@article {43054,
	title = {A cell-based framework for modeling cardiac mechanics},
	journal = {Biomechanics and Modeling in Mechanobiology},
	volume = {10101010},
	year = {2023},
	month = {01/2023},
	publisher = { Springer},
	keywords = {Cardiac Mechanics, cardiomyocyte contraction, cell geometries, intracellular and extracellular mechanics, microscale modeling},
	issn = {1617-7959},
	doi = {10.1007/s10237-022-01660-8},
	url = {https://link.springer.com/article/10.1007/s10237-022-01660-8},
	author = {Telle, {\r A}shild and James D. {Trotter} and Cai, Xing and Finsberg, Henrik and Kuchta, Miroslav and Sundnes, Joakim and Wall, Samuel}
}
@article {sundnes2023computational,
	title = {Editorial: Computational models of cardiovascular growth and remodeling},
	journal = {Frontiers in Physiology},
	volume = {14},
	year = {2023},
	pages = {56},
	publisher = {Frontiers},
	doi = { https://doi.org/10.3389/fphys.2023.1130420},
	url = {https://www.frontiersin.org/articles/10.3389/fphys.2023.1130420/full},
	author = {Sundnes, Joakim and Lik Chuan {Lee} and Wall, Samuel and Valdez-Jasso, Daniela}
}
@inbook {43294,
	title = {Impact of Pathological Vascular Remodelling on Right Ventricular Mechanics},
	booktitle = {Computational Physiology: Simula Summer School 2022- Student Reports},
	year = {2023},
	pages = {91{\textendash}109},
	publisher = {Springer},
	organization = {Springer},
	author = {Cui, Jiaxin and Mariluz Rojo {Domingo} and Konno, Ryan and Claudia A {Manetti} and Kagugube, George and Oscar O {Odeigah} and Sundnes, Joakim},
	editor = {Kimberly J {McCabe}}
}
@article {doi:10.1161/CIRCRESAHA.123.322588,
	title = {Stretch Harmonizes Sarcomere Strain Across the Cardiomyocyte},
	journal = {Circulation Research},
	year = {2023},
	month = {07/2023},
	publisher = {American Heart Association},
	abstract = {BACKGROUND:Increasing cardiomyocyte contraction during myocardial stretch serves as the basis for the Frank-Starling mechanism in the heart. However, it remains unclear how this phenomenon occurs regionally within cardiomyocytes, at the level of individual sarcomeres. We investigated sarcomere contractile synchrony and how intersarcomere dynamics contribute to increasing contractility during cell lengthening.METHODS:Sarcomere strain and Ca2+\&nbsp;were simultaneously recorded in isolated left ventricular cardiomyocytes during 1 Hz field stimulation at 37\&thinsp;\&deg;C, at resting length and following stepwise stretch.RESULTS:We observed that in unstretched rat cardiomyocytes, differential sarcomere deformation occurred during each beat. Specifically, while most sarcomeres shortened during the stimulus, \&asymp;10\% to 20\% of sarcomeres were stretched or remained stationary. This nonuniform strain was not traced to regional Ca2+\&nbsp;disparities but rather shorter resting lengths and lower force production in systolically stretched sarcomeres. Lengthening of the cell recruited additional shortening sarcomeres, which increased contractile efficiency as less negative, wasted work was performed by stretched sarcomeres. Given the known role of titin in setting sarcomere dimensions, we next hypothesized that modulating titin expression would alter intersarcomere dynamics. Indeed, in cardiomyocytes from mice with titin haploinsufficiency, we observed greater variability in resting sarcomere length, lower recruitment of shortening sarcomeres, and impaired work performance during cell lengthening.CONCLUSIONS:Graded sarcomere recruitment directs cardiomyocyte work performance, and harmonization of sarcomere strain increases contractility during cell stretch. By setting sarcomere dimensions, titin controls sarcomere recruitment, and its lowered expression in haploinsufficiency mutations impairs cardiomyocyte contractility.},
	url = {https://www.ahajournals.org/doi/abs/10.1161/CIRCRESAHA.123.322588},
	author = {Li, Jia and Sundnes, Joakim and Hou, Yufeng and Laasmaa, Martin and Ruud, Marianne and Unger, Andreas and Terje R. {Kolstad} and Frisk, Michael and Per A. {Norseng} and Yang, Limin and Ingunn E. {Setterberg} and Estela S. {Alves} and Kalakoutis, Michaeljohn and Ole M. {Sejersted} and Johanna T. {Lanner} and Wolfgang A. {Linke} and Ida G. {Lunde} and Pieter P. {de Tombe} and William E. {Louch}}
}
@article {kjeldsberg2023verified,
	title = {A verified and validated moving domain computational fluid dynamics solver with applications to cardiovascular flows},
	journal = {International journal for numerical methods in biomedical engineering},
	volume = {39},
	number = {6},
	year = {2023},
	pages = {e3703},
	publisher = { Wiley},
	author = {Kjeldsberg, Henrik and Sundnes, Joakim and Valen-Sendstad, Kristian}
}
@inbook {42581,
	title = {A Bayesian Approach to Parameter Estimation in Cardiac Mechanics},
	booktitle = {Solid (Bio) mechanics: Challenges of the Next Decade},
	year = {2022},
	month = {06/2022},
	pages = {245{\textendash}256},
	publisher = {Springer},
	organization = {Springer},
	address = {Cham},
	abstract = {Computational models of cardiac mechanics have been shown to capture the general mechanical function of the heart, and have been parameterized based on in vivo patient data to accurately reproduce the heart function of individual patients. Pre- vious attempts for creating such patient-specific problem have typically been based on solving a deterministic inverse problem, which minimizes the misfit between cer- tain model outputs and measured values. While this approach is robust and efficient, and has shown good agreement between model results and patient data, it does not provide any information about the uncertainty in the resulting model parameters. We here present a parameter estimation framework based on a Bayesian approach, which estimates probability density functions (PDFs) of material parameters based on uncertain input values. The method is based on sampling the parameter space and solving the associated forward model for each sample, which may lead to a substantial computational problem if multiple parameters are considered.\&nbsp;However,\&nbsp;the model also offers additional information in the form of univariate or multivariate PDFs for the estimated parameters. We investigate the potential of the methodology by solving a simple parameter estimation problem in passive left ventricular mechan- ics, and show that the results are in agreement with previous results obtained with a deterministic parameter estimation method.},
	issn = {ISBN 978-3-030-92338-9},
	doi = {10.1007/978-3-030-92339-6_10},
	url = {https://doi.org/10.1007/978-3-030-92339-6_10},
	author = {Sundnes, Joakim and Rodr{\'\i}guez-Cantano, Roc{\'\i}o},
	editor = {Sommer, Gerhard and Li, Kewei and Daniel Ch. {Haspinger} and Raymond W. {Ogden}}
}
@misc {42583,
	title = {A cell-based framework for modeling cardiac mechanics},
	howpublished = {International Symposium in honor of Professor Gerhard A. Holzapfel{\textquoteright}s 60th birthday, Graz, Austria},
	year = {2022},
	abstract = {The mechanical function of cardiac tissue results from the complex interplay ofcontracting cardiomyocytes and the passive extracellular matrix. Most computationalmodels of cardiac mechanics are based on a continuum approach, where the tissueis viewed as a continuous and homogeneous mix of cells and extracellular material.This approach has been successfully applied in numerous studies,and will undoubtedly remain a cornerstone of computational biomechanics.However, the extensive homogenization limits the models{\textquoteright} ability to give detailedinsight into the mechanical forces experienced by individual cardiac cells, andto delineate the mechanical contributions of myocytes and the extracellular matrix.More detailed models exist, in the form of continuum mechanics modelsof individual myocytes, but these are typically limited to a single myocyte anddo not consider the extracellular matrix.Computational models of cardiac electrophysiology are typically based on thesame continuous and homogenized concept as the mechanics model, with thebidomain model being the reference model for several decades. More recently,models have been developed that explicitly represent the cells, the membrane,and the domain between the cells. The approach is commonly referred to as the EMI(Extracellular-Membrane-Intracellular) model, and has been applied instudies of cardiac and neuronal electrophysiology. Natural extensions of theEMI framework include detailed models of intra- and extracellular ion concentrationsand electro-diffusion, as well as coupling to models for cell contraction and mechanics.We present a mechanical analogue of the EMI model, i.e., a continuum basedcardiac mechanics model that explicitly represents a three-dimensional networkof cells embedded in an extracellular matrix. Both the intra- and extracellular domainsare modeled as hyperelastic, with constitutive models based based onthe Holzapfel-Ogden model for passive myocardium. The two domainshave different passive mechanical properties, and the intracellular domain isactively contracting while the extracellular domain is completely passive.The active contraction is incorporated through a so-called active strain model,and in this first version of the model it is assumed to be synchronous and homogeneousacross the entire intracellular domain. The model was parameterized usingpublicly available experimental data for stretching and shear experiments,and was used in preliminary explorations of mechanical interactions betweenthe intra- and extracellular domains. In particular, we studied how myocytestress and strain are affected by the mechanical properties of the two domains,during passive stretching and active contraction. The results show considerablespatial variations in both stress and strain, and indicate that the detailedgeometrical representation of the cells may give improved insight into certainmechanisms of biomechanics and mechano-biology. Further development ofthe model should include a more detailed exploration of material parameters,cell geometry, and the mechanical coupling between the cells and the surroundingmatrix, as well as extending the framework to consider inhomogeneous contractionand potentially coupling of contraction to cell electrophysiology and calcium diffusion.},
	author = {Sundnes, Joakim and Telle, {\r A}shild and Wall, Samuel}
}
@article {koivumaki2022computational,
	title = {Computational cardiac physiology for new modelers: origins, foundations, and future},
	journal = {Acta Physiologica},
	volume = {236},
	number = {2},
	year = {2022},
	pages = {e13865},
	publisher = {Wiley},
	abstract = {Mathematical models of the cardiovascular system have come a long way since they were first introduced in the early 19th century. Driven by a rapid development of experimental techniques, numerical methods, and computer hardware, detailed models that describe physical scales from the molecular level up to organs and organ systems have been derived and used for physiological research. Mathematical and computational models can be seen as condensed and quantitative formulations of extensive physiological knowledge and are used for formulating and testing hypotheses, interpreting and directing experimental research, and have contributed substantially to our understanding of cardiovascular physiology. However, in spite of the strengths of mathematics to precisely describe complex relationships and the obvious need for the mathematical and computational models to be informed by experimental data, there still exist considerable barriers between experimental and computational physiological research. In this review, we present a historical overview of the development of mathematical and computational models in cardiovascular physiology, including the current state of the art. We further argue why a tighter integration is needed between experimental and computational scientists in physiology, and point out important obstacles and challenges that must be overcome in order to fully realize the synergy of experimental and computational physiological research.},
	author = {Jussi T {Koivum{\"a}ki} and Hoffman, Johan and Maleckar, Molly and Gaute T {Einevoll} and Sundnes, Joakim}
}
@misc {odeigah2022computational,
	title = {A computational model of right ventricular remodelling in the presence of pulmonary arterial hypertension},
	howpublished = {Biophysical Journal},
	year = {2022},
	month = {02/2022},
	publisher = {Elsevier},
	address = {Biophysical Society Annual Meeting, San Francisco, California, USA},
	abstract = {During early-stage pulmonary arterial hypertension (PAH), the right ventricle (RV) undergoes anatomical adaptation in the form of a thickened RV free wall, and material adaptation in the form of altered passive stiffness and contractility. The early-stage compensatory adaptations may help to preserve cardiac output but can later evolve into maladaptive remodelling and organ failure. The transition from compensatory to detrimental remodelling remains poorly understood.Using\&nbsp;in vivo\&nbsp;hemodynamic and morphological data from normotensive and hypertensive rats, we built idealized bi-ventricular finite element models representing different disease stages. We built a total of eight models, with RV wall thickness based on\&nbsp;ex vivo\&nbsp;measurements and passive material properties prescribed based on planar biaxial mechanical data obtained from the same animals. A previously developed inverse finite element framework was then used to fit the biventricular models to the\&nbsp;in-vivo\&nbsp;hemodynamic data, resulting in passive stiffness and contractility optimized to provide the best possible fit with the combined hemodynamic and biaxial data.Model simulations were then used to study how the presence of PAH affects the stress distribution in the right ventricular free wall, and how wall stress and RV function are altered by the induced changes in morphology, passive stiffness and contractility. Further numerical experiments were conducted to gain insight into the relative contribution of geometric and material adaptation to maintaining RV function in early-stage PAH, as well as the role of the septal wall. Such insights can facilitate a more comprehensive understanding of the compensatory remodeling that occurs during the disease progression.},
	author = {Odeigah, Oscar and Sundnes, Joakim and Bennington, Michael and Valdez-Jasso, Daniela}
}
@article {odeigah2022computational,
	title = {Computational models of ventricular mechanics and adaptation in response to right-ventricular pressure overload},
	journal = {Frontiers in Physiology},
	year = {2022},
	pages = {1774},
	publisher = {Frontiers},
	abstract = {Pulmonary arterial hypertension (PAH) is associated with substantial remodeling of the right ventricle (RV), which may at first be compensatory but at a later stage becomes detrimental to RV function and patient survival. Unlike the left ventricle (LV), the RV remains understudied, and with its thin-walled crescent shape, it is often modeled simply as an appendage of the LV. Furthermore, PAH diagnosis is challenging because it often leaves the LV and systemic circulation largely unaffected. Several treatment strategies such as atrial septostomy, right ventricular assist devices (RVADs) or RV resynchronization therapy have been shown to improve RV function and the quality of life in patients with PAH. However, evidence of their long-term efficacy is limited and lung transplantation is still the most effective and curative treatment option. As such, the clinical need for improved diagnosis and treatment of PAH drives a strong need for increased understanding of drivers and mechanisms of RV growth and remodeling (G\&amp;R), and more generally for targeted research into RV mechanics pathology. Computational models stand out as a valuable supplement to experimental research, offering detailed analysis of the drivers and consequences of G\&amp;R, as well as a virtual test bench for exploring and refining hypotheses of growth mechanisms. In this review we summarize the current efforts towards understanding RV G\&amp;R processes using computational approaches such as reduced-order models, three dimensional (3D) finite element (FE) models, and G\&amp;R models. In addition to an overview of the relevant literature of RV computational models, we discuss how the models have contributed to increased scientific understanding and to potential clinical treatment of PAH patients.},
	author = {Oscar O {Odeigah} and Valdez-Jasso, Daniela and Wall, Samuel and Sundnes, Joakim}
}
@inbook {42578,
	title = {Data aggregation and anonymization for mathematical modeling and epidemiological studies},
	booktitle = {Smittestopp - A Case Study on Digital Contact Tracing},
	volume = {11},
	year = {2022},
	pages = {121{\textendash}141},
	publisher = {Springer International Publishing},
	organization = {Springer International Publishing},
	address = {Cham},
	abstract = {An important secondary purpose of the Smittestopp development was to provide aggregated data sets describing mobility and social interactions in Norway{\textquoteright}s population. The data were to be used to monitor the effect of government regulations and recommendations, provide input to advanced computational models to predict the pandemic{\textquoteright}s spread, and provide input to fundamental epidemiology research. In this chapter we describe the challenges and technical solutions of Smittestopp{\textquoteright}s data aggregation, as well as preliminary results from the time period when the app was active.We first give a detailed overview of the requirements, specifying the types of data to be collected and the level of spatial and temporal aggregation. We then proceed to describe the concepts for anonymization via :-anonymity and Y-differential privacy (Y-DP ), and the technical solutions for collecting and aggregating data from the database. In particular, we present details of how GPS- and Bluetooth events were mapped to geographical regions and points of interest, and the solutions employed for efficient data retrieval and processing. The preliminary results demonstrate how the recorded GPS- and Bluetooth events match with expected temporal and spatial variations in mobility and social interactions, and indicate the usefulness of the aggregated data as a tool for pandemic monitoring and research. One of the main criticisms of Smittestopp concerns the centralized storage of individuals{\textquoteright} movements, even if such data were used and presented only at an aggregated and anonymized level. In this chapter, we also outline a completely different approach, where the GPS data do not leave the user{\textquoteright}s phone but are, instead, pre-processed to a much higher level of privacy before being dispatched to a server-side data aggregation algorithm. This approach, which would make the app significantly less intrusive, is made possible by recent advances in determining close contacts from Bluetooth data, either by a revised Smittestopp algorithm or by means of the Google/Apple Exposure Notification framework.},
	isbn = {978-3-031-05466-2},
	doi = {10.1007/978-3-031-05466-2_7},
	url = {https://doi.org/10.1007/978-3-031-05466-2_7},
	author = {Are Magnus {Bruaset} and Glenn T. {Lines} and Sundnes, Joakim},
	editor = {Elmokashfi, Ahmed and Lysne, Olav and Naumova, Valeriya}
}
@misc {43021,
	title = {Impact of Rigid Versus Dynamic Boundaries on Computational Fluid Dynamics Predictor of Left Atrial Appendage Thrombus Formation},
	year = {2022},
	address = {Computing in Cardiology},
	author = {Kjeldsberg, Henrik},
	editor = {Mill, Jordi and Carlos A. {Lucas} and David V. {Medel} and Camara, Oscar and Sundnes, Joakim and Valen-Sendstad, Kristian}
}
@misc {43023,
	title = {A mechanistic approach towards personalized treatment in patients with atrial fibrillation },
	howpublished = {University Heart \& Vascular Center Hamburg - UKE},
	year = {2022},
	author = {Kjeldsberg, Henrik and Sundnes, Joakim and Valen-Sendstad, Kristian}
}
@misc {42718,
	title = {Modeling cardiac mechanics using a cell-based framework},
	howpublished = {15th World Congress on Computational Mechanics (WCCM-XV), Yokohama, Japan},
	year = {2022},
	publisher = {15th World Congress on Computational Mechanics (WCCM-XV)},
	type = {Contributed},
	abstract = {Cardiac tissue primarily consists of interconnected cardiac cells which contract in a synchronized manner as the heart beats. Most computational models of cardiac tissue, however, homogenize out the individual cells and their surroundings. This approach has been immensely useful for describing cardiac mechanics on an overall level, but gives very limited understanding of the interaction between individual cells and their intermediate surroundings. Several models have been developed for single cells, see e.g. [1, 2]. In this work, we extend the mechanical part of these frameworks to a domain representing multiple cells, allowing us to investigate cell-matrix and cell-cell interactions. We present a mechanical model in which each cell and the extracellular matrix have an explicit geometrical representation, similar to the electrophysiological model presented in [3]. The strain energy functions are defined separately for each of the intracellular and extracellular subdomains, while we assume continuity of displacement and stresses along the membrane. Active tension is only assigned to the intracellular subdomain. For each state, we find an equilibrium solution using the finite element method. We explore passive and active mechanics for a single cell surrounded by an extracellular matrix and for small collections of cells combined into tissue blocks. The explicit geometric representation gives rise to highly varying strain and stress patterns. We show that the extracellular matrix stiffness highly influences the cardiomyocyte stresses during contraction. Through large-scale simulations enabled by high-performance computing, we also demonstrate that our model can be scaled to small collections of cells, resembling small cardiac tissue samples.

