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Grandits T, Augustin CM, Haase G, Jost N, Mirams GR, Niederer SA, Plank G, Varró A, Virág L, Jung A. Neural network emulation of the human ventricular cardiomyocyte action potential for more efficient computations in pharmacological studies. eLife 2024; 12:RP91911. [PMID: 38598284 PMCID: PMC11006416 DOI: 10.7554/elife.91911] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/11/2024] Open
Abstract
Computer models of the human ventricular cardiomyocyte action potential (AP) have reached a level of detail and maturity that has led to an increasing number of applications in the pharmaceutical sector. However, interfacing the models with experimental data can become a significant computational burden. To mitigate the computational burden, the present study introduces a neural network (NN) that emulates the AP for given maximum conductances of selected ion channels, pumps, and exchangers. Its applicability in pharmacological studies was tested on synthetic and experimental data. The NN emulator potentially enables massive speed-ups compared to regular simulations and the forward problem (find drugged AP for pharmacological parameters defined as scaling factors of control maximum conductances) on synthetic data could be solved with average root-mean-square errors (RMSE) of 0.47 mV in normal APs and of 14.5 mV in abnormal APs exhibiting early afterdepolarizations (72.5% of the emulated APs were alining with the abnormality, and the substantial majority of the remaining APs demonstrated pronounced proximity). This demonstrates not only very fast and mostly very accurate AP emulations but also the capability of accounting for discontinuities, a major advantage over existing emulation strategies. Furthermore, the inverse problem (find pharmacological parameters for control and drugged APs through optimization) on synthetic data could be solved with high accuracy shown by a maximum RMSE of 0.22 in the estimated pharmacological parameters. However, notable mismatches were observed between pharmacological parameters estimated from experimental data and distributions obtained from the Comprehensive in vitro Proarrhythmia Assay initiative. This reveals larger inaccuracies which can be attributed particularly to the fact that small tissue preparations were studied while the emulator was trained on single cardiomyocyte data. Overall, our study highlights the potential of NN emulators as powerful tool for an increased efficiency in future quantitative systems pharmacology studies.
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Affiliation(s)
- Thomas Grandits
- Department of Mathematics and Scientific Computing, University of GrazGrazAustria
- NAWI Graz, University of GrazGrazAustria
| | - Christoph M Augustin
- Gottfried Schatz Research Center for Cell Signaling, Metabolism and Aging - Division of Medical Physics and Biophysics, Medical University of GrazGrazAustria
- BioTechMed-GrazGrazAustria
| | - Gundolf Haase
- Department of Mathematics and Scientific Computing, University of GrazGrazAustria
| | - Norbert Jost
- Department of Pharmacology and Pharmacotherapy, University of SzegedSzegedHungary
- HUN-REN-TKI, Research Group of PharmacologyBudapestHungary
| | - Gary R Mirams
- Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of NottinghamNottinghamUnited Kingdom
| | - Steven A Niederer
- Division of Imaging Sciences & Biomedical Engineering, King’s College LondonLondonUnited Kingdom
| | - Gernot Plank
- Gottfried Schatz Research Center for Cell Signaling, Metabolism and Aging - Division of Medical Physics and Biophysics, Medical University of GrazGrazAustria
- BioTechMed-GrazGrazAustria
| | - András Varró
- Department of Pharmacology and Pharmacotherapy, University of SzegedSzegedHungary
- HUN-REN-TKI, Research Group of PharmacologyBudapestHungary
| | - László Virág
- Department of Pharmacology and Pharmacotherapy, University of SzegedSzegedHungary
| | - Alexander Jung
- Gottfried Schatz Research Center for Cell Signaling, Metabolism and Aging - Division of Medical Physics and Biophysics, Medical University of GrazGrazAustria
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2
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Raniga K, Nasir A, Vo NTN, Vaidyanathan R, Dickerson S, Hilcove S, Mosqueira D, Mirams GR, Clements P, Hicks R, Pointon A, Stebbeds W, Francis J, Denning C. Strengthening cardiac therapy pipelines using human pluripotent stem cell-derived cardiomyocytes. Cell Stem Cell 2024; 31:292-311. [PMID: 38366587 DOI: 10.1016/j.stem.2024.01.007] [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: 09/14/2023] [Revised: 11/27/2023] [Accepted: 01/19/2024] [Indexed: 02/18/2024]
Abstract
Advances in hiPSC isolation and reprogramming and hPSC-CM differentiation have prompted their therapeutic application and utilization for evaluating potential cardiovascular safety liabilities. In this perspective, we showcase key efforts toward the large-scale production of hiPSC-CMs, implementation of hiPSC-CMs in industry settings, and recent clinical applications of this technology. The key observations are a need for traceable gender and ethnically diverse hiPSC lines, approaches to reduce cost of scale-up, accessible clinical trial datasets, and transparent guidelines surrounding the safety and efficacy of hiPSC-based therapies.
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Affiliation(s)
- Kavita Raniga
- The Biodiscovery Institute, University of Nottingham, Nottingham NG7 2RD, UK; Pathology, Non-Clinical Safety, GlaxoSmithKline R&D, Stevenage SG1 2NY, UK.
| | - Aishah Nasir
- The Biodiscovery Institute, University of Nottingham, Nottingham NG7 2RD, UK
| | - Nguyen T N Vo
- The Biodiscovery Institute, University of Nottingham, Nottingham NG7 2RD, UK
| | | | | | | | - Diogo Mosqueira
- The Biodiscovery Institute, University of Nottingham, Nottingham NG7 2RD, UK
| | - Gary R Mirams
- Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK
| | - Peter Clements
- Pathology, Non-Clinical Safety, GlaxoSmithKline R&D, Stevenage SG1 2NY, UK
| | - Ryan Hicks
- BioPharmaceuticals R&D Cell Therapy Department, Research and Early Development, Cardiovascular, Renal, and Metabolism (CVRM), BioPharmaceuticals R&D, AstraZeneca, Gothenburg, Sweden; School of Cardiovascular and Metabolic Medicine & Sciences, King's College London, London WC2R 2LS, UK
| | - Amy Pointon
- Safety Sciences, Clinical Pharmacology and Safety Sciences, BioPharmaceuticals R&D, AstraZeneca, Cambridge CB2 0AA, UK
| | | | - Jo Francis
- Mechanstic Biology and Profiling, Discovery Sciences, BioPharmaceuticals R&D, AstraZeneca, Cambridge CB2 0AA, UK
| | - Chris Denning
- The Biodiscovery Institute, University of Nottingham, Nottingham NG7 2RD, UK.
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3
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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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4
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Grandits T, Augustin CM, Haase G, Jost N, Mirams GR, Niederer SA, Plank G, Varró A, Virág L, Jung A. Neural network emulation of the human ventricular cardiomyocyte action potential: a tool for more efficient computation in pharmacological studies. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.08.16.553497. [PMID: 38234850 PMCID: PMC10793461 DOI: 10.1101/2023.08.16.553497] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/19/2024]
Abstract
Computer models of the human ventricular cardiomyocyte action potential (AP) have reached a level of detail and maturity that has led to an increasing number of applications in the pharmaceutical sector. However, interfacing the models with experimental data can become a significant computational burden. To mitigate the computational burden, the present study introduces a neural network (NN) that emulates the AP for given maximum conductances of selected ion channels, pumps, and exchangers. Its applicability in pharmacological studies was tested on synthetic and experimental data. The NN emulator potentially enables massive speed-ups compared to regular simulations and the forward problem (find drugged AP for pharmacological parameters defined as scaling factors of control maximum conductances) on synthetic data could be solved with average root-mean-square errors (RMSE) of 0.47mV in normal APs and of 14.5mV in abnormal APs exhibiting early afterdepolarizations (72.5% of the emulated APs were alining with the abnormality, and the substantial majority of the remaining APs demonstrated pronounced proximity). This demonstrates not only very fast and mostly very accurate AP emulations but also the capability of accounting for discontinuities, a major advantage over existing emulation strategies. Furthermore, the inverse problem (find pharmacological parameters for control and drugged APs through optimization) on synthetic data could be solved with high accuracy shown by a maximum RMSE of 0.21 in the estimated pharmacological parameters. However, notable mismatches were observed between pharmacological parameters estimated from experimental data and distributions obtained from the Comprehensive in vitro Proarrhythmia Assay initiative. This reveals larger inaccuracies which can be attributed particularly to the fact that small tissue preparations were studied while the emulator was trained on single cardiomyocyte data. Overall, our study highlights the potential of NN emulators as powerful tool for an increased efficiency in future quantitative systems pharmacology studies.
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Affiliation(s)
- Thomas Grandits
- Department of Mathematics and Scientific Computing, University of Graz
- NAWI Graz, University of Graz
| | - Christoph M Augustin
- Gottfried Schatz Research Center for Cell Signaling, Metabolism and Aging - Division of Medical Physics and Biophysics, Medical University of Graz
- BioTechMed-Graz
| | - Gundolf Haase
- Department of Mathematics and Scientific Computing, University of Graz
| | - Norbert Jost
- Department of Pharmacology and Pharmacotherapy, University of Szeged
- HUN-REN-TKI, Research Group of Pharmacology
| | - Gary R Mirams
- Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham
| | - Steven A Niederer
- Division of Imaging Sciences & Biomedical Engineering, King's College London
| | - Gernot Plank
- Gottfried Schatz Research Center for Cell Signaling, Metabolism and Aging - Division of Medical Physics and Biophysics, Medical University of Graz
- BioTechMed-Graz
| | - András Varró
- Department of Pharmacology and Pharmacotherapy, University of Szeged
- HUN-REN-TKI, Research Group of Pharmacology
| | - László Virág
- Department of Pharmacology and Pharmacotherapy, University of Szeged
| | - Alexander Jung
- Gottfried Schatz Research Center for Cell Signaling, Metabolism and Aging - Division of Medical Physics and Biophysics, Medical University of Graz
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5
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Marzi SJ, Schilder BM, Nott A, Frigerio CS, Willaime-Morawek S, Bucholc M, Hanger DP, James C, Lewis PA, Lourida I, Noble W, Rodriguez-Algarra F, Sharif JA, Tsalenchuk M, Winchester LM, Yaman Ü, Yao Z, Ranson JM, Llewellyn DJ. Artificial intelligence for neurodegenerative experimental models. Alzheimers Dement 2023; 19:5970-5987. [PMID: 37768001 DOI: 10.1002/alz.13479] [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: 04/17/2023] [Revised: 08/11/2023] [Accepted: 08/14/2023] [Indexed: 09/29/2023]
Abstract
INTRODUCTION Experimental models are essential tools in neurodegenerative disease research. However, the translation of insights and drugs discovered in model systems has proven immensely challenging, marred by high failure rates in human clinical trials. METHODS Here we review the application of artificial intelligence (AI) and machine learning (ML) in experimental medicine for dementia research. RESULTS Considering the specific challenges of reproducibility and translation between other species or model systems and human biology in preclinical dementia research, we highlight best practices and resources that can be leveraged to quantify and evaluate translatability. We then evaluate how AI and ML approaches could be applied to enhance both cross-model reproducibility and translation to human biology, while sustaining biological interpretability. DISCUSSION AI and ML approaches in experimental medicine remain in their infancy. However, they have great potential to strengthen preclinical research and translation if based upon adequate, robust, and reproducible experimental data. HIGHLIGHTS There are increasing applications of AI in experimental medicine. We identified issues in reproducibility, cross-species translation, and data curation in the field. Our review highlights data resources and AI approaches as solutions. Multi-omics analysis with AI offers exciting future possibilities in drug discovery.
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Affiliation(s)
- Sarah J Marzi
- UK Dementia Research Institute, Imperial College London, London, UK
- Department of Brain Sciences, Imperial College London, London, UK
| | - Brian M Schilder
- UK Dementia Research Institute, Imperial College London, London, UK
- Department of Brain Sciences, Imperial College London, London, UK
| | - Alexi Nott
- UK Dementia Research Institute, Imperial College London, London, UK
- Department of Brain Sciences, Imperial College London, London, UK
| | | | | | - Magda Bucholc
- School of Computing, Engineering & Intelligent Systems, Ulster University, Derry, UK
| | - Diane P Hanger
- Institute of Psychiatry, Psychology and Neuroscience, King's College London, London, UK
| | | | - Patrick A Lewis
- Royal Veterinary College, London, UK
- Department of Neurodegenerative Disease, UCL Queen Square Institute of Neurology, London, UK
| | | | - Wendy Noble
- Faculty of Health and Life Sciences, University of Exeter, Exeter, UK
| | | | - Jalil-Ahmad Sharif
- UK Dementia Research Institute, Imperial College London, London, UK
- Department of Brain Sciences, Imperial College London, London, UK
| | - Maria Tsalenchuk
- UK Dementia Research Institute, Imperial College London, London, UK
- Department of Brain Sciences, Imperial College London, London, UK
| | | | - Ümran Yaman
- UK Dementia Research Institute at UCL, London, UK
| | | | | | - David J Llewellyn
- University of Exeter Medical School, Exeter, UK
- Alan Turing Institute, London, UK
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6
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Song E. Impact of noise on the instability of spiral waves in stochastic 2D mathematical models of human atrial fibrillation. J Biol Phys 2023; 49:521-533. [PMID: 37792115 PMCID: PMC10651617 DOI: 10.1007/s10867-023-09644-0] [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: 08/02/2023] [Accepted: 09/08/2023] [Indexed: 10/05/2023] Open
Abstract
Sustained spiral waves, also known as rotors, are pivotal mechanisms in persistent atrial fibrillation (AF). Stochasticity is inevitable in nonlinear biological systems such as the heart; however, it is unclear how noise affects the instability of spiral waves in human AF. This study presents a stochastic two-dimensional mathematical model of human AF and explores how Gaussian white noise affects the instability of spiral waves. In homogeneous tissue models, Gaussian white noise may lead to spiral-wave meandering and wavefront break-up. As the noise intensity increases, the spatial dispersion of phase singularity (PS) points increases. This finding indicates the potential AF-protective effects of cardiac system stochasticity by destabilizing the rotors. By contrast, Gaussian white noise is unlikely to affect the spiral-wave instability in the presence of localized scar or fibrosis regions. The PS points are located at the boundary or inside the scar/fibrosis regions. Localized scar or fibrosis may play a pivotal role in stabilizing spiral waves regardless of the presence of noise. This study suggests that fibrosis and scars are essential for stabilizing the rotors in stochastic mathematical models of AF. Further patient-derived realistic modeling studies are required to confirm the role of scar/fibrosis in AF pathophysiology.
