@book {43259,
	title = {Differential Equations for Studies in Computational Electrophysiology},
	number = {14},
	year = {2023},
	publisher = { Springer},
	organization = { Springer},
	address = {Simula SpringerBriefs on Computing},
	isbn = {978-3-031-30852-9},
	issn = {978-3-031-30851-2},
	doi = {https://doi.org/10.1007/978-3-031-30852-9},
	url = {https://link.springer.com/content/pdf/10.1007/978-3-031-30852-9.pdf?pdf=button\%20sticky},
	author = {Karoline Horgmo {J{\ae}ger} and Tveito, Aslak}
}
@article {43283,
	title = {Efficient, cell-based simulations of cardiac electrophysiology; The Kirchhoff Network Model (KNM)},
	journal = {npj Systems Biology and Applications},
	volume = {9},
	year = {2023},
	pages = {25},
	publisher = {Springer Nature},
	doi = {https://doi.org/10.1038/s41540-023-00288-3},
	url = {https://rdcu.be/detBd},
	author = {Karoline Horgmo {J{\ae}ger} and Tveito, Aslak}
}
@article {43164,
	title = {Nano-scale solution of the Poisson-Nernst-Planck (PNP) equations in a fraction of two neighboring cells reveals the magnitude of intercellular electrochemical waves},
	journal = {PLoS Computational Biology},
	volume = {19},
	year = {2023},
	pages = {e1010895},
	publisher = {Public Library of Science},
	abstract = {The basic building blocks of the electrophysiology of cardiomyocytes are ion channels integrated in the cell membranes. Close to the ion channels there are very strong electrical and chemical gradients. However, these gradients extend for only a few nano-meters and are therefore commonly ignored in mathematical models. The full complexity of the dynamics\&nbsp;is modelled by the Poisson-Nernst-Planck (PNP) equations but these equations must be solved using temporal and spatial scales of nano-seconds and nano-meters. Here we report solutions of the PNP equations in a fraction of two abuttal cells separated by a tiny extracellular space. We show that when only the potassium channels of the two cells are open, a stationary solution is reached with the well-known Debye layer close to the membranes. When the sodium channels of one of the cells are opened, a very strong and brief electrochemical wave emanates from the channels. If the extracellular space is sufficiently small and the number of sodium channels is sufficiently high, the wave extends all the way over to the neighboring cell and may therefore explain cardiac conduction even at very low levels of gap junctional coupling.},
	doi = {https://doi.org/10.1371/ journal.pcbi.1010895},
	url = {https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1010895},
	author = {Karoline Horgmo {J{\ae}ger} and Ivanovic, Ena and Jan P. {Kucera} and Tveito, Aslak}
}
@article {42456,
	title = {Arrhythmogenic influence of mutations in a myocyte-based computational model of the pulmonary vein sleeve},
	journal = {Nature Scientific Reports },
	volume = {12},
	year = {2022},
	pages = {7040},
	publisher = {Springer Nature},
	abstract = {In the heart, electrophysiological dysregulation arises from defects at many biological levels (from point mutations in ion channel proteins to gross structural abnormalities). These defects disrupt the normal pattern of electrical activation, producing ectopic activity and reentrant arrhythmia. To interrogate mechanisms that link these primary biological defects to macroscopic electrophysiologic dysregulation most prior computational studies have utilized either (i) detailed models of myocyte ion channel dynamics at limited spatial scales, or (ii) homogenized models of action potential conduction that reproduce arrhythmic activity at tissue and organ levels. Here we apply our recent model (EMI), which integrates electrical activation and propagation across these scales, to study human atrial arrhythmias originating in the pulmonary vein (PV) sleeves. These small structures initiate most supraventricular arrhythmias and include pronounced myocyte-to-myocyte heterogeneities in ion channel expression and intercellular coupling. To test EMI{\textquoteright}s cell-based architecture in this physiological context we asked whether ion channel mutations known to underlie atrial fibrillation are capable of initiating arrhythmogenic behavior via increased excitability or reentry in a schematic PV sleeve geometry. Our results illustrate that EMI{\textquoteright}s improved spatial resolution can directly interrogate how electrophysiological changes at the individual myocyte level manifest in tissue and as arrhythmia in the PV sleeve.},
	doi = {https://doi.org/10.1038/s41598-022-11110-1},
	url = {https://rdcu.be/cMntU},
	author = {Karoline Horgmo {J{\ae}ger} and Andrew G {Edwards} and Wayne R. {Giles} and Tveito, Aslak}
}
@article {28370,
	title = {Deriving the Bidomain Model of Cardiac Electrophysiology From a Cell-Based Model; Properties and Comparisons},
	journal = {Frontiers in Physiology},
	volume = {12},
	year = {2022},
	pages = {811029},
	publisher = {Frontiers},