[1] Tracqui, T. and Ohayon, J. An integrated formulation of anisotropic force{\textendash}calcium relations driving spatio-temporal contractions of cardiac myocytes. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences (2009).
[2] Ruiz-Baier, R. Gizzi, A., Rossi, S. Cherubini, C. Laadhari, A. Filippi, S. and Quarteroni, A. Mathematical modelling of active contraction in isolated cardiomyocytes. Mathematical Medicine and Biology (2014).
[3] Tveito, A., J{\ae}ger, KH. Kuchta, M. Mardal, K-A. and Rognes, ME. A cell-based framework for numerical modeling of electrical conduction in cardiac tissue. Frontiers in Physics (2017).
\end{thebibliography}
},
	keywords = {cardiomyocyte contraction, cell-based geometries, intracellular and extracellular mechanics, microscale cardiac mechanics},
	url = {https://prezi.com/view/uGIK0kQvrZ6G1CNOkc73/},
	author = {Telle, {\r A}shild and James D. {Trotter} and Cai, Xing and Kuchta, Miroslav and Finsberg, Henrik and Sundnes, Joakim and Wall, Samuel}
}
@article {albatat2022regional,
	title = {Regional Left Ventricular Fiber Stress Analysis for Cardiac Resynchronization Therapy Response},
	journal = {Annals of Biomedical Engineering},
	volume = {51},
	year = {2022},
	month = {07/2022},
	pages = {343{\textendash}351},
	publisher = {Springer},
	abstract = {Cardiac resynchronization therapy (CRT) is an effective treatment for a subgroup of heart failure (HF) patients, but more than 30\% of those selected do not improve after CRT implantation. Imperfect pre-procedural criteria for patient selection and optimization are the main causes of the high non-response rate. In this study, we evaluated a novel measure for assessing CRT response. We used a computational modeling framework to calculate the regional stress of the left ventricular wall of seven CRT patients and seven healthy controls. The standard deviation of regional wall stress at the time of mitral valve closure (SD_MVC) was used to quantify dyssynchrony and com- pared between patients and controls and among the patients. The results show that SD_MVC is significantly lower in controls than patients and correlates with long-term response in patients, based on end-diastolic volume reduction. In contrast to our initial hypothesis, patients with lower SD_MVC respond better to therapy. The patient with the highest SD_MVC was the only non-responder in the patient cohort. The distribution of fiber stress at the beginning of the isovolumetric phase seems to correlate with the degree of response and the use of this measurement could potentially improve selection criteria for CRT implantation. Further studies with a larger cohort of patients are needed to validate these results.},
	keywords = {Cardiac resynchronization therapy, Computational cardiology, electrophysiology, Heart failure},
	doi = {10.1007/s10439-022-03030-y},
	url = {https://doi.org/10.1007/s10439-022-03030-y},
	author = {Albatat, Mohammad and Finsberg, Henrik and Arevalo, Hermenegild and Sundnes, Joakim and Bergsland, Jacob and Balasingham, Ilangko and Hans Henrik {Odland}}
}
@misc {martinez2021assessment,
	title = {Assessment of left ventricular mechanics in right ventricular overload using in silico rat models},
	howpublished = {European Heart Journal},
	year = {2021},
	month = {08/2021},
	publisher = {Oxford University Press},
	address = {ESC Congress 2021},
	abstract = {BackgroundTo preserve cardiac function in overload conditions, the RV adapts by developing muscular hypertrophy through progressive tissue remodelling. This process may lead to a vicious cycle with detrimental effects on RV diastolic and systolic function, as seen in pulmonary arterial hypertension (PAH) patients. However, how RV overload affects LV function and remodelling remains an open question. Computational models of cardiac physiology offer an opportunity for investigating mechanisms difficult or impossible to analyse otherwise due to the existence of overlapping factors and technical limitations.AimThis study aims to assess the acute effects of RV overload and increased myocardial passive stiffness on the LV mechanical properties in an anatomically-based computational model of healthy rat heart.MethodsA computational simulation pipeline of cardiac mechanics based on the Holzapfel-Ogden model has been implemented using MR images from a healthy rat. Whereas LV function was modelled realistically using catheter measurements conducted on the same subject than the MR imaging, RV function was based on representative literature values for healthy and PAH rats with RV overload. The following cases were defined (Fig. 1): CTRL, with normal RV function; PAH1, with 30\% increase in RV ESV (end-systolic volume) and 15\% increase in RV ESP (end-systolic pressure) in comparison to CTRL; and PAH2, with 60\% increase in RV ESV and 30\% increase in RV ESP compared to CTRL. The cardiac cycle was simulated for all cases whilst fitting the experimentally measured LV pressure and volume values from a healthy rat, which allowed quantifying the effects of RV overload on LV function.ResultsThe increase of average circumferential strain in the LV correlated with the degree of RV overload simulated (CTRL: -8.7\%, PAH1: -8.9\%, PAH2: -9.2\%), whilst average radial (CTRL: 35.2\%, PAH1: 34.8\%, PAH2: 30.3\%) and longitudinal strains decreased (CTRL: -7.7\%, PAH1: -7.4\%, PAH2: -6.6\%), as seen in Fig.2. However, regional differences in strain were significant: under RV overload conditions, circumferential strain increased in the septum (-3.5\% difference in PAH2 vs. CTRL) but lower values were observed in the lateral wall (+1.7\% difference in PAH2 vs. CTRL). Cardiac function of case PAH2 was simulated also with increased myocardial passive stiffness (2.67 kPa instead of 1.34 kPa) which presented a mild strain increase in the mid LV ventricle in comparison to PAH2 with normal stiffness (circumferential strain: -0.8\%, radial strain: +0.5\%, longitudinal strain: -0.2\%).ConclusionOur study provides mechanistic evidence on how RV overload and increased passive myocardial stiffness causes a redistribution of strain and fibre stress in the LV, which may play a significant role in LV remodelling and function.\&nbsp;},
	doi = {10.1093/eurheartj/ehab724.3074},
	url = {https://doi.org/10.1093/eurheartj/ehab724.3074},
	author = {Martinez-Navarro, H and Espe, EKS and Odeigah, OO and Sjaastad, I and Sundnes, Joakim}
}
@article {shavik2021computational,
	title = {Computational Modeling Studies of the Roles of Left Ventricular Geometry, Afterload, and Muscle Contractility on Myocardial Strains in Heart Failure with Preserved Ejection Fraction},
	journal = {Journal of Cardiovascular Translational Research},
	volume = {14},
	year = {2021},
	pages = {1131{\textendash}1145},
	publisher = {Springer},
	author = {Sheikh Mohammad {Shavik} and Wall, Samuel and Sundnes, Joakim and Julius M {Guccione} and Sengupta, Partho and Scott D {Solomon} and Burkhoff, Daniel and Lik Chuan {Lee}}
}
@article {27783,
	title = {A computational study of the effects of tachycardia-induced remodelling on calcium wave propagation in rabbit atrial myocytes},
	journal = {Frontiers in Physiology},
	volume = {12},
	year = {2021},
	publisher = {Frontiers},
	abstract = {In atrial cardiomyocytes without a well-developed T-tubule system, calcium diffuses from the periphery towards the center creating a centripetal wave pattern. During atrial fibrillation, rapid activation of atrial myocytes induces complex remodelling in diffusion properties that result in failure of calcium to propagate in a fully regenerative manner towards the center; a phenomenon termed\&nbsp; {\textquoteleft}{\textquoteleft}calcium silencing{\textquoteright}{\textquoteright}. This has been observed in rabbit atrial myocytes after exposure to prolonged rapid\&nbsp; pacing. Although experimental studies have pointed to possible mechanisms underlying calcium silencing, their individual effects and relative importance remain largely unknown.In this study we used computational modelling of the rabbit atrial cardiomyocyte to query the individual effects and combined effects of the proposed mechanisms leading to calcium\&nbsp;silencing and abnormal calcium wave propagation. We employed a population of models obtained from a newly developed model of the rabbit atrial myocyte with spatial representation of intracellular calcium handling. We selected parameters in the model that represent experimentally observed cellular remodelling which have been implicated in calcium silencing, and scaled their values in the population to match experimental observations. In particular, we changed the maximum conductances of I_CaL I_NCX, and I_NaK, \&nbsp;RyR open probability, RyR density, Serca2a density, and calcium buffering strength. We incorporated remodelling in a population of 16 models by independently varying parameters that reproduce experimentally observed cellular remodelling, and quantified the resulting alterations in calcium dynamics and wave propagation patterns.The results show a strong effect of\&nbsp; I_CaL in driving calcium silencing, with I_NCX, \&nbsp;I_NaK, and RyR density also resulting in calcium silencing in some models. Calcium alternans was observed in some models where I_NCX and Serca2a density had been changed. Simultaneously incorporating changes in all remodelled parameters resulted in calcium\&nbsp;silencing in all models, indicating the predominant role of decreasing I_CaL in the population phenotype.},
	keywords = {calcium waves, computational model, population of models, rabbit atrial cardiomyocyte, spatial calcium dynamics, tachypacing},
	author = {Vagos, Marcia and Arevalo, Hermenegild and Heijman, Jordi and Schotten, Ulrich and Sundnes, Joakim}
}
@inbook {27570,
	title = {Modeling Cardiac Mechanics on a Sub-Cellular Scale},
	booktitle = {Modeling Excitable Tissue: The EMI Framework},
	volume = {7},
	year = {2021},
	month = {11/2020},
	pages = {28-43},
	publisher = { Springer International Publishing},
	organization = { Springer International Publishing},
	edition = {1},
	chapter = {3},
	address = {Cham},
	abstract = {We aim to extend existing models of single-cell mechanics to the EMI framework, to define spatially resolved mechanical models of cardiac myocytes embedded in a passive extracellular space. The models introduced here will be pure mechanics models employing fairly simple constitutive laws for active and passive mechanics. Future extensions of the models may include a coupling to the electrophysiology and electro-diffusion models described in the other chapters, to study the impact of spatially heterogeneous ion concentrations on the cell and tissue mechanics.},
	author = {Telle, {\r A}shild and Wall, Samuel and Sundnes, Joakim},
	editor = {Tveito, Aslak and Marie E. {Rognes} and Mardal, Kent-Andre}
}
@article {28029,
	title = {Nationwide rollout reveals efficacy of epidemic control through digital contact tracing},
	journal = {Nature Communications},
	volume = {12},
	number = {5918},
	year = {2021},
	publisher = {Springer Nature},
	doi = {https://doi.org/10.1038/s41467-021-26144-8},
	author = {Elmokashfi, Ahmed and Sundnes, Joakim and Kvalbein, Amund and Naumova, Valeriya and Reinemo, Sven-Arne and Per Magne {Florvaag} and H{\r a}kon Kvale {Stensland} and Lysne, Olav}
}
@article {27048,
	title = {A computational study on integrated mechanisms of mechano-electric feedback in ischemic arrhythmogenesis},
	journal = {SAGE},
	year = {2020},
	publisher = {Clinical Medicine Insights: Cardiology},
	author = {Timmermann, Viviane and Alexander T. {Quinn} and Sundnes, Joakim and Wall, Samuel and Andrew D. {McCulloch} and Andrew G {Edwards}}
}
@book {27741,
	title = {Introduction to scientific programming with Python},
	series = {Simula SpringerBriefs on Computing},
	number = {6},
	year = {2020},
	month = {08/2020},
	pages = {148},
	publisher = {Springer },
	organization = {Springer },
	address = {Switzerland},
	abstract = {The book provides a first introduction programming for scientific and computational applications using the Python programming language. The presentation is compact and example-based, and is suitable for students and researchers with little or no prior experience in programming. The book uses relevant examples from mathematics and natural sciences to introduce programming as a practical toolbox, that should quickly enable readers to write their own programs for data processing and mathematical modeling. These tools include file reading, plotting, simple text analysis, and using NumPy for numerical computations, which are fundamental building blocks of all programs in data science and computational science. At the same time, readers are introduced to the fundamental concepts of programming, including variables, functions, loops, classes, and object oriented programming. The book therefore gives a good foundation for further studies of computer science and programming.},
	isbn = {978-3-030-50355-0},
	issn = {978-3-030-50356-7},
	doi = {https://doi.org/10.1007/978-3-030-50356-7},
	url = {springer.com/gp/book/9783030503550},
	author = {Sundnes, Joakim}
}
@article {27176,
	title = {Multisite pacing and myocardial scars: a computational study},
	journal = {Computer Methods in Biomechanics and Biomedical Engineering},
	volume = {23},
	year = {2020},
	month = {01/2020},
	publisher = {Taylor and Francis},
	issn = {1025-5842},
	doi = {10.1080/10255842.2020.1711885},
	url = {https://www.tandfonline.com/doi/full/10.1080/10255842.2020.1711885},
	author = {Albatat, Mohammad and Bergsland, Jacob and Arevalo, Hermenegild and Hans Henrik {Odland} and Wall, Samuel and Sundnes, Joakim and Balasingham, Ilangko}
