@article {Land:2015dq,
	title = {Verification of cardiac mechanics software: benchmark problems and solutions for testing active and passive material behaviour},
	journal = {Proceedings of the Royal Society A},
	volume = {471},
	year = {2015},
	month = {12/2015},
	publisher = {The Royal Society},
	abstract = {Models of cardiac mechanics are increasingly used to investigate cardiac physiology. These models are characterized by a high level of complexity, including the particular anisotropic material properties of biological tissue and the actively contracting material. A large number of independent simulation codes have been developed, but a consistent way of verifying the accuracy and replicability of simulations is lacking. To aid in the verification of current and future cardiac mechanics solvers, this study provides three benchmark problems for cardiac mechanics. These benchmark problems test the ability to accurately simulate pressure-type forces that depend on the deformed objects geometry, anisotropic and spatially varying material properties similar to those seen in the left ventricle and active contractile forces. The benchmark was solved by 11 different groups to generate consensus solutions, with typical differences in higher-resolution solutions at approximately 0.5\%, and consistent results between linear, quadratic and cubic finite elements as well as different approaches to simulating incompressible materials. Online tools and solutions are made available to allow these tests to be effectively used in verification of future cardiac mechanics software.},
	author = {Land, Sander and Arens, Sander and Christoph M {Augustin} and Baron, Lukas and Castro, Sebastian and Crozier, Andrew and Favino, Marco and Thomas E {Fastl} and Fritz, Thomas and Gao, Hao and Gizzi, Alessio and Boyce E {Griffith} and Daniel E {Hurtado} and Krause, Rolf and Luo, Xiaoyu and Martyn P {Nash} and Pezzuto, Simone and Plank, Gernot and Rossi, Simone and Ruprecht, Daniel and Seemann, Gunnar and Nicolas P. {Smith} and Sundnes, Joakim and Rice, Jeremy and Natalia A. {Trayanova} and Wang, Dafang and Zhinuo Jenny {Wang} and Steven A {Niederer}}
}
@article {arevalo2013tachycardia,
	title = {Tachycardia in post-infarction hearts: insights from 3D image-based ventricular models},
	journal = {PLOS ONE},
	year = {2013},
	publisher = {PLOS ONE},
	author = {Arevalo, Hermenegild and Plank, Gernot and Helm, Patrick and Halperin, Henry and Natalia A. {Trayanova}}
}
@article {rantner2012three,
	title = {Three-dimensional mechanisms of increased vulnerability to electric shocks in myocardial infarction: Altered virtual electrode polarizations and conduction delay in the peri-infarct zone},
	journal = {Journal of Physiology},
	volume = {590},
	year = {2012},
	pages = {4537-51},
	publisher = {Blackwell Publishing Ltd},
	author = {Lukas J {Rantner} and Arevalo, Hermenegild and Jason L {Constantino} and Igor R {Efimov} and Plank, Gernot and Natalia A. {Trayanova}}
}
@article {Simula.simula.230,
	title = {N-Version Benchmark Evaluation of Cardiac Tissue Electrophysiology Simulators},
	journal = {Philosophical Transactions of the Royal Society A},
	volume = {369},
	number = {1954},
	year = {2011},
	month = {November},
	pages = {4331-51},
	abstract = {Ongoing developments in cardiac modelling have resulted, in particular, in the development of advanced and increasingly complex computational frameworks for simulating cardiac tissue electrophysiology. The goal of these simulations is often to represent the detailed physiology and pathologies of the heart using codes that exploit the computational potential of high-performance computing architectures. These developments have rapidly progressed the simulation capacity of cardiac virtual physiological human style models; however, they have also made it increasingly challenging to verify that a given code provides a faithful representation of the purported governing equations and corresponding solution techniques. This study provides the first cardiac tissue electrophysiology simulation benchmark to allow these codes to be verified. The benchmark was successfully evaluated on 11 simulation platforms to generate a consensus gold-standard converged solution. The benchmark definition in combination with the gold-standard solution can now be used to verify new simulation codes and numerical methods in the future.},
	doi = {10.1098/rsta.2011.0139},
	author = {Steven A {Niederer} and Kerfoot, Eric and Benson, Alana and Bernabeu, Miguel and Bernus, Olivier and Cherry, Elizabeth and Clayton, Richard and Fenton, Flavio and Garny, Alan and Heidenreich, Elvio and Land, Sander and Maleckar, Molly and Pathmanathan, Pras and Plank, Gernot and Rodriguez, Jose and Roy, Ishani and Sachse, Frank and Seemann, Gunnar and Skavhaug, Ola and Nicolas P. {Smith}}
}
@article {vadakkumpadan2010image,
	title = {Image-based models of cardiac structure in health and disease},
	journal = {Wiley Interdisciplinary Reviews: Systems Biology and Medicine},
	year = {2010},
	publisher = {John Wiley \& Sons, Inc.},
	author = {Vadakkumpadan, Fijoy and Arevalo, Hermenegild and Anton J {Prassl} and Chen, Junjie and Kickinger, Ferdinand and Kohl, Peter and Plank, Gernot and Natalia A. {Trayanova}}
}
@article {vigmond2009towards,
	title = {Towards predictive modelling of the electrophysiology of the heart},
	journal = {Experimental Physiology},
	year = {2009},
	publisher = {Blackwell Publishing Ltd},
	author = {Vigmond, Edward and Vadakkumpadan, Fijoy and Arevalo, Hermenegild and Deo, Makarand and Plank, Gernot and Natalia A. {Trayanova}}
}
