1
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Lei CL, Whittaker DG, Mirams GR. The impact of uncertainty in hERG binding mechanism on in silico predictions of drug-induced proarrhythmic risk. Br J Pharmacol 2024; 181:987-1004. [PMID: 37740435 DOI: 10.1111/bph.16250] [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: 03/14/2023] [Revised: 08/23/2023] [Accepted: 08/28/2023] [Indexed: 09/24/2023] Open
Abstract
BACKGROUND AND PURPOSE Drug-induced reduction of the rapid delayed rectifier potassium current carried by the human Ether-à-go-go-Related Gene (hERG) channel is associated with increased risk of arrhythmias. Recent updates to drug safety regulatory guidelines attempt to capture each drug's hERG binding mechanism by combining in vitro assays with in silico simulations. In this study, we investigate the impact on in silico proarrhythmic risk predictions due to uncertainty in the hERG binding mechanism and physiological hERG current model. EXPERIMENTAL APPROACH Possible pharmacological binding models were designed for the hERG channel to account for known and postulated small molecule binding mechanisms. After selecting a subset of plausible binding models for each compound through calibration to available voltage-clamp electrophysiology data, we assessed their effects, and the effects of different physiological models, on proarrhythmic risk predictions. KEY RESULTS For some compounds, multiple binding mechanisms can explain the same data produced under the safety testing guidelines, which results in different inferred binding rates. This can result in substantial uncertainty in the predicted torsade risk, which often spans more than one risk category. By comparison, we found that the effect of a different hERG physiological current model on risk classification was subtle. CONCLUSION AND IMPLICATIONS The approach developed in this study assesses the impact of uncertainty in hERG binding mechanisms on predictions of drug-induced proarrhythmic risk. For some compounds, these results imply the need for additional binding data to decrease uncertainty in safety-critical 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
| | - Dominic G Whittaker
- Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, UK
| | - Gary R Mirams
- Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, UK
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2
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Saghafi S, Rumbell T, Gurev V, Kozloski J, Tamagnini F, Wedgwood KCA, Diekman CO. Inferring Parameters of Pyramidal Neuron Excitability in Mouse Models of Alzheimer's Disease Using Biophysical Modeling and Deep Learning. Bull Math Biol 2024; 86:46. [PMID: 38528167 PMCID: PMC10963524 DOI: 10.1007/s11538-024-01273-5] [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: 02/28/2023] [Accepted: 02/19/2024] [Indexed: 03/27/2024]
Abstract
Alzheimer's disease (AD) is believed to occur when abnormal amounts of the proteins amyloid beta and tau aggregate in the brain, resulting in a progressive loss of neuronal function. Hippocampal neurons in transgenic mice with amyloidopathy or tauopathy exhibit altered intrinsic excitability properties. We used deep hybrid modeling (DeepHM), a recently developed parameter inference technique that combines deep learning with biophysical modeling, to map experimental data recorded from hippocampal CA1 neurons in transgenic AD mice and age-matched wildtype littermate controls to the parameter space of a conductance-based CA1 model. Although mechanistic modeling and machine learning methods are by themselves powerful tools for approximating biological systems and making accurate predictions from data, when used in isolation these approaches suffer from distinct shortcomings: model and parameter uncertainty limit mechanistic modeling, whereas machine learning methods disregard the underlying biophysical mechanisms. DeepHM addresses these shortcomings by using conditional generative adversarial networks to provide an inverse mapping of data to mechanistic models that identifies the distributions of mechanistic modeling parameters coherent to the data. Here, we demonstrated that DeepHM accurately infers parameter distributions of the conductance-based model on several test cases using synthetic data generated with complex underlying parameter structures. We then used DeepHM to estimate parameter distributions corresponding to the experimental data and infer which ion channels are altered in the Alzheimer's mouse models compared to their wildtype controls at 12 and 24 months. We found that the conductances most disrupted by tauopathy, amyloidopathy, and aging are delayed rectifier potassium, transient sodium, and hyperpolarization-activated potassium, respectively.
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Affiliation(s)
- Soheil Saghafi
- Department of Mathematical Sciences, New Jersey Institute of Technology, University Heights, Newark, NJ, 07102, USA
- Department of Biomedical Informatics, School of Medicine, Emory University, Atlanta, GA, 30322, USA
| | - Timothy Rumbell
- IBM T.J. Watson Research Center, Yorktown Heights, NY, 10598, USA
| | | | - James Kozloski
- IBM T.J. Watson Research Center, Yorktown Heights, NY, 10598, USA
| | | | | | - Casey O Diekman
- Department of Mathematical Sciences, New Jersey Institute of Technology, University Heights, Newark, NJ, 07102, USA.
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3
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Murphy RJ, Maclaren OJ, Simpson MJ. Implementing measurement error models with mechanistic mathematical models in a likelihood-based framework for estimation, identifiability analysis and prediction in the life sciences. J R Soc Interface 2024; 21:20230402. [PMID: 38290560 PMCID: PMC10827430 DOI: 10.1098/rsif.2023.0402] [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: 07/12/2023] [Accepted: 01/03/2024] [Indexed: 02/01/2024] Open
Abstract
Throughout the life sciences, we routinely seek to interpret measurements and observations using parametrized mechanistic mathematical models. A fundamental and often overlooked choice in this approach involves relating the solution of a mathematical model with noisy and incomplete measurement data. This is often achieved by assuming that the data are noisy measurements of the solution of a deterministic mathematical model, and that measurement errors are additive and normally distributed. While this assumption of additive Gaussian noise is extremely common and simple to implement and interpret, it is often unjustified and can lead to poor parameter estimates and non-physical predictions. One way to overcome this challenge is to implement a different measurement error model. In this review, we demonstrate how to implement a range of measurement error models in a likelihood-based framework for estimation, identifiability analysis and prediction, called profile-wise analysis. This frequentist approach to uncertainty quantification for mechanistic models leverages the profile likelihood for targeting parameters and understanding their influence on predictions. Case studies, motivated by simple caricature models routinely used in systems biology and mathematical biology literature, illustrate how the same ideas apply to different types of mathematical models. Open-source Julia code to reproduce results is available on GitHub.
