A mathematical model for the deformation of the eyeball by an elastic band

Mathematical Medicine and Biology

Volumn 26, Issue 2, 2009, Pages 165-185

  Keeling, Stephen L ^a   Propst, Georg ^a   Stadler, Georg ^b   Wackernagel, Werner ^c  

^a UNIVERSITY OF GRAZ   (Austria)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^c Universitats Augenklinik   (Austria)

Author keywords

Cerclage; Eyeball; Mathematical model

Indexed keywords

ORDINARY DIFFERENTIAL EQUATIONS; POTENTIAL ENERGY;

CERCLAGE; ELASTIC BANDS; EYEBALL; MODEL SOLUTION; NON LINEAR; PHYSICAL PRINCIPLES; SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS; SPHERICAL SYMMETRY; TWO POINT BOUNDARY VALUE PROBLEMS; VOLUME CONSTRAINT;

BOUNDARY VALUE PROBLEMS;

ALGORITHM; ARTICLE; COMPRESSION BANDAGE; EQUILIBRIUM CONSTANT; EYE DISEASE; EYEBALL; INTRAOCULAR PRESSURE; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; POSTOPERATIVE PERIOD; PREDICTION; STRETCHING; VALIDATION PROCESS;

EID: 67649099210     PISSN: 14778599     EISSN: 14778602     Source Type: Journal    
DOI: 10.1093/imammb/dqp008     Document Type: Article

References (24)

1. ADAMS, R. A. (1975) Sobblev Spaces. New York: Academic Press.
2. ADAMSON, A. (1997) Physical Chemistry of Surfaces, 6th edn. New York: Wiley.
3. ALASTRU, V., CALVO, B., PEÑA, E. & DOBLARÉ, M. (2006) Biomechanical modeling of refractive corneal surgery. J. Biomech. Eng., 128, 150-160.
4. BLYTH, M. G. & POZRIKIDIS, C. (2004) Solution space of axisymmetric capsules enclosed by elastic membranes. Eur J. Mech. A 23, 877-892.
5. BRYANT, M. R. & McDONNELL, P. J. (1996) Constitutive laws for biomechanical modeling of refractive surgery. J. Biomech. Eng., 118, 473-481.
6. CIARLET, P. G. (1978) The Finite Element Methodfor Elliptic Problems. Amsterdam: North-Holland.
7. COLLINS, R. & VAN DER WERFF, T. J. (1980) Mathematical Models of the Dynamics of the Human Eye. Lecture Notes in Biomathematics. Berlin: Springer.
8. ELSHEIKH, A., ALHASSO, D. & RAMA, P. (2008a) Biomechanical properties of human and porcine corneas. Exp. Eye Res., 86, 783-790.
9. ELSHEIKH, A., BROWN, M., ALHASSO, D., RAMA, P., CAMPANELLI, M. & GARWAY-HEATH, D. (2008b) Experimental assessment of corneal anisotropy. J. Refract. Surg., 24, 178-187.
10. FRIBERG, T. R. & LACE, J. W. (1988) A comparison of the elastic properties of human choroid and sclera. Exp. Eye Res., 47, 429-436.
11. GONIN, J. (1920) Pathogenie et anatomie pathalogique des decollements retiens. Bull. Mem. Soc. Fr Ophthalmol., 33, 1-123.
12. HEIMANN, H., BARTZ-SCHMIDT, K. U., BORNFELD, N., WEISS, C., HILGERS, R. D. & FOERSTER, M. H. (2007) Scleral buckling versus primary vitrectomy in rhegmatogenous retinal detachment: A prospective randomized multicenter clinical study. Ophthalmology, 114, 2142-2154.
13. HOELTZEL, D. A., ALTMAN, P., BUZARD, K. & CHOE, K. (1992) Strip extensiometry for comparison of the mechanical response of bovine, rabbit, and human corneas. J. Biomech. Eng., 114, 202-215.
14. MALUKIEWICZ-WINIEWSKA, G. & STAFIEJ, J. (1999) Changes in axial length after retinal detachment surgery. Eur J. Ophthalmol., 9 115-119.
15. PALLIKARIS, I. G., KYMIONIS, G. D., GINIS, H. S., KOUNIS, G. A. & TSILIMBARIS, M. K. (2005) Ocular rigidity in living human eyes. Irrvest. Ophthalmol. Vs. Sci., 46, 409-414.
16. PANDOLFI, A. & MANGANIELLO, F. (2006) A model for the human cornea: Constitutive formulation and numerical analysis. Biomech. Model. Mechanobiol., 5, 237-246.
17. PELLICER, J., MANZANARES, J. A. & MAFÉ, S. (1995) The physical description of elementary surface phenomena: Thermodynamics versus mechanics. Am. J. Phys., 63, 542-547.
18. PINSKY, P. M., VAN DER HEIDE, D. & CHERNYAK, D. (2005) Computational modeling of mechanical anisotropy in the cornea and sclera. J. Cataract Reftact. Surg., 31, 136-145.
19. PRESTON, S. P., JENSEN, O. E. & RICHARDSON, G. (2008) Buckling of an axisymmetric vesicle under compression: The effects of resistance to shear. Q. J. Mech. Appl. Math., 61, 1-24.
20. PURSLOW, P. P. & KARWATOWSKI, W. S. S. (1996) Ocular elasticity. Ophthalmology, 103, 1686-1692.
21. SCHEPENS, C. L., OKAMURA, L. D. & BOCKHURST, L. J. (1957) The scleral buckling procedures. I. Surgical techniques and management. AMA Arch. Ophthalmol., 58, 797-811.
22. SCHMITZ-VALCKENBERG, P. & MEYER-SCHWICKERATH, G. (1975) Kontrollierter Zug bei der Cerclage-Operation. Albrecht Von Graefes Arch. Klin. Exp. Ophthalmol., 197, 89-99.
23. SEO, G., PARK, C., ADLAND, Z. & LEE, J. (2003) Ocular mechanics - quantitative modeling and analyses of the eyeball. Report No. T3EyeFinalRep56603. Tucson, AZ: Department of Aerospace and Mechanical Engineering, University of Arizona.
24. SILVER, D. M. & GEYER, O. (2000) Pressure-volume relation for the living human eye. Curr Eye Res., 20, 115-120.