Skip to main content
Log in

Evolution of control system models of ocular accommodation, vergence and their interaction

  • Review
  • Published:
Medical and Biological Engineering and Computing Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

This paper reviews the evolution of inferential models describing ocular accommodation and vergence, which have been developed using the techniques of control engineering. The models are developed by inferring that the observed behaviour of the ocular systems could be produced by particular types of feedback control systems. The models are subsequently tested and improved by modifications resulting from the comparison of model predictions with physiological experimentation. Current models of accommodation and vergence have had considerable success in describing both the steady-state and dynamic behaviours of the individual systems. However, controversy currently exists among researchers, particularly with respect to the composition of models that describe the interaction of the two systems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Alpern, M., Kincaid, W., andLubeck, M. (1959): ‘Vergence and accommodation III: proposed definitions of the AC/A ratios’,Am. J. Ophthal.,48, pp. 141–148

    Google Scholar 

  • Brodkey, J., andStark, L. (1967a): ‘Feedback control analysis of accommodative convergence’,Am. J. Surg.,114, pp. 150–158

    Article  Google Scholar 

  • Brodkey, J., andStark, L. (1967b): ‘Accommodative convergence—an adaptive non-linear control system’,IEEE Trans.,SMC-3, pp. 121–133

    Google Scholar 

  • Burian, H. M., andVon Noorden, G. K. (1974): ‘Binocular vision and ocular motility’ (C. V. Mosby Ltd, St Louis, USA)

    Google Scholar 

  • Campbell, F. W., andWestheimer, G. (1960): ‘Dynamics of accommodation responses of the human eye’,J. Physiol.,151, pp. 285–295

    Google Scholar 

  • Charman, W. N. (1983): ‘The retinal image in the human eye’inOsborne, N., andChader, G. (Eds.): ‘Progress in retinal research’ Vol. 2. (Pergamon Press, Oxford) pp. 1–50

    Google Scholar 

  • Charman, W. N., andHeron, G. (1988): ‘Fluctuations in accommodation: a review’,Ophthal. Physiol. Opt.8, pp. 153–164

    Google Scholar 

  • Ciuffreda, K. J., andHung, G. K. (1992): ‘Symptoms related to abnormal tonic state: experimental results and computer simulations’,Optom. Vis. Sci.,69, pp. 283–288

    Article  Google Scholar 

  • Collewijn, H., andErkelens, C. J. (1990): ‘Binocular eye movements and the perception of depth’inKowler, E. (Ed.): ‘Eye movements and their role in visual and cognitive processes’ (Elsevier, Amsterdam) pp. 213–261

    Google Scholar 

  • Cook, G., andStark, L. (1967): ‘Derivation of a model for the human eye positioning system’,Bull. Math. Biophys.,29, pp. 153–173

    Article  Google Scholar 

  • Dazzo, J. J., andHoupis, C. H. (1988): ‘Linear control system analysis and design, conventional and modern’ (McGraw Hill, New York) 3rd edn.

    MATH  Google Scholar 

  • Fender, D. H. (1964a): ‘Control mechanisms of the eye’,Sci. Am.,211, pp. 24–33

    Article  Google Scholar 

  • Fender, D. H. (1964b): ‘Techniques of systems-analysis applied to feedback pathways in the control of eye movements’,Symp. Soc. Exp. Biol.,18, pp. 401–419

    Google Scholar 

  • Fender, D. H., andNye, P. W. (1961): ‘An investigation of the mechanisms of eye movement control’,Kybern.,1, pp. 81–88

    Article  Google Scholar 

  • Fincham, E. F. (1962): ‘Accommodation and convergence in the absence of retinal images’,Vis. Res.,1, pp. 425–440

    Article  Google Scholar 

  • Fincham, E. F., andWalton, J. (1957): ‘The reciprocal action of accommodation and vergence’,J. Physiol.,137, pp. 488–508

    Google Scholar 

  • Fry, G. A. (1939): ‘Further experiments on the accommodation convergence relationship’,Am. J. Optom.,16, pp. 325–336

    Google Scholar 

  • Gray, L., Winn, B., Gilmartin, B., andEadie, A. S. (1993): ‘The effect of mental effort on concurrent measures of open-loop accommodation and vergence’,Invest. Ophthal. Vis., Sci.,34, pp. 2996–3003

    Google Scholar 

  • Heath, G. G. (1956): ‘Components of accommodation’,Am. J. Optom. Arch. Am. Acad. Optom.,33, pp. 569–578

