Year 5 achievements

Abstract of the scientific program

There are two topics on which we will be working during the three years of the project. The first topic is conductivity parameters identification in the electrocardiography imaging inverse problem. The second topic concerns the ionic model parameters identification problem.
In the first topic, we will address the electrocardiography imaging inverse problem using new approaches. The novelty is that we will be optimizing the conductivities of the organs in the thoracic cage while constructing the electrical potential on the heart surface. This question has not been addressed before in the literature, although, we know that the electrical information is affected by the torso conductivity heterogeneity. The aim is to see if combining conductivities optimization with the electrical reconstruction allows significantly improving the quality of the reconstructed signals. In the second topic we will be using the dynamic model of the electrical activity of the heart which is generally based on the state-of-the-art monodomain, bidomain or Eikonal model, the pathological information that we will introduce to the numerical model are either structural information in this case they will be linked to the geometry (hypertrophy, hypotrophy, malformation,…) or they could be related to the functional aspect of electrical activity of the heart. In the latter case, the parameters of reaction- diffusion model like the conductivities (diffusion parameters) or the ionic model parameters (reaction parameters) have to be fitted to the patient condition. This topic is challenging in terms of mathematical analysis and numerical implementation. On the theoretical side, we will rely to the two following questions: 1) For a given electrical measurement taken from a patient (either in the heart or on the body surface), is there a unique set of parameters which allows the model to fit these measurements. 2) In case the identification problem has a unique solution, how sensitive is this solution to the errors in the measurements. On the numerical side, we will be using gradient descent methods, we will consider the adjoint problem corresponding to a given misfit functional representing the measure of the gap between the observations and the model.

Scientific progress program

In this year we continued our investigations in two topics: The first topic a theoretical study related to the identifiability of the ionic model parameters in cardiac electrophysiology modelling. This lead to a journal paper published in a topical issue in the MMNP journal. We also investigated the numerical estimation of these parameters. We used a descent gradient method where the gradient is computed by solving an adjoint problem. The originality of this work is that it shows that the number of observation we need should be at least as much as the number of the parameters to estimate. This work has been submitted to the journal of Mathematical Biology. The preprint version is available at https://hal.inria.fr/hal-02338984

The second topic concerns the formulation of the inverse problem in electrocardiography in terms of an artificial intelligence approach using deep leaning algorithms. We provided two formulation of the problem. The first formulation is based on learning on couples of: a) electrical potential on the heart surface and b) electrical potentials collected at the body surface. We used time-delayed approach that takes into account the evolution in time of the electrical potential. We also adapted this approach to the spatial domain using an adjacency matrix that relates the electrical potential in a given point to its neighbourhood. https://hal.inria.fr/hal-02154094

The second approach is built on couples of a) body surface potentials b) activation map at the heart surface. The idea is to predict the activation map of the patient from measurements on the torso.

On going work

With the PHD student A. Amri, we study the inverse problem of parameter identification in the case where the observations are collected from the body surface. We use the bidomain model coupled to a diffusion equation in the torso. As a first step, we succeed to establish a Carleman estimate for the coupled problem. We also started in September working with Wajih Mbarki (postdoc at FST) and a new PhD student Khouloud Kordoghli studying the inverse problem of parameters identification in the Purkinje myocardium coupled model. The goal of this work is to study the effect of the ionic model parameters in the genesis and the sustainability of arrhythmia.

Work plan for 2020

We will finalize with A. Amri the theoretical part related to the identifiability of the model parameters using body surface observations. We plan to start the work on the numerical estimation of these parameters. We also plan to continue the work that we just started with W. Mbarki on the identification of parameter in the purkinje model. On the other side, with A. Karoui we will investigate the potential of deep learning methods in the Electrocardiography Imaging inverse problem. Our aim in the next year is to make a comparative study between classical methods based on “mechanistic model” and the new methods based on AI approaches. Comparison would be performed on simulated data. Our aim in this year is also to work with clinicians in the CHU de Bordeaux to get data and make a proof of concept of the usefulness of the AI approach in the case of clinical data that are generally incomplete and non standardized.

Joint publications

Journal papers that have been published/accepted in 2019

We considerably participated in a special issue « Mathematical Modelling in cardiology » that would be published soon in the Mathematical Modelling and Natural Phenomena journal :

Year 5 achievements

Abstract of the scientific program

Scientific progress program

Joint publications

Journal papers that have been published/accepted in 2019

Previous years journal papers

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