@article {Simula.SC.508,
	title = {Stability of Two Time-Integrators for the Aliev-Panfilov System},
	journal = {International Journal of Numerical Analysis and Modeling},
	volume = {8},
	number = {3},
	year = {2011},
	pages = {427-442},
	author = {Hanslien, Monica and Artebrant, Robert and Tveito, Aslak and Glenn T. {Lines} and Cai, Xing}
}
@inproceedings {Simula.sc.1172,
	title = {A Note on Discontinuous Rate Functions for the Gate Variables in Mathematical Models of Cardiac Cells},
	journal = {Proceedings of the International Conference on Computational Science, ICCS},
	year = {2010},
	pages = {945-950},
	publisher = {Elsevier},
	type = {Conference},
	isbn = {1877-0509},
	author = {Hanslien, Monica and Holden, Nina and Sundnes, Joakim},
	editor = {Sloot, P.M.A. and van Albada, G.D. and Dongarra, J.}
}
@article {Simula.SC.134,
	title = {Numerical Solution of the Bidomain Equations},
	journal = {Philosophical Transactions of the Royal Society A},
	volume = {367},
	number = {1895},
	year = {2009},
	month = {May},
	pages = {1931-1951},
	abstract = {Knowledge of cardiac electrophysiology is e{ffi}ciently formulated in terms of mathematical models. Most of these models are, however, very complex and thus denies direct mathematical reasoning founded on classical and analytical considerations. This is particularly the case for the celebrated bidomain model, developed almost 40 years ago for concurrent analysis of extra- and intracellular electrical activity. Numerical simulations represent an indispensible tool to study electrophysiology based on this model. However, both steep gradients in the solutions and complicated geometries lead to extremely challenging computational problems. The greatest achievement in scienti{fi}c computing over the past 50 year was to enable solution of linear systems of algebraic equations arising from discretizations of partial di{ff}erential equations in an optimal manner; i.e. such that the CPU-e{ff}orts increases linearly in the number of computational nodes. Over the past decade such optimal methods have been introduced in simulation of electrophysiology. This development, together with the development of a{ff}ordable parallel computers, has enabled the solution of the bidomain model combined with accurate cellular models de{fi}ned on realistic geometries. However, in spite of recent progress, the full potential of modern computational methods has yet to be exploited for solution of the bidomain model. It is the purpose of this paper to review the development of numerical methods for solving the bidomain model. The {fi}eld is huge, and we have to restrict our focus to the development after year 2000.},
	author = {Linge, Svein and Sundnes, Joakim and Hanslien, Monica and Glenn T. {Lines} and Tveito, Aslak}
}
@article {Simula.SC.76,
	title = {An Unconditionally Stable Second Order Method for the Luo-Rudy 1 Model Used in Simulations of Defibrillation},
	journal = {International Journal of Numerical Analysis and Modeling},
	volume = {6},
	number = {4},
	year = {2009},
	pages = {627-641},
	abstract = {Simulations of cardiac defibrillation are associated with considerable numerical challenges. The cell models have traditionally been discretized by first order explicit schemes, which are associated with severe stability issues. The sharp transition layers in the solution call for stable and efficient solvers. We propose a second order accurate numerical method for the Luo-Rudy phase 1 model of electrical activity in a cardiac cell, which provides sequential update of each governing ODE. An \textit{a priori} estimate for the scheme is given, showing that the bounds of the variables typically observed during electric shocks constitute an invariant region for the system, regardless of the time step chosen. Thus the choice of time step is left as a matter of accuracy. Conclusively, we demonstrate the theoretical result by some numerical examples, illustrating second order convergence for the Luo-Rudy 1 model.},
	author = {Hanslien, Monica and Artebrant, Robert and Sundnes, Joakim and Tveito, Aslak}
}
@article {Simula.SC.146,
	title = {A Note on Discontinues Rate Functions for the Gate Variables in Mathematical Models of Cardiac Cells},
	journal = {Procedia Computer Science},