    Google Scholar 

  • Heron, G., andWinn, B. (1989): ‘Binocular accommodation reaction and response times for normal observers’,Ophthal. Physiol. Opt.,9, pp. 176–183

    Google Scholar 

  • Hung, G. K. (1990): ‘Fixation disparity under open and closed-loop accommodation’,Ophthal. Physiol. Opt.,10, pp. 211–213

    Google Scholar 

  • Hung, G. K. (1991): ‘A linear model of accommodation can account for discrepancies between AC/A measures using the fixation disparity and phoria methods’,Ophthal. Physiol. Opt.,11, pp. 275–278

    Article  MathSciNet  Google Scholar 

  • Hung, G. K. (1992a): ‘Adaptation model of accommodation and vergence’,Ophthal. Physiol. Opt.,12, pp. 319–326

    Article  Google Scholar 

  • Hung, G. K. (1992b): ‘A simple equation relating AC/A ratio to accommodative controller gain’,Ophthal. Physiol. Opt.,12, pp. 106–108

    Article  Google Scholar 

  • Hung, G. K. (1992c): ‘Quantitative anlaysis of associated and disassociated phorias’,IEEE Trans.,BME-39, pp. 135–145

    Google Scholar 

  • Hung, G. K., andCiuffreda, K. J. (1988): ‘Dual-mode behaviour in the human accommodation system’,Ophthal. Physiol. Opt.,8, pp. 327–332

    Article  Google Scholar 

  • Hung, G. K., Ciuffreda, K. J., andSemmlow, J. (1986a): ‘Static vergence and accommodation: population norms and orthoptic effects’,Doc. Ophthalmol.,62, pp. 165–179

    Article  Google Scholar 

  • Hung, G. K., Ciuffreda, K. J., Semmlow, J. L., andHokoda, S. C. (1983): ‘Model of static accommodative behaviour in human amblyopia’,IEEE Trans.,BME-30, pp. 665–671

    Google Scholar 

  • Hung, G. K., andSemmlow, J. L. (1980): ‘Static behaviour of accommodation and vergence computer simulation of a dual interaction feedback model’,IEEE Trans.,BME-27, pp. 439–447

    Google Scholar 

  • Hung, G. K., andSemmlow, J. L. (1982): ‘A quantitative theory of control sharing between accommodative and vergence controllers’,IEEE Trans.,BME-29, pp. 364–370

    Google Scholar 

  • Hung, G. K., andSemmlow, J. L., andCiuffreda, K. J. (1982): ‘Accommodative oscillation can enhance average accommodation response’,IEEE Trans.,SMC-12, pp. 594–598

    Google Scholar 

  • Hung, G. K., Semmlow, J. L., andCiuffreda, K. J. (1986b): ‘A dual-mode dynamic model of the vergence eye movement system’,IEEE Trans.,BME-3, pp. 1021–1028

    Google Scholar 

  • Judge, S. J. (1991): ‘Vergence’inCarpenter, R. H. S. (Ed.): ‘Eye movements’ (MacMillan, London) pp. 157–172

    Google Scholar 

  • Krall, A. M., andFarnaro, R. (1967): ‘An algorithm for generating root locus plots’,Commun. ACM,10, pp. 186–188

    Article  MATH  Google Scholar 

  • Krishnan, V. V., andStark, L. (1975): ‘Integral control in accommodation’,Comput. Programs Biomed.,4, pp. 237–245

    Article  Google Scholar 

  • Krishnan, V. V., andStark, L. (1977): ‘A heuristic model for the human vergence eye movement system’,IEEE Trans.,BME-24, pp. 44–49

    Google Scholar 

  • Maddox, E. E. (1886): ‘Investigations in the relationship between convergence and accommodation’,J. Anat.,21, pp. 475–505, pp. 565–584

    Google Scholar 

  • Miles, F. A. (1985): ‘Adaptive regulation in the vergence and accommodation control systems’inBerthoz, A., andMelvill Jones, G. (Eds.): ‘Adaptive mechanisms in gaze control’ (Elsevier, Amsterdam) pp. 81–94

    Google Scholar 

  • Milhorn, H. T. (1966): ‘The application of control theory to physiological systems’ (W. B. Saunders, Philadelphia)

    Google Scholar 

  • Morgan, M. W. (1957): ‘The resting state of accommodation’,Am. J. Optom. Arch. Am. Acad. Optom.,34, pp. 347–353

    Google Scholar 

  • O’Neill, W. D. (1969): ‘An interacting control systems analysis of the human lens accommodative controller’,Automatica,5, pp. 645–654

