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Filipe JA, Kyriazakis I. Bayesian, Likelihood-Free Modelling of Phenotypic Plasticity and Variability in Individuals and Populations. Front Genet 2019; 10:727. [PMID: 31616460 PMCID: PMC6764410 DOI: 10.3389/fgene.2019.00727] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2018] [Accepted: 07/11/2019] [Indexed: 12/17/2022] Open
Abstract
There is a paradigm shift from the traditional focus on the "average" individual towards the definition and analysis of trait variation within individual life-history and among individuals in populations. This is a result of increasing availability of individual phenotypic data. The shift allows the use of genetic and environment-driven variations to assess robustness to challenge, gain greater understanding of organismal biological processes, or deliver individual-targeted treatments or genetic selection. These consequences apply, in particular, to variation in ontogenetic growth. We propose an approach to parameterise mathematical models of individual traits (e.g., reaction norms, growth curves) that address two challenges: 1) Estimation of individual traits while making minimal assumptions about data distribution and correlation, addressed via Approximate Bayesian Computation (a form of nonparametric inference). We are motivated by the fact that available information on distribution of biological data is often less precise than assumed by conventional likelihood functions. 2) Scaling-up to population phenotype distributions while facilitating unbiased use of individual data; this is addressed via a probabilistic framework where population distributions build on separately-inferred individual distributions and individual-trait interpretability is preserved. The approach is tested against Bayesian likelihood-based inference, by fitting weight and energy intake growth models to animal data and normal- and skewed-distributed simulated data. i) Individual inferences were accurate and robust to changes in data distribution and sample size; in particular, median-based predictions were more robust than maximum- likelihood-based curves. These results suggest that the approach gives reliable inferences using few observations and monitoring resources. ii) At the population level, each individual contributed via a specific data distribution, and population phenotype estimates were not disproportionally influenced by outlier individuals. Indices measuring population phenotype variation can be derived for study comparisons. The approach offers an alternative for estimating trait variability in biological systems that may be reliable for various applications, for example, in genetics, health, and individualised nutrition, while using fewer assumptions and fewer empirical observations. In livestock breeding, the potentially greater accuracy of trait estimation (without specification of multitrait variance-covariance parameters) could lead to improved selection and to more decisive estimates of trait heritability.
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Affiliation(s)
- Joao A.N. Filipe
- Agriculture, School of Natural and Environmental Sciences, Newcastle University, Newcastle upon Tyne, United Kingdom
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Daly AC, Gavaghan D, Cooper J, Tavener S. Inference-based assessment of parameter identifiability in nonlinear biological models. J R Soc Interface 2019; 15:rsif.2018.0318. [PMID: 30021928 DOI: 10.1098/rsif.2018.0318] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2018] [Accepted: 06/21/2018] [Indexed: 11/12/2022] Open
Abstract
As systems approaches to the development of biological models become more mature, attention is increasingly focusing on the problem of inferring parameter values within those models from experimental data. However, particularly for nonlinear models, it is not obvious, either from inspection of the model or from the experimental data, that the inverse problem of parameter fitting will have a unique solution, or even a non-unique solution that constrains the parameters to lie within a plausible physiological range. Where parameters cannot be constrained they are termed 'unidentifiable'. We focus on gaining insight into the causes of unidentifiability using inference-based methods, and compare a recently developed measure-theoretic approach to inverse sensitivity analysis to the popular Markov chain Monte Carlo and approximate Bayesian computation techniques for Bayesian inference. All three approaches map the uncertainty in quantities of interest in the output space to the probability of sets of parameters in the input space. The geometry of these sets demonstrates how unidentifiability can be caused by parameter compensation and provides an intuitive approach to inference-based experimental design.
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Affiliation(s)
- Aidan C Daly
- Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford OX1 3QD, UK
| | - David Gavaghan
- Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford OX1 3QD, UK
| | - Jonathan Cooper
- Research IT Services, University College London, Gower Street, London WC1E 6BT, UK
| | - Simon Tavener
- Department of Mathematics, Colorado State University, Fort Collins, CO 80523, USA
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Sleutjes BTHM, Kovalchuk MO, Durmus N, Buitenweg JR, van Putten MJAM, van den Berg LH, Franssen H. Simulating perinodal changes observed in immune-mediated neuropathies: impact on conduction in a model of myelinated motor and sensory axons. J Neurophysiol 2019; 122:1036-1049. [PMID: 31291151 DOI: 10.1152/jn.00326.2019] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022] Open
Abstract
Immune-mediated neuropathies affect myelinated axons, resulting in conduction slowing or block that may affect motor and sensory axons differently. The underlying mechanisms of these neuropathies are not well understood. Using a myelinated axon model, we studied the impact of perinodal changes on conduction. We extended a longitudinal axon model (41 nodes of Ranvier) with biophysical properties unique to human myelinated motor and sensory axons. We simulated effects of temperature and axonal diameter on conduction and strength-duration properties. We then studied effects of impaired nodal sodium channel conductance and paranodal myelin detachment by reducing periaxonal resistance, as well as their interaction, on conduction in the 9 middle nodes and enclosed paranodes. Finally, we assessed the impact of reducing the affected region (5 nodes) and adding nodal widening. Physiological motor and sensory conduction velocities and changes to axonal diameter and temperature were observed. The sensory axon had a longer strength-duration time constant. Reducing sodium channel conductance and paranodal periaxonal resistance induced progressive conduction slowing. In motor axons, conduction block occurred with a 4-fold drop in sodium channel conductance or a 7.7-fold drop in periaxonal resistance. In sensory axons, block arose with a 4.8-fold drop in sodium channel conductance or a 9-fold drop in periaxonal resistance. This indicated that motor axons are more vulnerable to developing block. A boundary of block emerged when the two mechanisms interacted. This boundary shifted in opposite directions for a smaller affected region and nodal widening. These differences may contribute to the predominance of motor deficits observed in some immune-mediated neuropathies.NEW & NOTEWORTHY Immune-mediated neuropathies may affect myelinated motor and sensory axons differently. By the development of a computational model, we quantitatively studied the impact of perinodal changes on conduction in motor and sensory axons. Simulations of increasing nodal sodium channel dysfunction and paranodal myelin detachment induced progressive conduction slowing. Sensory axons were more resistant to block than motor axons. This could explain the greater predisposition of motor axons to functional deficits observed in some immune-mediated neuropathies.
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Affiliation(s)
- Boudewijn T H M Sleutjes
- Department of Neurology, Brain Center Utrecht, University Medical Center Utrecht, Utrecht, The Netherlands
| | - Maria O Kovalchuk
- Department of Neurology, Brain Center Utrecht, University Medical Center Utrecht, Utrecht, The Netherlands
| | - Naric Durmus
- Biomedical Signals and Systems, MIRA, Institute for Biomedical Technology and Technical Medicine, University of Twente, Enschede, The Netherlands.,Department of Clinical Neurophysiology, University of Twente, Enschede, The Netherlands
| | - Jan R Buitenweg
- Biomedical Signals and Systems, MIRA, Institute for Biomedical Technology and Technical Medicine, University of Twente, Enschede, The Netherlands
| | - Michel J A M van Putten
- Department of Clinical Neurophysiology, University of Twente, Enschede, The Netherlands.,Department of Neurology and Clinical Neurophysiology, Medisch Spectrum Twente, Enschede, The Netherlands
| | - Leonard H van den Berg
- Department of Neurology, Brain Center Utrecht, University Medical Center Utrecht, Utrecht, The Netherlands
| | - Hessel Franssen
- Department of Neurology, Brain Center Utrecht, University Medical Center Utrecht, Utrecht, The Netherlands
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54
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Lei CL, Clerx M, Gavaghan DJ, Polonchuk L, Mirams GR, Wang K. Rapid Characterization of hERG Channel Kinetics I: Using an Automated High-Throughput System. Biophys J 2019; 117:2438-2454. [PMID: 31447109 PMCID: PMC6990155 DOI: 10.1016/j.bpj.2019.07.029] [Citation(s) in RCA: 31] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/15/2019] [Revised: 06/20/2019] [Accepted: 07/17/2019] [Indexed: 11/27/2022] Open
Abstract
Predicting how pharmaceuticals may affect heart rhythm is a crucial step in drug development and requires a deep understanding of a compound’s action on ion channels. In vitro hERG channel current recordings are an important step in evaluating the proarrhythmic potential of small molecules and are now routinely performed using automated high-throughput patch-clamp platforms. These machines can execute traditional voltage-clamp protocols aimed at specific gating processes, but the array of protocols needed to fully characterize a current is typically too long to be applied in a single cell. Shorter high-information protocols have recently been introduced that have this capability, but they are not typically compatible with high-throughput platforms. We present a new 15 second protocol to characterize hERG (Kv11.1) kinetics, suitable for both manual and high-throughput systems. We demonstrate its use on the Nanion SyncroPatch 384PE, a 384-well automated patch-clamp platform, by applying it to Chinese hamster ovary cells stably expressing hERG1a. From these recordings, we construct 124 cell-specific variants/parameterizations of a hERG model at 25°C. A further eight independent protocols are run in each cell and are used to validate the model predictions. We then combine the experimental recordings using a hierarchical Bayesian model, which we use to quantify the uncertainty in the model parameters, and their variability from cell-to-cell; we use this model to suggest reasons for the variability. This study demonstrates a robust method to measure and quantify uncertainty and shows that it is possible and practical to use high-throughput systems to capture full hERG channel kinetics quantitatively and rapidly.
