Bulletin of Mathematical Biology

, Volume 64, Issue 2, pp 285–299 | Cite as

A dual-mode dynamic model of the human accommodation system

  • Madjid Khosroyani
  • George K. HungEmail author


The function of the accommodation system is to provide a clear retinal image of objects in the visual scene. The system was previously thought to be under simple continuous (i.e., single mode of operation) feedback control, but recent research has shown that it is under discontinuous (i.e., two stimulus-dependent modes of operation) feedback control by means of fast and slow processes. A model using MATLAB/SIMULINK was developed to simulate this dual-mode behavior. It consists of fast and slow components in a feedback loop. The fast component responds to step target disparity with an open-loop movement to nearly reach the desired level, and then the slow component uses closed-loop feedback to reduce the residual error to an acceptable small level. For slow ramps, the slow component provides smooth tracking of the stimulus, whereas for fast ramps, the fast component provides accurate staircase-like step responses. Simulation of this model using a variety of stimuli, including pulse, step, ramp, and sinusoid, showed good agreement with experimental results. Thus, this represents the first dynamic model of accommodation that can accurately simulate the complex dual-mode behavior seen experimentally. The biological significance of this model is that it can be used to quantitatively analyze clinical deficits such as amblyopia and accommodative insufficiency.


Slow Component Fast Component Amblyopia Ciliary Muscle Accommodative Response 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Benjamin, W. J. (1998). Borish’s Clinical Refraction, Philadelphia, PA: W. B. Saunders.Google Scholar
  2. Brodkey, J. D. and L. Stark (1967). Accommodative convergence—an adaptive nonlinear system. IEEE Trans. Syst. Sci. Cybern. 3, 121–133.Google Scholar
  3. Campbell, F. W., J. G. Robson and G. Westheimer (1959). Fluctuations of accommodation under steady viewing conditions. J. Physiol. 145, 579–594.Google Scholar
  4. Campbell, F. W. and G. Westheimer (1960). Dynamics of accommodation responses of the human eye. J. Physiol. 151, 285–295.Google Scholar
  5. Charman, W. N. and G. Heron (1988). Fluctuations in accommodation: a review. Ophthalmic. Physiol. Opt. 8, 153–164.Google Scholar
  6. Ciuffreda, K. J. (1991). Accommodation and its anomalies, in Vision and Visual Dysfunction: Visual Optics and Instrumentation, Vol. 1, W. N. Charman (Ed.), London: Macmillan, pp. 231–279.Google Scholar
  7. Eadie, A. S. and P. J. Carline (1995). Evolution of control system models of ocular accommodation, vergence and their interaction. Med. Biol. Eng. Comput. 33, 517–524.Google Scholar
  8. Fujii, K., K. Kondo and T. Kasai (1970). An analysis of the human eye accommodation system, Osaka University Technical Report No. 925, Vol. 20, pp. 221–236.Google Scholar
  9. Gilmartin, B. and R. E. Hogan (1985). The relationship between tonic accommodation and ciliary muscle innervation. Invest. Ophthalmol. Vis. Sci. 26, 1024–1028.Google Scholar
  10. Griffin, J. R. (1976). Binocular Anomalies—Procedures for Vision Therapy, Chicago, IL: Professional Press.Google Scholar
  11. Hung, G. K. (1997). Quantitative analysis of the accommodative convergence to accommodation ratio: linear and nonlinear models. IEEE Trans. Biomed. Eng. 44, 306–316.CrossRefGoogle Scholar
  12. Hung, G. K. (1998a). Dynamic model of the vergence eye movement system: simulation using MATLAB/SIMULINK. Comput. Methods Programs Biomed. 55, 59–68.CrossRefGoogle Scholar