	abstract = {The bidomain model is considered to be the gold standard for numerical simulation of the electrophysiology of cardiac tissue. The model provides important insights into the conduction properties of the electrochemical wave traversing the cardiac muscle in every heartbeat. However, in normal resolution, the model represents the average over a large number of cardiomyocytes, and more accurate models based on representations of all individual cells have therefore been introduced in order to gain insight into the conduction properties close to the myocytes. The more accurate model considered here is referred to as the EMI model since both the extracellular space (E), the cell membrane (M) and the intracellular space (I) are explicitly represented in the model. Here, we show that the bidomain model can be derived from the cell-based EMI model and we thus reveal the close relation between the two models, and obtain an indication of the error introduced in the approximation. Also, we present numerical simulations comparing the results of the two models and thereby highlight both similarities and differences between the models. We observe that the deviations between the solutions of the models become larger for larger cell sizes. Furthermore, we observe that the bidomain model provides solutions that are very similar to the EMI model when conductive properties of the tissue are in the normal range, but large deviations are present when the resistance between cardiomyocytes is increased.},
	doi = {doi: 10.3389/fphys.2021.811029},
	url = {https://www.frontiersin.org/articles/10.3389/fphys.2021.811029/full},
	author = {Karoline Horgmo {J{\ae}ger} and Tveito, Aslak}
}
@article {42717,
	title = {Metabolically driven maturation of human-induced-pluripotent-stem-cell-derived cardiac microtissues on microfluidic chips},
	journal = {Nature Biomedical Engineering},
	volume = {6},
	year = {2022},
	month = {Jan-04-2022},
	pages = {372 - 388},
	publisher = {Nature Publishing Group},
	address = {London, UK},
	doi = {10.1038/s41551-022-00884-4},
	url = {https://www.nature.com/articles/s41551-022-00884-4https://www.nature.com/articles/s41551-022-00884-4.pdfhttps://www.nature.com/articles/s41551-022-00884-4.pdfhttps://www.nature.com/articles/s41551-022-00884-4},
	author = {Huebsch, Nathaniel and Charrez, Berenice and Neiman, Gabriel and Siemons, Brian and Steven C. {Boggess} and Wall, Samuel and Charwat, Verena and Karoline Horgmo {J{\ae}ger} and Cleres, David and Telle, {\r A}shild and Felipe T. {Lee-Montiel} and Nicholas C. {Jeffreys} and Deveshwar, Nikhil and Andrew G {Edwards} and Serrano, Jonathan and Snuderl, Matija and Stahl, Andreas and Tveito, Aslak and Evan W. {Miller} and Kevin E. {Healy}}
}
@article {43086,
	title = {Validating the Arrhythmogenic Potential of High-, Intermediate-, and Low-Risk Drugs in a Human-Induced Pluripotent Stem Cell-Derived Cardiac Microphysiological System},
	journal = {ACS Pharmacology \& Translational Science},
	volume = {5},
	year = {2022},
	pages = {652{\textendash}667},
	publisher = {American Chemical Society},
	abstract = {Evaluation of arrhythmogenic drugs is required by regulatory agencies before any new compound can obtain market approval. Despite rigorous review, cardiac disorders remain the second most common cause for safety-related market withdrawal. On the other hand, false-positive preclinical findings prohibit potentially beneficial candidates from moving forward in the development pipeline. Complex\&nbsp;in vitro\&nbsp;models using cardiomyocytes derived from human-induced pluripotent stem cells (hiPSC-CM) have been identified as a useful tool that allows for rapid and cost-efficient screening of proarrhythmic drug risk. Currently available hiPSC-CM models employ simple two-dimensional (2D) culture formats with limited structural and functional relevance to the human heart muscle. Here, we present the use of our 3D cardiac microphysiological system (MPS), composed of a hiPSC-derived heart micromuscle, as a platform for arrhythmia risk assessment. We employed two different hiPSC lines and tested seven drugs with known ion channel effects and known clinical risk: dofetilide and bepridil (high risk); amiodarone and terfenadine (intermediate risk); and nifedipine, mexiletine, and lidocaine (low risk). The cardiac MPS successfully predicted drug cardiotoxicity risks based on changes in action potential duration, beat waveform (i.e., shape), and occurrence of proarrhythmic events of healthy patient hiPSC lines in the absence of risk cofactors. We showcase examples where the cardiac MPS outperformed existing hiPSC-CM 2D models.},
	doi = {https://doi.org/10.1021/acsptsci.2c00088},
	url = {https://pubs.acs.org/doi/abs/10.1021/acsptsci.2c00088},
	author = {Charwat, Verena and Charrez, B{\'e}r{\'e}nice and Brian A. {Siemons} and Finsberg, Henrik and Karoline Horgmo {J{\ae}ger} and Andrew G {Edwards} and Huebsch, Nathaniel and Wall, Samuel and Miller, Evan and Tveito, Aslak and Kevin E. {Healy}}
}
@article {27937,