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Affiliation(s)
- Ryan J. Murphy
- School of Mathematics and Statistics, The University of Melbourne, Parkville, Victoria, Australia
| | - Oliver J. Maclaren
- Department of Engineering Science and Biomedical Engineering, University of Auckland, Auckland, New Zealand
| | - Matthew J. Simpson
- Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
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4
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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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5
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Colebank MJ, Taylor R, Hacker TA, Chesler NC. Biventricular Interaction During Acute Left Ventricular Ischemia in Mice: A Combined In-Vivo and In-Silico Approach. Ann Biomed Eng 2023; 51:2528-2543. [PMID: 37453977 PMCID: PMC10598180 DOI: 10.1007/s10439-023-03293-z] [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: 01/27/2023] [Accepted: 06/17/2023] [Indexed: 07/18/2023]
Abstract
Computational models provide an efficient paradigm for integrating and linking multiple spatial and temporal scales. However, these models are difficult to parameterize and match to experimental data. Recent advances in both data collection and model analyses have helped overcome this limitation. Here, we combine a multiscale, biventricular interaction model with mouse data before and after left ventricular (LV) ischemia. Sensitivity analyses are used to identify the most influential parameters on pressure and volume predictions. The subset of influential model parameters are calibrated to biventricular pressure-volume loop data (n = 3) at baseline. Each mouse underwent left anterior descending coronary artery ligation, during which changes in fractional shortening and RV pressure-volume dynamics were recorded. Using the calibrated model, we simulate acute LV ischemia and contrast outputs at baseline and in simulated ischemia. Our baseline simulations align with the LV and RV data, and our predictions during ischemia complement recorded RV data and prior studies on LV function during myocardial infarction. We show that a model with both biventricular mechanical interaction and systems-level cardiovascular dynamics can quantitatively reproduce in-vivo data and qualitatively match prior findings from animal studies on LV ischemia.
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Affiliation(s)
- M J Colebank
- Edwards Lifesciences Foundation Cardiovascular Innovation and Research Center, and Department of Biomedical Engineering, University of California, Irvine, Irvine, CA, USA
| | - R Taylor
- Cardiovascular Research Center, University of Wisconsin-Madison, Madison, WI, USA
| | - T A Hacker
- Cardiovascular Research Center, University of Wisconsin-Madison, Madison, WI, USA
| | - N C Chesler
- Edwards Lifesciences Foundation Cardiovascular Innovation and Research Center, and Department of Biomedical Engineering, University of California, Irvine, Irvine, CA, USA.
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6
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Lei CL, Clerx M, Gavaghan DJ, Mirams GR. Model-driven optimal experimental design for calibrating cardiac electrophysiology models. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2023; 240:107690. [PMID: 37478675 DOI: 10.1016/j.cmpb.2023.107690] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2023] [Revised: 06/09/2023] [Accepted: 06/22/2023] [Indexed: 07/23/2023]
Abstract
BACKGROUND AND OBJECTIVE Models of the cardiomyocyte action potential have contributed immensely to the understanding of heart function, pathophysiology, and the origin of heart rhythm disturbances. However, action potential models are highly nonlinear, making them difficult to parameterise and limiting to describing 'average cell' dynamics, when cell-specific models would be ideal to uncover inter-cell variability but are too experimentally challenging to be achieved. Here, we focus on automatically designing experimental protocols that allow us to better identify cell-specific maximum conductance values for each major current type. METHODS AND RESULTS We developed an approach that applies optimal experimental designs to patch-clamp experiments, including both voltage-clamp and current-clamp experiments. We assessed the models calibrated to these new optimal designs by comparing them to the models calibrated to some of the commonly used designs in the literature. We showed that optimal designs are not only overall shorter in duration but also able to perform better than many of the existing experiment designs in terms of identifying model parameters and hence model predictive power. CONCLUSIONS For cardiac cellular electrophysiology, this approach will allow researchers to define their hypothesis of the dynamics of the system and automatically design experimental protocols that will result in theoretically optimal designs.
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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.
| | - Michael Clerx
- Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, United Kingdom
| | - David J Gavaghan
- Department of Computer Science, University of Oxford, Oxford, United Kingdom; Doctoral Training Centre, University of Oxford, Oxford, United Kingdom
| | - Gary R Mirams
- Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, United Kingdom.
