Skip to main content
Log in

A unifying theory of refractive error development

  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

While retinal defocus is believed to be myopigenic in nature, the underlying mechanism has remained elusive. We recently constructed a theory of refractive error development to investigate its fundamental properties. Our Incremental Retinal-Defocus Theory is based on the principle that the change in retinal-defocus magnitude during an increment of genetically-programmed ocular growth provides the requisite sign for the appropriate alteration in subsequent environmentally-induced ocular growth. This theory was tested under five experimental conditions: lenses, diffusers, occlusion, crystalline lens removal, and prolonged nearwork. Predictions of the theory were consistent with previous animal and human experimental findings. In addition, simulations using a MATLAB/SIMULINK model supported our theory by demonstrating quantitatively the appropriate directional changes in ocular growth rate. Thus, our Incremental Retinal-Defocus Theory provides a simple and logical unifying concept underlying the mechanism for the development of refractive error.

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

  • Abbott, M. L., K. L. Schmid and N. C. Strang (1998). Differences in the accommodation stimulus response curves of adult myopes and emmetropes. Ophthal. Physiol. Opt. 18, 13–20.

    Article  Google Scholar 

  • Adams, D. W. and N. A. McBrien (1992). Prevalence of myopia and myopic progression in a population of clinical microscopists. Optom. Vis. Sci. 69, 467–473.

    Google Scholar 

  • Bartmann, M. and F. Schaeffel (1994). A simple mechanism for emmetropization without cues from accommodation or colour. Vision Res. 34, 873–876.

    Article  Google Scholar 

  • Bennett, A. G. and R. B. Rabbetts (1989). Clinical Visual Optics, Woburn, MA: Butterworth-Heinemann, p. 75.

    Google Scholar 

  • Bjelke, B. et al. (1996). Dopaminergic transmission in the rat retina: evidence for volume transmission. Chem. Neuroanat. 12, 37–50.

    Article  Google Scholar 

  • Blackie, C. A. and H. C. Howland (1999). Extension of the Flitcroft model of emmetropization: inclusion of pupil size. Ophthalmic Physiol. Opt. 19, 112–125.

    Article  Google Scholar 

  • Bradley, D. V., A. Fernandes, M. Tigges and R. G. Boothe (1996). Diffuser contact lenses retard axial elongation in infant rhesus monkeys. Vision Res. 36, 509–514.

    Article  Google Scholar 

  • Christiansen, A. M. and J. Wallman (1991). Evidence that increased scleral growth underlies visual deprivation myopia in chicks. Invest. Ophthalmol. Vis. Sci. 32, 2134–2150.

    Google Scholar 

  • 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 

  • Ciuffreda, K. J. (1998). Accommodation, pupil, and presbyopia, in Borish’s Clinical Refraction, W. J. Benjamin (Ed.), Philadelphia, PA: W. B. Saunders Co, pp. 77–120.

    Google Scholar 

  • Ciuffreda, K. J. and R. V. Kenyon (1983). Accommodative vergence and accommodation in normals, amblyopes, and strabismics, in Vergence Eye Movements: Basic and Clinical Aspects, C. M. Schor and K. J. Ciuffreda (Eds), Boston, MA: Butterworths, pp. 101–173.

    Google Scholar 

  • Cohen, A. I. (1981). The retina and the optic nerve, in Adler’s Physiology of the Eye, Clinical Applications, R. A. Moses (Ed.), St. Louis, MO: C. V. Mosby Company, pp. 370–410.

    Google Scholar 

  • Dowling, J. E. (1996). Retinal processing of vision, in Comprehensive Human Physiology: From Cellular Mechanisms to Integration, Vol. 1, R. Greger and U. Windhorst (Eds), Berlin: Springer-Verlag, pp. 773–778.

    Google Scholar 

  • Fledelius, H. C. and M. Stubgaard (1986). Changes in refraction and corneal curvature during growth and adult life. A cross-sectional study. Acta Ophthalmol. 64, 487–491.

    Google Scholar 

  • Flitcroft, D. I. (1998). A model of the contribution of oculomotor and optical factors to emmetropization and myopia. Vision Res. 38, 2869–2879.

