Abstract

Since the characterization of the eye’s monochromatic aberration fluctuations in 2001, the power spectrum has remained the most widely used method for analyzing their dynamics. However, the power spectrum does not capture the complexities of the fluctuations. We measured the monochromatic aberration dynamics of six subjects using a Shack-Hartmann sensor sampling at 21 Hz. We characterized the dynamics using techniques from chaos theory. We found that the attractor embedding dimension for all aberrations, for all subjects, was equal to three. The embedding lag averaged across aberrations and subjects was 0.31 ± 0.07 s. The Lyapunov exponent of the rms wavefront error was positive for each subject, with an average value of 0.44 ± 0.15 µm/s. This indicates that the aberration dynamics are chaotic. Implications for future modeling are discussed.

© 2012 OSA

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2012 (1)

2011 (2)

K. M. Hampson and E. A. H. Mallen, “Multifractal nature of ocular aberration dynamics of the human eye,” Biomed. Opt. Express2(3), 464–470 (2011).
[CrossRef] [PubMed]

B. B. Ferreira, A. S. de Paula, and M. A. Savi, “Chaos control applied to heart rhythm dynamics,” Chaos Solitons Fractals44(8), 587–599 (2011).
[CrossRef]

2010 (3)

Z. Liu, “Chaotic time series analysis,” Math. Probl. Eng.2010, 720190 (2010).
[CrossRef]

M. Muma, D. R. Iskander, and M. J. Collins, “The role of cardiopulmonary signals in the dynamics of the eye’s wavefront aberrations,” IEEE Trans. Biomed. Eng.57(2), 373–383 (2010).
[CrossRef] [PubMed]

C. Leahy and C. Dainty, “A non-stationary model for simulating the dynamics of ocular aberrations,” Opt. Express18(20), 21386–21396 (2010).
[CrossRef] [PubMed]

2009 (3)

A. Mira-Agudelo, L. Lundström, and P. Artal, “Temporal dynamics of ocular aberrations: monocular vs binocular vision,” Ophthalmic Physiol. Opt.29(3), 256–263 (2009).
[CrossRef] [PubMed]

M. Day, D. Seidel, L. S. Gray, and N. C. Strang, “The effect of modulating ocular depth of focus upon accommodation microfluctuations in myopic and emmetropic subjects,” Vision Res.49(2), 211–218 (2009).
[CrossRef] [PubMed]

E. Gambra, L. Sawides, C. Dorronsoro, and S. Marcos, “Accommodative lag and fluctuations when optical aberrations are manipulated,” J. Vis.9(6), 4 (2009).
[CrossRef] [PubMed]

2008 (4)

Z. Y. Su, T. Wu, P. H. Yang, and Y. T. Wang, “Dynamic analysis of heartbeat rate signals of epileptics using multidimensional phase space reconstruction approach,” Physica A387(10), 2293–2305 (2008).
[CrossRef]

K. M. Hampson, S. S. Chin, and E. A. H. Mallen, “Binocular Shack-Hartmann sensor for the human eye,” J. Mod. Opt.55(4-5), 703–716 (2008).
[CrossRef]

K. M. Hampson, “Adaptive optics and vision,” J. Mod. Opt.55(21), 3425–3467 (2008).
[CrossRef]

S. S. Chin, K. M. Hampson, and E. A. H. Mallen, “Binocular correlation of ocular aberration dynamics,” Opt. Express16(19), 14731–14745 (2008).
[CrossRef] [PubMed]

2007 (1)

2006 (2)

K. M. Hampson, E. A. H. Mallen, and C. Dainty, “Coherence function analysis of the higher-order aberrations of the human eye,” Opt. Lett.31(2), 184–186 (2006).
[CrossRef] [PubMed]

M. Zhu, M. J. Collins, and D. R. Iskander, “The contribution of accommodation and the ocular surface to the microfluctuations of wavefront aberrations of the eye,” Ophthalmic Physiol. Opt.26(5), 439–446 (2006).
[CrossRef] [PubMed]

2005 (5)

M. A. Savi, “Chaos and order in biomedical rhythms,” J. Braz. Soc. Mech. Sci. Eng.27(2), 157–169 (2005).
[CrossRef]

S. Plainis, H. S. Ginis, and A. Pallikaris, “The effect of ocular aberrations on steady-state errors of accommodative response,” J. Vis.5(5), 7 (2005).
[CrossRef] [PubMed]

L. N. Davies, J. S. Wolffsohn, and B. Gilmartin, “Cognition, ocular accommodation, and cardiovascular function in emmetropes and late-onset myopes,” Invest. Ophthalmol. Vis. Sci.46(5), 1791–1796 (2005).
[CrossRef] [PubMed]

K. M. Hampson, I. Munro, C. Paterson, and C. Dainty, “Weak correlation between the aberration dynamics of the human eye and the cardiopulmonary system,” J. Opt. Soc. Am. A22(7), 1241–1250 (2005).
[CrossRef] [PubMed]

S. Gruppetta, F. Lacombe, and P. Puget, “Study of the dynamic aberrations of the human tear film,” Opt. Express13(19), 7631–7636 (2005).
[CrossRef] [PubMed]

2004 (2)

L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, “Accuracy and precision of objective refraction from wavefront aberrations,” J. Vis.4(4), 9 (2004).
[CrossRef] [PubMed]

M. Zhu, M. J. Collins, and D. Robert Iskander, “Microfluctuations of wavefront aberrations of the eye,” Ophthalmic Physiol. Opt.24(6), 562–571 (2004).
[CrossRef] [PubMed]

2003 (3)

2001 (1)

1999 (1)

M. L. Rosenberg and M. H. Kroll, “Pupillary hippus: an unrecognized example of biological chaos,” J. Biol. Syst.7(01), 85–94 (1999).
[CrossRef]