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7
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Farm HJ, Clerx M, Cooper F, Polonchuk L, Wang K, Gavaghan DJ, Lei CL. Importance of modelling hERG binding in predicting drug-induced action potential prolongations for drug safety assessment. Front Pharmacol 2023; 14:1110555. [PMID: 37021055 PMCID: PMC10067903 DOI: 10.3389/fphar.2023.1110555] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2022] [Accepted: 02/22/2023] [Indexed: 03/30/2023] Open
Abstract
Reduction of the rapid delayed rectifier potassium current (IKr) via drug binding to the human Ether-à-go-go-Related Gene (hERG) channel is a well recognised mechanism that can contribute to an increased risk of Torsades de Pointes. Mathematical models have been created to replicate the effects of channel blockers, such as reducing the ionic conductance of the channel. Here, we study the impact of including state-dependent drug binding in a mathematical model of hERG when translating hERG inhibition to action potential changes. We show that the difference in action potential predictions when modelling drug binding of hERG using a state-dependent model versus a conductance scaling model depends not only on the properties of the drug and whether the experiment achieves steady state, but also on the experimental protocols. Furthermore, through exploring the model parameter space, we demonstrate that the state-dependent model and the conductance scaling model generally predict different action potential prolongations and are not interchangeable, while at high binding and unbinding rates, the conductance scaling model tends to predict shorter action potential prolongations. Finally, we observe that the difference in simulated action potentials between the models is determined by the binding and unbinding rate, rather than the trapping mechanism. This study demonstrates the importance of modelling drug binding and highlights the need for improved understanding of drug trapping which can have implications for the uses in drug safety assessment.
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Affiliation(s)
- Hui Jia Farm
- Department of Computer Science, University of Oxford, Oxford, United Kingdom
| | - Michael Clerx
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, United Kingdom
| | - Fergus Cooper
- Doctoral Training Centre, University of Oxford, Oxford, United Kingdom
| | - Liudmila Polonchuk
- Roche Pharma Research and Early Development, Pharmaceutical Sciences, Roche Innovation Center Basel, F. Hoffmann-La Roche Ltd., Basel, Switzerland
| | - Ken Wang
- Roche Pharma Research and Early Development, Pharmaceutical Sciences, Roche Innovation Center Basel, F. Hoffmann-La Roche Ltd., Basel, Switzerland
| | - David J. Gavaghan
- Department of Computer Science, University of Oxford, Oxford, United Kingdom
- Doctoral Training Centre, University of Oxford, Oxford, United Kingdom
- *Correspondence: David J. Gavaghan, ; Chon Lok Lei,
| | - 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
- *Correspondence: David J. Gavaghan, ; Chon Lok Lei,
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8
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Lambert B, Lei CL, Robinson M, Clerx M, Creswell R, Ghosh S, Tavener S, Gavaghan DJ. Autocorrelated measurement processes and inference for ordinary differential equation models of biological systems. J R Soc Interface 2023. [PMCID: PMC9943878 DOI: 10.1098/rsif.2022.0725] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/24/2023] Open
Abstract
Ordinary differential equation models are used to describe dynamic processes across biology. To perform likelihood-based parameter inference on these models, it is necessary to specify a statistical process representing the contribution of factors not explicitly included in the mathematical model. For this, independent Gaussian noise is commonly chosen, with its use so widespread that researchers typically provide no explicit justification for this choice. This noise model assumes ‘random’ latent factors affect the system in the ephemeral fashion resulting in unsystematic deviation of observables from their modelled counterparts. However, like the deterministically modelled parts of a system, these latent factors can have persistent effects on observables. Here, we use experimental data from dynamical systems drawn from cardiac physiology and electrochemistry to demonstrate that highly persistent differences between observations and modelled quantities can occur. Considering the case when persistent noise arises owing only to measurement imperfections, we use the Fisher information matrix to quantify how uncertainty in parameter estimates is artificially reduced when erroneously assuming independent noise. We present a workflow to diagnose persistent noise from model fits and describe how to remodel accounting for correlated errors.
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Affiliation(s)
- Ben Lambert
- Department of Mathematics, University of Exeter, Exeter EX4 4PY, UK
| | - Chon Lok Lei
- Faculty of Health Sciences, Institute of Translational Medicine, University of Macau, Macau, People’s Republic of China
| | - Martin Robinson
- Department of Computer Science, University of Oxford, Oxford OX1 3QG, UK
| | - Michael Clerx
- School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK
| | - Richard Creswell
- Department of Computer Science, University of Oxford, Oxford OX1 3QG, UK
| | - Sanmitra Ghosh
- MRC Biostatistics Unit, University of Cambridge, Cambridge CB2 0SR, UK
| | - Simon Tavener
- Department of Mathematics, Colorado State University, Fort Collins, CO 80523, UK
| | - David J. Gavaghan
- Department of Computer Science, University of Oxford, Oxford OX1 3QG, UK
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9
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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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10
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Şengül Ayan S, Süleymanoğlu S, Özdoğan H. A pilot study of ion current estimation by ANN from action potential waveforms. J Biol Phys 2022; 48:461-475. [PMID: 36372807 PMCID: PMC9727005 DOI: 10.1007/s10867-022-09619-7] [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: 07/27/2022] [Accepted: 10/28/2022] [Indexed: 11/15/2022] Open
Abstract
Experiments using conventional experimental approaches to capture the dynamics of ion channels are not always feasible, and even when possible and feasible, some can be time-consuming. In this work, the ionic current-time dynamics during cardiac action potentials (APs) are predicted from a single AP waveform by means of artificial neural networks (ANNs). The data collection is accomplished by the use of a single-cell model to run electrophysiological simulations in order to identify ionic currents based on fluctuations in ion channel conductance. The relevant ionic currents, as well as the corresponding cardiac AP, are then calculated and fed into the ANN algorithm, which predicts the desired currents solely based on the AP curve. The validity of the proposed methodology for the Bayesian approach is demonstrated by the R (validation) scores obtained from training data, test data, and the entire data set. The Bayesian regularization's (BR) strength and dependability are further supported by error values and the regression presentations, all of which are positive indicators. As a result of the high convergence between the simulated currents and the currents generated by including the efficacy of a developed Bayesian solver, it is possible to generate behavior of ionic currents during time for the desired AP waveform for any electrical excitable cell.
