Abstract

We used adaptive optics to determine the effect of monochromatic aberration dynamics on the level of chaos in the accommodation control system. Four participants viewed a stationary target while the dynamics of their aberrations were either left uncorrected, defocus was corrected, or all aberrations except defocus were corrected. Chaos theory analysis was used to discern changes in the accommodative microfluctuations. We found a statistically significant reduction in the chaotic nature of the accommodation microfluctuations during correction of defocus, but not when all aberrations except defocus were corrected. The Lyapunov exponent decreased from 0.71±0.07D/s (baseline) to 0.55±0.03D/s (correction of defocus fluctuations). As the reduction of chaos in physiological signals is indicative of stress to the system, the results indicate that for the participants included in this study, fluctuations in defocus have a more profound effect than those of the other aberrations. There were no changes in the power spectrum between experimental conditions. Hence chaos theory analysis is a more subtle marker of changes in the accommodation control system and will be of value in the study of myopia onset and progression.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W. N. Charman and G. Heron, Ophthal. Physiol. Opt. 8, 153 (1988).
    [CrossRef]
  2. B. Winn, in Accommodation and Vergence Mechanisms in the Visual System, O. Franzén, H. Richter, and L. Stark, eds. (Birkhäuser Verlag, 2000), pp. 129–140.
  3. C. S. Poon and C. K. Merrill, Nature 389, 492 (1997).
    [CrossRef]
  4. K. M. Hampson and E. A. H. Mallen, Biomed. Opt. Express 3, 863 (2012).
    [CrossRef]
  5. J. E. Skinner, Biotechnology 12, 596 (1994).
    [CrossRef]
  6. P. P. Monticone and M. Menozzi, J. Eur. Opt. Soc. Rapid Pub. 6, 11003 (2011).
    [CrossRef]
  7. V. K. Yeragani, K. A. Rao, M. R. Smitha, R. B. Pohl, R. Balon, and K. Srinivasan, Biol. Psychiatry 51, 733 (2002).
    [CrossRef]
  8. H. Hofer, P. Artal, B. Singer, J. L. Aragón, and D. R. Williams, J. Opt. Soc. Am. A 18, 497 (2001).
    [CrossRef]
  9. E. J. Fernández and P. Artal, J. Opt. Soc. Am. A 22, 1732 (2005).
    [CrossRef]
  10. L. Chen, P. B. Kruger, H. Hofer, B. Singer, and D. R. Williams, J. Opt. Soc. Am. A 23, 1 (2006).
    [CrossRef]
  11. K. M. Hampson, S. S. Chin, and E. A. H. Mallen, Clin. Exp. Optom. 92, 227 (2009).
    [CrossRef]
  12. K. M. Hampson, S. S. Chin, and E. A. H. Mallen, Opt. Express 17, 18229 (2009).
    [CrossRef]
  13. E. Gambra, L. Sawides, C. Dorronsoro, and S. Marcos, J. Vis. 9(6), 4.1 (2009).
    [CrossRef]
  14. L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, J. Vis. 4(4), 329 (2004).
    [CrossRef]
  15. G. P. Williams, Chaos Theory Tamed (Joseph Henry, 1997).
  16. M. B. Kennel, R. Brown, and H. D. I. Abarbanel, Phys. Rev. A 45, 3403 (1992).
    [CrossRef]
  17. M. T. Rosenstein, J. J. Collins, and C. J. De Luca, Physica D 65, 117 (1993).
    [CrossRef]
  18. K. M. Hampson and E. A. H. Mallen, Opt. Lett. 38, 302 (2013).
    [CrossRef]
  19. S. S. Chin, “Adaptive optics, aberration dynamics and accommodation control,” Ph.D. thesis (University of Bradford, 2009).
  20. C. Leahy, C. Leroux, C. Dainty, and L. Diaz-Santana, Opt. Express 18, 2668 (2010).
    [CrossRef]
  21. B. Winn and B. Gilmartin, Opthal. Physiol. Opt. 12, 252 (1992).
    [CrossRef]
  22. N. S. Anstice and J. R. Phillips, Ophthalmology 118, 1152 (2011).
    [CrossRef]
  23. P. Cho and S. W. Cheung, Investig. Ophthalmol. Vis. Sci. 53, 7077 (2012).
    [CrossRef]

