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Jæger KH, Trotter JD, Cai X, Arevalo H, Tveito A. Evaluating computational efforts and physiological resolution of mathematical models of cardiac tissue. Sci Rep 2024; 14:16954. [PMID: 39043725 PMCID: PMC11266357 DOI: 10.1038/s41598-024-67431-w] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2024] [Accepted: 07/11/2024] [Indexed: 07/25/2024] Open
Abstract
Computational techniques have significantly advanced our understanding of cardiac electrophysiology, yet they have predominantly concentrated on averaged models that do not represent the intricate dynamics near individual cardiomyocytes. Recently, accurate models representing individual cells have gained popularity, enabling analysis of the electrophysiology at the micrometer level. Here, we evaluate five mathematical models to determine their computational efficiency and physiological fidelity. Our findings reveal that cell-based models introduced in recent literature offer both efficiency and precision for simulating small tissue samples (comprising thousands of cardiomyocytes). Conversely, the traditional bidomain model and its simplified counterpart, the monodomain model, are more appropriate for larger tissue masses (encompassing millions to billions of cardiomyocytes). For simulations requiring detailed parameter variations along individual cell membranes, the EMI model emerges as the only viable choice. This model distinctively accounts for the extracellular (E), membrane (M), and intracellular (I) spaces, providing a comprehensive framework for detailed studies. Nonetheless, the EMI model's applicability to large-scale tissues is limited by its substantial computational demands for subcellular resolution.
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Affiliation(s)
| | | | - Xing Cai
- Simula Research Laboratory, Oslo, Norway
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Grandits T, Augustin CM, Haase G, Jost N, Mirams GR, Niederer SA, Plank G, Varró A, Virág L, Jung A. Neural network emulation of the human ventricular cardiomyocyte action potential for more efficient computations in pharmacological studies. eLife 2024; 12:RP91911. [PMID: 38598284 PMCID: PMC11006416 DOI: 10.7554/elife.91911] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/11/2024] Open
Abstract
Computer models of the human ventricular cardiomyocyte action potential (AP) have reached a level of detail and maturity that has led to an increasing number of applications in the pharmaceutical sector. However, interfacing the models with experimental data can become a significant computational burden. To mitigate the computational burden, the present study introduces a neural network (NN) that emulates the AP for given maximum conductances of selected ion channels, pumps, and exchangers. Its applicability in pharmacological studies was tested on synthetic and experimental data. The NN emulator potentially enables massive speed-ups compared to regular simulations and the forward problem (find drugged AP for pharmacological parameters defined as scaling factors of control maximum conductances) on synthetic data could be solved with average root-mean-square errors (RMSE) of 0.47 mV in normal APs and of 14.5 mV in abnormal APs exhibiting early afterdepolarizations (72.5% of the emulated APs were alining with the abnormality, and the substantial majority of the remaining APs demonstrated pronounced proximity). This demonstrates not only very fast and mostly very accurate AP emulations but also the capability of accounting for discontinuities, a major advantage over existing emulation strategies. Furthermore, the inverse problem (find pharmacological parameters for control and drugged APs through optimization) on synthetic data could be solved with high accuracy shown by a maximum RMSE of 0.22 in the estimated pharmacological parameters. However, notable mismatches were observed between pharmacological parameters estimated from experimental data and distributions obtained from the Comprehensive in vitro Proarrhythmia Assay initiative. This reveals larger inaccuracies which can be attributed particularly to the fact that small tissue preparations were studied while the emulator was trained on single cardiomyocyte data. Overall, our study highlights the potential of NN emulators as powerful tool for an increased efficiency in future quantitative systems pharmacology studies.
