@article {42945,
	title = {Editorial: Dynamical Systems, PDEs and Networks for Biomedical Applications: Mathematical Modeling, Analysis and Simulations},
	journal = {Frontiers in Applied Mathematics and Statistics},
	year = {2023},
	publisher = {Frontiers},
	address = {Front. Phys. Sec. Statistical and Computational Physics},
	doi = {10.3389/fphy.2022.1101756},
	author = {Andr{\'e} H. {Erhardt} and Tsaneva-Atanasova, Krasimira and Glenn T. {Lines} and Erik Andreas {Martens}}
}
@article {42944,
	title = {Efficient computation of adjoint sensitivities at steady-state in ODE models of biochemical reaction networks},
	journal = {PLOS Computational Biology},
	year = {2023},
	publisher = {PLOS},
	author = {Lakrisenko, Polina and Stapor, Paul and Grein, Stephan and Paszkowski, Lukasz and Pathirana, Dilan and Fr{\"o}hlich, Fabian and Glenn T. {Lines} and Weindl, Daniel and Hasenauer, Jan}
}
@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}
}
@article {42943,
	title = {NEIL3-deficient bone marrow displays decreased hematopoietic capacity and reduced telomere length},
	journal = {Biochemistry and Biophysics Reports},
	volume = {29},
	year = {2022},
	month = {Jan-03-2022},
	pages = {101211},
	publisher = { Elsevier},
	issn = {24055808},
	doi = {10.1016/j.bbrep.2022.101211},
	url = {https://linkinghub.elsevier.com/retrieve/pii/S2405580822000127},
	author = {Tom Rune {Karlsen} and Maria B. {Olsen} and Xiang Y. {Kong} and Yang, Kuan and Quiles-Jim{\'e}nez, Ana and Kroustallaki, Penelope and Holm, Sverre and Glenn T. {Lines} and Aukrust, P{\r a}l and Skarpengland, Tonje and Bj{\o}r{\r a}s, Magnar and Tuva B. {Dahl} and Nilsen, Hilde and Gregersen, Ida and Halvorsen, Bente}
}
@inproceedings {26985,
	title = {Combining algorithmic rethinking and AVX-512 intrinsics for efficient simulation of subcellular calcium signaling},
	journal = {International Conference on Computational Science (ICCS 2019)},
	year = {2019},
	pages = {681-687},
	publisher = { Springer},
	abstract = {Calcium signaling is vital for the contraction of the heart. Physiologically realistic simulation of this subcellular process requires nanometer resolutions and a complicated mathematical model of differential equations. Since the subcellular space is composed of several irregularly-shaped and intricately-connected physiological domains with distinct properties, one particular challenge is to correctly compute the diffusion-induced calcium fluxes between the physiological domains. The common approach is to pre-calculate the effective diffusion coefficients between all pairs of neighboring computational voxels, and store them in large arrays. Such a strategy avoids complicated if-tests when looping through the computational mesh, but suffers from substantial memory overhead. In this paper, we adopt a memory-efficient strategy that uses a small lookup table of diffusion coefficients. The memory footprint and traffic are both drastically reduced, while also avoiding the if-tests. However, the new strategy induces more instructions on the processor level. To offset this potential performance pitfall, we use AVX-512 intrinsics to effectively vectorize the code. Performance measurements on a Knights Landing processor and a quad-socket Skylake server show a clear performance advantage of the manually vectorized implementation that uses lookup tables, over the counterpart using coefficient arrays.},
	doi = {10.1007/978-3-030-22750-0_66},
	author = {Jarvis, Chad and Glenn T. {Lines} and Langguth, Johannes and Nakajima, Kengo and Cai, Xing}
}
@inproceedings {26921,
	title = {Efficient computation of steady states in large-scale ODE models of biochemical reaction networks},
	journal = {8th IFAC Conference on Foundations of Systems Biology in Engineering},
	volume = {52},
	year = {2019},
	pages = {32-37},
	publisher = {Elsevier},
	author = {Glenn T. {Lines} and Paszkowski, Lukasz and Schmiester, Leonard and Weindl, Daniel and Stapor, Paul and Hasenauer, Jan}
}
@article {26345,
	title = {Evidence for heterogeneous subsarcolemmal Na+ levels in rat ventricular myocytes},
	journal = {AJP-Heart and Circulatory Physiology},
	volume = {6},
	year = {2019},
	publisher = {American Physiological Society},
	author = {Skogestad, Jonas and Glenn T. {Lines} and William E {Louch} and Ole M. {Sejersted} and Sjaastad, Ivar and Jan Magnus {Aronsen}}
}
@article {26199,
	title = {Computing Optimal Properties of Drugs Using Mathematical Models of Single Channel Dynamics},
	journal = {Computational and Mathematical Biophysics},
	volume = {6},
	year = {2018},
	month = {10/2018},
	pages = { 41-64},
	publisher = {DE GRUYTER},
	abstract = {Single channel dynamics can be modeled using stochastic differential equations, and the dynamics\&nbsp;of the state of the channel (e.g. open, closed, inactivated) can be represented using Markov models. Such\&nbsp;models can also be used to represent the effect of mutations as well as the effect of drugs used to alleviate\&nbsp;deleterious effects of mutations. Based on the Markov model and the stochastic models of the single channel,\&nbsp;it is possible to derive deterministic partial differential equations (PDEs) giving the probability density functions\&nbsp;(PDFs) of the states of the Markov model. In this study, we have analyzed PDEs modeling wild type (WT)\&nbsp;channels, mutant channels (MT) and mutant channels for which a drug has been applied (MTD). Our aim is\&nbsp;to show that it is possible to optimize the parameters of a given drug such that the solution of the MTD model\&nbsp;is very close to that of the WT: the mutation{\textquoteright}s effect is, theoretically, reduced significantly. We will present the\&nbsp;mathematical framework underpinning this\&nbsp;methodology and apply it to several examples. In particular, we\&nbsp;will show that it is possible to use the method to, theoretically, improve the properties of some well-known\&nbsp;existing drugs.},
	author = {Tveito, Aslak and Maleckar, Molly and Glenn T. {Lines}}
}
@article {26326,
	title = {Ryanodine Receptor Dispersion Disrupts Ca2+-Release in Failing Cardiac Myocytes},
	journal = {eLife},
	volume = {7},
	year = {2018},
	month = {10/2018},
	pages = {e39427},
	publisher = {eLife Sciences Publications},