1997 (2)

A. Casaleggio, S. Cerutti, and M. G. Signorini, “Study of the Lyapunov exponents in heart rate variability signals,” Methods Inf. Med.36(4-5), 274–277 (1997).
[PubMed]

C. S. Poon and C. K. Merrill, “Decrease of cardiac chaos in congestive heart failure,” Nature389(6650), 492–495 (1997).
[CrossRef] [PubMed]

1996 (1)

C. D. Wagner, B. Nafz, and P. B. Persson, “Chaos in blood pressure control,” Cardiovasc. Res.31(3), 380–387 (1996).
[PubMed]

1995 (2)

L. F. Schmetterer, F. Lexer, C. J. Unfried, H. Sattmann, and A. F. Fercher, “Topical measurement of fundus pulsations,” Opt. Eng.34(3), 711–716 (1995).
[CrossRef]

M. Collins, B. Davis, and J. Wood, “Microfluctuations of steady-state accommodation and the cardiopulmonary system,” Vision Res.35(17), 2491–2502 (1995).
[PubMed]

1994 (2)

S. J. Schiff, K. Jerger, D. H. Duong, T. Chang, M. L. Spano, and W. L. Ditto, “Controlling chaos in the brain,” Nature370(6491), 615–620 (1994).
[CrossRef] [PubMed]

A. S. Eadie, B. Winn, and J. R. Pugh, “The influence of arterial pulse on miniature eye movements,” Invest. Ophthalmol. Vis. Sci.35, 2037 (1994).

1993 (2)

M. T. Rosenstein, J. J. Collins, and C. J. De Luca, “A practical method for calculating largest Lyapunov exponents from small data sets,” Physica D65(1-2), 117–134 (1993).
[CrossRef]

R. E. Ganz, G. Weibels, K. H. Stäcker, P. M. Faustmann, and C. W. Zimmermann, “The Lyapunov exponent of heart rate dynamics as a sensitive marker of central autonomic organization: an exemplary study of early multiple sclerosis,” Int. J. Neurosci.71(1-4), 29–36 (1993).
[CrossRef] [PubMed]

1992 (2)

M. B. Kennel, R. Brown, and H. D. I. Abarbanel, “Determining embedding dimension for phase-space reconstruction using a geometrical construction,” Phys. Rev. A45(6), 3403–3411 (1992).
[CrossRef] [PubMed]

W. S. Pritchard and D. W. Duke, “Measuring chaos in the brain: a tutorial review of nonlinear dynamical EEG analysis,” Int. J. Neurosci.67(1-4), 31–80 (1992).
[CrossRef] [PubMed]

1991 (3)

D. R. Trew, C. B. James, S. H. L. Thomas, R. Sutton, and S. E. Smith, “Factors influencing the ocular pulse--the heart rate,” Graefes Arch. Clin. Exp. Ophthalmol.229(6), 553–556 (1991).
[CrossRef] [PubMed]

B. Gros, D. Pope, and T. Cohn, “Involuntary oculomotor events time-locked to the arterial pulse,” Invest. Ophthalmol. Vis. Sci.32, 895 (1991).

H. Yoshimatsu and M. Yamada, “High-dimensional chaos of miniature eye movements,” Proc. IEEE Eng. Med. Biol. Soc.13, 1513–1515 (1991).

1989 (1)

K. Nanba, T. Nakayama, and K. Iwata, “Variation of intraocular pressure by non-contact tonometry and cardiac pulse wave,” Nippon Ganka Gakkai Zasshi93(2), 155–160 (1989).
[PubMed]

1988 (2)

W. N. Charman and G. Heron, “Fluctuations in accommodation: a review,” Ophthalmic Physiol. Opt.8(2), 153–164 (1988).
[CrossRef] [PubMed]

C. Miege and P. Denieul, “Mean response and oscillations of accommodation for various stimulus vergences in relation to accommodation feedback control,” Ophthalmic Physiol. Opt.8(2), 165–171 (1988).
[CrossRef] [PubMed]

1986 (1)

J. C. Kotulak and C. M. Schor, “A computational model of the error detector of human visual accommodation,” Biol. Cybern.54(3), 189–194 (1986).
[CrossRef] [PubMed]

1982 (1)

K. M. Daum and G. A. Fry, “Pupillary micro movements apparently related to pulse frequency,” Vision Res.22(1), 173–177 (1982).
[CrossRef] [PubMed]

1962 (1)

I. Suzuki, “Corneal pulsation and corneal pulse waves,” Jpn. J. Ophthalmol.6, 190–194 (1962).

Abarbanel, H. D. I.

M. B. Kennel, R. Brown, and H. D. I. Abarbanel, “Determining embedding dimension for phase-space reconstruction using a geometrical construction,” Phys. Rev. A45(6), 3403–3411 (1992).
[CrossRef] [PubMed]

Applegate, R. A.

L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, “Accuracy and precision of objective refraction from wavefront aberrations,” J. Vis.4(4), 9 (2004).
[CrossRef] [PubMed]

Aragón, J. L.

Arden, G.

Artal, P.

A. Mira-Agudelo, L. Lundström, and P. Artal, “Temporal dynamics of ocular aberrations: monocular vs binocular vision,” Ophthalmic Physiol. Opt.29(3), 256–263 (2009).
[CrossRef] [PubMed]

H. Hofer, P. Artal, B. Singer, J. L. Aragón, and D. R. Williams, “J. L. Aragόn, and D. R. Williams, “Dynamics of the eye’s wave aberration,” J. Opt. Soc. Am. A18(3), 497–506 (2001).
[CrossRef]

Bille, J.

Bradley, A.

L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, “Accuracy and precision of objective refraction from wavefront aberrations,” J. Vis.4(4), 9 (2004).
[CrossRef] [PubMed]

Brown, R.