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Affiliation(s)
- Thomas Grandits
- Department of Mathematics and Scientific Computing, University of GrazGrazAustria
- NAWI Graz, University of GrazGrazAustria
| | - Christoph M Augustin
- Gottfried Schatz Research Center for Cell Signaling, Metabolism and Aging - Division of Medical Physics and Biophysics, Medical University of GrazGrazAustria
- BioTechMed-GrazGrazAustria
| | - Gundolf Haase
- Department of Mathematics and Scientific Computing, University of GrazGrazAustria
| | - Norbert Jost
- Department of Pharmacology and Pharmacotherapy, University of SzegedSzegedHungary
- HUN-REN-TKI, Research Group of PharmacologyBudapestHungary
| | - Gary R Mirams
- Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of NottinghamNottinghamUnited Kingdom
| | - Steven A Niederer
- Division of Imaging Sciences & Biomedical Engineering, King’s College LondonLondonUnited Kingdom
| | - Gernot Plank
- Gottfried Schatz Research Center for Cell Signaling, Metabolism and Aging - Division of Medical Physics and Biophysics, Medical University of GrazGrazAustria
- BioTechMed-GrazGrazAustria
| | - András Varró
- Department of Pharmacology and Pharmacotherapy, University of SzegedSzegedHungary
- HUN-REN-TKI, Research Group of PharmacologyBudapestHungary
| | - László Virág
- Department of Pharmacology and Pharmacotherapy, University of SzegedSzegedHungary
| | - Alexander Jung
- Gottfried Schatz Research Center for Cell Signaling, Metabolism and Aging - Division of Medical Physics and Biophysics, Medical University of GrazGrazAustria
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Grandits T, Augustin CM, Haase G, Jost N, Mirams GR, Niederer SA, Plank G, Varró A, Virág L, Jung A. Neural network emulation of the human ventricular cardiomyocyte action potential: a tool for more efficient computation in pharmacological studies. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.08.16.553497. [PMID: 38234850 PMCID: PMC10793461 DOI: 10.1101/2023.08.16.553497] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/19/2024]
Abstract
Computer models of the human ventricular cardiomyocyte action potential (AP) have reached a level of detail and maturity that has led to an increasing number of applications in the pharmaceutical sector. However, interfacing the models with experimental data can become a significant computational burden. To mitigate the computational burden, the present study introduces a neural network (NN) that emulates the AP for given maximum conductances of selected ion channels, pumps, and exchangers. Its applicability in pharmacological studies was tested on synthetic and experimental data. The NN emulator potentially enables massive speed-ups compared to regular simulations and the forward problem (find drugged AP for pharmacological parameters defined as scaling factors of control maximum conductances) on synthetic data could be solved with average root-mean-square errors (RMSE) of 0.47mV in normal APs and of 14.5mV in abnormal APs exhibiting early afterdepolarizations (72.5% of the emulated APs were alining with the abnormality, and the substantial majority of the remaining APs demonstrated pronounced proximity). This demonstrates not only very fast and mostly very accurate AP emulations but also the capability of accounting for discontinuities, a major advantage over existing emulation strategies. Furthermore, the inverse problem (find pharmacological parameters for control and drugged APs through optimization) on synthetic data could be solved with high accuracy shown by a maximum RMSE of 0.21 in the estimated pharmacological parameters. However, notable mismatches were observed between pharmacological parameters estimated from experimental data and distributions obtained from the Comprehensive in vitro Proarrhythmia Assay initiative. This reveals larger inaccuracies which can be attributed particularly to the fact that small tissue preparations were studied while the emulator was trained on single cardiomyocyte data. Overall, our study highlights the potential of NN emulators as powerful tool for an increased efficiency in future quantitative systems pharmacology studies.
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Affiliation(s)
- Thomas Grandits
- Department of Mathematics and Scientific Computing, University of Graz
- NAWI Graz, University of Graz
| | - Christoph M Augustin
- Gottfried Schatz Research Center for Cell Signaling, Metabolism and Aging - Division of Medical Physics and Biophysics, Medical University of Graz
- BioTechMed-Graz
| | - Gundolf Haase
- Department of Mathematics and Scientific Computing, University of Graz
| | - Norbert Jost
- Department of Pharmacology and Pharmacotherapy, University of Szeged
- HUN-REN-TKI, Research Group of Pharmacology
| | - Gary R Mirams
- Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham
| | - Steven A Niederer
- Division of Imaging Sciences & Biomedical Engineering, King's College London
| | - Gernot Plank
- Gottfried Schatz Research Center for Cell Signaling, Metabolism and Aging - Division of Medical Physics and Biophysics, Medical University of Graz
- BioTechMed-Graz
| | - András Varró
- Department of Pharmacology and Pharmacotherapy, University of Szeged
- HUN-REN-TKI, Research Group of Pharmacology
| | - László Virág
- Department of Pharmacology and Pharmacotherapy, University of Szeged
| | - Alexander Jung
- Gottfried Schatz Research Center for Cell Signaling, Metabolism and Aging - Division of Medical Physics and Biophysics, Medical University of Graz
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Computational analysis of arrhythmogenesis in KCNH2 T618I mutation-associated short QT syndrome and the pharmacological effects of quinidine and sotalol. NPJ Syst Biol Appl 2022; 8:43. [PMCID: PMC9636227 DOI: 10.1038/s41540-022-00254-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2022] [Accepted: 10/18/2022] [Indexed: 11/06/2022] Open
Abstract
Short QT syndrome (SQTS) is a rare but dangerous genetic disease. In this research, we conducted a comprehensive in silico investigation into the arrhythmogenesis in KCNH2 T618I-associated SQTS using a multi-scale human ventricle model. A Markov chain model of IKr was developed firstly to reproduce the experimental observations. It was then incorporated into cell, tissue, and organ models to explore how the mutation provided substrates for ventricular arrhythmias. Using this T618I Markov model, we explicitly revealed the subcellular level functional alterations by T618I mutation, particularly the changes of ion channel states that are difficult to demonstrate in wet experiments. The following tissue and organ models also successfully reproduced the changed dynamics of reentrant spiral waves and impaired rate adaptions in hearts of T618I mutation. In terms of pharmacotherapy, we replicated the different effects of a drug under various conditions using identical mathematical descriptions for drugs. This study not only simulated the actions of an effective drug (quinidine) at various physiological levels, but also elucidated why the IKr inhibitor sotalol failed in SQT1 patients through profoundly analyzing its mutation-dependent actions.
