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Jaffery OA, Melki L, Slabaugh G, Good WW, Roney CH. A Review of Personalised Cardiac Computational Modelling Using Electroanatomical Mapping Data. Arrhythm Electrophysiol Rev 2024; 13:e08. [PMID: 38807744 PMCID: PMC11131150 DOI: 10.15420/aer.2023.25] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 10/11/2023] [Accepted: 12/27/2023] [Indexed: 05/30/2024] Open
Abstract
Computational models of cardiac electrophysiology have gradually matured during the past few decades and are now being personalised to provide patient-specific therapy guidance for improving suboptimal treatment outcomes. The predictive features of these personalised electrophysiology models hold the promise of providing optimal treatment planning, which is currently limited in the clinic owing to reliance on a population-based or average patient approach. The generation of a personalised electrophysiology model entails a sequence of steps for which a range of activation mapping, calibration methods and therapy simulation pipelines have been suggested. However, the optimal methods that can potentially constitute a clinically relevant in silico treatment are still being investigated and face limitations, such as uncertainty of electroanatomical data recordings, generation and calibration of models within clinical timelines and requirements to validate or benchmark the recovered tissue parameters. This paper is aimed at reporting techniques on the personalisation of cardiac computational models, with a focus on calibrating cardiac tissue conductivity based on electroanatomical mapping data.
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Affiliation(s)
- Ovais A Jaffery
- School of Engineering and Materials Science, Queen Mary University of London London, UK
| | - Lea Melki
- R&D Algorithms, Acutus Medical Carlsbad, CA, US
| | - Gregory Slabaugh
- Digital Environment Research Institute, Queen Mary University of London London, UK
| | | | - Caroline H Roney
- School of Engineering and Materials Science, Queen Mary University of London London, UK
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2
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Masè M, Cristoforetti A, Pelloni S, Ravelli F. Systematic in-silico evaluation of fibrosis effects on re-entrant wave dynamics in atrial tissue. Sci Rep 2024; 14:11427. [PMID: 38763959 DOI: 10.1038/s41598-024-62002-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2023] [Accepted: 05/13/2024] [Indexed: 05/21/2024] Open
Abstract
Despite the key role of fibrosis in atrial fibrillation (AF), the effects of different spatial distributions and textures of fibrosis on wave propagation mechanisms in AF are not fully understood. To clarify these aspects, we performed a systematic computational study to assess fibrosis effects on the characteristics and stability of re-entrant waves in electrically-remodelled atrial tissues. A stochastic algorithm, which generated fibrotic distributions with controlled overall amount, average size, and orientation of fibrosis elements, was implemented on a monolayer spheric atrial model. 245 simulations were run at changing fibrosis parameters. The emerging propagation patterns were quantified in terms of rate, regularity, and coupling by frequency-domain analysis of correspondent synthetic bipolar electrograms. At the increase of fibrosis amount, the rate of reentrant waves significantly decreased and higher levels of regularity and coupling were observed (p < 0.0001). Higher spatial variability and pattern stochasticity over repetitions was observed for larger amount of fibrosis, especially in the presence of patchy and compact fibrosis. Overall, propagation slowing and organization led to higher stability of re-entrant waves. These results strengthen the evidence that the amount and spatial distribution of fibrosis concur in dictating re-entry dynamics in remodeled tissue and represent key factors in AF maintenance.
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Affiliation(s)
- Michela Masè
- Laboratory of Biophysics and Translational Cardiology, Department of Cellular, Computational and Integrative Biology-CIBIO, University of Trento, Via Sommarive 18, 38123, Povo, Trento, Italy.
| | - Alessandro Cristoforetti
- Laboratory of Biophysics and Translational Cardiology, Department of Cellular, Computational and Integrative Biology-CIBIO, University of Trento, Via Sommarive 18, 38123, Povo, Trento, Italy
| | - Samuele Pelloni
- Laboratory of Biophysics and Translational Cardiology, Department of Cellular, Computational and Integrative Biology-CIBIO, University of Trento, Via Sommarive 18, 38123, Povo, Trento, Italy
| | - Flavia Ravelli
- Laboratory of Biophysics and Translational Cardiology, Department of Cellular, Computational and Integrative Biology-CIBIO, University of Trento, Via Sommarive 18, 38123, Povo, Trento, Italy
- CISMed-Centre for Medical Sciences, University of Trento, 38122, Trento, Italy
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3
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Tikhomirov R, Oakley RH, Anderson C, Xiang Y, Al-Othman S, Smith M, Yaar S, Torre E, Li J, Wilson LR, Goulding DR, Donaldson I, Harno E, Soattin L, Shiels HA, Morris GM, Zhang H, Boyett MR, Cidlowski JA, Mesirca P, Mangoni ME, D'Souza A. Cardiac GR Mediates the Diurnal Rhythm in Ventricular Arrhythmia Susceptibility. Circ Res 2024; 134:1306-1326. [PMID: 38533639 PMCID: PMC11081863 DOI: 10.1161/circresaha.123.323464] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 08/03/2023] [Revised: 02/15/2024] [Accepted: 03/13/2024] [Indexed: 03/28/2024]
Abstract
BACKGROUND Ventricular arrhythmias (VAs) demonstrate a prominent day-night rhythm, commonly presenting in the morning. Transcriptional rhythms in cardiac ion channels accompany this phenomenon, but their role in the morning vulnerability to VAs and the underlying mechanisms are not understood. We investigated the recruitment of transcription factors that underpins transcriptional rhythms in ion channels and assessed whether this mechanism was pertinent to the heart's intrinsic diurnal susceptibility to VA. METHODS AND RESULTS Assay for transposase-accessible chromatin with sequencing performed in mouse ventricular myocyte nuclei at the beginning of the animals' inactive (ZT0) and active (ZT12) periods revealed differentially accessible chromatin sites annotating to rhythmically transcribed ion channels and distinct transcription factor binding motifs in these regions. Notably, motif enrichment for the glucocorticoid receptor (GR; transcriptional effector of corticosteroid signaling) in open chromatin profiles at ZT12 was observed, in line with the well-recognized ZT12 peak in circulating corticosteroids. Molecular, electrophysiological, and in silico biophysically-detailed modeling approaches demonstrated GR-mediated transcriptional control of ion channels (including Scn5a underlying the cardiac Na+ current, Kcnh2 underlying the rapid delayed rectifier K+ current, and Gja1 responsible for electrical coupling) and their contribution to the day-night rhythm in the vulnerability to VA. Strikingly, both pharmacological block of GR and cardiomyocyte-specific genetic knockout of GR blunted or abolished ion channel expression rhythms and abolished the ZT12 susceptibility to pacing-induced VA in isolated hearts. CONCLUSIONS Our study registers a day-night rhythm in chromatin accessibility that accompanies diurnal cycles in ventricular myocytes. Our approaches directly implicate the cardiac GR in the myocyte excitability rhythm and mechanistically link the ZT12 surge in glucocorticoids to intrinsic VA propensity at this time.
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Affiliation(s)
- Roman Tikhomirov
- Division of Cardiovascular Sciences (R.T., C.A., S.A.O., M.S., S.Y., L.S., H.A.S., G.M.M., A.D.), The University of Manchester, United Kingdom
- Myocardial Function Section, National Heart and Lung Institute, Imperial College London, United Kingdom (R.T., M.S., A.D.)
| | - Robert H Oakley
- Signal Transduction Laboratory, National Institute of Environmental Health Sciences, National Institutes of Health (R.H.O., J.L., L.R.W., D.R.G., J.A.C.)
| | - Cali Anderson
- Division of Cardiovascular Sciences (R.T., C.A., S.A.O., M.S., S.Y., L.S., H.A.S., G.M.M., A.D.), The University of Manchester, United Kingdom
| | - Yirong Xiang
- Department of Physics and Astronomy (Y.X., H.Z.), The University of Manchester, United Kingdom
| | - Sami Al-Othman
- Division of Cardiovascular Sciences (R.T., C.A., S.A.O., M.S., S.Y., L.S., H.A.S., G.M.M., A.D.), The University of Manchester, United Kingdom
| | - Matthew Smith
- Division of Cardiovascular Sciences (R.T., C.A., S.A.O., M.S., S.Y., L.S., H.A.S., G.M.M., A.D.), The University of Manchester, United Kingdom
- Myocardial Function Section, National Heart and Lung Institute, Imperial College London, United Kingdom (R.T., M.S., A.D.)
| | - Sana Yaar
- Division of Cardiovascular Sciences (R.T., C.A., S.A.O., M.S., S.Y., L.S., H.A.S., G.M.M., A.D.), The University of Manchester, United Kingdom
| | - Eleonora Torre
- Institut de Génomique Fonctionnelle, Université de Montpellier, Centre National de la Recherche Scientifique (CNRS), Institut National de la Santé et de la Recherche Médicale (INSERM), F-34094 Montpellier France (E.T., P.M., M.E.M.)
| | - Jianying Li
- Signal Transduction Laboratory, National Institute of Environmental Health Sciences, National Institutes of Health (R.H.O., J.L., L.R.W., D.R.G., J.A.C.)
| | - Leslie R Wilson
- Signal Transduction Laboratory, National Institute of Environmental Health Sciences, National Institutes of Health (R.H.O., J.L., L.R.W., D.R.G., J.A.C.)
| | - David R Goulding
- Signal Transduction Laboratory, National Institute of Environmental Health Sciences, National Institutes of Health (R.H.O., J.L., L.R.W., D.R.G., J.A.C.)
| | - Ian Donaldson
- Bioinformatics Core Facility (I.D.), The University of Manchester, United Kingdom
| | - Erika Harno
- Division of Diabetes, Endocrinology and Gastroenterology (E.H.), The University of Manchester, United Kingdom
| | - Luca Soattin
- Division of Cardiovascular Sciences (R.T., C.A., S.A.O., M.S., S.Y., L.S., H.A.S., G.M.M., A.D.), The University of Manchester, United Kingdom
| | - Holly A Shiels
- Division of Cardiovascular Sciences (R.T., C.A., S.A.O., M.S., S.Y., L.S., H.A.S., G.M.M., A.D.), The University of Manchester, United Kingdom
| | - Gwilym M Morris
- Division of Cardiovascular Sciences (R.T., C.A., S.A.O., M.S., S.Y., L.S., H.A.S., G.M.M., A.D.), The University of Manchester, United Kingdom
- Department of Cardiology, John Hunter Hospital, Newcastle, NSW, Australia (G.M.M.)
| | - Henggui Zhang
- Department of Physics and Astronomy (Y.X., H.Z.), The University of Manchester, United Kingdom
| | - Mark R Boyett
- Faculty of Life Sciences, University of Bradford, United Kingdom (M.R.B.)
| | - John A Cidlowski
- Signal Transduction Laboratory, National Institute of Environmental Health Sciences, National Institutes of Health (R.H.O., J.L., L.R.W., D.R.G., J.A.C.)
| | - Pietro Mesirca
- Institut de Génomique Fonctionnelle, Université de Montpellier, Centre National de la Recherche Scientifique (CNRS), Institut National de la Santé et de la Recherche Médicale (INSERM), F-34094 Montpellier France (E.T., P.M., M.E.M.)
| | - Matteo E Mangoni
- Institut de Génomique Fonctionnelle, Université de Montpellier, Centre National de la Recherche Scientifique (CNRS), Institut National de la Santé et de la Recherche Médicale (INSERM), F-34094 Montpellier France (E.T., P.M., M.E.M.)
| | - Alicia D'Souza
- Division of Cardiovascular Sciences (R.T., C.A., S.A.O., M.S., S.Y., L.S., H.A.S., G.M.M., A.D.), The University of Manchester, United Kingdom
- Myocardial Function Section, National Heart and Lung Institute, Imperial College London, United Kingdom (R.T., M.S., A.D.)
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4
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Tyree TJ, Murphy P, Rappel WJ. Annihilation dynamics during spiral defect chaos revealed by particle models. CHAOS (WOODBURY, N.Y.) 2024; 34:053131. [PMID: 38787314 PMCID: PMC11141445 DOI: 10.1063/5.0203319] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/12/2024] [Accepted: 04/30/2024] [Indexed: 05/25/2024]
Abstract
Pair-annihilation events are ubiquitous in a variety of spatially extended systems and are often studied using computationally expensive simulations. Here, we develop an approach in which we simulate the pair-annihilation of spiral wave tips in cardiac models using a computationally efficient particle model. Spiral wave tips are represented as particles with dynamics governed by diffusive behavior and short-ranged attraction. The parameters for diffusion and attraction are obtained by comparing particle motion to the trajectories of spiral wave tips in cardiac models during spiral defect chaos. The particle model reproduces the annihilation rates of the cardiac models and can determine the statistics of spiral wave dynamics, including its mean termination time. We show that increasing the attraction coefficient sharply decreases the mean termination time, making it a possible target for pharmaceutical intervention.
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Affiliation(s)
- Timothy J. Tyree
- Department of Physics, University of California San Diego, San Diego, California 92093, USA
| | - Patrick Murphy
- Department of Mathematics and Statistics, San Jose State University, San Jose, California 95192, USA
| | - Wouter-Jan Rappel
- Department of Physics, University of California San Diego, San Diego, California 92093, USA
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5
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Angelaki E, Lazarides N, Barmparis GD, Kourakis I, Marketou ME, Tsironis GP. T-wave inversion through inhomogeneous voltage diffusion within the FK3V cardiac model. CHAOS (WOODBURY, N.Y.) 2024; 34:043140. [PMID: 38629790 DOI: 10.1063/5.0187655] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/15/2023] [Accepted: 03/30/2024] [Indexed: 04/19/2024]
Abstract
The heart beats are due to the synchronized contraction of cardiomyocytes triggered by a periodic sequence of electrical signals called action potentials, which originate in the sinoatrial node and spread through the heart's electrical system. A large body of work is devoted to modeling the propagation of the action potential and to reproducing reliably its shape and duration. Connection of computational modeling of cells to macroscopic phenomenological curves such as the electrocardiogram has been also intense, due to its clinical importance in analyzing cardiovascular diseases. In this work, we simulate the dynamics of action potential propagation using the three-variable Fenton-Karma model that can account for both normal and damaged cells through a the spatially inhomogeneous voltage diffusion coefficient. We monitor the action potential propagation in the cardiac tissue and calculate the pseudo-electrocardiogram that reproduces the R and T waves. The R-wave amplitude varies according to a double exponential law as a function of the (spatially homogeneous, for an isotropic tissue) diffusion coefficient. The addition of spatial inhomogeneity in the diffusion coefficient by means of a defected region representing damaged cardiac cells may result in T-wave inversion in the calculated pseudo-electrocardiogram. The transition from positive to negative polarity of the T-wave is analyzed as a function of the length and the depth of the defected region.