	title = {A computational method for identifying an optimal combination of existing drugs to repair the action potentials of SQT1 ventricular myocytes},
	journal = {PLoS Computational Biology},
	volume = {17},
	number = {8},
	year = {2021},
	pages = {e1009233},
	publisher = {Public Library of Science},
	abstract = {Mutations are known to cause perturbations in essential functional features of integral membrane proteins, including ion channels. Even restricted or point mutations can result in substantially changed properties of ion currents. The additive effect of these alterations for a specific ion channel can result in significantly changed properties of the action potential (AP). Both AP shortening and AP prolongation can result from known mutations, and the consequences can be life-threatening. Here, we present a computational method for identifying new drugs utilizing combinations of existing drugs. Based on the knowledge of theoretical effects of existing drugs on individual ion currents, our aim is to compute optimal combinations that can {\textquoteleft}repair{\textquoteright} the mutant AP waveforms so that the baseline AP-properties are restored. More specifically, we compute optimal, combined, drug concentrations such that the waveforms of the transmembrane potential and the cytosolic calcium concentration of the mutant cardiomyocytes (CMs) becomes as similar as possible to their wild type coun- terparts after the drug has been applied. In order to demonstrate the utility of this method, we address the question of computing an optimal drug for the short QT syndrome type 1 (SQT1). For the SQT1 mutation N588K, there are available data sets that describe the effect of various drugs on the mutated K+ channel. These published findings are the basis for our computational analysis which can identify optimal compounds in the sense that the AP of the mutant CMs resembles essential biomarkers of the wild type CMs. Using recently developed insights regarding electrophysiological properties among myocytes from different species, we compute optimal drug combinations for hiPSC-CMs, rabbit ventricular CMs and adult human ventricular CMs with the SQT1 mutation. Since the {\textquoteleft}composition{\textquoteright} of ion channels that form the AP is different for the three types of myocytes under consideration, so is the composition of the optimal drug.},
	doi = {https://doi. org/10.1371/journal.pcbi.1009233},
	author = {Karoline Horgmo {J{\ae}ger} and Andrew G {Edwards} and Wayne R. {Giles} and Tveito, Aslak}
}
@article {27660,
	title = {Computational prediction of drug response in short QT syndrome type 1 based on measurements of compound effect in stem cell-derived cardiomyocytes},
	journal = {PLoS Computational Biology},
	volume = {17},
	year = {2021},
	pages = {e1008089},
	publisher = {Public Library of Science},
	abstract = {Short QT (SQT) syndrome is a genetic cardiac disorder characterized by an abbreviated QT interval of the patient{\textquoteright}s electrocardiogram. The syndrome is associated with increased risk of arrhythmia and sudden cardiac death and can arise from a number of ion channel mutations. Cardiomyocytes derived from induced pluripotent stem cells generated from SQT patients (SQT hiPSC-CMs) provide promising platforms for testing pharmacological treatments directly in human cardiac cells exhibiting mutations specific for the syndrome. How- ever, a difficulty is posed by the relative immaturity of hiPSC-CMs, with the possibility that drug effects observed in SQT hiPSC-CMs could be very different from the corresponding drug effect\&nbsp;in vivo. In this paper, we apply a multistep computational procedure for translating measured drug effects from these cells to human QT response. This process first detects drug effects on individual ion channels based on measurements of SQT hiPSC-CMs and then uses these results to estimate the drug effects on ventricular action potentials and QT intervals of adult SQT patients. We find that the procedure is able to identify IC50\&nbsp;values in line with measured values for the four drugs quinidine, ivabradine, ajmaline and mexiletine. In addition, the predicted effect of quinidine on the adult QT interval is in good agreement with measured effects of quinidine for adult patients. Consequently,\&nbsp;the computational procedure appears to be a useful tool for helping predicting adult drug responses from pure\&nbsp;in vitro\&nbsp;measurements of patient derived cell lines.},
	doi = {https://doi.org/10.1371/journal.pcbi.1008089},
	url = {https://journals.plos.org/ploscompbiol/article/file?id=10.1371/journal.pcbi.1008089\&type=printable},
	author = {Karoline Horgmo {J{\ae}ger} and Wall, Samuel and Tveito, Aslak}
}
@inbook {27507,
	title = {Derivation of a Cell-Based Mathematical Model of Excitable Cells},
	booktitle = {Modeling Excitable Tissue: The EMI Framework},
	volume = {7},
	year = {2021},
	pages = {1-13},
	publisher = {Springer International Publishing},
	organization = {Springer International Publishing},