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Affiliation(s)
- Euijun Song
- Yonsei University College of Medicine, Seoul, Republic of Korea.
- , Gyeonggi, Republic of Korea.
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7
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Shuttleworth JG, Lei CL, Whittaker DG, Windley MJ, Hill AP, Preston SP, Mirams GR. Empirical Quantification of Predictive Uncertainty Due to Model Discrepancy by Training with an Ensemble of Experimental Designs: An Application to Ion Channel Kinetics. Bull Math Biol 2023; 86:2. [PMID: 37999811 PMCID: PMC10673765 DOI: 10.1007/s11538-023-01224-6] [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: 01/31/2023] [Accepted: 10/09/2023] [Indexed: 11/25/2023]
Abstract
When using mathematical models to make quantitative predictions for clinical or industrial use, it is important that predictions come with a reliable estimate of their accuracy (uncertainty quantification). Because models of complex biological systems are always large simplifications, model discrepancy arises-models fail to perfectly recapitulate the true data generating process. This presents a particular challenge for making accurate predictions, and especially for accurately quantifying uncertainty in these predictions. Experimentalists and modellers must choose which experimental procedures (protocols) are used to produce data used to train models. We propose to characterise uncertainty owing to model discrepancy with an ensemble of parameter sets, each of which results from training to data from a different protocol. The variability in predictions from this ensemble provides an empirical estimate of predictive uncertainty owing to model discrepancy, even for unseen protocols. We use the example of electrophysiology experiments that investigate the properties of hERG potassium channels. Here, 'information-rich' protocols allow mathematical models to be trained using numerous short experiments performed on the same cell. In this case, we simulate data with one model and fit it with a different (discrepant) one. For any individual experimental protocol, parameter estimates vary little under repeated samples from the assumed additive independent Gaussian noise model. Yet parameter sets arising from the same model applied to different experiments conflict-highlighting model discrepancy. Our methods will help select more suitable ion channel models for future studies, and will be widely applicable to a range of biological modelling problems.
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Affiliation(s)
- Joseph G Shuttleworth
- Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK
| | - 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
| | - Dominic G Whittaker
- Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK
- 4 Systems Modeling & Translational Biology, Stevenage, GSK, UK
| | - Monique J Windley
- Computational Cardiology Laboratory, Victor Chang Cardiac Research Institute, Darlinghurst, NSW, Australia
- School of Clinical Medicine, Faculty of Medicine and Health, University of New South Wales, Sydney, NSW, Australia
| | - Adam P Hill
- Computational Cardiology Laboratory, Victor Chang Cardiac Research Institute, Darlinghurst, NSW, Australia
- School of Clinical Medicine, Faculty of Medicine and Health, University of New South Wales, Sydney, NSW, Australia
| | - Simon P Preston
- Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK
| | - Gary R Mirams
- Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK.
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Kopańska K, Rodríguez-Belenguer P, Llopis-Lorente J, Trenor B, Saiz J, Pastor M. Uncertainty assessment of proarrhythmia predictions derived from multi-level in silico models. Arch Toxicol 2023; 97:2721-2740. [PMID: 37528229 PMCID: PMC10474996 DOI: 10.1007/s00204-023-03557-6] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/28/2023] [Accepted: 07/12/2023] [Indexed: 08/03/2023]
Abstract
In silico methods can be used for an early assessment of arrhythmogenic properties of drug candidates. However, their use for decision-making is conditioned by the possibility to estimate the predictions' uncertainty. This work describes our efforts to develop uncertainty quantification methods for the predictions produced by multi-level proarrhythmia models. In silico models used in this field usually start with experimental or predicted IC50 values that describe drug-induced ion channel blockade. Using such inputs, an electrophysiological model computes how the ion channel inhibition, exerted by a drug in a certain concentration, translates to an altered shape and duration of the action potential in cardiac cells, which can be represented as arrhythmogenic risk biomarkers such as the APD90. Using this framework, we identify the main sources of aleatory and epistemic uncertainties and propose a method based on probabilistic simulations that replaces single-point estimates predicted using multiple input values, including the IC50s and the electrophysiological parameters, by distributions of values. Two selected variability types associated with these inputs are then propagated through the multi-level model to estimate their impact on the uncertainty levels in the output, expressed by means of intervals. The proposed approach yields single predictions of arrhythmogenic risk biomarkers together with value intervals, providing a more comprehensive and realistic description of drug effects on a human population. The methodology was tested by predicting arrhythmogenic biomarkers on a series of twelve well-characterised marketed drugs, belonging to different arrhythmogenic risk classes.
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Affiliation(s)
- Karolina Kopańska
- Research Programme on Biomedical Informatics (GRIB), Department of Medicine and Life Sciences, Universitat Pompeu Fabra, Hospital del Mar Research Institute, Barcelona, Spain
| | - Pablo Rodríguez-Belenguer
- Research Programme on Biomedical Informatics (GRIB), Department of Medicine and Life Sciences, Universitat Pompeu Fabra, Hospital del Mar Research Institute, Barcelona, Spain
- Department of Pharmacy and Pharmaceutical Technology and Parasitology, Universitat de València, Valencia, Spain
| | - Jordi Llopis-Lorente
- Centro de Investigación e Innovación en Bioingeniería (Ci2B), Universitat Politècnica de València, Valencia, Spain
| | - Beatriz Trenor
- Centro de Investigación e Innovación en Bioingeniería (Ci2B), Universitat Politècnica de València, Valencia, Spain
| | - Javier Saiz
- Centro de Investigación e Innovación en Bioingeniería (Ci2B), Universitat Politècnica de València, Valencia, Spain
| | - Manuel Pastor
- Research Programme on Biomedical Informatics (GRIB), Department of Medicine and Life Sciences, Universitat Pompeu Fabra, Hospital del Mar Research Institute, Barcelona, Spain.
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9
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Clark AP, Clerx M, Wei S, Lei CL, de Boer TP, Mirams GR, Christini DJ, Krogh-Madsen T. Leak current, even with gigaohm seals, can cause misinterpretation of stem cell-derived cardiomyocyte action potential recordings. Europace 2023; 25:euad243. [PMID: 37552789 PMCID: PMC10445319 DOI: 10.1093/europace/euad243] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2023] [Accepted: 06/18/2023] [Indexed: 08/10/2023] Open
Abstract
AIMS Human-induced pluripotent stem cell-derived cardiomyocytes (iPSC-CMs) have become an essential tool to study arrhythmia mechanisms. Much of the foundational work on these cells, as well as the computational models built from the resultant data, has overlooked the contribution of seal-leak current on the immature and heterogeneous phenotype that has come to define these cells. The aim of this study is to understand the effect of seal-leak current on recordings of action potential (AP) morphology. METHODS AND RESULTS Action potentials were recorded in human iPSC-CMs using patch clamp and simulated using previously published mathematical models. Our in silico and in vitro studies demonstrate how seal-leak current depolarizes APs, substantially affecting their morphology, even with seal resistances (Rseal) above 1 GΩ. We show that compensation of this leak current is difficult due to challenges with obtaining accurate measures of Rseal during an experiment. Using simulation, we show that Rseal measures (i) change during an experiment, invalidating the use of pre-rupture values, and (ii) are polluted by the presence of transmembrane currents at every voltage. Finally, we posit that the background sodium current in baseline iPSC-CM models imitates the effects of seal-leak current and is increased to a level that masks the effects of seal-leak current on iPSC-CMs. CONCLUSION Based on these findings, we make recommendations to improve iPSC-CM AP data acquisition, interpretation, and model-building. Taking these recommendations into account will improve our understanding of iPSC-CM physiology and the descriptive ability of models built from such data.
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Affiliation(s)
- Alexander P Clark
- Department of Biomedical Engineering, Cornell University, Ithaca, NY, USA
| | - Michael Clerx
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, UK
| | - Siyu Wei
- Department of Physiology and Pharmacology, SUNY Downstate Health Sciences University, Brooklyn, NY, USA
| | - 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
| | - Teun P de Boer
- Department of Medical Physiology, Division of Heart and Lungs, University Medical Center Utrecht, Utrecht, The Netherlands
| | - Gary R Mirams
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, UK
| | - David J Christini
- Department of Biomedical Engineering, Cornell University, Ithaca, NY, USA
- Department of Physiology and Pharmacology, SUNY Downstate Health Sciences University, Brooklyn, NY, USA
| | - Trine Krogh-Madsen
- Department of Physiology and Biophysics, Weill Cornell Medicine, 1300 York Avenue, Box 75, Room C501D, New York, 10065 NY, USA
- Institute for Computational Biomedicine, Weill Cornell Medicine, 1300 York Avenue, Box 75, Room C501D, New York, 10065 NY, USA
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10
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Strocchi M, Longobardi S, Augustin CM, Gsell MAF, Petras A, Rinaldi CA, Vigmond EJ, Plank G, Oates CJ, Wilkinson RD, Niederer SA. Cell to whole organ global sensitivity analysis on a four-chamber heart electromechanics model using Gaussian processes emulators. PLoS Comput Biol 2023; 19:e1011257. [PMID: 37363928 DOI: 10.1371/journal.pcbi.1011257] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2022] [Accepted: 06/09/2023] [Indexed: 06/28/2023] Open
Abstract
Cardiac pump function arises from a series of highly orchestrated events across multiple scales. Computational electromechanics can encode these events in physics-constrained models. However, the large number of parameters in these models has made the systematic study of the link between cellular, tissue, and organ scale parameters to whole heart physiology challenging. A patient-specific anatomical heart model, or digital twin, was created. Cellular ionic dynamics and contraction were simulated with the Courtemanche-Land and the ToR-ORd-Land models for the atria and the ventricles, respectively. Whole heart contraction was coupled with the circulatory system, simulated with CircAdapt, while accounting for the effect of the pericardium on cardiac motion. The four-chamber electromechanics framework resulted in 117 parameters of interest. The model was broken into five hierarchical sub-models: tissue electrophysiology, ToR-ORd-Land model, Courtemanche-Land model, passive mechanics and CircAdapt. For each sub-model, we trained Gaussian processes emulators (GPEs) that were then used to perform a global sensitivity analysis (GSA) to retain parameters explaining 90% of the total sensitivity for subsequent analysis. We identified 45 out of 117 parameters that were important for whole heart function. We performed a GSA over these 45 parameters and identified the systemic and pulmonary peripheral resistance as being critical parameters for a wide range of volumetric and hemodynamic cardiac indexes across all four chambers. We have shown that GPEs provide a robust method for mapping between cellular properties and clinical measurements. This could be applied to identify parameters that can be calibrated in patient-specific models or digital twins, and to link cellular function to clinical indexes.