	issn = {2050-084X},
	doi = {10.7554/eLife.39427},
	url = {https://elifesciences.org/articles/39427},
	author = {Terje R {Kolstad} and van den Brink, Jonas and MacQuaide, Niall and Per Kristian {Lunde} and Frisk, Michael and Jan Magnus {Aronsen} and Einar S {Norden} and Cataliotti, Alessandro and Sjaastad, Ivar and Ole M {Sejersted} and Andrew G {Edwards} and Glenn T. {Lines} and William E {Louch}}
}
@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 {25774,
	title = {Pleiotropic effects of schizophrenia-associated genetic variants in neuron firing and cardiac pacemaking revealed by computational modeling},
	journal = {Translational Psychiatry},
	volume = {7},
	number = {11},
	year = {2017},
	pages = {5},
	publisher = {Nature Publishing Group},
	author = {M{\"a}ki-Marttunen, Tuomo and Glenn T. {Lines} and Andrew G {Edwards} and Tveito, Aslak and Anders M {Dale} and Gaute T {Einevoll} and Ole A {Andreassen}}
}
@article {24963,
	title = {Studying dyadic structure-function relationships: a review of current modeling approaches and new insights into Ca2+ (mis)handling},
	journal = {Clinical Medicine Insights: Cardiology},
	volume = {11},
	year = {2017},
	month = {04/2017},
	pages = {1-11},
	publisher = {Libertas Academica},
	doi = { 10.1177/1179546817698602},
	url = {http://insights.sagepub.com/studying-dyadic-structurefunction-relationships-a-review-of-current-mo-article-a6287},
	author = {Maleckar, Molly and Andrew G {Edwards} and Louch, William and Glenn T. {Lines}}
}
@article {maleckar2017studying,
	title = {Studying dyadic structure{\textendash}function relationships: a review of current modeling approaches and new insights into ca2+ (mis) handling},
	journal = {Clinical Medicine Insights: Cardiology},
	volume = {11},
	year = {2017},
	pages = {1179546817698602},
	publisher = {{SAGE Publications Sage UK: London, England},
	author = {Maleckar, Molly and Andrew G {Edwards} and William E {Louch} and Glenn T. {Lines}}
}
@book {24058,
	title = {Computing characterizations of drugs for ion channels and receptors using Markov models},
	volume = {LNCSE Vol. 111. },
	year = {2016},
	pages = {261},
	publisher = {Springer},
	organization = {Springer},
	address = {Heidelberg, Germany},
	abstract = {Drugs are generally devised to alter the function of cells in a favorable manner. The actions of drugs can in some cases be represented by mathematical models often phrased in terms of differential equations. Our aim in these notes is to study such models and show how the effect of drugs can be optimized. More precisely, drugs are represented in terms of a set of parameters and we show how optimal drugs can be characterized by tuning the parameters. Our approach is to consider models of a healthy cell and a non-healthy cell and a model of a non-healthy cell to which a drug has been applied. The problem we are trying to resolve is how to tweak the parameters of the drug such that the drugged non-healthy cell behaves as similarly to the healthy cell as possible.},
	url = {http://tinyurl.com/zhazqv5},
	author = {Tveito, Aslak and Glenn T. {Lines}}
}
@article {24996,
	title = {Computing rates of Markov models of voltage-gated ion channels by inverting partial differential equations governing the probability density functions of the conducting and non-conducting states},
	journal = {Mathematical Biosciences},
	volume = {277},
	year = {2016},
	pages = {126-135},
	publisher = {Elsevier Inc},
	author = {Tveito, Aslak and Glenn T. {Lines} and Andrew G {Edwards} and Andrew D. {McCulloch}}
}
@article {24904,
	title = {Simple T wave metrics may better predict early ischemia as compared to ST segment},
	journal = {IEEE Transactions on Biomedical Engineering},
	volume = {64},
	number = {6},
	year = {2016},
	pages = {1305-1309},
	publisher = {IEEE},
	abstract = {There is pressing clinical need to identify developing heart attack (infarction) in patients as early as possible. However, current state-of-the-art tools in clinical practice, underpinned by evaluation of elevation of the ST-segment of the 12-lead electrocardiogram, do not identify all patients suffering from lack of blood flow to the heart muscle (cardiac ischemia), worsening the risk for further adverse events and patient outcome overall. In this study, we aimed to explore and compare the portions of cardiac repolarization in the ECG that best capture the electrophysiological changes associated with ischemia. We developed 3D electrophysiological models of the human ventricles and torso, incorporating biophysically-based membrane kinetics and realistic activation sequence, to compute simulated ECGs and their alteration with application of simulated ischemia of differing severity in diverse regions of the heart. Results suggest that metrics based on the T-wave in addition to the ST segment may be more sensitive to detecting ischemia than those using the ST segment alone. Further research into how such simulationaided risk assessment methods may aid workflows in extant clinical practice, with the ultimate goal of multi-modality clinical support, is warranted.},
	doi = {    10.1109/TBME.2016.2600198},
	author = {Glenn T. {Lines} and Bernardo Lino {de Oliveira} and Skavhaug, Ola and Maleckar, Molly}
}
@article {lines2016simple,
	title = {Simple t-wave metrics may better predict early ischemia as compared to st segment},
	journal = {IEEE Transactions on Biomedical Engineering},
	volume = {64},
	number = {6},
	year = {2016},
	pages = {1305{\textendash}1309},
	publisher = {{IEEE},
	author = {Glenn T. {Lines} and Bernardo Lino {de Oliveira} and Skavhaug, Ola and Maleckar, Molly}
}
@article {23456,
	title = {Scalable heterogeneous CPU-GPU computations for unstructured tetrahedral meshes},
	journal = {IEEE Micro},
	volume = {35},
	year = {2015},
	month = {07/2015},
	pages = {6-15},
	publisher = {ACM IEEE},
	abstract = {A recent trend in modern high-performance computing environments is the introduction of powerful, energy-efficient hardware accelerators such as GPUs and Xeon Phi coprocessors. These specialized computing devices coexist with CPUs and are optimized for highly parallel applications. In regular computing-intensive applications with predictable data access patterns, these devices often far outperform CPUs and thus relegate the latter to pure control functions instead of computations. For irregular applications, however, the performance gap can be much smaller and is sometimes even reversed. Thus, maximizing the overall performance on heterogeneous systems requires making full use of all available computational resources, including both accelerators and CPUs.},