	chapter = {1},
	address = {Cham},
	abstract = {Excitable cells are of vital importance in biology, and mathematical models have contributed significantly to understand their basic mechanisms. However, classical models of excitable cells are based on severe assumptions that may limit the accuracy of the simulation results. Here, we derive a more detailed approach to modeling that has recently been applied to study the electrical properties of both neurons and cardiomyocytes. The model is derived from first principles and opens up possibilities for studying detailed properties of excitable cells. We refer to the model as the EMI model because both the extracellular space (E), the cell membrane (M) and the intracellular space (I) are explicitly represented in the model, in contrast to classical spatial models of excitable cells. Later chapters of the present text will focus on numerical methods and software for solving the model. Also, in the next chapter, the model will be extended to account for ionic concentrations in the intracellular and extracellular spaces.},
	isbn = {978-3-030-61157-6},
	issn = {2512-1677},
	doi = {10.1007/978-3-030-61157-6_1},
	url = {https://link.springer.com/content/pdf/10.1007\%2F978-3-030-61157-6_1.pdf},
	author = {Karoline Horgmo {J{\ae}ger} and Tveito, Aslak},
	editor = {Tveito, Aslak and Mardal, Kent-Andre and Marie E. {Rognes}}
}
@article {27658,
	title = {Efficient numerical solution of the EMI model representing the extracellular space (E), cell membrane (M) and intracellular space (I) of a collection of cardiac cells},
	journal = {Frontiers in Physics},
	volume = {8},
	year = {2021},
	pages = {579461},
	publisher = {Frontiers},
	abstract = {The EMI model represents excitable cells in a more accurate manner than traditional homogenized models at the price of increased computational complexity. The increased complexity of solving the EMI model stems from a significant increase in the number of computational nodes and from the form of the linear systems that need to be solved. Here, we will show that the latter problem can be solved by careful use of operator splitting of the spatially coupled equations. By using this method, the linear systems can be broken into sub-problems that are of the classical type of linear, elliptic boundary value problems. Therefore, the vast collection of methods for solving linear, elliptic partial differential equations can be used. We demonstrate that this enables us to solve the systems using shared-memory parallel computers. The computing time scales perfectly with the number of physical cells. For a collection of 512{\texttimes}256 cells, we manage to solve linear systems with about 2.5{\texttimes}10^8 unknows. Since the computational effort scales linearly with the number of physical cells, we believe that larger computers can be used to simulate millions of excitable cells and thus allow careful analysis of physiological systems of great importance.},
	doi = {doi: 10.3389/fphy.2020.579461},
	url = {https://www.frontiersin.org/articles/10.3389/fphy.2020.579461/full},
	author = {Karoline Horgmo {J{\ae}ger} and Kristian Gregorius {Hustad} and Cai, Xing and Tveito, Aslak}
}
@article {28097,
	title = {From Millimeters to Micrometers; Re-introducing Myocytes in Models of Cardiac Electrophysiology},
	journal = {Frontiers in Physiology},
	volume = {12},
	year = {2021},
	pages = {763584},
	publisher = {Frontiers},
	abstract = {Computational modeling has contributed significantly to present understanding of cardiac electrophysiology including cardiac conduction, excitation-contraction coupling, and the effects and side-effects of drugs. However, the accuracy of\&nbsp;in silico\&nbsp;analysis of electrochemical wave dynamics in cardiac tissue is limited by the homogenization procedure (spatial averaging) intrinsic to standard continuum models of conduction. Averaged models cannot resolve the intricate dynamics in the vicinity of individual cardiomyocytes simply because the myocytes are not present in these models. Here we demonstrate how recently developed mathematical models based on representing every myocyte can significantly increase the accuracy, and thus the utility of modeling electrophysiological function and dysfunction in collections of coupled cardiomyocytes. The present gold standard of numerical simulation for cardiac electrophysiology is based on the bidomain model. In the bidomain model, the extracellular (E) space, the cell membrane (M) and the intracellular (I) space are all assumed to be present everywhere in the tissue. Consequently, it is impossible to study biophysical processes taking place close to individual myocytes. The bidomain model represents the tissue by averaging over several hundred myocytes and this inherently limits the accuracy of the model. In our alternative approach both E, M, and I are represented in the model which is therefore referred to as the EMI model. The EMI model approach allows for detailed analysis of the biophysical processes going on in functionally important spaces very close to individual myocytes, although at the cost of significantly increased CPU-requirements.},
