Share This Article:

Finite element modeling of the viscoelastic responses of the eye during microvolumetric changes

Abstract Full-Text HTML Download Download as PDF (Size:522KB) PP. 29-37
DOI: 10.4236/jbise.2013.612A005    2,816 Downloads   4,112 Views   Citations

ABSTRACT

A linear viscoelastic finite element model was built to investigate factors that influenced the intraocular pressure (IOP) elevations due to micro-volumetric changes in the eye at three different rates. The viscoelastic properties of the cornea and the sclera, including the instantaneous modulus, equilibrium modulus, and relaxation time constants, parametrically varied to examine their effects on IOP elevations at different rates of volumetric changes. The simulated responses were in good agreement with the previously reported experimental results obtained from porcine globes, showing the general trend of higher IOP elevations at faster rates. The simulations showed that all viscoelastic properties influenced the profile of the dynamic IOP due to volumetric changes, and the relative significance of a specific parameter was highly dependent on the rate of change.

 

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Perez, B. , Morris, H. , Hart, R. and Liu, J. (2013) Finite element modeling of the viscoelastic responses of the eye during microvolumetric changes. Journal of Biomedical Science and Engineering, 6, 29-37. doi: 10.4236/jbise.2013.612A005.

References

[1] Quigley, H.A. (1999) Neuronal death in glaucoma. Progress in Retinal and Eye Research, 18, 39-57.
http://dx.doi.org/10.1016/S1350-9462(98)00014-7
[2] Musch, D.C., Gillespie, B.W., Niziol, L.M., Lichter, P.R. and Varma, R. (2011) Intraocular pressure control and long-term visual field loss in the collaborative initial glaucoma treatment study. Ophthalmology, 118, 1766-1773. http://dx.doi.org/10.1016/j.ophtha.2011.01.047
[3] Liu, J.H.K., Zhang, X., Kripke, D.F. and Weinreb, R.N. (2003) Twenty-four-hour intraocular pressure pattern associated with early glaucomatous changes. Investigative Ophthalmology & Visual Science, 44, 1586-1590.
http://dx.doi.org/10.1167/iovs.02-0666
[4] Parsley, J., Powell, R.G., Keightley, S.J. and Elkington, A.R. (1987) Postural response of intraocular pressure in chronic open-angle glaucoma following trabeculectomy. British Journal of Ophthalmology, 71, 494-496.
http://dx.doi.org/10.1136/bjo.71.7.494
[5] Weinreb, R.N., Cook, J. and Friberg, T.R. (1984) Effect of inverted body position on intraocular pressure. American Journal of Ophthalmology, 98, 784-787.
[6] Rafuse, P.E., Mills, D.W., Hooper, P.L., Chang, T.S. and Wolf, R. (1994) Effects of Valsalva’s manoeuvre on intraocular pressure. Canadian Journal of Ophthalmology, 29, 73-76.
[7] Vieira, G.M., Oliveira, H.B., de Andrade, D.T., Bottaro, M. and Ritch, R. (2006) Intraocular pressure variation during weight lifting. Archives of Ophthalmology, 124, 1251-1254. http://dx.doi.org/10.1001/archopht.124.9.1251
[8] Susanna Jr., R., Vessani, R.M., Sakata, L., Zacarias, L.C. and Hatanaka, M. (2005) The relation between intraocular pressure peak in the water drinking test and visual field progression in glaucoma. British Journal of Ophthalmology, 89, 1298-1301.
http://dx.doi.org/10.1136/bjo.2005.070649
[9] Coleman, D.J. and Trokel, S. (1969) Direct-recorded intraocular pressure variations in a human subject. Archives of Ophthalmology, 82, 637-640.
http://dx.doi.org/10.1001/archopht.1969.00990020633011
[10] Kiuchi, T., Motoyama, Y. and Oshika, T. (2006) Relationship of progression of visual field damage to postural changes in intraocular pressure in patients with normaltension glaucoma. Ophthalmology, 113, 2150-2155.
http://dx.doi.org/10.1016/j.ophtha.2006.06.014
[11] Schuman, J.S., et al. (2000) Increased intraocular pressure and visual field defects in high resistance wind instrument players. Ophthalmology, 107, 127-133.
http://dx.doi.org/10.1016/S0161-6420(99)00015-9
[12] Sigal, I.A., Flanagan, J.G. and Ethier, C.R. (2005) Factors influencing optic nerve head biomechanics. Investigative Ophthalmology & Visual Science, 46, 4189-4199.
http://dx.doi.org/10.1167/iovs.05-0541
