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Nieto Ramos A, Fenton FH, Cherry EM. Bayesian inference for fitting cardiac models to experiments: estimating parameter distributions using Hamiltonian Monte Carlo and approximate Bayesian computation. Med Biol Eng Comput 2023; 61:75-95. [PMID: 36322242 DOI: 10.1007/s11517-022-02685-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/15/2022] [Accepted: 10/02/2022] [Indexed: 01/07/2023]
Abstract
Customization of cardiac action potential models has become increasingly important with the recognition of patient-specific models and virtual patient cohorts as valuable predictive tools. Nevertheless, developing customized models by fitting parameters to data poses technical and methodological challenges: despite noise and variability associated with real-world datasets, traditional optimization methods produce a single "best-fit" set of parameter values. Bayesian estimation methods seek distributions of parameter values given the data by obtaining samples from the target distribution, but in practice widely known Bayesian algorithms like Markov chain Monte Carlo tend to be computationally inefficient and scale poorly with the dimensionality of parameter space. In this paper, we consider two computationally efficient Bayesian approaches: the Hamiltonian Monte Carlo (HMC) algorithm and the approximate Bayesian computation sequential Monte Carlo (ABC-SMC) algorithm. We find that both methods successfully identify distributions of model parameters for two cardiac action potential models using model-derived synthetic data and an experimental dataset from a zebrafish heart. Although both methods appear to converge to the same distribution family and are computationally efficient, HMC generally finds narrower marginal distributions, while ABC-SMC is less sensitive to the algorithmic settings including the prior distribution.
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Affiliation(s)
- Alejandro Nieto Ramos
- School of Mathematical Sciences, Rochester Institute of Technology, 1 Lomb Memorial Drive, 14623, Rochester, NY, USA.,Epilepsy Center, Neurological Institute, Cleveland Clinic, 9500 Euclid Avenue, Cleveland, OH, 44195, USA
| | - Flavio H Fenton
- School of Physics, Georgia Institute of Technology, 837 State Street NW, 30332, Atlanta, GA, USA
| | - Elizabeth M Cherry
- School of Computational Science and Engineering, Georgia Institute of Technology, 756 West Peachtree Street, 30308, Atlanta, GA, USA.
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Sánchez J, Trenor B, Saiz J, Dössel O, Loewe A. Fibrotic Remodeling during Persistent Atrial Fibrillation: In Silico Investigation of the Role of Calcium for Human Atrial Myofibroblast Electrophysiology. Cells 2021; 10:cells10112852. [PMID: 34831076 PMCID: PMC8616446 DOI: 10.3390/cells10112852] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2021] [Revised: 10/08/2021] [Accepted: 10/19/2021] [Indexed: 12/20/2022] Open
Abstract
During atrial fibrillation, cardiac tissue undergoes different remodeling processes at different scales from the molecular level to the tissue level. One central player that contributes to both electrical and structural remodeling is the myofibroblast. Based on recent experimental evidence on myofibroblasts' ability to contract, we extended a biophysical myofibroblast model with Ca2+ handling components and studied the effect on cellular and tissue electrophysiology. Using genetic algorithms, we fitted the myofibroblast model parameters to the existing in vitro data. In silico experiments showed that Ca2+ currents can explain the experimentally observed variability regarding the myofibroblast resting membrane potential. The presence of an L-type Ca2+ current can trigger automaticity in the myofibroblast with a cycle length of 799.9 ms. Myocyte action potentials were prolonged when coupled to myofibroblasts with Ca2+ handling machinery. Different spatial myofibroblast distribution patterns increased the vulnerable window to induce arrhythmia from 12 ms in non-fibrotic tissue to 22 ± 2.5 ms and altered the reentry dynamics. Our findings suggest that Ca2+ handling can considerably affect myofibroblast electrophysiology and alter the electrical propagation in atrial tissue composed of myocytes coupled with myofibroblasts. These findings can inform experimental validation experiments to further elucidate the role of myofibroblast Ca2+ handling in atrial arrhythmogenesis.