M. B. Kennel, R. Brown, and H. D. I. Abarbanel, “Determining embedding dimension for phase-space reconstruction using a geometrical construction,” Phys. Rev. A45(6), 3403–3411 (1992).
[CrossRef] [PubMed]

Casaleggio, A.

A. Casaleggio, S. Cerutti, and M. G. Signorini, “Study of the Lyapunov exponents in heart rate variability signals,” Methods Inf. Med.36(4-5), 274–277 (1997).
[PubMed]

Cerutti, S.

A. Casaleggio, S. Cerutti, and M. G. Signorini, “Study of the Lyapunov exponents in heart rate variability signals,” Methods Inf. Med.36(4-5), 274–277 (1997).
[PubMed]

Chang, T.

S. J. Schiff, K. Jerger, D. H. Duong, T. Chang, M. L. Spano, and W. L. Ditto, “Controlling chaos in the brain,” Nature370(6491), 615–620 (1994).
[CrossRef] [PubMed]

Charman, W. N.

W. N. Charman and G. Heron, “Fluctuations in accommodation: a review,” Ophthalmic Physiol. Opt.8(2), 153–164 (1988).
[CrossRef] [PubMed]

Chin, S. S.

S. S. Chin, K. M. Hampson, and E. A. H. Mallen, “Binocular correlation of ocular aberration dynamics,” Opt. Express16(19), 14731–14745 (2008).
[CrossRef] [PubMed]

K. M. Hampson, S. S. Chin, and E. A. H. Mallen, “Binocular Shack-Hartmann sensor for the human eye,” J. Mod. Opt.55(4-5), 703–716 (2008).
[CrossRef]

Cohn, T.

B. Gros, D. Pope, and T. Cohn, “Involuntary oculomotor events time-locked to the arterial pulse,” Invest. Ophthalmol. Vis. Sci.32, 895 (1991).

Collins, J. J.

M. T. Rosenstein, J. J. Collins, and C. J. De Luca, “A practical method for calculating largest Lyapunov exponents from small data sets,” Physica D65(1-2), 117–134 (1993).
[CrossRef]

Collins, M.

M. Collins, B. Davis, and J. Wood, “Microfluctuations of steady-state accommodation and the cardiopulmonary system,” Vision Res.35(17), 2491–2502 (1995).
[PubMed]

Collins, M. J.

M. Muma, D. R. Iskander, and M. J. Collins, “The role of cardiopulmonary signals in the dynamics of the eye’s wavefront aberrations,” IEEE Trans. Biomed. Eng.57(2), 373–383 (2010).
[CrossRef] [PubMed]

M. Zhu, M. J. Collins, and D. R. Iskander, “The contribution of accommodation and the ocular surface to the microfluctuations of wavefront aberrations of the eye,” Ophthalmic Physiol. Opt.26(5), 439–446 (2006).
[CrossRef] [PubMed]

M. Zhu, M. J. Collins, and D. Robert Iskander, “Microfluctuations of wavefront aberrations of the eye,” Ophthalmic Physiol. Opt.24(6), 562–571 (2004).
[CrossRef] [PubMed]

Dainty, C.

Daum, K. M.

K. M. Daum and G. A. Fry, “Pupillary micro movements apparently related to pulse frequency,” Vision Res.22(1), 173–177 (1982).
[CrossRef] [PubMed]

Davies, L. N.

L. N. Davies, J. S. Wolffsohn, and B. Gilmartin, “Cognition, ocular accommodation, and cardiovascular function in emmetropes and late-onset myopes,” Invest. Ophthalmol. Vis. Sci.46(5), 1791–1796 (2005).
[CrossRef] [PubMed]

Davis, B.

M. Collins, B. Davis, and J. Wood, “Microfluctuations of steady-state accommodation and the cardiopulmonary system,” Vision Res.35(17), 2491–2502 (1995).
[PubMed]

Day, M.

M. Day, D. Seidel, L. S. Gray, and N. C. Strang, “The effect of modulating ocular depth of focus upon accommodation microfluctuations in myopic and emmetropic subjects,” Vision Res.49(2), 211–218 (2009).
[CrossRef] [PubMed]

De Luca, C. J.

M. T. Rosenstein, J. J. Collins, and C. J. De Luca, “A practical method for calculating largest Lyapunov exponents from small data sets,” Physica D65(1-2), 117–134 (1993).
[CrossRef]

de Paula, A. S.

B. B. Ferreira, A. S. de Paula, and M. A. Savi, “Chaos control applied to heart rhythm dynamics,” Chaos Solitons Fractals44(8), 587–599 (2011).
[CrossRef]

Denieul, P.

C. Miege and P. Denieul, “Mean response and oscillations of accommodation for various stimulus vergences in relation to accommodation feedback control,” Ophthalmic Physiol. Opt.8(2), 165–171 (1988).
[CrossRef] [PubMed]

Diaz-Santana, L.

Ditto, W. L.

S. J. Schiff, K. Jerger, D. H. Duong, T. Chang, M. L. Spano, and W. L. Ditto, “Controlling chaos in the brain,” Nature370(6491), 615–620 (1994).
[CrossRef] [PubMed]

Dorronsoro, C.

E. Gambra, L. Sawides, C. Dorronsoro, and S. Marcos, “Accommodative lag and fluctuations when optical aberrations are manipulated,” J. Vis.9(6), 4 (2009).
[CrossRef] [PubMed]

Duke, D. W.

W. S. Pritchard and D. W. Duke, “Measuring chaos in the brain: a tutorial review of nonlinear dynamical EEG analysis,” Int. J. Neurosci.67(1-4), 31–80 (1992).
[CrossRef] [PubMed]

Duong, D. H.

S. J. Schiff, K. Jerger, D. H. Duong, T. Chang, M. L. Spano, and W. L. Ditto, “Controlling chaos in the brain,” Nature370(6491), 615–620 (1994).
[CrossRef] [PubMed]

Eadie, A. S.

