AµT-OCE. A nearly incompressible transverse isotropic model was used to reconstruct moduli from AµT-OCE data. Independently, cornea elastic moduli were also measured with destructive mechanical tests (tensile extensometry and shear rheometry). Main Outcome Measures: Corneal elastic moduli (in-plane Young's modulus, E, in-plane, µ, and out-of-plane, G, shear moduli) can be evaluated in both normal and CXL treated tissues, as well as monitored during the CXL procedure using noncontact AµT-OCE. Results: Cross-linking induced a significant increase in both in-plane and out-of-plane elastic moduli in human cornea. The statistical mean in the paired study (presurgery and postsurgery, n = 7) of the in-plane Young's modulus, E = 3 µ , increased from 19 MPa to 43 MPa, while the out-of-plane shear modulus, G, increased from 188 kPa to 673 kPa. Mechanical tests in a separate subgroup support CXL-induced cornea moduli changes and generally agree with noncontact AµT-OCE measurements. Conclusions: The human cornea is a highly anisotropic material where in-plane mechanical properties are very different from those out-of-plane. Noncontact AµT-OCE can measure changes in the anisotropic elastic properties in human cornea as a result of ultraviolet CXL.

Spatial resolution in optical coherence elastography of bounded media.

Dynamic optical coherence elastography (OCE) tracks mechanical wave propagation in the subsurface region of tissue to image its shear modulus. For bulk shear waves, the lateral resolution of the reconstructed modulus map (i.e., elastographic resolution) can approach that of optical coherence tomography (OCT), typically a few tens of microns. Here we perform comprehensive numerical simulations and acoustic micro-tapping OCE experiments to show that for the typical situation of guided wave propagation in bounded media, such as cornea, the elastographic resolution cannot reach the OCT resolution and is mainly defined by the thickness of the bounded tissue layer. We considered the excitation of both broadband and quasi-harmonic guided waves in a bounded, isotropic medium. Leveraging the properties of broadband pulses, a robust method for modulus reconstruction with minimum artifacts at interfaces is demonstrated. In contrast, tissue bounding creates large instabilities in the phase of harmonic waves, leading to serious artifacts in modulus reconstructions.

Signatures of microstreaming patterns induced by non-spherically oscillating bubbles.

In this study, we report recent theoretical and experimental developments dealing with the axisymmetric flow surrounding non-spherically oscillating microbubbles. A wide variety of microstreaming patterns is revealed using a theoretical modeling providing exact analytical solutions of the second-order mean flows. The streaming pattern is highly dependent on the modal content of the bubble interface oscillation, including possibly spherical, translational, and nonspherical modes, as well as any combination of these modes. Experimental results on fluid flow induced by a single, non-spherically oscillating bubble in an unbounded fluid are presented and successfully compared to the theoretical predictions.

Induction of Microstreaming by Nonspherical Bubble Oscillations in an Acoustic Levitation System.

When located near biological barriers, oscillating microbubbles may increase cell membrane permeability, allowing for drug and gene internalization. Experimental observations suggest that the temporary permeabilization of these barriers may be due to shear stress that is exerted on cell tissues by cavitation microstreaming. Cavitation microstreaming is the generation of vortex flows which arise around oscillating ultrasound microbubbles. To produce such liquid flows, bubble oscillations must deviate from purely spherical oscillations and include either a translational instability or shape modes. Experimental studies of bubble-induced flows and shear stress on nearby surfaces are often restricted in their scope due to the difficulty of capturing shape deformations of microbubbles in a stable and controllable manner. We describe the design of an acoustic levitation chamber for the study of symmetry-controlled nonspherical oscillations. Such control is performed by using a coalescence technique between two approaching bubbles in a sufficiently intense ultrasound field. The control of nonspherical oscillations opens the way to a controlled cavitation microstreaming of a free surface-oscillating microbubble. High-frame rate cameras allow investigating quasi-simultaneously the nonspherical bubble dynamics at the acoustic timescale and the liquid flow at a lower timescale. It is shown that a large variety of fluid patterns may be obtained and that they are correlated to the modal content of the bubble interface. We demonstrate that even the high-order shape modes can create large-distance fluid patterns if the interface dynamics contain several modes, highlighting the potential of nonspherical oscillations for targeted and localized drug delivery.

Acoustic microstreaming produced by nonspherical oscillations of a gas bubble. IV. Case of modes n and m.

