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Multilevel optimization algorithm for Inverse Problem in Electrocardiography

Staff - Faculty of Informatics

Date: 17 March 2022 / 14:00 - 15:30

Online on MS Teams

You are cordially invited to attend the PhD Dissertation Defence of Fatemeh Chegini on Thursday 17 March 2022 at 14:00, you can join here.

Abstract:
The electric conductivity of cardiac tissue determines excitation propagation and is vital for quantifying ischemia and scar tissue and building personalized models. As scar tissue is generally characterized by different conduction of electrical excitation, we aim to estimate conductivity-related parameters in mathematical excitation models from endocardial mapping data, particularly the anisotropic conductivity tensor in the monodomain equation, which describes the cardiac excitation. Yet, estimating the distributed and anisotropic conductivity tensors reliably and efficiently from endocardial mapping data or electrocardiograms is a challenging inverse problem due to the computational complexity of the monodomain equation; Many expensive high-resolution computations for the monodomain equation on very fine space and time discretizations are involved. Thus, we aim at building an efficient multilevel method for accelerating the estimation procedure combining electrophysiology models of different complexity, which uses a computationally cheap eikonal model in addition to the more accurate monodomain model. Distributed parameter estimation, well-known as an ill-posed inverse problem, can be performed by minimizing the misfit between simulated and measured electrical activity on the endocardial surface subject to the monodomain model and some regularization, leading to a partial differential equation constrained optimization problem. We formulate this optimization problem, including scar tissue modeling and different regularizations, and design an efficient iterative solver. To this aim, we consider monodomain grid hierarchies, monodomain-eikonal model hierarchies, and the combination of both hierarchies in a recursive multilevel trust-region (RMTR) method. On the one hand, both the trust region method's estimation quality and efficiency, independent of the data, are investigated from several numerical examples. Endocardial mapping data of realistic density appears to be sufficient to provide quantitatively reasonable estimates of the location, size, and shape of scars close to the endocardial surface. In several situations, scar reconstruction based on eikonal and monodomain models differ significantly, suggesting the use of the more involved monodomain model for this purpose. Moreover, Eikonal models can accelerate the computations considerably, enabling the use of complex electrophysiology models for estimating myocardial scars from endocardial mapping data. In many situations, eikonal models approximate monodomain models well but are orders of magnitude faster to solve. Thus, eikonal models can utilize them to provide an RMTR acceleration with negligible overhead per iteration, resulting in a practical approach to estimating myocardial scars from endocardial mapping data. In addition, the multilevel solver is faster than a comparable single-level solver. On the other hand, we investigate different optimization approaches based on adjoint gradient computation for computing a maximum posterior estimate: steepest descent, limited memory BFGS, and recursive multilevel trust region methods using mesh hierarchies or heterogeneous model hierarchies. We compare overall performance, asymptotic convergence rate, and pre-asymptotic progress on selected examples in order to assess the benefit of our multifidelity acceleration. 

Dissertation Committee:
- Prof. Rolf Krause, Università della Svizzera italiana, Switzerland (Research Advisor)
- Prof. Martin Weiser, ZIB Berlin, Germany (Research co-Advisor)
- Prof. Michael Multerer, Università della Svizzera italiana, Switzerland (Internal Member)
- Prof. Igor Pivkin, Università della Svizzera italiana, Switzerland (Internal Member)
- Prof. Luca Pavarino, University of Pavia, Italy (External Member)
- Prof. Simone Scacchi, University of Milano, Italy (External Member)