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Affiliation(s)
- Sevgi Şengül Ayan
- Department of Engineering, Industrial Engineering, Antalya Bilim University, Döşemealtı, Antalya, Turkey
| | - Selim Süleymanoğlu
- Department of Engineering, Electrical and Computer Engineering, Antalya Bilim University, Döşemealtı, Antalya, Turkey
| | - Hasan Özdoğan
- Department of Medical Imaging Techniques, Vocational School of Health Services, Antalya Bilim University, Döşemealtı, Antalya, Turkey
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11
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Whittaker DG, Wang J, Shuttleworth JG, Venkateshappa R, Kemp JM, Claydon TW, Mirams GR. Ion channel model reduction using manifold boundaries. JOURNAL OF THE ROYAL SOCIETY, INTERFACE 2022; 19:20220193. [PMID: 35946166 PMCID: PMC9363999 DOI: 10.1098/rsif.2022.0193] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
Mathematical models of voltage-gated ion channels are used in basic research, industrial and clinical settings. These models range in complexity, but typically contain numerous variables representing the proportion of channels in a given state, and parameters describing the voltage-dependent rates of transition between states. An open problem is selecting the appropriate degree of complexity and structure for an ion channel model given data availability. Here, we simplify a model of the cardiac human Ether-à-go-go related gene (hERG) potassium ion channel, which carries cardiac IKr, using the manifold boundary approximation method (MBAM). The MBAM approximates high-dimensional model-output manifolds by reduced models describing their boundaries, resulting in models with fewer parameters (and often variables). We produced a series of models of reducing complexity starting from an established five-state hERG model with 15 parameters. Models with up to three fewer states and eight fewer parameters were shown to retain much of the predictive capability of the full model and were validated using experimental hERG1a data collected in HEK293 cells at 37°C. The method provides a way to simplify complex models of ion channels that improves parameter identifiability and will aid in future model development.
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Affiliation(s)
- Dominic G Whittaker
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, UK
| | - Jiahui Wang
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, UK
| | - Joseph G Shuttleworth
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, UK
| | | | - Jacob M Kemp
- Department of Biomedical Physiology and Kinesiology, Simon Fraser University, Burnaby, Canada
| | - Thomas W Claydon
- Department of Biomedical Physiology and Kinesiology, Simon Fraser University, Burnaby, Canada
| | - Gary R Mirams
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, UK
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12
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Simpson MJ, Baker RE, Buenzli PR, Nicholson R, Maclaren OJ. Reliable and efficient parameter estimation using approximate continuum limit descriptions of stochastic models. J Theor Biol 2022; 549:111201. [PMID: 35752285 DOI: 10.1016/j.jtbi.2022.111201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2022] [Revised: 06/08/2022] [Accepted: 06/10/2022] [Indexed: 11/28/2022]
Abstract
Stochastic individual-based mathematical models are attractive for modelling biological phenomena because they naturally capture the stochasticity and variability that is often evident in biological data. Such models also allow us to track the motion of individuals within the population of interest. Unfortunately, capturing this microscopic detail means that simulation and parameter inference can become computationally expensive. One approach for overcoming this computational limitation is to coarse-grain the stochastic model to provide an approximate continuum model that can be solved using far less computational effort. However, coarse-grained continuum models can be biased or inaccurate, particularly for certain parameter regimes. In this work, we combine stochastic and continuum mathematical models in the context of lattice-based models of two-dimensional cell biology experiments by demonstrating how to simulate two commonly used experiments: cell proliferation assays and barrier assays. Our approach involves building a simple statistical model of the discrepancy between the expensive stochastic model and the associated computationally inexpensive coarse-grained continuum model. We form this statistical model based on a limited number of expensive stochastic model evaluations at design points sampled from a user-chosen distribution, corresponding to a computer experiment design problem. With straightforward design point selection schemes, we show that using the statistical model of the discrepancy in tandem with the computationally inexpensive continuum model allows us to carry out prediction and inference while correcting for biases and inaccuracies due to the continuum approximation. We demonstrate this approach by simulating a proliferation assay, where the continuum limit model is the well-known logistic ordinary differential equation, as well as a barrier assay where the continuum limit model is closely related to the well-known Fisher-KPP partial differential equation. We construct an approximate likelihood function for parameter inference, both with and without discrepancy correction terms. Using maximum likelihood estimation, we provide point estimates of the unknown parameters, and use the profile likelihood to characterise the uncertainty in these estimates and form approximate confidence intervals. For the range of inference problems considered, working with the continuum limit model alone leads to biased parameter estimation and confidence intervals with poor coverage. In contrast, incorporating correction terms arising from the statistical model of the model discrepancy allows us to recover the parameters accurately with minimal computational overhead. The main tradeoff is that the associated confidence intervals are typically broader, reflecting the additional uncertainty introduced by the approximation process. All algorithms required to replicate the results in this work are written in the open source Julia language and are available at GitHub.
