Rareș Răhăian: The elliptic Cauchy problem with applications in Electrocardiographic Imaging (ECGi) (Seminar Talk)

On Wednesday 20th of May 2026 starting at 10am, Rareș Răhăian will give a talk at the Institute Seminar.

Title: The elliptic Cauchy problem with applications in Electrocardiographic Imaging (ECGi)

Abstract: This talk has two parts. In the first part, we introduce the main mathematical models used in electrocardiography, including the bidomain and monodomain models, ionic models, and torso models. We then present the forward problem of computing electrocardiograms (ECGs) and introduce the classical inverse problem of electrocardiography. Particular attention will be given to its connection with the elliptic Cauchy problem, as well as to its motivation and role in electrocardiographic imaging (ECGi).
In the second part, we focus on the numerical solution of the inverse problem of electrocardiography. For the elliptic Cauchy problem, we show how Lipschitz stability can be recovered under the assumption that the unknown Dirichlet trace belongs to a finite-dimensional subspace. This conditional stability is then used to derive an optimal numerical method for ECGi. In particular, we introduce a stabilised finite element method (stabFEM) enriched with a database of heart-surface potentials computed using the forward models discussed in the first part. This is joint work with Mihai Nechita.