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Affiliation(s)
- Chon Lok Lei
- Computational Biology, Department of Computer Science, University of Oxford, Oxford, United Kingdom
| | - Michael Clerx
- Computational Biology, Department of Computer Science, University of Oxford, Oxford, United Kingdom
| | - David J Gavaghan
- Computational Biology, Department of Computer Science, University of Oxford, Oxford, United Kingdom
| | - Liudmila Polonchuk
- Pharma Research and Early Development, Innovation Center Basel, F. Hoffmann-La Roche Ltd., Basel, Switzerland
| | - Gary R Mirams
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, United Kingdom.
| | - Ken Wang
- Pharma Research and Early Development, Innovation Center Basel, F. Hoffmann-La Roche Ltd., Basel, Switzerland
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Nelson T, Garg P, Clayton RH, Lee J. The Role of Cardiac MRI in the Management of Ventricular Arrhythmias in Ischaemic and Non-ischaemic Dilated Cardiomyopathy. Arrhythm Electrophysiol Rev 2019; 8:191-201. [PMID: 31463057 PMCID: PMC6702467 DOI: 10.15420/aer.2019.5.1] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 01/18/2019] [Accepted: 04/25/2019] [Indexed: 02/07/2023] Open
Abstract
Ventricular tachycardia (VT) and VF account for the majority of sudden cardiac deaths worldwide. Treatments for VT/VF include anti-arrhythmic drugs, ICDs and catheter ablation, but these treatments vary in effectiveness and carry substantial risks and/or expense. Current methods of selecting patients for ICD implantation are imprecise and fail to identify some at-risk patients, while leading to others being overtreated. In this article, the authors discuss the current role and future direction of cardiac MRI (CMRI) in refining diagnosis and personalising ventricular arrhythmia management. The capability of CMRI with gadolinium contrast delayed-enhancement patterns and, more recently, T1 mapping to determine the aetiology of patients presenting with heart failure is well established. Although CMRI imaging in patients with ICDs can be challenging, recent technical developments have started to overcome this. CMRI can contribute to risk stratification, with precise and reproducible assessment of ejection fraction, quantification of scar and 'border zone' volumes, and other indices. Detailed tissue characterisation has begun to enable creation of personalised computer models to predict an individual patient's arrhythmia risk. When patients require VT ablation, a substrate-based approach is frequently employed as haemodynamic instability may limit electrophysiological activation mapping. Beyond accurate localisation of substrate, CMRI could be used to predict the location of re-entrant circuits within the scar to guide ablation.
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Affiliation(s)
- Tom Nelson
- Sheffield Teaching Hospitals NHS Foundation TrustSheffield, UK
- Department of Immunity, Infection and Cardiovascular Disease, University of SheffieldSheffield, UK
| | - Pankaj Garg
- Sheffield Teaching Hospitals NHS Foundation TrustSheffield, UK
- Department of Immunity, Infection and Cardiovascular Disease, University of SheffieldSheffield, UK
| | - Richard H Clayton
- INSIGNEO Institute for In-Silico Medicine, University of SheffieldSheffield, UK
- Department of Computer Science, University of SheffieldSheffield, UK
| | - Justin Lee
- Sheffield Teaching Hospitals NHS Foundation TrustSheffield, UK
- Department of Immunity, Infection and Cardiovascular Disease, University of SheffieldSheffield, UK
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56
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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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57
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Pathmanathan P, Cordeiro JM, Gray RA. Comprehensive Uncertainty Quantification and Sensitivity Analysis for Cardiac Action Potential Models. Front Physiol 2019; 10:721. [PMID: 31297060 PMCID: PMC6607060 DOI: 10.3389/fphys.2019.00721] [Citation(s) in RCA: 42] [Impact Index Per Article: 8.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2018] [Accepted: 05/23/2019] [Indexed: 12/15/2022] Open
Abstract
Recent efforts to ensure the reliability of computational model-based predictions in healthcare, such as the ASME V&V40 Standard, emphasize the importance of uncertainty quantification (UQ) and sensitivity analysis (SA) when evaluating computational models. UQ involves empirically determining the uncertainty in model inputs-typically resulting from natural variability or measurement error-and then calculating the resultant uncertainty in model outputs. SA involves calculating how uncertainty in model outputs can be apportioned to input uncertainty. Rigorous comprehensive UQ/SA provides confidence that model-based decisions are robust to underlying uncertainties. However, comprehensive UQ/SA is not currently feasible for whole heart models, due to numerous factors including model complexity and difficulty in measuring variability in the many parameters. Here, we present a significant step to developing a framework to overcome these limitations. We: (i) developed a novel action potential (AP) model of moderate complexity (six currents, seven variables, 36 parameters); (ii) prescribed input variability for all parameters (not empirically derived); (iii) used a single "hyper-parameter" to study increasing levels of parameter uncertainty; (iv) performed UQ and SA for a range of model-derived quantities with physiological relevance; and (v) present quantitative and qualitative ways to analyze different behaviors that occur under parameter uncertainty, including "model failure". This is the first time uncertainty in every parameter (including conductances, steady-state parameters, and time constant parameters) of every ionic current in a cardiac model has been studied. This approach allowed us to demonstrate that, for this model, the simulated AP is fully robust to low levels of parameter uncertainty - to our knowledge the first time this has been shown of any cardiac model. A range of dynamics was observed at larger parameter uncertainty (e.g., oscillatory dynamics); analysis revealed that five parameters were highly influential in these dynamics. Overall, we demonstrate feasibility of performing comprehensive UQ/SA for cardiac cell models and demonstrate how to assess robustness and overcome model failure when performing cardiac UQ analyses. The approach presented here represents an important and significant step toward the development of model-based clinical tools which are demonstrably robust to all underlying uncertainties and therefore more reliable in safety-critical decision-making.
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Affiliation(s)
- Pras Pathmanathan
- Center for Devices and Radiological Health, U.S. Food and Drug Administration, Silver Spring, MD, United States
| | | | - Richard A. Gray
- Center for Devices and Radiological Health, U.S. Food and Drug Administration, Silver Spring, MD, United States
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58
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Li Z, Garnett C, Strauss DG. Quantitative Systems Pharmacology Models for a New International Cardiac Safety Regulatory Paradigm: An Overview of the Comprehensive In Vitro Proarrhythmia Assay In Silico Modeling Approach. CPT Pharmacometrics Syst Pharmacol 2019; 8:371-379. [PMID: 31044559 PMCID: PMC6617836 DOI: 10.1002/psp4.12423] [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: 02/12/2019] [Accepted: 04/15/2019] [Indexed: 12/17/2022] Open
Abstract
As a relatively new discipline, quantitative systems pharmacology has seen a significant increase in the application and utility of drug development. One area that could greatly benefit from such an approach is in the proarrhythmia assessment of new drugs. The Comprehensive In Vitro Proarrhythmia Assay (CiPA) Initiative is a global public-private partnership project that has developed an integrated approach using mechanistic in silico models for proarrhythmia risk prediction. Progress to date has led to the formation of the International Council on Harmonisation Implementation Working Group to revise regulatory guidelines via the Questions-and-Answers process to address the best practices for proarrhythmia models and how they can impact clinical drug development. This article reviews the CiPA in silico model-development process, focusing on its unique development and validation strategy, and summarizes the lessons learned as consideration points for the ongoing implementation of CiPA-like in silico models in drug development.
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Affiliation(s)
- Zhihua Li
- Division of Applied Regulatory ScienceOffice of Clinical PharmacologyOffice of Translational SciencesCenter for Drug Evaluation and ResearchUS Food and Drug AdministrationSilver SpringMarylandUSA
| | - Christine Garnett
- Division of Cardiovascular and Renal ProductsOffice of Drug Evaluation IOffice of New DrugsCenter for Drug Evaluation and ResearchUS Food and Drug AdministrationSilver SpringMarylandUSA
| | - David G. Strauss
- Division of Applied Regulatory ScienceOffice of Clinical PharmacologyOffice of Translational SciencesCenter for Drug Evaluation and ResearchUS Food and Drug AdministrationSilver SpringMarylandUSA
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Berg P, Voß S, Janiga G, Saalfeld S, Bergersen AW, Valen-Sendstad K, Bruening J, Goubergrits L, Spuler A, Chiu TL, Tsang ACO, Copelli G, Csippa B, Paál G, Závodszky G, Detmer FJ, Chung BJ, Cebral JR, Fujimura S, Takao H, Karmonik C, Elias S, Cancelliere NM, Najafi M, Steinman DA, Pereira VM, Piskin S, Finol EA, Pravdivtseva M, Velvaluri P, Rajabzadeh-Oghaz H, Paliwal N, Meng H, Seshadhri S, Venguru S, Shojima M, Sindeev S, Frolov S, Qian Y, Wu YA, Carlson KD, Kallmes DF, Dragomir-Daescu D, Beuing O. Multiple Aneurysms AnaTomy CHallenge 2018 (MATCH)-phase II: rupture risk assessment. Int J Comput Assist Radiol Surg 2019; 14:1795-1804. [PMID: 31054128 DOI: 10.1007/s11548-019-01986-2] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2019] [Accepted: 04/23/2019] [Indexed: 01/10/2023]
Abstract
PURPOSE Assessing the rupture probability of intracranial aneurysms (IAs) remains challenging. Therefore, hemodynamic simulations are increasingly applied toward supporting physicians during treatment planning. However, due to several assumptions, the clinical acceptance of these methods remains limited. METHODS To provide an overview of state-of-the-art blood flow simulation capabilities, the Multiple Aneurysms AnaTomy CHallenge 2018 (MATCH) was conducted. Seventeen research groups from all over the world performed segmentations and hemodynamic simulations to identify the ruptured aneurysm in a patient harboring five IAs. Although simulation setups revealed good similarity, clear differences exist with respect to the analysis of aneurysm shape and blood flow results. Most groups (12/71%) included morphological and hemodynamic parameters in their analysis, with aspect ratio and wall shear stress as the most popular candidates, respectively. RESULTS The majority of groups (7/41%) selected the largest aneurysm as being the ruptured one. Four (24%) of the participating groups were able to correctly select the ruptured aneurysm, while three groups (18%) ranked the ruptured aneurysm as the second most probable. Successful selections were based on the integration of clinically relevant information such as the aneurysm site, as well as advanced rupture probability models considering multiple parameters. Additionally, flow characteristics such as the quantification of inflow jets and the identification of multiple vortices led to correct predictions. CONCLUSIONS MATCH compares state-of-the-art image-based blood flow simulation approaches to assess the rupture risk of IAs. Furthermore, this challenge highlights the importance of multivariate analyses by combining clinically relevant metadata with advanced morphological and hemodynamic quantification.