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Affiliation(s)
- E Angelaki
- Department of Physics, and Institute of Theoretical and Computational Physics, University of Crete, Heraklion 70013, Greece
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
| | - N Lazarides
- Department of Mathematics, Khalifa University of Science and Technology, P.O. Box 127788, Abu Dhabi, United Arab Emirates
| | - G D Barmparis
- Department of Physics, and Institute of Theoretical and Computational Physics, University of Crete, Heraklion 70013, Greece
| | - Ioannis Kourakis
- Department of Mathematics, Khalifa University of Science and Technology, P.O. Box 127788, Abu Dhabi, United Arab Emirates
| | - Maria E Marketou
- School of Medicine, University of Crete, Heraklion 71500, Greece
- Department of Cardiology, Heraklion University Hospital, Heraklion 71110, Greece
| | - G P Tsironis
- Department of Physics, and Institute of Theoretical and Computational Physics, University of Crete, Heraklion 70013, Greece
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
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6
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Kabus D, De Coster T, de Vries AAF, Pijnappels DA, Dierckx H. Fast creation of data-driven low-order predictive cardiac tissue excitation models from recorded activation patterns. Comput Biol Med 2024; 169:107949. [PMID: 38199206 DOI: 10.1016/j.compbiomed.2024.107949] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/20/2023] [Revised: 12/07/2023] [Accepted: 01/01/2024] [Indexed: 01/12/2024]
Abstract
Excitable systems give rise to important phenomena such as heat waves, epidemics and cardiac arrhythmias. Understanding, forecasting and controlling such systems requires reliable mathematical representations. For cardiac tissue, computational models are commonly generated in a reaction-diffusion framework based on detailed measurements of ionic currents in dedicated single-cell experiments. Here, we show that recorded movies at the tissue-level of stochastic pacing in a single variable are sufficient to generate a mathematical model. Via exponentially weighed moving averages, we create additional state variables, and use simple polynomial regression in the augmented state space to quantify excitation wave dynamics. A spatial gradient-sensing term replaces the classical diffusion as it is more robust to noise. Our pipeline for model creation is demonstrated for an in-silico model and optical voltage mapping recordings of cultured human atrial myocytes and only takes a few minutes. Our findings have the potential for widespread generation, use and on-the-fly refinement of personalised computer models for non-linear phenomena in biology and medicine, such as predictive cardiac digital twins.
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Affiliation(s)
- Desmond Kabus
- Department of Mathematics, KU Leuven Campus Kortrijk (KULAK), Etienne Sabbelaan 53, 8500, Kortrijk, Belgium; Laboratory of Experimental Cardiology, Leiden University Medical Center (LUMC), Albinusdreef 2, 2333 ZA, Leiden, The Netherlands
| | - Tim De Coster
- Laboratory of Experimental Cardiology, Leiden University Medical Center (LUMC), Albinusdreef 2, 2333 ZA, Leiden, The Netherlands
| | - Antoine A F de Vries
- Laboratory of Experimental Cardiology, Leiden University Medical Center (LUMC), Albinusdreef 2, 2333 ZA, Leiden, The Netherlands
| | - Daniël A Pijnappels
- Laboratory of Experimental Cardiology, Leiden University Medical Center (LUMC), Albinusdreef 2, 2333 ZA, Leiden, The Netherlands
| | - Hans Dierckx
- Department of Mathematics, KU Leuven Campus Kortrijk (KULAK), Etienne Sabbelaan 53, 8500, Kortrijk, Belgium.
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7
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Ni H, Grandi E. Computational Modeling of Cardiac Electrophysiology. Methods Mol Biol 2024; 2735:63-103. [PMID: 38038844 DOI: 10.1007/978-1-0716-3527-8_5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/02/2023]
Abstract
Mathematical modeling and simulation are well-established and powerful tools to integrate experimental data of individual components of cardiac electrophysiology, excitation-contraction coupling, and regulatory signaling pathways, to gain quantitative and mechanistic insight into pathophysiological processes and guide therapeutic strategies. Here, we briefly describe the processes governing cardiac myocyte electrophysiology and Ca2+ handling and their regulation, as well as action potential propagation in tissue. We discuss the models and methods used to describe these phenomena, including procedures for model parameterization and validation, in addition to protocols for model interrogation and analysis and techniques that account for phenotypic variability and parameter uncertainty. Our objective is to provide a summary of basic concepts and approaches as a resource for scientists training in this discipline and for all researchers aiming to gain an understanding of cardiac modeling studies.
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Affiliation(s)
- Haibo Ni
- Department of Pharmacology, University of California, Davis, CA, USA.
| | - Eleonora Grandi
- Department of Pharmacology, University of California, Davis, CA, USA.
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8
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Hu W, Zhang W, Zhang K, Al-Moubarak E, Zhang Y, Harmer SC, Hancox JC, Zhang H. Evaluating pro-arrhythmogenic effects of the T634S-hERG mutation: insights from a simulation study. Interface Focus 2023; 13:20230035. [PMID: 38106919 PMCID: PMC10722218 DOI: 10.1098/rsfs.2023.0035] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2023] [Accepted: 11/06/2023] [Indexed: 12/19/2023] Open
Abstract
A mutation to serine of a conserved threonine (T634S) in the hERG K+ channel S6 pore region has been identified as a variant of uncertain significance, showing a loss-of-function effect. However, its potential consequences for ventricular excitation and arrhythmogenesis have not been reported. This study evaluated possible functional effects of the T634S-hERG mutation on ventricular excitation and arrhythmogenesis by using multi-scale computer models of the human ventricle. A Markov chain model of the rapid delayed rectifier potassium current (IKr) was reconstructed for wild-type and T634S-hERG mutant conditions and incorporated into the ten Tusscher et al. models of human ventricles at cell and tissue (1D, 2D and 3D) levels. Possible functional impacts of the T634S-hERG mutation were evaluated by its effects on action potential durations (APDs) and their rate-dependence (APDr) at the cell level; and on the QT interval of pseudo-ECGs, tissue vulnerability to unidirectional conduction block (VW), spiral wave dynamics and repolarization dispersion at the tissue level. It was found that the T634S-hERG mutation prolonged cellular APDs, steepened APDr, prolonged the QT interval, increased VW, destablized re-entry and augmented repolarization dispersion across the ventricle. Collectively, these results imply potential pro-arrhythmic effects of the T634S-hERG mutation, consistent with LQT2.
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Affiliation(s)
- Wei Hu
- Biological Physics Group, Department of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK
| | - Wenfeng Zhang
- College of Computer and Information Science, Chongqing Normal University, Chongqing, People's Republic of China
| | - Kevin Zhang
- Southmead Hospital, North Bristol Trust, Bristol, UK
| | - Ehab Al-Moubarak
- School of Physiology, Pharmacology and Neuroscience, University of Bristol, Biomedical Sciences Building, University Walk, Bristol BS8 1TD, UK
| | - Yihong Zhang
- School of Physiology, Pharmacology and Neuroscience, University of Bristol, Biomedical Sciences Building, University Walk, Bristol BS8 1TD, UK
| | - Stephen C. Harmer
- School of Physiology, Pharmacology and Neuroscience, University of Bristol, Biomedical Sciences Building, University Walk, Bristol BS8 1TD, UK
| | - Jules C. Hancox
- Biological Physics Group, Department of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK
- School of Physiology, Pharmacology and Neuroscience, University of Bristol, Biomedical Sciences Building, University Walk, Bristol BS8 1TD, UK
| | - Henggui Zhang
- Biological Physics Group, Department of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK
- Key Laboratory of Medical Electrophysiology of Ministry of Education and Medical Electrophysiological Key Laboratory of Sichuan Province, Institute of Cardiovascular Research, Southwest Medical University, Luzhou 646000, People's Republic of China
- Beijing Academy of Artificial Intelligence, Beijing 100084, People's Republic of China
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9
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Cloet M, Arno L, Kabus D, Van der Veken J, Panfilov AV, Dierckx H. Scroll Waves and Filaments in Excitable Media of Higher Spatial Dimension. PHYSICAL REVIEW LETTERS 2023; 131:208401. [PMID: 38039450 DOI: 10.1103/physrevlett.131.208401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2023] [Accepted: 08/30/2023] [Indexed: 12/03/2023]
Abstract
Excitable media are ubiquitous in nature, and in such systems the local excitation tends to self-organize in traveling waves, or in rotating spiral-shaped patterns in two or three spatial dimensions. Examples include waves during a pandemic or electrical scroll waves in the heart. Here we show that such phenomena can be extended to a space of four or more dimensions and propose that connections of excitable elements in a network setting can be regarded as additional spatial dimensions. Numerical simulations are performed in four dimensions using the FitzHugh-Nagumo model, showing that the vortices rotate around a two-dimensional surface which we define as the superfilament. Evolution equations are derived for general superfilaments of codimension two in an N-dimensional space, and their equilibrium configurations are proven to be minimal surfaces. We suggest that biological excitable systems, such as the heart or brain which have nonlocal connections can be regarded, at least partially, as multidimensional excitable media and discuss further possible studies in this direction.
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Affiliation(s)
- Marie Cloet
- Department of Mathematics, KU Leuven Campus Kortrijk (KULAK), Kortrijk 8500, Belgium
- iSi Health, Institute of Physics-based Modeling for In Silico Health, KU Leuven, Leuven 3000, Belgium
| | - Louise Arno
- Department of Mathematics, KU Leuven Campus Kortrijk (KULAK), Kortrijk 8500, Belgium
- iSi Health, Institute of Physics-based Modeling for In Silico Health, KU Leuven, Leuven 3000, Belgium
| | - Desmond Kabus
- Department of Mathematics, KU Leuven Campus Kortrijk (KULAK), Kortrijk 8500, Belgium
- iSi Health, Institute of Physics-based Modeling for In Silico Health, KU Leuven, Leuven 3000, Belgium
- Laboratory of Experimental Cardiology, Leiden University Medical Center (LUMC), Leiden 2333 ZA, Netherlands
| | | | - Alexander V Panfilov
- Department of Physics and Astronomy, Ghent University, Ghent 9000, Belgium
- Laboratory of Computational Biology and Medicine, Ural Federal University, Ekaterinburg 620002, Russia
- World-Class Research Center "Digital biodesign and personalized healthcare," Sechenov University, Moscow 119991, Russia
| | - Hans Dierckx
- Department of Mathematics, KU Leuven Campus Kortrijk (KULAK), Kortrijk 8500, Belgium
- iSi Health, Institute of Physics-based Modeling for In Silico Health, KU Leuven, Leuven 3000, Belgium
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10
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Gray RA, Franz MR. Amiodarone prevents wave front-tail interactions in patients with heart failure: an in silico study. Am J Physiol Heart Circ Physiol 2023; 325:H952-H964. [PMID: 37656133 PMCID: PMC10907032 DOI: 10.1152/ajpheart.00227.2023] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 04/20/2023] [Revised: 08/25/2023] [Accepted: 08/25/2023] [Indexed: 09/02/2023]
Abstract
Amiodarone (AM) is an antiarrhythmic drug whose chronic use has proved effective in preventing ventricular arrhythmias in a variety of patient populations, including those with heart failure (HF). AM has both class III [i.e., it prolongs the action potential duration (APD) via blocking potassium channels) and class I (i.e., it affects the rapid sodium channel) properties; however, the specific mechanism(s) by which it prevents reentry formation in patients with HF remains unknown. We tested the hypothesis that AM prevents reentry induction in HF during programmed electrical stimulation (PES) via its ability to induce postrepolarization refractoriness (PRR) via its class I effects on sodium channels. Here we extend our previous human action potential model to represent the effects of both HF and AM separately by calibrating to human tissue and clinical PES data, respectively. We then combine these models (HF + AM) to test our hypothesis. Results from simulations in cells and cables suggest that AM acts to increase PRR and decrease the elevation of takeoff potential. The ability of AM to prevent reentry was studied in silico in two-dimensional sheets in which a variety of APD gradients (ΔAPD) were imposed. Reentrant activity was induced in all HF simulations but was prevented in 23 of 24 HF + AM models. Eliminating the AM-induced slowing of the recovery of inactivation of the sodium channel restored the ability to induce reentry. In conclusion, in silico testing suggests that chronic AM treatment prevents reentry induction in patients with HF during PES via its class I effect to induce PRR.NEW & NOTEWORTHY This work presents a new model of the action potential of the human, which reproduces the complex dynamics during premature stimulation in heart failure patients with and without amiodarone. A specific mechanism of the ability of amiodarone to prevent reentrant arrhythmias is presented.
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Affiliation(s)
- Richard A Gray
- Division of Biomedical Physics, Office of Science and Engineering Laboratories, Center for Devices and Radiological Health, Food and Drug Administration, Silver Spring, Maryland, United States
| | - Michael R Franz
- Cardiology Division, Veteran Affairs Medical Center, Washington, District of Columbia, United States
- Department of Pharmacology, Georgetown University Medical Center, Washington, District of Columbia, United States
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11
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Tsumoto K, Shimamoto T, Aoji Y, Himeno Y, Kuda Y, Tanida M, Amano A, Kurata Y. Theoretical prediction of early afterdepolarization-evoked triggered activity formation initiating ventricular reentrant arrhythmias. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2023; 240:107722. [PMID: 37515880 DOI: 10.1016/j.cmpb.2023.107722] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2023] [Revised: 07/02/2023] [Accepted: 07/14/2023] [Indexed: 07/31/2023]
Abstract
BACKGROUND AND OBJECTIVE Excessive prolongation of QT interval on ECGs in patients with congenital/acquired long QT syndrome and heart failure is a sign suggesting the development of early afterdepolarization (EAD), an abnormal repolarization in the action potential of ventricular cardiomyocytes. The development of EAD has been believed to be a trigger for fatal tachyarrhythmia, which can be a risk for sudden cardiac death. The role of EAD in triggering ventricular tachycardia (VT) remains unclear. The aim of this study was to elucidate the mechanism of EAD-induced triggered activity formation that leads to the VT such as Torsades de Pointes. METHODS We investigated the relationship between EAD and tachyarrhythmia initiation by constructing homogeneous myocardial sheet models consisting of the mid-myocardial cell version of a human ventricular myocyte model and performing simulations of excitation propagation. RESULTS A solitary island-like (clustering) occurrence of EADs in the homogeneous myocardial sheet could induce a focal excitation wave. However, reentrant excitation, an entity of tachyarrhythmia, was not able to be triggered regardless of the EAD cluster size when the focal excitation wave formed a repolarization potential difference boundary consisting of only a convex surface. The discontinuous distribution of multiple EAD clusters in the ventricular tissue formed a specific repolarization heterogeneity due to the repolarization potential difference, the shape of which depended on EAD cluster size and placed intervals. We found that the triggered activity was formed in such a manner that the repolarization potential difference boundary included a concave surface. CONCLUSIONS The formation of triggered activity that led to tachyarrhythmia required not only the occurrence of EAD onset-mediated focal excitation wave but also a repolarization heterogeneity-based specific repolarization potential difference boundary shape formed within the tissue.