	doi = {10.1109/MM.2015.70},
	author = {Langguth, Johannes and Sourouri, Mohammed and Glenn T. {Lines} and Baden, Scott and Cai, Xing}
}
@article {Simula.simula.2246,
	title = {Towards Simulation of Subcellular Calcium Dynamics at Nanometre Resolution},
	journal = {International Journal of High Performance Computing Applications},
	volume = {29},
	year = {2015},
	pages = {51-63},
	publisher = {SAGE},
	abstract = {Numerical simulation of subcellular\&nbsp;\&nbsp;dynamics with a resolution down to one nanometre can be an important tool for discovering the physiological cause of many heart diseases. The requirement of enormous computational power, however, has made such simulations prohibitive so far. By using up to 12,288 Intel Xeon Phi 31S1P coprocessors on the new hybrid cluster Tianhe-2, which is the new number one supercomputer of the world, we have achieved 1.27 Pflop/s in double precision, which brings us much closer to the nanometre resolution. This is the result of efficiently using the hardware on different levels: (1) a single Xeon Phi (2) a single compute node that consists of a host and three coprocessors, and (3) a huge number of interconnected nodes. To overcome the challenge of programming Intel{\textquoteright}s new many-integrated core (MIC) architecture, we have adopted techniques such as vectorization, hierarchical data blocking, register data reuse, offloading computations to the coprocessors, and pipelining computations with intra-/inter-node communications.},
	doi = {10.1177/1094342013514465},
	author = {Chai, Jun and Johan Elon {Hake} and Wu, Nan and Wen, Mei and Cai, Xing and Glenn T. {Lines} and Yang, Jing and Su, Huayou and Zhang, Chunyuan and Liao, Xiangke}
}
@article {Simula.simula.3026,
	title = {NS5806 Partially Restores Action Potential Duration But Fails to Ameliorate Calcium Transient Dysfunction in a Computational Model of Canine Heart Failure},
	journal = {Europace},
	volume = {16},
	number = {4},
	year = {2014},
	month = {October},
	pages = {iv46-iv55},
	publisher = { },
	abstract = {Aims The study investigates how increased Ito, as mediated by the activator NS5806, affects excitation -contraction coupling in chronic heart failure (HF). We hypothesized that restoring spike-and-dome morphology of the action potential (AP) to a healthy phenotype would be insufficient to restore the intracellular Ca2+ transient (CaT), due to HF-induced remodelling of Ca2+ handling. Methods An existing mathematical model of the canine ventricular myocyte was modified to incorporate recent experimental data and results from healthy and failing myocytes, resulting in models of both healthy and HF epicardial, midmyocardial, and endocardial cell variants. Affects of NS5806 were also included in HF models through its direct interaction with Kv4.3 and Kv1.4. Single-cell simulations performed in all models (control, HF, and HF + drug) and variants (epi, mid, and endo) assessed AP morphology and underlying ionic processes with a focus on CaT, how these were altered in HF across the ventricular wall, and the subsequent effects of varying compound concentration in HF. Heart failure model variants recapitulated a characteristic increase in AP duration (APD) in the disease. The qualitative effects of application of half-maximal effective concentration (EC50) of NS5806 on APs and CaT are heterogeneous and non-linear. Deepening in the AP notch with drug is a direct effect of the activation of Ito; both Ito and consequent alteration of IK1 kinetics cause decrease in AP plateau. Decreased APD50 and APD90 are due to altered IK1. Analysis revealed that drug effects depend on transmurality. Ca2+ transient morphology changes-increased amplitude and shorter time to peak-are due to direct increase in ICa,L and indirect larger SR Ca2+ release subsequent to Ito activation. Conclusions Downstream effects of a compound acting exclusively on sarcolemmal ion channels are difficult to predict. Remediation of APD topre-failing state does not ameliorate dysfunction in CaT; however, restoration of notch depth appears to impart modest benefit and a likelihood of therapeutic value in modulating early repolarization.},
	author = {Maleckar, Molly and Glenn T. {Lines} and Koivum{\"a}ki, Jussi and Jonathan M. {Cordeiro} and Calloe, Kirstine}
}
@misc {Simula.simula.2784,
	title = {Supercomputing-Enabled Study of Subcellular Calcium Dynamics},
	year = {2014},
	type = {Article in "meta" - a magazine published by the notur project},
	author = {Cai, Xing and Johan Elon {Hake} and Glenn T. {Lines}}
}
@misc {Simula.simula.2720,
	title = {Ca2+-Transient Dysfunction and Ion Channel Therapy: What Can We Gather From a Computational Model of Canine Heart Failure?},
	howpublished = {  },
	year = {2013},
	month = {July},
	keywords = {Conference},
	author = {Maleckar, Molly and Glenn T. {Lines} and Koivum{\"a}ki, Jussi}
}
@article {Simula.simula.2274,
	title = {Mathematical Models of Cardiac Pacemaking Function},
	journal = {Frontiers in Physics},
	volume = {1},
	number = {20},
	year = {2013},
	month = {October 2013},
	abstract = {Over the past half century, there has been intense and fruitful interaction between experimental and computational investigations of cardiac function. This has led, for example, to more profound understanding of cardiac excitation-contraction coupling; how it works, as well as how it fails. However, many lines of inquiry remain unresolved, among them the initiation of each heartbeat. The sinoatrial node, a cluster of specialized pacemaking cells in the right atrium of the heart, spontaneously generates an electro-chemical wave that spreads through the atria and the cardiac conduction system to the ventricles, initiating the contraction of cardiac muscle essential for pumping blood to the body. Despite the fundamental importance of this primary pacemaker, this process is still not fully understood, and ionic mechanisms underlying cardiac pacemaking function are currently under heated debate. Several mathematical models of sinoatrial node cell membrane electrophysiology have been constructed as based on different experimental data sets and hypotheses. As could be expected, these differing models offer diverse predictions about cardiac pacemaking activities. This paper aims to present the current state of debate over the origins of the pacemaking function of the sinoatrial node. Here, we will specifically review the state-of-the-art of cardiac pacemaker modeling, with a special emphasis on current discrepancies, limitations, and future challenges.},
