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On the mechanics of myopia and its influence on retinal detachment

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Abstract

A mechanics-based mathematical model of retinal detachment due to the geometric changes of the eye associated with the evolution of myopia is developed. This includes deformation of the retina due to biological growth of the retina, as well as elastic deformation imposed on the retina by the myopic change in shape of the much stiffer choroid and sclera. The problem is formulated as a propagating boundary value problem in the calculus of variations, which yields self-consistent governing equations, boundary conditions, and transversality conditions that establish the location of the propagating boundaries that correspond to equilibrium configurations of the detaching ocular system. Axisymmetric conditions are considered, and exact, analytical solutions to the corresponding boundary value problem are obtained for detaching retinas with and without a tear. Based upon application of the model presented herein to the emmetropic retina, a value of the bond energy of the retina to retinal pigment epithelium interface is estimated using material properties found in the literature. Simulations based on the analytical solutions are performed for a detachment in the retina located at either the posterior or superior pole of the eye. The results support the clinical finding of an increased prevalence of retinal detachment in myopic eyes and provide insight into the potential causation for the increased prevalence.

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Notes

  1. Although the surface areas are of equal value, the final myopic state of the retina will not be stress free when \(\alpha =1\). This is due to the constrained shape that the outer eye imposes on the growth of the retina (Rodriguez et al. 1994; Skalak 1981).

  2. The bending measures are the components of the bending tensor, which are dependent on the derivatives of the rotation vector in a similar manner as the strain components are dependent on the derivatives of the displacement vector.

References

  • Akiba J (1993) Prevalence of posterior vitreous detachment in high myopia. Ophthalmology 100(9):1384–1388

    Article  Google Scholar 

  • Alkuraya H (2011) Myopic foveoschisis: a common complication in high myopia. Retinal Phys 8(2):47-49

    Google Scholar 

  • Atchison DA, Jones CE, Schmid KL, Pritchard N, Pope JM, Strugnell WE, Riley RA (2004) Eye shape in emmetropia and myopia. Invest Ophthalmol Vis Sci 45(10):3380–3386

    Article  Google Scholar 

  • Atchison DA, Pritchard N, Schmid KL, Scott DH, Jones CE, Pope JM (2005) Shape of the retinal surface in emmetropia and myopia. Invest Ophthalmol Vis Sci 46(8):2698–2707

    Article  Google Scholar 

  • Bottega WJ, Bishay PL, Prenner JL, Fine HF (2013) On the mechanics of a detaching retina. Math Med Biol 30(4):287–310

    Article  Google Scholar 

  • Celorio JM, Pruett RC (1991) Prevalence of lattice degeneration and its relation to axial length in severe myopia. Am J Ophthalmol 111(1):20–23

    Article  Google Scholar 

  • Chou T, Siegel M (2012) A mechanical model of retinal detachment. Phys Biol 9(4):046001

    Article  Google Scholar 

  • Feldkaemper M, Schaeffel F (2013) An updated view on the role of dopamine in myopia. Exp Eye Res 114:241–251

    Article  Google Scholar 

  • Flügge W (1960) Stesses in shells. Springer, Berlin

    Book  Google Scholar 

  • Gariano RF, Kim CH (2004) Evaluation and management of suspected retinal detachment. Am Fam Phys 69(7):1691–1698

    Google Scholar 

  • Gella L, Raman R, Sharma T (2011) Evaluation of in vivo human retinal morphology and function in myopes. Curr Eye Res 36(10):943–946

    Article  Google Scholar 

  • Gilmartin B, Nagra M, Logan NS (2013) Shape of the posterior vitreous chamber in human emmetropia and myopia. Invest Ophthalmol Vis Sci 54(12):7240–7251

    Article  Google Scholar 

  • Greene PR (1980) Mechanical considerations in myopia: relative effects of accommodation, convergence, intraocular pressure, and the extraocular muscles. Am J Optom Physiol Opt 57(12):902–914

    Article  Google Scholar 

  • Griffith AA (1921) The phenomena of rupture and flow in solids. Philos Trans R Soc Lond A 221:106–119

    Google Scholar 

  • Grytz R, El Hamdaoui M (2017) Multi-scale modeling of vision-guided remodeling and age-dependent growth of the tree shrew sclera during eye development and lens-induced myopia. J Elast 129(1–2):171–195

    Article  MathSciNet  Google Scholar 

  • Hung GK, Mahadas K, Mohammad F (2016) Eye growth and myopia development: unifying theory and Matlab model. Comput Biol Med 70:106–118

    Article  Google Scholar 

  • Ishii K, Iwata H, Oshika T (2011) Quantitative evaluation of changes in eyeball shape in emmetropization and myopic changes based on elliptic fourier descriptors. Invest Ophthalmol Vis Sci 52(12):8585–8591

    Article  Google Scholar 

  • Kain HL (1984) A new model for examining chorioretinal adhesion experimentally. Arch Ophthalmol 102(4):608–611

    Article  Google Scholar 

  • Kita M, Marmor MF (1992) Retinal adhesive force in living rabbit, cat, and monkey eyes. Normative data and enhancement by mannitol and acetazolamide. Invest Ophthalmol Vis Sci 33(6):1879–1882