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Affiliation(s)
- Kunichika Tsumoto
- Department of Physiology II, Kanazawa Medical University, Uchinada 920-0293, Japan.
| | - Takao Shimamoto
- Department of Bioinformatics, College of Life Sciences, Ritsumeikan University, Kusatsu 525-8577, Japan
| | - Yuma Aoji
- Department of Bioinformatics, College of Life Sciences, Ritsumeikan University, Kusatsu 525-8577, Japan
| | - Yukiko Himeno
- Department of Bioinformatics, College of Life Sciences, Ritsumeikan University, Kusatsu 525-8577, Japan
| | - Yuhichi Kuda
- Department of Physiology II, Kanazawa Medical University, Uchinada 920-0293, Japan
| | - Mamoru Tanida
- Department of Physiology II, Kanazawa Medical University, Uchinada 920-0293, Japan
| | - Akira Amano
- Department of Bioinformatics, College of Life Sciences, Ritsumeikan University, Kusatsu 525-8577, Japan
| | - Yasutaka Kurata
- Department of Physiology II, Kanazawa Medical University, Uchinada 920-0293, Japan.
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12
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Maciunas K, Snipas M, Kraujalis T, Kraujalienė L, Panfilov AV. The role of the Cx43/Cx45 gap junction voltage gating on wave propagation and arrhythmogenic activity in cardiac tissue. Sci Rep 2023; 13:14863. [PMID: 37684404 PMCID: PMC10491658 DOI: 10.1038/s41598-023-41796-w] [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] [Received: 03/25/2023] [Accepted: 08/31/2023] [Indexed: 09/10/2023] Open
Abstract
Gap junctions (GJs) formed of connexin (Cx) protein are the main conduits of electrical signals in the heart. Studies indicate that the transitional zone of the atrioventricular (AV) node contains heterotypic Cx43/Cx45 GJ channels which are highly sensitive to transjunctional voltage (Vj). To investigate the putative role of Vj gating of Cx43/Cx45 channels, we performed electrophysiological recordings in cell cultures and developed a novel mathematical/computational model which, for the first time, combines GJ channel Vj gating with a model of membrane excitability to simulate a spread of electrical pulses in 2D. Our simulation and electrophysiological data show that Vj transients during the spread of cardiac excitation can significantly affect the junctional conductance (gj) of Cx43/Cx45 GJs in a direction- and frequency-dependent manner. Subsequent simulation data indicate that such pulse-rate-dependent regulation of gj may have a physiological role in delaying impulse propagation through the AV node. We have also considered the putative role of the Cx43/Cx45 channel gating during pathological impulse propagation. Our simulation data show that Vj gating-induced changes in gj can cause the drift and subsequent termination of spiral waves of excitation. As a result, the development of fibrillation-like processes was significantly reduced in 2D clusters, which contained Vj-sensitive Cx43/Cx45 channels.
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Affiliation(s)
- Kestutis Maciunas
- Institute of Cardiology, Lithuanian University of Health Sciences, Kaunas, Lithuania
| | - Mindaugas Snipas
- Institute of Cardiology, Lithuanian University of Health Sciences, Kaunas, Lithuania.
- Department of Mathematical Modelling, Kaunas University of Technology, Kaunas, Lithuania.
| | - Tadas Kraujalis
- Institute of Cardiology, Lithuanian University of Health Sciences, Kaunas, Lithuania
- Department of Applied Informatics, Kaunas University of Technology, Kaunas, Lithuania
| | - Lina Kraujalienė
- Institute of Cardiology, Lithuanian University of Health Sciences, Kaunas, Lithuania
| | - Alexander V Panfilov
- Department of Physics and Astronomy, Ghent University, Ghent, Belgium
- Department of Cardiology, Leiden University Medical Center, Leiden, The Netherlands
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13
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Magtibay K, Massé S, Nanthakumar K, Umapathy K. Pro-arrhythmic role of adrenergic spatial densities in the human atria: An in-silico study. PLoS One 2023; 18:e0290676. [PMID: 37624832 PMCID: PMC10456151 DOI: 10.1371/journal.pone.0290676] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2023] [Accepted: 08/13/2023] [Indexed: 08/27/2023] Open
Abstract
Chronic stress among young patients (≤ 45 years old) could result in autonomic dysfunction. Autonomic dysfunction could be exhibited via sympathetic hyperactivity, sympathetic nerve sprouting, and diffuse adrenergic stimulation in the atria. Adrenergic spatial densities could alter atrial electrophysiology and increase arrhythmic susceptibility. Therefore, we examined the role of adrenergic spatial densities in creating arrhythmogenic substrates in silico. We simulated three 25 cm2 atrial sheets with varying adrenergic spatial densities (ASD), activation rates, and external transmembrane currents. We measured their effects on spatial and temporal heterogeneity of action potential durations (APD) at 50% and 20%. Increasing ASD shortens overall APD, and maximum spatial heterogeneity (31%) is achieved at 15% ASD. The addition of a few (5% to 10%) adrenergic elements decreases the excitation threshold, below 18 μA/cm2, while ASDs greater than 10% increase their excitation threshold up to 22 μA/cm2. Increase in ASD during rapid activation increases APD50 and APD20 by 21% and 41%, respectively. Activation times of captured beats during rapid activation could change by as much as 120 ms from the baseline cycle length. Rapidly activated atrial sheets with high ASDs significantly increase temporal heterogeneity of APD50 and APD20. Rapidly activated atrial sheets with 10% ASD have a high likelihood (0.7 ± 0.06) of fragmenting otherwise uniform wavefronts due to the transient inexcitability of adrenergically stimulated elements, producing an effective functional block. The likelihood of wave fragmentation due to ASD highly correlates with the spatial variations of APD20 (ρ = 0.90, p = 0.04). Our simulations provide a novel insight into the contributions of ASD to spatial and temporal heterogeneities of APDs, changes in excitation thresholds, and a potential explanation for wave fragmentation in the human atria due to sympathetic hyperactivity. Our work may aid in elucidating an electrophysiological link to arrhythmia initiation due to chronic stress among young patients.
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Affiliation(s)
- Karl Magtibay
- Biomedical Signal and Image Processing Laboratory, Faculty of Engineering and Architectural Science, Toronto Metropolitan University, Toronto, Ontario, Canada
| | - Stéphane Massé
- Toby Hull Cardiac Fibrillation Management Laboratory, Department of Medicine/Cardiology, Toronto General Hospital, University Health Network, Toronto, Ontario, Canada
| | - Kumaraswamy Nanthakumar
- Toby Hull Cardiac Fibrillation Management Laboratory, Department of Medicine/Cardiology, Toronto General Hospital, University Health Network, Toronto, Ontario, Canada
| | - Karthikeyan Umapathy
- Biomedical Signal and Image Processing Laboratory, Department of Electrical, Computer, and Biomedical Engineering, Faculty of Engineering and Architectural Science, Toronto Metropolitan University, Toronto, Ontario, Canada
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14
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Means SA, Roesler MW, Garrett AS, Cheng L, Clark AR. Steady-state approximations for Hodgkin-Huxley cell models: Reduction of order for uterine smooth muscle cell model. PLoS Comput Biol 2023; 19:e1011359. [PMID: 37647265 PMCID: PMC10468033 DOI: 10.1371/journal.pcbi.1011359] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2022] [Accepted: 07/14/2023] [Indexed: 09/01/2023] Open
Abstract
Multi-scale mathematical bioelectrical models of organs such as the uterus, stomach or heart present challenges both for accuracy and computational tractability. These multi-scale models are typically founded on models of biological cells derived from the classic Hodkgin-Huxley (HH) formalism. Ion channel behaviour is tracked with dynamical variables representing activation or inactivation of currents that relax to steady-state dependencies on cellular membrane voltage. Timescales for relaxation may be orders of magnitude faster than companion ion channel variables or phenomena of physiological interest for the entire cell (such as bursting sequences of action potentials) or the entire organ (such as electromechanical coordination). Exploiting these time scales with steady-state approximations for relatively fast-acting systems is a well-known but often overlooked approach as evidenced by recent published models. We thus investigate feasibility of an extensive reduction of order for an HH-type cell model with steady-state approximations to the full dynamical activation and inactivation ion channel variables. Our effort utilises a published comprehensive uterine smooth muscle cell model that encompasses 19 ordinary differential equations and 105 formulations overall. The numerous ion channel submodels in the published model exhibit relaxation times ranging from order 10-1 to 105 milliseconds. Substitution of the faster dynamic variables with steady-state formulations demonstrates both an accurate reproduction of the full model and substantial improvements in time-to-solve, for test cases performed. Our demonstration here of an effective and relatively straightforward reduction method underlines the particular importance of considering time scales for model simplification before embarking on large-scale computations or parameter sweeps. As a preliminary complement to more intensive reduction of order methods such as parameter sensitivity and bifurcation analysis, this approach can rapidly and accurately improve computational tractability for challenging multi-scale organ modelling efforts.
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Affiliation(s)
- Shawn A. Means
- Auckland Bioengineering Institute, University of Auckland, Auckland, New Zealand
| | - Mathias W. Roesler
- Auckland Bioengineering Institute, University of Auckland, Auckland, New Zealand
| | - Amy S. Garrett
- Auckland Bioengineering Institute, University of Auckland, Auckland, New Zealand
| | - Leo Cheng
- Auckland Bioengineering Institute, University of Auckland, Auckland, New Zealand
| | - Alys R. Clark
- Auckland Bioengineering Institute, University of Auckland, Auckland, New Zealand
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15
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Leenknegt L, Panfilov AV, Dierckx H. Impact of electrode orientation, myocardial wall thickness, and myofiber direction on intracardiac electrograms: numerical modeling and analytical solutions. Front Physiol 2023; 14:1213218. [PMID: 37492643 PMCID: PMC10364610 DOI: 10.3389/fphys.2023.1213218] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2023] [Accepted: 06/14/2023] [Indexed: 07/27/2023] Open
Abstract
Intracardiac electrograms (iEGMs) are time traces of the electrical potential recorded close to the heart muscle. We calculate unipolar and bipolar iEGMs analytically for a myocardial slab with parallel myofibers and validate them against numerical bidomain simulations. The analytical solution obtained via the method of mirrors is an infinite series of arctangents. It goes beyond the solid angle theory and is in good agreement with the simulations, even though bath loading effects were not accounted for in the analytical calculation. At a large distance from the myocardium, iEGMs decay as 1/R (unipolar), 1/R 2 (bipolar and parallel), and 1/R 3 (bipolar and perpendicular to the endocardium). At the endocardial surface, there is a mathematical branch cut. Here, we show how a thicker myocardium generates iEGMs with larger amplitudes and how anisotropy affects the iEGM width and amplitude. If only the leading-order term of our expansion is retained, it can be determined how the conductivities of the bath, torso, myocardium, and myofiber direction together determine the iEGM amplitude. Our results will be useful in the quantitative interpretation of iEGMs, the selection of thresholds to characterize viable tissues, and for future inferences of tissue parameters.
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Affiliation(s)
- Lore Leenknegt
- Department of Mathematics, KU Leuven Campus KULAK, KU Leuven, Kortrijk, Belgium
- iSi Health–KU Leuven Institute of Physics-based Modeling for In Silico Health, KU Leuven, Leuven, Belgium
| | | | - Hans Dierckx
- Department of Mathematics, KU Leuven Campus KULAK, KU Leuven, Kortrijk, Belgium
- iSi Health–KU Leuven Institute of Physics-based Modeling for In Silico Health, KU Leuven, Leuven, Belgium
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16
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Kervadec A, Kezos J, Ni H, Yu M, Marchant J, Spiering S, Kannan S, Kwon C, Andersen P, Bodmer R, Grandi E, Ocorr K, Colas AR. Multiplatform modeling of atrial fibrillation identifies phospholamban as a central regulator of cardiac rhythm. Dis Model Mech 2023; 16:dmm049962. [PMID: 37293707 PMCID: PMC10387351 DOI: 10.1242/dmm.049962] [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] [Received: 10/25/2022] [Accepted: 05/26/2023] [Indexed: 06/10/2023] Open
Abstract
Atrial fibrillation (AF) is a common and genetically inheritable form of cardiac arrhythmia; however, it is currently not known how these genetic predispositions contribute to the initiation and/or maintenance of AF-associated phenotypes. One major barrier to progress is the lack of experimental systems to investigate the effects of gene function on rhythm parameters in models with human atrial and whole-organ relevance. Here, we assembled a multi-model platform enabling high-throughput characterization of the effects of gene function on action potential duration and rhythm parameters using human induced pluripotent stem cell-derived atrial-like cardiomyocytes and a Drosophila heart model, and validation of the findings using computational models of human adult atrial myocytes and tissue. As proof of concept, we screened 20 AF-associated genes and identified phospholamban loss of function as a top conserved hit that shortens action potential duration and increases the incidence of arrhythmia phenotypes upon stress. Mechanistically, our study reveals that phospholamban regulates rhythm homeostasis by functionally interacting with L-type Ca2+ channels and NCX. In summary, our study illustrates how a multi-model system approach paves the way for the discovery and molecular delineation of gene regulatory networks controlling atrial rhythm with application to AF.