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Affiliation(s)
- Jorge Sánchez
- Institute of Biomedical Engineering, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany; (O.D.); (A.L.)
- Correspondence:
| | - Beatriz Trenor
- Centro de Investigación e Innovación en Bioingeniería (Ci2B), Universitàt Politècnica de València, 46022 Valencia, Spain; (B.T.); (J.S.)
| | - Javier Saiz
- Centro de Investigación e Innovación en Bioingeniería (Ci2B), Universitàt Politècnica de València, 46022 Valencia, Spain; (B.T.); (J.S.)
| | - Olaf Dössel
- Institute of Biomedical Engineering, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany; (O.D.); (A.L.)
| | - Axel Loewe
- Institute of Biomedical Engineering, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany; (O.D.); (A.L.)
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Coveney S, Corrado C, Oakley JE, Wilkinson RD, Niederer SA, Clayton RH. Bayesian Calibration of Electrophysiology Models Using Restitution Curve Emulators. Front Physiol 2021; 12:693015. [PMID: 34366883 PMCID: PMC8339909 DOI: 10.3389/fphys.2021.693015] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/09/2021] [Accepted: 06/28/2021] [Indexed: 11/13/2022] Open
Abstract
Calibration of cardiac electrophysiology models is a fundamental aspect of model personalization for predicting the outcomes of cardiac therapies, simulation testing of device performance for a range of phenotypes, and for fundamental research into cardiac function. Restitution curves provide information on tissue function and can be measured using clinically feasible measurement protocols. We introduce novel "restitution curve emulators" as probabilistic models for performing model exploration, sensitivity analysis, and Bayesian calibration to noisy data. These emulators are built by decomposing restitution curves using principal component analysis and modeling the resulting coordinates with respect to model parameters using Gaussian processes. Restitution curve emulators can be used to study parameter identifiability via sensitivity analysis of restitution curve components and rapid inference of the posterior distribution of model parameters given noisy measurements. Posterior uncertainty about parameters is critical for making predictions from calibrated models, since many parameter settings can be consistent with measured data and yet produce very different model behaviors under conditions not effectively probed by the measurement protocols. Restitution curve emulators are therefore promising probabilistic tools for calibrating electrophysiology models.
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Affiliation(s)
- Sam Coveney
- Insigneo Institute for In-Silico Medicine and Department of Computer Science, University of Sheffield, Sheffield, United Kingdom
| | - Cesare Corrado
- Division of Imaging Sciences and Biomedical Engineering, King's College London, London, United Kingdom
| | - Jeremy E Oakley
- School of Mathematics and Statistics, University of Sheffield, Sheffield, United Kingdom
| | - Richard D Wilkinson
- School of Mathematical Sciences, University of Nottingham, Nottingham, United Kingdom
| | - Steven A Niederer
- Division of Imaging Sciences and Biomedical Engineering, King's College London, London, United Kingdom
| | - Richard H Clayton
- Insigneo Institute for In-Silico Medicine and Department of Computer Science, University of Sheffield, Sheffield, United Kingdom
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Pouranbarani E, Weber dos Santos R, Nygren A. A robust multi-objective optimization framework to capture both cellular and intercellular properties in cardiac cellular model tuning: Analyzing different regions of membrane resistance profile in parameter fitting. PLoS One 2019; 14:e0225245. [PMID: 31730631 PMCID: PMC6857942 DOI: 10.1371/journal.pone.0225245] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2019] [Accepted: 10/31/2019] [Indexed: 02/07/2023] Open
Abstract
Mathematical models of cardiac cells have been established to broaden understanding of cardiac function. In the process of developing electrophysiological models for cardiac myocytes, precise parameter tuning is a crucial step. The membrane resistance (Rm) is an essential feature obtained from cardiac myocytes. This feature reflects intercellular coupling and affects important phenomena, such as conduction velocity, and early after-depolarizations, but it is often overlooked during the phase of parameter fitting. Thus, the traditional parameter fitting that only includes action potential (AP) waveform may yield incorrect values for Rm. In this paper, a novel multi-objective parameter fitting formulation is proposed and tested that includes different regions of the Rm profile as additional objective functions for optimization. As Rm depends on the transmembrane voltage (Vm) and exhibits singularities for some specific values of Vm, analyses are conducted to carefully select the regions of interest for the proper characterization of Rm. Non-dominated sorting genetic algorithm II is utilized to solve the proposed multi-objective optimization problem. To verify the efficacy of the proposed problem formulation, case studies and comparisons are carried out using multiple models of human cardiac ventricular cells. Results demonstrate Rm is correctly reproduced by the tuned cell models after considering the curve of Rm obtained from the late phase of repolarization and Rm value calculated in the rest phase as additional objectives. However, relative deterioration of the AP fit is observed, demonstrating trade-off among the objectives. This framework can be useful for a wide range of applications, including the parameters fitting phase of the cardiac cell model development and investigation of normal and pathological scenarios in which reproducing both cellular and intercellular properties are of great importance.