	doi = {https://doi.org/10.3389/fphys.2021.763584},
	url = {https://www.frontiersin.org/articles/10.3389/fphys.2021.763584/full},
	author = {Karoline Horgmo {J{\ae}ger} and Andrew G {Edwards} and Wayne R. {Giles} and Tveito, Aslak}
}
@article {27659,
	title = {Identifying drug response by combining measurements of the membrane potential, the cytosolic calcium concentration, and the extracellular potential in microphysiological systems},
	journal = {Frontiers in Pharmacology},
	volume = {11},
	year = {2021},
	pages = {569489},
	publisher = {Frontiers},
	abstract = {Cardiomyocytes derived from human induced pluripotent stem cells (hiPSC-CMs) offer a new means to study and understand the human cardiac action potential, and can give key insight into how compounds may interact with important molecular pathways to destabilize the electrical function of the heart. Important features of the action potential can be readily measured using standard experimental techniques, such as the use of voltage sensitive dyes and fluorescent genetic reporters to estimate transmembrane potentials and cytosolic calcium concentrations. Using previously introduced computational procedures, such measurements can be used to estimate the current density of major ion channels present in hiPSC-CMs, and how compounds may alter their behavior. However, due to the limitations of optical recordings, resolving the sodium current remains difficult from these data. Here we show that if these optical measurements are complemented with observations of the extracellular potential using multi electrode arrays (MEAs), we can accurately estimate the current density of the sodium channels. This inversion of the sodium current relies on observation of the conduction velocity which turns out to be straightforwardly computed using measurements of extracellular waves across the electrodes. The combined data including the membrane potential, the cytosolic calcium concentration and the extracellular potential further opens up for the possibility of accurately estimating the effect of novel drugs applied to hiPSC-CMs.},
	doi = {doi: 10.3389/fphar.2020.569489},
	url = {https://www.frontiersin.org/articles/10.3389/fphar.2020.569489/full},
	author = {Karoline Horgmo {J{\ae}ger} and Charwat, Verena and Wall, Samuel and Kevin E. {Healy} and Tveito, Aslak}
}
@inbook {27497,
	title = {Operator Splitting and Finite Difference Schemes for Solving the EMI Model},
	booktitle = {Modeling Excitable Tissue: The EMI Framework},
	volume = {7},
	year = {2021},
	pages = {44 - 55},
	publisher = {Springer International Publishing},
	organization = {Springer International Publishing},
	chapter = {4},
	address = {Cham},
	abstract = {We want to be able to perform accurate simulations of a large number of cardiac cells based on mathematical models where each individual cell is represented in the model. This implies that the computational mesh has to have a typical resolution of a few {\textmu}m leading to huge computational challenges. In this paper we use a certain operator splitting of the coupled equations and showthat this leads to systems that can be solved in parallel. This opens up for the possibility of simulating large numbers of coupled cardiac cells.},
	isbn = {978-3-030-61156-9},
	issn = {2512-1677},
	doi = {10.1007/978-3-030-61157-6_4},
	url = {http://link.springer.com/content/pdf/10.1007/978-3-030-61157-6_4},
	author = {Karoline Horgmo {J{\ae}ger} and Kristian Gregorius {Hustad} and Cai, Xing and Tveito, Aslak},
	editor = {Tveito, Aslak and Mardal, Kent-Andre and Marie E. {Rognes}}
}
@article {27367,
	title = {Computational translation of drug effects from animal experiments to human ventricular myocytes},
	journal = {Nature Scientific Reports },
	number = {10},
	year = {2020},
	pages = {10537},
	publisher = {Nature Publishing Group},
	abstract = {Using animal cells and tissues as precise measuring devices for developing new drugs presents a long- standing challenge for the pharmaceutical industry. Despite the very significant resources that continue to be dedicated to animal testing of new compounds, only qualitative results can be obtained. This often results in both false positives and false negatives. Here, we show how the effect of drugs applied to animal ventricular myocytes can be translated, quantitatively, to estimate a number of different effects of the same drug on human cardiomyocytes. We illustrate and validate our methodology by translating, from animal to human, the effect of dofetilide applied to dog cardiomyocytes, the effect\&nbsp;of E-4031 applied to zebrafish cardiomyocytes, and, finally, the effect of sotalol applied to rabbit cardiomyocytes. In all cases, the accuracy of our quantitative estimates are demonstrated. Our computations reveal that, in principle, electrophysiological data from testing using animal ventricular myocytes, can give precise, quantitative estimates of the effect of new compounds on human cardiomyocytes.},