	volume = {1},
	number = {1},
	year = {2008},
	pages = {945-950},
	abstract = {The gating mechanism of ionic channels in cardiac cells is often modeled by ordinary differential equations (ODEs) with voltage dependent rates of change. Some of these rate functions contain discontinuities or singularities, which are not physiologically founded but rather introduced to fit experimental data. Such non-smooth right hand sides of ODEs are associated with potential problems when the equations are solved numerically, in the form of reduced order of accuracy and inconsistent convergence. In this paper we propose to replace the discontinuous rates with smooth versions, by fitting functions of the form introduced by Noble (1962) to the original data found by Ebihara and Johnson (1980). We find that eliminating the discontinuities in the rate functions enables the numerical method to obtain the expected order of accuracy, and has a negligible effect on the kinetics of the membrane model.},
	author = {Hanslien, Monica and Sundnes, Joakim and Holden, Nina}
}
@misc {Simula.sc.882,
	title = {Stable Numerical Methods for Cell Models Used in Simulations of Ventricular Defibrillation},
	howpublished = {Talk at CBC, Seminar on Electrophysiology Modeling},
	year = {2007},
	month = {September},
	author = {Hanslien, Monica}
}
@article {Hanslien.2006.3,
	title = {An Unconditionally Stable Numerical Method for the Luo-Rudy 1 Model Used in Simulations of Defibrillation},
	journal = {Mathematical Biosciences},
	volume = {208},
	number = {2},
	year = {2007},
	month = {August},
	pages = {375-392},
	author = {Hanslien, Monica and Sundnes, Joakim and Tveito, Aslak}
}
@phdthesis {Hanslien.2006.2,
	title = {Analysis of Numerical Methods for Mathematical Models of Cardiac Electrical Activity},
	year = {2006},
	school = {Department of Informatics, University of Oslo},
	type = {phd},
	author = {Hanslien, Monica}
}
@article {Hanslien.2006.1,
	title = {On a Finite Difference Scheme for a Beeler-Reuter Based Model of Cardiac Electrical Activity},
	journal = {International Journal of Numerical Analysis and Modeling},
	volume = {3},
	number = {4},
	year = {2006},
	pages = {395-412},
	author = {Hanslien, Monica and K. H. {Karlsen} and Tveito, Aslak}
}
@misc {Simula.SC.107,
	title = {Simulating Electrical Activity in the Heart},
	howpublished = {Presented at St Jude Medical, Stockholm, Sweeden},
	year = {2006},
	author = {Hanslien, Monica and Sundnes, Joakim and Glenn T. {Lines} and Tveito, Aslak}
}
@misc {Simula.SC.108,
	title = {Simulations of Reentrant Arrhythmias in the Heart, and Defibrillation As a Treatment},
	howpublished = {Presented at NADA, KTH, Sweeden},
	year = {2006},
	author = {Hanslien, Monica and Sundnes, Joakim and Tveito, Aslak}
}
@article {Hanslien.2004.2,
	title = {A Maximum Principle for an Explicit Finite Difference Scheme Approximating the Hodgkin-Huxley Model},
	journal = {BIT},
	volume = {45},
	number = {4},
	year = {2005},
	month = {Dec},
	pages = {725-741},
	author = {Hanslien, Monica and K. H. {Karlsen} and Tveito, Aslak}
}
@inproceedings {Hanslien.2005.2,
	title = {Numerical Simulations of Cardiac Arrhythmias and Defibrillation},
	journal = {MekIT{\textquoteright}05 - Third national conference on Computational Mechanics, Trondheim, Norway May 11-12},
	year = {2005},
	pages = {135-144},
	publisher = {Tapir Academic Press},
	type = {1},
	address = {Trondheim},
	isbn = {82-519-2052-3},
	author = {Hanslien, Monica and Sundnes, Joakim and Glenn T. {Lines}},
	editor = {Bj{\o}rn H. {Skallerud} and Helge I. {Andersson}}
}
@misc {Sundnes.2005.4,
	title = {An Unconditionally Stable Numerical Method for the Luo-Rudy I Model Used in Defibrillation},
	howpublished = {Presented at Tulane University, New Orleans},
	year = {2005},
	note = {Computational science seminar, Tulane University, New Orleans, February 2005.},
	month = {February},
	author = {Sundnes, Joakim and Hanslien, Monica and Tveito, Aslak}
}
@techreport {SC.7.Nilssen.2004,
	title = {Resolution Requirements for a 1D Monodomain Model for Simulating},
	number = {2004-07},
	year = {2004},
	publisher = {Simula Research Laboratory},
	author = {Nilssen, Trygve Kastberg and Ingebrigtsen, L. and Hanslien, Monica and Glenn T. {Lines} and Tveito, Aslak}
}