A. S. Eadie, B. Winn, and J. R. Pugh, “The influence of arterial pulse on miniature eye movements,” Invest. Ophthalmol. Vis. Sci.35, 2037 (1994).

Faustmann, P. M.

R. E. Ganz, G. Weibels, K. H. Stäcker, P. M. Faustmann, and C. W. Zimmermann, “The Lyapunov exponent of heart rate dynamics as a sensitive marker of central autonomic organization: an exemplary study of early multiple sclerosis,” Int. J. Neurosci.71(1-4), 29–36 (1993).
[CrossRef] [PubMed]

Fercher, A. F.

L. F. Schmetterer, F. Lexer, C. J. Unfried, H. Sattmann, and A. F. Fercher, “Topical measurement of fundus pulsations,” Opt. Eng.34(3), 711–716 (1995).
[CrossRef]

Ferreira, B. B.

B. B. Ferreira, A. S. de Paula, and M. A. Savi, “Chaos control applied to heart rhythm dynamics,” Chaos Solitons Fractals44(8), 587–599 (2011).
[CrossRef]

Fry, G. A.

K. M. Daum and G. A. Fry, “Pupillary micro movements apparently related to pulse frequency,” Vision Res.22(1), 173–177 (1982).
[CrossRef] [PubMed]

Gambra, E.

E. Gambra, L. Sawides, C. Dorronsoro, and S. Marcos, “Accommodative lag and fluctuations when optical aberrations are manipulated,” J. Vis.9(6), 4 (2009).
[CrossRef] [PubMed]

Ganz, R. E.

R. E. Ganz, G. Weibels, K. H. Stäcker, P. M. Faustmann, and C. W. Zimmermann, “The Lyapunov exponent of heart rate dynamics as a sensitive marker of central autonomic organization: an exemplary study of early multiple sclerosis,” Int. J. Neurosci.71(1-4), 29–36 (1993).
[CrossRef] [PubMed]

Gasson, P.

Gilmartin, B.

L. N. Davies, J. S. Wolffsohn, and B. Gilmartin, “Cognition, ocular accommodation, and cardiovascular function in emmetropes and late-onset myopes,” Invest. Ophthalmol. Vis. Sci.46(5), 1791–1796 (2005).
[CrossRef] [PubMed]

Ginis, H. S.

S. Plainis, H. S. Ginis, and A. Pallikaris, “The effect of ocular aberrations on steady-state errors of accommodative response,” J. Vis.5(5), 7 (2005).
[CrossRef] [PubMed]

Gray, L. S.

M. Day, D. Seidel, L. S. Gray, and N. C. Strang, “The effect of modulating ocular depth of focus upon accommodation microfluctuations in myopic and emmetropic subjects,” Vision Res.49(2), 211–218 (2009).
[CrossRef] [PubMed]

D. Seidel, L. S. Gray, and G. Heron, “Retinotopic accommodation responses in myopia,” Invest. Ophthalmol. Vis. Sci.44(3), 1035–1041 (2003).
[CrossRef] [PubMed]

Gros, B.

B. Gros, D. Pope, and T. Cohn, “Involuntary oculomotor events time-locked to the arterial pulse,” Invest. Ophthalmol. Vis. Sci.32, 895 (1991).

Gruppetta, S.

Guériaux, V.

Hampson, K. M.

Harms, F.

Heron, G.

D. Seidel, L. S. Gray, and G. Heron, “Retinotopic accommodation responses in myopia,” Invest. Ophthalmol. Vis. Sci.44(3), 1035–1041 (2003).
[CrossRef] [PubMed]

W. N. Charman and G. Heron, “Fluctuations in accommodation: a review,” Ophthalmic Physiol. Opt.8(2), 153–164 (1988).
[CrossRef] [PubMed]

Hofer, H.

Hong, X.

L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, “Accuracy and precision of objective refraction from wavefront aberrations,” J. Vis.4(4), 9 (2004).
[CrossRef] [PubMed]

Iskander, D. R.

M. Muma, D. R. Iskander, and M. J. Collins, “The role of cardiopulmonary signals in the dynamics of the eye’s wavefront aberrations,” IEEE Trans. Biomed. Eng.57(2), 373–383 (2010).
[CrossRef] [PubMed]

M. Zhu, M. J. Collins, and D. R. Iskander, “The contribution of accommodation and the ocular surface to the microfluctuations of wavefront aberrations of the eye,” Ophthalmic Physiol. Opt.26(5), 439–446 (2006).
[CrossRef] [PubMed]

Iwata, K.

K. Nanba, T. Nakayama, and K. Iwata, “Variation of intraocular pressure by non-contact tonometry and cardiac pulse wave,” Nippon Ganka Gakkai Zasshi93(2), 155–160 (1989).
[PubMed]

James, C. B.

D. R. Trew, C. B. James, S. H. L. Thomas, R. Sutton, and S. E. Smith, “Factors influencing the ocular pulse--the heart rate,” Graefes Arch. Clin. Exp. Ophthalmol.229(6), 553–556 (1991).
[CrossRef] [PubMed]

Jerger, K.

S. J. Schiff, K. Jerger, D. H. Duong, T. Chang, M. L. Spano, and W. L. Ditto, “Controlling chaos in the brain,” Nature370(6491), 615–620 (1994).
[CrossRef] [PubMed]

Kennel, M. B.

M. B. Kennel, R. Brown, and H. D. I. Abarbanel, “Determining embedding dimension for phase-space reconstruction using a geometrical construction,” Phys. Rev. A45(6), 3403–3411 (1992).
[CrossRef] [PubMed]

Kotulak, J. C.