    Google Scholar 

  • Kita M, Negi A, Kawano S, Honda Y, Maegawa S (1990) Measurement of retinal adhesive force in the in vivo rabbit eye. Invest Ophthalmol Vis Sci 31(4):624–628

    Google Scholar 

  • Lakawicz JM, Bottega WJ, Prenner JL, Fine HF (2015) An analysis of the mechanical behaviour of a detaching retina. Math Med Biol 32(2):137–161

    Article  MathSciNet  Google Scholar 

  • Lin T, Grimes PA, Stone RA (1993) Expansion of the retinal pigment epithelium in experimental myopia. Vision Res 33(14):1881–1885

    Article  Google Scholar 

  • McBrien NA, Jobling AI, Gentle A (2009) Biomechanics of the sclera in myopia: extracellular and cellular factors. Optom Vis Sci 86(1):E23–E30

    Article  Google Scholar 

  • Meskauskas J, Repetto R, Siggers JH (2012) Shape change of the vitreous chamber influences retinal detachment and reattachment processes: is mechanical stress during eye rotations a factor? Invest Ophthalmol Vis Sci 53(10):6271–6281

    Article  Google Scholar 

  • Miles FA, Wallman J (1990) Local ocular compensation for imposed local refractive error. Vision Res 30(3):339–349

    Article  Google Scholar 

  • Mitry D, Charteris DG, Fleck BW, Campbell H, Singh J (2010) The epidemiology of rhegmatogenous retinal detachment: geographical variation and clinical associations. Br J Ophthalmol 94(6):678–684

    Article  Google Scholar 

  • Nelson MR, King JR, Jensen OE (2013) Buckling of a growing tissue and the emergence of two-dimensional patterns. Math Biosci 246(2):229–241

    Article  MathSciNet  Google Scholar 

  • Pruett RC (1988) Progressive myopia and intraocular pressure: what is the linkage?: A literature review. Acta Ophthalmol 66(S185):117–127

    Article  Google Scholar 

  • Repetto R, Tatone A, Testa A, Colangeli E (2011) Traction on the retina induced by saccadic eye movements in the presence of posterior vitreous detachment. Biomech Model Mechanobiol 10(2):191–202

    Article  Google Scholar 

  • Rodriguez EK, Hoger A, McCulloch AD (1994) Stress-dependent finite growth in soft elastic tissues. J Biomech 27(4):455–467

    Article  Google Scholar 

  • Rosenfield M, Gilmartin B (1998) Myopia and nearwork. Butterworth-Heinemann, Boston

    Google Scholar 

  • Schaeffel F, Glasser A, Howland HC (1988) Accommodation, refractive error and eye growth in chickens. Vision Res 28(5):639–657

    Article  Google Scholar 

  • Skalak R (1981) Growth as a finite displacement field. In: Proceedings of the IUTAM symposium on finite elasticity. Springer, Dordrecht, pp 347–355

  • Smith EL, Harwerth RS, Crawford ML, von Noorden GK (1987) Observations on the effects of form deprivation on the refractive status of the monkey. Invest Ophthalmol Vis Sci 28(8):1236–1245

    Google Scholar 

  • Timoshenko S, Woinowsky-Krieger S (1959) Theory of plates and shells. McGraw-Hill, New York

    MATH  Google Scholar 

  • Verkicharla PK, Mathur A, Mallen EA, Pope JM, Atchison DA (2012) Eye shape and retinal shape, and their relation to peripheral refraction. Ophthalmic Physiol Opt 32(3):184–199

    Article  Google Scholar 

  • Wilkinson RP, Rice TA (1997) Michels retinal detachment, 2nd edn. Mosby, St. Louis

    Google Scholar 

  • Wallman J, Turkel J, Trachtman J (1978) Extreme myopia produced by modest change in early visual experience. Science 201(4362):1249–1251

    Article  Google Scholar 

  • Wallman J, Gottlieb MD, Rajaram V, Fugate-Wentzek LA (1987) Local retinal regions control local eye growth and myopia. Science 237(4810):73–77

    Article  Google Scholar 

  • Wollensak G, Spoerl E, Grosse G, Wirbelauer C (2006) Biomechanical significance of the human internal limiting lamina. Retina 26(8):965–968

    Article  Google Scholar 

  • Young FA (1963) The effect of restricted visual space on the refractive error of the young monkey. Invest Ophthalmol Vis Sci 2(6):571–577

    Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, Rutgers University, Piscataway, NJ, 08854, USA

    Joseph M. Lakawicz & William J. Bottega

  2. NJ Retina, Robert Wood Johnson Medical School, Rutgers University, 10 Plum St., Suite 600, New Brunswick, NJ, 08901, USA

    Howard F. Fine & Jonathan L. Prenner

Authors
  1. Joseph M. Lakawicz
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  2. William J. Bottega
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  3. Howard F. Fine
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  4. Jonathan L. Prenner
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Correspondence to Joseph M. Lakawicz.

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Lakawicz, J.M., Bottega, W.J., Fine, H.F. et al. On the mechanics of myopia and its influence on retinal detachment. Biomech Model Mechanobiol 19, 603–620 (2020). https://doi.org/10.1007/s10237-019-01234-1

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  • DOI: https://doi.org/10.1007/s10237-019-01234-1

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