Abstract

The mechanical stability of the cornea is critical for maintaining its normal shape and refractive function. Here, we report an observation of the mechanical resonance modes of the cornea excited by sound waves and detected by using phase-sensitive optical coherence tomography. The cornea in bovine eye globes exhibited three resonance modes in a frequency range of 50-400 Hz. The vibration amplitude of the fundamental mode at 80-120 Hz was ~8 µm at a sound pressure level of 100 dB (2 Pa). Vibrography allows the visualization of the radially symmetric profiles of the resonance modes. A dynamic finite-element analysis supports our observation.

© 2015 Optical Society of America

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  4. G. Wollensak, E. Spoerl, and T. Seiler, “Riboflavin/ultraviolet-A-induced collagen crosslinking for the treatment of keratoconus,” Am. J. Ophthalmol. 135(5), 620–627 (2003).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  7. S. Bak-Nielsen, I. B. Pedersen, A. Ivarsen, and J. Hjortdal, “Dynamic Scheimpflug-based assessment of keratoconus and the effects of corneal cross-linking,” J. Refract. Surg. 30(6), 408–414 (2014).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  24. T. M. Nguyen, J. F. Aubry, D. Touboul, M. Fink, J. L. Gennisson, J. Bercoff, and M. Tanter, “Monitoring of cornea elastic properties changes during UV-A/riboflavin-induced corneal collagen cross-linking using supersonic shear wave imaging: a pilot study,” Invest. Ophthalmol. Vis. Sci. 53(9), 5948–5954 (2012).
    [Crossref] [PubMed]
  25. S. Kling, B. I. Akca, E. W. Chang, G. Scarcelli, N. Bekesi, S. H. Yun, and S. Marcos, “Numerical model of OCT-vibrography imaging to estimate corneal biomechanical properties,” J. R. Soc. Interface 11, 20140920 (2014).
    [Crossref] [PubMed]
  26. D. V. Litwiller, S. J. Lee, A. Kolipaka, Y. K. Mariappan, K. J. Glaser, J. S. Pulido, and R. L. Ehman, “MR elastography of the ex vivo bovine globe,” J. Magn. Reson. Imaging 32(1), 44–51 (2010).
    [Crossref] [PubMed]

2015 (1)

Z. Han, J. Li, M. Singh, S. R. Aglyamov, C. Wu, C. H. Liu, and K. V. Larin, “Analysis of the effects of curvature and thickness on elastic wave velocity in cornea-like structures by finite element modeling and optical coherence elastography,” Appl. Phys. Lett. 106(23), 233702 (2015).
[Crossref] [PubMed]

2014 (7)

S. Kling, B. I. Akca, E. W. Chang, G. Scarcelli, N. Bekesi, S. H. Yun, and S. Marcos, “Numerical model of OCT-vibrography imaging to estimate corneal biomechanical properties,” J. R. Soc. Interface 11, 20140920 (2014).
[Crossref] [PubMed]

T. M. Nguyen, S. Song, B. Arnal, E. Y. Wong, Z. Huang, R. K. Wang, and M. O’Donnell, “Shear wave pulse compression for dynamic elastography using phase-sensitive optical coherence tomography,” J. Biomed. Opt. 19(1), 016013 (2014).
[Crossref] [PubMed]

B. F. Kennedy, K. M. Kennedy, and D. D. Sampson, “A review of optical coherence elastography: fundamentals, techniques and prospects,” IEEE J. Sel. Top. Quantum Electron. 20(2), 272 (2014).
[Crossref]

S. Bak-Nielsen, I. B. Pedersen, A. Ivarsen, and J. Hjortdal, “Dynamic Scheimpflug-based assessment of keratoconus and the effects of corneal cross-linking,” J. Refract. Surg. 30(6), 408–414 (2014).
[Crossref] [PubMed]

S. Kling, N. Bekesi, C. Dorronsoro, D. Pascual, and S. Marcos, “Corneal viscoelastic properties from finite-element analysis of in vivo air-puff deformation,” PLoS One 9(8), e104904 (2014).
[Crossref] [PubMed]

S. Wang and K. V. Larin, “Shear wave imaging optical coherence tomography (SWI-OCT) for ocular tissue biomechanics,” Opt. Lett. 39(1), 41–44 (2014).
[Crossref] [PubMed]

M. D. Twa, J. Li, S. Vantipalli, M. Singh, S. Aglyamov, S. Emelianov, and K. V. Larin, “Spatial characterization of corneal biomechanical properties with optical coherence elastography after UV cross-linking,” Biomed. Opt. Express 5(5), 1419–1427 (2014).
[Crossref] [PubMed]

2013 (1)

E. W. Chang, J. T. Cheng, C. Röösli, J. B. Kobler, J. J. Rosowski, and S. H. Yun, “Simultaneous 3D imaging of sound-induced motions of the tympanic membrane and middle ear ossicles,” Hear. Res. 304, 49–56 (2013).
[Crossref] [PubMed]

2012 (4)

2011 (1)

M. R. Ford, W. J. Dupps, A. M. Rollins, A. S. Roy, and Z. Hu, “Method for optical coherence elastography of the cornea,” J. Biomed. Opt. 16(1), 016005 (2011).
[Crossref] [PubMed]

2010 (2)

D. V. Litwiller, S. J. Lee, A. Kolipaka, Y. K. Mariappan, K. J. Glaser, J. S. Pulido, and R. L. Ehman, “MR elastography of the ex vivo bovine globe,” J. Magn. Reson. Imaging 32(1), 44–51 (2010).
[Crossref] [PubMed]

S. G. Adie, X. Liang, B. F. Kennedy, R. John, D. D. Sampson, and S. A. Boppart, “Spectroscopic optical coherence elastography,” Opt. Express 18(25), 25519–25534 (2010).
[Crossref] [PubMed]

2009 (1)

M. Tanter, D. Touboul, J. L. Gennisson, J. Bercoff, and M. Fink, “High-resolution quantitative imaging of cornea elasticity using supersonic shear imaging,” IEEE Trans. Med. Imaging 28(12), 1881–1893 (2009).
[Crossref] [PubMed]

2008 (3)

C. Kirwan, D. O’Malley, and M. O’Keefe, “Corneal hysteresis and corneal resistance factor in keratoectasia: findings using the Reichert ocular response analyzer,” Ophthalmologica 222(5), 334–337 (2008).
[Crossref] [PubMed]

