PhD Position F/M Construction of a simulation-ready torso conductivity map library and data generation for the electrical impedance tomography (EIT) Bayesian inverse problem

The Inria centre at the University of Bordeaux is one of nine Inria centres in France and has around twenty research teams. The Inria centre is a major and recognised player in the field of digital sciences. It is at the heart of a rich ecosystem of R&D and innovation: highly innovative SMEs, major industrial groups, competitive clusters, research and higher education players, laboratories of excellence, technological research institutes, etc.

The aim of this thesis project is to study the reconstruction capabilities of Bayesian inference methods for the inverse problem of electrical impedance tomography of the human torso.

The project is related to the global topic of detecting cardiac arrhythmias, in particular ventricular fibrillation. More specifically, it aims to improve a medical imaging modality (electrocardiographic imaging - ECGi) used to non-invasively reconstruct the heart's electrical activity. One of the main aims of this imaging technique is to detect individuals at high risk of ventricular fibrillation. However, it is not yet possible to detect high-risk individuals in the general population, because current techniques for imaging the heart's electrical activity are not sufficiently accurate or reliable.

Electrical Impedance Tomography (EIT) is a potential solution for obtaining additional information. It is a non-invasive technique for reconstructing inclusions and internal conductivities from electrical measurements at the body surface. The direct problem of EIT is to determine the electrical potential in the domain for a given conductivity distribution and for a set of currents injected through the electrodes. The inverse problem involves estimating the conductivities themselves from measurements made at the body surface. Current applications of EIT include detecting breast cancer or acute strokes, monitoring lung ventilation and sometimes monitoring cardiac activity. However, to our knowledge, EIT has never been applied in ECGi to enrich the description of the volume of the torso and its internal conductivities.

The person recruited will work as part of the Inria CARMEN team (Inria Centre at the University of Bordeaux), which specialises in digital models dedicated to cardiac arrhythmias, at the IHU-Liryc, the Institute of Electrophysiology and Cardiac Modelling, dedicated to cardiac rhythm disorders. This project is part of a collaboration with an Inria Paris-Saclay researcher: Jing-Rebecca Li.

The aim of this project is to construct and incorporate statistical distributions of realistic human torso

volume geometries from a large set of realistic biological images. This a priori information will be obtained

from publicly available CT and MRI images as well as artificially generated images from training images. 

The CT images will be used to construct a library of realistic conductivity maps that serve as inputs to the

forward solver of the EIT problem. The forward solver will be an immersed boundary method to which

the pixelated conductivity maps can be coupled in a natural way. A large number of numerical simulations

will be performed to generate EIT data under a variety of experimental conditions for the conductivity maps in the library

in the library.

The constructed data libraries will be used to provide prior distribution information on the conductivity

maps to be estimated in the EIT torso inverse problem. We will also provide statistical distributions of

biological and geometrical parameters associated with the conductivity maps in the library. We expect to

incorporate the libraries and the statistical information in a Bayesian inversion algorithm.

The methodology will be developed in two dimensions and extended to three dimensions using HPC tools.

Both the conductivity map library and the simulated EIT data library will be made publicly available.

Numerical analysis of PDEs or analysis of PDEs with a strong interest in applications and programming. Some knowledge of probability would be desirable.

• Subsidised catering
• Public transport partially reimbursed 
• Leave: 7 weeks' annual leave + 10 days' RTT (full-time basis) + possibility of exceptional leave (e.g. sick children, moving house) 
• Possibility of partial teleworking and reorganisation of working hours 
• Professional equipment available (videoconferencing, loan of IT equipment, etc.) 
• Social, cultural and sports benefits (Association de gestion des œuvres sociales d'Inria)

The gross monthly salary will be €2,200 (before social security contributions and income tax) over 2025 and €2,300 from 01/01/2026.