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Affiliation(s)
- Matthew J Simpson
- School of Mathematical Sciences, Queensland University of Technology, Brisbane QLD 4001, Australia.
| | - Ruth E Baker
- Mathematical Institute, University of Oxford, Oxford, UK
| | - Pascal R Buenzli
- School of Mathematical Sciences, Queensland University of Technology, Brisbane QLD 4001, Australia
| | - Ruanui Nicholson
- Department of Engineering Science, University of Auckland, Auckland, 1142, New Zealand
| | - Oliver J Maclaren
- Department of Engineering Science, University of Auckland, Auckland, 1142, New Zealand
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13
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Xavier CR, Oliveira RS, Vieira VDF, Rocha BM, Reis RF, Quintela BDM, Lobosco M, Santos RWD. Timing the race of vaccination, new variants, and relaxing restrictions during COVID-19 pandemic. JOURNAL OF COMPUTATIONAL SCIENCE 2022; 61:101660. [PMID: 35432632 PMCID: PMC8990534 DOI: 10.1016/j.jocs.2022.101660] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2021] [Revised: 03/20/2022] [Accepted: 03/30/2022] [Indexed: 05/07/2023]
Abstract
Late in 2019, China identified a new type of coronavirus, SARS-CoV-2, and due to its fast spread, the World Health Organisation (WHO) declared a pandemic named COVID-19. Some variants of this virus were detected, including the Delta, which caused new waves of infections. This work uses an extended version of a SIRD model that includes vaccination effects to measure the impact of the Delta variant in three countries: Germany, Israel and Brazil. The calibrated models were able to reproduce the dynamics of the above countries. In addition, hypothetical scenarios were simulated to quantify the impact of vaccination and mitigation policies during the Delta wave. The results showed that the model could reproduce the complex dynamics observed in the different countries. The estimated increase of transmission rate due to the Delta variant was highest in Israel (7.9), followed by Germany (2.7) and Brazil (1.5). These values may support the hypothesis that people immunised against COVID-19 may lose their defensive antibodies with time since Israel, Germany, and Brazil fully vaccinated half of the population in March, July, and October. The scenario to study the impact of vaccination revealed relative reductions in the total number of deaths between 30% and 250%; an absolute reduction of 300 thousand deaths in Brazil due to vaccination during the Delta wave. The second hypothetical scenario revealed that mitigation policies saved up to 300 thousand Brazilians; relative reductions in the total number of deaths between 24% and 120% in the three analysed countries. Therefore, the results suggest that both vaccination and mitigation policies were crucial in decreasing the spread and the number of deaths during the Delta wave.
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Affiliation(s)
| | | | | | | | | | | | - Marcelo Lobosco
- Universidade Federal de Juiz de Fora, Juiz de Fora, MG, Brazil
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14
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Ribeiro Xavier C, Sachetto Oliveira R, da Fonseca Vieira V, Lobosco M, Weber dos Santos R. Characterisation of Omicron Variant during COVID-19 Pandemic and the Impact of Vaccination, Transmission Rate, Mortality, and Reinfection in South Africa, Germany, and Brazil. BIOTECH 2022; 11:biotech11020012. [PMID: 35822785 PMCID: PMC9264399 DOI: 10.3390/biotech11020012] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2022] [Revised: 04/21/2022] [Accepted: 04/21/2022] [Indexed: 02/05/2023] Open
Abstract
Several variants of SARS-CoV-2 have been identified in different parts of the world, including Gamma, detected in Brazil, Delta, detected in India, and the recent Omicron variant, detected in South Africa. The emergence of a new variant is a cause of great concern. This work considers an extended version of an SIRD model capable of incorporating the effects of vaccination, time-dependent transmissibility rates, mortality, and even potential reinfections during the pandemic. We use this model to characterise the Omicron wave in Brazil, South Africa, and Germany. During Omicron, the transmissibility increased by five for Brazil and Germany and eight for South Africa, whereas the estimated mortality was reduced by three-fold. We estimated that the reported cases accounted for less than 25% of the actual cases during Omicron. The mortality among the nonvaccinated population in these countries is, on average, three to four times higher than the mortality among the fully vaccinated. Finally, we could only reproduce the observed dynamics after introducing a new parameter that accounts for the percentage of the population that can be reinfected. Reinfection was as high as 40% in South Africa, which has only 29% of its population fully vaccinated and as low as 13% in Brazil, which has over 70% and 80% of its population fully vaccinated and with at least one dose, respectively. The calibrated models were able to estimate essential features of the complex virus and vaccination dynamics and stand as valuable tools for quantifying the impact of protocols and decisions in different populations.
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Affiliation(s)
- Carolina Ribeiro Xavier
- Department of Computer Science, Federal University of São João del-Rei, São João del-Rei 36301-360, MG, Brazil; (C.R.X.); (R.S.O.); (V.d.F.V.)
| | - Rafael Sachetto Oliveira
- Department of Computer Science, Federal University of São João del-Rei, São João del-Rei 36301-360, MG, Brazil; (C.R.X.); (R.S.O.); (V.d.F.V.)
| | - Vinícius da Fonseca Vieira
- Department of Computer Science, Federal University of São João del-Rei, São João del-Rei 36301-360, MG, Brazil; (C.R.X.); (R.S.O.); (V.d.F.V.)