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Affiliation(s)
| | - Samuel Voß
- University of Magdeburg, Magdeburg, Germany
| | | | | | | | | | | | | | | | | | | | | | - Benjamin Csippa
- Budapest University of Technology and Economics, Budapest, Hungary
| | - György Paál
- Budapest University of Technology and Economics, Budapest, Hungary
| | - Gábor Závodszky
- Budapest University of Technology and Economics, Budapest, Hungary
| | | | | | | | | | | | | | - Saba Elias
- Houston Methodist Research Institute, Houston, TX, USA
| | | | | | | | | | - Senol Piskin
- The University of Texas at San Antonio, San Antonio, TX, USA
| | - Ender A Finol
- The University of Texas at San Antonio, San Antonio, TX, USA
| | | | | | | | | | - Hui Meng
- State University of New York, Buffalo, NY, USA
| | | | | | | | | | | | - Yi Qian
- Macquarie University, Sydney, Australia
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Chemla D, Boulate D, Weatherald J, Lau EM, Attal P, Savale L, Montani D, Fadel E, Mercier O, Sitbon O, Humbert M, Hervé P. Golden Ratio and the Proportionality Between Pulmonary Pressure Components in Pulmonary Arterial Hypertension. Chest 2019; 155:991-998. [DOI: 10.1016/j.chest.2018.12.006] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/01/2018] [Revised: 11/13/2018] [Accepted: 12/03/2018] [Indexed: 12/14/2022] Open
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Nikishova A, Veen L, Zun P, Hoekstra AG. Semi-intrusive multiscale metamodelling uncertainty quantification with application to a model of in-stent restenosis. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2019; 377:20180154. [PMID: 30967038 PMCID: PMC6388010 DOI: 10.1098/rsta.2018.0154] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 10/10/2018] [Indexed: 05/02/2023]
Abstract
We explore the efficiency of a semi-intrusive uncertainty quantification (UQ) method for multiscale models as proposed by us in an earlier publication. We applied the multiscale metamodelling UQ method to a two-dimensional multiscale model for the wound healing response in a coronary artery after stenting (in-stent restenosis). The results obtained by the semi-intrusive method show a good match to those obtained by a black-box quasi-Monte Carlo method. Moreover, we significantly reduce the computational cost of the UQ. We conclude that the semi-intrusive metamodelling method is reliable and efficient, and can be applied to such complex models as the in-stent restenosis ISR2D model. This article is part of the theme issue 'Multiscale modelling, simulation and computing: from the desktop to the exascale'.
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Affiliation(s)
- A. Nikishova
- Computational Science Lab, Institute for Informatics, Faculty of Science, University of Amsterdam, 1098 XH Amsterdam, The Netherlands
| | - L. Veen
- Netherlands eScience Center, 1098 XG Amsterdam, The Netherlands
| | - P. Zun
- Computational Science Lab, Institute for Informatics, Faculty of Science, University of Amsterdam, 1098 XH Amsterdam, The Netherlands
- ITMO University, Saint Petersburg, 197101, Russia
| | - A. G. Hoekstra
- Computational Science Lab, Institute for Informatics, Faculty of Science, University of Amsterdam, 1098 XH Amsterdam, The Netherlands
- ITMO University, Saint Petersburg, 197101, Russia
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62
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Yang PC, Purawat S, Ieong PU, Jeng MT, DeMarco KR, Vorobyov I, McCulloch AD, Altintas I, Amaro RE, Clancy CE. A demonstration of modularity, reuse, reproducibility, portability and scalability for modeling and simulation of cardiac electrophysiology using Kepler Workflows. PLoS Comput Biol 2019; 15:e1006856. [PMID: 30849072 PMCID: PMC6426265 DOI: 10.1371/journal.pcbi.1006856] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/21/2018] [Revised: 03/20/2019] [Accepted: 02/08/2019] [Indexed: 01/18/2023] Open
Abstract
Multi-scale computational modeling is a major branch of computational biology as evidenced by the US federal interagency Multi-Scale Modeling Consortium and major international projects. It invariably involves specific and detailed sequences of data analysis and simulation, often with multiple tools and datasets, and the community recognizes improved modularity, reuse, reproducibility, portability and scalability as critical unmet needs in this area. Scientific workflows are a well-recognized strategy for addressing these needs in scientific computing. While there are good examples if the use of scientific workflows in bioinformatics, medical informatics, biomedical imaging and data analysis, there are fewer examples in multi-scale computational modeling in general and cardiac electrophysiology in particular. Cardiac electrophysiology simulation is a mature area of multi-scale computational biology that serves as an excellent use case for developing and testing new scientific workflows. In this article, we develop, describe and test a computational workflow that serves as a proof of concept of a platform for the robust integration and implementation of a reusable and reproducible multi-scale cardiac cell and tissue model that is expandable, modular and portable. The workflow described leverages Python and Kepler-Python actor for plotting and pre/post-processing. During all stages of the workflow design, we rely on freely available open-source tools, to make our workflow freely usable by scientists. We present a computational workflow as a proof of concept for integration and implementation of a reusable and reproducible cardiac multi-scale electrophysiology model that is expandable, modular and portable. This framework enables scientists to create intuitive, user-friendly and flexible end-to-end automated scientific workflows using a graphical user interface. Kepler is an advanced open-source platform that supports multiple models of computation. The underlying workflow engine handles scalability, provenance, reproducibility aspects of the code, performs orchestration of data flow, and automates execution on heterogeneous computing resources. One of the main advantages of workflow utilization is the integration of code written in multiple languages Standardization occurs at the interfaces of the workflow elements and allows for general applications and easy comparison and integration of code from different research groups or even multiple programmers coding in different languages for various purposes from the same group. A workflow driven problem-solving approach enables domain scientists to focus on resolving the core science questions, and delegates the computational and process management burden to the underlying Workflow. The workflow driven approach allows scaling the computational experiment with distributed data-parallel execution on multiple computing platforms, such as, HPC resources, GPU clusters, Cloud etc. The workflow framework tracks software version information along with hardware information to allow users an opportunity to trace any variation in workflow outcome to the system configurations.
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Affiliation(s)
- Pei-Chi Yang
- Department of Physiology and Membrane Biology, Department of Pharmacology, School of Medicine, University of California Davis, Davis, California, United States of America
| | - Shweta Purawat
- San Diego Supercomputer Center (SDSC), University of California, San Diego, La Jolla, California, United States of America
| | - Pek U. Ieong
- Department of Chemistry and Biochemistry, National Biomedical Computation Resource, Drug Design Data Resource (D3R), University of California San Diego, La Jolla, California, United States of America
| | - Mao-Tsuen Jeng
- Department of Physiology and Membrane Biology, Department of Pharmacology, School of Medicine, University of California Davis, Davis, California, United States of America
| | - Kevin R. DeMarco
- Department of Physiology and Membrane Biology, Department of Pharmacology, School of Medicine, University of California Davis, Davis, California, United States of America
| | - Igor Vorobyov
- Department of Physiology and Membrane Biology, Department of Pharmacology, School of Medicine, University of California Davis, Davis, California, United States of America
| | - Andrew D. McCulloch
- Departments of Bioengineering and Medicine, University of California, San Diego, La Jolla, California, United States of America
| | - Ilkay Altintas
- San Diego Supercomputer Center (SDSC), University of California, San Diego, La Jolla, California, United States of America
| | - Rommie E. Amaro
- Department of Chemistry and Biochemistry, National Biomedical Computation Resource, Drug Design Data Resource (D3R), University of California San Diego, La Jolla, California, United States of America
| | - Colleen E. Clancy
- Department of Physiology and Membrane Biology, Department of Pharmacology, School of Medicine, University of California Davis, Davis, California, United States of America
- * E-mail:
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63
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Makowiec D, Wdowczyk J, Struzik ZR. Heart Rhythm Insights Into Structural Remodeling in Atrial Tissue: Timed Automata Approach. Front Physiol 2019; 9:1859. [PMID: 30692928 PMCID: PMC6340163 DOI: 10.3389/fphys.2018.01859] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/07/2018] [Accepted: 12/11/2018] [Indexed: 12/19/2022] Open
Abstract
The heart rhythm of a person following heart transplantation (HTX) is assumed to display an intrinsic cardiac rhythm because it is significantly less influenced by the autonomic nervous system-the main source of heart rate variability in healthy people. Therefore, such a rhythm provides evidence for arrhythmogenic processes developing, usually silently, in the cardiac tissue. A model is proposed to simulate alterations in the cardiac tissue and to observe the effects of these changes on the resulting heart rhythm. The hybrid automata framework used makes it possible to represent reliably and simulate efficiently both the electrophysiology of a cardiac cell and the tissue organization. The curve fitting method used in the design of the hybrid automaton cycle follows the well-recognized physiological phases of the atrial myocyte membrane excitation. Moreover, knowledge of the complex architecture of the right atrium, the ability of the almost free design of intercellular connections makes the automata approach the only one possible. Two particular aspects are investigated: impairment of the impulse transmission between cells and structural changes in intercellular connections. The first aspect models the observed fatigue of cells due to specific cardiac tissue diseases. The second aspect simulates the increase in collagen deposition with aging. Finally, heart rhythms arising from the model are validated with the sinus heart rhythms recorded in HTX patients. The modulation in the impairment of the impulse transmission between cells reveals qualitatively the abnormally high heart rate variability observed in patients living long after HTX.