}
@article {27450,
	title = {A novel computational model of the rabbit atrial cardiomyocyte with spatial calcium dynamics},
	journal = {Frontiers in Physiology},
	volume = {11},
	year = {2020},
	pages = {1205},
	publisher = {Frontiers},
	author = {Vagos, Marcia and Arevalo, Hermenegild and Heijman, Jordi and Schotten, Ulrich and Sundnes, Joakim}
}
@article {27666,
	title = {Regional Left Ventricular Fiber Stress Analysis for Cardiac Resynchronization Therapy Response},
	journal = {Journal of Cardiovascular Electrophysiology},
	year = {2020},
	publisher = { Wiley},
	author = {Albatat, Mohammad and Finsberg, Henrik and Arevalo, Hermenegild and Sundnes, Joakim and Bergsland, Jacob and Balasingham, Ilangko and Hans Henrik {Odland}}
}
@article {campos2020uncertainty,
	title = {Uncertainty quantification and sensitivity analysis of left ventricular function during the full cardiac cycle},
	journal = {Philosophical Transactions of the Royal Society A},
	volume = {378},
	number = {2173},
	year = {2020},
	pages = {20190381},
	publisher = {The Royal Society Publishing},
	abstract = {Patient-specific computer simulations can be a powerful tool in clinical applications, helping in diagnostics and the development of new treatments. However, its practical use depends on the reliability of the models. The construction of cardiac simulations involves several steps with inherent uncertainties, including model parameters, the generation of personalized geometry and fibre orientation assignment, which are semi-manual processes subject to errors. Thus, it is important to quantify how these uncertainties impact model predictions. The present work performs uncertainty quantification and sensitivity analyses to assess the variability in important quantities of interest (QoI). Clinical quantities are analysed in terms of overall variability and to identify which parameters are the major contributors. The analyses are performed for simulations of the left ventricle function during the entire cardiac cycle. Uncertainties are incorporated in several model parameters, including regional wall thickness, fibre orientation, passive material parameters, active stress and the circulatory model. The results show that the QoI are very sensitive to active stress, wall thickness and fibre direction, where ejection fraction and ventricular torsion are the most impacted outputs. Thus, to improve the precision of models of cardiac mechanics, new methods should be considered to decrease uncertainties associated with geometrical reconstruction, estimation of active stress and of fibre orientation.},
	issn = {1364-503X},
	doi = {https://doi.org/10.1098/rsta.2019.0381},
	author = {Joventino Oliveira {Campos} and Sundnes, Joakim and Rodrigo Weber dos {Santos} and Bernardo Martins {Rocha}}
}
@article {timmermann2019arrhythmogenic,
	title = {Arrhythmogenic current generation by myofilament-triggered Ca2+ release and sarcomere heterogeneity},
	journal = {Biophysical Journal},
	volume = {117},
	year = {2019},
	pages = {2471-2485},
	publisher = {Cell Press},
	author = {Timmermann, Viviane and Andrew G {Edwards} and Wall, Samuel and Sundnes, Joakim and Andrew D. {McCulloch}}
}
@article {27087,
	title = {Computational quantification of patient-specific changes in ventricular dynamics associated with pulmonary hypertension},
	journal = {American Journal of Physiology-Heart and Circulatory Physiology},
	volume = {31711911},
	year = {2019},
	pages = {H1363 - H1375},
	publisher = {American Journal of Physiology},
	author = {Finsberg, Henrik and Xi, Ce and Zhao, Xiaodan and Le Tan, Ju and Genet, Martin and Sundnes, Joakim and Lik Chuan {Lee} and Zhong, Liang and Wall, Samuel}
}
@article {campos2019effects,
	title = {Effects of left ventricle wall thickness uncertainties on cardiac mechanics},
	journal = {Biomechanics and Modeling in Mechanobiology},
	volume = {18},
	number = {5},
	year = {2019},
	pages = {1415-1427},
	publisher = {Springer},
	address = {Berlin Heidelberg},
	author = {Joventino O {Campos} and Sundnes, Joakim and Rodrigo W dos {Santos} and Bernardo M {Rocha}}
}
@inproceedings {27043,
	title = {Mechano-electric feedback and arrhythmogenic current generation in a computational model of coupled myocytes},
	journal = {ICBME2019--YC Fung 100th Birthday Conference},
	year = {2019},
	publisher = {Tech Science Press},
	author = {Timmermann, Viviane and Vincent, Kevin and Sundnes, Joakim and Andrew D. {McCulloch}}
}
@misc {27046,
	title = {A one-dimensional computational study of mechano-electric feedback and arrhythmogenic current generation},
	howpublished = {Gordon Research Conference "Cardiac Arrhythmia Mechanisms", Barga, Italy},
	year = {2019},
	author = {Timmermann, Viviane and Sundnes, Joakim and Wall, Samuel and Andrew D. {McCulloch} and Andrew G {Edwards}}
}
@article {doi:10.1080/10255842.2019.1579312,
	title = {Sensitivity of stress and strain calculations to passive material parameters in cardiac mechanical models using unloaded geometries},
	journal = {Computer Methods in Biomechanics and Biomedical Engineering},
	volume = {22},
	number = {6},
	year = {2019},
	note = {PMID: 30822148},
	pages = {664-675},
	publisher = {Taylor \& Francis},
	doi = {10.1080/10255842.2019.1579312},
	url = {https://doi.org/10.1080/10255842.2019.1579312},
	author = {Kallhovd, Siri and Sundnes, Joakim and Wall, Samuel}
}
@article {25766,
	title = {Uncertainty in cardiac myofiber orientation and stiffnesses dominate the variability of left ventricle deformation response},
	journal = { International Journal for Numerical Methods in Biomedical Engineering},
	volume = {35},
	year = {2019},
	pages = {e3178},
	publisher = { Wiley},
	author = {Rodr{\'\i}guez-Cantano, Roc{\'\i}o and Sundnes, Joakim and Marie E. {Rognes}}
}
@inbook {28124,
	title = {Abnormal Tissue Zone Detection and Average Active Stress Estimation in Patients with LV Dysfunction},
	booktitle = {Medical and Biological Image Analysis},
	year = {2018},
	publisher = {{IntechOpen},
	organization = {{IntechOpen},
	author = {Behdadfar, Sareh and Navarro, Laurent and Sundnes, Joakim and Maleckar, Molly and Hans Henrik {Odland} and Avril, Stephane}
}
@inbook {26316,
	title = {Abnormal Tissue Zone Detection and Average Active Stress Estimation in Patients with LV Dysfunction},
	booktitle = {Medical and Biological Image Analysis},
	year = {2018},
	publisher = {IntechOpen},
	organization = {IntechOpen},
	author = {Behdadfar, Sareh and Navarro, Laurent and Sundnes, Joakim and Maleckar, Molly and Hans Henrik {Odland} and Avril, Stephane},
	editor = {Koprowski, Robert}
}
@misc {26382,
	title = {Adjoint Based Data Assimilation for Quantification of Dynamic Mechanical Behavior of the Heart},
	howpublished = {World Congress of Biomechanics, New York, USA},
	year = {2018},
	author = {Wall, Samuel and Finsberg, Henrik and Balaban, Gabriel and Sundnes, Joakim and Lik Chuan {Lee}}
}
@misc {26384,
	title = {Adjoint Based Personalization of Mechanical Models for Quantification of Right Ventricular Failure in Pulmonary Hypertension},
	year = {2018},
	address = {Heart by Numbers Conference, Berlin, Germany},
	author = {Finsberg, Henrik and Xi, Ce and Xiaodan, Zhao and Le Tan, Ju and Genet, Martin and Sundnes, Joakim and Lik Chuan {Lee} and Zhong, Liang and Wall, Samuel}
}
@article {behdadfar2018centerline,
	title = {A Centerline-Based Model Morphing Algorithm for Patient-Specific Finite Element Modeling of the Left Ventricle},
	journal = {IEEE Transactions on Biomedical Engineering},
	volume = {65},
	number = {6},
	year = {2018},
	pages = {1391{\textendash}1398},
	publisher = {IEEE},
	doi = {10.1109/TBME.2017.2754980},
	author = {Behdadfar, Sareh and Navarro, Laurent and Sundnes, Joakim and Maleckar, Molly and Ross, Stian and Hans Henrik {Odland} and Avril, Stephane}
}
@article {26116,
	title = {Computational Modeling of Electrophysiology and Pharmacotherapy of Atrial Fibrillation: Recent Advances and Future Challenges},
	journal = {Frontiers in Physiology},
	volume = {9},
	year = {2018},
	month = {Apr-09-2018},
	pages = {1221},
	publisher = {Frontiers in Physiology},
	doi = {10.3389/fphys.2018.01221},
	url = {https://www.frontiersin.org/article/10.3389/fphys.2018.01221/fullhttps://www.frontiersin.org/article/10.3389/fphys.2018.01221/full},
	author = {Vagos, Marcia and Ilsbeth Gerarda Ma {van Herck} and Sundnes, Joakim and Arevalo, Hermenegild and Andrew G {Edwards} and Koivum{\"a}ki, Jussi}
}
@misc {27045,
	title = {A computational study of the contribution of mechano-electric feedback to arrhythmogenic current generation},
	howpublished = {Berlin, Germany},
	year = {2018},
	publisher = {Heart by Numbers, Biophysical Society},
	author = {Timmermann, Viviane and Sundnes, Joakim and Wall, Samuel and Andrew D. {McCulloch} and Andrew G {Edwards}}
}
@article {25636,
	title = {Efficient estimation of personalized biventricular mechanical function employing gradient-based optimization},
	journal = { International Journal for Numerical Methods in Biomedical Engineering},
	volume = {34},
	year = {2018},
	publisher = {John Wiley \& Sons},
	doi = {10.1002/cnm.2982},
	author = {Finsberg, Henrik and Xi, Ce and Le Tan, Ju and Zhong, L and Genet, Martin and Sundnes, Joakim and Lik Chuan {Lee} and Wall, Samuel}
}
@inproceedings {26370,
	title = {Electromechanical Model to Predict Cardiac Resynchronization Therapy},
	journal = {2018 40th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC)},
	year = {2018},
	pages = {5446-5459},
	publisher = {IEEE},
	doi = {10.1109/EMBC.2018.8513539},
	author = {Albatat, Mohammad and King, Ryan and Unger, Laura and Arevalo, Hermenegild and Wall, Samuel and Sundnes, Joakim and Bergsland, Jacob and Balasingham, Ilangko}
}
@article {25968,
	title = {In vivo estimation of elastic heterogeneity in an infarcted human heart},
	journal = {Biomechanics and Modeling in Mechanobiology},
	volume = {17},
	year = {2018},
	month = {May-05-2019},
	pages = {1317{\textendash}1329},
	publisher = {Springer},
	address = {Berlin Heidelberg},
	abstract = {In myocardial infarction, muscle tissue of the heart is damaged as a result of ceased or severely impaired blood flow. Survivors have an increased risk of further complications, possibly leading to heart failure. Material properties play an important role in determining post-infarction outcome. Due to spatial variation in scarring, material properties can be expected to vary throughout the tissue of a heart after an infarction. In this study we propose a data assimilation technique that can efficiently estimate heterogeneous elastic material properties in a personalized model of cardiac mechanics. The proposed data assimilation is tested on a clinical dataset consisting of regional left ventricular strains and in vivo pressures during atrial systole from a human with a myocardial infarction. Good matches to regional strains are obtained, and simulated equi-biaxial tests are carried out to demonstrate regional heterogeneities in stress{\textendash}strain relationships. A synthetic data test shows a good match of estimated versus ground truth material parameter fields in the presence of no to low levels of noise. This study is the first to apply adjoint-based data assimilation to the important problem of estimating cardiac elastic heterogeneities in 3-D from medical images.},
	issn = {1617-7959},
	doi = {10.1007/s10237-018-1028-5},
	url = {http://link.springer.com/10.1007/s10237-018-1028-5},
	author = {Balaban, Gabriel and Finsberg, Henrik and Simon W {Funke} and Trine F. {H{\r a}land} and Hopp, Einar and Sundnes, Joakim and Wall, Samuel and Marie E. {Rognes}}
}
@misc {26368,
	title = {A Novel Computational Model of the Rabbit Atrial Myocyte Offers Insight into Calcium Wave Propagation Failure},
	howpublished = {Biophysical Journal},
	year = {2018},
	month = {Jan-02-2018},
	address = {Cambridge, USA},
	abstract = {Atrial cardiomyocytes have a less well-developed T-tubule system than ventricular cells, resulting in intracellular calcium waves propagating from the membrane to the center via centripetal calcium diffusion. Failure of centripetal calcium-wave propagation ({\textquoteleft}calcium silencing{\textquoteright}) has been observed in a rabbit model of rapid atrial pacing and in patients with atrial fibrillation, but the underlying mechanisms remain incompletely understood. The goal of this study was to develop a novel computational model of the rabbit atrial cardiomyocyte that incorporates detailed compartmentalization of intracellular calcium dynamics, which can be used to investigate the mechanisms underpinning calcium silencing.
We incorporated ion-current formulations reflecting rabbit electrophysiology into a previously published human atrial cardiomyocyte model. The model was validated with published experimental data and the effects of altered rate of calcium diffusion between the calcium-release-unit space and the cytosol (τdiff) were investigated. τdiff modulates local calcium levels available to activate neighboring calcium-release sites, affecting wave propagation.
Simulation results showed that calcium-wave propagation was highly sensitive to τdiff during normal pacing at 2 Hz. We observed impaired calcium-wave propagation for a range of values of τdiff, with full calcium-wave propagation for values of τdiff exceeding 12.7 ms, and calcium silencing for values of τdiff below 10.6 ms due to insufficient local positive feedback for calcium-induced calcium release to maintain centripetal wave propagation. We also observed calcium alternans between propagating and non-propagating waves for intermediate values of τdiff.
