Mathematics of electrical imaging: modeling, theory and implementation

Contribution List

3. Subspace surrogates for the parametric diffusion equation

Antti Hannukainen

6/12/23, 2:00 PM

In this talk, I consider efficient solution of the parametric diffusion equation for several parameter values. First, I study the dependency of the solution u from the parameter and establish that u can be approximated by low-dimensional subspace for any admissible parameter value. Then I propose an efficient method for approximately computing this subspace. I conclude with numerical examples...

2. Addressing Challenges in Modeling Human Head Anatomy for Stroke Monitoring with EIT

Anton Vavilov

6/12/23, 3:00 PM

In this talk, we explore the challenges encountered while implementing a computational framework for stroke monitoring using Electrical Impedance Tomography (EIT). Our focus is on accurately modeling human head anatomy based on a library of MRI scans and integrating real-world data obtained from physical experiments.

Accurately representing anatomical surfaces, such as the brain, skull,...

1. Electrocardiology modeling after pulsed field ablation relying on asymptotic analysis

Annabelle Collin

6/12/23, 4:00 PM

In healthy hearts, the propagation of electrical waves follows a predictable pattern, whereas in people suffering from arrhythmia, the electrical waves can become chaotic and directly affect the pumping function of the heart. One of the main treatments for these arrhythmias is catheter ablation, which destroys small areas of heart tissue to isolate or eliminate the cause of the rapid and...

4. EEG source localisation and cortical mapping

Masimba Nemaire

6/12/23, 5:00 PM

We present a theoretical and numerical framework for performing source lo-
calisation and cortical mapping using EEG data with various source models.
This framework is built on the idea that the problems of source localisation and
cortical mapping are different aspects of the same inverse problem rather than
independent inverse problems. This approach promises to improve numerical...

5. Liver tumor ablation by electroporation: mathematical modeling for clinical applications

Clair Poignard (INRIA & Université de Bordeaux)

6/13/23, 9:15 AM

Electropermeabilization (also called electroporation--EP) is a significant increase in the electrical conductivity and permeability of the cell membrane that occurs when pulses of large amplitude (a few hundred volts per centimeter) are applied to the cells: due to the electric field, the cell membrane is permeabilized. If the pulse duration is sufficiently short (a few milliseconds or a few...

6. EIT reconstruction using virtual X-rays and machine learning

Siiri Rautio

6/13/23, 10:15 AM

We introduce a new reconstruction algorithm for EIT, which provides a connection between EIT and traditional X-ray tomography, based on the idea of "virtual X-rays". We divide the exponentially ill-posed and nonlinear inverse problem of EIT into separate steps. We start by mathematically calculating so-called virtual X-ray projection data from the DN map. Then, we perform explicit algebraic...

7. Experimental Validation and Clinical Applications of ECGI

Laura Bear

6/13/23, 11:15 AM

Cardiac electrical diseases are a major cause of mortality in the world today. Many individuals are not identified as at risk, or incorrectly identified for treatment. These suboptimal results are mostly due to the limitations of current clinical methods to detect cardiac electrical activity. Real-time and panoramic images of cardiac electrical activity can be noninvasively reconstructed...

8. Numerical resolution of the inverse source problem for EEG

Marion Darbas

6/13/23, 2:00 PM

In the talk, I will present a numerical method for solving the EEG inverse source problem which is able to take into account the heterogeneity of the head tissues. One of the applications is to consider fontanels in the skull layer for neonates. The approach consists in firstly transmitting the recorded data from the scalp to the cortex using the
quasi-reversibility method. The second stage...

9. Immersed boundary method for electrical impedance tomography in the frame of Electrocardiography.

Niami Nasr

6/13/23, 3:00 PM

12. Monitoring of hemorrhagic stroke using electrical impedance tomography

Ville Kolehmainen

6/13/23, 4:00 PM

14. Parameter estimation in the eikonal equation

Jérôme Fehrenbach (IMT)

6/13/23, 5:00 PM

Electrical waves propagate at the surface of the heart, the simplest modelling is to describe them as a front propagating according to the eikonal equation. The propagation velocity is anisotropic since it occurs along fibers. For medical diagnosis purposes, we aim at finding the source location and the parameters of the velocity, either from measurements directly on the surface of the heart,...

10. Reconstruction of inclusions and cracks in Calderón's inverse conductivity problem

Henrik Garde

6/14/23, 9:15 AM

I will talk about the exact reconstruction of general inclusions in Calderón's inverse conductivity problem from boundary electrical measurements in the form of a local Neumann-to-Dirichlet map. Here "inclusion" means the support of perturbations to a known conductivity coefficient.

I will briefly cover the cases on open sets, where the perturbed coefficient can have finite positive and...

13. Multimodal analysis and inverse problems for brain imaging

Benjamin Sulis

6/14/23, 10:15 AM

The deeper understanding of brain activity is a major challenge for clinical and
mathematical research. In case of neurological disease, such as epilepsy, the main
objective is to better understand and diagnose the origin of the crisis in order to pro-
pose a proper treatment for each patient. Among the non-invasive imaging methods
used to study these pathologies, we are interested in the...

11. Some remarks on the quadratic nature of the matching to data operator

Marc Dambrine

6/14/23, 11:15 AM

We study the inverse problem of the reconstruction of an obstacle in an media from boundary measurements. We assume that the data is noised and that a statistical model for the data is at hand. We propose and study a reconstruction algorithm based a weighted combination of the first two moments of the Kohn-Vogelius criterion. By numerical results in dimension two, the applicability and...