This paper is the conclusion of work done in our previous papers [A. A. Doinikov et al., Phys. Rev. E 100, 033104 (2019)10.1103/PhysRevE.100.033104; Phys. Rev. E 100, 033105 (2019)10.1103/PhysRevE.100.033105]. The overall aim of the study is to develop a theory for modeling the velocity field of acoustic microstreaming produced by nonspherical oscillations of a gas bubble. In our previous papers, general equations were derived to describe the velocity field of acoustic microstreaming produced by modes m and n of bubble oscillations. Particular cases of mode interaction were derived, such as the 0-n, 1-1, 1-m, and n-n interactions. Here the general case of interaction between modes n and m, n>m, is solved analytically. Solutions are expressed in terms of complex mode amplitudes, meaning that the mode amplitudes are assumed to be known and serve as input data for the calculation of the velocity field of microstreaming. No restrictions are imposed on the ratio of the bubble radius to the viscous penetration depth. The n-m interaction results in specific streaming patterns: At large distance from the bubble interface the pattern exhibits 2|n-m| lobes, while 2min(m,n) lobes exist in the bubble vicinity. The spatial organization of the recirculation zones is unique for the interaction of two distinct nonspherical modes and therefore appears as a signature of the n-m interaction.

Secondary radiation force between two closely spaced acoustic bubbles.

Two acoustic bubbles may attract or repel due to the secondary radiation force acting on them. We use here a dual-frequency levitation chamber in order to trap two oscillating microbubbles at close, fixed distance, and to perform measurements of the interaction force. We successfully compare our measurements to a commonly used theoretical model that assumes linear spherical oscillations, and disregards attenuation and multiple scattering between bubbles. The deviation from the model arises when nonspherical surface oscillations are triggered, leading to an additional hydrodynamic force induced by second-order liquid flow.

Acoustic microstreaming produced by nonspherical oscillations of a gas bubble. III. Case of self-interacting modes n-n.

This paper is the continuation of work done in our previous papers [A. A. Doinikov et al., Phys. Rev. E 100, 033104 (2019)2470-004510.1103/PhysRevE.100.033104; Phys. Rev. E 100, 033105 (2019)].2470-004510.1103/PhysRevE.100.033105 The overall aim of the study is to develop a theory for modeling the velocity field of acoustic microstreaming produced by nonspherical oscillations of an acoustically driven gas bubble. In our previous papers, general equations have been derived to describe the velocity field of acoustic microstreaming produced by modes m and n of bubble oscillations. After solving these general equations for some particular cases of modal interactions (cases 0-n, 1-1, and 1-m), in this paper the general equations are solved analytically for the case that acoustic microstreaming results from the self-interaction of an arbitrary surface mode n≥1. Solutions are expressed in terms of complex mode amplitudes, meaning that the mode amplitudes are assumed to be known and serve as input data for the calculation of the velocity field of acoustic microstreaming. No restrictions are imposed on the ratio of the bubble radius to the viscous penetration depth. The self-interaction results in specific streaming patterns: a large-scale cross pattern and small recirculation zones in the vicinity of the bubble interface. Particularly the spatial organization of the recirculation zones is unique for a given surface mode and therefore appears as a signature of the n-n interaction. Experimental streaming patterns related to this interaction are obtained and good agreement is observed with the theoretical model.

Acoustic microstreaming produced by nonspherical oscillations of a gas bubble. I. Case of modes 0 and m.

A theory is developed that allows one to model the velocity field of acoustic microstreaming produced by nonspherical oscillations of an acoustically driven gas bubble. It is assumed that some of the bubble oscillation modes are excited parametrically and hence can oscillate at frequencies different from the driving frequency. Analytical solutions are derived in terms of complex amplitudes of oscillation modes, which means that the mode amplitudes are assumed to be known and serve as input data when the velocity field of acoustic microstreaming is calculated. No restrictions are imposed on the ratio of the bubble radius to the viscous penetration depth. The present paper is the first part of our study in which a general theory is developed and then applied to the case that acoustic microstreaming is generated by the interaction of the breathing mode (mode 0) with a mode of arbitrary order m≥1. Examples of numerical simulations and a comparison with experimental results are provided.

Acoustic microstreaming produced by nonspherical oscillations of a gas bubble. II. Case of modes 1 and m.

This paper continues a study that was started in our previous paper [A. A. Doinikov et al., Phys. Rev. E 100, 033104 (2019)10.1103/PhysRevE.100.033104]. The overall aim of the study is to develop a theory for modeling the velocity field of acoustic microstreaming produced by nonspherical oscillations of an acoustically driven gas bubble. In the previous paper, general equations were derived that describe the velocity field of acoustic microstreaming produced by modes n and m of bubble oscillations. In the present paper, the above equations are solved analytically in the case that acoustic microstreaming is the result of the interaction of the translational mode (mode 1) with a mode of arbitrary order m≥1. Solutions are expressed in terms of complex mode amplitudes, which means that the mode amplitudes are assumed to be known and serve as input data for the calculation of the velocity field of acoustic microstreaming. No restrictions are imposed on the ratio of the bubble radius to the viscous penetration depth. Analytical results are illustrated by numerical examples.