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Affiliation(s)
- Marina Strocchi
- 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
| | - Stefano Longobardi
- School of Biomedical Engineering and Imaging Sciences, King's College London, London, United Kingdom
| | | | | | - Argyrios Petras
- Johann Radon Institute for Computational and Applied Mathematics (RICAM), Linz, Austria
| | - Christopher A Rinaldi
- School of Biomedical Engineering and Imaging Sciences, King's College London, London, United Kingdom
- Guy's and St Thomas' NHS Foundation Trust, London, United Kingdom
| | - Edward J Vigmond
- University of Bordeaux, CNRS, Bordeaux, Talence, France
- IHU Liryc, Bordeaux, Talence, France
| | - Gernot Plank
- Medical University of Graz, Graz, Austria
- BioTechMed-Graz, Graz, Austria
| | - Chris J Oates
- Newcastle University, Newcastle upon Tyne, United Kingdom
| | | | - Steven A Niederer
- 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
- Alan Turing Institute, London, United Kingdom
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11
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Corrado C, Roney CH, Razeghi O, Lemus JAS, Coveney S, Sim I, Williams SE, O'Neill MD, Wilkinson RD, Clayton RH, Niederer SA. Quantifying the impact of shape uncertainty on predicted arrhythmias. Comput Biol Med 2023; 153:106528. [PMID: 36634600 DOI: 10.1016/j.compbiomed.2022.106528] [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: 09/09/2022] [Revised: 12/15/2022] [Accepted: 12/31/2022] [Indexed: 01/11/2023]
Abstract
BACKGROUND Personalised computer models are increasingly used to diagnose cardiac arrhythmias and tailor treatment. Patient-specific models of the left atrium are often derived from pre-procedural imaging of anatomy and fibrosis. These images contain noise that can affect simulation predictions. There are few computationally tractable methods for propagating uncertainties from images to clinical predictions. METHOD We describe the left atrium anatomy using our Bayesian shape model that captures anatomical uncertainty in medical images and has been validated on 63 independent clinical images. This algorithm describes the left atrium anatomy using Nmodes=15 principal components, capturing 95% of the shape variance and calculated from 70 clinical cardiac magnetic resonance (CMR) images. Latent variables encode shape uncertainty: we evaluate their posterior distribution for each new anatomy. We assume a normally distributed prior. We use the unscented transform to sample from the posterior shape distribution. For each sample, we assign the local material properties of the tissue using the projection of late gadolinium enhancement CMR (LGE-CMR) onto the anatomy to estimate local fibrosis. To test which activation patterns an atrium can sustain, we perform an arrhythmia simulation for each sample. We consider 34 possible outcomes (31 macro-re-entries, functional re-entry, atrial fibrillation, and non-sustained arrhythmia). For each sample, we determine the outcome by comparing pre- and post-ablation activation patterns following a cross-field stimulus. RESULTS We create patient-specific atrial electrophysiology models of ten patients. We validate the mean and standard deviation maps from the unscented transform with the same statistics obtained with 12,000 Monte Carlo (ground truth) samples. We found discrepancies <3% and <2% for the mean and standard deviation for fibrosis burden and activation time, respectively. For each patient case, we then compare the predicted outcome from a model built on the clinical data (deterministic approach) with the probability distribution obtained from the simulated samples. We found that the deterministic approach did not predict the most likely outcome in 80% of the cases. Finally, we estimate the influence of each source of uncertainty independently. Fixing the anatomy to the posterior mean and maintaining uncertainty in fibrosis reduced the prediction of self-terminating arrhythmias from ≃14% to ≃7%. Keeping the fibrosis fixed to the sample mean while retaining uncertainty in shape decreased the prediction of substrate-driven arrhythmias from ≃33% to ≃18% and increased the prediction of macro-re-entries from ≃54% to ≃68%. CONCLUSIONS We presented a novel method for propagating shape uncertainty in atrial models through to uncertainty in numerical simulations. The algorithm takes advantage of the unscented transform to compute the output distribution of the outcomes. We validated the unscented transform as a viable sampling strategy to deal with anatomy uncertainty. We then showed that the prediction computed with a deterministic model does not always coincide with the most likely outcome. Finally, we found that shape uncertainty affects the predictions of macro-re-entries, while fibrosis uncertainty affects the predictions of functional re-entries.
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Affiliation(s)
- Cesare Corrado
- Division of Imaging Sciences & Biomedical Engineering, King's College London, London SE17EH, United Kingdom.
| | - Caroline H Roney
- Division of Imaging Sciences & Biomedical Engineering, King's College London, London SE17EH, United Kingdom; School of Engineering and Materials Science, Queen Mary University of London, London, United Kingdom
| | - Orod Razeghi
- Division of Imaging Sciences & Biomedical Engineering, King's College London, London SE17EH, United Kingdom; UCL Centre for Advanced Research Computing, London, United Kingdom
| | - Josè Alonso Solís Lemus
- Division of Imaging Sciences & Biomedical Engineering, King's College London, London SE17EH, United Kingdom
| | - Sam Coveney
- Insigneo Institute for in-silico Medicine and Department of Computer Science, University of Sheffield, Sheffield, United Kingdom
| | - Iain Sim
- Division of Imaging Sciences & Biomedical Engineering, King's College London, London SE17EH, United Kingdom
| | - Steven E Williams
- Division of Imaging Sciences & Biomedical Engineering, King's College London, London SE17EH, United Kingdom
| | - Mark D O'Neill
- Division of Imaging Sciences & Biomedical Engineering, King's College London, London SE17EH, United Kingdom
| | - Richard D Wilkinson
- School of Mathematical Sciences, University of Nottingham, Nottingham, United Kingdom
| | - Richard H Clayton
- Insigneo Institute for in-silico Medicine and Department of Computer Science, University of Sheffield, Sheffield, United Kingdom
| | - Steven A Niederer
- Division of Imaging Sciences & Biomedical Engineering, King's College London, London SE17EH, United Kingdom
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12
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Monasterio V, Pueyo E, Rodríguez-Matas JF, Carro J. Cardiac cells stimulated with an axial current-like waveform reproduce electrophysiological properties of tissue fibers. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2022; 226:107121. [PMID: 36156439 DOI: 10.1016/j.cmpb.2022.107121] [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: 05/09/2022] [Revised: 09/01/2022] [Accepted: 09/07/2022] [Indexed: 06/16/2023]
Abstract
BACKGROUND AND OBJECTIVE In silico electrophysiological models are generally validated by comparing simulated results with experimental data. When dealing with single-cell and tissue scales simultaneously, as occurs frequently during model development and calibration, the effects of inter-cellular coupling should be considered to ensure the trustworthiness of model predictions. The hypothesis of this paper is that the cell-tissue mismatch can be reduced by incorporating the effects of conduction into the single-cell stimulation current. METHODS Five different stimulation waveforms were applied to the human ventricular O'Hara-Rudy cell model. The waveforms included the commonly used monophasic and biphasic (symmetric and asymmetric) pulses, a triangular waveform and a newly proposed asymmetric waveform (stimulation A) that resembles the transmembrane current associated with AP conduction in tissue. A comparison between single-cell and fiber simulated results was established by computing the relative difference between the values of AP-derived properties at different scales, and by evaluating the differences in the contributions of ionic conductances to each evaluated property. As a proof of the benefit, we investigated multi-scale differences in the simulation of the effects induced by dofetilide, a selective IKr blocker with high torsadogenic risk, on ventricular repolarization at different pacing rates. RESULTS Out of the five tested stimulation waveforms, stimulation A produced the closest correspondence between cell and tissue simulations in terms of AP properties at steady-state and under dynamic pacing and of ionic contributors to those AP properties. Also, stimulation A reproduced the effects of dofetilide better than the other alternative waveforms, mirroring the 'beat-skipping' behavior observed at fast pacing rates in experiments with human tissue. CONCLUSIONS The proposed stimulation current waveform accounts for inter-cellular coupling effects by mimicking cell excitation during AP conduction. The proposed waveform improves the correspondence between simulation scales, which could improve the trustworthiness of single-cell simulations without adding computational cost.
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Affiliation(s)
| | - Esther Pueyo
- Aragón Institute for Engineering Research, University of Zaragoza, IIS Aragón, Zaragoza, Spain; CIBER in Bioengineering, Biomaterials and Nanomedicine (CIBER-BBN), Spain
| | - José Félix Rodríguez-Matas
- LaBS, Department of Chemistry, Materials and Chemical Engineering "Giulio Natta", Politecnico di Milano, Italy
| | - Jesús Carro
- Universidad San Jorge, Villanueva de Gállego, Spain
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13
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Interpretable machine learning of action potential duration restitution kinetics in single-cell models of atrial cardiomyocytes. J Electrocardiol 2022; 74:137-145. [PMID: 36223672 DOI: 10.1016/j.jelectrocard.2022.09.010] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2022] [Revised: 08/28/2022] [Accepted: 09/19/2022] [Indexed: 12/13/2022]
Abstract
Action potential duration (APD) restitution curve and its maximal slope (Smax) reflect single cell-level dynamic instability for inducing chaotic heart rhythms. However, conventional parameter sensitivity analysis often fails to describe nonlinear relationships between ion channel parameters and electrophysiological phenotypes, such as Smax. We explored the parameter-phenotype mapping in a population of 5000 single-cell atrial cell models through interpretable machine learning (ML) approaches. Parameter sensitivity analyses could explain the linear relationships between parameters and electrophysiological phenotypes, including APD90, resting membrane potential, Vmax, refractory period, and APD/calcium alternans threshold, but not for Smax. However, neural network models had better prediction performance for Smax. To interpret the ML model, we evaluated the parameter importance at the global and local levels by computing the permutation feature importance and the local interpretable model-agnostic explanations (LIME) values, respectively. Increases in ICaL, INCX, and IKr, and decreases in IK1, Ib,Cl, IKur, ISERCA, and Ito are correlated with higher Smax values. The LIME algorithm determined that INaK plays a significant role in determining Smax as well as Ito and IKur. The atrial cardiomyocyte population was hierarchically clustered into three distinct groups based on the LIME values and the single-cell simulation confirmed that perturbations in INaK resulted in different behaviors of APD restitution curves in three clusters. Our combined top-down interpretable ML and bottom-up mechanistic simulation approaches uncovered the role of INaK in heterogeneous behaviors of Smax in the atrial cardiomyocyte population.
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14
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Dantas E, Orlande HRB, Dulikravich GS. Thermal ablation effects on rotors that characterize functional re-entry cardiac arrhythmia. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2022; 38:e3614. [PMID: 35543287 DOI: 10.1002/cnm.3614] [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: 02/17/2022] [Revised: 04/29/2022] [Accepted: 05/06/2022] [Indexed: 06/14/2023]
Abstract
Thermal ablation is a well-established successful treatment for cardiac arrhythmia, but it still presents limitations that require further studies and developments. In the rotor-driven functional re-entry arrhythmia, tissue heterogeneity results on the generation of spiral/scroll waves and wave break dynamics that may cause dangerous sustainable fibrillation. The selection of the target region to perform thermal ablation to mitigate this type of arrhythmia is challenging, since it considerably affects the local electrophysiology dynamics. This work deals with the numerical simulation of the thermal ablation of a cardiac muscle tissue and its effects on the dynamics of rotor-driven functional re-entry arrhythmia. A non-homogeneous two-dimensional rectangular region is used in the present numerical analysis, where radiofrequency ablation is performed. The electrophysiology problem for the propagation of the action potential in the cardiac tissue is simulated with the Fenton-Karma model. Thermal damage caused to the tissue by the radiofrequency heating is modeled by the Arrhenius equation. The effects of size and position of a heterogeneous region in the original muscle tissue were first analyzed, in order to verify the possible existence of the functional re-entry arrhythmia during the time period considered in the simulations. For each case that exhibited re-entry arrhythmia, six different ablation procedures were analyzed, depending on the position of the radiofrequency electrode and heating time. The obtained results revealed the effects of different model parameters on the existence and possible mitigation of the functional re-entry arrhythmia.
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Affiliation(s)
- Eber Dantas
- Department of Mechanical Engineering, Politécnica/COPPE, Federal University of Rio de Janeiro - UFRJ, Rio de Janeiro, Brazil
| | - Helcio R B Orlande
- Department of Mechanical Engineering, Politécnica/COPPE, Federal University of Rio de Janeiro - UFRJ, Rio de Janeiro, Brazil
| | - George S Dulikravich
- Department of Mechanical and Materials Engineering, MAIDROC Lab., Florida International University, Miami, Florida, USA
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15
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Sleutjes BTHM, Stikvoort García DJL, Kovalchuk MO, Heuberger JAAC, Groeneveld GJ, Franssen H, van den Berg LH. Acute retigabine-induced effects on myelinated motor axons in amyotrophic lateral sclerosis. Pharmacol Res Perspect 2022; 10:e00983. [PMID: 35881020 PMCID: PMC9318643 DOI: 10.1002/prp2.983] [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: 12/22/2021] [Revised: 06/11/2022] [Accepted: 06/15/2022] [Indexed: 11/24/2022] Open
Abstract
Altered motor neuron excitability in patients with amyotrophic lateral sclerosis (ALS) has been suggested to be an early pathophysiological mechanism associated with motor neuron death. Compounds that affect membrane excitability may therefore have disease‐modifying effects. Through which mechanism(s), these compounds modulate membrane excitability is mostly provided by preclinical studies, yet remains challenging to verify in clinical studies. Here, we investigated how retigabine affects human myelinated motor axons by applying computational modeling to interpret the complex excitability changes in a recent trial involving 18 ALS patients. Compared to baseline, the post‐dose excitability differences were modeled well by a hyperpolarizing shift of the half‐activation potential of slow potassium (K+)‐channels (till 2 mV). These findings verify that retigabine targets slow K+‐channel gating and highlight the usefulness of computational models. Further developments of this approach may facilitate the identification of early target engagement and ultimately aid selecting responders leading to more personalized treatment strategies.
