My thesis work

Summary of thesis work

Results and perspectives

This thesis focuses on the modeling of blood flows in arteries, by developing new one-dimensional and two-dimensional reduced models, and their numerical approximations via Discontinuous Galerkin methods.

The one-dimensional models, derived from the Navier-Stokes equations and adapted to arteries with simple geometry, include a hyperbolic model and a viscous extension describing a parabolic velocity profile. To solve these equations, RKDG and IIPG numerical methods are used.

However, to model arteries with complex geometry and non-uniform radial deformations, a two-dimensional model has been developed. The latter, obtained via an asymptotic analysis in a Serret-Frenet frame, offers better accuracy in real cases.

The thesis also includes a comparison of the models and a machine learning model, carried out within the framework of CEMRACS 2023, for the integration of complex functions. Keywords: Blood flow modeling, Discontinuous Galerkin methods, Dimensional reduced models

This thesis developed models to simulate blood flow in arteries, balancing computational efficiency and accuracy. The one-dimensional model is fast and suitable for simple scenarios, but its assumptions limit its application to complex cases.

A two-dimensional model was proposed to include more realistic geometries, such as curved arteries and non-circular sections. This model significantly improves accuracy in cases where the one-dimensional model is insufficient.

The uncertainty of real data, especially from deceased individuals, complicates model validation. These variations require special attention for reliable clinical applications.

Integrating these models with artificial intelligence could enable real-time and personalized simulations, paving the way for more accurate diagnoses and treatments.

1D

2D