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Affiliation(s)
- Danuta Makowiec
- Institute of Theoretical Physics and Astrophysics, University of Gdańsk, Gdansk, Poland
| | - Joanna Wdowczyk
- 1st Department of Cardiology, Medical University of Gdańsk, Gdansk, Poland
| | - Zbigniew R Struzik
- RIKEN Advanced Center for Computing and Communication, Wako, Japan.,Graduate School of Education, University of Tokyo, Tokyo, Japan
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64
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APPLICATION OF MATHEMATICAL APPROACHES IN MEDICINE ON THE EXAMPLE OF FOLLICULAR THYROCYTES SECRETORY ACTIVITY STUDY. WORLD OF MEDICINE AND BIOLOGY 2019. [DOI: 10.26724/2079-8334-2019-1-67-181] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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65
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Bowler LA, Gavaghan DJ, Mirams GR, Whiteley JP. Representation of Multiple Cellular Phenotypes Within Tissue-Level Simulations of Cardiac Electrophysiology. Bull Math Biol 2019; 81:7-38. [PMID: 30291590 PMCID: PMC6320359 DOI: 10.1007/s11538-018-0516-1] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2017] [Accepted: 07/31/2018] [Indexed: 12/12/2022]
Abstract
Distinct electrophysiological phenotypes are exhibited by biological cells that have differentiated into particular cell types. The usual approach when simulating the cardiac electrophysiology of tissue that includes different cell types is to model the different cell types as occupying spatially distinct yet coupled regions. Instead, we model the electrophysiology of well-mixed cells by using homogenisation to derive an extension to the commonly used monodomain or bidomain equations. These new equations permit spatial variations in the distribution of the different subtypes of cells and will reduce the computational demands of solving the governing equations. We validate the homogenisation computationally, and then use the new model to explain some experimental observations from stem cell-derived cardiomyocyte monolayers.
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Affiliation(s)
- Louise A Bowler
- Department of Computer Science, University of Oxford, Oxford, UK
| | - David J Gavaghan
- Department of Computer Science, University of Oxford, Oxford, UK
| | - Gary R Mirams
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, UK
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66
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Hu Z, Du D, Du Y. Generalized polynomial chaos-based uncertainty quantification and propagation in multi-scale modeling of cardiac electrophysiology. Comput Biol Med 2018; 102:57-74. [PMID: 30248513 DOI: 10.1016/j.compbiomed.2018.09.006] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/13/2018] [Revised: 09/11/2018] [Accepted: 09/11/2018] [Indexed: 11/19/2022]
Abstract
Uncertainty and physiological variability are ubiquitous in cardiac electrical signaling. It is important to address the uncertainty and variability in cardiac modeling to provide reliable and realistic predictions of heart function, thus ensuring trustworthy computer-aided medical decision-making and treatment planning. Statistical techniques such as Monte Carlo (MC) simulations have been applied to uncertainty quantification and propagation in cardiac modeling. However, MC simulation-based methods are computationally prohibitive for complex cardiac models with a great number of parameters and governing equations. In this paper, we propose to use the Generalized Polynomial Chaos (gPC) expansion in combination with Galerkin projection to analytically quantify parametric uncertainty in ion channel models of mouse ventricular cell, and further propagate the uncertainty across different organizational levels of cell and tissue. To identify the most significant parametric uncertainty in cardiac ion channel and cell models, variance decomposition-based sensitivity analysis was first performed. Following this, gPC was integrated with deterministic cardiac models to propagate uncertainty through ion current, ventricular cell, 1D cable, and 2D tissue to account for the stochasticity and cell-to-cell variability. As compared to MC, the gPC in this work shows the superior performance in terms of computational efficiency. In addition, the gPC models can provide a measure of confidence in model predictions, which can improve the reliability of computer simulations of cardiac electrophysiology for clinical applications.
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Affiliation(s)
- Zhiyong Hu
- Department of Industrial, Manufacturing and Systems Engineering, Texas Tech University, Lubbock, TX, 79409, USA
| | - Dongping Du
- Department of Industrial, Manufacturing and Systems Engineering, Texas Tech University, Lubbock, TX, 79409, USA.
| | - Yuncheng Du
- Department of Chemical and Biomolecular Engineering, Clarkson University, Potsdam, NY, 33613, USA.
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67
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Cellular function given parametric variation in the Hodgkin and Huxley model of excitability. Proc Natl Acad Sci U S A 2018; 115:E8211-E8218. [PMID: 30111538 PMCID: PMC6126753 DOI: 10.1073/pnas.1808552115] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022] Open
Abstract
How is reliable physiological function maintained in cells despite considerable variability in the values of key parameters of multiple interacting processes that govern that function? Here, we use the classic Hodgkin-Huxley formulation of the squid giant axon action potential to propose a possible approach to this problem. Although the full Hodgkin-Huxley model is very sensitive to fluctuations that independently occur in its many parameters, the outcome is in fact determined by simple combinations of these parameters along two physiological dimensions: structural and kinetic (denoted S and K, respectively). Structural parameters describe the properties of the cell, including its capacitance and the densities of its ion channels. Kinetic parameters are those that describe the opening and closing of the voltage-dependent conductances. The impacts of parametric fluctuations on the dynamics of the system-seemingly complex in the high-dimensional representation of the Hodgkin-Huxley model-are tractable when examined within the S-K plane. We demonstrate that slow inactivation, a ubiquitous activity-dependent feature of ionic channels, is a powerful local homeostatic control mechanism that stabilizes excitability amid changes in structural and kinetic parameters.
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68
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Ni H, Morotti S, Grandi E. A Heart for Diversity: Simulating Variability in Cardiac Arrhythmia Research. Front Physiol 2018; 9:958. [PMID: 30079031 PMCID: PMC6062641 DOI: 10.3389/fphys.2018.00958] [Citation(s) in RCA: 46] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2018] [Accepted: 06/29/2018] [Indexed: 12/31/2022] Open
Abstract
In cardiac electrophysiology, there exist many sources of inter- and intra-personal variability. These include variability in conditions and environment, and genotypic and molecular diversity, including differences in expression and behavior of ion channels and transporters, which lead to phenotypic diversity (e.g., variable integrated responses at the cell, tissue, and organ levels). These variabilities play an important role in progression of heart disease and arrhythmia syndromes and outcomes of therapeutic interventions. Yet, the traditional in silico framework for investigating cardiac arrhythmias is built upon a parameter/property-averaging approach that typically overlooks the physiological diversity. Inspired by work done in genetics and neuroscience, new modeling frameworks of cardiac electrophysiology have been recently developed that take advantage of modern computational capabilities and approaches, and account for the variance in the biological data they are intended to illuminate. In this review, we outline the recent advances in statistical and computational techniques that take into account physiological variability, and move beyond the traditional cardiac model-building scheme that involves averaging over samples from many individuals in the construction of a highly tuned composite model. We discuss how these advanced methods have harnessed the power of big (simulated) data to study the mechanisms of cardiac arrhythmias, with a special emphasis on atrial fibrillation, and improve the assessment of proarrhythmic risk and drug response. The challenges of using in silico approaches with variability are also addressed and future directions are proposed.
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Affiliation(s)
| | | | - Eleonora Grandi
- Department of Pharmacology, University of California, Davis, Davis, CA, United States
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69
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Morotti S, Grandi E. Quantitative systems models illuminate arrhythmia mechanisms in heart failure: Role of the Na + -Ca 2+ -Ca 2+ /calmodulin-dependent protein kinase II-reactive oxygen species feedback. WILEY INTERDISCIPLINARY REVIEWS-SYSTEMS BIOLOGY AND MEDICINE 2018; 11:e1434. [PMID: 30015404 DOI: 10.1002/wsbm.1434] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/22/2018] [Revised: 05/29/2018] [Accepted: 06/16/2018] [Indexed: 12/22/2022]
Abstract
Quantitative systems modeling aims to integrate knowledge in different research areas with models describing biological mechanisms and dynamics to gain a better understanding of complex clinical syndromes. Heart failure (HF) is a chronic complex cardiac disease that results from structural or functional disorders impairing the ability of the ventricle to fill with or eject blood. Highly interactive and dynamic changes in mechanical, structural, neurohumoral, metabolic, and electrophysiological properties collectively predispose the failing heart to cardiac arrhythmias, which are responsible for about a half of HF deaths. Multiscale cardiac modeling and simulation integrate structural and functional data from HF experimental models and patients to improve our mechanistic understanding of this complex arrhythmia syndrome. In particular, they allow investigating how disease-induced remodeling alters the coupling of electrophysiology, Ca2+ and Na+ handling, contraction, and energetics that lead to rhythm derangements. The Ca2+ /calmodulin-dependent protein kinase II, which expression and activity are enhanced in HF, emerges as a critical hub that modulates the feedbacks between these various subsystems and promotes arrhythmogenesis. This article is categorized under: Physiology > Mammalian Physiology in Health and Disease Models of Systems Properties and Processes > Mechanistic Models Models of Systems Properties and Processes > Cellular Models Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models.