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Affiliation(s)
- Anaïs Kervadec
- Sanford Burnham Prebys Medical Discovery Institute, La Jolla, CA 92037, USA
| | - James Kezos
- Sanford Burnham Prebys Medical Discovery Institute, La Jolla, CA 92037, USA
| | - Haibo Ni
- Department of Pharmacology, UC Davis, Davis, CA 95616, USA
| | - Michael Yu
- Sanford Burnham Prebys Medical Discovery Institute, La Jolla, CA 92037, USA
| | - James Marchant
- Sanford Burnham Prebys Medical Discovery Institute, La Jolla, CA 92037, USA
| | - Sean Spiering
- Sanford Burnham Prebys Medical Discovery Institute, La Jolla, CA 92037, USA
| | - Suraj Kannan
- Johns Hopkins University, Baltimore, MD 21205, USA
| | - Chulan Kwon
- Johns Hopkins University, Baltimore, MD 21205, USA
| | | | - Rolf Bodmer
- Sanford Burnham Prebys Medical Discovery Institute, La Jolla, CA 92037, USA
| | | | - Karen Ocorr
- Sanford Burnham Prebys Medical Discovery Institute, La Jolla, CA 92037, USA
| | - Alexandre R. Colas
- Sanford Burnham Prebys Medical Discovery Institute, La Jolla, CA 92037, USA
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17
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Alrabghi G, Liu Y, Hu W, Hancox JC, Zhang H. Human atrial fibrillation and genetic defects in transient outward currents: mechanistic insights from multi-scale computational models. Philos Trans R Soc Lond B Biol Sci 2023; 378:20220166. [PMID: 37122220 PMCID: PMC10150223 DOI: 10.1098/rstb.2022.0166] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/02/2023] Open
Abstract
Previous studies have linked dysfunctional Ito arising from mutations to KCND3-encoded Kv4.3 and KCND2-encoded Kv4.2 to atrial fibrillation. Using computational models, this study aimed to investigate the mechanisms underlying pro-arrhythmic effects of the gain-of-function Kv4.3 (T361S, A545P) and Kv4.2 (S447R) mutations. Wild-type and mutant Ito formulations were developed from and validated against experimental data and incorporated into the Colman et al. model of human atrial cells. Single-cell models were incorporated into one- (1D) and two-dimensional (2D) models of atrial tissue, and a three-dimensional (3D) realistic model of the human atria. The three gain-of-function mutations had similar, albeit quantitatively different, effects: shortening of the action potential duration; lowering the plateau membrane potential, abbreviating the effective refractory period (ERP) and the wavelength (WL) of atrial excitation at the tissue level. Restitution curves for the WL, the ERP and the conduction velocity were leftward shifted, facilitating the conduction of atrial excitation waves at high excitation rates. The mutations also increased lifespan and stationarity of re-entry in both 2D and 3D simulations, which further highlighted a mutation-induced increase in spatial dispersion of repolarization. Collectively, these changes account for pro-arrhythmic effects of these Kv4.3 and Kv4.2 mutations in facilitating AF. This article is part of the theme issue 'The heartbeat: its molecular basis and physiological mechanisms'.
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Affiliation(s)
- Ghadah Alrabghi
- Biological Physics Group, Department of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK
- Department of Physics, Faculty of Science, University of Jeddah, 21959 Jeddah, Saudi Arabia
| | - Yizhou Liu
- Biological Physics Group, Department of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK
| | - Wei Hu
- Biological Physics Group, Department of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK
| | - Jules C Hancox
- Biological Physics Group, Department of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK
- School of Physiology, Pharmacology and Neuroscience, Medical Sciences Building, University Walk, Bristol BS8 1TD, UK
| | - Henggui Zhang
- Biological Physics Group, Department of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK
- Key Laboratory of Medical Electrophysiology of Ministry of Education and Medical Electrophysiological Key Laboratory of Sichuan Province, Institute of Cardiovascular Research, Southwest Medical University, 646099 Luzhou, People's Republic of China
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18
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Scuderi M, Dermol-Černe J, Batista Napotnik T, Chaigne S, Bernus O, Benoist D, Sigg DC, Rems L, Miklavčič D. Characterization of Experimentally Observed Complex Interplay between Pulse Duration, Electrical Field Strength, and Cell Orientation on Electroporation Outcome Using a Time-Dependent Nonlinear Numerical Model. Biomolecules 2023; 13:727. [PMID: 37238597 PMCID: PMC10216437 DOI: 10.3390/biom13050727] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2023] [Revised: 04/17/2023] [Accepted: 04/18/2023] [Indexed: 05/28/2023] Open
Abstract
Electroporation is a biophysical phenomenon involving an increase in cell membrane permeability to molecules after a high-pulsed electric field is applied to the tissue. Currently, electroporation is being developed for non-thermal ablation of cardiac tissue to treat arrhythmias. Cardiomyocytes have been shown to be more affected by electroporation when oriented with their long axis parallel to the applied electric field. However, recent studies demonstrate that the preferentially affected orientation depends on the pulse parameters. To gain better insight into the influence of cell orientation on electroporation with different pulse parameters, we developed a time-dependent nonlinear numerical model where we calculated the induced transmembrane voltage and pores creation in the membrane due to electroporation. The numerical results show that the onset of electroporation is observed at lower electric field strengths for cells oriented parallel to the electric field for pulse durations ≥10 µs, and cells oriented perpendicular for pulse durations ~100 ns. For pulses of ~1 µs duration, electroporation is not very sensitive to cell orientation. Interestingly, as the electric field strength increases beyond the onset of electroporation, perpendicular cells become more affected irrespective of pulse duration. The results obtained using the developed time-dependent nonlinear model are corroborated by in vitro experimental measurements. Our study will contribute to the process of further development and optimization of pulsed-field ablation and gene therapy in cardiac treatments.
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Affiliation(s)
- Maria Scuderi
- Faculty of Electrical Engineering, University of Ljubljana, SI-1000 Ljubljana, Slovenia
| | - Janja Dermol-Černe
- Faculty of Electrical Engineering, University of Ljubljana, SI-1000 Ljubljana, Slovenia
| | - Tina Batista Napotnik
- Faculty of Electrical Engineering, University of Ljubljana, SI-1000 Ljubljana, Slovenia
| | - Sebastien Chaigne
- INSERM, CRCTB, U 1045, IHU Liryc, University of Bordeaux, F-33000 Bordeaux, France
| | - Olivier Bernus
- INSERM, CRCTB, U 1045, IHU Liryc, University of Bordeaux, F-33000 Bordeaux, France
| | - David Benoist
- INSERM, CRCTB, U 1045, IHU Liryc, University of Bordeaux, F-33000 Bordeaux, France
| | - Daniel C. Sigg
- Medtronic, Cardiac Ablation Solutions, Minneapolis, MN 55105, USA
| | - Lea Rems
- Faculty of Electrical Engineering, University of Ljubljana, SI-1000 Ljubljana, Slovenia
| | - Damijan Miklavčič
- Faculty of Electrical Engineering, University of Ljubljana, SI-1000 Ljubljana, Slovenia
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19
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Fassina D, M Costa C, Bishop M, Plank G, Whitaker J, Harding SE, Niederer SA. Assessing the arrhythmogenic risk of engineered heart tissue patches through in silico application on infarcted ventricle models. Comput Biol Med 2023; 154:106550. [PMID: 36701966 DOI: 10.1016/j.compbiomed.2023.106550] [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] [Received: 06/07/2022] [Revised: 01/02/2023] [Accepted: 01/11/2023] [Indexed: 01/15/2023]
Abstract
BACKGROUND Post myocardial infarction (MI) ventricles contain fibrotic tissue and may have disrupted electrical properties, both of which predispose to an increased risk of life-threatening arrhythmias. Application of epicardial patches obtained from human-induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) are a potential long-term therapy to treat heart failure resulting from post MI remodelling. However, whether the introduction of these patches is anti- or pro-arrhythmic has not been studied. METHODS We studied arrhythmic risk using in silico engineered heart tissue (EHT) patch engraftment on human post-MI ventricular models. Two patient models were studied, including one with a large dense scar and one with an apparent channel of preserved viability bordered on both sides by scar. In each heart model a virtual EHT patch was introduced as a layer of viable tissue overlying the scarred area, with hiPSC-CMs electrophysiological properties. The incidence of re-entrant and sustained activation in simulations with and without EHT patches was assessed and the arrhythmia inducibility compared in the context of different EHT patch properties (conduction velocity (CV) and action potential duration (APD)). The impact of the EHT patch on the likelihood of focal ectopic impulse propagation was estimated by assessing the minimum stimulus strength and duration required to generate a propagating impulse in the scar border zone (BZ) with and without patch. RESULTS We uncovered two main mechanisms by which ventricular tachycardia (VT) risk could be either augmented or attenuated by the interaction of the patch with the tissue. In the case of isthmus-related VT, our simulations predict that EHT patches can prevent the induction of VT when the, generally longer, hiPSC-CMs APD is reduced towards more physiological values. In the case of large dense scar, we found that, an EHT patch with CV similar to the host myocardium does not promote VT, while EHT patches with lower CV increase the risk of VT, by promoting both non-sustained and sustained re-entry. Finally, our simulations indicate that electrically coupled EHT patches reduce the likelihood of propagation of focal ectopic impulses. CONCLUSIONS The introduction of EHT patches as a treatment for heart failure has the potential to augment or attenuate the risk of ventricular arrhythmias, and variations in the anatomic configuration of the substrate, the functional properties of the BZ and the electrophysiologic properties of the patch itself will determine the overall impact. Planning for delivery of this therapy will need to consider the possible impact on arrhythmia.
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Affiliation(s)
- Damiano Fassina
- School of Biomedical Engineering and Imaging Sciences, King's College London, London, UK; National Heart and Lung Institute, Imperial College London, London, UK.
| | - Caroline M Costa
- School of Biomedical Engineering and Imaging Sciences, King's College London, London, UK
| | - Martin Bishop
- School of Biomedical Engineering and Imaging Sciences, King's College London, London, UK
| | | | | | - Sian E Harding
- National Heart and Lung Institute, Imperial College London, London, UK
| | - Steven A Niederer
- School of Biomedical Engineering and Imaging Sciences, King's College London, London, UK
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20
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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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21
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Galappaththige S, Gray RA, Costa CM, Niederer S, Pathmanathan P. Credibility assessment of patient-specific computational modeling using patient-specific cardiac modeling as an exemplar. PLoS Comput Biol 2022; 18:e1010541. [PMID: 36215228 PMCID: PMC9550052 DOI: 10.1371/journal.pcbi.1010541] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/21/2022] [Accepted: 09/02/2022] [Indexed: 11/07/2022] Open
Abstract
Reliable and robust simulation of individual patients using patient-specific models (PSMs) is one of the next frontiers for modeling and simulation (M&S) in healthcare. PSMs, which form the basis of digital twins, can be employed as clinical tools to, for example, assess disease state, predict response to therapy, or optimize therapy. They may also be used to construct virtual cohorts of patients, for in silico evaluation of medical product safety and/or performance. Methods and frameworks have recently been proposed for evaluating the credibility of M&S in healthcare applications. However, such efforts have generally been motivated by models of medical devices or generic patient models; how best to evaluate the credibility of PSMs has largely been unexplored. The aim of this paper is to understand and demonstrate the credibility assessment process for PSMs using patient-specific cardiac electrophysiological (EP) modeling as an exemplar. We first review approaches used to generate cardiac PSMs and consider how verification, validation, and uncertainty quantification (VVUQ) apply to cardiac PSMs. Next, we execute two simulation studies using a publicly available virtual cohort of 24 patient-specific ventricular models, the first a multi-patient verification study, the second investigating the impact of uncertainty in personalized and non-personalized inputs in a virtual cohort. We then use the findings from our analyses to identify how important characteristics of PSMs can be considered when assessing credibility with the approach of the ASME V&V40 Standard, accounting for PSM concepts such as inter- and intra-user variability, multi-patient and “every-patient” error estimation, uncertainty quantification in personalized vs non-personalized inputs, clinical validation, and others. The results of this paper will be useful to developers of cardiac and other medical image based PSMs, when assessing PSM credibility. Patient-specific models are computational models that have been personalized using data from a patient. After decades of research, recent computational, data science and healthcare advances have opened the door to the fulfilment of the enormous potential of such models, from truly personalized medicine to efficient and cost-effective testing of new medical products. However, reliability (credibility) of patient-specific models is key to their success, and there are currently no general guidelines for evaluating credibility of patient-specific models. Here, we consider how frameworks and model evaluation activities that have been developed for generic (not patient-specific) computational models, can be extended to patient specific models. We achieve this through a detailed analysis of the activities required to evaluate cardiac electrophysiological models, chosen as an exemplar field due to its maturity and the complexity of such models. This is the first paper on the topic of reliability of patient-specific models and will help pave the way to reliable and trusted patient-specific modeling across healthcare applications.
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Affiliation(s)
- Suran Galappaththige
- Center for Devices and Radiological Health, US Food and Drug Administration, Silver Spring, Maryland, United States of America
| | - Richard A. Gray
- Center for Devices and Radiological Health, US Food and Drug Administration, Silver Spring, Maryland, United States of America
| | - Caroline Mendonca Costa
- School of Biomedical Engineering & Imaging Sciences, King’s College London, London, United Kingdom
| | - Steven Niederer
- School of Biomedical Engineering & Imaging Sciences, King’s College London, London, United Kingdom
| | - Pras Pathmanathan
- Center for Devices and Radiological Health, US Food and Drug Administration, Silver Spring, Maryland, United States of America
- * E-mail:
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22
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Calibrating cardiac electrophysiology models using latent Gaussian processes on atrial manifolds. Sci Rep 2022; 12:16572. [PMID: 36195766 PMCID: PMC9532401 DOI: 10.1038/s41598-022-20745-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2022] [Accepted: 09/19/2022] [Indexed: 11/24/2022] Open
Abstract
Models of electrical excitation and recovery in the heart have become increasingly detailed, but have yet to be used routinely in the clinical setting to guide personalized intervention in patients. One of the main challenges is calibrating models from the limited measurements that can be made in a patient during a standard clinical procedure. In this work, we propose a novel framework for the probabilistic calibration of electrophysiology parameters on the left atrium of the heart using local measurements of cardiac excitability. Parameter fields are represented as Gaussian processes on manifolds and are linked to measurements via surrogate functions that map from local parameter values to measurements. The posterior distribution of parameter fields is then obtained. We show that our method can recover parameter fields used to generate localised synthetic measurements of effective refractory period. Our methodology is applicable to other measurement types collected with clinical protocols, and more generally for calibration where model parameters vary over a manifold.
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23
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Que W, Han C, Zhao X, Shi L. An ECG generative model of myocardial infarction. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2022; 225:107062. [PMID: 35994870 DOI: 10.1016/j.cmpb.2022.107062] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/21/2022] [Revised: 08/02/2022] [Accepted: 08/06/2022] [Indexed: 06/15/2023]
Abstract
Background and Objective Computer-aided diagnosis (CAD) of Myocardial Infarction (MI) using machine learning depends on a large amount of clinical Electrocardiogram (ECG) data. Existing infarct ECG databases face the problem of class imbalance. Data augmentation using generative simulation models is a new approach to effectively address this problem. Methods A multiscale ECG generative model was established for ECG data augmentation. In the cellular layer, an ischemic Action Potential (AP) model was established to generate APs in cardiomyocytes with different transmural regions of infraction or different ischemic durations. In the tissue layer, a probability-driven cellular automata excitation propagation model was established to simulate the propagation speed and direction of excitation. An infarct tissue model and a coronary artery model were established to describe the spatiotemporal diversity of MI. A ventricle model, a human torso model, and a computational model of surface ECG based on field source theory were established in the heart-torso layer. Results The model generated pathological 12-lead ECGs of MI with different topography and different extent. When simulating different ventricular wall infarction, the lesions appear in the same leads as the clinical 12-lead ECG. The ST-segment decreases and the T-wave amplitude decreases, similar to the clinical ECG features when simulating subendocardial ischemia. The average fidelity of the 12-lead ECG the model generated is 95.6%, according to the designed DTW-GRA distance algorithm. Conclusions The generative model considers the electrophysiological properties of the natural heart, the pathology of myocardial infarction, and the diversity of clinical ECGs. The model can provide many reliable samples for machine learning of MI.