| | - Marcelo Lobosco
- Department of Computer Science, Federal University of Juiz de Fora, Juiz de Fora 36036-330, MG, Brazil;
| | - Rodrigo Weber dos Santos
- Department of Computer Science, Federal University of Juiz de Fora, Juiz de Fora 36036-330, MG, Brazil;
- Correspondence:
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15
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Accurate in silico simulation of the rabbit Purkinje fiber electrophysiological assay to facilitate early pharmaceutical cardiosafety assessment: Dream or reality? J Pharmacol Toxicol Methods 2022; 115:107172. [DOI: 10.1016/j.vascn.2022.107172] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2021] [Revised: 03/31/2022] [Accepted: 04/08/2022] [Indexed: 11/24/2022]
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16
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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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17
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Rao P, Peyron Q, Burgner-Kahrs J. Shape Representation and Modeling of Tendon-Driven Continuum Robots Using Euler Arc Splines. IEEE Robot Autom Lett 2022. [DOI: 10.1109/lra.2022.3185377] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Affiliation(s)
- Priyanka Rao
- Continuum Robotics Laboratory, Department of Mathematical & Computational Sciences, University of Toronto, Toronto, ON, Canada
| | - Quentin Peyron
- Continuum Robotics Laboratory, Department of Mathematical & Computational Sciences, University of Toronto, Toronto, ON, Canada
| | - Jessica Burgner-Kahrs
- Continuum Robotics Laboratory, Department of Mathematical & Computational Sciences, University of Toronto, Toronto, ON, Canada
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18
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van Osta N, Kirkels FP, van Loon T, Koopsen T, Lyon A, Meiburg R, Huberts W, Cramer MJ, Delhaas T, Haugaa KH, Teske AJ, Lumens J. Uncertainty Quantification of Regional Cardiac Tissue Properties in Arrhythmogenic Cardiomyopathy Using Adaptive Multiple Importance Sampling. Front Physiol 2021; 12:738926. [PMID: 34658923 PMCID: PMC8514656 DOI: 10.3389/fphys.2021.738926] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/09/2021] [Accepted: 08/31/2021] [Indexed: 11/13/2022] Open
Abstract
Introduction: Computational models of the cardiovascular system are widely used to simulate cardiac (dys)function. Personalization of such models for patient-specific simulation of cardiac function remains challenging. Measurement uncertainty affects accuracy of parameter estimations. In this study, we present a methodology for patient-specific estimation and uncertainty quantification of parameters in the closed-loop CircAdapt model of the human heart and circulation using echocardiographic deformation imaging. Based on patient-specific estimated parameters we aim to reveal the mechanical substrate underlying deformation abnormalities in patients with arrhythmogenic cardiomyopathy (AC). Methods: We used adaptive multiple importance sampling to estimate the posterior distribution of regional myocardial tissue properties. This methodology is implemented in the CircAdapt cardiovascular modeling platform and applied to estimate active and passive tissue properties underlying regional deformation patterns, left ventricular volumes, and right ventricular diameter. First, we tested the accuracy of this method and its inter- and intraobserver variability using nine datasets obtained in AC patients. Second, we tested the trueness of the estimation using nine in silico generated virtual patient datasets representative for various stages of AC. Finally, we applied this method to two longitudinal series of echocardiograms of two pathogenic mutation carriers without established myocardial disease at baseline. Results: Tissue characteristics of virtual patients were accurately estimated with a highest density interval containing the true parameter value of 9% (95% CI [0-79]). Variances of estimated posterior distributions in patient data and virtual data were comparable, supporting the reliability of the patient estimations. Estimations were highly reproducible with an overlap in posterior distributions of 89.9% (95% CI [60.1-95.9]). Clinically measured deformation, ejection fraction, and end-diastolic volume were accurately simulated. In presence of worsening of deformation over time, estimated tissue properties also revealed functional deterioration. Conclusion: This method facilitates patient-specific simulation-based estimation of regional ventricular tissue properties from non-invasive imaging data, taking into account both measurement and model uncertainties. Two proof-of-principle case studies suggested that this cardiac digital twin technology enables quantitative monitoring of AC disease progression in early stages of disease.
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Affiliation(s)
- Nick van Osta
- Department of Biomedical Engineering, Cardiovascular Research Institute Maastricht, Maastricht University, Maastricht, Netherlands
| | - Feddo P Kirkels
- Division Heart and Lungs, Department of Cardiology, University Medical Center Utrecht, Utrecht, Netherlands
| | - Tim van Loon
- Department of Biomedical Engineering, Cardiovascular Research Institute Maastricht, Maastricht University, Maastricht, Netherlands
| | - Tijmen Koopsen
- Department of Biomedical Engineering, Cardiovascular Research Institute Maastricht, Maastricht University, Maastricht, Netherlands
| | - Aurore Lyon
- Department of Biomedical Engineering, Cardiovascular Research Institute Maastricht, Maastricht University, Maastricht, Netherlands
| | - Roel Meiburg
- Department of Biomedical Engineering, Cardiovascular Research Institute Maastricht, Maastricht University, Maastricht, Netherlands
| | - Wouter Huberts
- Department of Biomedical Engineering, Cardiovascular Research Institute Maastricht, Maastricht University, Maastricht, Netherlands
| | - Maarten J Cramer
- Division Heart and Lungs, Department of Cardiology, University Medical Center Utrecht, Utrecht, Netherlands
| | - Tammo Delhaas
- Department of Biomedical Engineering, Cardiovascular Research Institute Maastricht, Maastricht University, Maastricht, Netherlands
| | - Kristina H Haugaa
- Department of Cardiology, Oslo University Hospital, University of Oslo, Oslo, Norway
| | - Arco J Teske
- Division Heart and Lungs, Department of Cardiology, University Medical Center Utrecht, Utrecht, Netherlands
| | - Joost Lumens
- Department of Biomedical Engineering, Cardiovascular Research Institute Maastricht, Maastricht University, Maastricht, Netherlands
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19
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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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20
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Stage HB, Shingleton J, Ghosh S, Scarabel F, Pellis L, Finnie T. Shut and re-open: the role of schools in the spread of COVID-19 in Europe. Philos Trans R Soc Lond B Biol Sci 2021; 376:20200277. [PMID: 34053270 PMCID: PMC8165592 DOI: 10.1098/rstb.2020.0277] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 12/02/2020] [Indexed: 12/21/2022] Open
Abstract
We investigate the effect of school closure and subsequent reopening on the transmission of COVID-19, by considering Denmark, Norway, Sweden and German states as case studies. By comparing the growth rates in daily hospitalizations or confirmed cases under different interventions, we provide evidence that school closures contribute to a reduction in the growth rate approximately 7 days after implementation. Limited school attendance, such as older students sitting exams or the partial return of younger year groups, does not appear to significantly affect community transmission. In countries where community transmission is generally low, such as Denmark or Norway, a large-scale reopening of schools while controlling or suppressing the epidemic appears feasible. However, school reopening can contribute to statistically significant increases in the growth rate in countries like Germany, where community transmission is relatively high. In all regions, a combination of low classroom occupancy and robust test-and-trace measures were in place. Our findings underscore the need for a cautious evaluation of reopening strategies. This article is part of the theme issue 'Modelling that shaped the early COVID-19 pandemic response in the UK'.