	doi = {10.1038/s41598-018-35858-7},
	url = { https://rdcu.be/b5iBl},
	author = {Tveito, Aslak and Karoline Horgmo {J{\ae}ger} and Maleckar, Molly and Wayne R. {Giles} and Wall, Samuel}
}
@article {27079,
	title = {Improved computational identification of drug response using optical measurements of human stem cell derived cardiomyocytes in microphysiological systems},
	journal = {Frontiers in Pharmacology},
	volume = {10},
	number = {1648},
	year = {2020},
	month = {02/2020},
	publisher = {Frontiers},
	abstract = {Cardiomyocytes derived from human induced pluripotent stem cells (hiPSC-CMs) hold great potential for drug screening applications. However, their usefulness is limited by the relative immaturity of the cells{\textquoteright} electrophysiological properties as compared to native cardiomyocytes in the adult human heart. In this work, we extend and improve on methodology to address this limitation, building on previously introduced computational procedures which predict drug effects for adult cells based on changes in optical measurements of action potentials and calcium\&nbsp;transients made in stem cell derived cardiac microtissues. This methodology quantifies ion channel changes through the inversion of data into a mathematical model, and maps this response to an adult phenotype through the assumption of functional invariance of fundamental intracellular and membrane channels during maturation.\&nbsp;Here we utilize an updated action potential model to represent both hiPSC-CMs and adult cardiomyocytes, apply an IC50-based\&nbsp;model of dose-dependent drug effects, and introduce a continuation-based optimization algorithm for analysis of dose escalation measurements using five drugs with known effects. The improved methodology can identify drug induced changes more efficiently, and quantitate important metrics such as IC50 in line with published values. Consequently, the updated methodology is a step towards employing computational procedures to elucidate drug effects in adult cardiomyocytes for new drugs using stem cell-derived experimental tissues.\&nbsp;},
	doi = {10.3389/fphar.2019.01648},
	author = {Karoline Horgmo {J{\ae}ger} and Charwat, Verena and Charrez, B{\'e}r{\'e}nice and Finsberg, Henrik and Maleckar, Molly and Wall, Samuel and Kevin E. {Healy} and Tveito, Aslak}
}
@phdthesis {26642,
	title = {Cell-Based Mathematical Models of Small Collections of Excitable Cells},
	volume = {PhD},
	year = {2019},
	school = {Department of Informatics, University of Oslo},
	author = {Karoline Horgmo {J{\ae}ger}}
}
@article {26641,
	title = {Detecting undetectables: Can conductances of action potential models be changed without appreciable change in the transmembrane potential?},
	journal = {Chaos},
	volume = {29},
	number = {073102},
	year = {2019},
	month = {07/2019},
	publisher = {AIP},
	abstract = {Mathematical models describing the dynamics of the cardiac action potential are of great value for understanding how changes to the system can disrupt the normal electrical activity of cells and tissue in the heart. However, to represent specific data, these models must be parameterized, and adjustment of the maximum conductances of the individual contributing ionic currents is a commonly used method. Here, we present a method for investigating the uniqueness of such resulting parameterizations. Our key question is: Can the maximum conductances of a model be changed without giving any appreciable changes in the action potential? If so, the model parameters are not unique and this poses a major problem in using the models to identify changes in parameters from data, for instance, to evaluate potential drug effects. We propose a method for evaluating this uniqueness, founded on the singular value decomposition of a matrix consisting of the individual ionic currents. Small singular values of this matrix signify lack of parameter uniqueness and we show that the conclusion from linear analysis of the matrix carries over to provide insight into the uniqueness of the parameters in the nonlinear case. Using numerical experiments, we quantify the identifiability of the maximum conductances of well-known models of the cardiac action potential. Furthermore, we show how the identifiability depends on the time step used in the observation of the currents, how the application of drugs may change identifiability, and, finally, how the stimulation protocol can be used to improve the identifiability of a model.},
	doi = {10.1063/1.5087629},
	url = {https://aip.scitation.org/doi/10.1063/1.5087629},
	author = {Karoline Horgmo {J{\ae}ger} and Wall, Samuel and Tveito, Aslak}
}
@article {Buccino_2019,
	title = {How does the presence of neural probes affect extracellular potentials?},
	journal = {Journal of Neural Engineering},
	volume = {16},
	number = {2},