This study provided new insight into the mechanisms of calcium-wave propagation failure in rabbit atrial cardiomyocytes and motivates further investigation of the effects of altered calcium diffusion on wave-propagation abnormalities and calcium-dependent arrhythmogenesis. Moreover, the newly developed model will be a useful tool for studying conditions which permit restoration of normal calcium wave propagation.},
	issn = {00063495},
	doi = {10.1016/j.bpj.2017.11.680},
	url = {https://linkinghub.elsevier.com/retrieve/pii/S0006349517319124https://api.elsevier.com/content/article/PII:S0006349517319124?httpAccept=text/xmlhttps://api.elsevier.com/content/article/PII:S0006349517319124?httpAccept=text/plain},
	author = {Vagos, Marcia and Heijman, Jordi and Arevalo, Hermenegild and Maleckar, Molly and Bernardo Lino {de Oliveira} and Schotten, Ulrich and Sundnes, Joakim}
}
@article {vagos2018novel,
	title = {A Novel Computational Model of the Rabbit Atrial Myocyte Offers Insight into Calcium Wave Propagation Failure},
	journal = {Biophysical Journal},
	volume = {114},
	number = {3},
	year = {2018},
	pages = {119a},
	publisher = {{Elsevier},
	author = {M{\'a}rcia R {Vagos} and Heijman, Jordi and Arevalo, Hermenegild and Maleckar, Molly and Bernardo Lino {de Oliveira} and Schotten, Ulrich and Sundnes, Joakim}
}
@article {campos2018preconditioned,
	title = {Preconditioned augmented Lagrangian formulation for nearly incompressible cardiac mechanics},
	journal = {International Journal for Numerical Methods in Biomedical Engineering},
	volume = {34},
	number = {4},
	year = {2018},
	pages = {e2948},
	publisher = {Wiley Online Library},
	author = {Joventino Oliveira {Campos} and Rodrigo Weber dos {Santos} and Sundnes, Joakim and Bernardo Martins {Rocha}}
}
@misc {aboelkassem2018turning,
	title = {Turning the Azimuthal Motions of Adjacent Tropomyosins into a Coupled N-body Problem in a Brownian Model of Cardiac Thin Filament Activation},
	howpublished = {Biophysical Journal},
	year = {2018},
	publisher = {Elsevier},
	address = {San Francisco, California/U.S.A.},
	author = {Aboelkassem, Yasser and Kimberly J {McCabe} and Huber, Gary and Sundnes, Joakim and Andrew D. {McCulloch}}
}
@misc {25637,
	title = {Assessment of regional myocardial work through adjoint-based data assimilation},
	howpublished = {Oslo, Norway},
	year = {2017},
	type = {International Conference on Computational Science and Engineering,  In memory of Hans Petter Langtangen},
	abstract = {Assessment of regional myocardial work through adjoint-based data assimilationIntroductionTo achieve efficient pumping of blood to the body, the healthy heart contracts in a synchronous manner. However, heart disease can alter how the heart is activated during a beat, and dyssynchronous contraction can occur, reducing the overall pumping efficiency. Advanced treatments exist for such cases,\&nbsp;but selecting patients likely to respond can be challenging. The existing selection criteria, based on organ level measures of activation and contraction, have relatively low specificity. \&nbsp;It is therefore of interest to\&nbsp;extract new biomarkers to help better identify potential responders. Here we explore one example of a potential biomarker, the regional myocardial work [1], a measure of cardiac efficiency, using a computational model of cardiac mechanics optimized to patient specific data using a high level adjoint based data assimilation method.\&nbsp;\&nbsp;MethodsLeft ventricular (LV) geometry was obtained from 4D echocardiography, and the segmented chamber was modelled as an incompressible, continuous hyperelastic body described via an transversely isotropic material law[2]. \&nbsp;Active force development was modeled through additively decomposing stress into passive and active stresses, the latter added along the cardiac fiber direction, defined by a rule based architecture.\&nbsp;\&nbsp;The model was fit to 4D imaging of the LV through the cardiac cycle using an adjoint-based\&nbsp;data assimilation technique, which automatically solves for the gradient of the solution with respect to local active stress, for highly efficient minimization of model misfit against collected data. Simulations were optimized both globally and regionally in 17 delineated segments[3].\&nbsp;With these simulations, the amount of mechanical work performed between time point tm\&nbsp;and tn\&nbsp;could be regionally calculated through -W(tm,\&nbsp;tn)\&nbsp;=\&nbsp;∫ S:\&nbsp;∂tE dt = ∑i\&nbsp;S(ti-{\textonehalf}):\&nbsp;dE(ti-{\textonehalf})\&nbsp;where\&nbsp;S(ti-{\textonehalf}) = 0.5*(S(ti)+S(ti-1))\&nbsp;\&nbsp;and\&nbsp;\&nbsp;dE(ti-{\textonehalf}) = E(ti)-E(ti-1)\&nbsp;Here subscript t indicates the time point, S is the Second Piola-Kirchhoff stress tensor and E is the Green-Lagrange strain tensor.\&nbsp;ResultsWe tested the method on healthy control subjects and patients suffering from left bundle branch block (LBBB). The results show an excellent fit between\&nbsp;measured and simulated strain (R^2 = 0.8) and volume (R^2 = 1.0).\&nbsp;The estimated regional myocardial work, assessed in these segments, shows clear differences between the healthy and diseased patients (e.g Mid Septal longitudinal wasted work ratio[1]: 1.45 (LBBB), 0.24(Healthy)) and can potentially be used as a biomarker to map regional cardiac dysfunction.\&nbsp;References[1]\&nbsp;doi:10.1152/ajpheart.00191.2013\&nbsp;[2] doi:10.1098/rsta.2009.0091\&nbsp;[3] doi:10.1002/cnm.2863\&nbsp;},
	url = {https://cseconf2017.files.wordpress.com/2017/09/2017-09-28-cseconf2017-complete-program.pdf},
	author = {Finsberg, Henrik and Aalen, John and Larsen, Camilla and Remme, Espen and Sundnes, Joakim and Otto A. {Smiseth} and Wall, Samuel}
}
@article {25817,
	title = {A Centerline Based Model Morphing Algorithm for Patient-Specific Finite Element Modelling of the Left Ventricle},
	journal = {IEEE Transactions on Biomedical Engineering},
	year = {2017},
	month = {09/2017},
	publisher = {IEEE},
	issn = {0018-9294},
	doi = {10.1109/TBME.2017.2754980},
	author = {Behdadfar, Sareh and Navarro, L. and Sundnes, Joakim and Maleckar, Molly and Ross, Stian and Hans Henrik {Odland} and Avril, S.}
}
@article {behdadfar2017centerline,
	title = {A centerline-based model morphing algorithm for patient-specific finite element modeling of the left ventricle},
	journal = {IEEE Transactions on Biomedical Engineering},
	volume = {65},
	number = {6},
	year = {2017},
	pages = {1391{\textendash}1398},
	publisher = {{IEEE},
	author = {Behdadfar, Sareh and Navarro, Laurent and Sundnes, Joakim and Maleckar, Molly and Ross, Stian and Hans Henrik {Odland} and Avril, Stephane}
}
@article {vagos2017computational,
	title = {A computational framework for testing arrhythmia marker sensitivities to model parameters in functionally calibrated populations of atrial cells},
	journal = {Chaos: An Interdisciplinary Journal of Nonlinear Science},
	volume = {27},
	number = {9},
	year = {2017},
	pages = {093941},
	publisher = {{AIP Publishing LLC},
	author = {M{\'a}rcia R {Vagos} and Arevalo, Hermenegild and Bernardo Lino {de Oliveira} and Sundnes, Joakim and Maleckar, Molly}
}
@article {25392,
	title = {A computational framework for testing arrhythmia marker sensitivities to model parameters in functionally calibrated populations of atrial cells},
	journal = {Chaos},
	volume = {27},
	year = {2017},
	publisher = {AIP},
	doi = {10.1063/1.4999476},
	author = {Vagos, Marcia and Arevalo, Hermenegild and Bernardo Lino {de Oliveira} and Sundnes, Joakim and Maleckar, Molly}
}
@misc {25257,
	title = {A Computational Model for the Identification of Atrial Stunning Pathways},
	howpublished = {2017 EMI International Conference},
	year = {2017},
	author = {Bernardo Lino {de Oliveira} and Sundnes, Joakim}
}
@article {25635,
	title = {Estimating cardiac contraction through high resolution data assimilation of a personalized mechanical model},
	journal = {Journal of Computational Science},
	volume = {24},
	year = {2017},
	pages = {85-90},
	publisher = {Elsevier},
	keywords = {Adjoint Method, Cardiac Mechanics, Contractility, Data assimilation, PDE-constrained optimization},
	issn = {1877-7503},
	doi = {10.1016/j.jocs.2017.07.013},
	url = {http://www.sciencedirect.com/science/article/pii/S1877750317308190},
	author = {Finsberg, Henrik and Balaban, Gabriel and Ross, Stian and Trine F {H{\r a}land} and Hans Henrik {Odland} and Sundnes, Joakim and Wall, Samuel}
}
@article {24994,
	title = {An Evaluation of the Accuracy of Classical Models for Computing the Membrane Potential and Extracellular Potential for Neurons},
	journal = {Frontiers in Computational Neuroscience},
	volume = {11},
	year = {2017},
	pages = {27},
	publisher = {Frontiers Media SA},
	abstract = {Two mathematical models are part of the foundation of Computational neurophysiology; a) the Cable equation is used to compute the membrane potential of neurons, and, b) volume-conductor theory describes the extracellular potential around neurons. In the standard procedure for computing extracellular potentials, the transmembrane currents are computed by means of a) and the extracellular potentials are computed using an explicit sum over analytical point-current source solutions as prescribed by volume conductor theory. Both models are extremely useful as they allow huge simplifications of the computational efforts involved in computing extracellular potentials. However, there are more accurate, though\&nbsp;computationally very expensive, models available where the potentials inside and outside the neurons are computed simultaneously in a self-consistent scheme. In the present work we explore the accuracy of the classical models a) and b) by comparing them to these more accurate schemes.The main assumption of a) is that the ephaptic current can be ignored in the derivation of the Cable equation. We find, however, for our examples with stylized neurons, that the ephaptic current is comparable in magnitude to other currents involved in the computations, suggesting that it may be significant \&ndash; at least in parts of the simulation. The magnitude of the error introduced in the membrane potential is several millivolts, and this error also translates into errors in the predicted extracellular potentials. While the error becomes negligible if we assume the extracellular conductivity to be very large, this assumption is, unfortunately, not easy to justify a priori for all situations of interest.},
	issn = {1662-5188},
	doi = {10.3389/fncom.2017.00027},
	url = {http://journal.frontiersin.org/article/10.3389/fncom.2017.00027},
	author = {Tveito, Aslak and Karoline Horgmo {J{\ae}ger} and Glenn T. {Lines} and Paszkowski, {\L}ukasz and Sundnes, Joakim and Andrew G {Edwards} and M{\"a}ki-Marttunen, Tuomo and Halnes, Geir and Gaute T {Einevoll}}
}
@article {24721,
	title = {High resolution data assimilation of cardiac mechanics},
	journal = {International journal for numerical methods in biomedical engineering},
	volume = {33},
	number = {11},
	year = {2017},
	month = {04/2017},
	pages = {e2863},
	publisher = {John Wiley \& Sons, Ltd},
	doi = {10.1002/cnm.2863},
	author = {Balaban, Gabriel and Finsberg, Henrik and Hans Henrik {Odland} and Marie E. {Rognes} and Ross, Stian and Sundnes, Joakim and Wall, Samuel}
}
@article {behdadfar2017importance,
	title = {Importance of material parameters and strain energy function on the wall stresses in the left ventricle},
	journal = {Computer methods in biomechanics and biomedical engineering},
	volume = {20},
	number = {11},
	year = {2017},
	pages = {1223{\textendash}1232},
	publisher = {{Taylor \& Francis},
	author = {Behdadfar, Sareh and Navarro, Laurent and Sundnes, Joakim and Maleckar, Molly and Avril, Stephane}
}
@misc {25790,
	title = {Integrated Mechanisms of Mechano-Electric feedback in Ischemic Arrhythmogenesis},
	howpublished = {Bergen, Norway},
	year = {2017},
	author = {Timmermann, Viviane and Andrew G {Edwards} and Sundnes, Joakim and Andrew D. {McCulloch} and Wall, Samuel and T. A. {Quinn}}
}
@misc {25792,
	title = {Integrated Mechanisms of Mechano-Electric Feedback in Ischemic Arrhythmogenesis},
	year = {2017},
	month = {09/2017},
	address = {Oslo, Norway},
	author = {Timmermann, Viviane and Wall, Samuel and Sundnes, Joakim and T. A. {Quinn} and Andrew G {Edwards}}
}
@article {25788,
	title = {An integrative appraisal of mechano-electric feedback mechanisms in the heart},
	journal = {Progress in biophysics and molecular biology},
	volume = {130},
	year = {2017},
	pages = {404{\textendash}417},
	publisher = {Elsevier},
	author = {Timmermann, Viviane and Lars A {Dejgaard} and Kristina H {Haugaa} and Andrew G {Edwards} and Sundnes, Joakim and Andrew D. {McCulloch} and Wall, Samuel}
}
@misc {25457,
	title = {Mechanical Analysis of Pulmonary Hypertension via Adjoint based Data Assimilation of a Finite Element Model},
	year = {2017},
	month = {06/2017},
	address = {Summer Biomechanics, Bioengineering, and Biotransport Conference, Tuscon, USA},
	author = {Finsberg, Henrik and Xi, Ce and Tan, JL and Zhong, L and Lee, LC and Sundnes, Joakim and Wall, Samuel}
}
@article {24028,
	title = {Adjoint Multi-Start Based Estimation of Cardiac Hyperelastic Material Parameters using Shear Data},
	journal = {Biomechanics and Modeling in Mechanobiology},
	year = {2016},
	month = {23.03.2013},
	pages = {1-13},
	publisher = {Springer},
	author = {Balaban, Gabriel and Martin Sandve {Aln{\ae}s} and Sundnes, Joakim and Marie E. {Rognes}}
}
@inproceedings {25261,
	title = {Comparison of tetrahedral and hexahedral meshes for finite element simulation of cardiac electro-mechanics},
	journal = {VII European Congress on Computational Methods in Applied Sciences and Engineering},
	year = {2016},
	publisher = {National Technical University of Athens},
	author = {Bernardo Lino {de Oliveira} and Sundnes, Joakim},
	editor = {Papadrakakis, M. and Papadopoulos, V. and Stefanou, G. and Plevris, V.}
}
@misc {24969,
	title = {Impact of material parameter uncertainty on stress in patient specific models of the heart},
	howpublished = {SIAM Conference on uncertainty quantification, Lausanne, Switzerland},
	year = {2016},
	author = {Sundnes, Joakim and Kallhovd, Siri and Wall, Samuel}
}
@misc {24970,
	title = {Impact of material parameter variations on stress in patient specific models of the heart},
	howpublished = {World Congress on Computational Mechanics, Seoul, South Korea},
	year = {2016},
	author = {Sundnes, Joakim and Kallhovd, Siri and Wall, Samuel}
}
@article {25483,
	title = {An integrated electromechanical-growth heart model for simulating cardiac therapies},
	journal = {Biomechanics and modeling in mechanobiology},
	volume = {15},
	number = {4},
	year = {2016},
	pages = {791{\textendash}803},
	publisher = {{Springer Berlin Heidelberg},
	abstract = {An emerging class of models has been developed in recent years to predict cardiac growth and remodeling. We recently developed a cardiac  constitutive model that predicts remodeling in response to elevated hemodynamics loading, and a subsequent reversal of the remodeling process when the loading is reduced. Here, we describe the integration of this model to an existing strongly coupled electromechanical model of the heart. },
	author = {Lik Chuan {Lee} and Sundnes, Joakim and Genet, Martin and Jonathan F {Wenk} and Wall, Samuel}
}
@article {24968,
	title = {Methodology for morphometric analysis of modern human contralateral premolars},
	journal = {Journal of Computer Assisted Tomography},
	volume = {40},
	year = {2016},
	pages = {617-625},
	publisher = {Wolters Kluwer Health},
	abstract = {Objective: This study aimed at developing a standard methodology for morphometric analysis and comparison of contralateral human premolar pulp space using microcomputed tomography (micro-CT) and semi- automated software. The primary objective was to establish a method to compare the complex and minute morphological internal volumes of con- tralateral premolar pulp spaces and determine their degree of similarity. The secondary aim was to introduce new methodology for selecting contra- lateral premolars for the study of biomaterials and techniques. Methods: Forty-one intact human premolar pairs (n = 82) extracted from 28 patients were scanned with micro-CT. Quantitative comparative evalua- tion was performed through geometric morphometric deviation analysis of the pulp spaces after mirroring, automatic alignment, and coregistration with semiautomated software. Geometric parameters compared included volume, surface, and surface over volume. Shape deviation analysis of transformed mean distances and root mean square errors was conducted. Results: The geometric parameters of the contralateral premolar pulp spaces had significantly higher similarity coefficients than random pairs (P \&lt; 0.001). The shape deviation analysis and transformed mean distances had significantly lower values for contralaterals compared with random pairs (P \&lt; 0.001). The contralateral geometries had a statistically signifi- cant narrower distribution in deviation when compared with random pairs (P \&lt; 0.001).Conclusions: We present a methodology that sets a new standard for internal validation of the teeth to be used in ex vivo testing of endodon- tic materials and techniques. It also shows that the resolution of the CT scan is crucial and that studies using cone beam CT cannot be used for such studies.\&nbsp;},
	author = {Gaute Floer {Johnsen} and Sundnes, Joakim and Wengenroth, Jonas and H{\r a}vard Jostein {Haugen}}
}
@inproceedings {24567,
	title = {Optimization of a Spatially Varying Cardiac Contraction parameter using the Adjoint Method},
	journal = {FEniCS{\textquoteright}16},
	year = {2016},
	abstract = {A cardiac computational model is constrained using clinical measurements such as pressure, volume and regional strain. The problem is formulated as a PDE-constrained optimisation problem where the objective functional represents the misfit between measured and simulated data. The control parameter for the active phase is a spatially varying contraction parameter defined at every vertex in the mesh. This makes gradient calculations using the adjoint approach computationally advantageous over standard finite difference approximations.},