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Affiliation(s)
- Helena B. Stage
- Department of Mathematics, University of Manchester, Manchester, UK
| | | | - Sanmitra Ghosh
- MRC Biostatistics Unit, University of Cambridge, Cambridge, UK
| | - Francesca Scarabel
- Department of Mathematics, University of Manchester, Manchester, UK
- Laboratory of Industrial and Applied Mathematics, Department of Mathematics and Statistics, York University, Toronto Ontario, Canada
- CDLab - Computational Dynamics Laboratory, Department of Mathematics, Computer Science and Physics, University of Udine, Italy
| | - Lorenzo Pellis
- Department of Mathematics, University of Manchester, Manchester, UK
- The Alan Turing Institute, London, UK
| | - Thomas Finnie
- Emergency Response Department, Public Health England, London, UK
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21
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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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22
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Reis RF, Oliveira RS, Quintela BDM, Campos JDO, Gomes JM, Rocha BM, Lobosco M, Dos Santos RW. The Quixotic Task of Forecasting Peaks of COVID-19: Rather Focus on Forward and Backward Projections. Front Public Health 2021; 9:623521. [PMID: 33796495 PMCID: PMC8007858 DOI: 10.3389/fpubh.2021.623521] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2020] [Accepted: 02/10/2021] [Indexed: 12/23/2022] Open
Abstract
Over the last months, mathematical models have been extensively used to help control the COVID-19 pandemic worldwide. Although extremely useful in many tasks, most models have performed poorly in forecasting the pandemic peaks. We investigate this common pitfall by forecasting four countries' pandemic peak: Austria, Germany, Italy, and South Korea. Far from the peaks, our models can forecast the pandemic dynamics 20 days ahead. Nevertheless, when calibrating our models close to the day of the pandemic peak, all forecasts fail. Uncertainty quantification and sensitivity analysis revealed the main obstacle: the misestimation of the transmission rate. Inverse uncertainty quantification has shown that significant changes in transmission rate commonly precede a peak. These changes are a key factor in forecasting the pandemic peak. Long forecasts of the pandemic peak are therefore undermined by the lack of models that can forecast changes in the transmission rate, i.e., how a particular society behaves, changes of mitigation policies, or how society chooses to respond to them. In addition, our studies revealed that even short forecasts of the pandemic peak are challenging. Backward projections have shown us that the correct estimation of any temporal change in the transmission rate is only possible many days ahead. Our results suggest that the distance between a change in the transmission rate and its correct identification in the curve of active infected cases can be as long as 15 days. This is intrinsic to the phenomenon and how it affects epidemic data: a new case is usually only reported after an incubation period followed by a delay associated with the test. In summary, our results suggest the phenomenon itself challenges the task of forecasting the peak of the COVID-19 pandemic when only epidemic data is available. Nevertheless, we show that exciting results can be obtained when using the same models to project different scenarios of reduced transmission rates. Therefore, our results highlight that mathematical modeling can help control COVID-19 pandemic by backward projections that characterize the phenomena' essential features and forward projections when different scenarios and strategies can be tested and used for decision-making.
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Affiliation(s)
- Ruy Freitas Reis
- Departamento de Ciência da Computação, Universidade Federal de Juiz de Fora, Juiz de Fora, Brazil
| | - Rafael Sachetto Oliveira
- Departamento de Ciência da Computação, Universidade Federal de São João del-Rei, São João del-Rei, Brazil
| | - Bárbara de Melo Quintela
- Departamento de Ciência da Computação, Universidade Federal de Juiz de Fora, Juiz de Fora, Brazil
| | | | - Johnny Moreira Gomes
- Pós-Graduação em Modelagem Computacional, Universidade Federal de Juiz de Fora, Juiz de Fora, Brazil
| | - Bernardo Martins Rocha
- Departamento de Ciência da Computação, Universidade Federal de Juiz de Fora, Juiz de Fora, Brazil.,Pós-Graduação em Modelagem Computacional, Universidade Federal de Juiz de Fora, Juiz de Fora, Brazil
| | - Marcelo Lobosco
- Departamento de Ciência da Computação, Universidade Federal de Juiz de Fora, Juiz de Fora, Brazil.,Pós-Graduação em Modelagem Computacional, Universidade Federal de Juiz de Fora, Juiz de Fora, Brazil
| | - Rodrigo Weber Dos Santos
- Departamento de Ciência da Computação, Universidade Federal de Juiz de Fora, Juiz de Fora, Brazil.,Pós-Graduação em Modelagem Computacional, Universidade Federal de Juiz de Fora, Juiz de Fora, Brazil
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23
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McCabe KJ, Rangamani P. Computational modeling approaches to cAMP/PKA signaling in cardiomyocytes. J Mol Cell Cardiol 2021; 154:32-40. [PMID: 33548239 DOI: 10.1016/j.yjmcc.2021.01.008] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 10/15/2020] [Revised: 01/11/2021] [Accepted: 01/15/2021] [Indexed: 12/12/2022]
Abstract
The cAMP/PKA pathway is a fundamental regulator of excitation-contraction coupling in cardiomyocytes. Activation of cAMP has a variety of downstream effects on cardiac function including enhanced contraction, accelerated relaxation, adaptive stress response, mitochondrial regulation, and gene transcription. Experimental advances have shed light on the compartmentation of cAMP and PKA, which allow for control over the varied targets of these second messengers and is disrupted in heart failure conditions. Computational modeling is an important tool for understanding the spatial and temporal complexities of this system. In this review article, we outline the advances in computational modeling that have allowed for deeper understanding of cAMP/PKA dynamics in the cardiomyocyte in health and disease, and explore new modeling frameworks that may bring us closer to a more complete understanding of this system. We outline various compartmental and spatial signaling models that have been used to understand how β-adrenergic signaling pathways function in a variety of simulation conditions. We also discuss newer subcellular models of cardiovascular function that may be used as templates for the next phase of computational study of cAMP and PKA in the heart, and outline open challenges which are important to consider in future models.