    Article  Google Scholar 

  • O’Neill, W. D., andBrodkey, J. S. (1970): ‘A non-linear analysis of the mechanics of accommodation’,Vis. Res.,10, pp. 375–391

    Article  Google Scholar 

  • O’Neill, W. D., Sanathanan, C. K., andBrodkey, J. S. (1969): ‘A minimum variance, time optimal, control system model of human lens accommodation’,IEEE Trans.,SMC-5, pp. 290–299

    Google Scholar 

  • Ogle, K. N., Martens, T. G., andDyer, J. A. (1967): ‘Oculomotor imbalance and fixation disparity’ (Lea and Febiger, New York)

    Google Scholar 

  • Rashbass, C., andWestheimer, G. (1961): ‘Disjunctive eye movements’,J. Physiol.,159, pp. 339–364

    Google Scholar 

  • Robinson, D. A. (1981a): ‘The use of control systems analysis in the neurophysiology of eye movements’,Ann. Rev. Neurosci.,4, pp. 463–503

    Article  Google Scholar 

  • Robinson, D. A. (1981b): ‘Models of the mechanisms of eye movements’inZuber, B. L. (Ed.): ‘Models of oculomotor behaviour and control’ (CRC Press, Florida) pp. 22–40

    Google Scholar 

  • Robinson, D. A. (1986): ‘Is the oculomotor system a cartoon of motor control’,Prog. Brain Res.,64, pp. 411–417

    Article  Google Scholar 

  • Robinson, D. A., Gordon, J. L., andGordon, S. E. (1986): ‘A model of the smooth pursuit eye movement system’,Biol. Cybern.,55, pp. 43–57

    Article  Google Scholar 

  • Rusenfield, M., andGilmartin, B. (1988a): ‘Accommodative adaptation induced by sustained disparity-vergence’,Am. J. Optom. Physiol. Opt.,65, pp. 118–126

    Google Scholar 

  • Rosenfield, M., andGilmartin, B. (1988b): ‘The effect of vergence adaptation on convergent accommodation’,Ophthal. Physiol. Opt.,8, pp. 172–177

    Google Scholar 

  • Rosenfield, M., andGilmartin, B. (1989): ‘Temporal aspects of accommodation’,Optoml. Vis. Sci.,66, pp. 229–234

    Article  Google Scholar 

  • Schor, C. M. (1979): ‘The relationship between fusional vergence eye movements and fixation disparity’,Vis. Res.,19, pp. 1359–1367

    Article  Google Scholar 

  • Schor, C. M. (1980): ‘Fixation disparity: a steady state error of disparity induced vergence’,Am. J. Optom. Physiol. Opt.,57, pp. 618–631

    Google Scholar 

  • Schor, C. M. (1983): ‘Fixation disparity and vergence adaptation in vergence eye movements’inSchor, C. M., andCiuffreda, K. J. (Eds.): ‘Vergence eye movements’ (Butterworths, Boston)

    Google Scholar 

  • Schor, C. M. (1985): ‘Models of mutual interaction between accommodation and convergence’,Am. J. Optom. Physiol. Opt.,62, pp. 369–374

    Google Scholar 

  • Schor, C. M. (1986): ‘Adaptive regulation of accommodative vergence and vergence accommodation’,Am. J. Optom. Physiol. Opt.,63, pp. 587–609

    Google Scholar 

  • Schor, C. M. (1987): ‘Phasic-tonic organization of accommodation and vergence’inLennerstrand, G.et al. (Eds.): ‘Strabismus and amblyopia, experimental basis for advances in clinical management’ (Plenum Press, New York) pp. 111–120

    Google Scholar 

  • Schor, C. M. (1992): ‘A dynamic model of cross-coupling between accommodation and convergence: simulations of step and frequency responses’,Optom. Vis. Sci.,69, pp. 258–269

    Article  Google Scholar 

  • Schor, C. M., Alexander, J., Cormack, L., andStevenson, S. (1992): ‘Negative feedback control model of proximal convergence and accommodation’,Ophthal. Physiol. Opt.,12, pp. 307–318

    Article  Google Scholar 

  • Schor, C. M., andKotulak, J. C. (1986): ‘Dynamic interactions between accommodation and convergence are velocity sensitive’,Vis. Res.,26, pp. 927–943

    Article  Google Scholar 

  • Schor, C. M., andNaryan, V. (1982): ‘Graphical analysis of prism adaptation, convergence accommodation and accomodative convergence’,Am. J. Optom. Physiol. Opt.,59, pp. 774–784