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Affiliation(s)
- Wenge Que
- Department of Automation, Tsinghua University, Beijing 100084, China.
| | - Chuang Han
- School of Computer and Communication Engineering, Zhengzhou University of Light Industry, Zhengzhou 450000, China
| | - Xiliang Zhao
- Center for Coronary Artery Disease, Division of Cardiology, Beijing Anzhen Hospital, Capital Medical University, Beijing 100029, China.
| | - Li Shi
- Department of Automation, Tsinghua University, Beijing 100084, China; Beijing National Research Center for Information Science and Technology, Beijing 100084, China.
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24
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Kabus D, Arno L, Leenknegt L, Panfilov AV, Dierckx H. Numerical methods for the detection of phase defect structures in excitable media. PLoS One 2022; 17:e0271351. [PMID: 35819963 PMCID: PMC9275727 DOI: 10.1371/journal.pone.0271351] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2022] [Accepted: 06/12/2022] [Indexed: 11/19/2022] Open
Abstract
Electrical waves that rotate in the heart organize dangerous cardiac arrhythmias. Finding the region around which such rotation occurs is one of the most important practical questions for arrhythmia management. For many years, the main method for finding such regions was so-called phase mapping, in which a continuous phase was assigned to points in the heart based on their excitation status and defining the rotation region as a point of phase singularity. Recent analysis, however, showed that in many rotation regimes there exist phase discontinuities and the region of rotation must be defined not as a point of phase singularity, but as a phase defect line. In this paper, we use this novel methodology and perform a comparative study of three different phase definitions applied to in silico data and to experimental data obtained from optical voltage mapping experiments on monolayers of human atrial myocytes. We introduce new phase defect detection algorithms and compare them with those that appeared in literature already. We find that the phase definition is more important than the algorithm to identify sudden spatial phase variations. Sharp phase defect lines can be obtained from a phase derived from local activation times observed during one cycle of arrhythmia. Alternatively, similar quality can be obtained from a reparameterization of the classical phase obtained from observation of a single timeframe of transmembrane potential. We found that the phase defect line length was (35.9 ± 6.2)mm in the Fenton-Karma model and (4.01 ± 0.55)mm in cardiac human atrial myocyte monolayers. As local activation times are obtained during standard clinical cardiac mapping, the methods are also suitable to be applied to clinical datasets. All studied methods are publicly available and can be downloaded from an institutional web-server.
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Affiliation(s)
- Desmond Kabus
- Department of Mathematics, KU Leuven Campus Kortrijk (KULAK), Kortrijk, Belgium
- Laboratory of Experimental Cardiology, Leiden University Medical Center (LUMC), Leiden, The Netherlands
- iSi Health, Institute of Physics-based Modeling for In Silico Health, KU Leuven, Leuven, Belgium
| | - Louise Arno
- Department of Mathematics, KU Leuven Campus Kortrijk (KULAK), Kortrijk, Belgium
- iSi Health, Institute of Physics-based Modeling for In Silico Health, KU Leuven, Leuven, Belgium
| | - Lore Leenknegt
- Department of Mathematics, KU Leuven Campus Kortrijk (KULAK), Kortrijk, Belgium
- iSi Health, Institute of Physics-based Modeling for In Silico Health, KU Leuven, Leuven, Belgium
| | - Alexander V. Panfilov
- Department of Physics and Astronomy, Ghent University, Ghent, Belgium
- Laboratory of Computational Biology and Medicine, Ural Federal University, Ekaterinburg, Russia
- World-Class Research Center “Digital biodesign and personalized healthcare”, Sechenov University, Moscow, Russia
| | - Hans Dierckx
- Department of Mathematics, KU Leuven Campus Kortrijk (KULAK), Kortrijk, Belgium
- iSi Health, Institute of Physics-based Modeling for In Silico Health, KU Leuven, Leuven, Belgium
- * E-mail:
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25
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Hustad KG, Cai X. Resource-Efficient Use of Modern Processor Architectures For Numerically Solving Cardiac Ionic Cell Models. Front Physiol 2022; 13:904648. [PMID: 35923230 PMCID: PMC9342677 DOI: 10.3389/fphys.2022.904648] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2022] [Accepted: 04/27/2022] [Indexed: 11/13/2022] Open
Abstract
A central component in simulating cardiac electrophysiology is the numerical solution of nonlinear ordinary differential equations, also called cardiac ionic cell models, that describe cross-cell-membrane ion transport. Biophysically detailed cell models often require a considerable amount of computation, including calls to special mathematical functions. This paper systematically studies how to efficiently use modern multicore CPUs for this costly computational task. We start by investigating the code restructurings needed to effectively enable compiler-supported SIMD vectorisation, which is the most important performance booster in this context. It is found that suitable OpenMP directives are sufficient for achieving both vectorisation and parallelisation. We then continue with an evaluation of the performance optimisation technique of using lookup tables. Due to increased challenges for automated vectorisation, the obtainable benefits of lookup tables are dependent on the hardware platforms chosen. Throughout the study, we report detailed time measurements obtained on Intel Xeon, Xeon Phi, AMD Epyc and two ARM processors including Fujitsu A64FX, while attention is also paid to the impact of SIMD vectorisation and lookup tables on the computational accuracy. As a realistic example, the benefits of performance enhancement are demonstrated by a 109-run ensemble on the Oakforest-PACS system, where code restructurings and SIMD vectorisation yield an 84% reduction in computing time, corresponding to 63,270 node hours.
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Affiliation(s)
| | - Xing Cai
- Simula Research Laboratory, Oslo, Norway
- Department of Informatics, University of Oslo, Oslo, Norway
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26
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Falkenberg M, Coleman JA, Dobson S, Hickey DJ, Terrill L, Ciacci A, Thomas B, Sau A, Ng FS, Zhao J, Peters NS, Christensen K. Identifying locations susceptible to micro-anatomical reentry using a spatial network representation of atrial fibre maps. PLoS One 2022; 17:e0267166. [PMID: 35737662 PMCID: PMC9223322 DOI: 10.1371/journal.pone.0267166] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2021] [Accepted: 04/03/2022] [Indexed: 11/18/2022] Open
Abstract
Micro-anatomical reentry has been identified as a potential driver of atrial fibrillation (AF). In this paper, we introduce a novel computational method which aims to identify which atrial regions are most susceptible to micro-reentry. The approach, which considers the structural basis for micro-reentry only, is based on the premise that the accumulation of electrically insulating interstitial fibrosis can be modelled by simulating percolation-like phenomena on spatial networks. Our results suggest that at high coupling, where micro-reentry is rare, the micro-reentrant substrate is highly clustered in areas where the atrial walls are thin and have convex wall morphology, likely facilitating localised treatment via ablation. However, as transverse connections between fibres are removed, mimicking the accumulation of interstitial fibrosis, the substrate becomes less spatially clustered, and the bias to forming in thin, convex regions of the atria is reduced, possibly restricting the efficacy of localised ablation. Comparing our algorithm on image-based models with and without atrial fibre structure, we find that strong longitudinal fibre coupling can suppress the micro-reentrant substrate, whereas regions with disordered fibre orientations have an enhanced risk of micro-reentry. With further development, these methods may be useful for modelling the temporal development of the fibrotic substrate on an individualised basis.
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Affiliation(s)
- Max Falkenberg
- Centre for Complexity Science, Imperial College London, London, United Kingdom
- Department of Physics, Imperial College London, London, United Kingdom
- ElectroCardioMaths Programme, Imperial Centre for Cardiac Engineering, National Heart & Lung Institute, Imperial College London, London, United Kingdom
| | - James A. Coleman
- Department of Physics, Imperial College London, London, United Kingdom
| | - Sam Dobson
- Department of Physics, Imperial College London, London, United Kingdom
| | - David J. Hickey
- Department of Physics, Imperial College London, London, United Kingdom
| | - Louie Terrill
- Department of Physics, Imperial College London, London, United Kingdom
| | - Alberto Ciacci
- Centre for Complexity Science, Imperial College London, London, United Kingdom
- Department of Physics, Imperial College London, London, United Kingdom
- ElectroCardioMaths Programme, Imperial Centre for Cardiac Engineering, National Heart & Lung Institute, Imperial College London, London, United Kingdom
| | - Belvin Thomas
- Auckland Bioengineering Institute, The University of Auckland, Auckland, New Zealand
| | - Arunashis Sau
- ElectroCardioMaths Programme, Imperial Centre for Cardiac Engineering, National Heart & Lung Institute, Imperial College London, London, United Kingdom
| | - Fu Siong Ng
- ElectroCardioMaths Programme, Imperial Centre for Cardiac Engineering, National Heart & Lung Institute, Imperial College London, London, United Kingdom
| | - Jichao Zhao
- Auckland Bioengineering Institute, The University of Auckland, Auckland, New Zealand
| | - Nicholas S. Peters
- ElectroCardioMaths Programme, Imperial Centre for Cardiac Engineering, National Heart & Lung Institute, Imperial College London, London, United Kingdom
| | - Kim Christensen
- Centre for Complexity Science, Imperial College London, London, United Kingdom
- Department of Physics, Imperial College London, London, United Kingdom
- ElectroCardioMaths Programme, Imperial Centre for Cardiac Engineering, National Heart & Lung Institute, Imperial College London, London, United Kingdom
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27
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Wu C, Lorenzo G, Hormuth DA, Lima EABF, Slavkova KP, DiCarlo JC, Virostko J, Phillips CM, Patt D, Chung C, Yankeelov TE. Integrating mechanism-based modeling with biomedical imaging to build practical digital twins for clinical oncology. BIOPHYSICS REVIEWS 2022; 3:021304. [PMID: 35602761 PMCID: PMC9119003 DOI: 10.1063/5.0086789] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2022] [Accepted: 04/29/2022] [Indexed: 12/11/2022]
Abstract
Digital twins employ mathematical and computational models to virtually represent a physical object (e.g., planes and human organs), predict the behavior of the object, and enable decision-making to optimize the future behavior of the object. While digital twins have been widely used in engineering for decades, their applications to oncology are only just emerging. Due to advances in experimental techniques quantitatively characterizing cancer, as well as advances in the mathematical and computational sciences, the notion of building and applying digital twins to understand tumor dynamics and personalize the care of cancer patients has been increasingly appreciated. In this review, we present the opportunities and challenges of applying digital twins in clinical oncology, with a particular focus on integrating medical imaging with mechanism-based, tissue-scale mathematical modeling. Specifically, we first introduce the general digital twin framework and then illustrate existing applications of image-guided digital twins in healthcare. Next, we detail both the imaging and modeling techniques that provide practical opportunities to build patient-specific digital twins for oncology. We then describe the current challenges and limitations in developing image-guided, mechanism-based digital twins for oncology along with potential solutions. We conclude by outlining five fundamental questions that can serve as a roadmap when designing and building a practical digital twin for oncology and attempt to provide answers for a specific application to brain cancer. We hope that this contribution provides motivation for the imaging science, oncology, and computational communities to develop practical digital twin technologies to improve the care of patients battling cancer.
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Affiliation(s)
- Chengyue Wu
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas 78712, USA
| | | | | | | | - Kalina P. Slavkova
- Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA
| | | | | | - Caleb M. Phillips
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas 78712, USA
| | - Debra Patt
- Texas Oncology, Austin, Texas 78731, USA
| | - Caroline Chung
- Department of Radiation Oncology, MD Anderson Cancer Center, University of Texas, Houston, Texas 77030, USA
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28
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Greiner J, Sankarankutty AC, Seidel T, Sachse FB. Confocal microscopy-based estimation of intracellular conductivities in myocardium for modeling of the normal and infarcted heart. Comput Biol Med 2022; 146:105579. [PMID: 35588677 DOI: 10.1016/j.compbiomed.2022.105579] [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: 01/15/2022] [Revised: 04/12/2022] [Accepted: 04/30/2022] [Indexed: 11/03/2022]
Abstract
Ventricular arrhythmias are the leading cause of mortality in patients with ischemic heart diseases, such as myocardial infarction (MI). Computational simulation of cardiac electrophysiology provides insights into these arrhythmias and their treatment. However, only sparse information is available on crucial model parameters, for instance, the anisotropic intracellular electrical conductivities. Here, we introduced an approach to estimate these conductivities in normal and MI hearts. We processed and analyzed images from confocal microscopy of left ventricular tissue of a rabbit MI model to generate 3D reconstructions. We derived tissue features including the volume fraction of myocytes (Vmyo), gap junctions-containing voxels (Vgj), and fibrosis (Vfibrosis). We generated models of the intracellular space and intercellular coupling. Applying numerical methods for solving Poisson's equation for stationary electrical currents, we calculated normal (σmyo,n), longitudinal (σmyo,l), and transverse (σmyo,t) intracellular conductivities. Using linear regression analysis, we assessed relationships of conductivities to tissue features. Vgj and Vmyo were reduced in MI vs. control, but Vfibrosis was increased. Both σmyo,l and σmyo,n were lower in MI than in control. Differences of σmyo,t between control and MI were not significant. We found strong positive relationships of σmyo,l with Vmyo and Vgj, and a strong negative relationship with Vfibrosis. The relationships of σmyo,n with these tissue features were similar but less pronounced. Our study provides quantitative insights into the intracellular conductivities in the normal and MI heart. We suggest that our study establishes a framework for the estimation of intracellular electrical conductivities of myocardium with various pathologies.
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Affiliation(s)
- Joachim Greiner
- Institute for Experimental Cardiovascular Medicine, University Heart Center Freiburg·Bad Krozingen, Freiburg, Germany; Faculty of Medicine, University of Freiburg, Freiburg, Germany.
| | - Aparna C Sankarankutty
- Nora Eccles Harrison Cardiovascular Research and Training Institute, University of Utah, Salt Lake City, USA; Department of Biomedical Engineering, University of Utah, Salt Lake City, USA
| | - Thomas Seidel
- Institute of Cellular and Molecular Physiology, Friedrich-Alexander-University of Erlangen-Nürnberg, Erlangen, Germany
| | - Frank B Sachse
- Nora Eccles Harrison Cardiovascular Research and Training Institute, University of Utah, Salt Lake City, USA; Department of Biomedical Engineering, University of Utah, Salt Lake City, USA.