    Article  Google Scholar 

  • Garner, L. F., C. K. Meng, T. P. Grosvenor and N. Mohidin (1990). Ocular dimensions and refractive power in Malay and Melanesian children. Ophthalmic Physiol. Opt. 10, 234–238.

    Article  Google Scholar 

  • Goss, D. A. and P. Erickson (1987). Meridional corneal components of myopia progression in young adults and children. Am. J. Optom. Physiol. Opt. 64, 475–481.

    Google Scholar 

  • Goss, D. A. and T. W. Jackson (1993). Cross-sectional study of changes in the ocular components in school children. Appl. Opt. 32, 4169–4173.

    Article  Google Scholar 

  • Goss, D. A. and M. G. Wickham (1995). Retinal-image mediated ocular growth as a mechanism for juvenile onset myopia and for emmetropization. Doc. Ophthalmol. 90, 341–375.

    Article  Google Scholar 

  • Goss, D. A. and R. L. Winkler (1983). Progression of myopia in youth: age of cessation. Am. J. Optom. Physiol. Opt. 60, 651–658.

    Google Scholar 

  • Gottlieb, M. D., H. B. Joshi and D. L. Nickla (1990). Scleral changes in chicks with form-deprived myopia. Curr. Eye Res. 9, 1157–1165.

    Google Scholar 

  • Grosvenor, T. and D. A. Goss (1998). Role of the cornea in emmetropia and myopia. Optom. Vis. Sci. 75, 132–145.

    Google Scholar 

  • Grosvenor, T. and D. A. Goss (1999). Etiology of myopia, in Clinical Management of Myopia, Boston, MA: Butterworth-Heinemann, pp. 49–62.

    Google Scholar 

  • Gwiazda, J., F. Thorn, J. Bauer and R. Held (1993). Emmetropization and the progression of manifest refraction in children followed from infancy to puberty. Clin. Vis. Sci. 8, 337–344.

    Google Scholar 

  • Hung, G. K. (1998). Sensitivity analysis of the stimulus-response function of a static nonlinear accommodation model. IEEE Trans. Biomed. Eng. 45, 335–341.

    Article  Google Scholar 

  • Hung, G. K. and K. J. Ciuffreda (1999). Model of refractive error development. Curr. Eye Res. 19, 41–52.

    Article  Google Scholar 

  • Hung, G. K. and K. J. Ciuffreda (2000a). Differential retinal-defocus magnitude during eye growth provides the appropriate direction signal. Med. Sci. Monitor 6, 791–795.

    Google Scholar 

  • Hung, G. K. and K. J. Ciuffreda (2000b). Quantitative analysis of the effect of near lens addition on accommodation and myopigenesis. Curr. Eye Res. 20, 293–312.

    Article  Google Scholar 

  • Hung, L. F., J. Wallman and E. L. Smith (2000b). Vision-dependent changes in the choroidal thickness of Macaque monkeys. Invest. Ophthalmol Vis. Sci. 41, 1259–1269.

    Google Scholar 

  • Iuvone, P. M., M. Tigges, R. A. Stone, S. Lambert and A. M. Laties (1991). Effect of apomorphine, a dopamine receptor agonist, on ocular refraction and axial elongation in primate model of myopia. Invest. Ophthalmol Vis. Sci. 32, 1674–1677.

    Google Scholar 

  • Jiang, B. C. and W. M. Woessner (1996). Increase in axial length is responsible for late-onset myopia. Optom. Vis. Sci. 73, 231–234.

    Google Scholar 

  • Lin, L. L. K., Y. F. Shih, Y. C. Lee, P. T. Hung and P. K. Hou (1996). Changes in ocular refraction and its components among medical students—a 5-year longitudinal study. Optom. Vis. Sci. 73, 495–498.

    Google Scholar 

  • Marzani, D. and J. Wallman (1997). Growth of the two layers of the chick sclera is modulated reciprocally by visual conditions. Invest. Ophthalmol. Vis. Sci. 38, 1726–1739.

    Google Scholar 

  • McBrien, N. A., A. Gentle and C. Cottriall (1999). Optical correction of induced axial myopia in the tree shrew: implications for emmetropization. Optom. Vis. Sci. 76, 419–427.

    Google Scholar 

  • McBrien, N. A. and M. Millodot (1986). The effect of refractive error on the accommodative response gradient. Ophthalmic Physiol. Opt. 6, 145–149.