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Affiliation(s)
- Boudewijn T H M Sleutjes
- Department of Neurology, Brain Center Utrecht, University Medical Center Utrecht, Utrecht, The Netherlands
| | | | - Maria O Kovalchuk
- Department of Neurology, Brain Center Utrecht, University Medical Center Utrecht, Utrecht, The Netherlands
| | | | | | - Hessel Franssen
- Department of Neurology, Brain Center Utrecht, University Medical Center Utrecht, Utrecht, The Netherlands
| | - Leonard H van den Berg
- Department of Neurology, Brain Center Utrecht, University Medical Center Utrecht, Utrecht, The Netherlands
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16
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Marx L, Niestrawska JA, Gsell MA, Caforio F, Plank G, Augustin CM. Robust and efficient fixed-point algorithm for the inverse elastostatic problem to identify myocardial passive material parameters and the unloaded reference configuration. JOURNAL OF COMPUTATIONAL PHYSICS 2022; 463:111266. [PMID: 35662800 PMCID: PMC7612790 DOI: 10.1016/j.jcp.2022.111266] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
Image-based computational models of the heart represent a powerful tool to shed new light on the mechanisms underlying physiological and pathological conditions in cardiac function and to improve diagnosis and therapy planning. However, in order to enable the clinical translation of such models, it is crucial to develop personalized models that are able to reproduce the physiological reality of a given patient. There have been numerous contributions in experimental and computational biomechanics to characterize the passive behavior of the myocardium. However, most of these studies suffer from severe limitations and are not applicable to high-resolution geometries. In this work, we present a novel methodology to perform an automated identification of in vivo properties of passive cardiac biomechanics. The highly-efficient algorithm fits material parameters against the shape of a patient-specific approximation of the end-diastolic pressure-volume relation (EDPVR). Simultaneously, an unloaded reference configuration is generated, where a novel line search strategy to improve convergence and robustness is implemented. Only clinical image data or previously generated meshes at one time point during diastole and one measured data point of the EDPVR are required as an input. The proposed method can be straightforwardly coupled to existing finite element (FE) software packages and is applicable to different constitutive laws and FE formulations. Sensitivity analysis demonstrates that the algorithm is robust with respect to initial input parameters.
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Affiliation(s)
- Laura Marx
- Gottfried Schatz Research Center for Cell Signaling, Metabolism and Aging - Division of Biophysics, Medical University of Graz, Graz, Austria
- BioTechMed-Graz, Graz, Austria
| | - Justyna A. Niestrawska
- Gottfried Schatz Research Center for Cell Signaling, Metabolism and Aging - Division of Biophysics, Medical University of Graz, Graz, Austria
| | - Matthias A.F. Gsell
- Gottfried Schatz Research Center for Cell Signaling, Metabolism and Aging - Division of Biophysics, Medical University of Graz, Graz, Austria
| | - Federica Caforio
- Gottfried Schatz Research Center for Cell Signaling, Metabolism and Aging - Division of Biophysics, Medical University of Graz, Graz, Austria
- Institute of Mathematics and Scientific Computing, University of Graz, Graz, Austria
| | - Gernot Plank
- Gottfried Schatz Research Center for Cell Signaling, Metabolism and Aging - Division of Biophysics, Medical University of Graz, Graz, Austria
- BioTechMed-Graz, Graz, Austria
| | - Christoph M. Augustin
- Gottfried Schatz Research Center for Cell Signaling, Metabolism and Aging - Division of Biophysics, Medical University of Graz, Graz, Austria
- BioTechMed-Graz, Graz, Austria
- Corresponding author at: Gottfried Schatz Research Center: Division of Biophysics, Medical University of Graz, Neue Stiftingtalstrasse 6/D04, 8010 Graz, Austria. (C.M.Augustin)
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17
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Guan D, Gao H, Cai L, Luo X. A new active contraction model for the myocardium using a modified hill model. Comput Biol Med 2022; 145:105417. [DOI: 10.1016/j.compbiomed.2022.105417] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/29/2021] [Revised: 02/11/2022] [Accepted: 02/21/2022] [Indexed: 11/16/2022]
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18
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Lazarus A, Dalton D, Husmeier D, Gao H. Sensitivity analysis and inverse uncertainty quantification for the left ventricular passive mechanics. Biomech Model Mechanobiol 2022; 21:953-982. [PMID: 35377030 PMCID: PMC9132878 DOI: 10.1007/s10237-022-01571-8] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2021] [Accepted: 02/28/2022] [Indexed: 01/08/2023]
Abstract
Personalized computational cardiac models are considered to be a unique and powerful tool in modern cardiology, integrating the knowledge of physiology, pathology and fundamental laws of mechanics in one framework. They have the potential to improve risk prediction in cardiac patients and assist in the development of new treatments. However, in order to use these models for clinical decision support, it is important that both the impact of model parameter perturbations on the predicted quantities of interest as well as the uncertainty of parameter estimation are properly quantified, where the first task is a priori in nature (meaning independent of any specific clinical data), while the second task is carried out a posteriori (meaning after specific clinical data have been obtained). The present study addresses these challenges for a widely used constitutive law of passive myocardium (the Holzapfel-Ogden model), using global sensitivity analysis (SA) to address the first challenge, and inverse-uncertainty quantification (I-UQ) for the second challenge. The SA is carried out on a range of different input parameters to a left ventricle (LV) model, making use of computationally efficient Gaussian process (GP) surrogate models in place of the numerical forward simulator. The results of the SA are then used to inform a low-order reparametrization of the constitutive law for passive myocardium under consideration. The quality of this parameterization in the context of an inverse problem having observed noisy experimental data is then quantified with an I-UQ study, which again makes use of GP surrogate models. The I-UQ is carried out in a Bayesian manner using Markov Chain Monte Carlo, which allows for full uncertainty quantification of the material parameter estimates. Our study reveals insights into the relation between SA and I-UQ, elucidates the dependence of parameter sensitivity and estimation uncertainty on external factors, like LV cavity pressure, and sheds new light on cardio-mechanic model formulation, with particular focus on the Holzapfel-Ogden myocardial model.
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Affiliation(s)
- Alan Lazarus
- School of Mathematics and Statistics, University of Glasgow, Glasgow, UK
| | - David Dalton
- School of Mathematics and Statistics, University of Glasgow, Glasgow, UK
| | - Dirk Husmeier
- School of Mathematics and Statistics, University of Glasgow, Glasgow, UK
| | - Hao Gao
- School of Mathematics and Statistics, University of Glasgow, Glasgow, UK
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19
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Russo G, Parasiliti Palumbo GA, Pennisi M, Pappalardo F. Model verification tools: a computational framework for verification assessment of mechanistic agent-based models. BMC Bioinformatics 2022; 22:626. [PMID: 35590242 PMCID: PMC9117838 DOI: 10.1186/s12859-022-04684-0] [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: 04/05/2022] [Accepted: 04/11/2022] [Indexed: 11/10/2022] Open
Abstract
BACKGROUND Nowadays, the inception of computer modeling and simulation in life science is a matter of fact. This is one of the reasons why regulatory authorities are open in considering in silico trials evidence for the assessment of safeness and efficacy of medicinal products. In this context, mechanistic Agent-Based Models are increasingly used. Unfortunately, there is still a lack of consensus in the verification assessment of Agent-Based Models for regulatory approval needs. VV&UQ is an ASME standard specifically suited for the verification, validation, and uncertainty quantification of medical devices. However, it can also be adapted for the verification assessment of in silico trials for medicinal products. RESULTS Here, we propose a set of automatic tools for the mechanistic Agent-Based Model verification assessment. As a working example, we applied the verification framework to an Agent-Based Model in silico trial used in the COVID-19 context. CONCLUSIONS Using the described verification computational workflow allows researchers and practitioners to easily perform verification steps to prove Agent-Based Models robustness and correctness that provide strong evidence for further regulatory requirements.
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Affiliation(s)
- Giulia Russo
- Department of Drug and Health Sciences, University of Catania, 95125, Catania, Italy
| | | | - Marzio Pennisi
- Computer Science Institute, DiSIT, University of Eastern Piedmont, 15121, Alessandria, Italy
| | - Francesco Pappalardo
- Department of Drug and Health Sciences, University of Catania, 95125, Catania, Italy.
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20
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Jung A, Gsell MAF, Augustin CM, Plank G. An Integrated Workflow for Building Digital Twins of Cardiac Electromechanics—A Multi-Fidelity Approach for Personalising Active Mechanics. MATHEMATICS 2022; 10:823. [PMID: 35295404 PMCID: PMC7612499 DOI: 10.3390/math10050823] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
Personalised computer models of cardiac function, referred to as cardiac digital twins, are envisioned to play an important role in clinical precision therapies of cardiovascular diseases. A major obstacle hampering clinical translation involves the significant computational costs involved in the personalisation of biophysically detailed mechanistic models that require the identification of high-dimensional parameter vectors. An important aspect to identify in electromechanics (EM) models are active mechanics parameters that govern cardiac contraction and relaxation. In this study, we present a novel, fully automated, and efficient approach for personalising biophysically detailed active mechanics models using a two-step multi-fidelity solution. In the first step, active mechanical behaviour in a given 3D EM model is represented by a purely phenomenological, low-fidelity model, which is personalised at the organ scale by calibration to clinical cavity pressure data. Then, in the second step, median traces of nodal cellular active stress, intracellular calcium concentration, and fibre stretch are generated and utilised to personalise the desired high-fidelity model at the cellular scale using a 0D model of cardiac EM. Our novel approach was tested on a cohort of seven human left ventricular (LV) EM models, created from patients treated for aortic coarctation (CoA). Goodness of fit, computational cost, and robustness of the algorithm against uncertainty in the clinical data and variations of initial guesses were evaluated. We demonstrate that our multi-fidelity approach facilitates the personalisation of a biophysically detailed active stress model within only a few (2 to 4) expensive 3D organ-scale simulations—a computational effort compatible with clinical model applications.
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Affiliation(s)
- Alexander Jung
- Gottfried Schatz Research Center for Cell Signaling, Metabolism and Aging—Division of Biophysics, Medical University Graz, 8010 Graz, Austria
| | - Matthias A. F. Gsell
- Gottfried Schatz Research Center for Cell Signaling, Metabolism and Aging—Division of Biophysics, Medical University Graz, 8010 Graz, Austria
- NAWI Graz, Institute of Mathematics and Scientific Computing, University of Graz, 8010 Graz, Austria
| | - Christoph M. Augustin
- Gottfried Schatz Research Center for Cell Signaling, Metabolism and Aging—Division of Biophysics, Medical University Graz, 8010 Graz, Austria
- BioTechMed-Graz, 8010 Graz, Austria
- Correspondence:
| | - Gernot Plank
- Gottfried Schatz Research Center for Cell Signaling, Metabolism and Aging—Division of Biophysics, Medical University Graz, 8010 Graz, Austria
- BioTechMed-Graz, 8010 Graz, Austria
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21
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Sher A, Niederer SA, Mirams GR, Kirpichnikova A, Allen R, Pathmanathan P, Gavaghan DJ, van der Graaf PH, Noble D. A Quantitative Systems Pharmacology Perspective on the Importance of Parameter Identifiability. Bull Math Biol 2022; 84:39. [PMID: 35132487 PMCID: PMC8821410 DOI: 10.1007/s11538-021-00982-5] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2021] [Accepted: 11/30/2021] [Indexed: 12/31/2022]
Abstract
There is an inherent tension in Quantitative Systems Pharmacology (QSP) between the need to incorporate mathematical descriptions of complex physiology and drug targets with the necessity of developing robust, predictive and well-constrained models. In addition to this, there is no “gold standard” for model development and assessment in QSP. Moreover, there can be confusion over terminology such as model and parameter identifiability; complex and simple models; virtual populations; and other concepts, which leads to potential miscommunication and misapplication of methodologies within modeling communities, both the QSP community and related disciplines. This perspective article highlights the pros and cons of using simple (often identifiable) vs. complex (more physiologically detailed but often non-identifiable) models, as well as aspects of parameter identifiability, sensitivity and inference methodologies for model development and analysis. The paper distills the central themes of the issue of identifiability and optimal model size and discusses open challenges.
