1
|
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.
Collapse
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
| |
Collapse
|
2
|
Lei CL, Mirams GR. Neural Network Differential Equations For Ion Channel Modelling. Front Physiol 2021; 12:708944. [PMID: 34421652 PMCID: PMC8371386 DOI: 10.3389/fphys.2021.708944] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2021] [Accepted: 07/05/2021] [Indexed: 11/13/2022] Open
Abstract
Mathematical models of cardiac ion channels have been widely used to study and predict the behaviour of ion currents. Typically models are built using biophysically-based mechanistic principles such as Hodgkin-Huxley or Markov state transitions. These models provide an abstract description of the underlying conformational changes of the ion channels. However, due to the abstracted conformation states and assumptions for the rates of transition between them, there are differences between the models and reality-termed model discrepancy or misspecification. In this paper, we demonstrate the feasibility of using a mechanistically-inspired neural network differential equation model, a hybrid non-parametric model, to model ion channel kinetics. We apply it to the hERG potassium ion channel as an example, with the aim of providing an alternative modelling approach that could alleviate certain limitations of the traditional approach. We compare and discuss multiple ways of using a neural network to approximate extra hidden states or alternative transition rates. In particular we assess their ability to learn the missing dynamics, and ask whether we can use these models to handle model discrepancy. Finally, we discuss the practicality and limitations of using neural networks and their potential applications.
Collapse
Affiliation(s)
- Chon Lok Lei
- Institute of Translational Medicine, Faculty of Health Sciences, University of Macau, Macau, China
- Department of Biomedical Sciences, Faculty of Health Sciences, University of Macau, Macau, China
- School of Mathematical Sciences, Faculty of Science and Engineering, University of Nottingham, Ningbo, China
| | - Gary R. Mirams
- Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, United Kingdom
| |
Collapse
|
3
|
Amuzescu B, Airini R, Epureanu FB, Mann SA, Knott T, Radu BM. Evolution of mathematical models of cardiomyocyte electrophysiology. Math Biosci 2021; 334:108567. [PMID: 33607174 DOI: 10.1016/j.mbs.2021.108567] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2020] [Revised: 01/10/2021] [Accepted: 02/04/2021] [Indexed: 12/16/2022]
Abstract
Advanced computational techniques and mathematical modeling have become more and more important to the study of cardiac electrophysiology. In this review, we provide a brief history of the evolution of cardiomyocyte electrophysiology models and highlight some of the most important ones that had a major impact on our understanding of the electrical activity of the myocardium and associated transmembrane ion fluxes in normal and pathological states. We also present the use of these models in the study of various arrhythmogenesis mechanisms, particularly the integration of experimental pharmacology data into advanced humanized models for in silico proarrhythmogenic risk prediction as an essential component of the Comprehensive in vitro Proarrhythmia Assay (CiPA) drug safety paradigm.
Collapse
Affiliation(s)
- Bogdan Amuzescu
- Department of Anatomy, Animal Physiology and Biophysics, Faculty of Biology, University of Bucharest, 91-95 Splaiul Independentei, Bucharest 050095, Romania; Life, Environmental and Earth Sciences Division, Research Institute of the University of Bucharest (ICUB), 91-95 Splaiul Independentei, Bucharest 050095, Romania.