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Affiliation(s)
- Stefano Morotti
- Department of Pharmacology, University of California Davis, Davis, California
| | - Eleonora Grandi
- Department of Pharmacology, University of California Davis, Davis, California
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70
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Quaglino A, Pezzuto S, Koutsourelakis PS, Auricchio A, Krause R. Fast uncertainty quantification of activation sequences in patient-specific cardiac electrophysiology meeting clinical time constraints. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2018; 34:e2985. [PMID: 29577657 DOI: 10.1002/cnm.2985] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2017] [Revised: 01/16/2018] [Accepted: 03/15/2018] [Indexed: 06/08/2023]
Abstract
We present a fast, patient-specific methodology for uncertainty quantification in electrophysiology, aimed at meeting the time constraints of clinical practitioners. We focus on computing the statistics of the activation map, given the uncertainties associated with the conductivity tensor modeling the fiber orientation in the heart. We use a fast parallel solution method implemented on a graphics processing unit for the eikonal approximation, in order to compute the activation map and to sample the random fiber field with correlation on the basis of geodesic distances. While this enables to perform uncertainty quantification studies with a manageable computational effort, the required time frame still exceeds clinically suitable time expectations. In order to reduce it further by 2 orders of magnitude, we rely on Bayesian multifidelity methods. In particular, we propose a low-fidelity model that is patient-specific and free from the additional training cost associated with reduced models. This is achieved by a sound physics-based simplification of the full eikonal model. The low-fidelity output is then corrected by the standard multifidelity framework. In practice, the complete procedure only requires approximately 100 new runs of our eikonal graphics processing unit solver for producing the sought estimates and their associated credible intervals, enabling a full online analysis in less than 5 minutes.
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Affiliation(s)
- A Quaglino
- Center for Computational Medicine in Cardiology, Institute of Computational Science, Università della Svizzera italiana, Lugano, Switzerland
| | - S Pezzuto
- Center for Computational Medicine in Cardiology, Institute of Computational Science, Università della Svizzera italiana, Lugano, Switzerland
| | | | - A Auricchio
- Center for Computational Medicine in Cardiology, Institute of Computational Science, Università della Svizzera italiana, Lugano, Switzerland
- Division of Cardiology, Fondazione Cardiocentro Ticino, Lugano, Switzerland
| | - R Krause
- Center for Computational Medicine in Cardiology, Institute of Computational Science, Università della Svizzera italiana, Lugano, Switzerland
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71
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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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72
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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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73
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Pathmanathan P, Gray RA. Validation and Trustworthiness of Multiscale Models of Cardiac Electrophysiology. Front Physiol 2018; 9:106. [PMID: 29497385 PMCID: PMC5818422 DOI: 10.3389/fphys.2018.00106] [Citation(s) in RCA: 32] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2017] [Accepted: 01/31/2018] [Indexed: 02/06/2023] Open
Abstract
Computational models of cardiac electrophysiology have a long history in basic science applications and device design and evaluation, but have significant potential for clinical applications in all areas of cardiovascular medicine, including functional imaging and mapping, drug safety evaluation, disease diagnosis, patient selection, and therapy optimisation or personalisation. For all stakeholders to be confident in model-based clinical decisions, cardiac electrophysiological (CEP) models must be demonstrated to be trustworthy and reliable. Credibility, that is, the belief in the predictive capability, of a computational model is primarily established by performing validation, in which model predictions are compared to experimental or clinical data. However, there are numerous challenges to performing validation for highly complex multi-scale physiological models such as CEP models. As a result, credibility of CEP model predictions is usually founded upon a wide range of distinct factors, including various types of validation results, underlying theory, evidence supporting model assumptions, evidence from model calibration, all at a variety of scales from ion channel to cell to organ. Consequently, it is often unclear, or a matter for debate, the extent to which a CEP model can be trusted for a given application. The aim of this article is to clarify potential rationale for the trustworthiness of CEP models by reviewing evidence that has been (or could be) presented to support their credibility. We specifically address the complexity and multi-scale nature of CEP models which makes traditional model evaluation difficult. In addition, we make explicit some of the credibility justification that we believe is implicitly embedded in the CEP modeling literature. Overall, we provide a fresh perspective to CEP model credibility, and build a depiction and categorisation of the wide-ranging body of credibility evidence for CEP models. This paper also represents a step toward the extension of model evaluation methodologies that are currently being developed by the medical device community, to physiological models.
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Affiliation(s)
- Pras Pathmanathan
- Office of Science and Engineering Laboratories, Center for Devices and Radiological Health, U.S. Food and Drug Administration, Silver Spring, MD, United States
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74
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Affiliation(s)
- Peter J Hunter
- Auckland Bioengineering Institute, University of Auckland, Auckland, New Zealand
| | - Nicolas P Smith
- Faculty of Engineering, University of Auckland, Auckland, New Zealand
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75
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SEARCH FOR MARKERS OF CHANGES OF THE SYNTHETIC ACTIVITY OF THYROCYTE UNDER THE INFLUENCE OF IODINE RECEPTION IN IODINE DEFICIENCY CONDITIONS. WORLD OF MEDICINE AND BIOLOGY 2018. [DOI: 10.26724/2079-8334-2018-3-65-179-185] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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76
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Lawson BAJ, Drovandi CC, Cusimano N, Burrage P, Rodriguez B, Burrage K. Unlocking data sets by calibrating populations of models to data density: A study in atrial electrophysiology. SCIENCE ADVANCES 2018; 4:e1701676. [PMID: 29349296 PMCID: PMC5770172 DOI: 10.1126/sciadv.1701676] [Citation(s) in RCA: 47] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/19/2017] [Accepted: 12/08/2017] [Indexed: 05/08/2023]
Abstract
The understanding of complex physical or biological systems nearly always requires a characterization of the variability that underpins these processes. In addition, the data used to calibrate these models may also often exhibit considerable variability. A recent approach to deal with these issues has been to calibrate populations of models (POMs), multiple copies of a single mathematical model but with different parameter values, in response to experimental data. To date, this calibration has been largely limited to selecting models that produce outputs that fall within the ranges of the data set, ignoring any trends that might be present in the data. We present here a novel and general methodology for calibrating POMs to the distributions of a set of measured values in a data set. We demonstrate our technique using a data set from a cardiac electrophysiology study based on the differences in atrial action potential readings between patients exhibiting sinus rhythm (SR) or chronic atrial fibrillation (cAF) and the Courtemanche-Ramirez-Nattel model for human atrial action potentials. Not only does our approach accurately capture the variability inherent in the experimental population, but we also demonstrate how the POMs that it produces may be used to extract additional information from the data used for calibration, including improved identification of the differences underlying stratified data. We also show how our approach allows different hypotheses regarding the variability in complex systems to be quantitatively compared.
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Affiliation(s)
- Brodie A. J. Lawson
- Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers, School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
- Corresponding author.
| | - Christopher C. Drovandi
- Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers, School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
| | | | - Pamela Burrage
- Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers, School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
| | - Blanca Rodriguez
- Department of Computer Science, University of Oxford, Oxford, UK
| | - Kevin Burrage
- Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers, School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
- Department of Computer Science, University of Oxford, Oxford, UK
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77
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Lei CL, Wang K, Clerx M, Johnstone RH, Hortigon-Vinagre MP, Zamora V, Allan A, Smith GL, Gavaghan DJ, Mirams GR, Polonchuk L. Tailoring Mathematical Models to Stem-Cell Derived Cardiomyocyte Lines Can Improve Predictions of Drug-Induced Changes to Their Electrophysiology. Front Physiol 2017; 8:986. [PMID: 29311950 PMCID: PMC5732978 DOI: 10.3389/fphys.2017.00986] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2017] [Accepted: 11/17/2017] [Indexed: 01/27/2023] Open
Abstract
Human induced pluripotent stem cell derived cardiomyocytes (iPSC-CMs) have applications in disease modeling, cell therapy, drug screening and personalized medicine. Computational models can be used to interpret experimental findings in iPSC-CMs, provide mechanistic insights, and translate these findings to adult cardiomyocyte (CM) electrophysiology. However, different cell lines display different expression of ion channels, pumps and receptors, and show differences in electrophysiology. In this exploratory study, we use a mathematical model based on iPSC-CMs from Cellular Dynamic International (CDI, iCell), and compare its predictions to novel experimental recordings made with the Axiogenesis Cor.4U line. We show that tailoring this model to the specific cell line, even using limited data and a relatively simple approach, leads to improved predictions of baseline behavior and response to drugs. This demonstrates the need and the feasibility to tailor models to individual cell lines, although a more refined approach will be needed to characterize individual currents, address differences in ion current kinetics, and further improve these results.
