@misc{WeiserErdmannDeuflhard2008, author = {Weiser, Martin and Erdmann, Bodo and Deuflhard, Peter}, title = {On Efficiency and Accuracy in Cardioelectric Simulation}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10934}, number = {08-41}, year = {2008}, abstract = {Reasons for the failure of adaptive methods to deliver improved efficiency when integrating monodomain models for myocardiac excitation are discussed. Two closely related techniques for reducing the computational complexity of linearly implicit integrators, deliberate sparsing and splitting, are investigated with respect to their impact on computing time and accuracy.}, language = {en} } @misc{GoetschelNagaiahKunischetal.2013, author = {G{\"o}tschel, Sebastian and Nagaiah, Chamakuri and Kunisch, Karl and Weiser, Martin}, title = {Lossy Compression in Optimal Control of Cardiac Defibrillation}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-18566}, year = {2013}, abstract = {This paper presents efficient computational techniques for solving an optimization problem in cardiac defibrillation governed by the monodomain equations. Time-dependent electrical currents injected at different spatial positions act as the control. Inexact Newton-CG methods are used, with reduced gradient computation by adjoint solves. In order to reduce the computational complexity, adaptive mesh refinement for state and adjoint equations is performed. To reduce the high storage and bandwidth demand imposed by adjoint gradient and Hessian-vector evaluations, a lossy compression technique for storing trajectory data is applied. An adaptive choice of quantization tolerance based on error estimates is developed in order to ensure convergence. The efficiency of the proposed approach is demonstrated on numerical examples.}, language = {en} } @misc{Weiser2013, author = {Weiser, Martin}, title = {Faster SDC convergence on non-equidistant grids by DIRK sweeps}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-18662}, year = {2013}, abstract = {Spectral deferred correction methods for solving stiff ODEs are known to converge rapidly towards the collocation limit solution on equidistant grids, but show a much less favourable contraction on non-equidistant grids such as Radau-IIa points. We interprete SDC methods as fixed point iterations for the collocation system and propose new DIRK-type sweeps for stiff problems based on purely linear algebraic considerations. Good convergence is recovered also on non-equidistant grids. The properties of different variants are explored on a couple of numerical examples.}, language = {en} } @misc{Sali2016, author = {Sali, Adrian}, title = {Coupling of Monodomain and Eikonal Models for Cardiac Electrophysiology}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-60508}, year = {2016}, abstract = {The primary goal of this paper is to study the coupling of monodomain and eikonal models for the numerical simulation of cardiac electrophysiology. Eikonal models are nonlinear elliptic equations describing the excitation time of the cardiac tissue. They are often used as very fast approximations for monodomain or bidomain models - parabolic reaction-diffusion systems describing the excitation wavefront in terms of ionic currents. The excitation front is a thin region with high gradients, whereas excitation times vary over larger domains. Hence, eikonal equations can be solved on much coarser grids than monodomain equations. Moreover, as eikonal models are not time-dependent, no time integration is needed. Eikonal models are derived from monodomain models making additional assumptions and using certain approximations. While generally the approximation is rather good, several specific situations are not well captured by eikonal models. We consider coupling the two models, i.e. using the monodomain model in regions where more accurate results or the shape of the wavefront are needed, and the eikonal model in the remaining parts of the domain, where the excitation time is sufficient. Restricting the monodomain simulation to a small subdomain reduces the computational effort considerably. Numerical methods for the simulation of the individual models are presented, with the finite element method as the main ingredient. Coupling conditions as well as algorithms for implementing the coupling are explained. The approximation quality and efficiency of the coupled model is illustrated on simple geometries using an Aliev-Panfilov membrane model.}, language = {en} } @misc{Sali2016, type = {Master Thesis}, author = {Sali, Adrian}, title = {Coupling of Monodomain and Eikonal Models for Cardiac Electrophysiology}, pages = {63}, year = {2016}, abstract = {The primary goal of this paper is to study the coupling of monodomain and eikonal models for the numerical simulation of cardiac electrophysiology. Eikonal models are nonlinear elliptic equations describing the excitation time of the cardiac tissue. They are often used as very fast approximations for monodomain or bidomain models - parabolic reaction-diffusion systems describing the excitation wavefront in terms of ionic currents. The excitation front is a thin region with high gradients, whereas excitation times vary over larger domains. Hence, eikonal equations can be solved on much coarser grids than monodomain equations. Moreover, as eikonal models are not