2013

2012

K. M. Hampson and E. A. H. Mallen, Biomed. Opt. Express 3, 863 (2012).
[CrossRef]

P. Cho and S. W. Cheung, Investig. Ophthalmol. Vis. Sci. 53, 7077 (2012).
[CrossRef]

2011

P. P. Monticone and M. Menozzi, J. Eur. Opt. Soc. Rapid Pub. 6, 11003 (2011).
[CrossRef]

N. S. Anstice and J. R. Phillips, Ophthalmology 118, 1152 (2011).
[CrossRef]

2010

2009

K. M. Hampson, S. S. Chin, and E. A. H. Mallen, Clin. Exp. Optom. 92, 227 (2009).
[CrossRef]

K. M. Hampson, S. S. Chin, and E. A. H. Mallen, Opt. Express 17, 18229 (2009).
[CrossRef]

E. Gambra, L. Sawides, C. Dorronsoro, and S. Marcos, J. Vis. 9(6), 4.1 (2009).
[CrossRef]

2006

2005

2004

L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, J. Vis. 4(4), 329 (2004).
[CrossRef]

2002

V. K. Yeragani, K. A. Rao, M. R. Smitha, R. B. Pohl, R. Balon, and K. Srinivasan, Biol. Psychiatry 51, 733 (2002).
[CrossRef]

2001

1997

C. S. Poon and C. K. Merrill, Nature 389, 492 (1997).
[CrossRef]

1994

J. E. Skinner, Biotechnology 12, 596 (1994).
[CrossRef]

1993

M. T. Rosenstein, J. J. Collins, and C. J. De Luca, Physica D 65, 117 (1993).
[CrossRef]

1992

B. Winn and B. Gilmartin, Opthal. Physiol. Opt. 12, 252 (1992).
[CrossRef]

M. B. Kennel, R. Brown, and H. D. I. Abarbanel, Phys. Rev. A 45, 3403 (1992).
[CrossRef]

1988

W. N. Charman and G. Heron, Ophthal. Physiol. Opt. 8, 153 (1988).
[CrossRef]

Abarbanel, H. D. I.

M. B. Kennel, R. Brown, and H. D. I. Abarbanel, Phys. Rev. A 45, 3403 (1992).
[CrossRef]

Anstice, N. S.

N. S. Anstice and J. R. Phillips, Ophthalmology 118, 1152 (2011).
[CrossRef]

Applegate, R. A.

L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, J. Vis. 4(4), 329 (2004).
[CrossRef]

Aragón, J. L.

Artal, P.

Balon, R.

V. K. Yeragani, K. A. Rao, M. R. Smitha, R. B. Pohl, R. Balon, and K. Srinivasan, Biol. Psychiatry 51, 733 (2002).
[CrossRef]

Bradley, A.

L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, J. Vis. 4(4), 329 (2004).
[CrossRef]

Brown, R.

M. B. Kennel, R. Brown, and H. D. I. Abarbanel, Phys. Rev. A 45, 3403 (1992).
[CrossRef]

Charman, W. N.

W. N. Charman and G. Heron, Ophthal. Physiol. Opt. 8, 153 (1988).
[CrossRef]

Chen, L.

Cheung, S. W.

P. Cho and S. W. Cheung, Investig. Ophthalmol. Vis. Sci. 53, 7077 (2012).
[CrossRef]

Chin, S. S.

K. M. Hampson, S. S. Chin, and E. A. H. Mallen, Clin. Exp. Optom. 92, 227 (2009).
[CrossRef]

K. M. Hampson, S. S. Chin, and E. A. H. Mallen, Opt. Express 17, 18229 (2009).
[CrossRef]

S. S. Chin, “Adaptive optics, aberration dynamics and accommodation control,” Ph.D. thesis (University of Bradford, 2009).

