title: Verification of cardiac mechanics software: benchmark problems and solutions for testing active and passive material behaviour.
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.
authors.affiliation: Department of Biomedical Engineering, King's College London , London, UK.
authors.forename: Sander
authors.identifier: 0000-0001-8572-251X
authors.initials: S
authors.lastname: Land
authors.affiliation: Thomas J. Watson Research Center, IBM Research, Yorktown Heights , NY 10598, USA.
authors.forename: Viatcheslav
authors.initials: V
authors.lastname: Gurev
authors.affiliation: Department of Physics and Astronomy , Ghent University , Ghent, Belgium.
authors.forename: Sander
authors.initials: S
authors.lastname: Arens
authors.affiliation: Institute of Biophysics, Medical University of Graz , Graz, Austria.
authors.forename: Christoph M
authors.initials: CM
authors.lastname: Augustin
authors.affiliation: Institute of Biomedical Engineering, Karlsruhe Institute of Technology , Karlsruhe, Germany.
authors.forename: Lukas
authors.initials: L
authors.lastname: Baron
authors.affiliation: Department of Biomedical Engineering and Institute for Computational Medicine , Johns Hopkins University , Baltimore, MD 21218, USA.
authors.forename: Robert
authors.initials: R
authors.lastname: Blake
authors.affiliation: Auckland Bioengineering Institute, University of Auckland , Auckland, New Zealand.
authors.forename: Chris
authors.initials: C
authors.lastname: Bradley
authors.affiliation: Department of Structural and Geotechnical Engineering , Pontifica Universidad Católica de Chile , Chile.
authors.forename: Sebastian
authors.initials: S
authors.lastname: Castro
authors.affiliation: Institute of Biophysics, Medical University of Graz , Graz, Austria.
authors.forename: Andrew
authors.initials: A
authors.lastname: Crozier
authors.affiliation: Center for Computational Medicine in Cardiology , Institute of Computational Science, Università della Svizzera italiana , Lugano, Switzerland.
authors.forename: Marco
authors.initials: M
authors.lastname: Favino
authors.affiliation: Department of Biomedical Engineering, King's College London , London, UK.
authors.forename: Thomas E
authors.initials: TE
authors.lastname: Fastl
authors.affiliation: Institute of Biomedical Engineering, Karlsruhe Institute of Technology , Karlsruhe, Germany.
authors.forename: Thomas
authors.initials: T
authors.lastname: Fritz
authors.affiliation: School of Mathematics and Statistics, University of Glasgow , Glasgow, UK.
authors.forename: Hao
authors.initials: H
authors.lastname: Gao
authors.affiliation: Department of Engineering, Nonlinear Physics and Mathematical Modeling Lab , University Campus Bio-Medico of Rome , Rome, Italy.
authors.forename: Alessio
authors.initials: A
authors.lastname: Gizzi
authors.affiliation: Interdisciplinary Applied Mathematics Center , University of North Carolina at Chapel Hill , Chapel Hill, NC, USA.
authors.forename: Boyce E
authors.initials: BE
authors.lastname: Griffith
authors.affiliation: Department of Structural and Geotechnical Engineering , Pontifica Universidad Católica de Chile , Chile.
authors.forename: Daniel E
authors.initials: DE
authors.lastname: Hurtado
authors.affiliation: Center for Computational Medicine in Cardiology , Institute of Computational Science, Università della Svizzera italiana , Lugano, Switzerland.
authors.forename: Rolf
authors.initials: R
authors.lastname: Krause
authors.affiliation: School of Mathematics and Statistics, University of Glasgow , Glasgow, UK.
authors.forename: Xiaoyu
authors.initials: X
authors.lastname: Luo
authors.affiliation: Auckland Bioengineering Institute, University of Auckland, Auckland, New Zealand; Department of Engineering Science, University of Auckland, Auckland, New Zealand.
authors.forename: Martyn P
authors.initials: MP
authors.lastname: Nash
authors.affiliation: Center for Computational Medicine in Cardiology, Institute of Computational Science, Università della Svizzera italiana, Lugano, Switzerland; Simula Research Laboratory, Fornebu, Norway.
authors.forename: Simone
authors.initials: S
authors.lastname: Pezzuto
authors.affiliation: Institute of Biophysics, Medical University of Graz , Graz, Austria.
authors.forename: Gernot
authors.initials: G
authors.lastname: Plank
authors.affiliation: Civil and Environmental Engineering Department , Duke University , Durham, NC 27708-0287, USA.
authors.forename: Simone
authors.initials: S
authors.lastname: Rossi
authors.affiliation: Center for Computational Medicine in Cardiology , Institute of Computational Science, Università della Svizzera italiana , Lugano, Switzerland.
authors.forename: Daniel
authors.initials: D
authors.lastname: Ruprecht
authors.affiliation: Institute of Biomedical Engineering, Karlsruhe Institute of Technology , Karlsruhe, Germany.
authors.forename: Gunnar
authors.initials: G
authors.lastname: Seemann
authors.affiliation: Department of Biomedical Engineering, King's College London, London, UK; Department of Engineering Science, University of Auckland, Auckland, New Zealand.
authors.forename: Nicolas P
authors.initials: NP
authors.lastname: Smith
authors.affiliation: Simula Research Laboratory , Fornebu, Norway.
authors.forename: Joakim
authors.initials: J
authors.lastname: Sundnes
authors.affiliation: Thomas J. Watson Research Center, IBM Research, Yorktown Heights , NY 10598, USA.
authors.forename: J Jeremy
authors.initials: JJ
authors.lastname: Rice
authors.affiliation: Department of Biomedical Engineering and Institute for Computational Medicine , Johns Hopkins University , Baltimore, MD 21218, USA.
authors.forename: Natalia
authors.initials: N
authors.lastname: Trayanova
authors.affiliation: Department of Biomedical Engineering and Institute for Computational Medicine , Johns Hopkins University , Baltimore, MD 21218, USA.
authors.forename: Dafang
authors.initials: D
authors.lastname: Wang
authors.affiliation: Auckland Bioengineering Institute, University of Auckland , Auckland, New Zealand.
authors.forename: Zhinuo
authors.initials: Z
authors.lastname: Jenny Wang
authors.affiliation: Department of Biomedical Engineering, King's College London , London, UK.
authors.forename: Steven A
authors.initials: SA
authors.lastname: Niederer
keywords: VVUQ; benchmark; cardiac mechanics; verification