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Affiliation(s)
- Anna Sher
- Pfizer Worldwide Research, Development and Medical, Massachusetts, USA.
| | | | - Gary R Mirams
- Centre for Mathematical Medicine and Biology, Mathematical Sciences, University of Nottingham, Nottingham, UK
| | | | - Richard Allen
- Pfizer Worldwide Research, Development and Medical, Massachusetts, USA
| | - Pras Pathmanathan
- Center for Devices and Radiological Health, U.S. Food and Drug Administration, Maryland, USA
| | - David J Gavaghan
- Department of Computer Science, University of Oxford, Oxford, UK
| | | | - Denis Noble
- Department of Physiology, Anatomy and Genetics, University of Oxford, Oxford, UK
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22
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Sharifi H, Mann CK, Rockward AL, Mehri M, Mojumder J, Lee LC, Campbell KS, Wenk JF. Multiscale simulations of left ventricular growth and remodeling. Biophys Rev 2021; 13:729-746. [PMID: 34777616 PMCID: PMC8555068 DOI: 10.1007/s12551-021-00826-5] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/09/2021] [Accepted: 08/05/2021] [Indexed: 02/07/2023] Open
Abstract
Cardiomyocytes can adapt their size, shape, and orientation in response to altered biomechanical or biochemical stimuli. The process by which the heart undergoes structural changes-affecting both geometry and material properties-in response to altered ventricular loading, altered hormonal levels, or mutant sarcomeric proteins is broadly known as cardiac growth and remodeling (G&R). Although it is likely that cardiac G&R initially occurs as an adaptive response of the heart to the underlying stimuli, prolonged pathological changes can lead to increased risk of atrial fibrillation, heart failure, and sudden death. During the past few decades, computational models have been extensively used to investigate the mechanisms of cardiac G&R, as a complement to experimental measurements. These models have provided an opportunity to quantitatively study the relationships between the underlying stimuli (primarily mechanical) and the adverse outcomes of cardiac G&R, i.e., alterations in ventricular size and function. State-of-the-art computational models have shown promise in predicting the progression of cardiac G&R. However, there are still limitations that need to be addressed in future works to advance the field. In this review, we first outline the current state of computational models of cardiac growth and myofiber remodeling. Then, we discuss the potential limitations of current models of cardiac G&R that need to be addressed before they can be utilized in clinical care. Finally, we briefly discuss the next feasible steps and future directions that could advance the field of cardiac G&R.
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Affiliation(s)
- Hossein Sharifi
- Department of Mechanical Engineering, University of Kentucky, 269 Ralph G. Anderson Building, Lexington, KY 40506-0503 USA
| | - Charles K. Mann
- Department of Mechanical Engineering, University of Kentucky, 269 Ralph G. Anderson Building, Lexington, KY 40506-0503 USA
| | - Alexus L. Rockward
- Department of Mechanical Engineering, University of Kentucky, 269 Ralph G. Anderson Building, Lexington, KY 40506-0503 USA
| | - Mohammad Mehri
- Department of Mechanical Engineering, University of Kentucky, 269 Ralph G. Anderson Building, Lexington, KY 40506-0503 USA
| | - Joy Mojumder
- Department of Mechanical Engineering, Michigan State University, East Lansing, MI USA
| | - Lik-Chuan Lee
- Department of Mechanical Engineering, Michigan State University, East Lansing, MI USA
| | - Kenneth S. Campbell
- Department of Physiology & Division of Cardiovascular Medicine, University of Kentucky, Lexington, KY USA
| | - Jonathan F. Wenk
- Department of Mechanical Engineering, University of Kentucky, 269 Ralph G. Anderson Building, Lexington, KY 40506-0503 USA
- Department of Surgery, University of Kentucky, Lexington, KY USA
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23
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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.
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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
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24
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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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25
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Santos ARMP, Jang Y, Son I, Kim J, Park Y. Recapitulating Cardiac Structure and Function In Vitro from Simple to Complex Engineering. MICROMACHINES 2021; 12:mi12040386. [PMID: 33916254 PMCID: PMC8067203 DOI: 10.3390/mi12040386] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/03/2021] [Revised: 03/22/2021] [Accepted: 03/23/2021] [Indexed: 12/12/2022]
Abstract
Cardiac tissue engineering aims to generate in vivo-like functional tissue for the study of cardiac development, homeostasis, and regeneration. Since the heart is composed of various types of cells and extracellular matrix with a specific microenvironment, the fabrication of cardiac tissue in vitro requires integrating technologies of cardiac cells, biomaterials, fabrication, and computational modeling to model the complexity of heart tissue. Here, we review the recent progress of engineering techniques from simple to complex for fabricating matured cardiac tissue in vitro. Advancements in cardiomyocytes, extracellular matrix, geometry, and computational modeling will be discussed based on a technology perspective and their use for preparation of functional cardiac tissue. Since the heart is a very complex system at multiscale levels, an understanding of each technique and their interactions would be highly beneficial to the development of a fully functional heart in cardiac tissue engineering.
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Affiliation(s)
| | | | | | - Jongseong Kim
- Correspondence: (J.K.); (Y.P.); Tel.: +82-10-8858-7260 (J.K.); +82-10-4260-6460 (Y.P.)
| | - Yongdoo Park
- Correspondence: (J.K.); (Y.P.); Tel.: +82-10-8858-7260 (J.K.); +82-10-4260-6460 (Y.P.)
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26
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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.
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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
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27
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Paun LM, Husmeier D. Markov chain Monte Carlo with Gaussian processes for fast parameter estimation and uncertainty quantification in a 1D fluid-dynamics model of the pulmonary circulation. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2021; 37:e3421. [PMID: 33249755 PMCID: PMC7901000 DOI: 10.1002/cnm.3421] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/19/2020] [Revised: 11/07/2020] [Accepted: 11/18/2020] [Indexed: 06/12/2023]
Abstract
The past few decades have witnessed an explosive synergy between physics and the life sciences. In particular, physical modelling in medicine and physiology is a topical research area. The present work focuses on parameter inference and uncertainty quantification in a 1D fluid-dynamics model for quantitative physiology: the pulmonary blood circulation. The practical challenge is the estimation of the patient-specific biophysical model parameters, which cannot be measured directly. In principle this can be achieved based on a comparison between measured and predicted data. However, predicting data requires solving a system of partial differential equations (PDEs), which usually have no closed-form solution, and repeated numerical integrations as part of an adaptive estimation procedure are computationally expensive. In the present article, we demonstrate how fast parameter estimation combined with sound uncertainty quantification can be achieved by a combination of statistical emulation and Markov chain Monte Carlo (MCMC) sampling. We compare a range of state-of-the-art MCMC algorithms and emulation strategies, and assess their performance in terms of their accuracy and computational efficiency. The long-term goal is to develop a method for reliable disease prognostication in real time, and our work is an important step towards an automatic clinical decision support system.
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Affiliation(s)
- L. Mihaela Paun
- School of Mathematics and StatisticsUniversity of GlasgowGlasgowUK
| | - Dirk Husmeier
- School of Mathematics and StatisticsUniversity of GlasgowGlasgowUK
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28
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Building Models of Patient-Specific Anatomy and Scar Morphology from Clinical MRI Data. SYSTEMS MEDICINE 2021. [DOI: 10.1016/b978-0-12-801238-3.11663-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
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29
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Cai L, Ren L, Wang Y, Xie W, Zhu G, Gao H. Surrogate models based on machine learning methods for parameter estimation of left ventricular myocardium. ROYAL SOCIETY OPEN SCIENCE 2021; 8:201121. [PMID: 33614068 PMCID: PMC7890479 DOI: 10.1098/rsos.201121] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2020] [Accepted: 12/15/2020] [Indexed: 05/12/2023]
Abstract
A long-standing problem at the frontier of biomechanical studies is to develop fast methods capable of estimating material properties from clinical data. In this paper, we have studied three surrogate models based on machine learning (ML) methods for fast parameter estimation of left ventricular (LV) myocardium. We use three ML methods named K-nearest neighbour (KNN), XGBoost and multi-layer perceptron (MLP) to emulate the relationships between pressure and volume strains during the diastolic filling. Firstly, to train the surrogate models, a forward finite-element simulator of LV diastolic filling is used. Then the training data are projected in a low-dimensional parametrized space. Next, three ML models are trained to learn the relationships of pressure-volume and pressure-strain. Finally, an inverse parameter estimation problem is formulated by using those trained surrogate models. Our results show that the three ML models can learn the relationships of pressure-volume and pressure-strain very well, and the parameter inference using the surrogate models can be carried out in minutes. Estimated parameters from both the XGBoost and MLP models have much less uncertainties compared with the KNN model. Our results further suggest that the XGBoost model is better for predicting the LV diastolic dynamics and estimating passive parameters than other two surrogate models. Further studies are warranted to investigate how XGBoost can be used for emulating cardiac pump function in a multi-physics and multi-scale framework.
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Affiliation(s)
- Li Cai
- Xi’an Key Laboratory of Scientific Computation and Applied Statistics, Northwestern Polytechnical University, Xi’an 710129, China
- NPU-UoG International Cooperative Lab for Computation and Application in Cardiology, Northwestern Polytechnical University, Xi’an 710129, China
- School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710129, China
| | - Lei Ren
- Xi’an Key Laboratory of Scientific Computation and Applied Statistics, Northwestern Polytechnical University, Xi’an 710129, China
- NPU-UoG International Cooperative Lab for Computation and Application in Cardiology, Northwestern Polytechnical University, Xi’an 710129, China
- School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710129, China
| | - Yongheng Wang
- Xi’an Key Laboratory of Scientific Computation and Applied Statistics, Northwestern Polytechnical University, Xi’an 710129, China
- NPU-UoG International Cooperative Lab for Computation and Application in Cardiology, Northwestern Polytechnical University, Xi’an 710129, China
- School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710129, China
| | - Wenxian Xie
- Xi’an Key Laboratory of Scientific Computation and Applied Statistics, Northwestern Polytechnical University, Xi’an 710129, China
- NPU-UoG International Cooperative Lab for Computation and Application in Cardiology, Northwestern Polytechnical University, Xi’an 710129, China
- School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710129, China
| | - Guangyu Zhu
- School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China
| | - Hao Gao
- School of Mathematics and Statistics, University of Glasgow, Glasgow G12 8QQ, UK
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30
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Paun LM, Colebank MJ, Olufsen MS, Hill NA, Husmeier D. Assessing model mismatch and model selection in a Bayesian uncertainty quantification analysis of a fluid-dynamics model of pulmonary blood circulation. J R Soc Interface 2020; 17:20200886. [PMID: 33353505 PMCID: PMC7811590 DOI: 10.1098/rsif.2020.0886] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Abstract
This study uses Bayesian inference to quantify the uncertainty of model parameters and haemodynamic predictions in a one-dimensional pulmonary circulation model based on an integration of mouse haemodynamic and micro-computed tomography imaging data. We emphasize an often neglected, though important source of uncertainty: in the mathematical model form due to the discrepancy between the model and the reality, and in the measurements due to the wrong noise model (jointly called 'model mismatch'). We demonstrate that minimizing the mean squared error between the measured and the predicted data (the conventional method) in the presence of model mismatch leads to biased and overly confident parameter estimates and haemodynamic predictions. We show that our proposed method allowing for model mismatch, which we represent with Gaussian processes, corrects the bias. Additionally, we compare a linear and a nonlinear wall model, as well as models with different vessel stiffness relations. We use formal model selection analysis based on the Watanabe Akaike information criterion to select the model that best predicts the pulmonary haemodynamics. Results show that the nonlinear pressure-area relationship with stiffness dependent on the unstressed radius predicts best the data measured in a control mouse.
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Affiliation(s)
- L Mihaela Paun
- School of Mathematics and Statistics, University of Glasgow, Glasgow, G12 8QQ, UK
| | - Mitchel J Colebank
- Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA
| | - Mette S Olufsen
- Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA
| | - Nicholas A Hill
- School of Mathematics and Statistics, University of Glasgow, Glasgow, G12 8QQ, UK
| | - Dirk Husmeier
- School of Mathematics and Statistics, University of Glasgow, Glasgow, G12 8QQ, UK
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31
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Corral-Acero J, Margara F, Marciniak M, Rodero C, Loncaric F, Feng Y, Gilbert A, Fernandes JF, Bukhari HA, Wajdan A, Martinez MV, Santos MS, Shamohammdi M, Luo H, Westphal P, Leeson P, DiAchille P, Gurev V, Mayr M, Geris L, Pathmanathan P, Morrison T, Cornelussen R, Prinzen F, Delhaas T, Doltra A, Sitges M, Vigmond EJ, Zacur E, Grau V, Rodriguez B, Remme EW, Niederer S, Mortier P, McLeod K, Potse M, Pueyo E, Bueno-Orovio A, Lamata P. The 'Digital Twin' to enable the vision of precision cardiology. Eur Heart J 2020; 41:4556-4564. [PMID: 32128588 PMCID: PMC7774470 DOI: 10.1093/eurheartj/ehaa159] [Citation(s) in RCA: 193] [Impact Index Per Article: 48.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 09/06/2019] [Revised: 11/29/2019] [Accepted: 02/24/2020] [Indexed: 12/26/2022] Open
Abstract
Providing therapies tailored to each patient is the vision of precision medicine, enabled by the increasing ability to capture extensive data about individual patients. In this position paper, we argue that the second enabling pillar towards this vision is the increasing power of computers and algorithms to learn, reason, and build the 'digital twin' of a patient. Computational models are boosting the capacity to draw diagnosis and prognosis, and future treatments will be tailored not only to current health status and data, but also to an accurate projection of the pathways to restore health by model predictions. The early steps of the digital twin in the area of cardiovascular medicine are reviewed in this article, together with a discussion of the challenges and opportunities ahead. We emphasize the synergies between mechanistic and statistical models in accelerating cardiovascular research and enabling the vision of precision medicine.