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29
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Kulangareth NV, Magtibay K, Massé S, Krishnakumar Nair, Dorian P, Nanthakumar K, Umapathy K. An In-Silico model for evaluating the directional shock vectors in terminating and modulating rotors. Comput Biol Med 2022; 146:105665. [DOI: 10.1016/j.compbiomed.2022.105665] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2022] [Revised: 05/03/2022] [Accepted: 05/19/2022] [Indexed: 11/27/2022]
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30
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Woodworth LA, Cansız B, Kaliske M. Balancing conduction velocity error in cardiac electrophysiology using a modified quadrature approach. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2022; 38:e3589. [PMID: 35266643 DOI: 10.1002/cnm.3589] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/08/2021] [Revised: 01/20/2022] [Accepted: 02/28/2022] [Indexed: 06/14/2023]
Abstract
Conduction velocity error is often the main culprit behind the need for very fine spatial discretizations and high computational effort in cardiac electrophysiology problems. In light of this, a novel approach for simulating an accurate conduction velocity in coarse meshes with linear elements is suggested based on a modified quadrature approach. In this approach, the quadrature points are placed at arbitrary offsets of the isoparametric coordinates. A numerical study illustrates the dependence of the conduction velocity on the spatial discretization and the conductivity when using different quadrature rules and calculation approaches. Additionally, examples using the modified quadrature in coarse meshes for wave propagation demonstrate the improved accuracy of the conduction velocity with this method. This novel approach possesses great potential in reducing the computational effort required but remains limited to specific linear elements and experiences a reduction in accuracy for irregular meshes and heterogeneous conductivities. Further research can focus on developing an adaptive quadrature and extending the approach to other element formulations in order to make the approach more generally applicable.
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Affiliation(s)
- Lucas A Woodworth
- Institute for Structural Analysis, Technische Universität Dresden, Dresden, Germany
| | - Barış Cansız
- Institute for Structural Analysis, Technische Universität Dresden, Dresden, Germany
| | - Michael Kaliske
- Institute for Structural Analysis, Technische Universität Dresden, Dresden, Germany
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31
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Jian K, Li C, Hancox JC, Zhang H. Pro-Arrhythmic Effects of Discontinuous Conduction at the Purkinje Fiber-Ventricle Junction Arising From Heart Failure-Induced Ionic Remodeling - Insights From Computational Modelling. Front Physiol 2022; 13:877428. [PMID: 35547576 PMCID: PMC9081695 DOI: 10.3389/fphys.2022.877428] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2022] [Accepted: 03/18/2022] [Indexed: 11/18/2022] Open
Abstract
Heart failure is associated with electrical remodeling of the electrical properties and kinetics of the ion channels and transporters that are responsible for cardiac action potentials. However, it is still unclear whether heart failure-induced ionic remodeling can affect the conduction of excitation waves at the Purkinje fiber-ventricle junction contributing to pro-arrhythmic effects of heart failure, as the complexity of the heart impedes a detailed experimental analysis. The aim of this study was to employ computational models to investigate the pro-arrhythmic effects of heart failure-induced ionic remodeling on the cardiac action potentials and excitation wave conduction at the Purkinje fiber-ventricle junction. Single cell models of canine Purkinje fiber and ventricular myocytes were developed for control and heart failure. These single cell models were then incorporated into one-dimensional strand and three-dimensional wedge models to investigate the effects of heart failure-induced remodeling on propagation of action potentials in Purkinje fiber and ventricular tissue and at the Purkinje fiber-ventricle junction. This revealed that heart failure-induced ionic remodeling of Purkinje fiber and ventricular tissue reduced conduction safety and increased tissue vulnerability to the genesis of the unidirectional conduction block. This was marked at the Purkinje fiber-ventricle junction, forming a potential substrate for the genesis of conduction failure that led to re-entry. This study provides new insights into proarrhythmic consequences of heart failure-induced ionic remodeling.
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Affiliation(s)
- Kun Jian
- Biological Physics Group, Department of Physics and Astronomy, The University of Manchester, Manchester, United Kingdom
| | - Chen Li
- Biological Physics Group, Department of Physics and Astronomy, The University of Manchester, Manchester, United Kingdom
| | - Jules C. Hancox
- Biological Physics Group, Department of Physics and Astronomy, The University of Manchester, Manchester, United Kingdom
- School of Physiology, Pharmacology and Neuroscience, Medical Sciences Building, University Walk, Bristol, United Kingdom
| | - Henggui Zhang
- Biological Physics Group, Department of Physics and Astronomy, The University of Manchester, Manchester, United Kingdom
- Key Laboratory of Medical Electrophysiology of Ministry of Education and Medical Electrophysiological Key Laboratory of Sichuan Province, Institute of Cardiovascular Research, Southwest Medical University, Luzhou, China
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32
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Novaes GM, Alvarez-Lacalle E, Muñoz SA, dos Santos RW. An ensemble of parameters from a robust Markov-based model reproduces L-type calcium currents from different human cardiac myocytes. PLoS One 2022; 17:e0266233. [PMID: 35381041 PMCID: PMC8982880 DOI: 10.1371/journal.pone.0266233] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2021] [Accepted: 03/16/2022] [Indexed: 11/18/2022] Open
Abstract
The development of modeling structures at the channel level that can integrate subcellular and cell models and properly reproduce different experimental data is of utmost importance in cardiac electrophysiology. In contrast to gate-based models, Markov Chain models are well suited to promote the integration of the subcellular level of the cardiomyocyte to the whole cell. In this paper, we develop Markov Chain models for the L-type Calcium current that can reproduce the electrophysiology of two established human models for the ventricular and Purkinje cells. In addition, instead of presenting a single set of parameters, we present a collection of set of parameters employing Differential Evolution algorithms that can properly reproduce very different protocol data. We show the importance of using an ensemble of a set of parameter values to obtain proper results when considering a second protocol that suppresses calcium inactivation and mimics a pathological condition. We discuss how model discrepancy, data availability, and parameter identifiability can influence the choice of the size of the collection. In summary, we have modified two cardiac models by proposing new Markov Chain models for the L-type Calcium. We keep the original whole-cell dynamics by reproducing the same characteristic action potential and calcium dynamics, whereas the Markov chain-based description of the L-type Calcium channels allows novel small spatial scale simulations of subcellular processes. Finally, the use of collections of parameters was crucial for addressing model discrepancy, identifiability issues, and avoiding fitting parameters overly precisely, i.e., overfitting.
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Affiliation(s)
- Gustavo Montes Novaes
- Graduate Program in Computational Modeling, Federal University of Juiz de Fora, Juiz de Fora, MG, Brazil
- Department of Physics, Universitat Politècnica de Catalunya-BarcelonaTech, Barcelona, Spain
- Department of Computation and Mechanics, Federal Center of Technological Education of Minas Gerais, Leopoldina, MG, Brazil
- * E-mail:
| | | | - Sergio Alonso Muñoz
- Department of Physics, Universitat Politècnica de Catalunya-BarcelonaTech, Barcelona, Spain
| | - Rodrigo Weber dos Santos
- Graduate Program in Computational Modeling, Federal University of Juiz de Fora, Juiz de Fora, MG, Brazil
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Fassina D, Costa CM, Longobardi S, Karabelas E, Plank G, Harding SE, Niederer SA. Modelling the interaction between stem cells derived cardiomyocytes patches and host myocardium to aid non-arrhythmic engineered heart tissue design. PLoS Comput Biol 2022; 18:e1010030. [PMID: 35363778 PMCID: PMC9007348 DOI: 10.1371/journal.pcbi.1010030] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/03/2021] [Revised: 04/13/2022] [Accepted: 03/17/2022] [Indexed: 11/18/2022] Open
Abstract
Application of epicardial patches constructed from human-induced pluripotent stem cell- derived cardiomyocytes (hiPSC-CMs) has been proposed as a long-term therapy to treat scarred hearts post myocardial infarction (MI). Understanding electrical interaction between engineered heart tissue patches (EHT) and host myocardium represents a key step toward a successful patch engraftment. EHT retain different electrical properties with respect to the host heart tissue due to the hiPSC-CMs immature phenotype, which may lead to increased arrhythmia risk. We developed a modelling framework to examine the influence of patch design on electrical activation at the engraftment site. We performed an in silico investigation of different patch design approaches to restore pre-MI activation properties and evaluated the associated arrhythmic risk. We developed an in silico cardiac electrophysiology model of a transmural cross section of host myocardium. The model featured an infarct region, an epicardial patch spanning the infarct region and a bath region. The patch is modelled as a layer of hiPSC-CM, combined with a layer of conductive polymer (CP). Tissue and patch geometrical dimensions and conductivities were incorporated through 10 modifiable model parameters. We validated our model against 4 independent experimental studies and showed that it can qualitatively reproduce their findings. We performed a global sensitivity analysis (GSA) to isolate the most important parameters, showing that the stimulus propagation is mainly governed by the scar depth, radius and conductivity when the scar is not transmural, and by the EHT patch conductivity when the scar is transmural. We assessed the relevance of small animal studies to humans by comparing simulations of rat, rabbit and human myocardium. We found that stimulus propagation paths and GSA sensitivity indices are consistent across species. We explored which EHT design variables have the potential to restore physiological propagation. Simulations predict that increasing EHT conductivity from 0.28 to 1-1.1 S/m recovered physiological activation in rat, rabbit and human. Finally, we assessed arrhythmia risk related to increasing EHT conductivity and tested increasing the EHT Na+ channel density as an alternative strategy to match healthy activation. Our results revealed a greater arrhythmia risk linked to increased EHT conductivity compared to increased Na+ channel density. We demonstrated that our modeling framework could capture the interaction between host and EHT patches observed in in vitro experiments. We showed that large (patch and tissue dimensions) and small (cardiac myocyte electrophysiology) scale differences between small animals and humans do not alter EHT patch effect on infarcted tissue. Our model revealed that only when the scar is transmural do EHT properties impact activation times and isolated the EHT conductivity as the main parameter influencing propagation. We predicted that restoring physiological activation by tuning EHT conductivity is possible but may promote arrhythmic behavior. Finally, our model suggests that acting on hiPSC-CMs low action potential upstroke velocity and lack of IK1 may restore pre-MI activation while not promoting arrhythmia.
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Affiliation(s)
- Damiano Fassina
- School of Biomedical Engineering and Imaging Sciences, King’s College London, London, United Kingdom
- National Heart and Lung Institute, Imperial College London, London, United Kingdom
| | - Caroline M. Costa
- School of Biomedical Engineering and Imaging Sciences, King’s College London, London, United Kingdom
| | - Stefano Longobardi
- School of Biomedical Engineering and Imaging Sciences, King’s College London, London, United Kingdom
| | - Elias Karabelas
- Institute of Mathematics & Scientific Computing, University of Graz, Graz, Austria
| | - Gernot Plank
- Gottfried Schatz Research Center (for Cell Signaling, Metabolism and Aging), Division Biophysics, Medical University of Graz, Graz, Austria
| | - Sian E. Harding
- National Heart and Lung Institute, Imperial College London, London, United Kingdom
| | - Steven A. Niederer
- School of Biomedical Engineering and Imaging Sciences, King’s College London, London, United Kingdom
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Electro-anatomical computational cardiology in humans and experimental animal models. TRANSLATIONAL RESEARCH IN ANATOMY 2022. [DOI: 10.1016/j.tria.2022.100162] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022] Open
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Palmieri F, Gomis P, Ferreira D, Pueyo E, Martinez JP, Laguna P, Ramirez J. Weighted Time Warping Improves T-wave Morphology Markers Clinical Significance. IEEE Trans Biomed Eng 2022; 69:2787-2796. [PMID: 35196223 DOI: 10.1109/tbme.2022.3153791] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Background: T-wave (TW) morphology indices based on time-warping (dw) have shown significant cardiovascular risk stratification value. However, errors in the location of TW boundaries may impact their prognostic power. Our aim was to test the hypothesis that a weighted time-warping function (WF) would reduce the sensitivity of dw to these errors and improve their clinical significance. Methods: The WFs were proportional to (i) the reference TW (T), and (ii) the absolute value of its derivative (D). The index dw was recalculated using these WFs, and its performance was compared to the unweighted control case (C) in four different scenarios: 1) robustness against simulated TW boundaries location errors; 2) ability to retain physiological information in an electrophysiological cardiac model; 3) ability to monitor blood potassium concentration changes ([K+]) in 29 hemodialysis (HD) patients; 4) and the sudden cardiac death (SCD) risk stratification value of the TW morphology restitution (TMR) index, derived from dw, in 651 chronic heart failure (CHF) patients. Results and Discussion: The WFs led to a reduced sensitivity (R) of dw to TW boundary location errors as compared to C (median R=0.19 and 0.22 and 0.35 for T, D and C, respectively). They also preserved the physiological relationship between dw and repolarization dispersion changes at ventricular level. No improvements in [K+] tracking were observed for the HD patients (Pearsons median correlation [r] between [K+] and dw was 0.86r0.90 for T, D and C). In CHF patients, the SCD risk stratification value of TMR was improved by applying T (hazard ratio, HAR, of 2.80), followed by D (HAR=2.32) and C (HAR=2.23). Conclusions and Significance: The proposed WFs, with T showing the best performance, increased the robustness of time-warping based markers against TW location errors preserving their physiological information content and boosting their SCD risk stratification value. Results from this work support the use of T when deriving dw for future clinical applications.
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Herrero Martin C, Oved A, Chowdhury RA, Ullmann E, Peters NS, Bharath AA, Varela M. EP-PINNs: Cardiac Electrophysiology Characterisation Using Physics-Informed Neural Networks. Front Cardiovasc Med 2022; 8:768419. [PMID: 35187101 PMCID: PMC8850959 DOI: 10.3389/fcvm.2021.768419] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2021] [Accepted: 12/22/2021] [Indexed: 11/13/2022] Open
Abstract
Accurately inferring underlying electrophysiological (EP) tissue properties from action potential recordings is expected to be clinically useful in the diagnosis and treatment of arrhythmias such as atrial fibrillation. It is, however, notoriously difficult to perform. We present EP-PINNs (Physics Informed Neural Networks), a novel tool for accurate action potential simulation and EP parameter estimation from sparse amounts of EP data. We demonstrate, using 1D and 2D in silico data, how EP-PINNs are able to reconstruct the spatio-temporal evolution of action potentials, whilst predicting parameters related to action potential duration (APD), excitability and diffusion coefficients. EP-PINNs are additionally able to identify heterogeneities in EP properties, making them potentially useful for the detection of fibrosis and other localised pathology linked to arrhythmias. Finally, we show EP-PINNs effectiveness on biological in vitro preparations, by characterising the effect of anti-arrhythmic drugs on APD using optical mapping data. EP-PINNs are a promising clinical tool for the characterisation and potential treatment guidance of arrhythmias.