  13. Hung, G. K. (1998b). Sensitivity analysis of the stimulus/response function of a static nonlinear accommodation model. IEEE Trans. Biomed. Eng. 45, 335–341.CrossRefGoogle Scholar
  14. Hung, G. K. and K. J. Ciuffreda (1988). Dual-mode behaviour in the human accommodation system. Ophthalmic. Physiol. Opt. 8, 327–332.CrossRefGoogle Scholar
  15. Hung, G. K. and K. J. Ciuffreda (1994). Sensitivity analysis of relative accommodation and vergence. IEEE Trans. Biomed. Eng. 41, 241–248.CrossRefGoogle Scholar
  16. Hung, G. K., K. J. Ciuffreda, J. L. Semmlow and S. C. Hokoda (1983). Model of static accommodative behavior in human amblyopia. IEEE Trans. Biomed. Eng. 30, 665–672.Google Scholar
  17. Hung, G. K., J. L. Semmlow and K. J. Ciuffreda (1982). Accommodative oscillation can enhance average accommodation response: a simulation study. IEEE Trans. Syst. Man Cybern. 12, 594–598.Google Scholar
  18. Hung, G. K., J. L. Semmlow and K. J. Ciuffreda (1986). A dual-mode dynamic model of the vergence eye movement system. IEEE Trans. Biomed. Eng. 33, 1021–1028.Google Scholar
  19. Jiang, B-C. (2000). A modified control model for steady-state accommodation, in Accommodation and Vergence Mechanisms in the Visual System, O. Franzén, H. Richter and L. Stark (Eds), Basel: Birkhäuser Verlag, pp. 235–243.Google Scholar
  20. Kasai, T., M. Unno, K. Fujii, M. Sekiguchi and K. Shinohara (1971). Dynamic characteristics of human eye accommodation system, Osaka University Technical Report, Vol. 21, pp. 569.Google Scholar
  21. Khosroyani, M. (2000). Computer simulation of ocular accommodation and vergence models, MS thesis, Tarbiat Modarres University, Tehran.Google Scholar
  22. Krishnan, V. V. and L. Stark (1975). Integral control in accommodation. Comput. Programs Biomed. 4, 237–255.CrossRefGoogle Scholar
  23. Morgan, M. W. (1968). Accommodation and vergence. Am. J. Optom. Arch. Am. Acad. Optom. 45, 417–454.Google Scholar
  24. O’Neill, W. D. (1969). An interactive control system’s analysis of the human lens accommodative controller. Automatica 5, 645–654.CrossRefGoogle Scholar
  25. Poggio, G. F. and B. Fischer (1977). Binocular interaction and depth sensitivity in striate and prestriate cortex of behaving rhesus monkey. J. Neurophysiol. 40, 1392–1405.Google Scholar
  26. Semmlow, J. L., G. K. Hung and K. J. Ciuffreda (1986). Quantitative assessment of disparity vergence components. Invest. Ophthalmol. Vis. Sci. 27, 558–564.Google Scholar
  27. Stark, L. (1968). Neurological Control Systems, Studies in Bioengineering, New York: Plenum Press, pp. 369–403.Google Scholar
  28. Stark, L., Y. Takahashi and G. Zames (1965). Nonlinear servo-analysis of human lens accommodation. IEEE Trans. Sys. Sci. Cyber. 1, 75–83.CrossRefGoogle Scholar
  29. Sun, F. and L. Stark (1990). Switching control of accommodation: experimental and simulation responses to ramp inputs. IEEE Trans. Biomed. Eng. 37, 73–79.CrossRefGoogle Scholar
  30. Toates, F. M. (1972). Accommodation function of the human eye. Psychol. Rev. 52, 828–863.Google Scholar
  31. Tucker, J. and W. N. Charman (1979). Reaction and response times for accommodation. Am. J. Optom. Physiol. Opt. 56, 490–503.Google Scholar
  32. Winn, B., J. R. Pugh, B. Gilmartin and H. Owens (1990). Arterial pulse modulates steady-state ocular accommodation. Curr. Eye Res. 9, 971–974.Google Scholar

Copyright information

© Society for Mathematical Biology 2002

Authors and Affiliations

  1. 1.Department of Electrical EngineeringTarbiat Modarres UniversityTehranIran
  2. 2.Department of Biomedical EngineeringRutgers UniversityPiscatawayUSA

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