This contribution presents an ongoing work to implement a patient-specific mathematical virtual simulator for the eye. The aim is to create a multiscale and multiphysics model for the description of ocular biomechanics, fluid dynamics, and hemodynamics. This instrument may serve to illustrate and estimate some clinically relevant parameters, as well as predict their spatial and temporal evolution adopting forward-looking numerical techniques.
Sala L, Prudhomme C, Prada D, et al. Patient-specific virtual simulator of tissue perfusion in the lamina cribrosa. In: Annual Meeting of the Association for Research in Vision and Ophthalmology. 7-11 May 2017. Baltimore, MD, USA.
Causin P, Guidoboni G, Harris A, Prada D, Sacco R, Terragni S. A poroelastic model for the perfusion of the lamina cribrosa in the optic nerve head. Math Biosci. 2015; 257:33-41.
Prada D. A hybridizable discontinuous Galerkin method for nonlinear porous media viscoelasticity with applications in ophthalmology. PhD thesis at IUPUI. 2016. Indianapolis (IN) USA.
Cockburn B, Gopalakrishnan J, Lazarov R. Unified hybridization of discontinuous Galerkin, mixed, and continuous Galerkin methods for second order elliptic problems. SIAM J Numer Anal. 2009;47(2):1319–1365.
Prud'Homme C, Chabannes V, Doyeux V, Ismail M, Samake A, Pena G. Feel++: A Computational Framework for Galerkin Methods and Advanced Numerical Methods ESAIM: Proceedings, EDP Sciences. 2012; 38: pp. 429-455. doi: 10.1051/proc/201238024
Carichino L, Guidoboni G, Szopos M. Operator splitting approach for coupling Stokes flow and nonlinear systems of ODEs. In: 7th International Conference on Computational Methods for Coupled Problems in Science and Engineering. 2017. Rhodes, Greece.
Sala L, Hild R, Prud’Homme C, et al. An implementation of HDG methods with Feel++. Application to problems with integral boundary condition. In preparation. 2017.
Yan DB, Coloma FM, Metheetrairut A, Trope GE, Heathcote JG, Ethier CR. Deformation of the lamina cribrosa by elevated intraocular pressure. Br J Ophthalmol. 1994;78(8):643-648.
Sigal IA, Flanagan JG, Tertinegg I, Ethier CR. Finite element modeling of optic nerve head biomechanics. Invest Ophthalmol Vis Sci. 2004;45(12):4378-4387.
Guidoboni G, Harris A, Cassani S, et al. Intraocular pressure, blood pressure, and retinal blood flow autoregulation: A mathematical model to clarify their relationship and clinical relevance. Invest Ophthalmol Vis Sci. 2014;55(7):4105-4118.
Williamson TH, Harris A. Color Doppler ultrasound imaging of the eye and orbit. Surv Ophthalmol. 1996;40(4):255-267.