×

zbMATH — the first resource for mathematics

On the behavior of an eye encircled by a scleral buckle. (English) Zbl 1357.92021
Summary: A mechanics based mathematical model for the behavior of an eye encircled by a scleral buckle, a procedure used by surgeons to correct retinal detachment, is developed. Closed form analytical solutions are obtained, and results of numerical simulations based on those solutions are presented. The effects of material and geometric parameters of the scleral buckle, as well as of the ocular pressure, on the deformation and volume change of the eye are studied. Critical behavior is identified, and correlations are drawn with regard to the properties of the buckle, the associated deformation of the eye, and the ocular pressure. The results indicate that a judicious choice of the buckle parameters is advisable for planning surgery. In particular, the initial (undeformed) radius of the buckle is seen to have the dominant influence with regard to deformation of the eye, while the thickness (height) and width, and hence the shape, of the buckle are seen to have minimal influence and may be chosen for other reasons, such as to maximize the comfort of the patient.

MSC:
92C30 Physiology (general)
92C50 Medical applications (general)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bauer, SM; Tovstik, PE; Katchanov, AB, On the stability of the eye shell under an encircling band, Tech Mech., 1995, 183-190, (1995)
[2] Bottega, WJ; Bishay, PL; Prenner, JL; Fine, HF, On the mechanics of a detaching retina, Math Med Biol, 30, 287-310, (2013) · Zbl 1278.92008
[3] Chou T, Siegel M (2013) The mechanics of retinal detachment. Bull Am Phys Soc 58
[4] Flugge W (1960) Stresses in shells. Julius Springer, Berlin · Zbl 0092.41504
[5] Foster, WJ; Dowla, N; Joshi, SY; Nikolaou, M, The fluid mechanics of scleral buckling surgery for the repair of retinal detachment, Graefe’s Arch Clin Exp Ophthalmol, 248, 31-36, (2010)
[6] Ge P (2014) On the mechanics of contact and reattachment in layered aerospace and ocular structures, Ph.D. Dissertation. Rutgers University, Piscatway
[7] Ge P, Bottega WJ, Prenner JL, Fine HF (2015) On the influence of an equatorial cerclage on closure of posterior retinal detachment. Math Med Biol. doi:10.1093/imammb/dqv028 (published online ahead of print, September 8, 2015) · Zbl 1400.92254
[8] Jones, I; Warner, M; Stevens, J, Mathematical modelling of the elastic properties of retina: a determination of young’s modulus, Eye, 6, 556-559, (1992)
[9] Keeling, SL; Propst, G; Stadler, G; Wackernagel, W, A mathematical model for the deformation of the eyeball by an elastic band, Math Med Biol, 26, 165-185, (2009) · Zbl 1163.92015
[10] Kim YJ, Na YJ, Kim J, Seo JM (2012) Quantitative analysis of ocular structure after scleral buckle encircling. In: Proc. 5th European Conference of the International Federation for Medical and Biological Engineering. Springer, New York, pp 267-270
[11] Lakawicz, JM; Bottega, WJ; Prenner, JL; Fine, HF, An analysis of the mechanical behaviour of a detaching retina, Math Med Biol, 32, 1. 37-1. 61, (2014) · Zbl 1351.92007
[12] Lincoff, H; Stopa, M; Kreissig, I; Madjarov, B; Sarup, V; Saxena, S; Brodie, S, Cutting the encircling band, Retina, 26, 650-654, (2006)
[13] Meskauskas, J; Repetto, R; Stiggers, JH, Shape change of the vitreous chamber influences retinal detachment and reattachment processes: is mechanical stress during eye rotations a factor?, Investig Ophthalmol Vis Sci, 53, 6271-6281, (2012)
[14] Seo, JM; Park, KS; Yu, HG; Chung, H, Geometric changes of the eye with an encircling scleral buckle, J Korean Ophthalmol Soc, 43, 1072-1080, (2002)
[15] Sigal, I; Grimm, J; Schuman, J; Kagemann, L; Ishikawa, H; Wollstein, G, A method to estimate biomechanics and mechanical properties of optic nerve head tssues from parameters measurable using optical coherence tomography, IEEE Trans Med Imaging, 33, 1381-1389, (2014)
[16] Thompson, JT; Michels, RG, Volume displacement of scleral buckles, Arch Ophthalmol, 103, 1822-1824, (1985)
[17] Timoshenko S, Woinowsky-Krieger S, Woinowsky S (1959) Theory of plates and shells. McGraw-hill, New York · Zbl 0114.40801
[18] Uchio, E; Ohno, S; Kudoh, J; Aoki, K; Kisielewicz, LT, Simulation model of an eyeball based on finite element analysis on a supercomputer, Br J Ophthalmol, 83, 1106-1111, (1999)
[19] Wilkinson CP, Rice TA (1997) Michels’s retinal detachment, 2nd edn. Mosby, St. Louis
[20] Wollensak, G; Spoerl, E, Biomechanical characteristics of the retina, Retina, 24, 967-970, (2004)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.