	doi = {10.3389/fphy.2013.00020},
	author = {Li, Pan and Glenn T. {Lines} and Maleckar, Molly and Tveito, Aslak}
}
@misc {Simula.simula.2716,
	title = {NS5806 Partially Restores APD But Fails to Ameliorate Ca2+ Transient Dysfunction in a Computational Model of Canine Heart Failure},
	howpublished = {Europace 2014},
	year = {2013},
	month = {October},
	keywords = {Conference},
	author = {Maleckar, Molly and Glenn T. {Lines} and Koivum{\"a}ki, Jussi and Calloe, Kirstine and Cordeiro, JM}
}
@inproceedings {Simula.simula.2692,
	title = {Observability of Ischemia and the Need for Patient Specific Geometrical Models in Inverse ECG},
	journal = {Computing in Cardiology Conference (CinC)},
	year = {2013},
	publisher = {IEEE},
	type = {Conference},
	author = {Glenn T. {Lines} and Ola Marius {Lysaker} and Nielsen, Bj{\o}rn Fredrik},
	editor = {Murray, Alan}
}
@misc {Simula.simula.2214,
	title = {Observability of Ischemia and the Need for Patient Specific Geometrical Models in Inverse ECG},
	howpublished = {Computing in Cardiology, Zaragoza, Spain},
	year = {2013},
	author = {Glenn T. {Lines} and Ola Marius {Lysaker} and Nielsen, Bj{\o}rn Fredrik}
}
@article {Simula.simula.542,
	title = {An Analysis of the Shock Strength Needed to Achieve Defibrillation in a Simplified Mathematical Model of Cardiac Tissue},
	journal = {International Journal of Numerical Analysis and Modeling},
	volume = {9},
	number = {3},
	year = {2012},
	pages = {644-657},
	author = {Tveito, Aslak and Glenn T. {Lines} and Marie E. {Rognes} and Maleckar, Molly}
}
@misc {Simula.simula.1740,
	title = {Elements of Scientific Computing},
	howpublished = {3-day intensive course given at National University of Defence Technology, China, October 16-18},
	year = {2012},
	author = {Glenn T. {Lines} and Cai, Xing}
}
@article {Simula.simula.720,
	title = {Instabilities of the Resting State in a Mathematical Model of Calcium Handling in Cardiac Myocytes},
	journal = {Mathematical Biosciences},
	volume = {236},
	number = {2},
	year = {2012},
	pages = {97-107},
	publisher = {Elsevier},
	doi = {http://dx.doi.org/10.1016/j.mbs.2012.02.005},
	author = {Tveito, Aslak and Glenn T. {Lines} and Johan Elon {Hake} and Andrew G {Edwards}}
}
@article {Simula.camo.14,
	title = {A Note on a Possible Pro-Arrhythmic Property of Anti-Arrhythmic Drugs Aimed at Improving Gap-Junction Coupling},
	journal = {Biophysical Journal},
	volume = {102},
	number = {2},
	year = {2012},
	month = {November},
	pages = {231-237},
	author = {Tveito, Aslak and Glenn T. {Lines} and Maleckar, Molly}
}
@article {Slow-Calcium-Depolarization-Calcium,
	title = {Slow Calcium-Depolarization-Calcium Waves May Initiate Fast Local Depolarization Waves in Ventricular Tissue},
	journal = {Progress in Biophysics and Molecular Biology},
	volume = {110},
	number = {2-3},
	year = {2012},
	month = {July 24},
	pages = {295-304},
	abstract = {Intercellular calcium waves in cardiac myocytes are a well-recognized, if incompletely understood, phenomenon. In a	variety of preparations, investigators have reported multi-cellular calcium waves or triggered propagated contractions, but the	mechanisms of propagation and pathological importance of these events remain unclear. Here, we review existing experimental data and present a computational approach to investigate the mechanisms of multi-cellular calcium wave propagation. Over the past 50 years, the standard modeling paradigm for excitable cardiac tissue	has seen increasingly detailed models of the dynamics of individual cells coupled in tissue solely by intercellular and interstitial current flow. Although very successful, this modeling regime has been unable to capture two important phenomena: 1) the slow intercellular calcium waves observed experimentally, and 2) how intercellular calcium events resulting in delayed after depolarizations at the cellular level could overcome a source-sink mismatch to initiate depolarization waves in tissue. In this paper, we introduce a mathematical model with subcellular spatial resolution, in which we allow both inter- and intracellular current flow and calcium diffusion. In simulations of coupled cells employing this model, we observe: a) slow inter-cellular calcium waves propagating at about 0.1 mm/s, b) faster Calcium-Depolarization-Calcium (CDC) waves, traveling at about 1 mm/s, and c) CDC- waves that can set off fast depolarization-waves (50 cm/s) in tissue with varying gap-junction conductivity.},
	author = {Tveito, Aslak and Glenn T. {Lines} and Andrew G {Edwards} and Maleckar, Molly and Anushka P. {Michailova} and Johan Elon {Hake} and Andrew D. {McCulloch}}
}
@article {Simula.SC.488,
	title = {Computing the Stability of Steady-State Solutions of Mathematical Models of the Electrical Activity in the Heart},
	journal = {Mathematical Biosciences and Engineering},
	volume = {41},
	number = {8},
	year = {2011},
	pages = {611-618},
	doi = {10.1016/j.compbiomed.2011.05.011},
	author = {Tveito, Aslak and Skavhaug, Ola and Glenn T. {Lines} and Artebrant, Robert}
}
@article {Simula.SC.644,
	title = {On Defining Candidate Drug Characteristics for Long-QT},
	journal = {Mathematical Biosciences and Engineering},
	volume = {8},
	number = {3},
	year = {2011},
	pages = {861-873},