| | - Razvan Airini
- Department of Anatomy, Animal Physiology and Biophysics, Faculty of Biology, University of Bucharest, 91-95 Splaiul Independentei, Bucharest 050095, Romania; Life, Environmental and Earth Sciences Division, Research Institute of the University of Bucharest (ICUB), 91-95 Splaiul Independentei, Bucharest 050095, Romania
| | - Florin Bogdan Epureanu
- Department of Anatomy, Animal Physiology and Biophysics, Faculty of Biology, University of Bucharest, 91-95 Splaiul Independentei, Bucharest 050095, Romania; Life, Environmental and Earth Sciences Division, Research Institute of the University of Bucharest (ICUB), 91-95 Splaiul Independentei, Bucharest 050095, Romania
| | - Stefan A Mann
- Cytocentrics Bioscience GmbH, Nattermannallee 1, 50829 Cologne, Germany
| | - Thomas Knott
- CytoBioScience Inc., 3463 Magic Drive, San Antonio, TX 78229, USA
| | - Beatrice Mihaela Radu
- Department of Anatomy, Animal Physiology and Biophysics, Faculty of Biology, University of Bucharest, 91-95 Splaiul Independentei, Bucharest 050095, Romania; Life, Environmental and Earth Sciences Division, Research Institute of the University of Bucharest (ICUB), 91-95 Splaiul Independentei, Bucharest 050095, Romania
| |
Collapse
|
4
|
Pouranbarani E, Berg LA, Oliveira RS, Dos Santos RW, Nygren A. Improved Accuracy of Cardiac Tissue-Level Simulations by Considering Membrane Resistance as a Cellular-Level Optimization Objective. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2020; 2020:2487-2490. [PMID: 33018511 DOI: 10.1109/embc44109.2020.9176128] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
Cardiac cellular models are utilized as the building blocks for tissue simulation. One of the imprecisions of conventional cellular modeling, especially when the models are used in tissue-level modeling, stems from the mere consideration of cellular properties (e.g., action potential shape) in parameter tuning of the model. In our previous work, we put forward an accurate framework in which membrane resistance (Rm) reflecting inter-cellular characteristics, i.e., electrotonic effects, was considered alongside cellular features in cellular model fitting. This paper, for the first time, examines the hypothesis that considering Rm as an additional optimization objective improves the accuracy of tissue-level modeling. To study this hypothesis, after cellular-level optimization of a well-known model, source-sink mismatch configurations in a 2-dimensional model are investigated. The results demonstrate that including Rm in the optimization protocol yields a substantial improvement in the relative error of the critical transition border which is defined as the minimum window size between source and sink that wave propagates. Model developers can utilize the proposed concept during parameter tuning to increase the accuracy of models.
Collapse
|
5
|
Lei CL, Ghosh S, Whittaker DG, Aboelkassem Y, Beattie KA, Cantwell CD, Delhaas T, Houston C, Novaes GM, Panfilov AV, Pathmanathan P, Riabiz M, dos Santos RW, Walmsley J, Worden K, Mirams GR, Wilkinson RD. Considering discrepancy when calibrating a mechanistic electrophysiology model. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2020; 378:20190349. [PMID: 32448065 PMCID: PMC7287333 DOI: 10.1098/rsta.2019.0349] [Citation(s) in RCA: 32] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 04/21/2020] [Indexed: 05/21/2023]
Abstract
Uncertainty quantification (UQ) is a vital step in using mathematical models and simulations to take decisions. The field of cardiac simulation has begun to explore and adopt UQ methods to characterize uncertainty in model inputs and how that propagates through to outputs or predictions; examples of this can be seen in the papers of this issue. In this review and perspective piece, we draw attention to an important and under-addressed source of uncertainty in our predictions-that of uncertainty in the model structure or the equations themselves. The difference between imperfect models and reality is termed model discrepancy, and we are often uncertain as to the size and consequences of this discrepancy. Here, we provide two examples of the consequences of discrepancy when calibrating models at the ion channel and action potential scales. Furthermore, we attempt to account for this discrepancy when calibrating and validating an ion channel model using different methods, based on modelling the discrepancy using Gaussian processes and autoregressive-moving-average models, then highlight the advantages and shortcomings of each approach. Finally, suggestions and lines of enquiry for future work are provided. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.