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Affiliation(s)
- Clara Herrero Martin
- Department of Bioengineering, Imperial College London, London, United Kingdom
- ITACA Institute, Universitat Politècnica de València, Valencia, Spain
| | - Alon Oved
- Department of Computing, Imperial College London, London, United Kingdom
| | - Rasheda A. Chowdhury
- National Heart and Lung Institute, Imperial College London, London, United Kingdom
| | - Elisabeth Ullmann
- Department of Mathematics, Technical University of Munich, Munich, Germany
| | - Nicholas S. Peters
- National Heart and Lung Institute, Imperial College London, London, United Kingdom
| | - Anil A. Bharath
- Department of Bioengineering, Imperial College London, London, United Kingdom
| | - Marta Varela
- National Heart and Lung Institute, Imperial College London, London, United Kingdom
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37
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Zaman MS, Dhamala J, Bajracharya P, Sapp JL, Horácek BM, Wu KC, Trayanova NA, Wang L. Fast Posterior Estimation of Cardiac Electrophysiological Model Parameters via Bayesian Active Learning. Front Physiol 2021; 12:740306. [PMID: 34759835 PMCID: PMC8573318 DOI: 10.3389/fphys.2021.740306] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2021] [Accepted: 09/24/2021] [Indexed: 11/13/2022] Open
Abstract
Probabilistic estimation of cardiac electrophysiological model parameters serves an important step toward model personalization and uncertain quantification. The expensive computation associated with these model simulations, however, makes direct Markov Chain Monte Carlo (MCMC) sampling of the posterior probability density function (pdf) of model parameters computationally intensive. Approximated posterior pdfs resulting from replacing the simulation model with a computationally efficient surrogate, on the other hand, have seen limited accuracy. In this study, we present a Bayesian active learning method to directly approximate the posterior pdf function of cardiac model parameters, in which we intelligently select training points to query the simulation model in order to learn the posterior pdf using a small number of samples. We integrate a generative model into Bayesian active learning to allow approximating posterior pdf of high-dimensional model parameters at the resolution of the cardiac mesh. We further introduce new acquisition functions to focus the selection of training points on better approximating the shape rather than the modes of the posterior pdf of interest. We evaluated the presented method in estimating tissue excitability in a 3D cardiac electrophysiological model in a range of synthetic and real-data experiments. We demonstrated its improved accuracy in approximating the posterior pdf compared to Bayesian active learning using regular acquisition functions, and substantially reduced computational cost in comparison to existing standard or accelerated MCMC sampling.
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Affiliation(s)
- Md Shakil Zaman
- Rochester Institute of Technology, Rochester, NY, United States
| | - Jwala Dhamala
- Rochester Institute of Technology, Rochester, NY, United States
| | | | - John L Sapp
- Department of Medicine, Dalhousie University, Halifax, NS, Canada
| | - B Milan Horácek
- Department of Electrical and Computer Engineering, Halifax, NS, Canada
| | - Katherine C Wu
- Department of Medicine, Johns Hopkins University, Baltimore, MD, United States
| | - Natalia A Trayanova
- Department of Biomedical Engineering, Johns Hopkins University, Baltimore, MD, United States
| | - Linwei Wang
- Rochester Institute of Technology, Rochester, NY, United States
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38
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Davidović A, Coudière Y, Bourgault Y. Modelling the action potential propagation in a heart with structural heterogeneities: From high-resolution MRI to numerical simulations. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2021; 37:e3322. [PMID: 32052589 DOI: 10.1002/cnm.3322] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/03/2019] [Revised: 01/28/2020] [Accepted: 02/03/2020] [Indexed: 06/10/2023]
Abstract
Mathematical modelling and numerical simulation in cardiac electrophysiology have already been studied extensively. However, there is a clear lack of techniques and methodologies for studying the propagation of action potential in a heart with structural defects. In this article, we present a modified version of the bidomain model, derived using homogenisation techniques with the assumption of existence of diffusive inclusions in the cardiac tissue. The diffusive inclusions represent regions without electrically active myocytes, for example, fat, fibrosis, and so forth. We present an application of this model to a rat heart. Starting from high-resolution MRI, the geometry of the heart is built and meshed using image processing techniques. We perform a study of the effects of tissue heterogeneities induced by diffusive inclusions on the velocity and shape of the depolarisation wavefront. We present several test cases with different geometries of diffusive inclusions. We reach the conclusion that the conduction velocity is not affected in the best cases, while it is affected by up to 76% in the worst case scenario. Additionally, the shape of the wavefront was affected in some cases.
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Affiliation(s)
- Anđela Davidović
- Carmen Team, Inria Bordeaux-Sud-Ouest, Bordeaux, France
- Calcul scientifique et Modélisation, Institut de Mathématiques de Bordeaux, CNRS UMR 5251, Université de Bordeaux, Bordeaux, France
- L'Institut de RYthmologie et Modélisation Cardiaque-LIRYC, Bordeaux, France
- Department of Computational Biology, CNRS USR 3756, Institut Pasteur, Paris, France
| | - Yves Coudière
- Carmen Team, Inria Bordeaux-Sud-Ouest, Bordeaux, France
- Calcul scientifique et Modélisation, Institut de Mathématiques de Bordeaux, CNRS UMR 5251, Université de Bordeaux, Bordeaux, France
- L'Institut de RYthmologie et Modélisation Cardiaque-LIRYC, Bordeaux, France
| | - Yves Bourgault
- Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario, Canada
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39
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Biasi N, Tognetti A. A computationally efficient dynamic model of human epicardial tissue. PLoS One 2021; 16:e0259066. [PMID: 34699557 PMCID: PMC8547700 DOI: 10.1371/journal.pone.0259066] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2021] [Accepted: 10/11/2021] [Indexed: 11/29/2022] Open
Abstract
We present a new phenomenological model of human ventricular epicardial cells and we test its reentry dynamics. The model is derived from the Rogers-McCulloch formulation of the FitzHugh-Nagumo equations and represents the total ionic current divided into three contributions corresponding to the excitatory, recovery and transient outward currents. Our model reproduces the main characteristics of human epicardial tissue, including action potential amplitude and morphology, upstroke velocity, and action potential duration and conduction velocity restitution curves. The reentry dynamics is stable, and the dominant period is about 270 ms, which is comparable to clinical values. The proposed model is the first phenomenological model able to accurately resemble human experimental data by using only 3 state variables and 17 parameters. Indeed, it is more computationally efficient than existing models (i.e., almost two times faster than the minimal ventricular model). Beyond the computational efficiency, the low number of parameters facilitates the process of fitting the model to the experimental data.
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Affiliation(s)
- Niccoló Biasi
- Department of Information Engineering, University of Pisa, Pisa, Italy
| | - Alessandro Tognetti
- Department of Information Engineering, University of Pisa, Pisa, Italy.,Research Centre "E. Piaggio", University of Pisa, Pisa, Italy
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40
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Fresca S, Manzoni A, Dedè L, Quarteroni A. POD-Enhanced Deep Learning-Based Reduced Order Models for the Real-Time Simulation of Cardiac Electrophysiology in the Left Atrium. Front Physiol 2021; 12:679076. [PMID: 34630131 PMCID: PMC8493298 DOI: 10.3389/fphys.2021.679076] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2021] [Accepted: 08/10/2021] [Indexed: 12/22/2022] Open
Abstract
The numerical simulation of multiple scenarios easily becomes computationally prohibitive for cardiac electrophysiology (EP) problems if relying on usual high-fidelity, full order models (FOMs). Likewise, the use of traditional reduced order models (ROMs) for parametrized PDEs to speed up the solution of the aforementioned problems can be problematic. This is primarily due to the strong variability characterizing the solution set and to the nonlinear nature of the input-output maps that we intend to reconstruct numerically. To enhance ROM efficiency, we proposed a new generation of non-intrusive, nonlinear ROMs, based on deep learning (DL) algorithms, such as convolutional, feedforward, and autoencoder neural networks. In the proposed DL-ROM, both the nonlinear solution manifold and the nonlinear reduced dynamics used to model the system evolution on that manifold can be learnt in a non-intrusive way thanks to DL algorithms trained on a set of FOM snapshots. DL-ROMs were shown to be able to accurately capture complex front propagation processes, both in physiological and pathological cardiac EP, very rapidly once neural networks were trained, however, at the expense of huge training costs. In this study, we show that performing a prior dimensionality reduction on FOM snapshots through randomized proper orthogonal decomposition (POD) enables to speed up training times and to decrease networks complexity. Accuracy and efficiency of this strategy, which we refer to as POD-DL-ROM, are assessed in the context of cardiac EP on an idealized left atrium (LA) geometry and considering snapshots arising from a NURBS (non-uniform rational B-splines)-based isogeometric analysis (IGA) discretization. Once the ROMs have been trained, POD-DL-ROMs can efficiently solve both physiological and pathological cardiac EP problems, for any new scenario, in real-time, even in extremely challenging contexts such as those featuring circuit re-entries, that are among the factors triggering cardiac arrhythmias.
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Affiliation(s)
- Stefania Fresca
- MOX, Dipartimento di Matematica, Politecnico di Milano, Milan, Italy
| | - Andrea Manzoni
- MOX, Dipartimento di Matematica, Politecnico di Milano, Milan, Italy
| | - Luca Dedè
- MOX, Dipartimento di Matematica, Politecnico di Milano, Milan, Italy
| | - Alfio Quarteroni
- MOX, Dipartimento di Matematica, Politecnico di Milano, Milan, Italy.,Mathematics Institute, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
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41
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Johnston BM, Johnston PR. Which bidomain conductivity is the most important for modelling heart and torso surface potentials during ischaemia? Comput Biol Med 2021; 137:104830. [PMID: 34534792 DOI: 10.1016/j.compbiomed.2021.104830] [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: 07/14/2021] [Revised: 08/29/2021] [Accepted: 08/31/2021] [Indexed: 10/20/2022]
Abstract
Mathematical simulations using the bidomain model, which represents cardiac tissue as consisting of an intracellular and an extracellular space, are a key approach that can be used to improve understanding of heart conditions such as ischaemia. However, key inputs to these models, such as the bidomain conductivity values, are not known with any certainty. Since efforts are underway to measure these values, it would be useful to be able to quantify the effect on model outputs of uncertainty in these inputs, and also to determine, if possible, which are the most important values to focus on in experimental studies. Our previous work has systematically studied the sensitivity of heart surface potentials to the bidomain conductivity values, and this was performed using a half-ellipsoidal model of the left ventricle. This study uses a bi-ventricular heart in a torso model and this time looks at the sensitivity of the torso surface potentials, as well as the heart surface potentials, to various conductivity values (blood, torso and the six bidomain conductivities). We found that both epicardial and torso potentials are the most sensitive to the intracellular longitudinal (along the cardiac fibres) conductivity (gil) with more minor sensitivity to the torso conductivity, and that changes in gil have a significant effect on the surface potential distributions on both the torso and the heart.
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Affiliation(s)
- Barbara M Johnston
- School of Environment and Science, Griffith University, Nathan, Queensland, 4111, Australia.
| | - Peter R Johnston
- School of Environment and Science, Griffith University, Nathan, Queensland, 4111, Australia
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42
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Bi X, Zhang S, Jiang H, Wei Z. A Multi-Scale Computational Model for the Rat Ventricle: Construction, Parallelization, and Applications. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2021; 208:106289. [PMID: 34303152 DOI: 10.1016/j.cmpb.2021.106289] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2021] [Accepted: 07/10/2021] [Indexed: 06/13/2023]
Abstract
BACKGROUND Cardiovascular diseases are the top killer of human beings. The ventricular arrhythmia, as a type of malignant cardiac arrhythmias, typically leads to death if not treated within minutes. The multi-scale virtual heart provides an idealized tool for exploring the underlying mechanisms, by means of incorporating abundant experimental data at the level of ion channels and analyzing the subsequent pathological changes at organ levels. However, there are few studies on building a virtual heart model for rats-a species most widely used in experiments. OBJECTIVE To build a multi-scale computational model for rats, with detailed methodology for the model construction, computational optimization, and its applications. METHODS First, approaches for building multi-scale models ranging from cellular to 3-D organ levels are introduced, with detailed descriptions of handling the ventricular myocardium heterogeneity, geometry processing, and boundary conditions, etc. Next, for dealing with the expensive computational costs of 3-D models, optimization approaches including an optimized representation and a GPU-based parallelization method are introduced. Finally, methods for reproducing of some key phenomenon (e.g., electrocardiograph, spiral/scroll waves) are demonstrated. RESULTS Three types of heterogeneity, including the transmural heterogeneity, the interventricular heterogeneity, and the base-apex heterogeneity are incorporated into the model. The normal and reentrant excitation waves, as well as the corresponding pseudo-ECGs are reproduced by the constructed ventricle model. In addition, the temporal and spatial vulnerability to reentry arrhythmias are quantified based on the evaluation experiments of vulnerable window and the critical length. CONCLUSIONS The constructed multi-scale rat ventricle model is able to reproduce both the physiological and the pathological phenomenon in different scales. Evaluation experiments suggest that the apex is the most susceptible area to arrhythmias. The model can be a promising tool for the investigation of arrhythmogenesis and the screening of anti-arrhythmic drugs.
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Affiliation(s)
- Xiangpeng Bi
- College of Computer Science and Technology, Ocean University of China, Qingdao 266100, China
| | - Shugang Zhang
- College of Computer Science and Technology, Ocean University of China, Qingdao 266100, China; High Performance Computing Center, Pilot National Laboratory for Marine Science and Technology (Qingdao), Qingdao 266237, China.
| | - Huasen Jiang
- College of Computer Science and Technology, Ocean University of China, Qingdao 266100, China
| | - Zhiqiang Wei
- College of Computer Science and Technology, Ocean University of China, Qingdao 266100, China; High Performance Computing Center, Pilot National Laboratory for Marine Science and Technology (Qingdao), Qingdao 266237, China
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Personalized Evaluation of Atrial Complexity of Patients Undergoing Atrial Fibrillation Ablation: A Clinical Computational Study. BIOLOGY 2021; 10:biology10090838. [PMID: 34571716 PMCID: PMC8469429 DOI: 10.3390/biology10090838] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/13/2021] [Revised: 08/24/2021] [Accepted: 08/25/2021] [Indexed: 11/17/2022]
Abstract
Simple Summary Atrial fibrillation is a type of arrhythmia that occurs when the electrical activity of the heart in the atrium is not coordinated, and its consequences can be lethal. The driving source that initiates this chaotic activity can be located anywhere in the atrium, but most frequently appears in certain areas such as the pulmonary veins. In this study, we developed a new estimation method to evaluate possible source location and complexity of the arrhythmia using computer simulations. This method represents mathematical descriptions of natural processes that can be used to mimic a real scenario, including specific information such as the atrial anatomy. Here, we identified a specific biomarker the enabled obtaining a foci distribution map and found that elimination of pulmonary vein drivers was associated with a successful long-term ablation outcome. This study could, therefore, help to identify and characterize patients in order to better plan the ablation procedure. Abstract Current clinical guidelines establish Pulmonary Vein (PV) isolation as the indicated treatment for Atrial Fibrillation (AF). However, AF can also be triggered or sustained due to atrial drivers located elsewhere in the atria. We designed a new simulation workflow based on personalized computer simulations to characterize AF complexity of patients undergoing PV ablation, validated with non-invasive electrocardiographic imaging and evaluated at one year after ablation. We included 30 patients using atrial anatomies segmented from MRI and simulated an automata model for the electrical modelling, consisting of three states (resting, excited and refractory). In total, 100 different scenarios were simulated per anatomy varying rotor number and location. The 3 states were calibrated with Koivumaki action potential, entropy maps were obtained from the electrograms and compared with ECGi for each patient to analyze PV isolation outcome. The completion of the workflow indicated that successful AF ablation occurred in patients with rotors mainly located at the PV antrum, while unsuccessful procedures presented greater number of driving sites outside the PV area. The number of rotors attached to the PV was significantly higher in patients with favorable long-term ablation outcome (1-year freedom from AF: 1.61 ± 0.21 vs. AF recurrence: 1.40 ± 0.20; p-value = 0.018). The presented workflow could improve patient stratification for PV ablation by screening the complexity of the atria.