	keywords = {Adjoint Method, Cardiac Mechanics, parameter estimation, PDE-constrained optimization},
	author = {Finsberg, Henrik and Balaban, Gabriel and Marie E. {Rognes} and Sundnes, Joakim and Wall, Samuel}
}
@misc {24417,
	title = {Patient Specific Modeling of Cardiac Mechanics using the Active Strain Formulation},
	howpublished = {Geilo Winter School},
	year = {2016},
	author = {Finsberg, Henrik and Balaban, Gabriel and Wall, Samuel and Sundnes, Joakim and Marie E. {Rognes}}
}
@inproceedings {24991,
	title = {Personalized Cardiac Mechanical Model using a High Resolution Contraction Field},
	journal = {VPH16 Translating VPH to the Clinic},
	year = {2016},
	author = {Finsberg, Henrik and Balaban, Gabriel and Sundnes, Joakim and Marie E. {Rognes} and Hans Henrik {Odland} and Ross, Stian and Wall, Samuel}
}
@article {24650,
	title = {Physics-based computer simulation of the long-term effects of cardiac regenerative therapies},
	journal = {Technology},
	volume = {4},
	number = {01},
	year = {2016},
	pages = {23{\textendash}29},
	publisher = {{World Scientific Publishing Co./Imperial College Press},
	author = {Lik Chuan {Lee} and Sundnes, Joakim and Genet, Martin and Wall, Samuel}
}
@misc {25791,
	title = {Role of Electromechanical Feedback in Mitral Valve Prolapse Arrhythmia},
	year = {2016},
	month = {09/2016},
	publisher = {Conference on Cardiac Mechano-Electric Couping and Arrhythmias},
	address = {Freiburg, Germany},
	author = {Timmermann, Viviane and Andrew G {Edwards} and Sundnes, Joakim and Andrew D. {McCulloch} and Wall, Samuel}
}
@article {Pezzuto2016,
	title = {Space-discretization error analysis and stabilization schemes for conduction velocity in cardiac electrophysiology},
	journal = {International Journal for Numerical Methods in Biomedical Engineering},
	volume = {32},
	number = {10},
	year = {2016},
	publisher = {Wiley},
	abstract = {The paper discusses spatial discretization techniques for the bidomain model of cardiac electrophysiology. A detailed error analysis for the conduction velocity is presented, which shed light on several questions and previous result in the literature concerning mass lumping and current interpolation methodologies. Based on the results of the analysis, we introduce a stabilized scheme with artificial conductivity, which tends to correct the conduction velocity on coarse grids. Finally, a weighted mass lumping scheme is shown to be super-convergent on uniform grids.},
	doi = {https://dx.doi.org/10.1002/cnm.2762},
	author = {Pezzuto, Simone and Johan Elon {Hake} and Sundnes, Joakim}
}
@inbook {23986,
	title = {Bidomain Model: Computation},
	booktitle = {Encyclopedia of Applied and Computational Mathematics},
	year = {2015},
	month = {11/2015},
	pages = {125-128},
	publisher = {Springer Berlin Heidelberg},
	organization = {Springer Berlin Heidelberg},
	isbn = {978-3-540-70528-4},
	doi = {10.1007/978-3-540-70529-1_294},
	url = {http://dx.doi.org/10.1007/978-3-540-70529-1_294},
	author = {Sundnes, Joakim},
	editor = {Engquist, Bj{\"o}rn}
}
@misc {23710,
	title = {Computational models of electro-mechanical interactions in the heart},
	howpublished = {University of Uppsala},
	year = {2015},
	author = {Sundnes, Joakim and Sjur Urdson {Gjerald} and Wall, Samuel}
}
@misc {23855,
	title = {Dyssynchronous Left Ventricular Stress Estimation},
	howpublished = {Workshop on Advanced Numerical Techniques in Biomedical Computing: Simula Research Laboratory},
	year = {2015},
	abstract = {The heart is a muscular pump that moves approximatly 8,000 litres per day through the human body. It manages to this by a combination of contraction/relaxation along muscle fibers and elastic recoil. These two effects are indistinguishable in a medical image, but can be estimated using a computational model.In our work we use adjoint based optimization techniques in order to determine muscle contraction and elastic recoil in a patient specific left ventricular geometry based on echocardiography and pressure catheter data. Possible applications of the technique include mechanical stress estimation and hypothesis testing in cardiac resynchronization therapy research.},
	author = {Balaban, Gabriel},
	editor = {Finsberg, Henrik and Marie E. {Rognes} and Sundnes, Joakim and Wall, Samuel and Hans Henrik {Odland} and Ross, Stian}
}
@inbook {23987,
	title = {Electro-Mechanical Coupling in Cardiac Tissue},
	booktitle = {Encyclopedia of Applied and Computational Mathematics},
	year = {2015},
	publisher = {Springer Berlin Heidelberg},
	organization = {Springer Berlin Heidelberg},
	isbn = {978-3-540-70528-4},
	doi = {10.1007/978-3-540-70529-1_481},
	url = {http://dx.doi.org/10.1007/978-3-540-70529-1_481},
	author = {Sundnes, Joakim},
	editor = {Engquist, Bj{\"o}rn}
}
@misc {23581,
	title = {Identifying the Parameters of the Heart: Variational Data Assimilation in Cardiac Mechanics Using Dolfin-Adjoint},
	howpublished = {FEniCS {\textquoteright}15, Imperial College London, UK},
	year = {2015},
	type = {Featured presentation},
	author = {Marie E. {Rognes} and Balaban, Gabriel and Sundnes, Joakim and Martin Sandve {Aln{\ae}s}}
}
@article {Simula.simula.2704,
	title = {Increased Membrane Capacitance Is the Dominant Mechanism of Stretch-Dependent Conduction Slowing in the Rabbit Heart: a Computational Study},
	journal = {Cellular and Molecular Bioengineering},
	volume = {8},
	year = {2015},
	pages = {237-246},
	publisher = { },
	abstract = {Volume loading of the cardiac ventricles is known to slow electrical conduction in the rabbit heart, but the mech- anisms remain unclear. Previous experimental and modeling studies have investigated some of these mechanisms, including stretch-activated membrane currents, reduced gap junctional conductance, and altered cell membrane capacitance. In order to quantify the relative contributions of these mechanisms, we combined a monomain model of rabbit ventricular electrophysiology with a hyperelastic model of passive ventricular mechanics. After a simplied geometric model with prescribed homogeneous deformation had been used to t model parameters and charcterize individual MEF mechanisms, a 3D model of the rabbit left and right ventricles was compared with experimental measurements from optical electrical mapping studies in the isolated rabbit heart. The model was in ated to an end-diastolic pressure of 30 mmHg, resulting in epicardial strains comparable to those measured in the anterior left ventricular free wall. While the e ects of stretch activated channels did alter epicardial conduction velocity, an increase in cellular capacitance was required to explain previously reported experimental results. The new results suggest that for large strains, various mechanisms can combine and produce a biphasic relationship between strain and conduction velocity. However, at the moderate strains generated by high end-diastolic pressure, a stretch- induced increase in myocyte membrane capacitance is the dominant driver of conduction slowing during ventricular volume loading.},
	author = {Bernardo Lino {de Oliveira} and Sundnes, Joakim and Wall, Samuel and Andrew D. {McCulloch}}
}
@article {23708,
	title = {An integrated electromechanical-growth heart model for simulating cardiac therapies},
	journal = {Biomechanics and Modeling in Mechanobiology},
	volume = {15},
	year = {2015},
	pages = {791-803},
	publisher = {Springer Berlin Heidelberg},
	author = {Lik Chuan {Lee} and Sundnes, Joakim and Genet, Martin and Jonathan F {Wenk} and Wall, Samuel}
}
@misc {23711,
	title = {Mechano-electric feedback as a source of ectopic activity},
	howpublished = {Gordon Research Conference on Arrhythmia Mechanisms, Lucca, Italy},
	year = {2015},
	month = {03/2015},
	address = {Gordon Research Conference on Arrhythmia Mechanisms, Lucca, Italy},
	author = {Sundnes, Joakim and Wall, Samuel and Timmermann, Viviane and Tveito, Aslak}
}
@misc {23812,
	title = {Modeling growth and remodeling in heart muscle tissue},
	howpublished = {SIAM Conference on Computational Science and Engineering},
	year = {2015},
	type = {Minisymposium },
	author = {Sundnes, Joakim and Wall, Samuel}
}
@inproceedings {23709,
	title = {Patient{\textendash}Specific Parameter Estimation for a Transversely Isotropic Active Strain Model of Left Ventricular Mechanics},
	journal = {Statistical Atlases and Computational Models of the Heart-Imaging and Modelling Challenges},
	year = {2015},
	pages = {93-104},
	publisher = {Springer International Publishing},
	author = {Sjur Urdson {Gjerald} and Johan Elon {Hake} and Pezzuto, Simone and Sundnes, Joakim and Wall, Samuel}
}
@inproceedings {23720,
	title = {Personalization of a Cardiac Compuational Model using Clinical Measurements},
	journal = {28th Nordic Seminar on Computational Mechanics},
	volume = {28},
	year = {2015},
	month = {10/2015},
	pages = {47-50},
	publisher = {Proceedings of NSCM-28},
	address = {Tallin, Estonia},
	abstract = {Important features in cardiac mechanics that cannot easily be measured in the clinic, can be computed using a computational model that is calibrated to behave in the same way as a patient{\textquoteright}s heart. To construct such a model, clinical measurements such as strain, volume and cavity pressure are used to personalize the mechanics of a cardiac computational model. The problem is formulated as a PDE-constrained optimization problem where the minimization functional represents the misfit between the measured and simulated data. The target parameters are material parameters and a spatially varying contraction parameter. The minimization is carried out using a gradient based optimization algorithm and an automatically derived adjoint equation. The method has been tested on synthetic data, and is able to reproduce a prescribed contraction pattern on the left ventricle.},
	author = {Finsberg, Henrik and Balaban, Gabriel and Sundnes, Joakim and Marie E. {Rognes} and Wall, Samuel}
}
@misc {23937,
	title = {Significance of passive material parameters in mechanical models of the heart},
	howpublished = {Lugano, Switzerland},
	year = {2015},
	type = {Conference presentation at MALT 2015 },
	abstract = {Significance of passive material parameters in mechanicalmodels of the heart},
	author = {Kallhovd, Siri and Sundnes, Joakim and Wall, Samuel}
}
@misc {23713,
	title = {Simulations of Heart Function (editorial)},
	howpublished = {BioMed Research International},
	year = {2015},
	pages = { 3 pages},
	publisher = {Hindawi Publishing Corporation},
	author = {Rodrigo Weber dos {Santos} and Alonso, Sergio and Elizabeth M {Cherry} and Sundnes, Joakim}
}
@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}}
}
@misc {Simula.simula.3020,
	title = {Computational Models of Electro-Mechanical Interactions in the Heart},
	howpublished = {Invited mini symposium presentation at the European Conference for Mathematics in Industry, Taormina, Italy.},
	year = {2014},
	month = {June},
	keywords = {Conference},
	author = {Sundnes, Joakim and Wall, Samuel and Pezzuto, Simone and Johan Elon {Hake} and Bernardo Lino {de Oliveira}}
}
@misc {23454,
	title = {Computational Models of Electro-Mechanical Interactions in the Heart},
	howpublished = {The Nordic Seminar on Computational Mechanics, Stockholm},
	year = {2014},
	type = {Keynote talk},
	author = {Sundnes, Joakim}
}
@misc {Simula.simula.3022,
	title = {A Continuum Model for Active Cardiac Muscle},
	howpublished = {World congress on Computational Mechanics, Barcelona, Spain},
	year = {2014},
	month = {July},
	keywords = {Conference},
	author = {Sundnes, Joakim and Narayanan, Harish}
}
@article {Simula.simula.1594,
	title = {Improved Discretisation and Linearisation of Active Tension in Strongly Coupled Cardiac Electro-Mechanics Simulations},
	journal = {Computer Methods in Biomechanics and Biomedical Engineering},
	volume = {17},
	number = {6},
	year = {2014},
	pages = {604-15},
	publisher = { },
	abstract = {Mathematical models of cardiac electro-mechanics typically consist of three tightly coupled parts: systems of ordinary differential equations describing electro-chemical reactions and cross-bridge dynamics in the muscle cells, a system of partial differential equations modelling the propagation of the electrical activation through the tissue and a nonlinear elasticity problem describing the mechanical deformations of the heart muscle. The complexity of the mathematical model motivates numerical methods based on operator splitting, but simple explicit splitting schemes have been shown to give severe stability problems for realistic models of cardiac electro-mechanical coupling. The stability may be improved by adopting semi-implicit schemes, but these give rise to challenges in updating and linearising the active tension. In this paper we present an operator splitting framework for strongly coupled electro-mechanical simulations and discuss alternative strategies for updating and linearising the active stress component. Numerical experiments demonstrate considerable performance increases from an update method based on a generalised Rush-Larsen scheme and a consistent linearisation of active stress based on the first elasticity tensor.},
	author = {Sundnes, Joakim and Wall, Samuel and Osnes, Harald and Thorvaldsen, Tom and Andrew D. {McCulloch}}
}
@inproceedings {Simula.simula.3088,
	title = {Least Squares Fitting of a Cardiac Hyperelasticity Model Using an Automatically Derived Adjoint Equation},
	journal = {Proceedings of NSCM-27: the 27th Nordic Seminar on Computational Mechanics},
	volume = {27},
	year = {2014},
	month = {October},
	pages = {272-275},
	publisher = {KTH Stockholm Royal Institute of Technology},
	type = {Workshop},
	address = {Drottning Kristinas v{\"a}g 53},
	abstract = {A Cardiac hyperelasticity model is successfully calibrated using an adjoint based least squares minimization and synthetic data.},
	keywords = {Conference},
	author = {Balaban, Gabriel and Sundnes, Joakim and Martin Sandve {Aln{\ae}s} and Marie E. {Rognes}},
	editor = {Eriksson, Anders and Kulachenko, Artem and Mihaescu, Mihai and Tibert, Gunnar}
}
@misc {Simula.simula.3018,
	title = {Patient Specific Models of Cardiac Electro-Mechanics},
	howpublished = {Seminar at Ecole des Mines, St Etienne, France},
	year = {2014},
	month = {February},
	author = {Sundnes, Joakim and Wall, Samuel and Sjur Urdson {Gjerald} and Johan Elon {Hake} and Bernardo Lino {de Oliveira}}
}
@inbook {gjerald2014patient,
	title = {Patient{\textendash}Specific Parameter Estimation for a Transversely Isotropic Active Strain Model of Left Ventricular Mechanics},
	booktitle = {Lecture Notes in Computer Science},
	volume = {8896},
	year = {2014},
	pages = {93{\textendash}104},
	publisher = {Springer International Publishing},
	organization = {Springer International Publishing},
	author = {Sjur Urdson {Gjerald} and Johan Elon {Hake} and Pezzuto, Simone and Sundnes, Joakim and Wall, Samuel}
}
@article {stablebidomain,
	title = {Stable Time Integration Suppresses Unphysical Oscillations in the Bidomain Model},
	journal = {Frontiers in Physics},
	volume = {2},
	year = {2014},
	publisher = { },
	abstract = {The bidomain model is a popular model for simulating electrical activity in cardiac tissue. It is a continuum-based model consisting of non-linear ordinary differential equations (ODEs) describing spatially averaged cellular reactions and a system of partial differential equations (PDEs) describing electrodiffusion on tissue level. Because of this multi-scale, ODE/PDE structure of the model, operator-splitting methods that treat the ODEs and PDEs in separate steps are natural candidates as numerical solution methods. Second-order methods can generally be expected to be more effective than first-order methods under normal accuracy requirements. However, the simplest and the most commonly applied second-order method for the PDE step, the Crank-Nicolson (CN) method, may generate unphysical oscillations. In this paper, we investigate the performance of a two-stage, L-stable singly diagonally implicit Runge-Kutta method for solving the PDEs of the bidomain model. Numerical experiments show that the enhanced stability property of this method leads to more physically realistic numerical simulations compared to both the CN and backward Euler methods.},
	author = {Saeed Torabi {Ziaratgahi} and Marsh, Megan and Sundnes, Joakim and Raymond J. {Spiteri}}
}
@inproceedings {Simula.simula.2708,
	title = {3D Heart Modeling With Cellular Automata, Mass-Spring System and CUDA},
	journal = {Parallel computing technologies},
	volume = {7979},
	year = {2013},
	pages = {296-309},
	publisher = {Springer},
	type = {Conference},
	abstract = {The mechanical behavior of the heart is guided by the propagation of an electrical wave, called action potential. Many diseases have multiple effects on both electrical and mechanical cardiac physiology. To support a better understanding of the multi-scale and multi-physics processes involved in physiological and pathological cardiac conditions, a lot of work has been done in developing computational tools to simulate the electro-mechanical behavior of the heart. In this work, we implemented an aplication to mimic the heart tissue behavior, based on cellular automaton, mass-spring system and parallel computing with CUDA. Our application performed 3D simulations in a very short time. In order to assess the simulation results, we compared them with another synthetic model based on well-known partial differential equations(PDE). Preliminary results suggest our application was able to reproduce the PDE results with much less computational effort.},
	author = {Ricardo Silva {Campos} and Ronan Mendonca {Amorim} and Bernardo Lino {de Oliveira} and Sundnes, Joakim and Luis Paulo da S {Barra} and Lobosco, Marcelo and Rodrigo Weber dos {Santos}},
	editor = {Malyshkin, Victor}
}
@misc {Simula.simula.2706,
	title = {Computational Models of Electro-Mechanical Interactions in the Heart},
	howpublished = {SIAM conference on computational science and engineering, Boston},
	year = {2013},
	month = {February},
	keywords = {Conference},
	author = {Sundnes, Joakim and Wall, Samuel}
}
@article {Simula.simula.1440,
	title = {Effects of Deformation on Transmural Dispersion of Repolarization Using in Silico Models of Human Left Ventricular Wedge},
	journal = {International Journal for Numerical Methods in Biomedical Engineering},