	abstract = {Mutations of the SCN5A gene can significantly alter the function of cardiac myocyte sodium channels leading to increased risk of ventricular arrhythmia. Several gain-of-function mutations associated with long QT intervals result in a persistent late current that prolongs the cardiac action potential. Over the past decade, Markov models of the action potential of wild type and mutant cardiac cells have been developed. The effects of drugs on mutant cells have also been incorporated into some of these models. It is the purpose of this paper to predict the effects on sodium currents and whole cell action potentials of theoretical drugs targeting the mutant sodium channel. Our aim is to compute advantageous properties of a hypothetical drug by deriving Markov model parameters of the drug action that: (a) restores the steady-state open probability of the mutant channel to that of normal wildtype channels; and (b) minimizes the difference between whole cell currents in drugged mutant and wildtype cells. The difference in the electrochemical state vector of the cell can be measured in a norm taking all components and their dynamical properties into account. Measured with this norm, the difference between the state of the mutant and wild type cell was reduced by a factor of 36 after the drug was introduced and by factors of 4 over mexitiline and 25 over lidocaine. The results suggest the potential to synthesize more effective drugs based on mechanisms of action of existing compounds.},
	author = {Tveito, Aslak and Glenn T. {Lines} and Li, Pan and Andrew D. {McCulloch}}
}
@article {Simula.sc.838,
	title = {Existence of Excitation Waves for a Collection of Cardiomyocytes Electrically Coupled to Fibroblasts},
	journal = {Mathematical Biosciences},
	volume = {230},
	year = {2011},
	pages = {79-86},
	publisher = {Elsevier},
	abstract = {We consider mathematical models of a collection of cardiomyocytes (myocardial tissue) coupled to a varying number of fibroblasts. Our aim is to understand how conductivity (δ) and fibroblast density (η) affect the stability of the myocardial tissue. We provide mathematical and computational arguments indicating that there is a region of instability in the η-δ space. Mathematical arguments, based on a simplified model of the coupled myocyte-fibroblast system, show that for certain parameter choices, a stationary solution cannot exist. Numerical experiments (1D,2D) are based on a recently developed model of electro-chemical coupling between a human atrial myocyte and a number of associated atrial fibroblasts.},
	doi = {10.1016/j.mbs.2011.01.004},
	author = {Tveito, Aslak and Glenn T. {Lines} and Artebrant, Robert and Skavhaug, Ola and Maleckar, Molly}
}
@article {Simula.SC.508,
	title = {Stability of Two Time-Integrators for the Aliev-Panfilov System},
	journal = {International Journal of Numerical Analysis and Modeling},
	volume = {8},
	number = {3},
	year = {2011},
	pages = {427-442},
	author = {Hanslien, Monica and Artebrant, Robert and Tveito, Aslak and Glenn T. {Lines} and Cai, Xing}
}
@misc {Simula.simula.964,
	title = {A Stochastic Model of the Ryanodine Receptor Featuring Coupled Gating and Competitive Binding of Luminal and Cytosolic Ca2+ and Mg2+},
	year = {2011},
	author = {Johan Elon {Hake} and William E. {Louch} and Haugen, K. and Sjaastad, Ivar and Ole M. {Sejersted} and Andrew D. {McCulloch} and Anushka P. {Michailova} and Glenn T. {Lines}}
}
@article {Simula.simula.228,
	title = {Unstable Eigenmodes As Possible Drivers for Cardiac Arrhythmias},
	journal = {Journal of the Royal Society Interface},
	volume = {8},
	number = {61},
	year = {2011},
	month = {August},
	pages = {1212-6},
	author = {Tveito, Aslak and Glenn T. {Lines} and Skavhaug, Ola and Maleckar, Molly}
}
@article {Simula.simula.122,
	title = {Control of Ca2+ Release by Action Potential Configuration in Normal and Failing Murine Cardiomyocytes},
	journal = {Biophysical Journal},
	volume = {99},
	number = {5},
	year = {2010},
	month = {September},
	pages = {1377-1386},
	author = {William E. {Louch} and Johan Elon {Hake} and Guro Five {J{\o}lle} and Halvor K. {M{\o}rk} and Sjaastad, Ivar and Glenn T. {Lines} and Ole M. {Sejersted}}
}
@article {Simula.SC.464,
	title = {A Method for Analyzing the Stability of the Resting State for a Model of Pacemaker Cells Surrounded by Stable Cells},
	journal = {Mathematical Biosciences and Engineering},
	volume = {7},
	number = {3},
	year = {2010},
	pages = {505-526},
	abstract = {The purpose of this paper is to derive and analyze methods for examining the stability of solutions of partial differential equations modeling collections of excitable cells. In particular, we derive methods for estimating the principal eigenvalue of a linearized version of the Luo-Rudy I model close to an equilibrium solution. It has been suggested that the stability of a collection of unstable cells surrounded by a large collection of stable cells can be studied by considering only a collection of unstable cells equipped with a Dirichlet type boundary condition. This method has earlier been applied to analytically assess the stability of a reduced version the Luo-Rudy I model. In this paper we analyze the accuracy of this technique and apply it to the full Luo-Rudy I model. Furthermore, we extend the method to provide analytical results for the FitzHugh-Nagumo model in the case where a collection of unstable cells is surrounded by a collection of stable cells. All our analytical findings are complemented by numerical computations computing the principal eigenvalue of a discrete version of linearized models.},
	author = {Artebrant, Robert and Tveito, Aslak and Glenn T. {Lines}}
}
@article {Simula.SC.29,
	title = {Adaptive Finite Element Simulation of Ventricular Fibrillation Dynamics},
	journal = {Computing and Visualization in Science},
	volume = {12},
	number = {5},
	year = {2009},
	pages = {201-205},
	author = {Deuflhard, Peter and Erdmann, Bodo and Roitzsch, Rainer and Glenn T. {Lines}}
}
@misc {Simula.sc.840,
	title = {Antiarrhythmic Drug Identifaction},
	howpublished = {Presented at the Bidomain Workshop, Graz, Austria},
	year = {2009},
	note = {Presented at the Bidomain Workshop, Graz, Austria},
	author = {Glenn T. {Lines} and Tveito, Aslak and Li, Pan}
}
@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}
}
@article {Simula.SC.116,
	title = {A Note on a Method for Determining Advantageous Properties of an Anti-Arrhythmic Drug Based on a Mathematical Model of Cardiac Cells},
	journal = {Mathematical Biosciences},
	volume = {217},
	number = {2},