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Affiliation(s)
- Chon Lok Lei
- Computational Biology, Department of Computer Science, University of Oxford, Oxford, United Kingdom
| | - Ken Wang
- Roche Pharma Research and Early Development, Roche Innovation Center Basel, F. Hoffmann-La Roche Ltd., Basel, Switzerland
| | - Michael Clerx
- Computational Biology, Department of Computer Science, University of Oxford, Oxford, United Kingdom
| | - Ross H Johnstone
- Computational Biology, Department of Computer Science, University of Oxford, Oxford, United Kingdom
| | | | - Victor Zamora
- Clyde Biosciences, BioCity Scotland, Newhouse, United Kingdom
| | - Andrew Allan
- Clyde Biosciences, BioCity Scotland, Newhouse, United Kingdom
| | - Godfrey L Smith
- Clyde Biosciences, BioCity Scotland, Newhouse, United Kingdom
| | - David J Gavaghan
- Computational Biology, Department of Computer Science, University of Oxford, Oxford, United Kingdom
| | - Gary R Mirams
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, United Kingdom
| | - Liudmila Polonchuk
- Roche Pharma Research and Early Development, Roche Innovation Center Basel, F. Hoffmann-La Roche Ltd., Basel, Switzerland
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78
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Abstract
Respiratory disease is a significant problem worldwide, and it is a problem with increasing prevalence. Pathology in the upper airways and lung is very difficult to diagnose and treat, as response to disease is often heterogeneous across patients. Computational models have long been used to help understand respiratory function, and these models have evolved alongside increases in the resolution of medical imaging and increased capability of functional imaging, advances in biological knowledge, mathematical techniques and computational power. The benefits of increasingly complex and realistic geometric and biophysical models of the respiratory system are that they are able to capture heterogeneity in patient response to disease and predict emergent function across spatial scales from the delicate alveolar structures to the whole organ level. However, with increasing complexity, models become harder to solve and in some cases harder to validate, which can reduce their impact clinically. Here, we review the evolution of complexity in computational models of the respiratory system, including successes in translation of models into the clinical arena. We also highlight major challenges in modelling the respiratory system, while making use of the evolving functional data that are available for model parameterisation and testing.
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Affiliation(s)
- Alys R Clark
- 1 Auckland Bioengineering Institute, The University of Auckland, Auckland, New Zealand
| | - Haribalan Kumar
- 1 Auckland Bioengineering Institute, The University of Auckland, Auckland, New Zealand
| | - Kelly Burrowes
- 2 Department of Chemical and Materials Engineering, The University of Auckland, Auckland, New Zealand
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79
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Chang KC, Dutta S, Mirams GR, Beattie KA, Sheng J, Tran PN, Wu M, Wu WW, Colatsky T, Strauss DG, Li Z. Uncertainty Quantification Reveals the Importance of Data Variability and Experimental Design Considerations for in Silico Proarrhythmia Risk Assessment. Front Physiol 2017; 8:917. [PMID: 29209226 PMCID: PMC5702340 DOI: 10.3389/fphys.2017.00917] [Citation(s) in RCA: 56] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2017] [Accepted: 10/30/2017] [Indexed: 12/19/2022] Open
Abstract
The Comprehensive in vitro Proarrhythmia Assay (CiPA) is a global initiative intended to improve drug proarrhythmia risk assessment using a new paradigm of mechanistic assays. Under the CiPA paradigm, the relative risk of drug-induced Torsade de Pointes (TdP) is assessed using an in silico model of the human ventricular action potential (AP) that integrates in vitro pharmacology data from multiple ion channels. Thus, modeling predictions of cardiac risk liability will depend critically on the variability in pharmacology data, and uncertainty quantification (UQ) must comprise an essential component of the in silico assay. This study explores UQ methods that may be incorporated into the CiPA framework. Recently, we proposed a promising in silico TdP risk metric (qNet), which is derived from AP simulations and allows separation of a set of CiPA training compounds into Low, Intermediate, and High TdP risk categories. The purpose of this study was to use UQ to evaluate the robustness of TdP risk separation by qNet. Uncertainty in the model parameters used to describe drug binding and ionic current block was estimated using the non-parametric bootstrap method and a Bayesian inference approach. Uncertainty was then propagated through AP simulations to quantify uncertainty in qNet for each drug. UQ revealed lower uncertainty and more accurate TdP risk stratification by qNet when simulations were run at concentrations below 5× the maximum therapeutic exposure (Cmax). However, when drug effects were extrapolated above 10× Cmax, UQ showed that qNet could no longer clearly separate drugs by TdP risk. This was because for most of the pharmacology data, the amount of current block measured was <60%, preventing reliable estimation of IC50-values. The results of this study demonstrate that the accuracy of TdP risk prediction depends both on the intrinsic variability in ion channel pharmacology data as well as on experimental design considerations that preclude an accurate determination of drug IC50-values in vitro. Thus, we demonstrate that UQ provides valuable information about in silico modeling predictions that can inform future proarrhythmic risk evaluation of drugs under the CiPA paradigm.
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Affiliation(s)
- Kelly C Chang
- Division of Applied Regulatory Science, Center for Drug Evaluation and Research, Office of Translational Sciences, Office of Clinical Pharmacology, Food and Drug Administration, Silver Spring, MD, United States
| | - Sara Dutta
- Division of Applied Regulatory Science, Center for Drug Evaluation and Research, Office of Translational Sciences, Office of Clinical Pharmacology, Food and Drug Administration, Silver Spring, MD, United States
| | - Gary R Mirams
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, United Kingdom
| | - Kylie A Beattie
- Division of Applied Regulatory Science, Center for Drug Evaluation and Research, Office of Translational Sciences, Office of Clinical Pharmacology, Food and Drug Administration, Silver Spring, MD, United States
| | - Jiansong Sheng
- Division of Applied Regulatory Science, Center for Drug Evaluation and Research, Office of Translational Sciences, Office of Clinical Pharmacology, Food and Drug Administration, Silver Spring, MD, United States
| | - Phu N Tran
- Division of Applied Regulatory Science, Center for Drug Evaluation and Research, Office of Translational Sciences, Office of Clinical Pharmacology, Food and Drug Administration, Silver Spring, MD, United States
| | - Min Wu
- Division of Applied Regulatory Science, Center for Drug Evaluation and Research, Office of Translational Sciences, Office of Clinical Pharmacology, Food and Drug Administration, Silver Spring, MD, United States
| | - Wendy W Wu
- Division of Applied Regulatory Science, Center for Drug Evaluation and Research, Office of Translational Sciences, Office of Clinical Pharmacology, Food and Drug Administration, Silver Spring, MD, United States
| | - Thomas Colatsky
- Marshview Life Science Advisors, Seabrook Island, SC, United States
| | - David G Strauss
- Division of Applied Regulatory Science, Center for Drug Evaluation and Research, Office of Translational Sciences, Office of Clinical Pharmacology, Food and Drug Administration, Silver Spring, MD, United States
| | - Zhihua Li
- Division of Applied Regulatory Science, Center for Drug Evaluation and Research, Office of Translational Sciences, Office of Clinical Pharmacology, Food and Drug Administration, Silver Spring, MD, United States
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80
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Mangion K, Gao H, Husmeier D, Luo X, Berry C. Advances in computational modelling for personalised medicine after myocardial infarction. Heart 2017; 104:550-557. [PMID: 29127185 DOI: 10.1136/heartjnl-2017-311449] [Citation(s) in RCA: 31] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 05/15/2017] [Revised: 10/24/2017] [Accepted: 10/25/2017] [Indexed: 11/04/2022] Open
Abstract
Myocardial infarction (MI) is a leading cause of premature morbidity and mortality worldwide. Determining which patients will experience heart failure and sudden cardiac death after an acute MI is notoriously difficult for clinicians. The extent of heart damage after an acute MI is informed by cardiac imaging, typically using echocardiography or sometimes, cardiac magnetic resonance (CMR). These scans provide complex data sets that are only partially exploited by clinicians in daily practice, implying potential for improved risk assessment. Computational modelling of left ventricular (LV) function can bridge the gap towards personalised medicine using cardiac imaging in patients with post-MI. Several novel biomechanical parameters have theoretical prognostic value and may be useful to reflect the biomechanical effects of novel preventive therapy for adverse remodelling post-MI. These parameters include myocardial contractility (regional and global), stiffness and stress. Further, the parameters can be delineated spatially to correspond with infarct pathology and the remote zone. While these parameters hold promise, there are challenges for translating MI modelling into clinical practice, including model uncertainty, validation and verification, as well as time-efficient processing. More research is needed to (1) simplify imaging with CMR in patients with post-MI, while preserving diagnostic accuracy and patient tolerance (2) to assess and validate novel biomechanical parameters against established prognostic biomarkers, such as LV ejection fraction and infarct size. Accessible software packages with minimal user interaction are also needed. Translating benefits to patients will be achieved through a multidisciplinary approach including clinicians, mathematicians, statisticians and industry partners.
