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Multilevel Methods and Uncertainty Quantification in Cardiac Electrophysiology

Applicant Harbrecht Helmut
Number 169599
Funding scheme Project funding
Research institution Fachbereich Mathematik Departement Mathematik und Informatik Universität Basel
Institution of higher education University of Basel - BS
Main discipline Mathematics
Start/End 01.10.2016 - 31.01.2020
Approved amount 368'016.00
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Keywords (3)

uncertainty quantification; multigrid methods; cardiac electrophysiology

Lay Summary (German)

Lead
Millionen von Menschen in aller Welt sind von Herzinsuffizienz betoffen. Diese verursacht immense direkte und indirekte Kosten für ihre Prävention, Diagnose und Behandlung. Speziell wird eine hohe Anzahl von Todesfällen durch die Krankheit verursacht. Ein verbessertes Verständnis der zugrundeliegenden Ursachen wird daher einen grossen Einfluss auf die Auswahl der wirksamsten Behandlung der einzelnen Patienten haben.
Lay summary

Diese Projekt wird einen signifikanten Fortschritt in der verlässlichen Computersimulation von Herzgewebe darstellen. Dies unterstützt die wissenschaftliche Herzforschung und verbessert medizinische Therapien. Die Ziele des Projekts sind (i) die Untersuchung und rigorose Fundierung der zugrundeliegenden mathematischen Modelle und (ii) die Entwicklung einer effiziente Software für die wirklichkeitsnahe Computersimulation von elektrophysiologischer Diagnostik und Therapie.

Direct link to Lay Summary Last update: 27.09.2016

Responsible applicant and co-applicants

Employees

Publications

Publication
Multilevel quadrature for elliptic problems on random domains by the coupling of FEM and BEM
Harbrecht Helmut, Schmidlin Marc (2021), Multilevel quadrature for elliptic problems on random domains by the coupling of FEM and BEM, in Stochastics and Partial Differential Equations: Analysis and Computations.
Space-time multilevel Monte Carlo methods and their application to cardiac electrophysiology
Ben Bader S., Benedusi P., Quaglino A., Zulian P., Krause R. (2021), Space-time multilevel Monte Carlo methods and their application to cardiac electrophysiology, in Journal of Computational Physics, 433, 110164-110164.
Multilevel methods for uncertainty quantification of elliptic PDEs with random anisotropic diffusion
Harbrecht Helmut, Schmidlin Marc (2020), Multilevel methods for uncertainty quantification of elliptic PDEs with random anisotropic diffusion, in Stochastics and Partial Differential Equations: Analysis and Computations, 8(1), 54-81.
Uncertainty quantification for PDEs with anisotropic random diffusion
Harbrecht Helmut, Peters Michael, Schmidlin Marc (2017), Uncertainty quantification for PDEs with anisotropic random diffusion, in SIAM J. Numer. Anal., 55(2), 1002-1023.

Collaboration

Group / person Country
Types of collaboration
Frits Prinzen (Maastricht University) Netherlands (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
Mark Potse (USI Lugano) Switzerland (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
Michael Griebel (University of Bonn) Germany (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
Uli Schotten (Maastricht University) Netherlands (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
Christoph Schwab (ETH Zurich) Switzerland (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
Angelo Auricchio (Cardiocentro Ticino) Switzerland (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Publication

Scientific events

Active participation

Title Type of contribution Title of article or contribution Date Place Persons involved
Workshop “Uncertainty Quantification” Talk given at a conference Modelling and simulation of partial differential equations on random domains 25.11.2019 Canberra, Australia Harbrecht Helmut;
MAFELAP 2019 Talk given at a conference Multilevel quadrature for elliptic problems on random domains by the coupling of FEM and BEM 18.06.2019 Uxbridge, Great Britain and Northern Ireland Schmidlin Marc;
Swiss Numerics Day 2019 Talk given at a conference Multilevel Quadrature for Elliptic Problems on Random Domains by the Coupling of FEM and BEM 10.05.2019 Lugano, Switzerland Schmidlin Marc;
Sixth Chilean Workshop on Numerical Analysis of Partial Differential Equations - WONAPDE 2019 Talk given at a conference Uncertainty Quantification for elliptic PDEs with Random Anisotropic Diffusion 21.01.2019 Concepcion, Chile Schmidlin Marc;
16th Workshop on fast boundary element methods in industrial applications Talk given at a conference Multilevel quadrature for elliptic problems on random do- mains by the coupling of FEM and BEM 04.10.2018 Hirschegg, Austria Harbrecht Helmut;
31st Chemnitz Finite Element Symposium Talk given at a conference Multilevel quadrature for elliptic problems on random domains by the coupling of FEM and BEM 24.09.2018 Chemnitz, Germany Schmidlin Marc;
The 40th Conference on Stochastic Processes and their Applications – SPA 2018 Talk given at a conference Uncertainty Quantification for elliptic PDEs with Random Anisotropic Diffusion 11.06.2018 Gothenburg, Sweden Schmidlin Marc;
ENUMATH 2017 Talk given at a conference Uncertainty Quantification for PDEs with Anisotropic Random Diffusion 25.09.2017 Voss, Norway Schmidlin Marc;
NumPDE Summer Retreat 2017 Talk given at a conference Uncertainty Quantification for PDEs with Random Anisotropic Diffusion 09.08.2017 Disentis, Switzerland Schmidlin Marc;
FOMICS Winter School on Uncertainty Quantification Talk given at a conference Uncertainty quantification for PDEs with anisotropic random diffusion 15.12.2016 Lugano, Switzerland Schmidlin Marc;


Associated projects

Number Title Start Funding scheme
137669 Rapid solution of boundary value problems on stochastic domains 01.11.2011 Project funding
149828 A Flexible High Performance Approach to Cardiac Electromechanics 01.04.2014 Project funding

Abstract

Computational models and numerical analysis play an increasingly important role in many medical and biomedical applications. As a matter of fact, mathematical modeling and numerical simulations allow for the creation of - prototypical or patient-specific - models, which can be used to study, e.g., the function of organs such as the human heart, or to evaluate and plan for individualized therapies.Using established forward models, different studies have been carried out, providing sensitivity analysis on the basis of forward simulations and a more or less straightforward sampling of the parameter spaces. However, the newly developed ideas and mathematical insights from Uncertainty Quantification (UQ) do allow for a much more precise and efficient quantification of important sensitivities in cardiac simulations.It is therefore the goal of this proposal to exploit ideas and techniques from UQ for simulations in cardiology, in particular electrophysiology, and to develop simulation tools, which in the very end will provide reliable estimates of parameter sensitivities to the clinician for patient-specific simulations in electrophysiology. More precisely, we plan to consider the equations modeling the bioelectrical activity of the cardiac tissue, which are parametrized by conductivity tensor fields that, in practice, are not known exactly. This motivates to model them as random fields which, in turn, yields a solution that is a random field.By combining the expertise of the two PIs in the fields of uncertainty quantification and large-scale parallel computations and model development for electrophysiology, the project will reach the following goals: (i) new theoretical results on the solution’s stochastic regularity will be derived for the rigorous foundation of multilevel adaptive stochastic techniques; (ii) these new techniques will be integrated into existing, deterministic large-scale solvers in order to provide efficient software for reliable and realistic stochastic simulations in cardiac electrophysiology.
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