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Affiliation(s)
- Elnaz Pouranbarani
- Department of Electrical and Computer Engineering, University of Calgary, Calgary, Alberta, Canada
- * E-mail:
| | - Rodrigo Weber dos Santos
- Department of Computer Science and the Graduate Program of Computational Modeling, Federal University of Juiz de Fora, Juiz de Fora, Minas Gerais, Brazil
| | - Anders Nygren
- Department of Electrical and Computer Engineering, University of Calgary, Calgary, Alberta, Canada
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Pouranbarani E, Nygren A. A Novel Bi-Level Framework for Fitting the Parameters in Cardiac Cellular Models. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2019; 2018:2370-2373. [PMID: 30440883 DOI: 10.1109/embc.2018.8512883] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
Cardiac models constructed from sets of differential equations provide invaluable information about heart mechanism and disorder of both human and animals. As tuning the parameters is a profoundly important step of modeling, this paper presents a novel parametrization technique based on a bilevel framework that benefits from two solution approaches, namely mixed integer genetic algorithm (MIGA) and linear least squares (LLS). In the upper-level optimization step, the action potential (AP) of the model is fitted to the reference AP using MIGA. In the lower-level optimization step, the mismatch between the total current of the model and reference is minimized via a clamp concept-based linearization and LLS solution approach. Notably, the clamp concept can diminish the nonlinearity of the parameter fitting problem. The issue of dependency on initial parameters in the lower-level problem, as well as the sensitivity of model parameters to linearization, are circumvented by MIGA in the upper-level optimization. For evaluation of MIGA-LLS performance, two complex human ventricular models are employed. The results demonstrate that in comparison to the genetic algorithm (GA)-based approach, the proposed framework significantly reduces the average and variation of normalized root-mean-squared error (NRMSE) in terms of the AP and total current in different trials. Variability in the resulting parameter values is considerably decreased as well.
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Clerx M, Beattie KA, Gavaghan DJ, Mirams GR. Four Ways to Fit an Ion Channel Model. Biophys J 2019; 117:2420-2437. [PMID: 31493859 PMCID: PMC6990153 DOI: 10.1016/j.bpj.2019.08.001] [Citation(s) in RCA: 35] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/15/2019] [Revised: 06/20/2019] [Accepted: 08/01/2019] [Indexed: 12/16/2022] Open
Abstract
Mathematical models of ionic currents are used to study the electrophysiology of the heart, brain, gut, and several other organs. Increasingly, these models are being used predictively in the clinic, for example, to predict the risks and results of genetic mutations, pharmacological treatments, or surgical procedures. These safety-critical applications depend on accurate characterization of the underlying ionic currents. Four different methods can be found in the literature to fit voltage-sensitive ion channel models to whole-cell current measurements: method 1, fitting model equations directly to time-constant, steady-state, and I-V summary curves; method 2, fitting by comparing simulated versions of these summary curves to their experimental counterparts; method 3, fitting to the current traces themselves from a range of protocols; and method 4, fitting to a single current trace from a short and rapidly fluctuating voltage-clamp protocol. We compare these methods using a set of experiments in which hERG1a current was measured in nine Chinese hamster ovary cells. In each cell, the same sequence of fitting protocols was applied, as well as an independent validation protocol. We show that methods 3 and 4 provide the best predictions on the independent validation set and that short, rapidly fluctuating protocols like that used in method 4 can replace much longer conventional protocols without loss of predictive ability. Although data for method 2 are most readily available from the literature, we find it performs poorly compared to methods 3 and 4 both in accuracy of predictions and computational efficiency. Our results demonstrate how novel experimental and computational approaches can improve the quality of model predictions in safety-critical applications.