time-dependent, no time integration is needed. Eikonal models are derived from monodomain models making additional assumptions and using certain approximations. While generally the approximation is rather good, several specific situations are not well captured by eikonal models. We consider coupling the two models, i.e. using the monodomain model in regions where more accurate results or the shape of the wavefront are needed, and the eikonal model in the remaining parts of the domain, where the excitation time is sufficient. Restricting the monodomain simulation to a small subdomain reduces the computational effort considerably. Numerical methods for the simulation of the individual models are presented, with the finite element method as the main ingredient. Coupling conditions as well as algorithms for implementing the coupling are explained. The approximation quality and efficiency of the coupled model is illustrated on simple geometries using an Aliev-Panfilov membrane model.}, language = {en} } @article{DeuflhardErdmannRoitzschetal.2009, author = {Deuflhard, Peter and Erdmann, Bodo and Roitzsch, Rainer and Lines, Glenn Terje}, title = {Adaptive Finite Element Simulation of Ventricular Dynamics}, volume = {12}, journal = {J. Computing and Visualization in Science}, pages = {201 -- 205}, year = {2009}, language = {en} } @article{Weiser2009, author = {Weiser, Martin}, title = {Pointwise Nonlinear Scaling for Reaction-Diffusion Equations}, volume = {59}, journal = {Appl. Num. Math.}, number = {8}, pages = {1858 -- 1869}, year = {2009}, language = {en} } @article{GoetschelNagaiahKunischetal.2014, author = {G{\"o}tschel, Sebastian and Nagaiah, Chamakuri and Kunisch, Karl and Weiser, Martin}, title = {Lossy Compression in Optimal Control of Cardiac Defibrillation}, volume = {60}, journal = {J. Sci. Comput.}, number = {1}, doi = {10.1007/s10915-013-9785-x}, pages = {35 -- 59}, year = {2014}, abstract = {This paper presents efficient computational techniques for solving an optimization problem in cardiac defibrillation governed by the monodomain equations. Time-dependent electrical currents injected at different spatial positions act as the control. Inexact Newton-CG methods are used, with reduced gradient computation by adjoint solves. In order to reduce the computational complexity, adaptive mesh refinement for state and adjoint equations is performed. To reduce the high storage and bandwidth demand imposed by adjoint gradient and Hessian-vector evaluations, a lossy compression technique for storing trajectory data is applied. An adaptive choice of quantization tolerance based on error estimates is developed in order to ensure convergence. The efficiency of the proposed approach is demonstrated on numerical examples.}, language = {en} } @article{TierneyMiraReinholdetal.2018, author = {Tierney, Nicholas J. and Mira, Antonietta and Reinhold, J. Jost and Weiser, Martin and Burkart, Roman and Benvenuti, Claudio and Auricchio, Angelo}, title = {Novel relocation methods for automatic external defibrillator improve out-of-hospital cardiac arrest coverage under limited resources}, journal = {Resuscitation}, number = {125}, doi = {10.1016/j.resuscitation.2018.01.055}, pages = {83 -- 89}, year = {2018}, abstract = {Background Mathematical optimisation models have recently been applied to identify ideal Automatic External Defibrillator (AED) locations that maximise coverage of Out of Hospital Cardiac Arrest (OHCA). However, these fixed location models cannot relocate existing AEDs in a flexible way, and have nearly exclusively been applied to urban regions. We developed a flexible location model for AEDs, compared its performance to existing fixed location and population models, and explored how these perform across urban and rural regions. Methods Optimisation techniques were applied to AED deployment and OHCA coverage was assessed. A total of 2802 geolocated OHCAs occurred in Canton Ticino, Switzerland, from January 1st 2005 to December 31st 2015. Results There were 719 AEDs in Canton Ticino. 635 (23\%) OHCA events occurred within 100m of an AED, with 306 (31\%) in urban, and 329 (18\%) in rural areas. Median distance from OHCA events to the nearest AED was 224m (168m urban vs. 269m rural). Flexible location models performed better than fixed location and population models, with the cost to deploy 20 new AEDs instead relocating 171 existing AEDs to new locations, improving OHCA coverage to 38\%, compared to 26\% using fixed models, and 24\% with the population based model. Conclusions Optimisation models for AEDs placement are superior to population models and should be strongly considered by communities when selecting areas for AED deployment. Compared to other models, flexible location models increase overall OHCA coverage, and decreases the distance to nearby AEDs, even in rural areas, while saving significant financial resources.}, language = {en} } @inproceedings{LameckerMansiRelanetal.2009, author = {Lamecker, Hans and Mansi, Tomaso and Relan, Jatin and Billet, Florence and Sermesant, Maxime and Ayache, Nicholas and Delingette, Herv{\´e}}, title = {Adaptive Tetrahedral Meshing for Personalized Cardiac Simulations}, booktitle = {Proc. MICCAI Workshop on Cardiovascular Interventional Imaging and Biophysical Modelling (CI2BM)}, pages = {149 -- 158}, year = {2009}, language = {en} }