D. G. Dawson, J. B. Randleman, H. E. Grossniklaus, T. P. O’Brien, S. R. Dubovy, I. Schmack, R. D. Stulting, and H. F. Edelhauser, “Corneal ectasia after excimer laser keratorefractive surgery: histopathology, ultrastructure, and pathophysiology,” Ophthalmology 115(12), 2181–2191 (2008).
[Crossref] [PubMed]

G. Scarcelli and S. H. Yun, “Confocal Brillouin microscopy for three-dimensional mechanical imaging,” Nat. Photonics 2(1), 39–43 (2008).
[Crossref] [PubMed]

2007 (1)

N. Morishige, A. J. Wahlert, M. C. Kenney, D. J. Brown, K. Kawamoto, T. Chikama, T. Nishida, and J. V. Jester, “Second-harmonic imaging microscopy of normal human and keratoconus cornea,” Invest. Ophthalmol. Vis. Sci. 48(3), 1087–1094 (2007).
[Crossref] [PubMed]

2006 (1)

W. J. Dupps and S. E. Wilson, “Biomechanics and wound healing in the cornea,” Exp. Eye Res. 83(4), 709–720 (2006).
[Crossref] [PubMed]

2005 (1)

D. A. Luce, “Determining in vivo biomechanical properties of the cornea with an ocular response analyzer,” J. Cataract Refract. Surg. 31(1), 156–162 (2005).
[Crossref] [PubMed]

2003 (1)

G. Wollensak, E. Spoerl, and T. Seiler, “Riboflavin/ultraviolet-A-induced collagen crosslinking for the treatment of keratoconus,” Am. J. Ophthalmol. 135(5), 620–627 (2003).
[Crossref] [PubMed]

Adie, S. G.

Aglyamov, S.

Aglyamov, S. R.

Z. Han, J. Li, M. Singh, S. R. Aglyamov, C. Wu, C. H. Liu, and K. V. Larin, “Analysis of the effects of curvature and thickness on elastic wave velocity in cornea-like structures by finite element modeling and optical coherence elastography,” Appl. Phys. Lett. 106(23), 233702 (2015).
[Crossref] [PubMed]

Akca, B. I.

S. Kling, B. I. Akca, E. W. Chang, G. Scarcelli, N. Bekesi, S. H. Yun, and S. Marcos, “Numerical model of OCT-vibrography imaging to estimate corneal biomechanical properties,” J. R. Soc. Interface 11, 20140920 (2014).
[Crossref] [PubMed]

Arnal, B.

T. M. Nguyen, S. Song, B. Arnal, E. Y. Wong, Z. Huang, R. K. Wang, and M. O’Donnell, “Shear wave pulse compression for dynamic elastography using phase-sensitive optical coherence tomography,” J. Biomed. Opt. 19(1), 016013 (2014).
[Crossref] [PubMed]

Aubry, J. F.

T. M. Nguyen, J. F. Aubry, D. Touboul, M. Fink, J. L. Gennisson, J. Bercoff, and M. Tanter, “Monitoring of cornea elastic properties changes during UV-A/riboflavin-induced corneal collagen cross-linking using supersonic shear wave imaging: a pilot study,” Invest. Ophthalmol. Vis. Sci. 53(9), 5948–5954 (2012).
[Crossref] [PubMed]

Bak-Nielsen, S.

S. Bak-Nielsen, I. B. Pedersen, A. Ivarsen, and J. Hjortdal, “Dynamic Scheimpflug-based assessment of keratoconus and the effects of corneal cross-linking,” J. Refract. Surg. 30(6), 408–414 (2014).
[Crossref] [PubMed]

Bekesi, N.

S. Kling, N. Bekesi, C. Dorronsoro, D. Pascual, and S. Marcos, “Corneal viscoelastic properties from finite-element analysis of in vivo air-puff deformation,” PLoS One 9(8), e104904 (2014).
[Crossref] [PubMed]

S. Kling, B. I. Akca, E. W. Chang, G. Scarcelli, N. Bekesi, S. H. Yun, and S. Marcos, “Numerical model of OCT-vibrography imaging to estimate corneal biomechanical properties,” J. R. Soc. Interface 11, 20140920 (2014).
[Crossref] [PubMed]

Bercoff, J.

T. M. Nguyen, J. F. Aubry, D. Touboul, M. Fink, J. L. Gennisson, J. Bercoff, and M. Tanter, “Monitoring of cornea elastic properties changes during UV-A/riboflavin-induced corneal collagen cross-linking using supersonic shear wave imaging: a pilot study,” Invest. Ophthalmol. Vis. Sci. 53(9), 5948–5954 (2012).
[Crossref] [PubMed]

M. Tanter, D. Touboul, J. L. Gennisson, J. Bercoff, and M. Fink, “High-resolution quantitative imaging of cornea elasticity using supersonic shear imaging,” IEEE Trans. Med. Imaging 28(12), 1881–1893 (2009).
[Crossref] [PubMed]

Boppart, S. A.

Brown, D. J.

N. Morishige, A. J. Wahlert, M. C. Kenney, D. J. Brown, K. Kawamoto, T. Chikama, T. Nishida, and J. V. Jester, “Second-harmonic imaging microscopy of normal human and keratoconus cornea,” Invest. Ophthalmol. Vis. Sci. 48(3), 1087–1094 (2007).
[Crossref] [PubMed]

Chang, E. W.

S. Kling, B. I. Akca, E. W. Chang, G. Scarcelli, N. Bekesi, S. H. Yun, and S. Marcos, “Numerical model of OCT-vibrography imaging to estimate corneal biomechanical properties,” J. R. Soc. Interface 11, 20140920 (2014).
[Crossref] [PubMed]

E. W. Chang, J. T. Cheng, C. Röösli, J. B. Kobler, J. J. Rosowski, and S. H. Yun, “Simultaneous 3D imaging of sound-induced motions of the tympanic membrane and middle ear ossicles,” Hear. Res. 304, 49–56 (2013).
[Crossref] [PubMed]

E. W. Chang, J. B. Kobler, and S. H. Yun, “Subnanometer optical coherence tomographic vibrography,” Opt. Lett. 37(17), 3678–3680 (2012).
[Crossref] [PubMed]

Cheng, J. T.

