Mathematical modelling and simulation of ocular blood flows and their interactions.

Abstract : Optic neuropathies such as glaucoma are often late-onset, progressive and incurable diseases. Despite the recent progress in clinical research, there are still numerous open questions regarding the etiology of these disorders and their pathophysiology. Furthermore, data on ocular posterior tissues are difficult to estimate noninvasively and their clinical interpretation remains challenging due to the interaction among multiple factors that are not easily isolated. The recent use of mathematical models applied to biomedical problems has helped unveiling complex mechanisms of the human physiology. In this very compelling context, our contribution is devoted to designing a mathematical and computational model coupling tissue perfusion and biomechanics within the human eye. In this thesis we have developed a patient-specific Ocular Mathematical Virtual Simulator (OMVS), which is able to disentangle multiscale and multiphysics factors in a accessible environment by employing advanced and innovative mathematical models and numerical methods. Moreover, the proposed framework may serve as a complementary method for data analysis and visualization for clinical and experimental research, and a training application for educational purposes. In the first part of the thesis, we describe the anatomy of the eye and the pathophysiology of glaucoma. Next, we define the modeling choices and the mathematical architecture of the OMVS (Part II). In part III we present the complex ocular geometry and mesh along with the new numerical methods we have developed, namely the Hybridizable Discontinuous Galerkin method with Integral Boundary Conditions, and the operator splitting technique for solving coupled PDE-ODE systems. The fourth part of the thesis gathers all the C++ libraries that have been implemented to create and solve the OMVS. Part V illustrates the OMVS simulation results, specifically the verification and the validation strategy, and some clinically meaningful virtual experiments. Then, we propose a preliminary uncertainty quantification study, in particular an analysis on the propagation of uncertainties and a sensitivity analysis using Sobol indices (Part VI). Finally, in the last part of the thesis, we draw the conclusions and characterize different projects that can be integrated in the OMVS in the future.
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Submitted on : Wednesday, September 11, 2019 - 3:41:05 PM
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Lorenzo Sala. Mathematical modelling and simulation of ocular blood flows and their interactions.. Numerical Analysis [math.NA]. Université de Strasbourg, IRMA, 2019. English. ⟨tel-02284233⟩

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