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Affiliation(s)
- Michael Clerx
- Computational Biology & Health Informatics, Department of Computer Science, University of Oxford, Oxford, United Kingdom
| | - Kylie A Beattie
- Computational Biology & Health Informatics, Department of Computer Science, University of Oxford, Oxford, United Kingdom
| | - David J Gavaghan
- Computational Biology & Health Informatics, Department of Computer Science, 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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Aronis KN, Ali RL, Liang JA, Zhou S, Trayanova NA. Understanding AF Mechanisms Through Computational Modelling and Simulations. Arrhythm Electrophysiol Rev 2019; 8:210-219. [PMID: 31463059 PMCID: PMC6702471 DOI: 10.15420/aer.2019.28.2] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 03/08/2019] [Accepted: 06/17/2019] [Indexed: 12/21/2022] Open
Abstract
AF is a progressive disease of the atria, involving complex mechanisms related to its initiation, maintenance and progression. Computational modelling provides a framework for integration of experimental and clinical findings, and has emerged as an essential part of mechanistic research in AF. The authors summarise recent advancements in development of multi-scale AF models and focus on the mechanistic links between alternations in atrial structure and electrophysiology with AF. Key AF mechanisms that have been explored using atrial modelling are pulmonary vein ectopy; atrial fibrosis and fibrosis distribution; atrial wall thickness heterogeneity; atrial adipose tissue infiltration; development of repolarisation alternans; cardiac ion channel mutations; and atrial stretch with mechano-electrical feedback. They review modelling approaches that capture variability at the cohort level and provide cohort-specific mechanistic insights. The authors conclude with a summary of future perspectives, as envisioned for the contributions of atrial modelling in the mechanistic understanding of AF.
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Affiliation(s)
- Konstantinos N Aronis
- Department of Biomedical Engineering and the Institute for Computational Medicine, Johns Hopkins UniversityBaltimore, MD, US
- Division of Cardiology, Johns Hopkins HospitalBaltimore, MD, US
| | - Rheeda L Ali
- Department of Biomedical Engineering and the Institute for Computational Medicine, Johns Hopkins UniversityBaltimore, MD, US
| | - Jialiu A Liang
- Department of Biomedical Engineering and the Institute for Computational Medicine, Johns Hopkins UniversityBaltimore, MD, US
| | - Shijie Zhou
- Department of Biomedical Engineering and the Institute for Computational Medicine, Johns Hopkins UniversityBaltimore, MD, US
| | - Natalia A Trayanova
- Department of Biomedical Engineering and the Institute for Computational Medicine, Johns Hopkins UniversityBaltimore, MD, US
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Reproducible model development in the cardiac electrophysiology Web Lab. PROGRESS IN BIOPHYSICS AND MOLECULAR BIOLOGY 2018; 139:3-14. [PMID: 29842853 PMCID: PMC6288479 DOI: 10.1016/j.pbiomolbio.2018.05.011] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/31/2018] [Revised: 05/01/2018] [Accepted: 05/23/2018] [Indexed: 12/18/2022]
Abstract
The modelling of the electrophysiology of cardiac cells is one of the most mature areas of systems biology. This extended concentration of research effort brings with it new challenges, foremost among which is that of choosing which of these models is most suitable for addressing a particular scientific question. In a previous paper, we presented our initial work in developing an online resource for the characterisation and comparison of electrophysiological cell models in a wide range of experimental scenarios. In that work, we described how we had developed a novel protocol language that allowed us to separate the details of the mathematical model (the majority of cardiac cell models take the form of ordinary differential equations) from the experimental protocol being simulated. We developed a fully-open online repository (which we termed the Cardiac Electrophysiology Web Lab) which allows users to store and compare the results of applying the same experimental protocol to competing models. In the current paper we describe the most recent and planned extensions of this work, focused on supporting the process of model building from experimental data. We outline the necessary work to develop a machine-readable language to describe the process of inferring parameters from wet lab datasets, and illustrate our approach through a detailed example of fitting a model of the hERG channel using experimental data. We conclude by discussing the future challenges in making further progress in this domain towards our goal of facilitating a fully reproducible approach to the development of cardiac cell models.