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Affiliation(s)
- Kenneth Mangion
- BHF Glasgow Cardiovascular Research Centre, University of Glasgow, Glasgow, UK.,West of Scotland Heart and Lung Centre, Golden Jubilee National Hospital, Clydebank, UK
| | - Hao Gao
- Department of Mathematics and Statistics, University of Glasgow, Glasgow, UK
| | - Dirk Husmeier
- Department of Mathematics and Statistics, University of Glasgow, Glasgow, UK
| | - Xiaoyu Luo
- Department of Mathematics and Statistics, University of Glasgow, Glasgow, UK
| | - Colin Berry
- BHF Glasgow Cardiovascular Research Centre, University of Glasgow, Glasgow, UK.,West of Scotland Heart and Lung Centre, Golden Jubilee National Hospital, Clydebank, UK
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81
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Xiao M, Adams MP, Willis A, Burford MA, O'Brien KR. Variation within and between cyanobacterial species and strains affects competition: Implications for phytoplankton modelling. HARMFUL ALGAE 2017; 69:38-47. [PMID: 29122241 DOI: 10.1016/j.hal.2017.10.001] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/06/2017] [Revised: 10/02/2017] [Accepted: 10/03/2017] [Indexed: 06/07/2023]
Abstract
Cyanobacteria Microcystis aeruginosa and Cylindrospermopsis raciborskii are two harmful species which co-occur and successively dominate in freshwaters globally. Within-species strain variability affects cyanobacterial population responses to environmental conditions, and it is unclear which species/strain would dominate under different environmental conditions. This study applied a Monte Carlo approach to a phytoplankton dynamic growth model to identify how growth variability of multiple strains of these two species affects their competition. Pairwise competition between four M. aeruginosa and eight C. raciborskii strains was simulated using a deterministic model, parameterized with laboratory measurements of growth and light attenuation for all strains, and run at two temperatures and light intensities. 17 000 runs were simulated for each pair using a statistical distribution with Monte Carlo approach. The model results showed that cyanobacterial competition was highly variable, depending on strains present, light and temperature conditions. There was no absolute 'winner' under all conditions as there were always strains predicted to coexist with the dominant strains, which were M. aeruginosa strains at 20°C and C. raciborskii strains at 28°C. The uncertainty in prediction of species competition outcomes was due to the substantial variability of growth responses within and between strains. Overall, this study demonstrates that within-species strain variability has a potentially large effect on cyanobacterial population dynamics, and therefore this variability may substantially reduce confidence in predicting outcomes of phytoplankton competition in deterministic models, that are based on only one set of parameters for each species or strain.
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Affiliation(s)
- Man Xiao
- Australian Rivers Institute, Griffith University, 170 Kessels Road, Nathan, QLD 4111, Australia; School of Environment, Griffith University, 170 Kessels Road, Nathan, QLD 4111, Australia.
| | - Matthew P Adams
- School of Chemical Engineering, University of Queensland, St Lucia, QLD 4072, Australia
| | - Anusuya Willis
- Australian Rivers Institute, Griffith University, 170 Kessels Road, Nathan, QLD 4111, Australia
| | - Michele A Burford
- Australian Rivers Institute, Griffith University, 170 Kessels Road, Nathan, QLD 4111, Australia; School of Environment, Griffith University, 170 Kessels Road, Nathan, QLD 4111, Australia
| | - Katherine R O'Brien
- School of Chemical Engineering, University of Queensland, St Lucia, QLD 4072, Australia
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82
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Trenor B, Cardona K, Saiz J, Noble D, Giles W. Cardiac action potential repolarization revisited: early repolarization shows all-or-none behaviour. J Physiol 2017; 595:6599-6612. [PMID: 28815597 PMCID: PMC5663823 DOI: 10.1113/jp273651] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2017] [Accepted: 08/09/2017] [Indexed: 12/15/2022] Open
Abstract
In healthy mammalian hearts the action potential (AP) waveform initiates and modulates each contraction, or heartbeat. As a result, AP height and duration are key physiological variables. In addition, rate-dependent changes in ventricular AP duration (APD), and variations in APD at a fixed heart rate are both reliable biomarkers of electrophysiological stability. Present guidelines for the likelihood that candidate drugs will increase arrhythmias rely on small changes in APD and Q-T intervals as criteria for safety pharmacology decisions. However, both of these measurements correspond to the final repolarization of the AP. Emerging clinical evidence draws attention to the early repolarization phase of the action potential (and the J-wave of the ECG) as an additional important biomarker for arrhythmogenesis. Here we provide a mechanistic background to this early repolarization syndrome by summarizing the evidence that both the initial depolarization and repolarization phases of the cardiac action potential can exhibit distinct time- and voltage-dependent thresholds, and also demonstrating that both can show regenerative all-or-none behaviour. An important consequence of this is that not all of the dynamics of action potential repolarization in human ventricle can be captured by data from single myocytes when these results are expressed as 'repolarization reserve'. For example, the complex pattern of cell-to-cell current flow that is responsible for AP conduction (propagation) within the mammalian myocardium can change APD and the Q-T interval of the electrocardiogram alter APD stability, and modulate responsiveness to pharmacological agents (such as Class III anti-arrhythmic drugs).
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Affiliation(s)
- Beatriz Trenor
- Centro de Investigación e BioingenieríaUniversitat Politècnica de ValènciaValenciaSpain
| | - Karen Cardona
- Centro de Investigación e BioingenieríaUniversitat Politècnica de ValènciaValenciaSpain
| | - Javier Saiz
- Centro de Investigación e BioingenieríaUniversitat Politècnica de ValènciaValenciaSpain
| | - Denis Noble
- University Laboratory of PhysiologyUniversity of OxfordOxfordOX1 3PTUK
| | - Wayne Giles
- Faculties of Kinesiology and MedicineUniversity of CalgaryCalgaryAlbertaCanadaT2N 1N4
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83
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McMillan B, Gavaghan DJ, Mirams GR. Early afterdepolarisation tendency as a simulated pro-arrhythmic risk indicator. Toxicol Res (Camb) 2017; 6:912-921. [PMID: 29456831 PMCID: PMC5779076 DOI: 10.1039/c7tx00141j] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2017] [Accepted: 09/12/2017] [Indexed: 12/19/2022] Open
Abstract
Drug-induced Torsades de Pointes (TdP) arrhythmia is of major interest in predictive toxicology. Drugs which cause TdP block the hERG cardiac potassium channel. However, not all drugs that block hERG cause TdP. As such, further understanding of the mechanistic route to TdP is needed. Early afterdepolarisations (EADs) are a cell-level phenomenon in which the membrane of a cardiac cell depolarises a second time before repolarisation, and EADs are seen in hearts during TdP. Therefore, we propose a method of predicting TdP using induced EADs combined with multiple ion channel block in simulations using biophysically-based mathematical models of human ventricular cell electrophysiology. EADs were induced in cardiac action potential models using interventions based on diseases that are known to cause EADs, including: increasing the conduction of the L-type calcium channel, decreasing the conduction of the hERG channel, and shifting the inactivation curve of the fast sodium channel. The threshold of intervention that was required to cause an EAD was used to classify drugs into clinical risk categories. The metric that used L-type calcium induced EADs was the most accurate of the EAD metrics at classifying drugs into the correct risk categories, and increased in accuracy when combined with action potential duration measurements. The EAD metrics were all more accurate than hERG block alone, but not as predictive as simpler measures such as simulated action potential duration. This may be because different routes to EADs represent risk well for different patient subgroups, something that is difficult to assess at present.
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Affiliation(s)
- Beth McMillan
- Computational Biology , Dept. of Computer Science , University of Oxford , Oxford , OX1 3QD , UK . ; ; Tel: +44 (0)1865 273838
| | - David J Gavaghan
- Computational Biology , Dept. of Computer Science , University of Oxford , Oxford , OX1 3QD , UK . ; ; Tel: +44 (0)1865 273838
| | - Gary R Mirams
- Centre for Mathematical Biology , School of Mathematical Sciences , University of Nottingham , Nottingham , NG7 2RD , UK
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84
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Wiśniowska B, Tylutki Z, Polak S. Humans Vary, So Cardiac Models Should Account for That Too! Front Physiol 2017; 8:700. [PMID: 28983251 PMCID: PMC5613127 DOI: 10.3389/fphys.2017.00700] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2017] [Accepted: 08/30/2017] [Indexed: 12/25/2022] Open
Abstract
The utilization of mathematical modeling and simulation in drug development encompasses multiple mathematical techniques and the location of a drug candidate in the development pipeline. Historically speaking they have been used to analyze experimental data (i.e., Hill equation) and clarify the involved physical and chemical processes (i.e., Fick laws and drug molecule diffusion). In recent years the advanced utilization of mathematical modeling has been an important part of the regulatory review process. Physiologically based pharmacokinetic (PBPK) models identify the need to conduct specific clinical studies, suggest specific study designs and propose appropriate labeling language. Their application allows the evaluation of the influence of intrinsic (e.g., age, gender, genetics, disease) and extrinsic [e.g., dosing schedule, drug-drug interactions (DDIs)] factors, alone or in combinations, on drug exposure and therefore provides accurate population assessment. A similar pathway has been taken for the assessment of drug safety with cardiac safety being one the most advanced examples. Mechanistic mathematical model-informed safety evaluation, with a focus on drug potential for causing arrhythmias, is now discussed as an element of the Comprehensive in vitro Proarrhythmia Assay. One of the pillars of this paradigm is the use of an in silico model of the adult human ventricular cardiomyocyte to integrate in vitro measured data. Existing examples (in vitro—in vivo extrapolation with the use of PBPK models) suggest that deterministic, epidemiological and clinical data based variability models can be merged with the mechanistic models describing human physiology. There are other methods available, based on the stochastic approach and on population of models generated by randomly assigning specific parameter values (ionic current conductance and kinetic) and further pruning. Both approaches are briefly characterized in this manuscript, in parallel with the drug-specific variability.
