Modeling Excitable Tissue

1. Front Matter

   Pages i-xvii

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2. Derivation of a Cell-Based Mathematical Model of Excitable Cells

   • Karoline Horgmo Jæger, Aslak Tveito

   Pages 1-13Open Access

3. A Cell-Based Model for Ionic Electrodiffusion in Excitable Tissue

   • Ada J. Ellingsrud, Cécile Daversin-Catty, Marie E. Rognes

   Pages 14-27Open Access

4. Modeling Cardiac Mechanics on a Sub-Cellular Scale

   • Åshild Telle, Samuel T. Wall, Joakim Sundnes

   Pages 28-43Open Access

5. Operator Splitting and Finite Difference Schemes for Solving the EMI Model

   • Karoline Horgmo Jæger, Kristian Gregorius Hustad, Xing Cai, Aslak Tveito

   Pages 44-55Open Access

6. Solving the EMI Equations using Finite Element Methods

   • Miroslav Kuchta, Kent-André Mardal, Marie E. Rognes

   Pages 56-69Open Access

7. Iterative Solvers for EMI Models

   • Miroslav Kuchta, Kent-André Mardal

   Pages 70-86Open Access

8. Improving Neural Simulations with the EMI Model

   • Alessio Paolo Buccino, Miroslav Kuchta, Jakob Schreiner, Kent-André Mardal

   Pages 87-98Open Access

9. Back Matter

   Pages 99-100

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This open access volume presents a novel computational framework for understanding how collections of excitable cells work. The key approach in the text is to model excitable tissue by representing the individual cells constituting the tissue. This is in stark contrast to the common approach where homogenization is used to develop models where the cells are not explicitly present. The approach allows for very detailed analysis of small collections of excitable cells, but computational challenges limit the applicability in the presence of large collections of cells.

• applied mathematics
• scientific computing
• computational physiology
• finite element methods
• cardiac modelling
• biomechanics
• computational physiology
• numerical methods
• preconditioning
• open access

• Simula Research Laboratory, Fornebu, Norway

  Aslak Tveito, Marie E. Rognes

• Department of Mathematics, University of Oslo, Oslo, Norway

  Kent-Andre Mardal

Kent-Andre Mardal is a professor of mechanics at the University of Oslo and an adjunct research scientist at Simula Research Laboratory. He has published more than 90 scientific publications, including journal papers, two co-authored books and the co-edited the book about the FEniCS project, for which he was a core developer for many years.  Research interests include computational modeling of various life science applications and robust, stable and accurate numerical schemes.

Marie E. Rognes is a research professor at Simula Research Laboratory and a founding member of the Young Academy of Norway. She has over 50 scientific publications and has delivered numerous keynote addresses and invited talks, including a TEDx talk. Her research is primarily focused on mathematical and computational modelling of fluid flow in the brain, and this work has been partially funded by an ERC starting grant.

Aslak Tveito is a professor of scientific computing at the University of Oslo, and the CEO of Simula Research Laboratory. He has co-authored three text books, one research monograph and many journal papers on computational physiology. His research interests are related to the use of computational methods to understand the dynamics of collections of excitable cells.