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Mazola Y, Márquez Montesinos JCE, Ramírez D, Zúñiga L, Decher N, Ravens U, Yarov-Yarovoy V, González W. Common Structural Pattern for Flecainide Binding in Atrial-Selective Kv1.5 and Nav1.5 Channels: A Computational Approach. Pharmaceutics 2022; 14:pharmaceutics14071356. [PMID: 35890252 PMCID: PMC9318806 DOI: 10.3390/pharmaceutics14071356] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/14/2022] [Revised: 06/20/2022] [Accepted: 06/20/2022] [Indexed: 02/04/2023] Open
Abstract
Atrial fibrillation (AF) is the most common cardiac arrhythmia. Its treatment includes antiarrhythmic drugs (AADs) to modulate the function of cardiac ion channels. However, AADs have been limited by proarrhythmic effects, non-cardiovascular toxicities as well as often modest antiarrhythmic efficacy. Theoretical models showed that a combined blockade of Nav1.5 (and its current, INa) and Kv1.5 (and its current, IKur) ion channels yield a synergistic anti-arrhythmic effect without alterations in ventricles. We focused on Kv1.5 and Nav1.5 to search for structural similarities in their binding site (BS) for flecainide (a common blocker and widely prescribed AAD) as a first step for prospective rational multi-target directed ligand (MTDL) design strategies. We present a computational workflow for a flecainide BS comparison in a flecainide-Kv1.5 docking model and a solved structure of the flecainide-Nav1.5 complex. The workflow includes docking, molecular dynamics, BS characterization and pattern matching. We identified a common structural pattern in flecainide BS for these channels. The latter belongs to the central cavity and consists of a hydrophobic patch and a polar region, involving residues from the S6 helix and P-loop. Since the rational MTDL design for AF is still incipient, our findings could advance multi-target atrial-selective strategies for AF treatment.
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Affiliation(s)
- Yuliet Mazola
- Center for Bioinformatics, Simulation and Modeling (CBSM), Universidad de Talca, Talca 3460000, Chile; (Y.M.); (J.C.E.M.M.)
| | - José C. E. Márquez Montesinos
- Center for Bioinformatics, Simulation and Modeling (CBSM), Universidad de Talca, Talca 3460000, Chile; (Y.M.); (J.C.E.M.M.)
| | - David Ramírez
- Departamento de Farmacología, Facultad de Ciencias Biológicas, Universidad de Concepción, Concepción 4030000, Chile;
| | - Leandro Zúñiga
- Escuela de Medicina, Centro de Investigaciones Médicas, Universidad de Talca, Talca 3460000, Chile;
| | - Niels Decher
- Institute for Physiology and Pathophysiology, Vegetative Physiology, Philipps-University of Marburg, 35043 Marburg, Germany;
| | - Ursula Ravens
- Institut für Experimentelle Kardiovaskuläre Medizin, Universitäts-Herzzentrum Freiburg Bad Krotzingen, 79110 Freiburg im Breisgau, Germany;
| | - Vladimir Yarov-Yarovoy
- Department of Physiology and Membrane Biology, University of California, Davis, CA 95616, USA;
| | - Wendy González
- Center for Bioinformatics, Simulation and Modeling (CBSM), Universidad de Talca, Talca 3460000, Chile; (Y.M.); (J.C.E.M.M.)
- Millennium Nucleus of Ion Channels-Associated Diseases (MiNICAD), Talca 3530000, Chile
- Correspondence:
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Jæger KH, Edwards AG, Giles WR, Tveito A. Arrhythmogenic influence of mutations in a myocyte-based computational model of the pulmonary vein sleeve. Sci Rep 2022; 12:7040. [PMID: 35487957 PMCID: PMC9054808 DOI: 10.1038/s41598-022-11110-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2022] [Accepted: 04/12/2022] [Indexed: 11/09/2022] Open
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'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'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.
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Affiliation(s)
| | | | - Wayne R Giles
- Simula Research Laboratory, Oslo, Norway.,Department of Physiology and Pharmacology, Cumming School of Medicine, University of Calgary, Calgary, Canada
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