Niami Nasr (Université de Rouen Normandie): Immersed Boundary Method for Electrical Impedance Tomography

In this talk, we focus on a medical imaging technique called electrical impedance tomography (EIT). In EIT, a set of electrodes is placed around the body, through which electrical currents are applied. By measuring the resulting voltages at these electrodes, we aim to reconstruct the conductivity map inside the body.
However, in an experimental EIT setting, there can be additional unknowns, such as the contact impedance or unperfect information regarding moving boundary problem (e.g. patient respiration, organ motion). Moreover, these quantities may be imperfectly known, which leads to a moving and unknown boundary problem.
Mathematically speaking, this is called an inverse problem: from observations, we aim to identify the parameters responsible for these observations. To solve such problems, one must implement numerical methods to simulate the underlying physical phenomena. Traditional numerical methods require the computational grid to closely match the geometry, which means the grid must be rebuilt whenever the geometry changes—a process that can be very time-consuming.
We present an immersed boundary method that overcomes this limitation by representing boundaries implicitly. As a result, moving or changing geometries can be handled without rebuilding the computational grid, making the simulations much more efficient.
We will present the method and evaluate its performance using synthetic data. We will also discuss the additional challenges that must be addressed in order to achieve reliable reconstructions in more realistic and experimental settings.