	volume = {29},
	number = {12},
	year = {2013},
	pages = {1323-1337},
	abstract = {Mechanical deformation affects the electrical activity of the heart through multiple feedback loops. The purpose of this work is to study the effect of deformation on transmural dispersion of repolarization and on surface electrograms using an in silico human ventricular wedge. To achieve this purpose, we developed a strongly coupled electromechanical cell model by coupling a human left ventricle electrophysiology model and an active contraction model reparameterized for human cells. This model was then embedded in tissue simulations on the basis of bidomain equations and nonlinear solid mechanics. The coupled model was used to evaluate effects of mechanical deformation on important features of repolarization and electrograms. Our results indicate an increase in the T-wave amplitude of the surface electrograms in simulations that account for the effects of cardiac deformation. This increased T-wave amplitude can be explained by changes to the coupling between neighboring myocytes, also known as electrotonic effect. The thickening of the ventricular wall during repolarization contributes to the decoupling of cells in the transmural direction, enhancing action potential heterogeneity and increasing both transmural repolarization dispersion and T-wave amplitude of surface electrograms. The simulations suggest that a considerable percentage of the T-wave amplitude (15\%) may be related to cardiac deformation.},
	author = {Bernardo Lino {de Oliveira} and Luis Paulo da S {Barra} and Elson Magalh{\~a}es {Toledo} and Sundnes, Joakim and Rodrigo Weber dos {Santos}}
}
@misc {Simula.simula.2694,
	title = {The Effects of Mechanoelectrical Feedback on Conduction Velocity: a Computational Study},
	year = {2013},
	publisher = {Cardiac Physiome Workshop},
	abstract = {Mechanical deformation is know to have an influence on the velocity of the electrical conduction in cardiac tissue. Several experimental and computational studies have investigated this and a wide variety of different strain-conduction velocity relationships have been reported. In short, there are increasing, decreasing, constant and biphasic relationships reported. The objective of this study is to develop a computational model that includes multiple mechanoelectrical feedback mechanisms and is capable of reproducing the different strain-conduction velocity relationships reported.},
	author = {Bernardo Lino {de Oliveira} and Wall, Samuel and Sundnes, Joakim}
}
@misc {Simula.simula.2696,
	title = {Evaluation of Cardiac Tissue Engineering Applications Using Strongly Coupled Electromechanical Models of the Left Ventricle},
	howpublished = {Computer Methods in Biomechanics and Biomedical Engineering, Utah},
	year = {2013},
	keywords = {Internal Seminar, University of Oslo},
	author = {Wall, Samuel and Sundnes, Joakim and Guccione, Julius}
}
@misc {Simula.simula.2578,
	title = {Patient-Specific Models of Cardiac Electro-Mechanics},
	howpublished = {Federal University of Juiz de Fora},
	year = {2013},
	month = {October},
	author = {Sundnes, Joakim and Wall, Samuel and Sjur Urdson {Gjerald} and Johan Elon {Hake} and Bernardo Lino {de Oliveira}}
}
@misc {Simula.simula.2700,
	title = {Strongly Coupled Electromechanical Models of the Heart},
	howpublished = {Biomechanics and Medical Imaging Mini-Symposium, UCSF},
	year = {2013},
	keywords = {Conference},
	author = {Wall, Samuel and Sundnes, Joakim}
}
@misc {Simula.simula.1620,
	title = {Computational Models of Electro-Mechanical Interactions in the Infarct Injured Heart},
	howpublished = {National PhD conference in medical Imaging, Trondheim, Norway},
	year = {2012},
	author = {Sundnes, Joakim and Wall, Samuel}
}
@misc {Simula.simula.1610,
	title = {Computer Models of Electro-Mechanical Interactions in the Contracting Heart},
	howpublished = {Workshop on computational models in biomedicine, Federal University of Juiz de Fora, Brazil},
	year = {2012},
	month = {July},
	author = {Sundnes, Joakim and Wall, Samuel}
}
@misc {Simula.simula.1614,
	title = {Computer Models of Electro-Mechanical Interactions in the Contracting Heart},
	howpublished = {Seminar at the Norwegian Defence Research Establishment},
	year = {2012},
	month = {September},
	author = {Sundnes, Joakim and Wall, Samuel}
}
@misc {Simula.simula.1606,
	title = {Computer Simulations of Electro-Mechanical Interactions in the Heart},
	howpublished = {CBC Workshop on Adjoint-Based Methods for Transient Problems: Software and Applications},
	year = {2012},
	month = {March},
	author = {Sundnes, Joakim and Wall, Samuel}
}
@article {Simula.simula.544,
	title = {Electromechanical Feedback With Reduced Cellular Connectivity Alters Electrical Activity in an Infarct Injured Left Ventricle - a Finite Element Model Study},
	journal = {American Journal of Physiology - Heart and Circulatory Physiology},
	number = {302},
	year = {2012},
	month = {Jan},
	pages = {H206-H214},
	abstract = {Myocardial infarction (MI) significantly alters the structure and function of the heart. As abnormal strain may drive heart failure and the generation of arrhythmias, we used computational methods to simulate a left ventricle with an MI over the course of a heartbeat to investigate strains and their potential implications to electrophysiology. We created a fully coupled finite element model of myocardial electromechanics consisting of a cellular physiological model, a bidomain electrical diffusion solver, and a nonlinear mechanics solver. A geometric mesh built from magnetic resonance imaging (MRI) measurements of an ovine left ventricle suffering from a surgically induced anteroapical infarct was used in the model, cycled through the cardiac loop of inflation, isovolumic contraction, ejection, and isovolumic relaxation. Stretch-activated currents were added as a mechanism of mechanoelectric feedback. Elevated fiber and cross fiber strains were observed in the area immediately adjacent to the aneurysm throughout the cardiac cycle, with a more dramatic increase in cross fiber strain than fiber strain. Stretch-activated channels decreased action potential (AP) dispersion in the remote myocardium while increasing it in the border zone. Decreases in electrical connectivity dramatically increased the changes in AP dispersion. The role of cross fiber strain in MI-injured hearts should be investigated more closely, since results indicate that these are more highly elevated than fiber strain in the border of the infarct. Decreases in connectivity may play an important role in the development of altered electrophysiology in the high-stretch regions of the heart.},
	keywords = {Workshop},
	doi = {10.1152/ajpheart.00272.2011},
	author = {Wall, Samuel and Guccione, Julius and Ratcliffe, Mark and Sundnes, Joakim}
}
@misc {Simula.simula.2192,
	title = {Impact of Mechanical Deformation on Conduction Velocity of Cardiac Tissue},
	howpublished = {World Congress on Computational Mechanics},
	year = {2012},
	abstract = {Impact of mechanical deformation on conduction velocity of cardiac tissue The heart is an electromechanical pump responsible of circulating blood in the body. The contraction of the heart is initiated by an electrical wave which spreads through the tissue. This stimulus triggers a chain of reactions that generates active force and consequently contraction, the so-called excitation-contraction coupling. However, there are several feedback loops that enable mechanical deformation to regulate the electrical activity, commonly referred to as mechano-electric feedback. Some examples of these mechanisms are deformation dependent conductivities, length and tension dependent binding rates, and stretch-activation channels, among others. The relevance of each of these mechanisms and the relationships between them are still poorly understood and need to be further investigated. Computational models that account both excitation-contraction and mechano-electric feedback are called strongly coupled models. These models are very complex and have already demonstrated to be an important tool to test new hypothesis and enhance understanding. Studies have investigated the relations between mechanical deformation and changes on electrical conduction velocity on mammalian ventricles. Some models try to mimic this effect by including deformation dependent conductivity, but, there is no detailed experimental data to support these assumptions. In this work a strongly coupled cardiac electromechanics simulation framework was developed, based on bidomain equations and large deformation theory. The simulations were used to compare different approaches and develop a model capable of better representing the dependency of conduction velocity on mechanical deformation that was reported in recent experimental studies.},
	keywords = {Conference},
	author = {Bernardo Lino {de Oliveira} and Wall, Samuel and Sundnes, Joakim}
}
@misc {Simula.simula.2194,
	title = {Multiple Mechanoelectrical Feedback Mechanisms Affect Conduction Velocity},
	howpublished = {CaMo/CMRG Workshop, San Diego},
	year = {2012},
	abstract = {Mechanical deformation is know to have an influence on the velocity of the electrical conduction in cardiac tissue. Although this is an acknowledged phenomenon, there is still controversy with respect to the underlying biophysical mechanisms. Several experimental and computational studies have investigated this and a wide variety of different strain-conduction velocity relationships have been reported. In short, there are increasing, decreasing, constant and biphasic relationships reported. The objective of this study is to develop a computational model that includes multiple mechanoelectrical feedback mechanisms and is capable of reproducing different strain-conduction velocity relationships reported on experiments.},
	author = {Bernardo Lino {de Oliveira} and Wall, Samuel and Sundnes, Joakim}
}
@misc {Simula.simula.2702,
	title = {Multiple Mechanoelectrical Feedback Mechanisms Affect Conduction Velocity},
	year = {2012},
	publisher = {Cardiac Physiome Workshop},
	abstract = {Mechanical deformation is know to have an influence on the velocity of the electrical conduction in cardiac tissue. Although this is an acknowledged phenomenon, there is still controversy with respect to the underlying biophysical mechanisms. Several experimental and computational studies have investigated this and a wide variety of different strain-conduction velocity relationships have been reported. In short, there are increasing, decreasing, constant and biphasic relationships reported. The objective of this study is to develop a computational model that includes multiple mechanoelectrical feedback mechanisms and is capable of reproducing different strain-conduction velocity relationships reported on experiments.},
	author = {Bernardo Lino {de Oliveira} and Wall, Samuel and Sundnes, Joakim}
}
@misc {Simula.simula.1608,
	title = {Numerical Methods for Strongly Coupled Simulations of Cardiac Electro-Mechanics},
	howpublished = {Workshop on efficient solvers in biomedical applications, Graz, Austria},
	year = {2012},
	month = {July},
	author = {Sundnes, Joakim and Wall, Samuel}
}
@misc {Simula.simula.1612,
	title = {On the Stability of Operator Splitting Schemes for Strongly Coupled Cardiac Electro-Mechanics},
	howpublished = {World Congress on Computational Mechanics, Sao Paulo, Brazil},
	year = {2012},
	month = {July},
	author = {Sundnes, Joakim and Wall, Samuel}
}
@misc {Simula.simula.1618,
	title = {Strongly Coupled Simulations of Cardiac Electro-Mechanics},
	howpublished = {CBC seminar},
	year = {2012},
	month = {November},
	author = {Sundnes, Joakim and Wall, Samuel}
}
@misc {Simula.simula.1616,
	title = {Towards Patient-Specific Models of Strongly Coupled Cardiac Electro-Mechanics},
	howpublished = {Cardiac Physiome Workshop, San Diego},
	year = {2012},
	month = {November},
	author = {Sundnes, Joakim and Wall, Samuel and Sjur Urdson {Gjerald}}
}
@article {heartmech-uncertainty,
	title = {Uncertainty Analysis of Ventricular Mechanics Using the Probabilistic Collocation Method},
	journal = {IEEE Transactions on Biomedical Engineering},
	volume = {59},
	number = {8},
	year = {2012},
	month = {August},
	pages = {2171-2179},
	abstract = {Uncertainty and variability in material parameters are fundamental challenges in computational biomechanics. Analyzing and quantifying the resulting uncertainty in computed results with parameter sweeps or Monte Carlo methods has become very computationally demanding. In this paper we consider a stochastic method named the probabilistic collocation method, and investigate its applicability for uncertainty analysis in computing the passive mechanical behaviour of the left ventricle. Specifically, we study the effect of uncertainties in material input parameters upon response properties such as the increase in cavity volume, the elongation of the ventricle, the increase in inner radius, the decrease in wall thickness and the rotation at apex. The numerical simulations conducted herein indicate that the method is well suited for the problem of consideration, and is far more efficient than the Monte Carlo simulation method for obtaining a detailed uncertainty quantification. The numerical experiments also give interesting indications on which material parameters are most critical for accurately determining various global responses.},
	author = {Osnes, Harald and Sundnes, Joakim}
}
@misc {Simula.simula.1604,
	title = {Kan Vi Regne Ut Hvordan Hjertet Virker?},
	howpublished = {Idefestivalen, University of Oslo},
	year = {2011},
	month = {October},
	author = {Sundnes, Joakim}
}
@misc {Simula.simula.1600,
	title = {Strongly Coupled Electro-Mechanics Simulations of the Infarct Injured Heart},
	howpublished = {Computational Science Seminar, University of Basel, Switzerland},
	year = {2011},
	author = {Sundnes, Joakim and Wall, Samuel}
}
@misc {Simula.simula.1602,
	title = {Strongly Coupled Electro-Mechanics Simulations of the Infarct Injured Heart},
	howpublished = {International Conference on Numerical Methods and Applied Mathematics, Greece},
	year = {2011},
	month = {September},
	author = {Sundnes, Joakim and Wall, Samuel}
}
@misc {Simula.simula.1598,
	title = {Strongly Coupled Electro-Mechanics Simulations of the Infarct Injured Heart},
	howpublished = {Workshop on cardiac modeling, Federal University of Juiz de Fora, Brazil},
	year = {2011},
	month = {January},
	keywords = {Conference},
	author = {Sundnes, Joakim and Wall, Samuel}
}
@misc {Simula.simula.269,
	title = {The Baby Justicia Project: Biomechanical Investigations of the Shaken Baby Syndrome (SBS)},
	howpublished = {WCB2010, Seminar session, Head/Brain Injury - Models},
	year = {2010},
	month = {August},
	author = {Blechingberg, Anna and Mardal, Kent-Andre and Strisland, Frode and Sundnes, Joakim and Torleiv Ole {Rognum} and Vege, {\r A}shild and Weensvangen, Morten and Stray-Pedersen, Arne}
}
@inproceedings {Simula.sc.1170,
	title = {Biomedical and Bioinformatics Challenges to Computer Science},
	journal = {Proceedings of the International Conference on Computational Science, ICCS},
	year = {2010},
	publisher = {Elsevier},
	type = {1},
	isbn = {1877-0509},
	author = {Cannataro, Mario and Rodrigo Weber dos {Santos} and Sundnes, Joakim},
	editor = {Sloot, P.M.A. and van Albada, G.D. and Dongarra, J.}
}
@inproceedings {Simula.sc.1182,
	title = {The Development of a New Computational Model for the Electromechanics of the Human Myocyte},
	journal = {2010 Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC)},
	year = {2010},
	publisher = {IEEE},
	type = {Conference},
	isbn = {978-1-4244-4124-2},
	author = {Bernardo Lino {de Oliveira} and Sundnes, Joakim and Rodrigo Weber dos {Santos}},
	editor = {Nigel Lovell et {al}}
}
@misc {Simula.simula.1596,
	title = {Discontinuous Rate Function in Cardiac Cell Models},
	year = {2010},
	month = {June},
	keywords = {Conference},
	author = {Sundnes, Joakim}
}
@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.602,
	title = {Aproaching Cardiac Modeling Challenges to Computer Science With CellMl-Based Web Tools},
	journal = {Future Generation Computer Systems},
	volume = {26},
	number = {3},
	year = {2009},
	pages = {462-470},
	publisher = {Elsevier},
	author = {Ricardo Silva {Campos} and Ronan Mendonca {Amorim} and C. M. {Costa} and Bernardo Lino {de Oliveira} and Barbosa, C. and Sundnes, Joakim and Rodrigo Weber dos {Santos}}
}
@inproceedings {Simula.sc.1164,
	title = {Bioinformatics{\textquoteright} Challenges to Computer Science: Bioinformatics Tools and Biomedical Modeling},
	journal = {Proceedings of the International Conference on Computational Science, ICCS},
	year = {2009},
	publisher = {Springer},
	type = {1},
	isbn = {978-3-642-01969-2},
	author = {Cannataro, Mario and Rodrigo Weber dos {Santos} and Sundnes, Joakim},
	editor = {Allen, G. and Nabrzyski, J. and Seidel, E. and G. D. {van Albada} and Dongarra, J. and P. M. A. {Sloot}}
}
@article {Simula.SC.73,
	title = {A Computationally Efficient Method for Determining the Size and Location of Myocardial Ischemia},
	journal = {IEEE Transactions on Biomedical Engineering},
	volume = {56},
	number = {2},
	year = {2009},
	month = {February},
	pages = {263-272},
	author = {Tomas Syrstad {Ruud} and Nielsen, Bj{\o}rn Fredrik and Ola Marius {Lysaker} and Sundnes, Joakim}
}
@misc {Simula.sc.712,
	title = {Computer Modeling of Cardiac Electro-Mechanics - Models and Numerical Methods},
	howpublished = {Talk at Cardiac Modeling seminar, Simula Research Laboratory},
	year = {2009},
	month = {February},
	author = {Sundnes, Joakim and Wall, Samuel and Osnes, Harald}
}
@inbook {Simula.SC.536,
	title = {Computer Simulations of the Heart},
	booktitle = {Simula Research Laboratory - by thinking constantly about it},
	year = {2009},
	pages = {259-276},
	publisher = {Springer},
	organization = {Springer},
	chapter = {20},
	address = {Heidelberg},
	isbn = {978-3-642-01155-9},
	author = {Glenn T. {Lines} and Sundnes, Joakim},
	editor = {Tveito, Aslak and Are Magnus {Bruaset} and Lysne, Olav}
}
@misc {Simula.simula.562,
	title = {Electromechanical Modeling of the Infarct Injured Failing Ovine Heart},
	year = {2009},
	author = {Wall, Samuel and Sundnes, Joakim and Ratcliffe, Mark and Guccione, Julius}
