5,442 research outputs found
Identification of weakly coupled multiphysics problems. Application to the inverse problem of electrocardiography
This work addresses the inverse problem of electrocardiography from a new
perspective, by combining electrical and mechanical measurements. Our strategy
relies on the defini-tion of a model of the electromechanical contraction which
is registered on ECG data but also on measured mechanical displacements of the
heart tissue typically extracted from medical images. In this respect, we
establish in this work the convergence of a sequential estimator which combines
for such coupled problems various state of the art sequential data assimilation
methods in a unified consistent and efficient framework. Indeed we ag-gregate a
Luenberger observer for the mechanical state and a Reduced Order Unscented
Kalman Filter applied on the parameters to be identified and a POD projection
of the electrical state. Then using synthetic data we show the benefits of our
approach for the estimation of the electrical state of the ventricles along the
heart beat compared with more classical strategies which only consider an
electrophysiological model with ECG measurements. Our numerical results
actually show that the mechanical measurements improve the identifiability of
the electrical problem allowing to reconstruct the electrical state of the
coupled system more precisely. Therefore, this work is intended to be a first
proof of concept, with theoretical justifications and numerical investigations,
of the ad-vantage of using available multi-modal observations for the
estimation and identification of an electromechanical model of the heart
Numerical simulation of electrocardiograms for full cardiac cycles in healthy and pathological conditions
This work is dedicated to the simulation of full cycles of the electrical
activity of the heart and the corresponding body surface potential. The model
is based on a realistic torso and heart anatomy, including ventricles and
atria. One of the specificities of our approach is to model the atria as a
surface, which is the kind of data typically provided by medical imaging for
thin volumes. The bidomain equations are considered in their usual formulation
in the ventricles, and in a surface formulation on the atria. Two ionic models
are used: the Courtemanche-Ramirez-Nattel model on the atria, and the "Minimal
model for human Ventricular action potentials" (MV) by Bueno-Orovio, Cherry and
Fenton in the ventricles. The heart is weakly coupled to the torso by a Robin
boundary condition based on a resistor- capacitor transmission condition.
Various ECGs are simulated in healthy and pathological conditions (left and
right bundle branch blocks, Bachmann's bundle block, Wolff-Parkinson-White
syndrome). To assess the numerical ECGs, we use several qualitative and
quantitative criteria found in the medical literature. Our simulator can also
be used to generate the signals measured by a vest of electrodes. This
capability is illustrated at the end of the article
三次元心臓モデルと不均一振動モデルによる心臓活動電位のコンピュータシミュレーション
Tohoku University西條芳文論
Doctor of Philosophy
dissertationInverse Electrocardiography (ECG) aims to noninvasively estimate the electrophysiological activity of the heart from the voltages measured at the body surface, with promising clinical applications in diagnosis and therapy. The main challenge of this emerging technique lies in its mathematical foundation: an inverse source problem governed by partial differential equations (PDEs) which is severely ill-conditioned. Essential to the success of inverse ECG are computational methods that reliably achieve accurate inverse solutions while harnessing the ever-growing complexity and realism of the bioelectric simulation. This dissertation focuses on the formulation, optimization, and solution of the inverse ECG problem based on finite element methods, consisting of two research thrusts. The first thrust explores the optimal finite element discretization specifically oriented towards the inverse ECG problem. In contrast, most existing discretization strategies are designed for forward problems and may become inappropriate for the corresponding inverse problems. Based on a Fourier analysis of how discretization relates to ill-conditioning, this work proposes refinement strategies that optimize approximation accuracy o f the inverse ECG problem while mitigating its ill-conditioning. To fulfill these strategies, two refinement techniques are developed: one uses hybrid-shaped finite elements whereas the other adapts high-order finite elements. The second research thrust involves a new methodology for inverse ECG solutions called PDE-constrained optimization, an optimization framework that flexibly allows convex objectives and various physically-based constraints. This work features three contributions: (1) fulfilling optimization in the continuous space, (2) formulating rigorous finite element solutions, and (3) fulfilling subsequent numerical optimization by a primal-dual interiorpoint method tailored to the given optimization problem's specific algebraic structure. The efficacy o f this new method is shown by its application to localization o f cardiac ischemic disease, in which the method, under realistic settings, achieves promising solutions to a previously intractable inverse ECG problem involving the bidomain heart model. In summary, this dissertation advances the computational research of inverse ECG, making it evolve toward an image-based, patient-specific modality for biomedical research
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