J. C. Kotulak and C. M. Schor, “A computational model of the error detector of human visual accommodation,” Biol. Cybern.54(3), 189–194 (1986).
[CrossRef] [PubMed]

Kroll, M. H.

M. L. Rosenberg and M. H. Kroll, “Pupillary hippus: an unrecognized example of biological chaos,” J. Biol. Syst.7(01), 85–94 (1999).
[CrossRef]

Lacombe, F.

Lamory, B.

Leahy, C.

Levecq, X.

Lexer, F.

L. F. Schmetterer, F. Lexer, C. J. Unfried, H. Sattmann, and A. F. Fercher, “Topical measurement of fundus pulsations,” Opt. Eng.34(3), 711–716 (1995).
[CrossRef]

Liu, Z.

Z. Liu, “Chaotic time series analysis,” Math. Probl. Eng.2010, 720190 (2010).
[CrossRef]

Lundström, L.

A. Mira-Agudelo, L. Lundström, and P. Artal, “Temporal dynamics of ocular aberrations: monocular vs binocular vision,” Ophthalmic Physiol. Opt.29(3), 256–263 (2009).
[CrossRef] [PubMed]

Mallen, E. A. H.

Marcos, S.

E. Gambra, L. Sawides, C. Dorronsoro, and S. Marcos, “Accommodative lag and fluctuations when optical aberrations are manipulated,” J. Vis.9(6), 4 (2009).
[CrossRef] [PubMed]

Merrill, C. K.

C. S. Poon and C. K. Merrill, “Decrease of cardiac chaos in congestive heart failure,” Nature389(6650), 492–495 (1997).
[CrossRef] [PubMed]

Miege, C.

C. Miege and P. Denieul, “Mean response and oscillations of accommodation for various stimulus vergences in relation to accommodation feedback control,” Ophthalmic Physiol. Opt.8(2), 165–171 (1988).
[CrossRef] [PubMed]

Mira-Agudelo, A.

A. Mira-Agudelo, L. Lundström, and P. Artal, “Temporal dynamics of ocular aberrations: monocular vs binocular vision,” Ophthalmic Physiol. Opt.29(3), 256–263 (2009).
[CrossRef] [PubMed]

Muma, M.

M. Muma, D. R. Iskander, and M. J. Collins, “The role of cardiopulmonary signals in the dynamics of the eye’s wavefront aberrations,” IEEE Trans. Biomed. Eng.57(2), 373–383 (2010).
[CrossRef] [PubMed]

Munro, I.

Nafz, B.

C. D. Wagner, B. Nafz, and P. B. Persson, “Chaos in blood pressure control,” Cardiovasc. Res.31(3), 380–387 (1996).
[PubMed]

Nakayama, T.

K. Nanba, T. Nakayama, and K. Iwata, “Variation of intraocular pressure by non-contact tonometry and cardiac pulse wave,” Nippon Ganka Gakkai Zasshi93(2), 155–160 (1989).
[PubMed]

Nanba, K.

K. Nanba, T. Nakayama, and K. Iwata, “Variation of intraocular pressure by non-contact tonometry and cardiac pulse wave,” Nippon Ganka Gakkai Zasshi93(2), 155–160 (1989).
[PubMed]

Nirmaier, T.

Pallikaris, A.

S. Plainis, H. S. Ginis, and A. Pallikaris, “The effect of ocular aberrations on steady-state errors of accommodative response,” J. Vis.5(5), 7 (2005).
[CrossRef] [PubMed]

Paterson, C.

Persson, P. B.

C. D. Wagner, B. Nafz, and P. B. Persson, “Chaos in blood pressure control,” Cardiovasc. Res.31(3), 380–387 (1996).
[PubMed]

Plainis, S.

S. Plainis, H. S. Ginis, and A. Pallikaris, “The effect of ocular aberrations on steady-state errors of accommodative response,” J. Vis.5(5), 7 (2005).
[CrossRef] [PubMed]

Poon, C. S.

C. S. Poon and C. K. Merrill, “Decrease of cardiac chaos in congestive heart failure,” Nature389(6650), 492–495 (1997).
[CrossRef] [PubMed]

Pope, D.

B. Gros, D. Pope, and T. Cohn, “Involuntary oculomotor events time-locked to the arterial pulse,” Invest. Ophthalmol. Vis. Sci.32, 895 (1991).

Pritchard, W. S.

W. S. Pritchard and D. W. Duke, “Measuring chaos in the brain: a tutorial review of nonlinear dynamical EEG analysis,” Int. J. Neurosci.67(1-4), 31–80 (1992).
[CrossRef] [PubMed]

Pudasaini, G.

Puget, P.

Pugh, J. R.

A. S. Eadie, B. Winn, and J. R. Pugh, “The influence of arterial pulse on miniature eye movements,” Invest. Ophthalmol. Vis. Sci.35, 2037 (1994).

Robert Iskander, D.

M. Zhu, M. J. Collins, and D. Robert Iskander, “Microfluctuations of wavefront aberrations of the eye,” Ophthalmic Physiol. Opt.24(6), 562–571 (2004).
[CrossRef] [PubMed]

Rosenberg, M. L.

M. L. Rosenberg and M. H. Kroll, “Pupillary hippus: an unrecognized example of biological chaos,” J. Biol. Syst.7(01), 85–94 (1999).
[CrossRef]

Rosenstein, M. T.

M. T. Rosenstein, J. J. Collins, and C. J. De Luca, “A practical method for calculating largest Lyapunov exponents from small data sets,” Physica D65(1-2), 117–134 (1993).
[CrossRef]

Sahin, B.

Sattmann, H.

L. F. Schmetterer, F. Lexer, C. J. Unfried, H. Sattmann, and A. F. Fercher, “Topical measurement of fundus pulsations,” Opt. Eng.34(3), 711–716 (1995).
[CrossRef]

Savi, M. A.

