Skip to Main content Skip to Navigation
Theses

Variability modeling and numerical biomarkers design in cardiac electrophysiology

Abstract : This PhD thesis is dedicated to the study of the variability observed in cardiac electrophysiology (i.e. the electrical activity of biological tissues) measurements and to the design of numerical biomarkers extracted from these measurements. The potential applications are numerous, ranging from a better understanding of existing electrophysiology models to the assessment of adverse effects of drugs or the diagnosis of cardiac pathologies. The cardiac electrophysiology models considered in the present work are either ODEs or PDEs depending on whether we focus on the cell scale or the tissue scale. In both cases, these models are highly non-linear and computationally intensive. We proceed as follows: first we develop numerical tools that address general issues and that are applicable beyond the scope of cardiac electrophysiology. Then, we apply those tools to synthetic electrophysiology measurements in various realistic scenarios and, when available, to real experimental data. In the first part of this thesis, we present a general method for estimating the probability density function (PDF) of uncertain parameters of models based on ordinary differential equations (ODEs) or partial differential equations (PDEs). The method is non-instrusive and relies on offline evaluations of the forward model, making it computationally cheap in practice compared to more sophisticated approaches. The method is illustrated with generic PDE and ODE models. It is then applied to synthetic and experimental electrophysiology measurements. In the second part of this thesis, we present a method to extract and select biomarkers from models outputs in view of performing classication tasks or solving parameter identification problems. The method relies on the resolution of a sparse optimization problem. The method is illustrated with simple models and then applied to synthetic measurements, including electrocardiogram recordings, and to experimental data obtained from micro-electrode array measurements.
Document type :
Theses
Complete list of metadatas

Cited literature [144 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-01697112
Contributor : Abes Star :  Contact
Submitted on : Thursday, March 8, 2018 - 10:07:08 AM
Last modification on : Sunday, October 25, 2020 - 5:41:22 PM
Long-term archiving on: : Saturday, June 9, 2018 - 1:34:47 PM

File

2017PA066325.pdf
Version validated by the jury (STAR)

Identifiers

  • HAL Id : tel-01697112, version 2

Citation

Eliott Tixier. Variability modeling and numerical biomarkers design in cardiac electrophysiology. General Mathematics [math.GM]. Université Pierre et Marie Curie - Paris VI, 2017. English. ⟨NNT : 2017PA066325⟩. ⟨tel-01697112v2⟩

Share

Metrics

Record views

569

Files downloads

345