E. W. Chang, J. T. Cheng, C. Röösli, J. B. Kobler, J. J. Rosowski, and S. H. Yun, “Simultaneous 3D imaging of sound-induced motions of the tympanic membrane and middle ear ossicles,” Hear. Res. 304, 49–56 (2013).
[Crossref] [PubMed]

Chikama, T.

N. Morishige, A. J. Wahlert, M. C. Kenney, D. J. Brown, K. Kawamoto, T. Chikama, T. Nishida, and J. V. Jester, “Second-harmonic imaging microscopy of normal human and keratoconus cornea,” Invest. Ophthalmol. Vis. Sci. 48(3), 1087–1094 (2007).
[Crossref] [PubMed]

Dawson, D. G.

D. G. Dawson, J. B. Randleman, H. E. Grossniklaus, T. P. O’Brien, S. R. Dubovy, I. Schmack, R. D. Stulting, and H. F. Edelhauser, “Corneal ectasia after excimer laser keratorefractive surgery: histopathology, ultrastructure, and pathophysiology,” Ophthalmology 115(12), 2181–2191 (2008).
[Crossref] [PubMed]

Dorronsoro, C.

S. Kling, N. Bekesi, C. Dorronsoro, D. Pascual, and S. Marcos, “Corneal viscoelastic properties from finite-element analysis of in vivo air-puff deformation,” PLoS One 9(8), e104904 (2014).
[Crossref] [PubMed]

C. Dorronsoro, D. Pascual, P. Pérez-Merino, S. Kling, and S. Marcos, “Dynamic OCT measurement of corneal deformation by an air puff in normal and cross-linked corneas,” Biomed. Opt. Express 3(3), 473–487 (2012).
[Crossref] [PubMed]

Dubovy, S. R.

D. G. Dawson, J. B. Randleman, H. E. Grossniklaus, T. P. O’Brien, S. R. Dubovy, I. Schmack, R. D. Stulting, and H. F. Edelhauser, “Corneal ectasia after excimer laser keratorefractive surgery: histopathology, ultrastructure, and pathophysiology,” Ophthalmology 115(12), 2181–2191 (2008).
[Crossref] [PubMed]

Dupps, W. J.

M. R. Ford, W. J. Dupps, A. M. Rollins, A. S. Roy, and Z. Hu, “Method for optical coherence elastography of the cornea,” J. Biomed. Opt. 16(1), 016005 (2011).
[Crossref] [PubMed]

W. J. Dupps and S. E. Wilson, “Biomechanics and wound healing in the cornea,” Exp. Eye Res. 83(4), 709–720 (2006).
[Crossref] [PubMed]

Edelhauser, H. F.

D. G. Dawson, J. B. Randleman, H. E. Grossniklaus, T. P. O’Brien, S. R. Dubovy, I. Schmack, R. D. Stulting, and H. F. Edelhauser, “Corneal ectasia after excimer laser keratorefractive surgery: histopathology, ultrastructure, and pathophysiology,” Ophthalmology 115(12), 2181–2191 (2008).
[Crossref] [PubMed]

Ehman, R. L.

D. V. Litwiller, S. J. Lee, A. Kolipaka, Y. K. Mariappan, K. J. Glaser, J. S. Pulido, and R. L. Ehman, “MR elastography of the ex vivo bovine globe,” J. Magn. Reson. Imaging 32(1), 44–51 (2010).
[Crossref] [PubMed]

Emelianov, S.

Fink, M.

T. M. Nguyen, J. F. Aubry, D. Touboul, M. Fink, J. L. Gennisson, J. Bercoff, and M. Tanter, “Monitoring of cornea elastic properties changes during UV-A/riboflavin-induced corneal collagen cross-linking using supersonic shear wave imaging: a pilot study,” Invest. Ophthalmol. Vis. Sci. 53(9), 5948–5954 (2012).
[Crossref] [PubMed]

M. Tanter, D. Touboul, J. L. Gennisson, J. Bercoff, and M. Fink, “High-resolution quantitative imaging of cornea elasticity using supersonic shear imaging,” IEEE Trans. Med. Imaging 28(12), 1881–1893 (2009).
[Crossref] [PubMed]

Ford, M. R.

M. R. Ford, W. J. Dupps, A. M. Rollins, A. S. Roy, and Z. Hu, “Method for optical coherence elastography of the cornea,” J. Biomed. Opt. 16(1), 016005 (2011).
[Crossref] [PubMed]

Gennisson, J. L.

T. M. Nguyen, J. F. Aubry, D. Touboul, M. Fink, J. L. Gennisson, J. Bercoff, and M. Tanter, “Monitoring of cornea elastic properties changes during UV-A/riboflavin-induced corneal collagen cross-linking using supersonic shear wave imaging: a pilot study,” Invest. Ophthalmol. Vis. Sci. 53(9), 5948–5954 (2012).
[Crossref] [PubMed]

M. Tanter, D. Touboul, J. L. Gennisson, J. Bercoff, and M. Fink, “High-resolution quantitative imaging of cornea elasticity using supersonic shear imaging,” IEEE Trans. Med. Imaging 28(12), 1881–1893 (2009).
[Crossref] [PubMed]

Glaser, K. J.

D. V. Litwiller, S. J. Lee, A. Kolipaka, Y. K. Mariappan, K. J. Glaser, J. S. Pulido, and R. L. Ehman, “MR elastography of the ex vivo bovine globe,” J. Magn. Reson. Imaging 32(1), 44–51 (2010).
[Crossref] [PubMed]

Grossniklaus, H. E.

D. G. Dawson, J. B. Randleman, H. E. Grossniklaus, T. P. O’Brien, S. R. Dubovy, I. Schmack, R. D. Stulting, and H. F. Edelhauser, “Corneal ectasia after excimer laser keratorefractive surgery: histopathology, ultrastructure, and pathophysiology,” Ophthalmology 115(12), 2181–2191 (2008).
[Crossref] [PubMed]

Guan, G.

Han, Z.

Z. Han, J. Li, M. Singh, S. R. Aglyamov, C. Wu, C. H. Liu, and K. V. Larin, “Analysis of the effects of curvature and thickness on elastic wave velocity in cornea-like structures by finite element modeling and optical coherence elastography,” Appl. Phys. Lett. 106(23), 233702 (2015).
[Crossref] [PubMed]

Hjortdal, J.