Cho, P.

P. Cho and S. W. Cheung, Investig. Ophthalmol. Vis. Sci. 53, 7077 (2012).
[CrossRef]

Collins, J. J.

M. T. Rosenstein, J. J. Collins, and C. J. De Luca, Physica D 65, 117 (1993).
[CrossRef]

Dainty, C.

De Luca, C. J.

M. T. Rosenstein, J. J. Collins, and C. J. De Luca, Physica D 65, 117 (1993).
[CrossRef]

Diaz-Santana, L.

Dorronsoro, C.

E. Gambra, L. Sawides, C. Dorronsoro, and S. Marcos, J. Vis. 9(6), 4.1 (2009).
[CrossRef]

Fernández, E. J.

Gambra, E.

E. Gambra, L. Sawides, C. Dorronsoro, and S. Marcos, J. Vis. 9(6), 4.1 (2009).
[CrossRef]

Gilmartin, B.

B. Winn and B. Gilmartin, Opthal. Physiol. Opt. 12, 252 (1992).
[CrossRef]

Hampson, K. M.

Heron, G.

W. N. Charman and G. Heron, Ophthal. Physiol. Opt. 8, 153 (1988).
[CrossRef]

Hofer, H.

Hong, X.

L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, J. Vis. 4(4), 329 (2004).
[CrossRef]

Kennel, M. B.

M. B. Kennel, R. Brown, and H. D. I. Abarbanel, Phys. Rev. A 45, 3403 (1992).
[CrossRef]

Kruger, P. B.

Leahy, C.

Leroux, C.

Mallen, E. A. H.

Marcos, S.

E. Gambra, L. Sawides, C. Dorronsoro, and S. Marcos, J. Vis. 9(6), 4.1 (2009).
[CrossRef]

Menozzi, M.

P. P. Monticone and M. Menozzi, J. Eur. Opt. Soc. Rapid Pub. 6, 11003 (2011).
[CrossRef]

Merrill, C. K.

C. S. Poon and C. K. Merrill, Nature 389, 492 (1997).
[CrossRef]

Monticone, P. P.

P. P. Monticone and M. Menozzi, J. Eur. Opt. Soc. Rapid Pub. 6, 11003 (2011).
[CrossRef]

Phillips, J. R.

N. S. Anstice and J. R. Phillips, Ophthalmology 118, 1152 (2011).
[CrossRef]

Pohl, R. B.

V. K. Yeragani, K. A. Rao, M. R. Smitha, R. B. Pohl, R. Balon, and K. Srinivasan, Biol. Psychiatry 51, 733 (2002).
[CrossRef]

Poon, C. S.

C. S. Poon and C. K. Merrill, Nature 389, 492 (1997).
[CrossRef]

Rao, K. A.

V. K. Yeragani, K. A. Rao, M. R. Smitha, R. B. Pohl, R. Balon, and K. Srinivasan, Biol. Psychiatry 51, 733 (2002).
[CrossRef]

Rosenstein, M. T.

M. T. Rosenstein, J. J. Collins, and C. J. De Luca, Physica D 65, 117 (1993).
[CrossRef]

Sawides, L.

E. Gambra, L. Sawides, C. Dorronsoro, and S. Marcos, J. Vis. 9(6), 4.1 (2009).
[CrossRef]

Singer, B.

Skinner, J. E.

J. E. Skinner, Biotechnology 12, 596 (1994).
[CrossRef]

Smitha, M. R.

V. K. Yeragani, K. A. Rao, M. R. Smitha, R. B. Pohl, R. Balon, and K. Srinivasan, Biol. Psychiatry 51, 733 (2002).
[CrossRef]

Srinivasan, K.

V. K. Yeragani, K. A. Rao, M. R. Smitha, R. B. Pohl, R. Balon, and K. Srinivasan, Biol. Psychiatry 51, 733 (2002).
[CrossRef]

Thibos, L. N.