B. B. Ferreira, A. S. de Paula, and M. A. Savi, “Chaos control applied to heart rhythm dynamics,” Chaos Solitons Fractals44(8), 587–599 (2011).
[CrossRef]

M. A. Savi, “Chaos and order in biomedical rhythms,” J. Braz. Soc. Mech. Sci. Eng.27(2), 157–169 (2005).
[CrossRef]

Sawides, L.

E. Gambra, L. Sawides, C. Dorronsoro, and S. Marcos, “Accommodative lag and fluctuations when optical aberrations are manipulated,” J. Vis.9(6), 4 (2009).
[CrossRef] [PubMed]

Schiff, S. J.

S. J. Schiff, K. Jerger, D. H. Duong, T. Chang, M. L. Spano, and W. L. Ditto, “Controlling chaos in the brain,” Nature370(6491), 615–620 (1994).
[CrossRef] [PubMed]

Schmetterer, L. F.

L. F. Schmetterer, F. Lexer, C. J. Unfried, H. Sattmann, and A. F. Fercher, “Topical measurement of fundus pulsations,” Opt. Eng.34(3), 711–716 (1995).
[CrossRef]

Schor, C. M.

J. C. Kotulak and C. M. Schor, “A computational model of the error detector of human visual accommodation,” Biol. Cybern.54(3), 189–194 (1986).
[CrossRef] [PubMed]

Seidel, D.

M. Day, D. Seidel, L. S. Gray, and N. C. Strang, “The effect of modulating ocular depth of focus upon accommodation microfluctuations in myopic and emmetropic subjects,” Vision Res.49(2), 211–218 (2009).
[CrossRef] [PubMed]

D. Seidel, L. S. Gray, and G. Heron, “Retinotopic accommodation responses in myopia,” Invest. Ophthalmol. Vis. Sci.44(3), 1035–1041 (2003).
[CrossRef] [PubMed]

Signorini, M. G.

A. Casaleggio, S. Cerutti, and M. G. Signorini, “Study of the Lyapunov exponents in heart rate variability signals,” Methods Inf. Med.36(4-5), 274–277 (1997).
[PubMed]

Singer, B.

Smith, S. E.

D. R. Trew, C. B. James, S. H. L. Thomas, R. Sutton, and S. E. Smith, “Factors influencing the ocular pulse--the heart rate,” Graefes Arch. Clin. Exp. Ophthalmol.229(6), 553–556 (1991).
[CrossRef] [PubMed]

Spano, M. L.

S. J. Schiff, K. Jerger, D. H. Duong, T. Chang, M. L. Spano, and W. L. Ditto, “Controlling chaos in the brain,” Nature370(6491), 615–620 (1994).
[CrossRef] [PubMed]

Stäcker, K. H.

R. E. Ganz, G. Weibels, K. H. Stäcker, P. M. Faustmann, and C. W. Zimmermann, “The Lyapunov exponent of heart rate dynamics as a sensitive marker of central autonomic organization: an exemplary study of early multiple sclerosis,” Int. J. Neurosci.71(1-4), 29–36 (1993).
[CrossRef] [PubMed]

Strang, N. C.

M. Day, D. Seidel, L. S. Gray, and N. C. Strang, “The effect of modulating ocular depth of focus upon accommodation microfluctuations in myopic and emmetropic subjects,” Vision Res.49(2), 211–218 (2009).
[CrossRef] [PubMed]

Su, Z. Y.

Z. Y. Su, T. Wu, P. H. Yang, and Y. T. Wang, “Dynamic analysis of heartbeat rate signals of epileptics using multidimensional phase space reconstruction approach,” Physica A387(10), 2293–2305 (2008).
[CrossRef]

Sutton, R.

D. R. Trew, C. B. James, S. H. L. Thomas, R. Sutton, and S. E. Smith, “Factors influencing the ocular pulse--the heart rate,” Graefes Arch. Clin. Exp. Ophthalmol.229(6), 553–556 (1991).
[CrossRef] [PubMed]

Suzuki, I.

I. Suzuki, “Corneal pulsation and corneal pulse waves,” Jpn. J. Ophthalmol.6, 190–194 (1962).

Thibos, L. N.

L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, “Accuracy and precision of objective refraction from wavefront aberrations,” J. Vis.4(4), 9 (2004).
[CrossRef] [PubMed]

Thomas, S. H. L.

D. R. Trew, C. B. James, S. H. L. Thomas, R. Sutton, and S. E. Smith, “Factors influencing the ocular pulse--the heart rate,” Graefes Arch. Clin. Exp. Ophthalmol.229(6), 553–556 (1991).
[CrossRef] [PubMed]

Torti, C.

Trew, D. R.

D. R. Trew, C. B. James, S. H. L. Thomas, R. Sutton, and S. E. Smith, “Factors influencing the ocular pulse--the heart rate,” Graefes Arch. Clin. Exp. Ophthalmol.229(6), 553–556 (1991).
[CrossRef] [PubMed]

Unfried, C. J.

L. F. Schmetterer, F. Lexer, C. J. Unfried, H. Sattmann, and A. F. Fercher, “Topical measurement of fundus pulsations,” Opt. Eng.34(3), 711–716 (1995).
[CrossRef]

Wagner, C. D.

C. D. Wagner, B. Nafz, and P. B. Persson, “Chaos in blood pressure control,” Cardiovasc. Res.31(3), 380–387 (1996).
[PubMed]

Wang, Y. T.

Z. Y. Su, T. Wu, P. H. Yang, and Y. T. Wang, “Dynamic analysis of heartbeat rate signals of epileptics using multidimensional phase space reconstruction approach,” Physica A387(10), 2293–2305 (2008).
[CrossRef]

Weibels, G.