S. Bak-Nielsen, I. B. Pedersen, A. Ivarsen, and J. Hjortdal, “Dynamic Scheimpflug-based assessment of keratoconus and the effects of corneal cross-linking,” J. Refract. Surg. 30(6), 408–414 (2014).
[Crossref] [PubMed]

Hu, Z.

M. R. Ford, W. J. Dupps, A. M. Rollins, A. S. Roy, and Z. Hu, “Method for optical coherence elastography of the cornea,” J. Biomed. Opt. 16(1), 016005 (2011).
[Crossref] [PubMed]

Huang, Z.

T. M. Nguyen, S. Song, B. Arnal, E. Y. Wong, Z. Huang, R. K. Wang, and M. O’Donnell, “Shear wave pulse compression for dynamic elastography using phase-sensitive optical coherence tomography,” J. Biomed. Opt. 19(1), 016013 (2014).
[Crossref] [PubMed]

C. Li, G. Guan, Z. Huang, M. Johnstone, and R. K. Wang, “Noncontact all-optical measurement of corneal elasticity,” Opt. Lett. 37(10), 1625–1627 (2012).
[Crossref] [PubMed]

Ivarsen, A.

S. Bak-Nielsen, I. B. Pedersen, A. Ivarsen, and J. Hjortdal, “Dynamic Scheimpflug-based assessment of keratoconus and the effects of corneal cross-linking,” J. Refract. Surg. 30(6), 408–414 (2014).
[Crossref] [PubMed]

Jester, J. V.

N. Morishige, A. J. Wahlert, M. C. Kenney, D. J. Brown, K. Kawamoto, T. Chikama, T. Nishida, and J. V. Jester, “Second-harmonic imaging microscopy of normal human and keratoconus cornea,” Invest. Ophthalmol. Vis. Sci. 48(3), 1087–1094 (2007).
[Crossref] [PubMed]

John, R.

Johnstone, M.

Kawamoto, K.

N. Morishige, A. J. Wahlert, M. C. Kenney, D. J. Brown, K. Kawamoto, T. Chikama, T. Nishida, and J. V. Jester, “Second-harmonic imaging microscopy of normal human and keratoconus cornea,” Invest. Ophthalmol. Vis. Sci. 48(3), 1087–1094 (2007).
[Crossref] [PubMed]

Kennedy, B. F.

B. F. Kennedy, K. M. Kennedy, and D. D. Sampson, “A review of optical coherence elastography: fundamentals, techniques and prospects,” IEEE J. Sel. Top. Quantum Electron. 20(2), 272 (2014).
[Crossref]

S. G. Adie, X. Liang, B. F. Kennedy, R. John, D. D. Sampson, and S. A. Boppart, “Spectroscopic optical coherence elastography,” Opt. Express 18(25), 25519–25534 (2010).
[Crossref] [PubMed]

Kennedy, K. M.

B. F. Kennedy, K. M. Kennedy, and D. D. Sampson, “A review of optical coherence elastography: fundamentals, techniques and prospects,” IEEE J. Sel. Top. Quantum Electron. 20(2), 272 (2014).
[Crossref]

Kenney, M. C.

N. Morishige, A. J. Wahlert, M. C. Kenney, D. J. Brown, K. Kawamoto, T. Chikama, T. Nishida, and J. V. Jester, “Second-harmonic imaging microscopy of normal human and keratoconus cornea,” Invest. Ophthalmol. Vis. Sci. 48(3), 1087–1094 (2007).
[Crossref] [PubMed]

Kirwan, C.

C. Kirwan, D. O’Malley, and M. O’Keefe, “Corneal hysteresis and corneal resistance factor in keratoectasia: findings using the Reichert ocular response analyzer,” Ophthalmologica 222(5), 334–337 (2008).
[Crossref] [PubMed]

Kling, S.

S. Kling, N. Bekesi, C. Dorronsoro, D. Pascual, and S. Marcos, “Corneal viscoelastic properties from finite-element analysis of in vivo air-puff deformation,” PLoS One 9(8), e104904 (2014).
[Crossref] [PubMed]

S. Kling, B. I. Akca, E. W. Chang, G. Scarcelli, N. Bekesi, S. H. Yun, and S. Marcos, “Numerical model of OCT-vibrography imaging to estimate corneal biomechanical properties,” J. R. Soc. Interface 11, 20140920 (2014).
[Crossref] [PubMed]

C. Dorronsoro, D. Pascual, P. Pérez-Merino, S. Kling, and S. Marcos, “Dynamic OCT measurement of corneal deformation by an air puff in normal and cross-linked corneas,” Biomed. Opt. Express 3(3), 473–487 (2012).
[Crossref] [PubMed]

Kobler, J. B.

E. W. Chang, J. T. Cheng, C. Röösli, J. B. Kobler, J. J. Rosowski, and S. H. Yun, “Simultaneous 3D imaging of sound-induced motions of the tympanic membrane and middle ear ossicles,” Hear. Res. 304, 49–56 (2013).
[Crossref] [PubMed]

E. W. Chang, J. B. Kobler, and S. H. Yun, “Subnanometer optical coherence tomographic vibrography,” Opt. Lett. 37(17), 3678–3680 (2012).
[Crossref] [PubMed]

Kolipaka, A.

D. V. Litwiller, S. J. Lee, A. Kolipaka, Y. K. Mariappan, K. J. Glaser, J. S. Pulido, and R. L. Ehman, “MR elastography of the ex vivo bovine globe,” J. Magn. Reson. Imaging 32(1), 44–51 (2010).
[Crossref] [PubMed]

Larin, K. V.

Lee, S. J.

D. V. Litwiller, S. J. Lee, A. Kolipaka, Y. K. Mariappan, K. J. Glaser, J. S. Pulido, and R. L. Ehman, “MR elastography of the ex vivo bovine globe,” J. Magn. Reson. Imaging 32(1), 44–51 (2010).
[Crossref] [PubMed]

Li, C.

Li, J.

Z. Han, J. Li, M. Singh, S. R. Aglyamov, C. Wu, C. H. Liu, and K. V. Larin, “Analysis of the effects of curvature and thickness on elastic wave velocity in cornea-like structures by finite element modeling and optical coherence elastography,” Appl. Phys. Lett. 106(23), 233702 (2015).
[Crossref] [PubMed]

M. D. Twa, J. Li, S. Vantipalli, M. Singh, S. Aglyamov, S. Emelianov, and K. V. Larin, “Spatial characterization of corneal biomechanical properties with optical coherence elastography after UV cross-linking,” Biomed. Opt. Express 5(5), 1419–1427 (2014).
[Crossref] [PubMed]

Liang, X.