    Google Scholar 

  • Semmlow, J. L. (1981): ‘Oculomotor responses to near stimuli: the near triad’inZuber, B. L. (Ed.): ‘Models of oculomotor behaviour and control’ (CRC Press, Florida) pp. 161–191

    Google Scholar 

  • Semmlow, J. L., Hung, G. K., Horng, J. L., andCiuffreda, K. (1993): ‘Initial control component in disparity vergence eye movements’,Ophthal. Physiol. Opt.,13, pp. 48–55

    Google Scholar 

  • Semmlow, J. L., Hung, G. K., andCiuffreda, K. J. (1986): ‘Quantitative aspects of disparity vergence components’,Invest. Ophthal. Vis. Sci.,27, pp. 558–564

    Google Scholar 

  • Semmlow, J. L., Hung, G. K., Horng, J. L., andCiuffreda, K. J. (1993): ‘The initial control component in disparity vergence eye movements’,Ophthal. Physiol. Opt.,13, pp. 48–55

    Google Scholar 

  • Stark, L., andTakahashi, Y. (1965): ‘Absence of an odd-error signal mechanism in human accommodation’,IEEE Trans.,BME-12, pp. 138–146

    Google Scholar 

  • Stark, L., Takahashi, Y., andZames, G. (1965): ‘Nonlinear servoanalysis of human lens accommodation’,IEEE Trans.,SMC-1, pp. 76–83

    Google Scholar 

  • Toates, F. M. (1968): ‘Control of the eyes intrinsic muscles’,Meas. Control,1, pp. 129–132

    Google Scholar 

  • Toates, F. M. (1969): ‘Accommodation and convergence in the human eye’,Meas. Control.2, pp. 29–33

    Google Scholar 

  • Toates, F. M. (1970): ‘A model of accommodation’,Vis. Res.,10, pp. 1069–1076

    Article  Google Scholar 

  • Toates, F. M. (1972a): ‘Accommodation function of the human eye’,Physiol. Rev.,52, pp. 828–863

    Google Scholar 

  • Toates, F. M. (1972b): ‘Studies on the control of accommodation and convergence’,Meas. Control,5, pp. 58–61

    Google Scholar 

  • Toates, F. M. (1974): ‘Vergence eye movements’,Doc. Ophthalmol.,37, pp. 153–214

    Article  Google Scholar 

  • Toates, F. M. (1975): ‘Control theory in biology and experimental psychology’ (Hutchison, London)

    Google Scholar 

  • Westheimer, G. (1966): ‘Focusing responses of the human eye’,Am. J. Optom. Arch. Am. Acad. Optom.,43, pp. 221–232

    Google Scholar 

  • Westheimer, G., andMitchell, A. M. (1956): ‘Eye movement responses to convergent stimuli’,AMA Arch. Ophthalmol.,54, pp. 848–856

    Google Scholar 

  • Wick, B., andCurrie, D. (1991): ‘Dynamic demonstration of proximal vergence and proximal accommodation’,Optom. Vis. Sci.,68, pp. 163–167

    Article  Google Scholar 

  • Winn, B., andGilmartin, B. (1992): ‘A current perspective on accommodation microfluctuations’,Ophthal. Physiol. Opt.,12, pp. 252–256

    Google Scholar 

  • Winn, G., Gilmartin, B., Mortimer, L. C., andEdwards, N. R. (1991): ‘The effect of mental effort on open and closed-loop accommodation’,Ophthal. Physiol. Opt.,11, pp. 335–339

    Article  Google Scholar 

  • Young, L. R. (1981): ‘The sampled data model and foveal dead zone for saccadesinZuber, B. L. (Ed.): ‘Models of oculomotor behaviour and control’ (CRC Press, Florida) pp. 43–74

    Google Scholar 

  • Young, L. R., andStark, L. (1963): ‘Variable feedback experiments testing a sampled data model for eye tracking movements’,IEEE Trans.,HFE-4, pp. 38–51

    Google Scholar 

  • Zuber, B. L. (1971): ‘The control of vergence eye movements’inBach-Y-Rita, P., andCollins, C. C. (Eds.): ‘The control of eye movements’ (Academic Press, New York) pp. 447–470

    Google Scholar 

  • Zuber, B. L., andStark, L. (1968): ‘Dynamical characteristics of fusional vergence eye movements’,IEEE Trans.,SMC-4, pp. 72–79

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Eadie, A.S., Carlin, P.J. Evolution of control system models of ocular accommodation, vergence and their interaction. Med. Biol. Eng. Comput. 33, 517–524 (1995). https://doi.org/10.1007/BF02522508

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02522508

Keywords

Navigation