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Peirlinck M, Sahli Costabal F, Kuhl E. Sex Differences in Drug-Induced Arrhythmogenesis. Front Physiol 2021; 12:708435. [PMID: 34489728 PMCID: PMC8417068 DOI: 10.3389/fphys.2021.708435] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2021] [Accepted: 07/14/2021] [Indexed: 12/25/2022] Open
Abstract
The electrical activity in the heart varies significantly between men and women and results in a sex-specific response to drugs. Recent evidence suggests that women are more than twice as likely as men to develop drug-induced arrhythmia with potentially fatal consequences. Yet, the sex-specific differences in drug-induced arrhythmogenesis remain poorly understood. Here we integrate multiscale modeling and machine learning to gain mechanistic insight into the sex-specific origin of drug-induced cardiac arrhythmia at differing drug concentrations. To quantify critical drug concentrations in male and female hearts, we identify the most important ion channels that trigger male and female arrhythmogenesis, and create and train a sex-specific multi-fidelity arrhythmogenic risk classifier. Our study reveals that sex differences in ion channel activity, tissue conductivity, and heart dimensions trigger longer QT-intervals in women than in men. We quantify the critical drug concentration for dofetilide, a high risk drug, to be seven times lower for women than for men. Our results emphasize the importance of including sex as an independent biological variable in risk assessment during drug development. Acknowledging and understanding sex differences in drug safety evaluation is critical when developing novel therapeutic treatments on a personalized basis. The general trends of this study have significant implications on the development of safe and efficacious new drugs and the prescription of existing drugs in combination with other drugs.
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Affiliation(s)
- Mathias Peirlinck
- Department of Mechanical Engineering, Stanford University, Stanford, CA, United States
| | - Francisco Sahli Costabal
- Department of Mechanical and Metallurgical Engineering, School of Engineering, Pontificia Universidad Católica de Chile, Santiago, Chile
- Institute for Biological and Medical Engineering, Schools of Engineering, Medicine and Biological Sciences, Pontificia Universidad Católica de Chile, Santiago, Chile
- Millennium Nucleus for Cardiovascular Magnetic Resonance, Santiago, Chile
| | - Ellen Kuhl
- Department of Mechanical Engineering, Stanford University, Stanford, CA, United States
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Theoretical Investigation of the Mechanism by which A Gain-of-Function Mutation of the TRPM4 Channel Causes Conduction Block. Int J Mol Sci 2021; 22:ijms22168513. [PMID: 34445219 PMCID: PMC8395173 DOI: 10.3390/ijms22168513] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/25/2021] [Revised: 07/26/2021] [Accepted: 08/04/2021] [Indexed: 11/17/2022] Open
Abstract
In the heart, TRPM4 is most abundantly distributed in the conduction system. Previously, a single mutation, 'E7K', was identified in its distal N-terminus to cause conduction disorder because of enhanced cell-surface expression. It remains, however, unclear how this expression increase leads to conduction failure rather than abnormally enhanced cardiac excitability. To address this issue theoretically, we mathematically formulated the gating kinetics of the E7K-mutant TRPM4 channel by a combined use of voltage jump analysis and ionomycin-perforated cell-attached recording technique and incorporated the resultant rate constants of opening and closing into a human Purkinje fiber single-cell action potential (AP) model (Trovato model) to perform 1D-cable simulations. The results from TRPM4 expressing HEK293 cells showed that as compared with the wild-type, the open state is much preferred in the E7K mutant with increased voltage-and Ca2+-sensitivities. These theoretical predictions were confirmed by power spectrum and single channel analyses of expressed wild-type and E7K-mutant TRPM4 channels. In our modified Trovato model, the facilitated opening of the E7K mutant channel markedly prolonged AP duration with concomitant depolarizing shifts of the resting membrane potential in a manner dependent on the channel density (or maximal activity). This was, however, little evident in the wild-type TRPM4 channel. Moreover, 1D-cable simulations with the modified Trovato model revealed that increasing the density of E7K (but not of wild-type) TRPM4 channels progressively reduced AP conduction velocity eventually culminating in complete conduction block. These results clearly suggest the brady-arrhythmogenicity of the E7K mutant channel which likely results from its pathologically enhanced activity.
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Bai J, Lu Y, Zhu Y, Wang H, Yin D, Zhang H, Franco D, Zhao J. Understanding PITX2-Dependent Atrial Fibrillation Mechanisms through Computational Models. Int J Mol Sci 2021; 22:7681. [PMID: 34299303 PMCID: PMC8307824 DOI: 10.3390/ijms22147681] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2021] [Revised: 07/14/2021] [Accepted: 07/16/2021] [Indexed: 01/11/2023] Open
Abstract
Atrial fibrillation (AF) is a common arrhythmia. Better prevention and treatment of AF are needed to reduce AF-associated morbidity and mortality. Several major mechanisms cause AF in patients, including genetic predispositions to AF development. Genome-wide association studies have identified a number of genetic variants in association with AF populations, with the strongest hits clustering on chromosome 4q25, close to the gene for the homeobox transcription PITX2. Because of the inherent complexity of the human heart, experimental and basic research is insufficient for understanding the functional impacts of PITX2 variants on AF. Linking PITX2 properties to ion channels, cells, tissues, atriums and the whole heart, computational models provide a supplementary tool for achieving a quantitative understanding of the functional role of PITX2 in remodelling atrial structure and function to predispose to AF. It is hoped that computational approaches incorporating all we know about PITX2-related structural and electrical remodelling would provide better understanding into its proarrhythmic effects leading to development of improved anti-AF therapies. In the present review, we discuss advances in atrial modelling and focus on the mechanistic links between PITX2 and AF. Challenges in applying models for improving patient health are described, as well as a summary of future perspectives.
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Affiliation(s)
- Jieyun Bai
- College of Information Science and Technology, Jinan University, Guangzhou 510632, China; (Y.L.); (Y.Z.)
- Auckland Bioengineering Institute, University of Auckland, Auckland 1010, New Zealand
| | - Yaosheng Lu
- College of Information Science and Technology, Jinan University, Guangzhou 510632, China; (Y.L.); (Y.Z.)
| | - Yijie Zhu
- College of Information Science and Technology, Jinan University, Guangzhou 510632, China; (Y.L.); (Y.Z.)
| | - Huijin Wang
- College of Information Science and Technology, Jinan University, Guangzhou 510632, China; (Y.L.); (Y.Z.)
| | - Dechun Yin
- Department of Cardiology, First Affiliated Hospital of Harbin Medical University, Harbin 150000, China;
| | - Henggui Zhang
- Biological Physics Group, School of Physics & Astronomy, The University of Manchester, Manchester M13 9PL, UK;
| | - Diego Franco
- Department of Experimental Biology, University of Jaen, 23071 Jaen, Spain;
| | - Jichao Zhao
- Auckland Bioengineering Institute, University of Auckland, Auckland 1010, New Zealand
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Cusimano N, Gerardo-Giorda L, Gizzi A. A space-fractional bidomain framework for cardiac electrophysiology: 1D alternans dynamics. CHAOS (WOODBURY, N.Y.) 2021; 31:073123. [PMID: 34340362 DOI: 10.1063/5.0050897] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/19/2021] [Accepted: 06/23/2021] [Indexed: 06/13/2023]
Abstract
Cardiac electrophysiology modeling deals with a complex network of excitable cells forming an intricate syncytium: the heart. The electrical activity of the heart shows recurrent spatial patterns of activation, known as cardiac alternans, featuring multiscale emerging behavior. On these grounds, we propose a novel mathematical formulation for cardiac electrophysiology modeling and simulation incorporating spatially non-local couplings within a physiological reaction-diffusion scenario. In particular, we formulate, a space-fractional electrophysiological framework, extending and generalizing similar works conducted for the monodomain model. We characterize one-dimensional excitation patterns by performing an extended numerical analysis encompassing a broad spectrum of space-fractional derivative powers and various intra- and extracellular conductivity combinations. Our numerical study demonstrates that (i) symmetric properties occur in the conductivity parameters' space following the proposed theoretical framework, (ii) the degree of non-local coupling affects the onset and evolution of discordant alternans dynamics, and (iii) the theoretical framework fully recovers classical formulations and is amenable for parametric tuning relying on experimental conduction velocity and action potential morphology.
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Affiliation(s)
| | | | - Alessio Gizzi
- Department of Engineering, Campus Bio-Medico University of Rome, 00128 Rome, Italy
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A modified approach to determine the six cardiac bidomain conductivities. Comput Biol Med 2021; 135:104549. [PMID: 34171640 PMCID: PMC10183296 DOI: 10.1016/j.compbiomed.2021.104549] [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: 04/08/2021] [Revised: 05/31/2021] [Accepted: 06/01/2021] [Indexed: 11/23/2022]
Abstract
Accurate values for the six cardiac bidomain conductivities are crucial for meaningful computational studies of conduction in cardiac tissue, and are yet to be determined by experimental means. Although previous studies have proposed an approach using a multi-electrode array to measure potentials, from which the conductivities can be determined, it has been found that the conductivities cannot be retrieved consistently when the noise in the potentials varies. This paper presents a protocol, which not only has been shown to retrieve the conductivities to a reasonable accuracy, but does so under the presence of a more appropriate additive Gaussian noise model, while using fewer computational resources. Through repetitions of the protocol, a comparison of two pre-fabricated 128 electrode arrays, one array with a square arrangement of electrodes and the other with a rectangular arrangement, was made against a 75-electrode array proposed in previous studies. Results indicated that the two pre-fabricated arrays were generally more capable of obtaining the cardiac conductivities to a higher degree of accuracy than the 75-electrode array. The 128-electrode rectangular array was orientated such that the length of the array first ran along the direction of the fibres, then was reorientated such that the length of the array ran perpendicular to the direction of the fibres. The 128-electrode rectangular array, when orientated in this manner, was more capable of retrieving the conductivities than the remainder of the arrays tested, and thus we suggest this arrangement be used during experimental trials.
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Krause AL, Klika V, Maini PK, Headon D, Gaffney EA. Isolating Patterns in Open Reaction-Diffusion Systems. Bull Math Biol 2021; 83:82. [PMID: 34089093 PMCID: PMC8178156 DOI: 10.1007/s11538-021-00913-4] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2020] [Accepted: 05/13/2021] [Indexed: 01/14/2023]
Abstract
Realistic examples of reaction-diffusion phenomena governing spatial and spatiotemporal pattern formation are rarely isolated systems, either chemically or thermodynamically. However, even formulations of 'open' reaction-diffusion systems often neglect the role of domain boundaries. Most idealizations of closed reaction-diffusion systems employ no-flux boundary conditions, and often patterns will form up to, or along, these boundaries. Motivated by boundaries of patterning fields related to the emergence of spatial form in embryonic development, we propose a set of mixed boundary conditions for a two-species reaction-diffusion system which forms inhomogeneous solutions away from the boundary of the domain for a variety of different reaction kinetics, with a prescribed uniform state near the boundary. We show that these boundary conditions can be derived from a larger heterogeneous field, indicating that these conditions can arise naturally if cell signalling or other properties of the medium vary in space. We explain the basic mechanisms behind this pattern localization and demonstrate that it can capture a large range of localized patterning in one, two, and three dimensions and that this framework can be applied to systems involving more than two species. Furthermore, the boundary conditions proposed lead to more symmetrical patterns on the interior of the domain and plausibly capture more realistic boundaries in developmental systems. Finally, we show that these isolated patterns are more robust to fluctuations in initial conditions and that they allow intriguing possibilities of pattern selection via geometry, distinct from known selection mechanisms.
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Affiliation(s)
- Andrew L Krause
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK.
| | - Václav Klika
- Department of Mathematics, FNSPE, Czech Technical University in Prague, Trojanova 13, 120 00, Praha, Czech Republic
| | - Philip K Maini
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK
| | - Denis Headon
- The Roslin Institute and Royal (Dick) School of Veterinary Studies, University of Edinburgh, Easter Bush Campus, Midlothian, EH25 9RG, UK
| | - Eamonn A Gaffney
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK
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Pagani S, Manzoni A. Enabling forward uncertainty quantification and sensitivity analysis in cardiac electrophysiology by reduced order modeling and machine learning. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2021; 37:e3450. [PMID: 33599106 PMCID: PMC8244126 DOI: 10.1002/cnm.3450] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Revised: 02/05/2021] [Accepted: 02/07/2021] [Indexed: 06/12/2023]
Abstract
We present a new, computationally efficient framework to perform forward uncertainty quantification (UQ) in cardiac electrophysiology. We consider the monodomain model to describe the electrical activity in the cardiac tissue, coupled with the Aliev-Panfilov model to characterize the ionic activity through the cell membrane. We address a complete forward UQ pipeline, including both: (i) a variance-based global sensitivity analysis for the selection of the most relevant input parameters, and (ii) a way to perform uncertainty propagation to investigate the impact of intra-subject variability on outputs of interest depending on the cardiac potential. Both tasks exploit stochastic sampling techniques, thus implying overwhelming computational costs because of the huge amount of queries to the high-fidelity, full-order computational model obtained by approximating the coupled monodomain/Aliev-Panfilov system through the finite element method. To mitigate this computational burden, we replace the full-order model with computationally inexpensive projection-based reduced-order models (ROMs) aimed at reducing the state-space dimensionality. Resulting approximation errors on the outputs of interest are finally taken into account through artificial neural network (ANN)-based models, enhancing the accuracy of the whole UQ pipeline. Numerical results show that the proposed physics-based ROMs outperform regression-based emulators relying on ANNs built with the same amount of training data, in terms of both numerical accuracy and overall computational efficiency.
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Affiliation(s)
- Stefano Pagani
- MOX, Dipartimento di MatematicaPolitecnico di MilanoMilanItaly
| | - Andrea Manzoni
- MOX, Dipartimento di MatematicaPolitecnico di MilanoMilanItaly
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