Litwiller, D. V.

D. V. Litwiller, S. J. Lee, A. Kolipaka, Y. K. Mariappan, K. J. Glaser, J. S. Pulido, and R. L. Ehman, “MR elastography of the ex vivo bovine globe,” J. Magn. Reson. Imaging 32(1), 44–51 (2010).
[Crossref] [PubMed]

Liu, C. H.

Z. Han, J. Li, M. Singh, S. R. Aglyamov, C. Wu, C. H. Liu, and K. V. Larin, “Analysis of the effects of curvature and thickness on elastic wave velocity in cornea-like structures by finite element modeling and optical coherence elastography,” Appl. Phys. Lett. 106(23), 233702 (2015).
[Crossref] [PubMed]

Luce, D. A.

D. A. Luce, “Determining in vivo biomechanical properties of the cornea with an ocular response analyzer,” J. Cataract Refract. Surg. 31(1), 156–162 (2005).
[Crossref] [PubMed]

Marcos, S.

S. Kling, N. Bekesi, C. Dorronsoro, D. Pascual, and S. Marcos, “Corneal viscoelastic properties from finite-element analysis of in vivo air-puff deformation,” PLoS One 9(8), e104904 (2014).
[Crossref] [PubMed]

S. Kling, B. I. Akca, E. W. Chang, G. Scarcelli, N. Bekesi, S. H. Yun, and S. Marcos, “Numerical model of OCT-vibrography imaging to estimate corneal biomechanical properties,” J. R. Soc. Interface 11, 20140920 (2014).
[Crossref] [PubMed]

C. Dorronsoro, D. Pascual, P. Pérez-Merino, S. Kling, and S. Marcos, “Dynamic OCT measurement of corneal deformation by an air puff in normal and cross-linked corneas,” Biomed. Opt. Express 3(3), 473–487 (2012).
[Crossref] [PubMed]

Mariappan, Y. K.

D. V. Litwiller, S. J. Lee, A. Kolipaka, Y. K. Mariappan, K. J. Glaser, J. S. Pulido, and R. L. Ehman, “MR elastography of the ex vivo bovine globe,” J. Magn. Reson. Imaging 32(1), 44–51 (2010).
[Crossref] [PubMed]

Morishige, N.

N. Morishige, A. J. Wahlert, M. C. Kenney, D. J. Brown, K. Kawamoto, T. Chikama, T. Nishida, and J. V. Jester, “Second-harmonic imaging microscopy of normal human and keratoconus cornea,” Invest. Ophthalmol. Vis. Sci. 48(3), 1087–1094 (2007).
[Crossref] [PubMed]

Nguyen, T. M.

T. M. Nguyen, S. Song, B. Arnal, E. Y. Wong, Z. Huang, R. K. Wang, and M. O’Donnell, “Shear wave pulse compression for dynamic elastography using phase-sensitive optical coherence tomography,” J. Biomed. Opt. 19(1), 016013 (2014).
[Crossref] [PubMed]

T. M. Nguyen, J. F. Aubry, D. Touboul, M. Fink, J. L. Gennisson, J. Bercoff, and M. Tanter, “Monitoring of cornea elastic properties changes during UV-A/riboflavin-induced corneal collagen cross-linking using supersonic shear wave imaging: a pilot study,” Invest. Ophthalmol. Vis. Sci. 53(9), 5948–5954 (2012).
[Crossref] [PubMed]

Nishida, T.

N. Morishige, A. J. Wahlert, M. C. Kenney, D. J. Brown, K. Kawamoto, T. Chikama, T. Nishida, and J. V. Jester, “Second-harmonic imaging microscopy of normal human and keratoconus cornea,” Invest. Ophthalmol. Vis. Sci. 48(3), 1087–1094 (2007).
[Crossref] [PubMed]

O’Brien, T. P.

D. G. Dawson, J. B. Randleman, H. E. Grossniklaus, T. P. O’Brien, S. R. Dubovy, I. Schmack, R. D. Stulting, and H. F. Edelhauser, “Corneal ectasia after excimer laser keratorefractive surgery: histopathology, ultrastructure, and pathophysiology,” Ophthalmology 115(12), 2181–2191 (2008).
[Crossref] [PubMed]

O’Donnell, M.

T. M. Nguyen, S. Song, B. Arnal, E. Y. Wong, Z. Huang, R. K. Wang, and M. O’Donnell, “Shear wave pulse compression for dynamic elastography using phase-sensitive optical coherence tomography,” J. Biomed. Opt. 19(1), 016013 (2014).
[Crossref] [PubMed]

O’Keefe, M.

C. Kirwan, D. O’Malley, and M. O’Keefe, “Corneal hysteresis and corneal resistance factor in keratoectasia: findings using the Reichert ocular response analyzer,” Ophthalmologica 222(5), 334–337 (2008).
[Crossref] [PubMed]

O’Malley, D.

C. Kirwan, D. O’Malley, and M. O’Keefe, “Corneal hysteresis and corneal resistance factor in keratoectasia: findings using the Reichert ocular response analyzer,” Ophthalmologica 222(5), 334–337 (2008).
[Crossref] [PubMed]

Pascual, D.

S. Kling, N. Bekesi, C. Dorronsoro, D. Pascual, and S. Marcos, “Corneal viscoelastic properties from finite-element analysis of in vivo air-puff deformation,” PLoS One 9(8), e104904 (2014).
[Crossref] [PubMed]

C. Dorronsoro, D. Pascual, P. Pérez-Merino, S. Kling, and S. Marcos, “Dynamic OCT measurement of corneal deformation by an air puff in normal and cross-linked corneas,” Biomed. Opt. Express 3(3), 473–487 (2012).
[Crossref] [PubMed]

Pedersen, I. B.

S. Bak-Nielsen, I. B. Pedersen, A. Ivarsen, and J. Hjortdal, “Dynamic Scheimpflug-based assessment of keratoconus and the effects of corneal cross-linking,” J. Refract. Surg. 30(6), 408–414 (2014).
[Crossref] [PubMed]

Pérez-Merino, P.

Pulido, J. S.