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Affiliation(s)
| | - Francesca Margara
- Department of Computer Science, British Heart Foundation Centre of Research Excellence, University of Oxford, Oxford, UK
| | - Maciej Marciniak
- Department of Biomedical Engineering, Division of Imaging Sciences and Biomedical Engineering, King’s College London, London, UK
| | - Cristobal Rodero
- Department of Biomedical Engineering, Division of Imaging Sciences and Biomedical Engineering, King’s College London, London, UK
| | - Filip Loncaric
- Institut Clínic Cardiovascular, Hospital Clínic, Universitat de Barcelona, Institut d’Investigacions Biomèdiques August Pi i Sunyer (IDIBAPS), Barcelona, Spain
| | - Yingjing Feng
- IHU Liryc, Electrophysiology and Heart Modeling Institute, fondation Bordeaux Université, Pessac-Bordeaux F-33600, France
- IMB, UMR 5251, University of Bordeaux, Talence F-33400, France
| | | | - Joao F Fernandes
- Department of Biomedical Engineering, Division of Imaging Sciences and Biomedical Engineering, King’s College London, London, UK
| | - Hassaan A Bukhari
- IMB, UMR 5251, University of Bordeaux, Talence F-33400, France
- Aragón Institute of Engineering Research, Universidad de Zaragoza, IIS Aragón, Zaragoza, Spain
| | - Ali Wajdan
- The Intervention Centre, Oslo University Hospital, Rikshospitalet, Oslo, Norway
| | | | | | - Mehrdad Shamohammdi
- CARIM School for Cardiovascular Diseases, Maastricht University, Maastricht, The Netherlands
| | - Hongxing Luo
- CARIM School for Cardiovascular Diseases, Maastricht University, Maastricht, The Netherlands
| | - Philip Westphal
- Medtronic PLC, Bakken Research Center, Maastricht, the Netherlands
| | - Paul Leeson
- Radcliffe Department of Medicine, Division of Cardiovascular Medicine, Oxford Cardiovascular Clinical Research Facility, John Radcliffe Hospital, University of Oxford, Oxford, UK
| | - Paolo DiAchille
- Healthcare and Life Sciences Research, IBM T.J. Watson Research Center, Yorktown Heights, NY, USA
| | - Viatcheslav Gurev
- Healthcare and Life Sciences Research, IBM T.J. Watson Research Center, Yorktown Heights, NY, USA
| | - Manuel Mayr
- King’s British Heart Foundation Centre, King’s College London, London, UK
| | - Liesbet Geris
- Virtual Physiological Human Institute, Leuven, Belgium
| | - Pras Pathmanathan
- Center for Devices and Radiological Health, U.S. Food and Drug Administration, Silver Spring, MD, USA
| | - Tina Morrison
- Center for Devices and Radiological Health, U.S. Food and Drug Administration, Silver Spring, MD, USA
| | | | - Frits Prinzen
- CARIM School for Cardiovascular Diseases, Maastricht University, Maastricht, The Netherlands
| | - Tammo Delhaas
- CARIM School for Cardiovascular Diseases, Maastricht University, Maastricht, The Netherlands
| | - Ada Doltra
- Institut Clínic Cardiovascular, Hospital Clínic, Universitat de Barcelona, Institut d’Investigacions Biomèdiques August Pi i Sunyer (IDIBAPS), Barcelona, Spain
| | - Marta Sitges
- Institut Clínic Cardiovascular, Hospital Clínic, Universitat de Barcelona, Institut d’Investigacions Biomèdiques August Pi i Sunyer (IDIBAPS), Barcelona, Spain
- CIBERCV, Instituto de Salud Carlos III, (CB16/11/00354), CERCA Programme/Generalitat de, Catalunya, Spain
| | - Edward J Vigmond
- IHU Liryc, Electrophysiology and Heart Modeling Institute, fondation Bordeaux Université, Pessac-Bordeaux F-33600, France
- IMB, UMR 5251, University of Bordeaux, Talence F-33400, France
| | - Ernesto Zacur
- Department of Engineering Science, University of Oxford, Oxford, UK
| | - Vicente Grau
- Department of Engineering Science, University of Oxford, Oxford, UK
| | - Blanca Rodriguez
- Department of Computer Science, British Heart Foundation Centre of Research Excellence, University of Oxford, Oxford, UK
| | - Espen W Remme
- The Intervention Centre, Oslo University Hospital, Rikshospitalet, Oslo, Norway
| | - Steven Niederer
- Department of Biomedical Engineering, Division of Imaging Sciences and Biomedical Engineering, King’s College London, London, UK
| | | | | | - Mark Potse
- IHU Liryc, Electrophysiology and Heart Modeling Institute, fondation Bordeaux Université, Pessac-Bordeaux F-33600, France
- IMB, UMR 5251, University of Bordeaux, Talence F-33400, France
- Inria Bordeaux Sud-Ouest, CARMEN team, Talence F-33400, France
| | - Esther Pueyo
- Aragón Institute of Engineering Research, Universidad de Zaragoza, IIS Aragón, Zaragoza, Spain
- CIBER in Bioengineering, Biomaterials and Nanomedicine (CIBER‐BBN), Madrid, Spain
| | - Alfonso Bueno-Orovio
- Department of Computer Science, British Heart Foundation Centre of Research Excellence, University of Oxford, Oxford, UK
| | - Pablo Lamata
- Department of Biomedical Engineering, Division of Imaging Sciences and Biomedical Engineering, King’s College London, London, UK
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32
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Browning AP, Warne DJ, Burrage K, Baker RE, Simpson MJ. Identifiability analysis for stochastic differential equation models in systems biology. J R Soc Interface 2020; 17:20200652. [PMID: 33323054 PMCID: PMC7811582 DOI: 10.1098/rsif.2020.0652] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2020] [Accepted: 11/24/2020] [Indexed: 12/26/2022] Open
Abstract
Mathematical models are routinely calibrated to experimental data, with goals ranging from building predictive models to quantifying parameters that cannot be measured. Whether or not reliable parameter estimates are obtainable from the available data can easily be overlooked. Such issues of parameter identifiability have important ramifications for both the predictive power of a model, and the mechanistic insight that can be obtained. Identifiability analysis is well-established for deterministic, ordinary differential equation (ODE) models, but there are no commonly adopted methods for analysing identifiability in stochastic models. We provide an accessible introduction to identifiability analysis and demonstrate how existing ideas for analysis of ODE models can be applied to stochastic differential equation (SDE) models through four practical case studies. To assess structural identifiability, we study ODEs that describe the statistical moments of the stochastic process using open-source software tools. Using practically motivated synthetic data and Markov chain Monte Carlo methods, we assess parameter identifiability in the context of available data. Our analysis shows that SDE models can often extract more information about parameters than deterministic descriptions. All code used to perform the analysis is available on Github.
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Affiliation(s)
- Alexander P. Browning
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
- ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Brisbane, Australia
| | - David J. Warne
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
- ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Brisbane, Australia
| | - Kevin Burrage
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
- ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Brisbane, Australia
- ARC Centre of Excellence for Plant Success in Nature and Agriculture, Queensland University of Technology, Brisbane, Australia
- Department of Computer Science, University of Oxford, Oxford, UK
| | - Ruth E. Baker
- Mathematical Institute, University of Oxford, Oxford, UK
| | - Matthew J. Simpson
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
- ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Brisbane, Australia
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33
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Morrison RE. Data-Driven Corrections of Partial Lotka-Volterra Models. ENTROPY 2020; 22:e22111313. [PMID: 33287078 PMCID: PMC7712089 DOI: 10.3390/e22111313] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/02/2020] [Revised: 11/03/2020] [Accepted: 11/16/2020] [Indexed: 11/16/2022]
Abstract
In many applications of interacting systems, we are only interested in the dynamic behavior of a subset of all possible active species. For example, this is true in combustion models (many transient chemical species are not of interest in a given reaction) and in epidemiological models (only certain subpopulations are consequential). Thus, it is common to use greatly reduced or partial models in which only the interactions among the species of interest are known. In this work, we explore the use of an embedded, sparse, and data-driven discrepancy operator to augment these partial interaction models. Preliminary results show that the model error caused by severe reductions-e.g., elimination of hundreds of terms-can be captured with sparse operators, built with only a small fraction of that number. The operator is embedded within the differential equations of the model, which allows the action of the operator to be interpretable. Moreover, it is constrained by available physical information and calibrated over many scenarios. These qualities of the discrepancy model-interpretability, physical consistency, and robustness to different scenarios-are intended to support reliable predictions under extrapolative conditions.
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Affiliation(s)
- Rebecca E Morrison
- Department of Computer Science, University of Colorado Boulder, 1111 Engineering Drive, Boulder, CO 80309, USA
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34
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Fresca S, Manzoni A, Dedè L, Quarteroni A. Deep learning-based reduced order models in cardiac electrophysiology. PLoS One 2020; 15:e0239416. [PMID: 33002014 PMCID: PMC7529269 DOI: 10.1371/journal.pone.0239416] [Citation(s) in RCA: 23] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/09/2020] [Accepted: 09/06/2020] [Indexed: 01/06/2023] Open
Abstract
Predicting the electrical behavior of the heart, from the cellular scale to the tissue level, relies on the numerical approximation of coupled nonlinear dynamical systems. These systems describe the cardiac action potential, that is the polarization/depolarization cycle occurring at every heart beat that models the time evolution of the electrical potential across the cell membrane, as well as a set of ionic variables. Multiple solutions of these systems, corresponding to different model inputs, are required to evaluate outputs of clinical interest, such as activation maps and action potential duration. More importantly, these models feature coherent structures that propagate over time, such as wavefronts. These systems can hardly be reduced to lower dimensional problems by conventional reduced order models (ROMs) such as, e.g., the reduced basis method. This is primarily due to the low regularity of the solution manifold (with respect to the problem parameters), as well as to the nonlinear nature of the input-output maps that we intend to reconstruct numerically. To overcome this difficulty, in this paper we propose a new, nonlinear approach relying on deep learning (DL) algorithms—such as deep feedforward neural networks and convolutional autoencoders—to obtain accurate and efficient ROMs, whose dimensionality matches the number of system parameters. We show that the proposed DL-ROM framework can efficiently provide solutions to parametrized electrophysiology problems, thus enabling multi-scenario analysis in pathological cases. We investigate four challenging test cases in cardiac electrophysiology, thus demonstrating that DL-ROM outperforms classical projection-based ROMs.
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Affiliation(s)
- Stefania Fresca
- MOX - Dipartimento di Matematica, Politecnico di Milano, Milano, Italy
- * E-mail:
| | - Andrea Manzoni
- MOX - Dipartimento di Matematica, Politecnico di Milano, Milano, Italy
| | - Luca Dedè
- MOX - Dipartimento di Matematica, Politecnico di Milano, Milano, Italy
| | - Alfio Quarteroni
- MOX - Dipartimento di Matematica, Politecnico di Milano, Milano, Italy
- Mathematics Institute, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
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35
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Whittaker DG, Clerx M, Lei CL, Christini DJ, Mirams GR. Calibration of ionic and cellular cardiac electrophysiology models. WILEY INTERDISCIPLINARY REVIEWS. SYSTEMS BIOLOGY AND MEDICINE 2020; 12:e1482. [PMID: 32084308 PMCID: PMC8614115 DOI: 10.1002/wsbm.1482] [Citation(s) in RCA: 41] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/30/2019] [Revised: 01/17/2020] [Accepted: 01/18/2020] [Indexed: 12/30/2022]
Abstract
Cardiac electrophysiology models are among the most mature and well-studied mathematical models of biological systems. This maturity is bringing new challenges as models are being used increasingly to make quantitative rather than qualitative predictions. As such, calibrating the parameters within ion current and action potential (AP) models to experimental data sets is a crucial step in constructing a predictive model. This review highlights some of the fundamental concepts in cardiac model calibration and is intended to be readily understood by computational and mathematical modelers working in other fields of biology. We discuss the classic and latest approaches to calibration in the electrophysiology field, at both the ion channel and cellular AP scales. We end with a discussion of the many challenges that work to date has raised and the need for reproducible descriptions of the calibration process to enable models to be recalibrated to new data sets and built upon for new studies. This article is categorized under: Analytical and Computational Methods > Computational Methods Physiology > Mammalian Physiology in Health and Disease Models of Systems Properties and Processes > Cellular Models.
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Affiliation(s)
- Dominic G. Whittaker
- Centre for Mathematical Medicine & Biology, School of Mathematical SciencesUniversity of NottinghamNottinghamUK
| | - Michael Clerx
- Computational Biology & Health Informatics, Department of Computer ScienceUniversity of OxfordOxfordUK
| | - Chon Lok Lei
- Computational Biology & Health Informatics, Department of Computer ScienceUniversity of OxfordOxfordUK
| | | | - Gary R. Mirams
- Centre for Mathematical Medicine & Biology, School of Mathematical SciencesUniversity of NottinghamNottinghamUK
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36
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Houston C, Marchand B, Engelbert L, Cantwell CD. Reducing complexity and unidentifiability when modelling human atrial cells. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2020. [PMID: 32448063 DOI: 10.5061/dryad.p2ngf1vmc] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
Mathematical models of a cellular action potential (AP) in cardiac modelling have become increasingly complex, particularly in gating kinetics, which control the opening and closing of individual ion channel currents. As cardiac models advance towards use in personalized medicine to inform clinical decision-making, it is critical to understand the uncertainty hidden in parameter estimates from their calibration to experimental data. This study applies approximate Bayesian computation to re-calibrate the gating kinetics of four ion channels in two existing human atrial cell models to their original datasets, providing a measure of uncertainty and indication of potential issues with selecting a single unique value given the available experimental data. Two approaches are investigated to reduce the uncertainty present: re-calibrating the models to a more complete dataset and using a less complex formulation with fewer parameters to constrain. The re-calibrated models are inserted back into the full cell model to study the overall effect on the AP. The use of more complete datasets does not eliminate uncertainty present in parameter estimates. The less complex model, particularly for the fast sodium current, gave a better fit to experimental data alongside lower parameter uncertainty and improved computational speed. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.