L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, J. Vis. 4(4), 329 (2004).
[CrossRef]

Williams, D. R.

Williams, G. P.

G. P. Williams, Chaos Theory Tamed (Joseph Henry, 1997).

Winn, B.

B. Winn and B. Gilmartin, Opthal. Physiol. Opt. 12, 252 (1992).
[CrossRef]

B. Winn, in Accommodation and Vergence Mechanisms in the Visual System, O. Franzén, H. Richter, and L. Stark, eds. (Birkhäuser Verlag, 2000), pp. 129–140.

Yeragani, V. K.

V. K. Yeragani, K. A. Rao, M. R. Smitha, R. B. Pohl, R. Balon, and K. Srinivasan, Biol. Psychiatry 51, 733 (2002).
[CrossRef]

Biol. Psychiatry

V. K. Yeragani, K. A. Rao, M. R. Smitha, R. B. Pohl, R. Balon, and K. Srinivasan, Biol. Psychiatry 51, 733 (2002).
[CrossRef]

Biomed. Opt. Express

Biotechnology

J. E. Skinner, Biotechnology 12, 596 (1994).
[CrossRef]

Clin. Exp. Optom.

K. M. Hampson, S. S. Chin, and E. A. H. Mallen, Clin. Exp. Optom. 92, 227 (2009).
[CrossRef]

Investig. Ophthalmol. Vis. Sci.

P. Cho and S. W. Cheung, Investig. Ophthalmol. Vis. Sci. 53, 7077 (2012).
[CrossRef]

J. Eur. Opt. Soc. Rapid Pub.

P. P. Monticone and M. Menozzi, J. Eur. Opt. Soc. Rapid Pub. 6, 11003 (2011).
[CrossRef]

J. Opt. Soc. Am. A

J. Vis.

E. Gambra, L. Sawides, C. Dorronsoro, and S. Marcos, J. Vis. 9(6), 4.1 (2009).
[CrossRef]

L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, J. Vis. 4(4), 329 (2004).
[CrossRef]

Nature

C. S. Poon and C. K. Merrill, Nature 389, 492 (1997).
[CrossRef]

Ophthal. Physiol. Opt.

W. N. Charman and G. Heron, Ophthal. Physiol. Opt. 8, 153 (1988).
[CrossRef]

Ophthalmology

N. S. Anstice and J. R. Phillips, Ophthalmology 118, 1152 (2011).
[CrossRef]

Opt. Express

Opt. Lett.

Opthal. Physiol. Opt.

B. Winn and B. Gilmartin, Opthal. Physiol. Opt. 12, 252 (1992).
[CrossRef]

Phys. Rev. A

M. B. Kennel, R. Brown, and H. D. I. Abarbanel, Phys. Rev. A 45, 3403 (1992).
[CrossRef]

Physica D

M. T. Rosenstein, J. J. Collins, and C. J. De Luca, Physica D 65, 117 (1993).
[CrossRef]

Other

S. S. Chin, “Adaptive optics, aberration dynamics and accommodation control,” Ph.D. thesis (University of Bradford, 2009).

G. P. Williams, Chaos Theory Tamed (Joseph Henry, 1997).

B. Winn, in Accommodation and Vergence Mechanisms in the Visual System, O. Franzén, H. Richter, and L. Stark, eds. (Birkhäuser Verlag, 2000), pp. 129–140.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1.
Fig. 1.

Principle of constructing a multidimensional phase space from a one-dimensional time series. (a) The time series. (b) The phase space plot. In this example, the embedding lag is three data points and the embedding dimension is two.

Fig. 2.
Fig. 2.

Divergence plot for each condition averaged over trials and participants. The slope of the linear rise region is the Lyapunov exponent. The length of time of the linear rise region is the limit of predictability. The plots have been displaced for clarity.

Tables (1)

Tables Icon

Table 1. Chaos Theory Analysis Results for Each Condition Averaged Across Trials and Participants

Equations (1)

Equations on this page are rendered with MathJax. Learn more.

dj(i)=CeL(iΔt),

Metrics