[13] Palko, J.R., Pan, X. and Liu, J. (2011) Dynamic testing of regional viscoelastic behavior of canine sclera. Experimental Eye Research, 93, 825-832.
http://dx.doi.org/10.1016/j.exer.2011.09.018
[14] Downs, J.C., et al. (2005) Viscoelastic material properties of the peripapillary sclera in normal and early-glaucoma monkey eyes. Investigative Ophthalmology & Visual Science, 46, 540-546. http://dx.doi.org/10.1167/iovs.04-0114
[15] Girard, M., Suh, J.-K.F., Hart, R.T., Burgoyne, C.F. and Downs, J.C. (2007) Effects of storage time on the mechanical properties of rabbit peripapillary sclera after enucleation. Current Eye Research, 32, 465-470.
http://dx.doi.org/10.1080/02713680701273792
[16] Downs, J.C., et al. (2003) Viscoelastic characterization of peripapillary sclera: Material properties by quadrant in rabbit and monkey eyes. Journal of Biomechanical Engineering, 125, 124-131.
http://dx.doi.org/10.1115/1.1536930
[17] Eilaghi, A., et al. (2010) Biaxial mechanical testing of human sclera. Journal of Biomechanics, 43, 1696-1701.
http://dx.doi.org/10.1016/j.jbiomech.2010.02.031
[18] Fazio, M.A., et al. (2012) Regional variations in mechanical strain in the posterior human sclera. Investigative Ophthalmology & Visual Science, 53, 5326-5333.
http://dx.doi.org/10.1167/iovs.12-9668
[19] Coudrillier, B., et al. (2012) Biomechanics of the human posterior sclera: Ageand glaucoma-related changes measured using inflation testing. Investigative Ophthalmology & Visual Science, 53, 1714-1728.
http://dx.doi.org/10.1167/iovs.11-8009
[20] Girard, M.J.A., Downs, J.C., Bottlang, M., Burgoyne, C.F. and Suh, J.K.F. (2009) Peripapillary and posterior scleral mechanics—Part II: Experimental and inverse finite element characterization. Journal of Biomechanical Engineering, 131, Article ID: 051012.
http://dx.doi.org/10.1115/1.3113683
[21] Girard, M.J.A., Downs, J.C., Burgoyne, C.F. and Suh, J.K.F. (2008) Experimental surface strain mapping of porcine peripapillary sclera due to elevations of intraocular pressure. Journal of Biomechanical Engineering, 130, Article ID: 041017. http://dx.doi.org/10.1115/1.2948416
[22] Tang, J. and Liu, J. (2012) Ultrasonic measurement of scleral cross-sectional strains during elevations of intraocular pressure: Method validation and initial results in posterior porcine sclera. Journal of Biomechanical Engineering, 134, Article ID: 091007.
http://dx.doi.org/10.1115/1.4007365
[23] Nguyen, T. and Boyce, B. (2011) An inverse finite element method for determining the anisotropic properties of the cornea. Biomechanics and Modeling in Mechanobiology, 10, 323-337.
http://dx.doi.org/10.1007/s10237-010-0237-3
[24] Nguyen, T.D., Jones, R.E. and Boyce, B.L. (2008) A nonlinear anisotropic viscoelastic model for the tensile behavior of the corneal stroma. Journal of Biomechanical Engineering, 130, Article ID: 041020.
http://dx.doi.org/10.1115/1.2947399
[25] Elsheikh, A. and Anderson, K. (2005) Comparative study of corneal strip extensometry and inflation tests. Journal of the Royal Society Interface, 2, 177-185.
http://dx.doi.org/10.1098/rsif.2005.0034
[26] He, X. and Liu, J. (2009) A quantitative ultrasonic spectroscopy method for noninvasive determination of corneal biomechanical properties. Investigative Ophthalmology & Visual Science, 50, 5148-5154.
http://dx.doi.org/10.1167/iovs.09-3439
[27] Liu, J. and He, X. (2009) Corneal stiffness affects IOP elevation during rapid volume change in the eye. Investigative Ophthalmology & Visual Science, 50, 2224-2229.
http://dx.doi.org/10.1167/iovs.08-2365
[28] Morris, H.J., et al. (2013) Correlation between biomechanical responses of posterior sclera and IOP elevations during micro intraocular volume change. IOVS, Under Review.
[29] Sródka, W. (2010) Goldmann applanation tonometry— Not as good as gold. Acta of Bioengineering and Biomechanics/Wroclaw University of Technology, 12, 39-47.
[30] Anderson, K., El-Sheikh, A. and Newson, T. (2004) Application of structural analysis to the mechanical behaviour of the cornea. Journal of the Royal Society Interface, 1, 3-15. http://dx.doi.org/10.1098/rsif.2004.0002
[31] Asejczyk-Widlicka, M., Schachar, R.A. and Pierscionek, B.K. (2008) Optical coherence tomography measurements of the fresh porcine eye and response of the outer coats of the eye to volume increase. Journal of Biomedical Optics, 13, Article ID: 024002.