    Article  Google Scholar 

  • Medina, A. (1987). A model of emmetropization, the effect of corrective lenses. Acta Ophthalmol. 65, 585–571.

    Article  Google Scholar 

  • Norton, T. T. (1999). Animal models of myopia: learning how vision controls the size of the eye. Instit. Lab. Animal Res. J. 40, 59–77.

    Google Scholar 

  • Norton, T. T. and J. A. Rada (1995). Reduced extracellular matrix in mammalian sclera with induced myopia. Vision Res. 35, 1271–1281.

    Article  Google Scholar 

  • O’Leary, D. J., K. M. Chung and S. Othman (1992). Contrast reduction without myopia induction in monkey. Invest. Ophthalmol. Vis. Sci. 33(Suppl.), 712.

    Google Scholar 

  • Ong, E. and K. J. Ciuffreda (1997). Accommodation, Nearwork, and Myopia: Optometric Extension Program Foundation, Inc, Santa Ana, CA, pp. 76–96, 177–201.

    Google Scholar 

  • Ong, E., K. J. Ciuffreda and B. Tannen (1993). Static accommodation in congenital nystagmus. Invest. Ophthalmol. Vis. Sci. 34, 194–204.

    Google Scholar 

  • Rada, J. A., A. L. McFarland, P. K. Cornuet and J. R. Hassell (1992). Proteoglycan synthesis by scleral chondrocytes is modulated by a vision dependent mechanism. Curr. Eye Res. 11, 767–782.

    Google Scholar 

  • Rosenfield, M. and B. Gilmartin (1998). Myopia and nearwork: causation or merely association? in Myopia and Nearwork, M. Rosenfield and B. Gilmartin (Eds), Oxford: Butterworth-Heinemann, pp. 193–206.

    Google Scholar 

  • Scammon, R. E. and E. L. Armstrong (1925). On the growth of the human eyeball and optic nerve. J. Comp. Neurol. 38, 165–219.

    Article  Google Scholar 

  • Schaeffel, F. and H. C. Howland (1988). Mathematical model of emmetropization in the chicken. J. Opt. Soc. Am. A 5, 2080–2086.

    Article  Google Scholar 

  • Schaeffel, F., D. Troilo, J. Wallman and H. C. Howland (1990). Developing eyes that lack accommodation grow to compensate for imposed defocus. Vis. Neurosci. 4, 177–183.

    Article  Google Scholar 

  • Siegwart, J. T. Jr. and T. T. Norton (1998). A susceptible period for deprivation-induced myopia in tree shrew. Vision Res. 38, 3505–3515.

    Article  Google Scholar 

  • Siegwart, J. T. Jr. and T. T. Norton (1999). Regulation of the mechanical properties of tree shrew sclera by the visual environment. Vision Res. 39, 387–407.

    Article  Google Scholar 

  • Smith, E. L. and L. F. Hung (1999). The role of optical defocus in regulating refractive development in infant monkeys. Vision Res. 39, 1415–1435.

    Article  Google Scholar 

  • Smith, E. L. and L. F. Hung (2000). Form deprivation myopia in monkeys is a graded phenomenon. Vision Res. 40, 371–381.

    Article  Google Scholar 

  • Smith, G. and D. A. Atchison (1997). The Eye and Visual Optical Instruments, Cambridge, United Kingdom: Cambridge University Press, pp. 274, 796.

    Google Scholar 

  • Sorsby, A., B. Benjamin and M. Sheridan (1961). Refraction and its Components During the Growth of the Eye from the Age of Three, Med Res Council Report Series 301, London: Her Majesty’s Stationery Office.

    Google Scholar 

  • Sperduto, R. D., D. Seigel, J. Roberts and M. Rowland (1983). Prevalence of myopia in the United States. Arch. Ophthalmol. 101, 405–407.

    Google Scholar 

  • Stark, L. (1968). Neurological Control Systems, Studies in Bioengineering, New York: Plenum Press, pp. 205–219.

    Google Scholar 

  • Stone, R. A., T. Lin and A. M. Laties (1989). Retinal dopamine and form-deprivation myopia. Proc. Natl. Acad. Sci. 86, 704–706.