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Roney CH, Bayer JD, Cochet H, Meo M, Dubois R, Jaïs P, Vigmond EJ. Variability in pulmonary vein electrophysiology and fibrosis determines arrhythmia susceptibility and dynamics. PLoS Comput Biol 2018; 14:e1006166. [PMID: 29795549 PMCID: PMC5997352 DOI: 10.1371/journal.pcbi.1006166] [Citation(s) in RCA: 35] [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: 12/15/2017] [Revised: 06/12/2018] [Accepted: 04/30/2018] [Indexed: 11/28/2022] Open
Abstract
Success rates for catheter ablation of persistent atrial fibrillation patients are currently low; however, there is a subset of patients for whom electrical isolation of the pulmonary veins alone is a successful treatment strategy. It is difficult to identify these patients because there are a multitude of factors affecting arrhythmia susceptibility and maintenance, and the individual contributions of these factors are difficult to determine clinically. We hypothesised that the combination of pulmonary vein (PV) electrophysiology and atrial body fibrosis determine driver location and effectiveness of pulmonary vein isolation (PVI). We used bilayer biatrial computer models based on patient geometries to investigate the effects of PV properties and atrial fibrosis on arrhythmia inducibility, maintenance mechanisms, and the outcome of PVI. Short PV action potential duration (APD) increased arrhythmia susceptibility, while longer PV APD was found to be protective. Arrhythmia inducibility increased with slower conduction velocity (CV) at the LA/PV junction, but not for cases with homogeneous CV changes or slower CV at the distal PV. Phase singularity (PS) density in the PV region for cases with PV fibrosis was increased. Arrhythmia dynamics depend on both PV properties and fibrosis distribution, varying from meandering rotors to PV reentry (in cases with baseline or long APD), to stable rotors at regions of high fibrosis density. Measurement of fibrosis and PV properties may indicate patient specific susceptibility to AF initiation and maintenance. PV PS density before PVI was higher for cases in which AF terminated or converted to a macroreentry; thus, high PV PS density may indicate likelihood of PVI success. Atrial fibrillation is the most commonly encountered cardiac arrhythmia, affecting a significant portion of the population. Currently, ablation is the most effective treatment but success rates are less than optimal, being 70% one-year post-treatment. There is a large effort to find better ablation strategies to permanently cure the condition. Pulmonary vein isolation by ablation is more or less the standard of care, but many questions remain since pulmonary vein ectopy by itself does not explain all of the clinical successes or failures. We used computer simulations to investigate how electrophysiological properties of the pulmonary veins can affect rotor formation and maintenance in patients suffering from atrial fibrillation. We used complex, biophysical representations of cellular electrophysiology in highly detailed geometries constructed from patient scans. We heterogeneously varied electrophysiological and structural properties to see their effects on rotor initiation and maintenance. Our study suggests a metric for indicating the likelihood of success of pulmonary vein isolation. Thus either measuring this clinically, or running patient-specific simulations to estimate this metric may suggest whether ablation in addition to pulmonary vein isolation should be performed. Our study provides motivation for a retrospective clinical study or experimental study into this metric.