D. V. Litwiller, S. J. Lee, A. Kolipaka, Y. K. Mariappan, K. J. Glaser, J. S. Pulido, and R. L. Ehman, “MR elastography of the ex vivo bovine globe,” J. Magn. Reson. Imaging 32(1), 44–51 (2010).
[Crossref] [PubMed]

Randleman, J. B.

D. G. Dawson, J. B. Randleman, H. E. Grossniklaus, T. P. O’Brien, S. R. Dubovy, I. Schmack, R. D. Stulting, and H. F. Edelhauser, “Corneal ectasia after excimer laser keratorefractive surgery: histopathology, ultrastructure, and pathophysiology,” Ophthalmology 115(12), 2181–2191 (2008).
[Crossref] [PubMed]

Rollins, A. M.

M. R. Ford, W. J. Dupps, A. M. Rollins, A. S. Roy, and Z. Hu, “Method for optical coherence elastography of the cornea,” J. Biomed. Opt. 16(1), 016005 (2011).
[Crossref] [PubMed]

Röösli, C.

E. W. Chang, J. T. Cheng, C. Röösli, J. B. Kobler, J. J. Rosowski, and S. H. Yun, “Simultaneous 3D imaging of sound-induced motions of the tympanic membrane and middle ear ossicles,” Hear. Res. 304, 49–56 (2013).
[Crossref] [PubMed]

Rosowski, J. J.

E. W. Chang, J. T. Cheng, C. Röösli, J. B. Kobler, J. J. Rosowski, and S. H. Yun, “Simultaneous 3D imaging of sound-induced motions of the tympanic membrane and middle ear ossicles,” Hear. Res. 304, 49–56 (2013).
[Crossref] [PubMed]

Roy, A. S.

M. R. Ford, W. J. Dupps, A. M. Rollins, A. S. Roy, and Z. Hu, “Method for optical coherence elastography of the cornea,” J. Biomed. Opt. 16(1), 016005 (2011).
[Crossref] [PubMed]

Sampson, D. D.

B. F. Kennedy, K. M. Kennedy, and D. D. Sampson, “A review of optical coherence elastography: fundamentals, techniques and prospects,” IEEE J. Sel. Top. Quantum Electron. 20(2), 272 (2014).
[Crossref]

S. G. Adie, X. Liang, B. F. Kennedy, R. John, D. D. Sampson, and S. A. Boppart, “Spectroscopic optical coherence elastography,” Opt. Express 18(25), 25519–25534 (2010).
[Crossref] [PubMed]

Scarcelli, G.

S. Kling, B. I. Akca, E. W. Chang, G. Scarcelli, N. Bekesi, S. H. Yun, and S. Marcos, “Numerical model of OCT-vibrography imaging to estimate corneal biomechanical properties,” J. R. Soc. Interface 11, 20140920 (2014).
[Crossref] [PubMed]

G. Scarcelli and S. H. Yun, “Confocal Brillouin microscopy for three-dimensional mechanical imaging,” Nat. Photonics 2(1), 39–43 (2008).
[Crossref] [PubMed]

Schmack, I.

D. G. Dawson, J. B. Randleman, H. E. Grossniklaus, T. P. O’Brien, S. R. Dubovy, I. Schmack, R. D. Stulting, and H. F. Edelhauser, “Corneal ectasia after excimer laser keratorefractive surgery: histopathology, ultrastructure, and pathophysiology,” Ophthalmology 115(12), 2181–2191 (2008).
[Crossref] [PubMed]

Seiler, T.

G. Wollensak, E. Spoerl, and T. Seiler, “Riboflavin/ultraviolet-A-induced collagen crosslinking for the treatment of keratoconus,” Am. J. Ophthalmol. 135(5), 620–627 (2003).
[Crossref] [PubMed]

Singh, M.

Z. Han, J. Li, M. Singh, S. R. Aglyamov, C. Wu, C. H. Liu, and K. V. Larin, “Analysis of the effects of curvature and thickness on elastic wave velocity in cornea-like structures by finite element modeling and optical coherence elastography,” Appl. Phys. Lett. 106(23), 233702 (2015).
[Crossref] [PubMed]

M. D. Twa, J. Li, S. Vantipalli, M. Singh, S. Aglyamov, S. Emelianov, and K. V. Larin, “Spatial characterization of corneal biomechanical properties with optical coherence elastography after UV cross-linking,” Biomed. Opt. Express 5(5), 1419–1427 (2014).
[Crossref] [PubMed]

Song, S.

T. M. Nguyen, S. Song, B. Arnal, E. Y. Wong, Z. Huang, R. K. Wang, and M. O’Donnell, “Shear wave pulse compression for dynamic elastography using phase-sensitive optical coherence tomography,” J. Biomed. Opt. 19(1), 016013 (2014).
[Crossref] [PubMed]

Spoerl, E.

G. Wollensak, E. Spoerl, and T. Seiler, “Riboflavin/ultraviolet-A-induced collagen crosslinking for the treatment of keratoconus,” Am. J. Ophthalmol. 135(5), 620–627 (2003).
[Crossref] [PubMed]

Stulting, R. D.

D. G. Dawson, J. B. Randleman, H. E. Grossniklaus, T. P. O’Brien, S. R. Dubovy, I. Schmack, R. D. Stulting, and H. F. Edelhauser, “Corneal ectasia after excimer laser keratorefractive surgery: histopathology, ultrastructure, and pathophysiology,” Ophthalmology 115(12), 2181–2191 (2008).
[Crossref] [PubMed]

Tanter, M.

T. M. Nguyen, J. F. Aubry, D. Touboul, M. Fink, J. L. Gennisson, J. Bercoff, and M. Tanter, “Monitoring of cornea elastic properties changes during UV-A/riboflavin-induced corneal collagen cross-linking using supersonic shear wave imaging: a pilot study,” Invest. Ophthalmol. Vis. Sci. 53(9), 5948–5954 (2012).
[Crossref] [PubMed]

M. Tanter, D. Touboul, J. L. Gennisson, J. Bercoff, and M. Fink, “High-resolution quantitative imaging of cornea elasticity using supersonic shear imaging,” IEEE Trans. Med. Imaging 28(12), 1881–1893 (2009).
[Crossref] [PubMed]

Touboul, D.