R. E. Ganz, G. Weibels, K. H. Stäcker, P. M. Faustmann, and C. W. Zimmermann, “The Lyapunov exponent of heart rate dynamics as a sensitive marker of central autonomic organization: an exemplary study of early multiple sclerosis,” Int. J. Neurosci.71(1-4), 29–36 (1993).
[CrossRef] [PubMed]

Williams, D. R.

Winn, B.

A. S. Eadie, B. Winn, and J. R. Pugh, “The influence of arterial pulse on miniature eye movements,” Invest. Ophthalmol. Vis. Sci.35, 2037 (1994).

Wolffsohn, J. S.

L. N. Davies, J. S. Wolffsohn, and B. Gilmartin, “Cognition, ocular accommodation, and cardiovascular function in emmetropes and late-onset myopes,” Invest. Ophthalmol. Vis. Sci.46(5), 1791–1796 (2005).
[CrossRef] [PubMed]

Wood, J.

M. Collins, B. Davis, and J. Wood, “Microfluctuations of steady-state accommodation and the cardiopulmonary system,” Vision Res.35(17), 2491–2502 (1995).
[PubMed]

Wu, T.

Z. Y. Su, T. Wu, P. H. Yang, and Y. T. Wang, “Dynamic analysis of heartbeat rate signals of epileptics using multidimensional phase space reconstruction approach,” Physica A387(10), 2293–2305 (2008).
[CrossRef]

Yamada, M.

H. Yoshimatsu and M. Yamada, “High-dimensional chaos of miniature eye movements,” Proc. IEEE Eng. Med. Biol. Soc.13, 1513–1515 (1991).

Yang, P. H.

Z. Y. Su, T. Wu, P. H. Yang, and Y. T. Wang, “Dynamic analysis of heartbeat rate signals of epileptics using multidimensional phase space reconstruction approach,” Physica A387(10), 2293–2305 (2008).
[CrossRef]

Yoshimatsu, H.

H. Yoshimatsu and M. Yamada, “High-dimensional chaos of miniature eye movements,” Proc. IEEE Eng. Med. Biol. Soc.13, 1513–1515 (1991).

Zhu, M.

M. Zhu, M. J. Collins, and D. R. Iskander, “The contribution of accommodation and the ocular surface to the microfluctuations of wavefront aberrations of the eye,” Ophthalmic Physiol. Opt.26(5), 439–446 (2006).
[CrossRef] [PubMed]

M. Zhu, M. J. Collins, and D. Robert Iskander, “Microfluctuations of wavefront aberrations of the eye,” Ophthalmic Physiol. Opt.24(6), 562–571 (2004).
[CrossRef] [PubMed]

Zimmermann, C. W.

R. E. Ganz, G. Weibels, K. H. Stäcker, P. M. Faustmann, and C. W. Zimmermann, “The Lyapunov exponent of heart rate dynamics as a sensitive marker of central autonomic organization: an exemplary study of early multiple sclerosis,” Int. J. Neurosci.71(1-4), 29–36 (1993).
[CrossRef] [PubMed]

Biol. Cybern. (1)

J. C. Kotulak and C. M. Schor, “A computational model of the error detector of human visual accommodation,” Biol. Cybern.54(3), 189–194 (1986).
[CrossRef] [PubMed]

Biomed. Opt. Express (2)

Cardiovasc. Res. (1)

C. D. Wagner, B. Nafz, and P. B. Persson, “Chaos in blood pressure control,” Cardiovasc. Res.31(3), 380–387 (1996).
[PubMed]

Chaos Solitons Fractals (1)

B. B. Ferreira, A. S. de Paula, and M. A. Savi, “Chaos control applied to heart rhythm dynamics,” Chaos Solitons Fractals44(8), 587–599 (2011).
[CrossRef]

Graefes Arch. Clin. Exp. Ophthalmol. (1)

D. R. Trew, C. B. James, S. H. L. Thomas, R. Sutton, and S. E. Smith, “Factors influencing the ocular pulse--the heart rate,” Graefes Arch. Clin. Exp. Ophthalmol.229(6), 553–556 (1991).
[CrossRef] [PubMed]

IEEE Trans. Biomed. Eng. (1)

M. Muma, D. R. Iskander, and M. J. Collins, “The role of cardiopulmonary signals in the dynamics of the eye’s wavefront aberrations,” IEEE Trans. Biomed. Eng.57(2), 373–383 (2010).
[CrossRef] [PubMed]

Int. J. Neurosci. (2)

W. S. Pritchard and D. W. Duke, “Measuring chaos in the brain: a tutorial review of nonlinear dynamical EEG analysis,” Int. J. Neurosci.67(1-4), 31–80 (1992).
[CrossRef] [PubMed]

R. E. Ganz, G. Weibels, K. H. Stäcker, P. M. Faustmann, and C. W. Zimmermann, “The Lyapunov exponent of heart rate dynamics as a sensitive marker of central autonomic organization: an exemplary study of early multiple sclerosis,” Int. J. Neurosci.71(1-4), 29–36 (1993).
[CrossRef] [PubMed]

Invest. Ophthalmol. Vis. Sci. (4)

L. N. Davies, J. S. Wolffsohn, and B. Gilmartin, “Cognition, ocular accommodation, and cardiovascular function in emmetropes and late-onset myopes,” Invest. Ophthalmol. Vis. Sci.46(5), 1791–1796 (2005).
[CrossRef] [PubMed]

B. Gros, D. Pope, and T. Cohn, “Involuntary oculomotor events time-locked to the arterial pulse,” Invest. Ophthalmol. Vis. Sci.32, 895 (1991).

A. S. Eadie, B. Winn, and J. R. Pugh, “The influence of arterial pulse on miniature eye movements,” Invest. Ophthalmol. Vis. Sci.35, 2037 (1994).