http://dx.doi.org/10.1117/1.2907453
[32] Callister, W.D. (2003) Materials science and engineering an introduction. John Wiley & Sons, New York.
[33] Mase, G.T. and Mase, G.E. (2010) Continuum mechanics for engineers. 3rd Edition, Taylor & Francis, London.
[34] Ethier, C.R., Johnson, M. and Ruberti, J. (2004) Ocular biomechanics and biotransport. Annual Review of Biomedical Engineering, 6, 249-273.
http://dx.doi.org/10.1146/annurev.bioeng.6.040803.140055
[35] Woo, S.L.Y., Kobayashi, A.S., Schlegel, W.A. and Lawrence, C. (1972) Nonlinear material properties of intact cornea and sclera. Experimental Eye Research, 14, 29-39.
http://dx.doi.org/10.1016/0014-4835(72)90139-X
[36] Pierscionek, B.K., Asejczyk-Widlicka, M. and Schachar, R.A. (2007) The effect of changing intraocular pressure on the corneal and scleral curvatures in the fresh porcine eye. The British Journal of Ophthalmology, 91, 801-803. http://dx.doi.org/10.1136/bjo.2006.110221
[37] Caprioli, J. and Coleman, A.L. (2008) Intraocular pressure fluctuation: A risk factor for visual field progression at low intraocular pressures in the advanced glaucoma intervention study. Ophthalmology, 115, 1123-1129.e3.
http://dx.doi.org/10.1016/j.ophtha.2007.10.031
[38] Resta, V., Novelli, E., Vozzi, G., Scarpa, C., Caleo, M., Ahluwalia, A., Solini, A., Santini, E., Parisi, V., Di Virgilio, F. and Galli-Resta, L. (2007) Acute retinal ganglion cell injury caused by intraocular pressure spikes is mediated by endogenous extracellular ATP. European Journal of Neuroscience, 25, 2741-2754.
http://dx.doi.org/10.1111/j.1460-9568.2007.05528.x
[39] Epstein, D.L., Rowlette, L.L. and Roberts, B.C. (1999) Acto-myosin drug effects and aqueous outflow function. Investigative Ophthalmology & Visual Science, 40, 74-81.
[40] Tang, H., Buehler, M.J. and Moran, B. (2009) A constitutive model of soft tissue: From nanoscale collagen to tissue continuum. Annals of Biomedical Engineering, 37, 1117-1130. http://dx.doi.org/10.1007/s10439-009-9679-0
[41] Comninou, M. and Yannas, I.V. (1976) Dependence of stress-strain nonlinearity of connective tissues on the geometry of collagen fibers. Journal of Biomechanics, 9, 427-433. http://dx.doi.org/10.1016/0021-9290(76)90084-1
[42] Maceri, F., Marino, M. and Vairo, G. (2012) An insight on multiscale tendon modeling in muscle-tendon integrated behavior. Biomechanics and Modeling in Mechanobiology, 11, 505-517.
http://dx.doi.org/10.1007/s10237-011-0329-8
[43] Maceri, F., Marino, M. and Vairo, G. (2010) A unified multiscale mechanical model for soft collagenous tissues with regular fiber arrangement. Journal of Biomechanics, 43, 355-363.
http://dx.doi.org/10.1016/j.jbiomech.2009.07.040
[44] Marino, M. and Vairo, G. (2012) Stress and strain localization in stretched collagenous tissues via a multiscale modelling approach. Computer Methods in Biomechanics and Biomedical Engineering, 2012, 1-20.
http://dx.doi.org/10.1080/10255842.2012.658043
[45] Pinsky, P.M., van der Heide, D. and Chernyak, D. (2005) Computational modeling of mechanical anisotropy in the cornea and sclera. Journal of Cataract & Refractive Surgery, 31, 136-145.
http://dx.doi.org/10.1016/j.jcrs.2004.10.048
[46] Girard, M.J.A., Downs, J.C., Burgoyne, C.F. and Suh, J.K.F. (2009) Peripapillary and posterior scleral mechanics—Part I: Development of an anisotropic hyperelastic constitutive model. Journal of Biomechanical Engineering, 131, Article ID: 051011. http://dx.doi.org/10.1115/1.3113682
[47] Grytz, R., Sigal, I.A., Ruberti, J.W., Meschke, G. and Downs, J.C. (2012) Lamina cribrosa thickening in early glaucoma predicted by a microstructure motivated growth and remodeling approach. Mechanics of Materials, 44, 99-109. http://dx.doi.org/10.1016/j.mechmat.2011.07.004
[48] Grytz, R., Meschke, G. and Jonas, J. (2011) The collagen fibril architecture in the lamina cribrosa and peripapillary sclera predicted by a computational remodeling approach. Biomechanics and Modeling in Mechanobiology, 10, 371-382. http://dx.doi.org/10.1007/s10237-010-0240-8

  
comments powered by Disqus

Copyright © 2019 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.