	year = {2019},
	month = {feb},
	pages = {026030},
	publisher = {IOP} Publishing},
	abstract = {{Objective. Mechanistic modeling of neurons is an essential component of computational neuroscience that enables scientists to simulate, explain, and explore neural activity. The conventional approach to simulation of extracellular neural recordings first computes transmembrane currents using the cable equation and then sums their contribution to model the extracellular potential. This two-step approach relies on the assumption that the extracellular space is an infinite and homogeneous conductive medium, while measurements are performed using neural probes. The main purpose of this paper is to assess to what extent the presence of the neural probes of varying shape and size impacts the extracellular field and how to correct for them. Approach. We apply a detailed modeling framework allowing explicit representation of the neuron and the probe to study the effect of the probes and thereby estimate the effect of ignoring it. We use meshes with simplified neurons and different types of probe and compare the extracellular action potentials with and without the probe in the extracellular space. We then compare various solutions to account for the probes{\textquoteright} presence and introduce an efficient probe correction method to include the probe effect in modeling of extracellular potentials. Main results. Our computations show that microwires hardly influence the extracellular electric field and their effect can therefore be ignored. In contrast, multi-electrode arrays (MEAs) significantly affect the extracellular field by magnifying the recorded potential. While MEAs behave similarly to infinite insulated planes, we find that their effect strongly depends on the neuron-probe alignment and probe orientation. Significance. Ignoring the probe effect might be deleterious in some applications, such as neural localization and parameterization of neural models from extracellular recordings. Moreover, the presence of the probe can improve the interpretation of extracellular recordings, by providing a more accurate estimation of the extracellular potential generated by neuronal models.},
	doi = {10.1088/1741-2552/ab03a1},
	url = {https://doi.org/10.1088\%2F1741-2552\%2Fab03a1},
	author = {Alessio Paolo {Buccino} and Kuchta, Miroslav and Karoline Horgmo {J{\ae}ger} and Torbj{\o}rn Vefferstad {Ness} and Berthet, Pierre and Mardal, Kent-Andre and Cauwenberghs, Gert and Tveito, Aslak}
}
@inproceedings {27157,
	title = {Investigating the Pro- and Anti-Arrhythmic Properties of Human Induced Pluripotent Stem Cell-Derived Cardiomyocytes in Post-Infarction Patient Hearts: A Modeling Study},
	journal = {6th International Conference on Computational and Mathematical Biomedical Engineering},
	volume = {1},
	year = {2019},
	pages = {357-360},
	publisher = {Zeta Computational Resources Ltd.},
	issn = {2227-9385},
	author = {Arevalo, Hermenegild and Karoline Horgmo {J{\ae}ger} and Wall, Samuel}
}
@article {26640,
	title = {Properties of cardiac conduction in a cell-based computational model},
	journal = {PLoS Computational Biology},
	volume = {15},
	number = {e1007042},
	year = {2019},
	month = {05/2019},
	publisher = {Public Library of Science},
	abstract = {The conduction of electrical signals through cardiac tissue is essential for maintaining the function of the heart, and conduction abnormalities are known to potentially lead to life-threatening arrhythmias. The properties of cardiac conduction have therefore been the topic of intense study for decades, but a number of questions related to the mechanisms of conduction still remain unresolved. In this paper, we demonstrate how the so-called EMI model may be used to study some of these open questions. In the EMI model, the extracellular space, the cell membrane, the intracellular space and the cell connections are all represented as separate parts of the computational domain, and the model therefore allows for study of local properties that are hard to represent in the classical homogenized bidomain or monodomain models commonly used to study cardiac conduction. We conclude that a non-uniform sodium channel distribution increases the conduction velocity and decreases the time delays over gap junctions of reduced coupling in the EMI model simulations. We also present a theoretical optimal cell length with respect to conduction velocity and consider the possibility of ephaptic coupling (i.e. cell-to-cell coupling through the extracellular potential) acting as an alternative or supporting mechanism to gap junction coupling. We conclude that for a non-uniform distribution of sodium channels and a sufficiently small intercellular distance, ephaptic coupling can influence the dynamics of the sodium channels and potentially provide cell-to-cell coupling when the gap junction connection is absent.},
	doi = {10.1371/journal.pcbi.1007042},
	url = {https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1007042},