D. Seidel, L. S. Gray, and G. Heron, “Retinotopic accommodation responses in myopia,” Invest. Ophthalmol. Vis. Sci.44(3), 1035–1041 (2003).
[CrossRef] [PubMed]

J. Biol. Syst. (1)

M. L. Rosenberg and M. H. Kroll, “Pupillary hippus: an unrecognized example of biological chaos,” J. Biol. Syst.7(01), 85–94 (1999).
[CrossRef]

J. Braz. Soc. Mech. Sci. Eng. (1)

M. A. Savi, “Chaos and order in biomedical rhythms,” J. Braz. Soc. Mech. Sci. Eng.27(2), 157–169 (2005).
[CrossRef]

J. Mod. Opt. (2)

K. M. Hampson, S. S. Chin, and E. A. H. Mallen, “Binocular Shack-Hartmann sensor for the human eye,” J. Mod. Opt.55(4-5), 703–716 (2008).
[CrossRef]

K. M. Hampson, “Adaptive optics and vision,” J. Mod. Opt.55(21), 3425–3467 (2008).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Vis. (3)

L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, “Accuracy and precision of objective refraction from wavefront aberrations,” J. Vis.4(4), 9 (2004).
[CrossRef] [PubMed]

E. Gambra, L. Sawides, C. Dorronsoro, and S. Marcos, “Accommodative lag and fluctuations when optical aberrations are manipulated,” J. Vis.9(6), 4 (2009).
[CrossRef] [PubMed]

S. Plainis, H. S. Ginis, and A. Pallikaris, “The effect of ocular aberrations on steady-state errors of accommodative response,” J. Vis.5(5), 7 (2005).
[CrossRef] [PubMed]

Jpn. J. Ophthalmol. (1)

I. Suzuki, “Corneal pulsation and corneal pulse waves,” Jpn. J. Ophthalmol.6, 190–194 (1962).

Math. Probl. Eng. (1)

Z. Liu, “Chaotic time series analysis,” Math. Probl. Eng.2010, 720190 (2010).
[CrossRef]

Methods Inf. Med. (1)

A. Casaleggio, S. Cerutti, and M. G. Signorini, “Study of the Lyapunov exponents in heart rate variability signals,” Methods Inf. Med.36(4-5), 274–277 (1997).
[PubMed]

Nature (2)

C. S. Poon and C. K. Merrill, “Decrease of cardiac chaos in congestive heart failure,” Nature389(6650), 492–495 (1997).
[CrossRef] [PubMed]

S. J. Schiff, K. Jerger, D. H. Duong, T. Chang, M. L. Spano, and W. L. Ditto, “Controlling chaos in the brain,” Nature370(6491), 615–620 (1994).
[CrossRef] [PubMed]

Nippon Ganka Gakkai Zasshi (1)

K. Nanba, T. Nakayama, and K. Iwata, “Variation of intraocular pressure by non-contact tonometry and cardiac pulse wave,” Nippon Ganka Gakkai Zasshi93(2), 155–160 (1989).
[PubMed]

Ophthalmic Physiol. Opt. (5)

A. Mira-Agudelo, L. Lundström, and P. Artal, “Temporal dynamics of ocular aberrations: monocular vs binocular vision,” Ophthalmic Physiol. Opt.29(3), 256–263 (2009).
[CrossRef] [PubMed]

M. Zhu, M. J. Collins, and D. R. Iskander, “The contribution of accommodation and the ocular surface to the microfluctuations of wavefront aberrations of the eye,” Ophthalmic Physiol. Opt.26(5), 439–446 (2006).
[CrossRef] [PubMed]

M. Zhu, M. J. Collins, and D. Robert Iskander, “Microfluctuations of wavefront aberrations of the eye,” Ophthalmic Physiol. Opt.24(6), 562–571 (2004).
[CrossRef] [PubMed]

W. N. Charman and G. Heron, “Fluctuations in accommodation: a review,” Ophthalmic Physiol. Opt.8(2), 153–164 (1988).
[CrossRef] [PubMed]

C. Miege and P. Denieul, “Mean response and oscillations of accommodation for various stimulus vergences in relation to accommodation feedback control,” Ophthalmic Physiol. Opt.8(2), 165–171 (1988).
[CrossRef] [PubMed]

Opt. Eng. (1)

L. F. Schmetterer, F. Lexer, C. J. Unfried, H. Sattmann, and A. F. Fercher, “Topical measurement of fundus pulsations,” Opt. Eng.34(3), 711–716 (1995).
[CrossRef]

Opt. Express (6)

Opt. Lett. (1)

Phys. Rev. A (1)

M. B. Kennel, R. Brown, and H. D. I. Abarbanel, “Determining embedding dimension for phase-space reconstruction using a geometrical construction,” Phys. Rev. A45(6), 3403–3411 (1992).
[CrossRef] [PubMed]

Physica A (1)

Z. Y. Su, T. Wu, P. H. Yang, and Y. T. Wang, “Dynamic analysis of heartbeat rate signals of epileptics using multidimensional phase space reconstruction approach,” Physica A387(10), 2293–2305 (2008).
[CrossRef]

Physica D (1)

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Proc. IEEE Eng. Med. Biol. Soc. (1)

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M. Day, D. Seidel, L. S. Gray, and N. C. Strang, “The effect of modulating ocular depth of focus upon accommodation microfluctuations in myopic and emmetropic subjects,” Vision Res.49(2), 211–218 (2009).
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S. S. Chin, “Adaptive optics, aberration dynamics and accommodation control,” Ph.D. thesis (Bradford School of Optometry and vision science, University of Bradford, Bradford, 2009).

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B. Winn, “Accommodative microfluctuations: a mechanism for steady-state control of accommodation,” in Accommodation and Vergence Mechanisms in the Visual System, O. Franzén, H. Richter, and L. Stark, eds. (Birkhäuser Verlag Basel, Switzerland, 2000), pp. 129–140.

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