    Article  Google Scholar 

  • Tigges, M., J. Tigges, A. Fernendes, H. M. Effers and J. A. Gammon (1990). Postnatal axial eye elongation in normal and visually deprived rhesus monkeys. Invest. Ophthalmol. Vis. Sci. 31, 1035–1046.

    Google Scholar 

  • Troilo, D. (1989). The visual control of eye growth in chicks, PhD dissertation, City College of the City University of New York, New York.

    Google Scholar 

  • Troilo, D., M. D. Gottlieb and J. Wallman (1987). Visual deprivation causes myopia in chicks with optic nerve section. Curr. Eye Res. 6, 993–999.

    Google Scholar 

  • Troilo, D., D. L. Nickla and J. Wallman (2000a). Choroidal thickness changes during altered eye growth and refractive state in a primate. Invest. Ophthalmol. Vis. Sci. 41, 1249–1258.

    Google Scholar 

  • Troilo, D., D. L. Nickla and C. F. Wildsoet (2000b). Form deprivation myopia in mature common Marmoset (Callitbrix jaccbus). Invest. Ophthalmol. Vis. Sci. 41, 2043–2049.

    Google Scholar 

  • Van Alphen, G. W. (1961). On emmetropia and ametropia. Acta Ophthalmol 142(Suppl.), Karger, Basel, pp. 1–92.

    Google Scholar 

  • Wallman, J. (1997). Can myopia be prevented? in 14th Biennial Research to Prevent Blindness Science Writers Seminar in Ophthalmology, New York: Research to Prevent Blindness, pp. 50–52.

    Google Scholar 

  • Weale, R. A. (1982). A Biography of the Eye: Development, Growth, Age, London: H. K. Lewis.

    Google Scholar 

  • Westheimer, G. (1981). Visual acuity, in Adler’s Physiology of the Eye, R. A. Moses (Ed.), St. Louis: C.V. Mosby Co., pp. 530–544.

    Google Scholar 

  • Wildsoet, C. F. (1998). Structural correlates of myopia, in Myopia and Nearwork, M. Rosenfield and B. Gilmartin (Eds), Oxford: Butterworth-Heinemann, pp. 32–51.

    Google Scholar 

  • Wildsoet, C. F. and M. J. Collins (2000). Competing defocus stimuli of opposite sign produce opposite effects in eyes with intact and section optic nerves in the chick. Invest. Ophthalmol. Vis. Sci. 41, S738.

    Google Scholar 

  • Wildsoet, C. F. and J. D. Pettigrew (1988). Experimental myopia and anomalous eye growth patterns unaffected by optic nerve section in chickens: Evidence for local control of eye growth. Clin. Vis. Sci. 3, 99–107.

    Google Scholar 

  • Wilson, J. R., A. Fernandes, C. V. Chankler, M. Tigges, R. G. Boothe and J. A. Gammon (1987). Abnormal development of the axial length of aphakic monkey eyes. Invest. Ophthalmol. Vis. Sci. 28, 2096–2099.

    Google Scholar 

  • Winauer, J. A., X. Zhu, T. Park and J. Wallman (2000). Is myopic blur more important than sharp vision for positive-lens compensation? Invest. Ophthalmol. Vis. Sci. 41, S136.

    Google Scholar 

  • Windhorst, U. (1996). Specific networks of the cerebral cortex: functional organization and plasticity, in Comprehensive Human Physiology: From Cellular Mechanisms to Integration, Vol. 1, R. Greger and U. Windhorst (Eds), Berlin: Springer-Verlag, pp. 1105–1136.

    Google Scholar 

  • Yackle, K. and D. E. Fitzgerald (1999). Emmetropization: an overview. J. Behav. Optom. 10, 38–43.

    Google Scholar 

  • York, M. A. and R. B. Mandell (1969). A new calibration system for photokeratoscopy. II. Corneal contour measurements. Am. J. Optom. Arch. Am. Acad. Optom. 46, 818–825.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to George K. Hung.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hung, G.K., Ciuffreda, K.J. A unifying theory of refractive error development. Bull. Math. Biol. 62, 1087–1108 (2000). https://doi.org/10.1006/bulm.2000.0199

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1006/bulm.2000.0199

Keywords

Navigation