Automatized Patient-Specific Methodology for Numerical Determination of Biomechanical Corneal Response
Tóm tắt
This work presents a novel methodology for building a three-dimensional patient-specific eyeball model suitable for performing a fully automatic finite element (FE) analysis of the corneal biomechanics. The reconstruction algorithm fits and smooths the patient’s corneal surfaces obtained in clinic with corneal topographers and creates an FE mesh for the simulation. The patient’s corneal elevation and pachymetry data is kept where available, to account for all corneal geometric features (central corneal thickness–CCT and curvature). Subsequently, an iterative free-stress algorithm including a fiber’s pull-back is applied to incorporate the pre-stress field to the model. A convergence analysis of the mesh and a sensitivity analysis of the parameters involved in the numerical response is also addressed to determine the most influential features of the FE model. As a final step, the methodology is applied on the simulation of a general non-commercial non-contact tonometry diagnostic test over a large set of 130 patients—53 healthy, 63 keratoconic (KTC) and 14 post-LASIK surgery eyes. Results show the influence of the CCT, intraocular pressure (IOP) and fibers (87%) on the numerical corneal displacement
$$({{U}}_{{Num}}),$$
the good agreement of the
$${{U}}_{{Num}}$$
with clinical results, and the importance of considering the corneal pre-stress in the FE analysis. The potential and flexibility of the methodology can help improve understanding of the eye biomechanics, to help to plan surgeries, or to interpret the results of new diagnosis tools (i.e., non-contact tonometers).
Tài liệu tham khảo
Alastrué, V., Calvo, B, Peña, E, and Doblaré, M. Biomechanical odeling of refractive corneal surgery. J. Biomech. Eng., 128(1):150–160, 2006.
Ariza-Gracia, M. Á., Zurita, J. F., Piñero, D. P., Rodriguez-Matas, J. F., and Calvo, B. coupled biomechanical response of the cornea assessed by non–contact tonometry. a simulation study. PLoS One 10(3):e0121486. doi10.1371/journal.pone.0121486.
Bourges, J. L., Alfonsi, N., Laliberté, J. F., Chagnon, M., Renard, G., Legeais, J. M., and Brunette I. Average 3-dimensional models for the comparison of orbscan ii and pentacam pachymetry maps in normal corneas. Ophthalmology, 116(11):2064–2071, 2009.
Bryant, M. R. and McDonnell, P.J. Constitutive laws for biomechanical modeling of refractive surgery. J. Biomech. Eng., 118(4):473–481, 1996.
Cotter, S. C. A screening design for factorial experiments with interactions.Biometrika 66(2):317–320, 1979.
Coudrillier, B., Pijanka, J. K., Jefferys, J., Sorensen, T., Quigley, H.A., Boote, C., and Nguyen, T. D. Effects of age and diabetes on scleral dtiffness. J. Biomech. Eng., 137:061004, 2015. doi:10.1115/1.4029986.
Eilaghi, A., Flanagan, J. G., Tertinegg, I., Simmons, C. A., Brodland, G. W., Ethier C.R. and Biaxial. Mechanical testing of human sclera. J. Biomech., 43(9):1696–1701, 2010.
Elsheikh, A., Whitford, C., Hamarashid, R., Kassem, W., Joda, A., and Büchler, P. Stress free configuration of the human eye. Med. Eng. Phys., 35(2):211–216, 2013.
Gasser, T. C., Ogden, R. W., and Holzapfel, G. A. Hyperelastic modeling of arterial layers with distributed collagen fiber orientations. J. R. Soc. Interface, 3(6):15–35, 2006.
Girard, M. J. A., Downs, J. C., Bottlang, M., Burgoyne, C. F., and Suh, J.-K. F. Peripapillary and posterior scleral mechanics-part II: experimental and inverse finite element characterization. J. Biomech. Eng., 131(5):051012, 2009.
Girard, M. J. A., Downs, J. C., Bottlang, M., Burgoyne, C. F., and Suh J.-.K. F. Peripapillary and posterior scleral mechanics-part I: development of an anisotropic hyperelastic constitutive model.J. Biomech. Eng. 131(5):051011, 2009.
Hassan, Z., Modis, L., Szalai, E., Berta, A., and Nemeth, G. examination of ocular biomechanics with a new Scheimpflug technology after corneal refractive surgery. Cont. Lens Anterior Eye, 37:337–341, 2014.
Holzapfel, G. A., Gasser, T. C., and Ogden R. W. A new constitutive framework for arterial wall mechanics and a comparative study of material models. J. Elast. Phys. Sci. Solids, 61(1–3):1–48, 2000.