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Affiliation(s)
- Caroline H. Roney
- IHU Liryc, Electrophysiology and Heart Modeling Institute, foundation Bordeaux Université, F-33600 Pessac- Bordeaux, France
- Division of Imaging Sciences and Biomedical Engineering, King’s College London, London, United Kingdom
| | - Jason D. Bayer
- IHU Liryc, Electrophysiology and Heart Modeling Institute, foundation Bordeaux Université, F-33600 Pessac- Bordeaux, France
- Univ. Bordeaux, IMB UMR 5251, CNRS, F-33400 Talence, France
| | - Hubert Cochet
- IHU Liryc, Electrophysiology and Heart Modeling Institute, foundation Bordeaux Université, F-33600 Pessac- Bordeaux, France
- Hôpital Cardiologique du Haut-L’évêque, Université de Bordeaux, LIRYC Institute: IHU LIRYC ANR-10-IAHU-04 and Equipex MUSIC ANR-11-EQPX-0030, Bordeaux, France
| | - Marianna Meo
- IHU Liryc, Electrophysiology and Heart Modeling Institute, foundation Bordeaux Université, F-33600 Pessac- Bordeaux, France
| | - Rémi Dubois
- IHU Liryc, Electrophysiology and Heart Modeling Institute, foundation Bordeaux Université, F-33600 Pessac- Bordeaux, France
| | - Pierre Jaïs
- IHU Liryc, Electrophysiology and Heart Modeling Institute, foundation Bordeaux Université, F-33600 Pessac- Bordeaux, France
- Hôpital Cardiologique du Haut-L’évêque, Université de Bordeaux, LIRYC Institute: IHU LIRYC ANR-10-IAHU-04 and Equipex MUSIC ANR-11-EQPX-0030, Bordeaux, France
| | - Edward J. Vigmond
- IHU Liryc, Electrophysiology and Heart Modeling Institute, foundation Bordeaux Université, F-33600 Pessac- Bordeaux, France
- Univ. Bordeaux, IMB UMR 5251, CNRS, F-33400 Talence, France
- * E-mail:
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10
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Beattie KA, Hill AP, Bardenet R, Cui Y, Vandenberg JI, Gavaghan DJ, de Boer TP, Mirams GR. Sinusoidal voltage protocols for rapid characterisation of ion channel kinetics. J Physiol 2018; 596:1813-1828. [PMID: 29573276 PMCID: PMC5978315 DOI: 10.1113/jp275733] [Citation(s) in RCA: 43] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2017] [Accepted: 02/19/2018] [Indexed: 12/21/2022] Open
Abstract
Key points Ion current kinetics are commonly represented by current–voltage relationships, time constant–voltage relationships and subsequently mathematical models fitted to these. These experiments take substantial time, which means they are rarely performed in the same cell. Rather than traditional square‐wave voltage clamps, we fitted a model to the current evoked by a novel sum‐of‐sinusoids voltage clamp that was only 8 s long. Short protocols that can be performed multiple times within a single cell will offer many new opportunities to measure how ion current kinetics are affected by changing conditions. The new model predicts the current under traditional square‐wave protocols well, with better predictions of underlying currents than literature models. The current under a novel physiologically relevant series of action potential clamps is predicted extremely well. The short sinusoidal protocols allow a model to be fully fitted to individual cells, allowing us to examine cell–cell variability in current kinetics for the first time.
Abstract Understanding the roles of ion currents is crucial to predict the action of pharmaceuticals and mutations in different scenarios, and thereby to guide clinical interventions in the heart, brain and other electrophysiological systems. Our ability to predict how ion currents contribute to cellular electrophysiology is in turn critically dependent on our characterisation of ion channel kinetics – the voltage‐dependent rates of transition between open, closed and inactivated channel states. We present a new method for rapidly exploring and characterising ion channel kinetics, applying it to the hERG potassium channel as an example, with the aim of generating a quantitatively predictive representation of the ion current. We fitted a mathematical model to currents evoked by a novel 8 second sinusoidal voltage clamp in CHO cells overexpressing hERG1a. The model was then used to predict over 5 minutes of recordings in the same cell in response to further protocols: a series of traditional square step voltage clamps, and also a novel voltage clamp comprising a collection of physiologically relevant action potentials. We demonstrate that we can make predictive cell‐specific models that outperform the use of averaged data from a number of different cells, and thereby examine which changes in gating are responsible for cell–cell variability in current kinetics. Our technique allows rapid collection of consistent and high quality data, from single cells, and produces more predictive mathematical ion channel models than traditional approaches. Ion current kinetics are commonly represented by current–voltage relationships, time constant–voltage relationships and subsequently mathematical models fitted to these. These experiments take substantial time, which means they are rarely performed in the same cell. Rather than traditional square‐wave voltage clamps, we fitted a model to the current evoked by a novel sum‐of‐sinusoids voltage clamp that was only 8 s long. Short protocols that can be performed multiple times within a single cell will offer many new opportunities to measure how ion current kinetics are affected by changing conditions. The new model predicts the current under traditional square‐wave protocols well, with better predictions of underlying currents than literature models. The current under a novel physiologically relevant series of action potential clamps is predicted extremely well. The short sinusoidal protocols allow a model to be fully fitted to individual cells, allowing us to examine cell–cell variability in current kinetics for the first time.