Collapse
Affiliation(s)
- Chon Lok Lei
- Computational Biology and Health Informatics, Department of Computer Science, University of Oxford, Oxford, UK
| | - Sanmitra Ghosh
- MRC Biostatistics Unit, University of Cambridge, Cambridge, UK
| | - Dominic G. Whittaker
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, UK
| | - Yasser Aboelkassem
- Department of Bioengineering, University of California San Diego, La Jolla, CA, USA
| | - Kylie A. Beattie
- Systems Modeling and Translational Biology, GlaxoSmithKline R&D, Stevenage, UK
| | - Chris D. Cantwell
- ElectroCardioMaths Programme, Centre for Cardiac Engineering, Imperial College London, London, UK
| | - Tammo Delhaas
- CARIM School for Cardiovascular Diseases, Maastricht University, Maastricht, The Netherlands
| | - Charles Houston
- ElectroCardioMaths Programme, Centre for Cardiac Engineering, Imperial College London, London, UK
| | - Gustavo Montes Novaes
- Graduate Program in Computational Modeling, Universidade Federal de Juiz de Fora, Juiz de Fora, Brazil
| | - Alexander V. Panfilov
- Department of Physics and Astronomy, Ghent University, Ghent, Belgium
- Laboratory of Computational Biology and Medicine, Ural Federal University, Ekaterinburg, Russia
| | - Pras Pathmanathan
- US Food and Drug Administration, Center for Devices and Radiological Health, Office of Science and Engineering Laboratories, Silver Spring, MD, USA
| | - Marina Riabiz
- Department of Biomedical Engineering King’s College London and Alan Turing Institute, London, UK
| | - Rodrigo Weber dos Santos
- Graduate Program in Computational Modeling, Universidade Federal de Juiz de Fora, Juiz de Fora, Brazil
| | - John Walmsley
- James T. Willerson Center for Cardiovascular Modeling and Simulation, Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX, USA
| | - Keith Worden
- Dynamics Research Group, Department of Mechanical Engineering, University of Sheffield, Sheffield, UK
| | - Gary R. Mirams
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, UK
| | | |
Collapse
|
6
|
Clayton RH, Aboelkassem Y, Cantwell CD, Corrado C, Delhaas T, Huberts W, Lei CL, Ni H, Panfilov AV, Roney C, dos Santos RW. An audit of uncertainty in multi-scale cardiac electrophysiology models. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2020; 378:20190335. [PMID: 32448070 PMCID: PMC7287340 DOI: 10.1098/rsta.2019.0335] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 03/16/2020] [Indexed: 05/21/2023]
Abstract
Models of electrical activation and recovery in cardiac cells and tissue have become valuable research tools, and are beginning to be used in safety-critical applications including guidance for clinical procedures and for drug safety assessment. As a consequence, there is an urgent need for a more detailed and quantitative understanding of the ways that uncertainty and variability influence model predictions. In this paper, we review the sources of uncertainty in these models at different spatial scales, discuss how uncertainties are communicated across scales, and begin to assess their relative importance. We conclude by highlighting important challenges that continue to face the cardiac modelling community, identifying open questions, and making recommendations for future studies. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.
Collapse
Affiliation(s)
- Richard H. Clayton
- Insigneo institute for in-silico Medicine and Department of Computer Science, University of Sheffield, Sheffield, UK
- e-mail:
| | - Yasser Aboelkassem
- Department of Bioengineering, University of California, San Diego, CA, USA
| | | | - Cesare Corrado
- Division of Imaging Sciences and Biomedical Engineering, King’s College London, London, UK
| | - Tammo Delhaas
- School of Cardiovascular Diseases, Maastricht University, Maastricht, The Netherlands
| | - Wouter Huberts
- School of Cardiovascular Diseases, Maastricht University, Maastricht, The Netherlands
- Department of Biomedical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands
| | - Chon Lok Lei
- Computational Biology and Health Informatics, Department of Computer Science, University of Oxford, Oxford, UK
| | - Haibo Ni
- Department of Pharmacology, University of California, Davis, CA, USA
| | - Alexander V. Panfilov
- Department of Physics and Astronomy, University of Gent, Gent, Belgium
- Laboratory of Computational Biology and Medicine, Ural Federal University, Ekaterinburg, Russia
| | - Caroline Roney
- Division of Imaging Sciences and Biomedical Engineering, King’s College London, London, UK
| | | |
Collapse
|