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Affiliation(s)
- Kimberly J McCabe
- Simula Research Laboratory, Department of Computational Physiology, PO Box 134, 1325 Lysaker, Norway.
| | - Padmini Rangamani
- University of California San Diego, Department of Mechanical and Aerospace Engineering, 9500 Gilman Drive MC 0411, La Jolla, CA 92093, United States of America
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24
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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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25
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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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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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Pathmanathan P, Galappaththige SK, Cordeiro JM, Kaboudian A, Fenton FH, Gray RA. Data-Driven Uncertainty Quantification for Cardiac Electrophysiological Models: Impact of Physiological Variability on Action Potential and Spiral Wave Dynamics. Front Physiol 2020; 11:585400. [PMID: 33329034 PMCID: PMC7711195 DOI: 10.3389/fphys.2020.585400] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2020] [Accepted: 10/20/2020] [Indexed: 12/23/2022] Open
Abstract
Computational modeling of cardiac electrophysiology (EP) has recently transitioned from a scientific research tool to clinical applications. To ensure reliability of clinical or regulatory decisions made using cardiac EP models, it is vital to evaluate the uncertainty in model predictions. Model predictions are uncertain because there is typically substantial uncertainty in model input parameters, due to measurement error or natural variability. While there has been much recent uncertainty quantification (UQ) research for cardiac EP models, all previous work has been limited by either: (i) considering uncertainty in only a subset of the full set of parameters; and/or (ii) assigning arbitrary variation to parameters (e.g., ±10 or 50% around mean value) rather than basing the parameter uncertainty on experimental data. In our recent work we overcame the first limitation by performing UQ and sensitivity analysis using a novel canine action potential model, allowing all parameters to be uncertain, but with arbitrary variation. Here, we address the second limitation by extending our previous work to use data-driven estimates of parameter uncertainty. Overall, we estimated uncertainty due to population variability in all parameters in five currents active during repolarization: inward potassium rectifier, transient outward potassium, L-type calcium, rapidly and slowly activating delayed potassium rectifier; 25 parameters in total (all model parameters except fast sodium current parameters). A variety of methods was used to estimate the variability in these parameters. We then propagated the uncertainties through the model to determine their impact on predictions of action potential shape, action potential duration (APD) prolongation due to drug block, and spiral wave dynamics. Parameter uncertainty had a significant effect on model predictions, especially L-type calcium current parameters. Correlation between physiological parameters was determined to play a role in physiological realism of action potentials. Surprisingly, even model outputs that were relative differences, specifically drug-induced APD prolongation, were heavily impacted by the underlying uncertainty. This is the first data-driven end-to-end UQ analysis in cardiac EP accounting for uncertainty in the vast majority of parameters, including first in tissue, and demonstrates how future UQ could be used to ensure model-based decisions are robust to all underlying parameter uncertainties.
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Affiliation(s)
- Pras Pathmanathan
- U.S. Food and Drug Administration, Center for Devices and Radiological Health, Silver Spring, MD, United States
| | - Suran K. Galappaththige
- U.S. Food and Drug Administration, Center for Devices and Radiological Health, Silver Spring, MD, United States
| | - Jonathan M. Cordeiro
- Department of Experimental Cardiology, Masonic Medical Research Institute, Utica, NY, United States
| | - Abouzar Kaboudian
- School of Physics, Georgia Institute of Technology, Atlanta, GA, United States
| | - Flavio H. Fenton
- School of Physics, Georgia Institute of Technology, Atlanta, GA, United States
| | - Richard A. Gray
- U.S. Food and Drug Administration, Center for Devices and Radiological Health, Silver Spring, MD, United States
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28
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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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29
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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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30
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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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31
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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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32
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Mirams GR, Niederer SA, Clayton RH. The fickle heart: uncertainty quantification in cardiac and cardiovascular modelling and simulation. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2020; 378:20200119. [PMID: 32448073 PMCID: PMC7287327 DOI: 10.1098/rsta.2020.0119] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Affiliation(s)
- Gary R. Mirams
- School of Mathematical Sciences, University of Nottingham, Mathematical Sciences Building, University Park, Nottingham, Nottinghamshire NG7 2RD, UK
- e-mail:
| | - Steven A. Niederer
- Division of Imaging Sciences and Biomedical Engineering, Kings College London, The Rayne Institute, 4th Floor, Lambeth Wing, St Thomas’ Hospital, London SE1 7EH, UK
| | - Richard H. Clayton
- Computer Science, University of Sheffield, Regent Court, 211 Portobello, Sheffield S1 4DP, UK
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