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Affiliation(s)
- C Houston
- ElectroCardioMaths Programme, Centre for Cardiac Engineering, Imperial College, London, UK
- Department of Aeronautics, Imperial College, London, UK
| | - B Marchand
- Department of Aeronautics, Imperial College, London, UK
| | - L Engelbert
- Department of Aeronautics, Imperial College, London, UK
| | - C D Cantwell
- ElectroCardioMaths Programme, Centre for Cardiac Engineering, Imperial College, London, UK
- Department of Aeronautics, Imperial College, London, UK
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37
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Hoffman MJ, Cherry EM. Sensitivity of a data-assimilation system for reconstructing three-dimensional cardiac electrical dynamics. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2020; 378:20190388. [PMID: 32448069 PMCID: PMC7287341 DOI: 10.1098/rsta.2019.0388] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 02/25/2020] [Indexed: 05/21/2023]
Abstract
Modelling of cardiac electrical behaviour has led to important mechanistic insights, but important challenges, including uncertainty in model formulations and parameter values, make it difficult to obtain quantitatively accurate results. An alternative approach is combining models with observations from experiments to produce a data-informed reconstruction of system states over time. Here, we extend our earlier data-assimilation studies using an ensemble Kalman filter to reconstruct a three-dimensional time series of states with complex spatio-temporal dynamics using only surface observations of voltage. We consider the effects of several algorithmic and model parameters on the accuracy of reconstructions of known scroll-wave truth states using synthetic observations. In particular, we study the algorithm's sensitivity to parameters governing different parts of the process and its robustness to several model-error conditions. We find that the algorithm can achieve an acceptable level of error in many cases, with the weakest performance occurring for model-error cases and more extreme parameter regimes with more complex dynamics. Analysis of the poorest-performing cases indicates an initial decrease in error followed by an increase when the ensemble spread is reduced. Our results suggest avenues for further improvement through increasing ensemble spread by incorporating additive inflation or using a parameter or multi-model ensemble. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.
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Affiliation(s)
- Matthew J. Hoffman
- School of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY 14623, USA
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38
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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'.
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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
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Lawson BAJ, Oliveira RS, Berg LA, Silva PAA, Burrage K, dos Santos RW. Variability in electrophysiological properties and conducting obstacles controls re-entry risk in heterogeneous ischaemic tissue. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2020; 378:20190341. [PMID: 32448068 PMCID: PMC7287337 DOI: 10.1098/rsta.2019.0341] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/07/2023]
Abstract
Ischaemia, in which inadequate blood supply compromises and eventually kills regions of cardiac tissue, can cause many types of arrhythmia, some life-threatening. A significant component of this is the effects of the resulting hypoxia, and concomitant hyperklaemia and acidosis, on the electrophysiological properties of myocytes. Clinical and experimental data have also shown that regions of structural heterogeneity (fibrosis, necrosis, fibro-fatty infiltration) can act as triggers for arrhythmias under acute ischaemic conditions. Mechanistic models have successfully captured these effects in silico. However, the relative significance of these separate facets of the condition, and how sensitive arrhythmic risk is to the extents of each, is far less explored. In this work, we use partitioned Gaussian process emulation and new metrics for source-sink mismatch that rely on simulations of bifurcating cardiac fibres to interrogate a model of heterogeneous ischaemic tissue. Re-entries were most sensitive to the level of hypoxia and the fraction of non-excitable tissue. In addition, our results reveal both protective and pro-arrhythmic effects of hyperklaemia, and present the levels of hyperklaemia, hypoxia and percentage of non-excitable tissue that pose the highest arrhythmic risks. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.
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Affiliation(s)
- Brodie A. J. Lawson
- ARC Centre of Excellence for Mathematical and Statistical Frontiers Queensland University of Technology, Brisbane, Australia
| | - Rafael S. Oliveira
- Department of Computer Science, Universidade Federal de São João del-Rei, São João del-Rei, Brazil
| | - Lucas A. Berg
- Graduate Program in Computational Modelling, Universidade Federal de Juiz de Fora, Juiz de Fora, Brazil
| | - Pedro A. A. Silva
- Graduate Program in Computational Modelling, Universidade Federal de Juiz de Fora, Juiz de Fora, Brazil
| | - Kevin Burrage
- ARC Centre of Excellence for Mathematical and Statistical Frontiers Queensland University of Technology, Brisbane, Australia
- Visiting Professor, Department of Computer Science, University of Oxford, Oxford, UK
| | - Rodrigo Weber dos Santos
- Graduate Program in Computational Modelling, Universidade Federal de Juiz de Fora, Juiz de Fora, Brazil
- e-mail:
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40
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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'.
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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
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41
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Lei CL, Clerx M, Whittaker DG, Gavaghan DJ, de Boer TP, Mirams GR. Accounting for variability in ion current recordings using a mathematical model of artefacts in voltage-clamp experiments. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2020; 378:20190348. [PMID: 32448060 PMCID: PMC7287334 DOI: 10.1098/rsta.2019.0348] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 04/08/2020] [Indexed: 05/21/2023]
Abstract
Mathematical models of ion channels, which constitute indispensable components of action potential models, are commonly constructed by fitting to whole-cell patch-clamp data. In a previous study, we fitted cell-specific models to hERG1a (Kv11.1) recordings simultaneously measured using an automated high-throughput system, and studied cell-cell variability by inspecting the resulting model parameters. However, the origin of the observed variability was not identified. Here, we study the source of variability by constructing a model that describes not just ion current dynamics, but the entire voltage-clamp experiment. The experimental artefact components of the model include: series resistance, membrane and pipette capacitance, voltage offsets, imperfect compensations made by the amplifier for these phenomena, and leak current. In this model, variability in the observations can be explained by either cell properties, measurement artefacts, or both. Remarkably, by assuming that variability arises exclusively from measurement artefacts, it is possible to explain a larger amount of the observed variability than when assuming cell-specific ion current kinetics. This assumption also leads to a smaller number of model parameters. This result suggests that most of the observed variability in patch-clamp data measured under the same conditions is caused by experimental artefacts, and hence can be compensated for in post-processing by using our model for the patch-clamp experiment. This study has implications for the question of the extent to which cell-cell variability in ion channel kinetics exists, and opens up routes for better correction of artefacts in patch-clamp data. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.
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Affiliation(s)
- Chon Lok Lei
- Computational Biology & Health Informatics, Department of Computer Science, University of Oxford, Oxford, UK
| | - Michael Clerx
- Computational Biology & Health Informatics, Department of Computer Science, University of Oxford, Oxford, UK
| | - Dominic G. Whittaker
- Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, UK
| | - David J. Gavaghan
- Computational Biology & Health Informatics, Department of Computer Science, University of Oxford, Oxford, UK
| | - Teun P. de Boer
- Department of Medical Physiology, Division Heart & Lungs, University Medical Center Utrecht, Utrecht, the Netherlands
| | - Gary R. Mirams
- Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, UK
- e-mail:
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42
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Houston C, Marchand B, Engelbert L, Cantwell CD. Reducing complexity and unidentifiability when modelling human atrial cells. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2020; 378:20190339. [PMID: 32448063 PMCID: PMC7287336 DOI: 10.1098/rsta.2019.0339] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/07/2023]
Abstract
Mathematical models of a cellular action potential (AP) in cardiac modelling have become increasingly complex, particularly in gating kinetics, which control the opening and closing of individual ion channel currents. As cardiac models advance towards use in personalized medicine to inform clinical decision-making, it is critical to understand the uncertainty hidden in parameter estimates from their calibration to experimental data. This study applies approximate Bayesian computation to re-calibrate the gating kinetics of four ion channels in two existing human atrial cell models to their original datasets, providing a measure of uncertainty and indication of potential issues with selecting a single unique value given the available experimental data. Two approaches are investigated to reduce the uncertainty present: re-calibrating the models to a more complete dataset and using a less complex formulation with fewer parameters to constrain. The re-calibrated models are inserted back into the full cell model to study the overall effect on the AP. The use of more complete datasets does not eliminate uncertainty present in parameter estimates. The less complex model, particularly for the fast sodium current, gave a better fit to experimental data alongside lower parameter uncertainty and improved computational speed. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.
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Affiliation(s)
- C. Houston
- ElectroCardioMaths Programme, Centre for Cardiac Engineering, Imperial College, London, UK
- Department of Aeronautics, Imperial College, London, UK
- e-mail:
| | - B. Marchand
- Department of Aeronautics, Imperial College, London, UK
| | - L. Engelbert
- Department of Aeronautics, Imperial College, London, UK
| | - C. D. Cantwell
- ElectroCardioMaths Programme, Centre for Cardiac Engineering, Imperial College, London, UK
- Department of Aeronautics, Imperial College, London, UK
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43
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Cao S, Aboelkassem Y, Wang A, Valdez-Jasso D, Saucerman JJ, Omens JH, McCulloch AD. Quantification of model and data uncertainty in a network analysis of cardiac myocyte mechanosignalling. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2020; 378:20190336. [PMID: 32448062 PMCID: PMC7287329 DOI: 10.1098/rsta.2019.0336] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 04/14/2020] [Indexed: 05/21/2023]
Abstract
Cardiac myocytes transduce changes in mechanical loading into cellular responses via interacting cell signalling pathways. We previously reported a logic-based ordinary differential equation model of the myocyte mechanosignalling network that correctly predicts 78% of independent experimental results not used to formulate the original model. Here, we use Monte Carlo and polynomial chaos expansion simulations to examine the effects of uncertainty in parameter values, model logic and experimental validation data on the assessed accuracy of that model. The prediction accuracy of the model was robust to parameter changes over a wide range being least sensitive to uncertainty in time constants and most affected by uncertainty in reaction weights. Quantifying epistemic uncertainty in the reaction logic of the model showed that while replacing 'OR' with 'AND' reactions greatly reduced model accuracy, replacing 'AND' with 'OR' reactions was more likely to maintain or even improve accuracy. Finally, data uncertainty had a modest effect on assessment of model accuracy. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.
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Affiliation(s)
- Shulin Cao
- Department of Bioengineering, University of California San Diego, La Jolla, CA 92093, USA
| | - Yasser Aboelkassem
- Department of Bioengineering, University of California San Diego, La Jolla, CA 92093, USA
| | - Ariel Wang
- Department of Bioengineering, University of California San Diego, La Jolla, CA 92093, USA
| | - Daniela Valdez-Jasso
- Department of Bioengineering, University of California San Diego, La Jolla, CA 92093, USA
| | - Jeffrey J. Saucerman
- Department of Biomedical Engineering, University of Virginia, Charlottesville, VA 22904, USA
| | - Jeffrey H. Omens
- Department of Bioengineering, University of California San Diego, La Jolla, CA 92093, USA
- Department of Medicine, University of California San Diego, La Jolla, CA 92093, USA
| | - Andrew D. McCulloch
- Department of Bioengineering, University of California San Diego, La Jolla, CA 92093, USA
- Department of Medicine, University of California San Diego, La Jolla, CA 92093, USA
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44
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Wang A, Cao S, Aboelkassem Y, Valdez-Jasso D. Quantification of uncertainty in a new network model of pulmonary arterial adventitial fibroblast pro-fibrotic signalling. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2020; 378:20190338. [PMID: 32448066 PMCID: PMC7287331 DOI: 10.1098/rsta.2019.0338] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 03/16/2020] [Indexed: 05/21/2023]
Abstract
Here, we present a novel network model of the pulmonary arterial adventitial fibroblast (PAAF) that represents seven signalling pathways, confirmed to be important in pulmonary arterial fibrosis, as 92 reactions and 64 state variables. Without optimizing parameters, the model correctly predicted 80% of 39 results of input-output and inhibition experiments reported in 20 independent papers not used to formulate the original network. Parameter uncertainty quantification (UQ) showed that this measure of model accuracy is robust to changes in input weights and half-maximal activation levels (EC50), but is more affected by uncertainty in the Hill coefficient (n), which governs the biochemical cooperativity or steepness of the sigmoidal activation function of each state variable. Epistemic uncertainty in model structure, due to the reliance of some network components and interactions on experiments using non-PAAF cell types, suggested that this source of uncertainty had a smaller impact on model accuracy than the alternative of reducing the network to only those interactions reported in PAAFs. UQ highlighted model parameters that can be optimized to improve prediction accuracy and network modules where there is the greatest need for new experiments. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.