T. M. Nguyen, J. F. Aubry, D. Touboul, M. Fink, J. L. Gennisson, J. Bercoff, and M. Tanter, “Monitoring of cornea elastic properties changes during UV-A/riboflavin-induced corneal collagen cross-linking using supersonic shear wave imaging: a pilot study,” Invest. Ophthalmol. Vis. Sci. 53(9), 5948–5954 (2012).
[Crossref] [PubMed]

M. Tanter, D. Touboul, J. L. Gennisson, J. Bercoff, and M. Fink, “High-resolution quantitative imaging of cornea elasticity using supersonic shear imaging,” IEEE Trans. Med. Imaging 28(12), 1881–1893 (2009).
[Crossref] [PubMed]

Twa, M. D.

Vantipalli, S.

Wahlert, A. J.

N. Morishige, A. J. Wahlert, M. C. Kenney, D. J. Brown, K. Kawamoto, T. Chikama, T. Nishida, and J. V. Jester, “Second-harmonic imaging microscopy of normal human and keratoconus cornea,” Invest. Ophthalmol. Vis. Sci. 48(3), 1087–1094 (2007).
[Crossref] [PubMed]

Wang, R. K.

T. M. Nguyen, S. Song, B. Arnal, E. Y. Wong, Z. Huang, R. K. Wang, and M. O’Donnell, “Shear wave pulse compression for dynamic elastography using phase-sensitive optical coherence tomography,” J. Biomed. Opt. 19(1), 016013 (2014).
[Crossref] [PubMed]

C. Li, G. Guan, Z. Huang, M. Johnstone, and R. K. Wang, “Noncontact all-optical measurement of corneal elasticity,” Opt. Lett. 37(10), 1625–1627 (2012).
[Crossref] [PubMed]

Wang, S.

Wilson, S. E.

W. J. Dupps and S. E. Wilson, “Biomechanics and wound healing in the cornea,” Exp. Eye Res. 83(4), 709–720 (2006).
[Crossref] [PubMed]

Wollensak, G.

G. Wollensak, E. Spoerl, and T. Seiler, “Riboflavin/ultraviolet-A-induced collagen crosslinking for the treatment of keratoconus,” Am. J. Ophthalmol. 135(5), 620–627 (2003).
[Crossref] [PubMed]

Wong, E. Y.

T. M. Nguyen, S. Song, B. Arnal, E. Y. Wong, Z. Huang, R. K. Wang, and M. O’Donnell, “Shear wave pulse compression for dynamic elastography using phase-sensitive optical coherence tomography,” J. Biomed. Opt. 19(1), 016013 (2014).
[Crossref] [PubMed]

Wu, C.

Z. Han, J. Li, M. Singh, S. R. Aglyamov, C. Wu, C. H. Liu, and K. V. Larin, “Analysis of the effects of curvature and thickness on elastic wave velocity in cornea-like structures by finite element modeling and optical coherence elastography,” Appl. Phys. Lett. 106(23), 233702 (2015).
[Crossref] [PubMed]

Yun, S. H.

S. Kling, B. I. Akca, E. W. Chang, G. Scarcelli, N. Bekesi, S. H. Yun, and S. Marcos, “Numerical model of OCT-vibrography imaging to estimate corneal biomechanical properties,” J. R. Soc. Interface 11, 20140920 (2014).
[Crossref] [PubMed]

E. W. Chang, J. T. Cheng, C. Röösli, J. B. Kobler, J. J. Rosowski, and S. H. Yun, “Simultaneous 3D imaging of sound-induced motions of the tympanic membrane and middle ear ossicles,” Hear. Res. 304, 49–56 (2013).
[Crossref] [PubMed]

E. W. Chang, J. B. Kobler, and S. H. Yun, “Subnanometer optical coherence tomographic vibrography,” Opt. Lett. 37(17), 3678–3680 (2012).
[Crossref] [PubMed]

G. Scarcelli and S. H. Yun, “Confocal Brillouin microscopy for three-dimensional mechanical imaging,” Nat. Photonics 2(1), 39–43 (2008).
[Crossref] [PubMed]

Am. J. Ophthalmol. (1)

G. Wollensak, E. Spoerl, and T. Seiler, “Riboflavin/ultraviolet-A-induced collagen crosslinking for the treatment of keratoconus,” Am. J. Ophthalmol. 135(5), 620–627 (2003).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

Z. Han, J. Li, M. Singh, S. R. Aglyamov, C. Wu, C. H. Liu, and K. V. Larin, “Analysis of the effects of curvature and thickness on elastic wave velocity in cornea-like structures by finite element modeling and optical coherence elastography,” Appl. Phys. Lett. 106(23), 233702 (2015).
[Crossref] [PubMed]

Biomed. Opt. Express (2)

Exp. Eye Res. (1)

W. J. Dupps and S. E. Wilson, “Biomechanics and wound healing in the cornea,” Exp. Eye Res. 83(4), 709–720 (2006).
[Crossref] [PubMed]

Hear. Res. (1)

E. W. Chang, J. T. Cheng, C. Röösli, J. B. Kobler, J. J. Rosowski, and S. H. Yun, “Simultaneous 3D imaging of sound-induced motions of the tympanic membrane and middle ear ossicles,” Hear. Res. 304, 49–56 (2013).
[Crossref] [PubMed]

IEEE J. Sel. Top. Quantum Electron. (1)

B. F. Kennedy, K. M. Kennedy, and D. D. Sampson, “A review of optical coherence elastography: fundamentals, techniques and prospects,” IEEE J. Sel. Top. Quantum Electron. 20(2), 272 (2014).
[Crossref]

IEEE Trans. Med. Imaging (1)

M. Tanter, D. Touboul, J. L. Gennisson, J. Bercoff, and M. Fink, “High-resolution quantitative imaging of cornea elasticity using supersonic shear imaging,” IEEE Trans. Med. Imaging 28(12), 1881–1893 (2009).
[Crossref] [PubMed]

Invest. Ophthalmol. Vis. Sci. (2)

N. Morishige, A. J. Wahlert, M. C. Kenney, D. J. Brown, K. Kawamoto, T. Chikama, T. Nishida, and J. V. Jester, “Second-harmonic imaging microscopy of normal human and keratoconus cornea,” Invest. Ophthalmol. Vis. Sci. 48(3), 1087–1094 (2007).
[Crossref] [PubMed]