	year = {2009},
	pages = {167-173},
	doi = {10.1016/j.mbs.2008.12.001},
	author = {Tveito, Aslak and Glenn T. {Lines}}
}
@article {Simula.SC.134,
	title = {Numerical Solution of the Bidomain Equations},
	journal = {Philosophical Transactions of the Royal Society A},
	volume = {367},
	number = {1895},
	year = {2009},
	month = {May},
	pages = {1931-1951},
	abstract = {Knowledge of cardiac electrophysiology is e{ffi}ciently formulated in terms of mathematical models. Most of these models are, however, very complex and thus denies direct mathematical reasoning founded on classical and analytical considerations. This is particularly the case for the celebrated bidomain model, developed almost 40 years ago for concurrent analysis of extra- and intracellular electrical activity. Numerical simulations represent an indispensible tool to study electrophysiology based on this model. However, both steep gradients in the solutions and complicated geometries lead to extremely challenging computational problems. The greatest achievement in scienti{fi}c computing over the past 50 year was to enable solution of linear systems of algebraic equations arising from discretizations of partial di{ff}erential equations in an optimal manner; i.e. such that the CPU-e{ff}orts increases linearly in the number of computational nodes. Over the past decade such optimal methods have been introduced in simulation of electrophysiology. This development, together with the development of a{ff}ordable parallel computers, has enabled the solution of the bidomain model combined with accurate cellular models de{fi}ned on realistic geometries. However, in spite of recent progress, the full potential of modern computational methods has yet to be exploited for solution of the bidomain model. It is the purpose of this paper to review the development of numerical methods for solving the bidomain model. The {fi}eld is huge, and we have to restrict our focus to the development after year 2000.},
	author = {Linge, Svein and Sundnes, Joakim and Hanslien, Monica and Glenn T. {Lines} and Tveito, Aslak}
}
@article {Simula.SC.12,
	title = {Synchronizing Computer Simulations With Measurement Data for a Case of Atrial Flutter},
	journal = {Annals of Biomedical Engineering},
	volume = {37},
	number = {7},
	year = {2009},
	pages = {1287-1293},
	abstract = {When the function of the atria is hampered by irregular electrical activation, radiofrequency ablation therapy can be used to restore normal activation and rhythm. Electroanatomical mapping systems provide the clinician with a picture of the activation sequence, from which he/she can determine where to ablate. The purpose of this paper is to present an algorithm for incorporating data from these mapping systems into a numerical simulator of the atria. The method is applied to 3D test problems with synthetic mapping data. Convergence to the correct solution is observed provided that a sufficient number of mapping sites are used. For our simulations, we use the monodomain model coupled with FitzHugh-Nagumo cell dynamics.},
	author = {Glenn T. {Lines} and Linge, Svein and Mary C. {MacLachlan} and Tveito, Aslak}
}
@article {Simula.SC.100,
	title = {A Condition for Setting Off Ectopic Waves in Computational Models of Excitable Cells},
	journal = {Mathematical Biosciences},
	volume = {213},
	number = {2},
	year = {2008},
	pages = {141-150},
	doi = {10.1016/j.mbs.2008.04.001},
	author = {Tveito, Aslak and Glenn T. {Lines}}
}
@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}
}
@misc {Simula.SC.170,
	title = {Modelling the Mesoscopic Length Scale of EC Coupling: the Diadic Cleft},
	howpublished = {Invited talk at {\textquoteright}European Conference on Mathematical and Theoretical Biology{\textquoteright}},
	year = {2008},
	month = {june},
	abstract = {Ca2+ signalling in the dyadic cleft plays an important role in the excitation contraction (EC) coupling in ventricular myocytes. The cleft is a fuzzy space between the T-tubule and the Sarcoplasmic reticulum (SR). An action potential triggers the opening of L-type Ca2+ channels that let Ca2+ ions into the cleft. Most of the ions diffuses into the cytosole; but some bind to Ryanodine receptors (RyR), which are situated in clusters at the SR membrane, triggering further Ca 2+ release from SR. The signal is conveyed by a small number of diffusing Ca2+ ions, and is therefor fundamentally stochastic. The small number of Ca2+ ions involved in the process would suggest that diffusion in the dyadic cleft have to be modelled using Random Walk methods, making a deterministic and continuous model of diffusion useless. However the signal is not conveyed by Ca2+ ions in the cleft but rather by Ca2+ ions binding to single RyRs. To study the mesoscopic scale for this process we compared the event of single Ca2+ ions binding to RyRs in the cleft using two different models of diffusion: a stochastic and discrete Random Walk (RW) model, and a deterministic continuous model. We investigate whether the latter model, together with a stochastic receptor model, can reproduce binding events registered in fully stochastic RW simulations. By evaluating the continuous model goodness-of-fit, for a large range of parameters, we present evidence that it can. The large fluctuations in binding rate observed at the level of single time steps are integrated and smoothed at the larger time scale of single binding events, explaining the continuous model goodness-of-fit. Three parameters, which are combined into a dimensionless parameter: the diffusion constant of Ca2+, the binding rate of Ca2+ to the RyRs, and the diffusion length of the RW model, defines an upper limit for the agreement between the two models. As a result these parameters set the mesoscopic scale for the EC coupling.},
	author = {Johan Elon {Hake} and Glenn T. {Lines}}
}
@article {Simula.SC.40,
	title = {Stochastic Binding of Ca2+ in the Dyadic Cleft: Continuous Vs. Random-Walk Description of Diffusion.},
	journal = {Biophysical Journal},
	volume = {94},
	number = {11},
	year = {2008},
	month = {juni},
	pages = {4184-4201},
