Parameter Identification in Cardiac Electrophysiology Using Proper Orthogonal Decomposition Method

Abstract

Abstract. We consider the problem of estimating some parameters (like ionic models or parameters involved in the initial stimulation) of a model of electrocardiograms (ECG) from the data of the Einthoven leads. This problem can be viewed as a first attempt to identify or to locate a pathology. The direct model is based on the bidomain equations in the heart and a Poisson equation in the torso and. To keep the computational time reasonable, the evaluation of the direct problem is approximated with a reduced order model based on Proper Orthogonal Decomposition (POD). The optimization problem is solved using a genetic algorithm. Numerical tests show that, with noisy synthetic data, the proposed procedure allows to recover ionic parameters and initial activation regions with a fair accuracy.

Efficient estimation of cardiac conductivities via POD-DEIM model order reduction

“…We have observed that the DOE of a POD basis based on a single generating parameter is narrow, especially when the amplitude of the conductivity value is small. This phenomena has also been shown in [7] where POD was applied to estimate ionic model parameters. The situation in our case is even worse, considering the fact that we can not group snapshots for basis construction from different generating parameters, due to the strong sensitivity of the transmembrane potential to the conductivities.…”

“…In constructing a reduced basis for the parameterized Monodomain model, two ways can be followed as mentioned in [7]. One is to store a set of solutions of the full-order model computed at different instants with a set of different parameter values in a given sample space, then collect all these solutions to build a unique snapshot matrix, upon which the POD basis is finally built.…”

“…The POD approach has been used in numerous fields of science and engineering such as fluid-structure interaction [6] and aerodynamics [11], but its practical application in electrocardiology only starts from 2011 [7,8,18]. In these references, the POD method allows reasonable estimation of cardiac ionic model parameters, however, no systematic study on the improvement of efficiency of solving the full nonlinear electrocardiological model is available.…”

Reduced‐order modeling for cardiac electrophysiology. Application to parameter identification

“…This may have interesting applications for long time simulations, for example to compute a restitution curve, or to estimate the ionic current parameters in an optimization loop. Second, a reduced-order model based on a single simulation is totally inadequate to approximate a situation with a spatial change in the parameter: this has been shown in the present study for an infarcted region; in [4] the same observation was made for the initial activation region. A natural strategy consisting of precomputing several POD bases with different sets of parameters, or a single POD basis from different experiments, proved to be satisfactory in the cases we have considered.…”

Le cœur numérique personnalisé

“…• des mesures moins invasives pour la personnalisation du modèle, remplaçant la mesure de potentiels électriques dans les ventricules par des mesures acquises sur le thorax du patient (ECG, VCG, cartes de potentiels thoraciques) [33]; • une simulation plus fine de la mécanique des fluides sanguins [34], qui peut bénéficier de techniques modernes d'imagerie comme l'IRM à contraste de phase; • une modélisation et une simulation plus fines de diverses formes de thérapie (resynchronisation cardiaque, ablation radiofréquence, chirurgie, pose de valves, etc.) [35]; • la simulation du remodelage du coeur après une thérapie et la modélisation du développement du coeur chez l'enfant [36] ; • la prise en compte des incertitudes de mesure et de modélisation [37] ;…”