	author = {Karoline Horgmo {J{\ae}ger} and Andrew G {Edwards} and Andrew D. {McCulloch} and Tveito, Aslak}
}
@misc {26385,
	title = {In Silico - Augmented Cardiac Microphysiological Systems for Evaluating Cardiac Drug Effects},
	year = {2018},
	address = {BMES Conference, Atlanta, USA},
	author = {Wall, Samuel and Karoline Horgmo {J{\ae}ger} and Huebsch, Nathaniel and Charrez, B{\'e}r{\'e}nice and Healy, Kevin and Tveito, Aslak}
}
@misc {26386,
	title = {In Silico - Augmented Cardiac Microphysiological Systems for Evaluating Cardiac Drug Effects},
	year = {2018},
	address = {Keystone Organ on Chip Symposium, Montana, USA},
	author = {Wall, Samuel and Karoline Horgmo {J{\ae}ger} and Huebsch, Nathaniel and Charrez, B{\'e}r{\'e}nice and Healy, Kevin and Tveito, Aslak}
}
@misc {26383,
	title = {In Silico Modeling of Cardiac Microphysiological  Systems for Evaluating Drug Side Effects},
	howpublished = {Heart By Numbers Conference, Berlin, Germany},
	year = {2018},
	author = {Wall, Samuel and Tveito, Aslak and Karoline Horgmo {J{\ae}ger} and Andrew G {Edwards} and Healy, Kevin and Huebsch, Nathaniel and Charrez, B{\'e}r{\'e}nice}
}
@article {26238,
	title = {Inversion and computational maturation of drug response using human stem cell derived cardiomyocytes in microphysiological systems},
	journal = {Nature Scientific Reports },
	volume = {8},
	number = {17626},
	year = {2018},
	month = {12/2018},
	publisher = {Springer Nature},
	abstract = {While cardiomyocytes differentiated from human induced pluripotent stems cells (hiPSCs) hold great promise for drug screening, the electrophysiological properties of these cells can be variable and immature, producing results that are significantly different from their human adult counterparts. Here, we describe a computational framework to address this limitation, and show how in silico methods, applied to measurements on immature cardiomyocytes, can be used to both identify drug action and to predict its effect in mature cells. Our synthetic and experimental results indicate that optically obtained waveforms of voltage and calcium from microphysiological systems can be inverted into information on drug ion channel blockage, and then, through assuming functional invariance of proteins during maturation, this data can be used to predict drug induced changes in mature ventricular cells. Together, this pipeline of measurements and computational analysis could significantly improve the ability of hiPSC derived cardiomycocytes to predict dangerous drug side effects.},
	doi = {10.1038/s41598-018-35858-7},
	url = {https://doi.org/10.1038/s41598-018-35858-7},
	author = {Tveito, Aslak and Karoline Horgmo {J{\ae}ger} and Huebsch, Nathaniel and Charrez, B{\'e}r{\'e}nice and Andrew G {Edwards} and Wall, Samuel and Kevin E. {Healy}}
}
@article {25486,
	title = {A cell-based framework for numerical modelling of electrical conduction in cardiac tissue},
	journal = {Frontiers in Physics, Computational Physics},
	volume = {5},
	year = {2017},
	month = {10/2017},
	publisher = {Frontiers},
	doi = {https://doi.org/10.3389/fphy.2017.00048},
	url = {https://www.frontiersin.org/articles/10.3389/fphy.2017.00048/full?\&utm_source=Email_to_authors_\&utm_medium=Email\&utm_content=T1_11.5e1_author\&utm_campaign=Email_publication\&field=\&journalName=Frontiers_in_Physics\&id=289187},
	author = {Tveito, Aslak and Karoline Horgmo {J{\ae}ger} and Kuchta, Miroslav and Mardal, Kent-Andre and Marie E. {Rognes}}
}
@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}}
}
@mastersthesis {26643,
	title = {An Investigation of Necessary Grid Resolution for Numerical Simulations of Calcium Dynamics in Cardiac Cells},
	journal = {The University of Oslo},
	year = {2015},
	publisher = {Department of Mathematics, University of Oslo},
	abstract = {One of the challenges related to modelling calcium dynamics in cardiac cells is the large difference in the length scales involved. The dyad, where important processes take place, is very small compared to the whole cell. Therefore, resolutions fine enough to capture the details of what happens in the dyad result in huge computational problems for whole-cell simulations, and the exact choice of resolution has a substantial effect on the problem size.In this thesis, we investigate what grid resolution is necessary to capture the details of what happens in the dyad. We study simple mathematical models of calcium dynamics in the dyad and find analytical solutions to some of these simple models. Numerical simulations of the models are carried out for different resolutions using finite difference methods in 1D and 2D and a finite volume method in 3D. The accuracy of the numerical simulations is then studied by comparing the numerical solutions to analytical solutions and fine-grid numerical solutions, and the results suggest necessary resolutions in the nanometre range.},
	url = {https://www.duo.uio.no/handle/10852/45312},
	author = {Karoline Horgmo {J{\ae}ger}}
}