	abstract = {Ca2+ signaling in the dyadic cleft in ventricular myocytes is fundamentally discrete and stochastic. We study the stochastic binding of single Ca2+ ions to receptors in the cleft using two different models of diffusion: a stochastic and discrete Random Walk (RW) model, and a deterministic continuous model. We investigate whether the latter model, together with a stochastic receptor model, can reproduce binding events registered in fully stochastic RW simulations. By evaluating the continuous model goodness-of-fit for a large range of parameters, we present evidence that it can. Further, we show that the large fluctuations in binding rate observed at the level of single time-steps are integrated and smoothed at the larger timescale of binding events, which explains the continuous model goodness-of-fit. With these results we demonstrate that the stochasticity and discreteness of the Ca2+ signaling in the dyadic cleft, determined by single binding events, can be described using a deterministic model of Ca2+ diffusion together with a stochastic model of the binding events, for a specific range of physiological relevant parameters. Time-consuming RW simulations can thus be avoided. We also present a new analytical model of bimolecular binding probabilities, which we use in the RW simulations and the statistical analysis.},
	doi = {10.1529/biophysj.106.103523},
	author = {Johan Elon {Hake} and Glenn T. {Lines}}
}
@article {Schroll.2005.2,
	title = {On the Accuracy of Operator Splitting As Applied to Discretized Reaction Diffusion Systems},
	journal = {International Journal of Computer Mathematics},
	volume = {84},
	number = {6},
	year = {2007},
	pages = {871-885},
	author = {Schroll, Achim and Glenn T. {Lines} and Tveito, Aslak}
}
@misc {Simula.sc.890,
	title = {Cardiac Computing at Simula},
	howpublished = {Talk at CBC Workshop on Biomedical Computing},
	year = {2007},
	month = {June},
	author = {Glenn T. {Lines}}
}
@article {Nielsen.2006.7,
	title = {Optimal Monodomain Approximations of the Bidomain Equations},
	journal = {Applied Mathematics and Computation},
	volume = {184},
	number = {2},
	year = {2007},
	month = {January},
	pages = {276-290},
	author = {Nielsen, Bj{\o}rn Fredrik and Tomas Syrstad {Ruud} and Glenn T. {Lines} and Tveito, Aslak}
}
@misc {Simula.sc.892,
	title = {Overview of the Cardiac Computations Project},
	howpublished = {Talk at CBC, Seminar on Electrophysiology Modeling},
	year = {2007},
	month = {September},
	author = {Glenn T. {Lines}}
}
@misc {Simula.SC.38,
	title = {Stochastic Binding of Ca2+ Ions in the Dyadic Cleft Continuous Vs Random Walk Description of Diffusion},
	howpublished = {Presentation at ICIAM 07},
	year = {2007},
	note = {Contributed talk},
	month = {July},
	author = {Johan Elon {Hake} and Glenn T. {Lines}}
}
@misc {Simula.SC.37,
	title = {Stochastic Binding of Ca2+ Ions in the Dyadic Cleft Continuous Vs Random Walk Description of Diffusion},
	howpublished = {Poster presentation at 5th Annual CHFR Symposium},
	year = {2007},
	month = {October},
	author = {Johan Elon {Hake} and Glenn T. {Lines}}
}
@article {Mardal.2006.7,
	title = {Using Python to Solve Partial Differential Equations},
	journal = {Computing in Science \& Engineering},
	volume = {9},
	number = {3},
	year = {2007},
	month = {May/June},
	pages = {48-51},
	author = {Mardal, Kent-Andre and Skavhaug, Ola and Glenn T. {Lines} and Gunnar Andreas {Staff} and {\O}deg{\r a}rd, {\r A}smund}
}
@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}
}
@article {Lines.2006.1,
	title = {Contribution of the Na/Ca Exchanger to Rapid Ca Release in Cardiomyocytes},
	journal = {Biophysical Journal},
	volume = {91},
	number = {3},
	year = {2006},
	pages = {779-792},
	abstract = {Trigger Ca is considered to be the Ca current through the L-type Ca channel (LTCC) that causes release of Ca from the sarcoplasmic reticulum (SR). However, cell contraction also occurs in the absence of the LTCC current (ICa). In this paper we investigate the contribution of the Na/Ca -exchanger (NCX) to the trigger Ca. Experimental data from rat cardiomyocytes using confocal microscopy indicating that inhibition of reverse mode Na/Ca -exchange delays the Ca transient by 3-4 ms, served as a basis for the mathematical model. A detailed computational model of the dyadic cleft (fuzzy space) is presented where the diffusion of both Na and Ca is taken into account. Ionic channels are included at discrete locations, making it possible to study the effect of channel position and colocalization. The simulations indicate that if a Na channel is present in the fuzzy space, the NCX is able to bring enough Ca into the cell to affect the timing of release. However, this critically depends on channel placement and local diffusion properties. With fuzzy space diffusion in the order of 1\% compared to bulk diffusion, triggering through LTCC alone was 3-4 ms slower than with the presence of a Na channel and NCX.},
	author = {Glenn T. {Lines} and J{\o}rn Bodvar {Sande} and William E. {Louch} and Halvor K. {M{\o}rk} and Gr{\o}ttum, Per and Ole M. {Sejersted}}
}
@inbook {Cai.2006.3,
	title = {Full-Scale Simulation of Cardiac Electrophysiology on Parallel Computers},
	booktitle = {Numerical Solution of Partial Differential Equations on Parallel Computers},
	series = {Lecture Notes in Computational Science and Engineering},
	year = {2006},
	pages = {385-411},
	publisher = {Springer},
	organization = {Springer},
	author = {Cai, Xing and Glenn T. {Lines}},
	editor = {Are Magnus {Bruaset} and Tveito, Aslak}
}
@misc {Simula.SC.107,
	title = {Simulating Electrical Activity in the Heart},
	howpublished = {Presented at St Jude Medical, Stockholm, Sweeden},
	year = {2006},
	author = {Hanslien, Monica and Sundnes, Joakim and Glenn T. {Lines} and Tveito, Aslak}
}
@misc {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}
}
@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}
}
@techreport {25345,
	title = {Optimal Monodomain Approximations of the Bidomain Equations},
	year = {2005},
	note = {This technical report is an earlier version of a published journal article. The published version can be found here:https://www.simula.no/publications/optimal-monodomain-approximations-bidomain-equations},
	publisher = {Simula Research Laboratory},
	author = {Nielsen, Bj{\o}rn Fredrik and Tomas Syrstad {Ruud} 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 {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}}