T. M. Nguyen, J. F. Aubry, D. Touboul, M. Fink, J. L. Gennisson, J. Bercoff, and M. Tanter, “Monitoring of cornea elastic properties changes during UV-A/riboflavin-induced corneal collagen cross-linking using supersonic shear wave imaging: a pilot study,” Invest. Ophthalmol. Vis. Sci. 53(9), 5948–5954 (2012).
[Crossref] [PubMed]

J. Biomed. Opt. (2)

M. R. Ford, W. J. Dupps, A. M. Rollins, A. S. Roy, and Z. Hu, “Method for optical coherence elastography of the cornea,” J. Biomed. Opt. 16(1), 016005 (2011).
[Crossref] [PubMed]

T. M. Nguyen, S. Song, B. Arnal, E. Y. Wong, Z. Huang, R. K. Wang, and M. O’Donnell, “Shear wave pulse compression for dynamic elastography using phase-sensitive optical coherence tomography,” J. Biomed. Opt. 19(1), 016013 (2014).
[Crossref] [PubMed]

J. Cataract Refract. Surg. (1)

D. A. Luce, “Determining in vivo biomechanical properties of the cornea with an ocular response analyzer,” J. Cataract Refract. Surg. 31(1), 156–162 (2005).
[Crossref] [PubMed]

J. Magn. Reson. Imaging (1)

D. V. Litwiller, S. J. Lee, A. Kolipaka, Y. K. Mariappan, K. J. Glaser, J. S. Pulido, and R. L. Ehman, “MR elastography of the ex vivo bovine globe,” J. Magn. Reson. Imaging 32(1), 44–51 (2010).
[Crossref] [PubMed]

J. R. Soc. Interface (1)

S. Kling, B. I. Akca, E. W. Chang, G. Scarcelli, N. Bekesi, S. H. Yun, and S. Marcos, “Numerical model of OCT-vibrography imaging to estimate corneal biomechanical properties,” J. R. Soc. Interface 11, 20140920 (2014).
[Crossref] [PubMed]

J. Refract. Surg. (1)

S. Bak-Nielsen, I. B. Pedersen, A. Ivarsen, and J. Hjortdal, “Dynamic Scheimpflug-based assessment of keratoconus and the effects of corneal cross-linking,” J. Refract. Surg. 30(6), 408–414 (2014).
[Crossref] [PubMed]

Nat. Photonics (1)

G. Scarcelli and S. H. Yun, “Confocal Brillouin microscopy for three-dimensional mechanical imaging,” Nat. Photonics 2(1), 39–43 (2008).
[Crossref] [PubMed]

Ophthalmologica (1)

C. Kirwan, D. O’Malley, and M. O’Keefe, “Corneal hysteresis and corneal resistance factor in keratoectasia: findings using the Reichert ocular response analyzer,” Ophthalmologica 222(5), 334–337 (2008).
[Crossref] [PubMed]

Ophthalmology (1)

D. G. Dawson, J. B. Randleman, H. E. Grossniklaus, T. P. O’Brien, S. R. Dubovy, I. Schmack, R. D. Stulting, and H. F. Edelhauser, “Corneal ectasia after excimer laser keratorefractive surgery: histopathology, ultrastructure, and pathophysiology,” Ophthalmology 115(12), 2181–2191 (2008).
[Crossref] [PubMed]

Opt. Express (1)

Opt. Lett. (3)

PLoS One (1)

S. Kling, N. Bekesi, C. Dorronsoro, D. Pascual, and S. Marcos, “Corneal viscoelastic properties from finite-element analysis of in vivo air-puff deformation,” PLoS One 9(8), e104904 (2014).
[Crossref] [PubMed]

Other (2)

D. J. Ewins, Modal Testing: theory, practice and application (Wiley, 2001).

S. S. Rao, Vibration of continuous systems (Wiley, 2007).

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Figures (7)

Fig. 1
Fig. 1 Methods for analyzing the mechanical stability of the cornea. (a) A simple model of the cornea under in-plane membrane tension and IOP. (b) Conventional air-puff method. (c) The proposed method based on sound-induced vibrations.
Fig. 2
Fig. 2 (a) Schematic of the experimental setup. The sound wave emitted from a loudspeaker is directed toward the eyeball, and the motion of the cornea is captured and recorded by the OCT system. A needle syringe connected to a water column (not shown in this picture) is placed into the globe, by which the IOP was set to 6 mmHg. (b) Signal processing sequence for the measurement of vibration spectrum at a fixed spatial location in the cornea. (c) Signal processing sequence to generate vibrography images at a specific sound frequency.
Fig. 3
Fig. 3 Frequency-domain response. (a) The amplitude of sound-induced vibration measured at the center of the cornea in a bovine eye globe ex vivo, in comparison with the vibration of the sample mount. (b) The induced stress calculated from the amplitude spectra. There are three distinct resonance peaks at 86, 200, and 310 Hz, respectively, which correspond to the first three symmetric modes, [0,1], [0,2], and [0,3] modes. The SPL was 100 dB.
Fig. 4
Fig. 4 Resonance frequencies of 12 bovine eyeballs ex vivo. (a) Frequency response curves of four sample groups divided by their weights and ages (unspecified). Each group consists of three eyeballs with similar weights (the mean value is given). For each eyeball, the resonance frequencies of three modes—[0,1], [0,2] and [0,3]—are plotted. (b) The ratio of the resonance frequencies of the [0,2] or [0,3] mode to the fundamental [0,1] mode. Dotted lines, linear fit.
Fig. 5
Fig. 5 Experimentally measured vibration modes of the bovine cornea. The timing of the snapshot images corresponds to a zero phase when the potential energy of vibration is the maximum. (a) Cross-sectional OCT vibrography images for sound frequencies at 86 Hz, 200 Hz, and 310 Hz. (b) 3-D rendered vibrography images. Color scale represents anterior-posterior (vertical, upward normal to the corneal surface) displacement.
Fig. 6
Fig. 6 (a) A schematic of the eye model used in numerical finite-element analysis. Vibration excited by sound pressure is primarily localized in the cornea. Vibration of the aqueous humor (fluid) is also seen. (b) Simulation reproduces three resonance peaks in good agreement with the experiments results.
Fig. 7
Fig. 7 Simulated vibration modes. (a) Cross-sectional vibration profile for sound frequencies at 86, 200, and 310 Hz, respectively. (b) 3-D rendered vibration modes with exaggerated deformation. The color scale represents normalized anterior-posterior (vertical) displacement.

Equations (1)

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f m,n = λ m,n 2πa V m,n .

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