}
@misc {Simula.sc.714,
	title = {Multiscale Models of Physiological Systems},
	howpublished = {Guest lecture at the course Bioinformatics for molecular biology, University of Oslo},
	year = {2009},
	month = {October},
	author = {Sundnes, Joakim}
}
@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}
}
@inbook {Simula.SC.514,
	title = {Scientific Computing: Why - How - What - What{\textquoteright}s Next},
	booktitle = {Simula Research Laboratory - by thinking constantly about it},
	year = {2009},
	pages = {237-248},
	publisher = {Springer},
	organization = {Springer},
	chapter = {18},
	isbn = {978-3-642-01155-9},
	author = {Hans Petter {Langtangen} and Sundnes, Joakim},
	editor = {Tveito, Aslak and Are Magnus {Bruaset} and Lysne, Olav}
}
@article {Simula.SC.114,
	title = {A Second Order Algorithm for Solving Dynamic Cell Membrane Equations},
	journal = {IEEE Transactions on Biomedical Engineering},
	volume = {56},
	number = {10},
	year = {2009},
	pages = {2546-2548},
	abstract = {This paper describes an extension of the so-called Rush-Larsen scheme, which is a widely used numerical method for solving dynamic models of cardiac cell electrophysiology. The proposed method applies a local linearization of non-linear terms in combination with the analytical solution of linear ordinary differential equations, to obtain a second order accurate numerical scheme. We compare the error and computational load of the second order scheme to the original Rush-Larsen method. For a given error tolerance, the second order method is from nine to 500 times faster than the original scheme, depending on the choice of model and tolerance.},
	author = {Sundnes, Joakim and Artebrant, Robert and Skavhaug, Ola and Tveito, Aslak}
}
@misc {Simula.sc.716,
	title = {Simulation of Strongly Coupled Electro-Mechanics in an Infarcted Left Ventricle},
	howpublished = {Invited talk at the workshop Bidomain 2009, University of Graz},
	year = {2009},
	author = {Sundnes, Joakim and Wall, Samuel and Osnes, Harald}
}
@article {Simula.SC.442,
	title = {Towards a Computational Method for Imaging the Extracellular Potassium Concentration During Regional Ischemia},
	journal = {Mathematical Biosciences},
	volume = {220},
	number = {2},
	year = {2009},
	pages = {118-130},
	doi = {10.1016/j.mbs.2009.05.004},
	author = {Nielsen, Bj{\o}rn Fredrik and Cai, Xing and Sundnes, Joakim and Tveito, Aslak}
}
@inproceedings {Simula.SC.598,
	title = {A Two Dimensional Model of Coupled Electromechanics in Cardiac Tissue},
	journal = {Proceedings of the World Congress on Medical Physics and Biomedical Engineering},
	year = {2009},
	publisher = {Springer},
	type = {Conference},
	isbn = {978-3-642-03881-5},
	author = {Bernardo Martins {Rocha} and Bernardo Lino {de Oliveira} and Rodrigo Weber dos {Santos} and E. T. {Magalh{\~a}es} and Luis Paulo da S {Barra} and Sundnes, Joakim},
	editor = {Schlegel, W. and D{\"o}ssel, O.}
}
@inproceedings {Simula.sc.820,
	title = {Uncertainty Analysis of the Mechanics of the Heart},
	journal = {Proceedings of the Twenty Second Nordic Seminar on Computational Mechanics},
	number = {11},
	year = {2009},
	publisher = {Aalborg University. Department of Civil Engineering},
	type = {1},
	chapter = {245-248},
	isbn = {1901-7278},
	author = {Osnes, Harald and Clark, Stuart and Sundnes, Joakim},
	editor = {Damkilde, L. and Andersen, L. and Kristensen, A.S. and Lund, E.}
}
@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}
}
@inproceedings {Simula.sc.1168,
	title = {Bioinformatics{\textquoteright} Challenges to Computer Science},
	journal = {Proceedings of the 8th international conference on Computational Science, Part III},
	year = {2008},
	pages = {67-69},
	publisher = {Springer},
	type = {Conference},
	isbn = {978-3-540-69383-3},
	doi = {10.1007/978-3-540-69389-5\_9},
	author = {Cannataro, Mario and Romberg, Mathilde and Rodrigo Weber dos {Santos} and Sundnes, Joakim},
	editor = {Bubak, Marian and Geert Dick {van Albada} and Dongarra, Jack and Peter M.A. {Sloot}}
}
@misc {Simula.SC.506,
	title = {Computational Challenges in Mathematical Models of the Heart},
	howpublished = {Talk at Norwegian University of Life Sciences, January 30th},
	year = {2008},
	author = {Sundnes, Joakim}
}
@article {Simula.SC.27,
	title = {On the Frequency of Automaticity During Ischemia in Simulations Based on Stochastic Perturbations of the Luo-Rudy 1 Model},
	journal = {Computers in Biology and Medicine},
	volume = {38},
	year = {2008},
	pages = {1218-1227},
	author = {Linge, Svein and Glenn T. {Lines} 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.23,
	title = {Application of Symbolic Finite Element Tools to Nonlinear Hyperelasticity},
	howpublished = {Talk at MekIT{\textquoteright}07: Fourth National Conference on Computational Mechanics},
	year = {2007},
	month = {May},
	author = {Martin Sandve {Aln{\ae}s} and Mardal, Kent-Andre and Sundnes, Joakim}
}
@inproceedings {Simula.SC.22,
	title = {Application of Symbolic Finite Element Tools to Nonlinear Hyperelasticity},
	journal = {Fourth national conference on Computational Mechanics (MekIT{\textquoteright}07)},
	year = {2007},
	month = {May},
	pages = {87-101},
	publisher = {Tapir Academic Press},
	type = {Conference},
	address = {NO-7005 Trondheim},
	abstract = {The present paper addresses the use of high level languages, symbolic mathematical tools and code generation in an implementation of the finite element method, using a nonlinear hyperelasticity equation as example. Advantages of the software development method that will be demonstrated include closeness to the mathematics, enabling high human efficiency with easy to use high level languages, while still keeping a high computational efficiency by generating tailored inner loop code for the problem at hand. The application we have in mind for the equations presented here is the simulation of the passive elastic properties of heart and blood vessel tissue.},
	isbn = {978-82-519-2235-7},
	author = {Martin Sandve {Aln{\ae}s} and Mardal, Kent-Andre and Sundnes, Joakim},
	editor = {Bj{\o}rn H. {Skallerud} and Andersson, H.I.}
}
@article {Maclachlan.2005.3,
	title = {A Comparison of Non-Standard Solvers for ODEs Describing Cellular Reactions in the Heart},
	journal = {Computer Methods in Biomechanics and Biomedical Engineering},
	volume = {10},
	number = {5},
	year = {2007},
	month = {October},
	pages = {317-326},
	author = {Mary C. {MacLachlan} and Sundnes, Joakim and Raymond J. {Spiteri}}
}
@misc {Simula.SC.59,
	title = {Computational Techniques for Heart Muscle Mechanics},
	howpublished = {Minisymposium talk at ICIAM 07, Zurich},
	year = {2007},
	month = {July},
	abstract = {The heart occupies the most central role of the cardiovascular system, with the crucial role of supplying a continuous flow of blood through the vast network of vessels composing the circulatory system. Mathematical models of the heart in health and disease is an increasingly important tool for improving our understanding of this vital organ, and thereby help to reduce health problems and costs related to cardiovascular disorders. In this talk we give an overview of computational challenges and techniques related to modelling the mechanical function of the heart muscle. Models applied for this purpose vary in complexity from the simplest pressure-volume relations based on a given time varying elastance, to systems of differential equations that give a detailed description of cardiac electro-mechanical interaction. The primary focus of the talk will be on finite element modeling of the heart muscle, which includes modeling the passive mechanical properties of the tissue as well as the active muscle contraction and its coupling to electrophysiology. The heart muscle is normally modeled as a hyper-elastic material, with strongly non-linear and anisotropic material behavior. The resulting mathematical model consists of a large-strain elasticity equation, which is coupled to DAE systems that describe electro-chemical reactions on cell level, and also to a system of PDEs that describe the conduction of the electrical signal in the tissue. We discuss some approaches for solving this system, which offer a varying degree of coupling and feedback between electrophysiology and mechanics. We also discuss different approaches for coupling the heart muscle models to the rest of the circulatory system. The latter topic will also be covered in more detail in the other talks of the minisymposium.},
	author = {Sundnes, Joakim}
}
@misc {Simula.SC.61,
	title = {A Finite Element Model of Cardiac Electrophysiology and Mechanics},
	howpublished = {VII International conference on computational plasticity},
	year = {2007},
	month = {September},
	abstract = {Background Computer models of heart function has the potential to become a valuable tool both for medical research and clinical practice. Simulations based on accurate biophysical models increase our understanding of heart physiology and pathology, and may also predict the outcome of therapeutic interventions and drugs. This has been an active research area for decades, but the models, and in particular their application in clinical practice, are still in an early development stage. Unresolved challenges in the field include the extreme complexity of the biological processes involved, and the multiscale nature of the problem, covering processes from molecular level to the complete organ system. Models and methods Passive heart tissue is commonly modeled as a hyperelastic material, which undergoes large deformations during normal heart function. We apply an exponential stress-strain relation, resulting in a strongly non-linear elasticity equation describing the deformations of the muscle. In order to model the actively contracting muscle, the elasticity equation is coupled to systems of ordinary differential equations (ODEs) which describes the electrical activation and active force development in the muscle cells. These systems are in turn coupled to a system of partial differential equations (PDEs) known as the bidomain model, which describes propagation of the electrical signal through the heart muscle. We apply operator splitting to divide the complete model into two separate PDE systems, describing electrophysiology and mechanics on tissue level, and one system of ODEs that describes electro-mechanical coupling on cell level. These individual systems are then discretized in time with implicit schemes of first or second order, and in space with the finite element method. Simple no-flux boundary conditions are applied for the electrophysiology problem, but the mechanics problem is subject to fairly complex dynamic boundary conditions resulting from the interaction with the blood flow. To avoid solving a fluid-structure interaction problem involving the full Navier-Stokes equation for blood flow, we employ a lumped parameter model to describe the circulation. This model is a system of ODEs that describes pressures, volumes and flows through a simplified, closed loop vessel system. When this model is coupled to the finite element model for the heart muscle the result is an index one differential-algebraic (DAE) system, where the algebraic part contains the finite element based electro-mechanics model. We propose to solve the DAE system with a Runge-Kutta method of Radau type, where the time step is automatically adjusted to the different phases of the heart cycle. Results Combining the Radau solver with operator splitting and finite element discretization results in a fairly robust method, which is flexible with respect to changing or replacing individual parts of the model. Initial test results confirm the robustness and convergence of the algorithm, and verifies that the mechanics part of the problem can be solved with good accuracy. The elecrophysiology part, which contains very steep gradients, has still not been solved with the desired accuracy.},
	author = {Sundnes, Joakim and Martin Sandve {Aln{\ae}s} and Mardal, Kent-Andre}
}
@article {Maclachlan.2006.2,
	title = {A Linear System of Partial Differential Equations Modeling the Resting Potential of a Heart With Regional Ischemia},
	journal = {Mathematical Biosciences},
	volume = {210},
	number = {1},
	year = {2007},
	month = {November},
	pages = {238-252},
	author = {Mary C. {MacLachlan} and Sundnes, Joakim and Skavhaug, Ola and Ola Marius {Lysaker} and Nielsen, Bj{\o}rn Fredrik and Tveito, Aslak}
}
@misc {Simula.SC.60,
	title = {Software Components for Biomedical Flows},
	howpublished = {National seminar on medical technology, NFA (Norsk forening for automatisering)},
	year = {2007},
	month = {September},
	author = {Sundnes, Joakim}
}
@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}
}
@misc {Simula.SC.58,
	title = {Using Mathematical Models to Test Physiological Hypotheses},
	howpublished = {Invited talk at the annual meeting of the Scandinavian Physiological Society},
	year = {2007},
	month = {August},
	abstract = {Mathematical models have been used in physiological research for centuries, but they have so far played a less important role than in many other branches of science. Important reasons for this include the extreme complexity and multi-scale nature of biological systems, which makes it challenging both to derive accurate models and to solve the resulting mathematical equations. With the increasing availabilty of powerful computer hardware and numerical software, accompanied by a revolutionary increase of knowledge in molecular biology, this situation is currently about to change. The last ten years in particular, we have seen the advent of increasingly accurate mathematical models of physiological systems, linking biophysical processes across a wide range of spatial and temporal scales. An illustrative example is mathematical models of heart electrophysiology and mechanics, where models have been derived that link processes on cellular and sub-cellular level to the function of the complete organ. Although modeling of other components of the body lags behind that of the cardiovascular system, there is an ongoing development to model other organs and organ systems. Profiled initiatives in this direction include the IUPS Physiome project (http://www.physiome.org.nz) and the Virtual Physiological Human (http://www.europhysiome.org). Although slightly differing in focus, the vision of both these initiatives is to construct advanced computational models of the complete human body, which may be used both for clinical work and as test beds for new physiological hypotheses. In this talk we present a few examples of mathematical models describing physiological phenomena, and how they have been used to verify and quantify physiological and clinical knowledge. The focus will be on mathematical models of the cardiovascular system.},
	author = {Sundnes, Joakim}
}
@article {Sundnes.2006.1,
	title = {On the Computational Complexity of the Bidomain and the Monodomain Models of Electrophysiology},
	journal = {Annals of Biomedical Engineering},
	volume = {34},
	number = {7},
	year = {2006},
	month = {July},
	pages = {1088-1097},
	author = {Sundnes, Joakim and Nielsen, Bj{\o}rn Fredrik and Mardal, Kent-Andre and Cai, Xing and Glenn T. {Lines} and Tveito, Aslak}
}
@misc {Nielsen.2006.3,
	title = {Computational Issues in Heart Modeling},
	howpublished = {Presented at the Johann Radon Institute for Computational and Applied Mathematics, Linz, Austria},
	year = {2006},
	month = {April},
	author = {Nielsen, Bj{\o}rn Fredrik and Ola Marius {Lysaker} and Cai, Xing and Mardal, Kent-Andre and Tarrou, Christian and Mary C. {MacLachlan} and Sundnes, Joakim and Glenn T. {Lines} and Tveito, Aslak}
}
@book {Sundnes.2006.2,
	title = {Computing the Electrical Activity in the Heart},
	year = {2006},
	publisher = {Springer},
	organization = {Springer},
	address = {Berlin Heidelberg},
	abstract = {This book describes mathematical models and numerical techniques for simulating the electrical activity in the heart. The book gives an introduction to the most important models of the field, followed by a detailed description of numerical techniques for the models. Particular focus is on efficient numerical methods for large scale simulations on both scalar and parallel computers. The results presented in the book will be of particular interest to researchers in bioengineering and computational biology, who face the challenge of solving these complex mathematical models efficiently. The book will also serve as a valuable introduction to a new and exciting field for computational scientists and applied mathematicians.},
	isbn = {3-540-33432-7},
	author = {Sundnes, Joakim and Glenn T. {Lines} and Cai, Xing and Nielsen, Bj{\o}rn Fredrik and Mardal, Kent-Andre and Tveito, Aslak}
}
@misc {Langtangen.2006.5,
	title = {Introduction to Heart Muscle Mechanics-Basic Concepts of Muscle Contraction and Soft Tissue Mechanics.},
	howpublished = {Lecture at Svalbard summer school},
	year = {2006},
	note = {European Mathematical Society Summer School Mathematical Modeling of the Heart, Longyearbyen, Svalbard, Norway. Presented by J. Sundnes.},
	month = {may},
	author = {Hans Petter {Langtangen} and Sundnes, Joakim}
}
@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}
}
@misc {Nielsen.2006.10,
	title = {On the Use of the Bidomain Equations for Computing the Transmembrane Potential Throughout the Heart Wall: an Inverse Problem},
	howpublished = {Presented at the Computers in Cardiology conference in Valencia, Spain},
	year = {2006},
	month = {September},
	author = {Nielsen, Bj{\o}rn Fredrik and Ola Marius {Lysaker} and Tarrou, Christian and Sundnes, Joakim and Cai, Xing and Mardal, Kent-Andre}
}
@inproceedings {Nielsen.2006.9,
	title = {On the Use of the Bidomain Equations for Computing the Transmembrane Potential Throughout the Heart Wall: an Inverse Problem},
	journal = {Computers in Cardiology 2006},
	year = {2006},
	note = {ISSN 0276-6547},
	pages = {797-800},
	publisher = {Computers in Cardiology},
	type = {Conference},
	isbn = {0276-6547},
	author = {Nielsen, Bj{\o}rn Fredrik and Ola Marius {Lysaker} and Tarrou, Christian and Sundnes, Joakim and Cai, Xing and Mardal, Kent-Andre},
	editor = {Murray, A.}
}
@misc {Sundnes.2005.5,
	title = {Computing the Electrical Activity in the Heart},