}
@inbook {SC.5.Cai.2004.b,
	title = {Parallel Solution of the Bidomain Equations With High Resolutions},
	booktitle = {Parallel Computing: Software Technology, Algorithms, Architectures \& Applications},
	year = {2004},
	pages = {837-844},
	publisher = {Elsevier Science},
	organization = {Elsevier Science},
	author = {Cai, Xing and Glenn T. {Lines} and Tveito, Aslak},
	editor = {G. R. {Joubert} and W. E. {Nagel} and F. J. {Peters} and W. V. {Walter}}
}
@misc {SC.8.Nielsen.2004,
	title = {Parameter Identification Problems for Infarction Modelling},
	howpublished = {Presented at the 2004 SIAM Conference on the Life Sciences, Portland, Oregon, USA},
	year = {2004},
	month = {July},
	author = {Nielsen, Bj{\o}rn Fredrik and Ola Marius {Lysaker} and Glenn T. {Lines} and Tveito, Aslak}
}
@techreport {SC.7.Nilssen.2004,
	title = {Resolution Requirements for a 1D Monodomain Model for Simulating},
	number = {2004-07},
	year = {2004},
	publisher = {Simula Research Laboratory},
	author = {Nilssen, Trygve Kastberg and Ingebrigtsen, L. and Hanslien, Monica and Glenn T. {Lines} and Tveito, Aslak}
}
@article {SC.4.Lines.2003.c,
	title = {Co-Localization of Sodium Transporters in Isolated Cardiac Cell Membrane; a Model Study},
	journal = {International Journal of Bioelectromagnetism},
	volume = {5},
	number = {1},
	year = {2003},
	pages = {179-180},
	author = {Glenn T. {Lines} and J{\o}rn Bodvar {Sande} and Gr{\o}ttum, P. and T. A. {Str{\o}mme} and Ole M. {Sejersted}}
}
@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}
}
@misc {SC.8.Nielsen.2003,
	title = {Determining the Size and Location of a Myocardial Infarction; a Scientific Computing Framework},
	howpublished = {Presented at the European Conference on Numerical Mathematics and Advanced Applications, Prague, Czech Republic},
	year = {2003},
	month = {August},
	author = {Nielsen, Bj{\o}rn Fredrik and Glenn T. {Lines} and Tveito, Aslak}
}
@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}
}
@article {SC.4.Lines.2003,
	title = {Modeling the Electrical Activity of the Heart -A Bidomain Model of the Ventricles Embedded in a Torso},
	journal = {Computing and Visualization in Science},
	volume = {5},
	number = {4},
	year = {2003},
	pages = {195-213},
	abstract = {In this paper a model for the electrical activity of the heart will be presented and an approach to solve the resulting numerical problem will be suggested. The Bidomain Model is used to compute the spatial distribution of the electrical potential. The partial differential equations are discretized with the finite element method and the multigrid method is used to solve the corresponding linear equations. Adaptivity is applied to resolve the steep gradients in the solution.},
	author = {Glenn T. {Lines} and Gr{\o}ttum, P. 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}
}
@inbook {SC.5.Cai.2003.c,
	title = {Performance Modeling of PDE Solvers},
	booktitle = {Advanced Topics in Computational Partial Differential Equations - Numerical Methods and Diffpack Programming},
	series = {Lecture Notes in Computational Science and Engineering},
	year = {2003},
	pages = {361-399},
	publisher = {Springer},
	organization = {Springer},
	author = {Cai, Xing and Are Magnus {Bruaset} and Hans Petter {Langtangen} and Glenn T. {Lines} and Samuelsson, K. and Shen, W. and Tveito, Aslak and Zumbusch, G.},
	editor = {Hans Petter {Langtangen} and Tveito, Aslak}
}
@misc {Cai.2003.1,
	title = {Toward Extremely High-Resolution Simulation of Human Heart},
	howpublished = {Talk at the ParCo 2003 Conference, 2 - 5 September 2003, Dresden, Germany},
	year = {2003},
	author = {Cai, Xing and Glenn T. {Lines} and Tveito, Aslak}
}
@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}
}
@inproceedings {SC.5.Cai.2002.b,
	title = {Enabling Numerical and Software Technologies for Studying the Electrical Activity in Human Heart},
	journal = {Applied Parallel Computing - Advanced Scientific Computing, 6th International Conference, PARA 2002},
	year = {2002},
	pages = {3-17},
	publisher = {Springer-Verlag},
	type = {1},
	address = {Espoo, Finland},
	author = {Cai, Xing and Glenn T. {Lines}},
	editor = {Fagerholm, J.}
}
@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}
}
@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}
}
@techreport {SC.7.Lines.2001,
	title = {A Parallel Solution of the Bidomain Equations Modeling the Electrical Activity of the Heart},
	year = {2001},
	publisher = {Simula Research Laboratory},
	author = {Glenn T. {Lines} and Cai, Xing 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}
}
@phdthesis {SC.3.Lines.1999,
	title = {Simulating the Electrical Activity in the Heart - a Bidomain Model of the Ventrciles Embedded in a Torso},
	year = {1999},
	school = {Department of Informatics, University of Oslo},
	type = {phd},
	author = {Glenn T. {Lines}}
}
@inproceedings {SC.5.Lines.1998.a,
	title = {A Coupled Torso and Myocardium Simulator Using the Luo-Rudy Cell Model - Implementation and Results},
	journal = {Proceedings of the XXVth International Congress on Electrocardiology},
	year = {1998},
	pages = {75-79,},
	type = {1},
	author = {Glenn T. {Lines} and Gr{\o}ttum, P. and Tveito, Aslak},
	editor = {Preda, Istvan}
}
@techreport {SC.7.Cai.1998,
	title = {Performance Modeling of PDE Solvers},
	number = {1998-3},
	year = {1998},
	publisher = {Department of Informatics, University of Oslo},
	author = {Cai, Xing and Are Magnus {Bruaset} and Hans Petter {Langtangen} and Glenn T. {Lines} and Samuelsson, K. and Shen, W. and Tveito, Aslak and Zumbusch, G.}
}
@article {SC.4.Johansen.1997,
	title = {Calibration of an FT-IR Spectrometer for Ambient Air Monitoring Using PLS},
	journal = {Applied Spectroscopy},
	volume = {51},
	number = {10,},
	year = {1997},
	author = {Johansen, I-R and Glenn T. {Lines} and Honne, A. and Midtgaard, T.}
}
@inbook {SC.5.Lines.1996,
	title = {The Equivalence of Spline Models and Fuzzy Logic Applied to Model Construction and Interpretation},
	booktitle = {Neural Adaptive Control Theory},
	year = {1996},
	publisher = {World Scientific},
	organization = {World Scientific},
	author = {Glenn T. {Lines} and Kavli, T.},
	editor = {Zbikowski, R. and Hunt, K.J.}
}