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Affiliation(s)
- Kylie A Beattie
- Computational Biology, Department of Computer Science, University of Oxford, Oxford, OX1 3QD, UK.,Division of Applied Regulatory Science, Office of Clinical Pharmacology, Office of Translational Sciences, Center for Drug Evaluation and Research, Food and Drug Administration, Silver Spring, MD, USA
| | - Adam P Hill
- Department of Molecular Cardiology and Biophysics, Victor Chang Cardiac Research Institute, Sydney, NSW, 2010, Australia.,St Vincent's Clinical School, UNSW Sydney, Darlinghurst, NSW, 2010, Australia
| | - Rémi Bardenet
- CNRS & CRIStAL, Université de Lille, 59651 Villeneuve d'Ascq, Lille, France
| | - Yi Cui
- Safety Evaluation and Risk Management, Global Clinical Safety and Pharmacovigilance, GlaxoSmithKline, Uxbridge, UB11 1BS, UK
| | - Jamie I Vandenberg
- Department of Molecular Cardiology and Biophysics, Victor Chang Cardiac Research Institute, Sydney, NSW, 2010, Australia.,St Vincent's Clinical School, UNSW Sydney, Darlinghurst, NSW, 2010, Australia
| | - David J Gavaghan
- Computational Biology, Department of Computer Science, University of Oxford, Oxford, OX1 3QD, UK
| | - Teun P de Boer
- Department of Medical Physiology, Division of 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, NG7 2RD, UK
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11
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Cairns DI, Fenton FH, Cherry EM. Efficient parameterization of cardiac action potential models using a genetic algorithm. CHAOS (WOODBURY, N.Y.) 2017; 27:093922. [PMID: 28964158 DOI: 10.1063/1.5000354] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Finding appropriate values for parameters in mathematical models of cardiac cells is a challenging task. Here, we show that it is possible to obtain good parameterizations in as little as 30-40 s when as many as 27 parameters are fit simultaneously using a genetic algorithm and two flexible phenomenological models of cardiac action potentials. We demonstrate how our implementation works by considering cases of "model recovery" in which we attempt to find parameter values that match model-derived action potential data from several cycle lengths. We assess performance by evaluating the parameter values obtained, action potentials at fit and non-fit cycle lengths, and bifurcation plots for fidelity to the truth as well as consistency across different runs of the algorithm. We also fit the models to action potentials recorded experimentally using microelectrodes and analyze performance. We find that our implementation can efficiently obtain model parameterizations that are in good agreement with the dynamics exhibited by the underlying systems that are included in the fitting process. However, the parameter values obtained in good parameterizations can exhibit a significant amount of variability, raising issues of parameter identifiability and sensitivity. Along similar lines, we also find that the two models differ in terms of the ease of obtaining parameterizations that reproduce model dynamics accurately, most likely reflecting different levels of parameter identifiability for the two models.
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Affiliation(s)
- Darby I Cairns
- School of Mathematical Sciences, Rochester Institute of Technology, Rochester, New York 14623, USA
| | - Flavio H Fenton
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - E M Cherry
- School of Mathematical Sciences, Rochester Institute of Technology, Rochester, New York 14623, USA
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