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Affiliation(s)
| | | | | | - Daniela Valdez-Jasso
- Department of Bioengineering, University of California San Diego, La Jolla, CA 92092, USA
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45
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Coveney S, Clayton RH. Sensitivity and Uncertainty Analysis of Two Human Atrial Cardiac Cell Models Using Gaussian Process Emulators. Front Physiol 2020; 11:364. [PMID: 32390867 PMCID: PMC7191317 DOI: 10.3389/fphys.2020.00364] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2019] [Accepted: 03/30/2020] [Indexed: 12/20/2022] Open
Abstract
Biophysically detailed cardiac cell models reconstruct the action potential and calcium dynamics of cardiac myocytes. They aim to capture the biophysics of current flow through ion channels, pumps, and exchangers in the cell membrane, and are highly detailed. However, the relationship between model parameters and model outputs is difficult to establish because the models are both complex and non-linear. The consequences of uncertainty and variability in model parameters are therefore difficult to determine without undertaking large numbers of model evaluations. The aim of the present study was to demonstrate how sensitivity and uncertainty analysis using Gaussian process emulators can be used for a systematic and quantitive analysis of biophysically detailed cardiac cell models. We selected the Courtemanche and Maleckar models of the human atrial action potential for analysis because these models describe a similar set of currents, with different formulations. In our approach Gaussian processes emulate the main features of the action potential and calcium transient. The emulators were trained with a set of design data comprising samples from parameter space and corresponding model outputs, initially obtained from 300 model evaluations. Variance based sensitivity indices were calculated using the emulators, and first order and total effect indices were calculated for each combination of parameter and output. The differences between the first order and total effect indices indicated that the effect of interactions between parameters was small. A second set of emulators were then trained using a new set of design data with a subset of the model parameters with a sensitivity index of more than 0.1 (10%). This second stage analysis enabled comparison of mechanisms in the two models. The second stage sensitivity indices enabled the relationship between the L-type Ca 2+ current and the action potential plateau to be quantified in each model. Our quantitative analysis predicted that changes in maximum conductance of the ultra-rapid K + channel I Kur would have opposite effects on action potential duration in the two models, and this prediction was confirmed by additional simulations. This study has demonstrated that Gaussian process emulators are an effective tool for sensitivity and uncertainty analysis of biophysically detailed cardiac cell models.
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Affiliation(s)
| | - Richard H. Clayton
- Insigneo Institute for in-silico Medicine and Department of Computer Science, University of Sheffield, Sheffield, United Kingdom
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46
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Corrado C, Razeghi O, Roney C, Coveney S, Williams S, Sim I, O'Neill M, Wilkinson R, Oakley J, Clayton RH, Niederer S. Quantifying atrial anatomy uncertainty from clinical data and its impact on electro-physiology simulation predictions. Med Image Anal 2020; 61:101626. [PMID: 32000114 DOI: 10.1016/j.media.2019.101626] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2019] [Revised: 11/05/2019] [Accepted: 12/05/2019] [Indexed: 12/11/2022]
Abstract
Patient-specific computational models of structure and function are increasingly being used to diagnose disease and predict how a patient will respond to therapy. Models of anatomy are often derived after segmentation of clinical images or from mapping systems which are affected by image artefacts, resolution and contrast. Quantifying the impact of uncertain anatomy on model predictions is important, as models are increasingly used in clinical practice where decisions need to be made regardless of image quality. We use a Bayesian probabilistic approach to estimate the anatomy and to quantify the uncertainty about the shape of the left atrium derived from Cardiac Magnetic Resonance images. We show that we can quantify uncertain shape, encode uncertainty about the left atrial shape due to imaging artefacts, and quantify the effect of uncertain shape on simulations of left atrial activation times.
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Affiliation(s)
- Cesare Corrado
- Division of Imaging Sciences & Biomedical Engineering, King's College London, London SE17EH, United Kingdom.
| | - Orod Razeghi
- Division of Imaging Sciences & Biomedical Engineering, King's College London, London SE17EH, United Kingdom
| | - Caroline Roney
- Division of Imaging Sciences & Biomedical Engineering, King's College London, London SE17EH, United Kingdom
| | - Sam Coveney
- Insigneo Institute for in-silico Medicine and Department of Computer Science, University of Sheffield, Sheffield, United Kingdom
| | - Steven Williams
- Division of Imaging Sciences & Biomedical Engineering, King's College London, London SE17EH, United Kingdom
| | - Iain Sim
- Division of Imaging Sciences & Biomedical Engineering, King's College London, London SE17EH, United Kingdom
| | - Mark O'Neill
- Division of Imaging Sciences & Biomedical Engineering, King's College London, London SE17EH, United Kingdom
| | - Richard Wilkinson
- School of Mathematics and Statistics, University of Sheffield, Sheffield, United Kingdom
| | - Jeremy Oakley
- School of Mathematics and Statistics, University of Sheffield, Sheffield, United Kingdom
| | - Richard H Clayton
- Insigneo Institute for in-silico Medicine and Department of Computer Science, University of Sheffield, Sheffield, United Kingdom
| | - Steven Niederer
- Division of Imaging Sciences & Biomedical Engineering, King's College London, London SE17EH, United Kingdom
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Li Z, Mirams GR, Yoshinaga T, Ridder BJ, Han X, Chen JE, Stockbridge NL, Wisialowski TA, Damiano B, Severi S, Morissette P, Kowey PR, Holbrook M, Smith G, Rasmusson RL, Liu M, Song Z, Qu Z, Leishman DJ, Steidl‐Nichols J, Rodriguez B, Bueno‐Orovio A, Zhou X, Passini E, Edwards AG, Morotti S, Ni H, Grandi E, Clancy CE, Vandenberg J, Hill A, Nakamura M, Singer T, Polonchuk L, Greiter‐Wilke A, Wang K, Nave S, Fullerton A, Sobie EA, Paci M, Musuamba Tshinanu F, Strauss DG. General Principles for the Validation of Proarrhythmia Risk Prediction Models: An Extension of the CiPA In Silico Strategy. Clin Pharmacol Ther 2020; 107:102-111. [PMID: 31709525 PMCID: PMC6977398 DOI: 10.1002/cpt.1647] [Citation(s) in RCA: 52] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2019] [Accepted: 09/06/2019] [Indexed: 12/27/2022]
Abstract
This white paper presents principles for validating proarrhythmia risk prediction models for regulatory use as discussed at the In Silico Breakout Session of a Cardiac Safety Research Consortium/Health and Environmental Sciences Institute/US Food and Drug Administration-sponsored Think Tank Meeting on May 22, 2018. The meeting was convened to evaluate the progress in the development of a new cardiac safety paradigm, the Comprehensive in Vitro Proarrhythmia Assay (CiPA). The opinions regarding these principles reflect the collective views of those who participated in the discussion of this topic both at and after the breakout session. Although primarily discussed in the context of in silico models, these principles describe the interface between experimental input and model-based interpretation and are intended to be general enough to be applied to other types of nonclinical models for proarrhythmia assessment. This document was developed with the intention of providing a foundation for more consistency and harmonization in developing and validating different models for proarrhythmia risk prediction using the example of the CiPA paradigm.
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Viceconti M, Juarez MA, Curreli C, Pennisi M, Russo G, Pappalardo F. Credibility of In Silico Trial Technologies-A Theoretical Framing. IEEE J Biomed Health Inform 2019; 24:4-13. [PMID: 31670687 DOI: 10.1109/jbhi.2019.2949888] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Different research communities have developed various approaches to assess the credibility of predictive models. Each approach usually works well for a specific type of model, and under some epistemic conditions that are normally satisfied within that specific research domain. Some regulatory agencies recently started to consider evidences of safety and efficacy on new medical products obtained using computer modelling and simulation (which is referred to as In Silico Trials); this has raised the attention in the computational medicine research community on the regulatory science aspects of this emerging discipline. But this poses a foundational problem: in the domain of biomedical research the use of computer modelling is relatively recent, without a widely accepted epistemic framing for model credibility. Also, because of the inherent complexity of living organisms, biomedical modellers tend to use a variety of modelling methods, sometimes mixing them in the solution of a single problem. In such context merely adopting credibility approaches developed within other research communities might not be appropriate. In this paper we propose a theoretical framing for assessing the credibility of a predictive models for In Silico Trials, which accounts for the epistemic specificity of this research field and is general enough to be used for different type of models.
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Parikh J, Di Achille P, Kozloski J, Gurev V. Global Sensitivity Analysis of Ventricular Myocyte Model-Derived Metrics for Proarrhythmic Risk Assessment. Front Pharmacol 2019; 10:1054. [PMID: 31680938 PMCID: PMC6797832 DOI: 10.3389/fphar.2019.01054] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2019] [Accepted: 08/20/2019] [Indexed: 01/08/2023] Open
Abstract
Multiscale computational models of the heart are being extensively investigated for improved assessment of drug-induced torsades de pointes (TdP) risk, a fatal side effect of many drugs. Model-derived metrics such as action potential duration and net charge carried by ionic currents (qNet) have been proposed as potential candidates for TdP risk stratification after being tested on small datasets. Unlike purely statistical approaches, model-derived metrics are thought to provide mechanism-based classification. In particular, qNet has been recently proposed as a surrogate metric for early afterdepolarizations (EADs), which are known to be cellular triggers of TdP. Analysis of critical model components and of the ion channels that have major impact on model-derived metrics can lead to improvements in the confidence of the prediction. In this paper, we analyze large populations of virtual drugs to systematically examine the influence of different ion channels on model-derived metrics that have been proposed for proarrhythmic risk assessment. We demonstrate via global sensitivity analysis (GSA) that model-derived metrics are most sensitive to different sets of input parameters. Similarly, important differences in sensitivity to specific channel blocks are highlighted when classifying drugs into different risk categories by either qNet or a metric directly based on simulated EADs. In particular, the higher sensitivity of qNet to the block of the late sodium channel might explain why its classification accuracy is better than that of the EAD-based metric, as shown for a small set of known drugs. Our results highlight the need for a better mechanistic interpretation of promising metrics like qNet based on a formal analysis of models. GSA should, therefore, constitute an essential component of the in silico workflow for proarrhythmic risk assessment, as an improved understanding of the structure of model-derived metrics could increase confidence in model-predicted risk.
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Cosi FG, Giese W, Neubert W, Luther S, Chamakuri N, Parlitz U, Falcke M. Multiscale Modeling of Dyadic Structure-Function Relation in Ventricular Cardiac Myocytes. Biophys J 2019; 117:2409-2419. [PMID: 31635789 PMCID: PMC6990380 DOI: 10.1016/j.bpj.2019.09.023] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2019] [Revised: 09/11/2019] [Accepted: 09/16/2019] [Indexed: 01/20/2023] Open
Abstract
Cardiovascular disease is often related to defects of subcellular components in cardiac myocytes, specifically in the dyadic cleft, which include changes in cleft geometry and channel placement. Modeling of these pathological changes requires both spatially resolved cleft as well as whole cell level descriptions. We use a multiscale model to create dyadic structure-function relationships to explore the impact of molecular changes on whole cell electrophysiology and calcium cycling. This multiscale model incorporates stochastic simulation of individual L-type calcium channels and ryanodine receptor channels, spatially detailed concentration dynamics in dyadic clefts, rabbit membrane potential dynamics, and a system of partial differential equations for myoplasmic and lumenal free Ca2+ and Ca2+-binding molecules in the bulk of the cell. We found action potential duration, systolic, and diastolic [Ca2+] to respond most sensitively to changes in L-type calcium channel current. The ryanodine receptor channel cluster structure inside dyadic clefts was found to affect all biomarkers investigated. The shape of clusters observed in experiments by Jayasinghe et al. and channel density within the cluster (characterized by mean occupancy) showed the strongest correlation to the effects on biomarkers.
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Affiliation(s)
- Filippo G Cosi
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany; Georg-August-Universität Göttingen, Institute for the Dynamics of Complex Systems, Göttingen, Germany; DZHK (German Center for Cardiovascular Research), Partner Site Göttingen, Göttingen, Germany
| | - Wolfgang Giese
- Max Delbrück Center for Molecular Medicine in the Helmholtz Association, Berlin, Germany
| | - Wilhelm Neubert
- Max Delbrück Center for Molecular Medicine in the Helmholtz Association, Berlin, Germany
| | - Stefan Luther
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany; Georg-August-Universität Göttingen, Institute for the Dynamics of Complex Systems, Göttingen, Germany; DZHK (German Center for Cardiovascular Research), Partner Site Göttingen, Göttingen, Germany
| | - Nagaiah Chamakuri
- Institute of Applied Mathematics, University of Hohenheim, Stuttgart, Germany
| | - Ulrich Parlitz
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany; Georg-August-Universität Göttingen, Institute for the Dynamics of Complex Systems, Göttingen, Germany; DZHK (German Center for Cardiovascular Research), Partner Site Göttingen, Göttingen, Germany
| | - Martin Falcke
- Max Delbrück Center for Molecular Medicine in the Helmholtz Association, Berlin, Germany; DZHK (German Center for Cardiovascular Research), Partner Site Berlin, Berlin, Germany; Department of Physics, Humboldt University Berlin, Germany.
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