Hong, J., Xu, J., Wei, A., Deng, S. X., Cui, X., Yu, X., and Sun X. A new tonometer-the CorVis ST tonometer: clinical comparison with noncontact and goldmann applanation tonometers. Invest. Ophthalmol. Vis. Sci., 54(1):659–665, 2013.
Huseynova, T., Waring, G.O., Roberts, C., Krueger, R. R., and Tomita M. Corneal biomechanics as a function of intraocular pressure and pachymetry by dynamic infrared signal and Scheimpflug imaging analysis in normal eyes. Am. J. Ophthalmol., 157(4):885–893, 2014.
Kling, S. and Marcos, S. Contributing factors to corneal deformation in air puff measurements. Invest. Ophthalmol. Vis. Sci., 54(7):5078–5085, 2013.
Kling, S., Bekesi, N., Dorronsoro, C., Pascual, D., and Marcos, S. Contributing factors to corneal deformation in air puff measurements. PLoS One, 9(8):e104904, 2014.
Lanchares, E., Calvo, B., Cristóbal, J. A., and Doblaré, M. Finite element simulation of arcuates for astigmatism vorrection. J. Biomech., 41(4):797–805, 2008.
Meek, K. M. and Boote, C. The use of X-ray scattering techniques to quantify the orientation and distribution of collagen in the corneal stroma. Prog. Retin Eye Res. 28(5):369–392, 2009.
Montgomery D. C. Design and Analysis of Experiments New York: Wiley, 5th edition, 1997. ISBN 0-471-31649−0
Newton, R. H. and Meek, K. M. The integration of the corneal and limbal fibrils in the human eye. Biophys. J., 75(5):2508–2512, 1998.
Ogbuehi, K. C. and Osuagwu, U. L. Corneal biomechanical properties: precision and influence on tonometry. Cont. Lens Anterior Eye, 37(3):124–131, 2014.
Pandolfi, A. and Manganiello, F. A model for the human cornea: constitutive formulation and numerical analysis. Biomech. Model. Mechanobiol., 5(4):237–246, 2006.
Pandolfi, A. and Holzapfel, G. A. Three-dimensional modeling and computational analysis of the human cornea considering distributed collagen fibril orientations. J. Biomech. Eng., 130(6):061006, 2008.
Pinsky, P. M, van der Heide, D., and Chernyak, D. Computational modeling of mechanical anisotropy in the cornea and sclera. J. Cataract. Refract. Surg., 31(1):136–145, 2005.
Rabinowitz, Y. S. Keratoconus. Surv. Ophthalmol., 42(4):297–319, 1998.
Riveros, F., Chandra, S., Finol, E. A., Gasser, T. G., and Rodriguez, J. F. Pull-back algorithm to determine the unloaded vascular geometry in anisotropic hyperelastic aaa passive mechanics. Ann. Biomed. Eng., 41(4):694–708, 2013.
Roberts C. A journey through the biomechanics of the cornea. In Conference ESOIRS. The Ohio State University: Ohio, 2012.
Roy, A. S. and Dupps, W. J. Patient-specific modeling of corneal refractive surgery outcomes and inverse estimation of elastic property changes. J. Biomech. Eng., 133(1):011002, 2011.
Ruiseñor Vázquez, P. R., Galletti, J. D., Minguez, N., Delrivo, M., Fuentes Bonthoux, F., Pförtner, T., and Galletti, J. G. Pentacam Scheimpflug tomography findings in topographically normal patients and subclinical keratoconus cases. Am. J. Ophthalmol., 158(1):32–40.e2, 2014.
Runger, G.C. and Montgomery, D. C. Applied Statistics and Probability for Engineers, Vol.1. New York: Wiley, 2nd edn, 1999.
Studer, H. P., Riedwyl, H., Amstutz, C. A., Hanson, J. V. M., and Büchler P. Patient-specific finite-element simulation of the human cornea: a clinical validation study on cataract surgery. J. Biomech., 46(4):751–758, 2013.
Thompson, J. F., Soni, B. K., and Weatherill, H. P. Handbook of Grid Generation. Boca Raton: CRC Press, 1998.
Valbon, B. F., Ambrósio, R., Fontes, B. M, and Alves, M. R. Effects of age on corneal deformation by non-contact tonometry integrated with an ultra-high-speed (UHS) Scheimpflug camera. Arq. Bras. Oftalmol., 76 (4):229–232, 2013.
Whitford, C., Studer, H. P., Boote, C., Meek, K. M., and Elsheikh, A. Biomechanical model of the human cornea: considering shear stiffness and regional variation of collagen anisotropy and density. J. Mech. Behav. Biomed. Mater., 42:76–87, 2015.