	howpublished = {Presented at the Department of Mathematics, University of Oslo},
	year = {2005},
	note = {Popmat seminar, April 2005.},
	month = {April},
	author = {Sundnes, Joakim}
}
@misc {Lysaker.2005.2,
	title = {Kan Man Simulere Et Hjerteslag?},
	howpublished = {LAMIS - SOMMERKURS Matematikk - med r{\o}tter og vinger, Asker},
	year = {2005},
	month = {07.08 - 10.08. 2005},
	author = {Ola Marius {Lysaker} and Nielsen, Bj{\o}rn Fredrik and Tveito, Aslak and Glenn T. {Lines} and Sundnes, Joakim and Tarrou, Christian}
}
@misc {Thorvaldsen.2005.3,
	title = {A Mixed FEM for Modeling the Passive Mechanical Properties of the Myocardium},
	howpublished = {Talk at the SIAM Conference on Computational Science \& Engineering},
	year = {2005},
	month = {February},
	author = {Thorvaldsen, Tom and Osnes, Harald and Sundnes, Joakim}
}
@article {Thorvaldsen.2005.1,
	title = {A Mixed Finite Element Formulation for a Nonlinear, Transversely Isotropic Material Model for the Cardiac Tissue},
	journal = {Computer Methods in Biomechanics and Biomedical Engineering},
	volume = {8},
	number = {6},
	year = {2005},
	month = {December},
	pages = {369-379},
	abstract = {In this paper we present a mixed finite element method for modeling the passive properties of the myocardium. The passive properties are described by a non-linear, transversely isotropic, hyperelastic material model, and the myocardium is assumed to be almost incompressible. Single-field, pure displacement-based formulations are known to cause numerical difficulties when applied to incompressible or slightly compressible material cases. This paper presents an alternative approach in the form of a mixed formulation, where a separately interpolated pressure field is introduced as a primary unknown in addition to the displacement field. Moreover, a constraint term is included in the formulation to enforce (almost) incompressibility. Numerical results presented in the paper demonstrate the difficulties related to employing a pure displacement-based method, applying a set of physically relevant material parameter values for the cardiac tissue. The same problems are not experienced for the proposed mixed method. We show that the mixed formulation provides reasonable numerical results for compressible as well as nearly incompressible cases, also in situations of large fiber stretches. There is good agreement between the numerical results and the underlying analytical models.},
	author = {Thorvaldsen, Tom and Osnes, Harald and Sundnes, Joakim}
}
@inproceedings {Thorvaldsen.2005.2,
	title = {A Mixed Formulation for Modeling the Mechanical Bahavior of the Heart},
	journal = {MekIt05 - Third national conference om Computational Mechanics, Trondheim May 11-12},
	year = {2005},
	month = {May},
	pages = {327-341},
	publisher = {Tapir Academic Press},
	type = {1},
	abstract = {In this paper we present a mixed finite element formulation for modeling the mechanical behavior of the cardiac tissue. The modeling may be divided into a passive and an active part. The passive properties are in this work described by a transversely isotropic, hyperelastic material model. Moreover, the myocardium is assumed to be almost incompressible. In advanced models the active contraction is strongly connected to electro-physiological processes in the muscle cells. In this paper we simplify the active stress contribution by modeling it as a linear function in time. Due to the fact that the heart muscle undergoes large deformations during contraction, both material and geometrical non-linearities must be taken into account in the analysis. Numerical results are presented for different activation patterns applied to a box-shaped test specimen, which represents a piece of the myocardial wall. The proposed mixed method offers reasonable results in the modeling of the mechanical behavior of the test specimen.},
	author = {Thorvaldsen, Tom and Sundnes, Joakim and Osnes, Harald},
	editor = {Bj{\o}rn H. {Skallerud} and Helge I. {Andersson}}
}
@techreport {Thorvaldsen.2005.4,
	title = {Non-Linear Elasticity With Applications to Heart Mechanics},
	number = {2005-16},
	year = {2005},
	publisher = {Simula Research Laboratory},
	abstract = {This report gives an introduction to mathematical and numerical modeling of large-deformation elasticity problems. Basic non-linear continuum mechanics is presented along with a set of hyperelastic material models. Two alternative finite element formulations are described for solving such problems, for compressible and almost incompressible materials. Simulation results are presented for both methods. The elasticity solver is employed in simulating the mechanical behavior of the heart. Mathematical models are presented for describing the passive behavior of cardiac tissue and the active force development. Moreover, we show mathematical models and numerical algorithms for simulating the large deformations of the left ventricle during a heart beat.},
	author = {Thorvaldsen, Tom and Sundnes, Joakim and Osnes, Harald}
}
@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}}
}
@article {Sundnes.2005.2,
	title = {An Operator Splitting Method for Solving the Bidomain Equations Coupled to a Volume Conductor Model for the Torso},
	journal = {Mathematical Biosciences},
	volume = {194},
	number = {2},
	year = {2005},
	month = {April},
	pages = {233-248},
	abstract = {In this paper we present a numerical method for the bidomain model, which describes the electrical activity in the heart. The model consists of two partial differential equations (PDEs), which are coupled to systems of ordinary differential equations (ODEs) describing electrochemical reactions in the cardiac cells. Many applications require coupling these equations to a third PDE, describing the electrical fields in the torso surrounding the heart. The resulting system is challenging to solve numerically, because of its complexity and very strict resolution requirements in time and space. We propose a method based on operator splitting and a fully coupled discretization of the three PDEs. Numerical experiments show that for simple simulation cases and fine discretizations, the algorithm is second-order accurate in space and time.},
	author = {Sundnes, Joakim and Glenn T. {Lines} and Tveito, Aslak}
}
@article {Maclachlan.2005.1,
	title = {Simulation of ST Segment Changes During Subendocardial Ischemia Using a Realistic 3-D Cardiac Geometry},
	journal = {IEEE Transactions on Biomedical Engineering},
	volume = {52},
	number = {5},
	year = {2005},
	month = {May},
	pages = {799-807},
	author = {Mary C. {MacLachlan} and Sundnes, Joakim and Glenn T. {Lines}}
}
@article {Linge.2005.1,
	title = {Solving the Heart Mechanics Equations With Newton and Quasi Newton Methods - a Comparison},
	journal = {Computer Methods in Biomechanics and Biomedical Engineering},
	volume = {8},
	number = {1},
	year = {2005},
	pages = {1-8},
	abstract = {The non-linear elasticity equations of heart mechancis are solved while emulating the effects of a propagating activation wave. The dynamics of a 1 cm^3 slab of active cardiac tissue was simulated as the electrical wave traversed the muscular heart wall transmurally. The regular Newton (Newton-Raphson) method was compared to two modified Newton approaches, and also to a third approach that delayed update only of some selected Jacobian elements. In addition, the impact of changing the time step (0.01 ms, 0.1 ms and 1 ms) and the relative nonlinear convergence tolerance (10^-4, 10^-3 and 10^-2) was investigated. Updating the Jacobian only when slow convergence occured was by far the most efficient approach, giving time savings of 83-96\%. For each of the four methods, CPU times were reduced by 48-90\% when the time step was increased by a factor 10. Increasing the convergence tolerance by the same factor gave time savings of 3-71\%. Different combinations of activation wave speed, stress rate and bulk modulus revealed that the fastest method became relatively even faster as stress rate and bulk modulus were decreased, while the activation speed had negligible influence in this respect.},
	author = {Linge, Svein and Glenn T. {Lines} and Sundnes, Joakim}
}
@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}
}
@misc {SC.8.Sundnes.2004,
	title = {Challenges in Mathematical Models of the Heart},
	howpublished = {Presented at the SIAM Annual meeting, Portland, Oregon},
	year = {2004},
	month = {July},
	author = {Sundnes, Joakim and Glenn T. {Lines} and Tveito, Aslak}
}
@misc {Maclachlan.2004.1,
	title = {Modelling ST Segment Changes During Myocardial Ischemia},
	howpublished = {Presented at the SIAM Conference on the Life Sciences: Portland, Oregon},
	year = {2004},
	author = {Mary C. {MacLachlan} and Sundnes, Joakim and Glenn T. {Lines}}
}
@techreport {SC.7.Thorvaldsen.2004,
	title = {Numerical Modeling of Isotropic, Hyperelastic Materials Undergoing Large Deformations},
	number = {2004-06},
	year = {2004},
	publisher = {Simula Research Laboratory},
	author = {Thorvaldsen, Tom and Sundnes, Joakim and Osnes, Harald}
}
@inbook {SC.5.Mardal.2003.b,
	title = {Block Preconditioning and Systems of PDEs},
	booktitle = {Advanced Topics in Computational Partial Differential Equations - Numerical Methods and Diffpack Programming},
	series = {Lecture Notes in Computational Science and Engineering},
	year = {2003},
	pages = {199-236},
	publisher = {Springer},
	organization = {Springer},
	author = {Mardal, Kent-Andre and Sundnes, Joakim and Hans Petter {Langtangen} and Tveito, Aslak},
	editor = {Hans Petter {Langtangen} and Tveito, Aslak}
}
@misc {SC.8.Lines.2003,
	title = {Computing the Electrical Activity in the Human Heart},
	howpublished = {Presented at the Centre of Mathematics for Applications, Oslo},
	year = {2003},
	author = {Glenn T. {Lines} and Nielsen, Bj{\o}rn Fredrik and Tveito, Aslak and Sundnes, Joakim and Gr{\o}ttum, P. and Cai, Xing and Mardal, Kent-Andre}
}
@misc {SC.8.Tveito.2003,
	title = {Computing the Electrical Activity in the Human Heart},
	howpublished = {Presented at the European Conference on Numerical Mathematics and Advanced Applications, Prague, Czech Republic},
	year = {2003},
	month = {August},
	author = {Tveito, Aslak and Glenn T. {Lines} and Sundnes, Joakim and Nielsen, Bj{\o}rn Fredrik and Gr{\o}ttum, P. and Cai, Xing and Mardal, Kent-Andre}
}
@misc {SC.8.Tveito.2003.b,
	title = {Computing the Heart},
	howpublished = {Presented at the 21st CAD-FEM users{\textquoteright} meeting 2003 - International congress on FEM technology, Potsdam, Germany},
	year = {2003},
	month = {November},
	author = {Tveito, Aslak and Glenn T. {Lines} and Nielsen, Bj{\o}rn Fredrik and Sundnes, Joakim and Gr{\o}ttum, P. and Cai, Xing and Mardal, Kent-Andre}
}
@inbook {SC.5.Sundnes.2003,
	title = {Electrical Activity in the Human Heart},
	booktitle = {Advanced Topics in Computational Partial Differential Equations - Numerical Methods and Diffpack Programming},
	series = {Lecture Notes in Computational Science and Engineering},
	year = {2003},
	pages = {401-449},
	publisher = {Springer},
	organization = {Springer},
	chapter = {10},
	author = {Sundnes, Joakim and Glenn T. {Lines} and Gr{\o}ttum, P. and Tveito, Aslak},
	editor = {Hans Petter {Langtangen} and Tveito, Aslak}
}
@article {SC.4.Lines.2003.b,
	title = {Mathematical Models and Numerical Methods for the Forward Problem in Cardiac Electrophysiology},
	journal = {Computing and Visualization in Science},
	volume = {5},
	number = {4},
	year = {2003},
	pages = {215-239},
	author = {Glenn T. {Lines} and M. L. {Buist} and Gr{\o}ttum, P. and A. J. {Pullan} and Sundnes, Joakim and Tveito, Aslak}
}
@inproceedings {SC.6.Sundnes.2003,
	title = {Modeling the Electro-Mechanical Behavior of an Infarcted Heart},
	journal = {Proceedings from MekIT{\textquoteright}03, Second national conference on Computational Mechanics},
	year = {2003},
	month = {8-9 May},
	type = {1},
	address = {Trondheim},
	author = {Sundnes, Joakim and Glenn T. {Lines}}
}
@misc {Lines.2003.1,
	title = {Parallel Algorithms for Simulating the Electrical Activity of the Heart},
	howpublished = {Presented at the Dagstuhl seminar Challenges in computational science and engineering},
	year = {2003},
	note = {Presented by Joakim Sundnes, March 2003.},
	month = {March},
	author = {Glenn T. {Lines} and Cai, Xing and Sundnes, Joakim}
}
@misc {SC.8.Lines.2002,
	title = {Diffpack Simulation of the Electrical Activity in the Heart},
	howpublished = {Invited minisymposium talk at the 20th CAD-FEM User{\textquoteright}s Meeting, Friedrichshafen, Germany},
	year = {2002},
	note = {Presented by A. M. Bruaset},
	month = {October},
	author = {Glenn T. {Lines} and Sundnes, Joakim and Tveito, Aslak and Cai, Xing and Mardal, Kent-Andre and Are Magnus {Bruaset}}
}
@article {SC.4.Lines.2002.b,
	title = {A Domain Embedding Strategy for Solving the Bidomain Equations on Complicated Geometries},
	journal = {International Journal of Bioelectromagnetism},
	volume = {4},
	number = {2},
	year = {2002},
	pages = {53-54},
	author = {Glenn T. {Lines} and Sundnes, Joakim and Tveito, Aslak}
}
@article {SC.4.Sundnes.2002,
	title = {Multigrid Block Preconditioning for a Coupled System of Partial Differential Equations Modeling the Electrical Activity in the Heart},
	journal = {Computer Methods in Biomechanics and Biomedical Engineering},
	volume = {5},
	number = {6},
	year = {2002},
	author = {Sundnes, Joakim and Glenn T. {Lines} and Mardal, Kent-Andre and Tveito, Aslak}
}
@phdthesis {SC.3.Sundnes.2002,
	title = {Numerical Methods for Simulating the Electrical Activity of the Heart},
	year = {2002},
	school = {Department of Informatics, University of Oslo},
	type = {phd},
	author = {Sundnes, Joakim}
}
@article {SC.4.Sundnes.2002.b,
	title = {ODE Solvers for a Stiff System Arising in the Modeling of the Electrical Activity of the Heart},
	journal = {International Journal of Nonlinear Sciences and Numerical Simulation},
	volume = {3},
	number = {3},
	year = {2002},
	author = {Sundnes, Joakim and Glenn T. {Lines} and Tveito, Aslak}
}
@article {SC.4.Sundnes.2002.a,
	title = {A Second Order Scheme for Solving the Bidomain and Forward Problem},
	journal = {International Journal of Bioelectromagnetism},
	volume = {4},
	number = {2},
	year = {2002},
	pages = {51-52},
	author = {Sundnes, Joakim and Glenn T. {Lines} and Tveito, Aslak}
}
@article {SC.4.Sundnes.2001,
	title = {Efficient Solution of Ordinary Differential Equations Modeling Electrical Activity in Cardiac Cells},
	journal = {Mathematical Biosciences},
	year = {2001},
	pages = {55-72},
	author = {Sundnes, Joakim and Glenn T. {Lines} and Tveito, Aslak}
}
@misc {Sundnes.2001.1,
	title = {On Numerical Techniques for the Bidomain Model},
	howpublished = {Presented at the SIAM Annual meeting, San Diego, California},
	year = {2001},
	month = {July},
	author = {Sundnes, Joakim and Glenn T. {Lines} and Mardal, Kent-Andre and Tveito, Aslak}
}
@misc {Sundnes.2000.1,
	title = {Efficient Solution of ODEs Modeling Electrical Activity in Cardiac Cells},
	howpublished = {DIFTA seminar, Norwegian University of Science and Technology},
	year = {2000},
	note = {Presented by Joakim Sundnes, October 2000.},
	author = {Sundnes, Joakim and Glenn T. {Lines} and Tveito, Aslak}
}
@techreport {SC.7.Sundnes.2000,
	title = {An Investigation of Different Solvers for Stiff ODE Systems},
	year = {2000},
	publisher = {Department of Informatics, University of Oslo},
	author = {Sundnes, Joakim and Glenn T. {Lines} and Tveito, Aslak}
}
@article {doi:10.14814/phy2.13392,
	title = {Organ-level validation of a cross-bridge cycling descriptor in a left ventricular finite element model: effects of ventricular loading on myocardial strains},
	journal = {Physiological Reports},
	volume = {5},
	number = {21},
	pages = {e13392},
	publisher = { Wiley},
	abstract = {Abstract Although detailed cell-based descriptors of cross-bridge cycling have been applied in finite element (FE) heart models to describe ventricular mechanics, these multiscale models have never been tested rigorously to determine if these descriptors, when scaled up to the organ-level, are able to reproduce well-established organ-level physiological behaviors. To address this void, we here validate a left ventricular (LV) FE model that is driven by a cell-based cross-bridge cycling descriptor against key organ-level heart physiology. The LV FE model was coupled to a closed-loop lumped parameter circulatory model to simulate different ventricular loading conditions (preload and afterload) and contractilities. We show that our model is able to reproduce a linear end-systolic pressure volume relationship, a curvilinear end-diastolic pressure volume relationship and a linear relationship between myocardial oxygen consumption and pressure{\^a}volume area. We also show that the validated model can predict realistic LV strain-time profiles in the longitudinal, circumferential, and radial directions. The predicted strain-time profiles display key features that are consistent with those measured in humans, such as having similar peak strains, time-to-peak-strain, and a rapid change in strain during atrial contraction at late-diastole. Our model shows that the myocardial strains are sensitive to not only LV contractility, but also to the LV loading conditions, especially to a change in afterload. This result suggests that caution must be exercised when associating changes in myocardial strain with changes in LV contractility. The methodically validated multiscale model will be used in future studies to understand human heart diseases.},
	keywords = {Cardiac energetics, finite element modeling, left ventricle, myocardial strain},
	doi = {10.14814/phy2.13392},
	url = {https://physoc.onlinelibrary.wiley.com/doi/abs/10.14814/phy2.13392},
	author = {Sheikh Mohammad {Shavik} and Wall, Samuel and Sundnes, Joakim and Burkhoff, Daniel and Lik Chuan {Lee}}
}
@article {campos2018preconditioned,
	title = {Preconditioned augmented Lagrangian formulation for nearly incompressible cardiac mechanics},
	journal = {International journal for numerical methods in biomedical engineering},
	volume = {34},
	number = {4},
	pages = {e2948},
	publisher = {Wiley},
	author = {Joventino Oliveira {Campos} and Rodrigo Weber dos {Santos} and Sundnes, Joakim and Bernardo Martins {Rocha}}
}