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Affiliation(s)
- Barbara Wiśniowska
- Pharmacoepidemiology and Pharmacoeconomics Unit, Faculty of Pharmacy, Jagiellonian University Medical CollegeKrakow, Poland
| | - Zofia Tylutki
- Pharmacoepidemiology and Pharmacoeconomics Unit, Faculty of Pharmacy, Jagiellonian University Medical CollegeKrakow, Poland
| | - Sebastian Polak
- Pharmacoepidemiology and Pharmacoeconomics Unit, Faculty of Pharmacy, Jagiellonian University Medical CollegeKrakow, Poland.,SimcypCertara, Sheffield, United Kingdom
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85
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Hartung T, FitzGerald RE, Jennings P, Mirams GR, Peitsch MC, Rostami-Hodjegan A, Shah I, Wilks MF, Sturla SJ. Systems Toxicology: Real World Applications and Opportunities. Chem Res Toxicol 2017; 30:870-882. [PMID: 28362102 PMCID: PMC5396025 DOI: 10.1021/acs.chemrestox.7b00003] [Citation(s) in RCA: 68] [Impact Index Per Article: 9.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2017] [Indexed: 01/14/2023]
Abstract
Systems Toxicology aims to change the basis of how adverse biological effects of xenobiotics are characterized from empirical end points to describing modes of action as adverse outcome pathways and perturbed networks. Toward this aim, Systems Toxicology entails the integration of in vitro and in vivo toxicity data with computational modeling. This evolving approach depends critically on data reliability and relevance, which in turn depends on the quality of experimental models and bioanalysis techniques used to generate toxicological data. Systems Toxicology involves the use of large-scale data streams ("big data"), such as those derived from omics measurements that require computational means for obtaining informative results. Thus, integrative analysis of multiple molecular measurements, particularly acquired by omics strategies, is a key approach in Systems Toxicology. In recent years, there have been significant advances centered on in vitro test systems and bioanalytical strategies, yet a frontier challenge concerns linking observed network perturbations to phenotypes, which will require understanding pathways and networks that give rise to adverse responses. This summary perspective from a 2016 Systems Toxicology meeting, an international conference held in the Alps of Switzerland, describes the limitations and opportunities of selected emerging applications in this rapidly advancing field. Systems Toxicology aims to change the basis of how adverse biological effects of xenobiotics are characterized, from empirical end points to pathways of toxicity. This requires the integration of in vitro and in vivo data with computational modeling. Test systems and bioanalytical technologies have made significant advances, but ensuring data reliability and relevance is an ongoing concern. The major challenge facing the new pathway approach is determining how to link observed network perturbations to phenotypic toxicity.
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Affiliation(s)
- Thomas Hartung
- Center
for Alternatives to Animal Testing (CAAT), Johns Hopkins Bloomberg School of Public Health, Baltimore, Maryland 21205, United States
- University
of Konstanz, CAAT-Europe, 78457 Konstanz, Germany
| | - Rex E. FitzGerald
- Swiss
Centre for Applied Human Toxicology, University
of Basel, 4055 Basel, Switzerland
| | - Paul Jennings
- Division
of Physiology, Department of Physiology and Medical Physics, Medical University of Innsbruck, 6020 Innsbruck, Austria
| | - Gary R. Mirams
- Centre
for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, U.K.
| | - Manuel C. Peitsch
- Department
of Research and Development, Philip Morris
International, 2000 Neuchâtel, Switzerland
| | - Amin Rostami-Hodjegan
- Centre
for Applied Pharmacokinetic Research, University
of Manchester, Manchester M13 9PL, U.K.
- Simcyp
Limited (a Certara Company), Blades Enterprise
Centre, Sheffield S2 4SU, U.K.
| | - Imran Shah
- National
Center for Computational Toxicology, Research Triangle Park, North Carolina 27711, United States
| | - Martin F. Wilks
- Swiss
Centre for Applied Human Toxicology, University
of Basel, 4055 Basel, Switzerland
| | - Shana J. Sturla
- Department
of Health Sciences and Technology, ETH Zurich, 8092 Zurich, Switzerland
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86
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Johnstone RH, Bardenet R, Gavaghan DJ, Mirams GR. Hierarchical Bayesian inference for ion channel screening dose-response data. Wellcome Open Res 2016. [PMID: 27918599 DOI: 10.12688/wellcomeopenres.9945.1] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022] Open
Abstract
Dose-response (or 'concentration-effect') relationships commonly occur in biological and pharmacological systems and are well characterised by Hill curves. These curves are described by an equation with two parameters: the inhibitory concentration 50% (IC50); and the Hill coefficient. Typically just the 'best fit' parameter values are reported in the literature. Here we introduce a Python-based software tool, PyHillFit , and describe the underlying Bayesian inference methods that it uses, to infer probability distributions for these parameters as well as the level of experimental observation noise. The tool also allows for hierarchical fitting, characterising the effect of inter-experiment variability. We demonstrate the use of the tool on a recently published dataset on multiple ion channel inhibition by multiple drug compounds. We compare the maximum likelihood, Bayesian and hierarchical Bayesian approaches. We then show how uncertainty in dose-response inputs can be characterised and propagated into a cardiac action potential simulation to give a probability distribution on model outputs.
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Affiliation(s)
- Ross H Johnstone
- Computational Biology, Department of Computer Science, University of Oxford, Oxford, UK
| | | | - David J Gavaghan
- Computational Biology, Department of Computer Science, University of Oxford, Oxford, UK
| | - Gary R Mirams
- Computational Biology, Department of Computer Science, University of Oxford, Oxford, UK.,Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, UK
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87
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Johnstone RH, Bardenet R, Gavaghan DJ, Mirams GR. Hierarchical Bayesian inference for ion channel screening dose-response data. Wellcome Open Res 2016; 1:6. [PMID: 27918599 PMCID: PMC5134333 DOI: 10.12688/wellcomeopenres.9945.2] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022] Open
Abstract
Dose-response (or ‘concentration-effect’) relationships commonly occur in biological and pharmacological systems and are well characterised by Hill curves. These curves are described by an equation with two parameters: the inhibitory concentration 50% (IC50); and the Hill coefficient. Typically just the ‘best fit’ parameter values are reported in the literature. Here we introduce a Python-based software tool,
PyHillFit , and describe the underlying Bayesian inference methods that it uses, to infer probability distributions for these parameters as well as the level of experimental observation noise. The tool also allows for hierarchical fitting, characterising the effect of inter-experiment variability. We demonstrate the use of the tool on a recently published dataset on multiple ion channel inhibition by multiple drug compounds. We compare the maximum likelihood, Bayesian and hierarchical Bayesian approaches. We then show how uncertainty in dose-response inputs can be characterised and propagated into a cardiac action potential simulation to give a probability distribution on model outputs.
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Affiliation(s)
- Ross H Johnstone
- Computational Biology, Department of Computer Science, University of Oxford, Oxford, UK
| | | | - David J Gavaghan
- Computational Biology, Department of Computer Science, University of Oxford, Oxford, UK
| | - Gary R Mirams
- Computational Biology, Department of Computer Science, University of Oxford, Oxford, UK.,Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, UK
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88
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Jousset F, Maguy A, Rohr S, Kucera JP. Myofibroblasts Electrotonically Coupled to Cardiomyocytes Alter Conduction: Insights at the Cellular Level from a Detailed In silico Tissue Structure Model. Front Physiol 2016; 7:496. [PMID: 27833567 PMCID: PMC5081362 DOI: 10.3389/fphys.2016.00496] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2016] [Accepted: 10/11/2016] [Indexed: 01/05/2023] Open
Abstract
Fibrotic myocardial remodeling is typically accompanied by the appearance of myofibroblasts (MFBs). In vitro, MFBs were shown to slow conduction and precipitate ectopic activity following gap junctional coupling to cardiomyocytes (CMCs). To gain further mechanistic insights into this arrhythmogenic MFB-CMC crosstalk, we performed numerical simulations in cell-based high-resolution two-dimensional tissue models that replicated experimental conditions. Cell dimensions were determined using confocal microscopy of single and co-cultured neonatal rat ventricular CMCs and MFBs. Conduction was investigated as a function of MFB density in three distinct cellular tissue architectures: CMC strands with endogenous MFBs, CMC strands with coating MFBs of two different sizes, and CMC strands with MFB inserts. Simulations were performed to identify individual contributions of heterocellular gap junctional coupling and of the specific electrical phenotype of MFBs. With increasing MFB density, both endogenous and coating MFBs slowed conduction. At MFB densities of 5-30%, conduction slowing was most pronounced in strands with endogenous MFBs due to the MFB-dependent increase in axial resistance. At MFB densities >40%, very slow conduction and spontaneous activity was primarily due to MFB-induced CMC depolarization. Coating MFBs caused non-uniformities of resting membrane potential, which were more prominent with large than with small MFBs. In simulations of MFB inserts connecting two CMC strands, conduction delays increased with increasing insert lengths and block appeared for inserts >1.2 mm. Thus, electrophysiological properties of engineered CMC-MFB co-cultures depend on MFB density, MFB size and their specific positioning in respect to CMCs. These factors may influence conduction characteristics in the heterocellular myocardium.
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Affiliation(s)
- Florian Jousset
- Department of Physiology, University of Bern Bern, Switzerland
| | - Ange Maguy
- Department of Physiology, University of Bern Bern, Switzerland
| | - Stephan Rohr
- Department of Physiology, University of Bern Bern, Switzerland
| | - Jan P Kucera
- Department of Physiology, University of Bern Bern, Switzerland
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89
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Johnstone RH, Bardenet R, Gavaghan DJ, Polonchuk L, Davies MR, Mirams GR. Hierarchical Bayesian Modelling of Variability and Uncertainty in Synthetic Action Potential Traces. COMPUTING IN CARDIOLOGY 2016; 43:1089-1092. [PMID: 37551270 PMCID: PMC7614890 DOI: 10.22489/cinc.2016.313-458] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/09/2023]
Abstract
There are many sources of uncertainty in the recording and modelling of membrane action potentials (APs) from cardiomyocytes. For example, there are measurement, parameter, and model uncertainties. There is also extrinsic variability between cells, and intrinsic beat-to-beat variability within a single cell. These combined uncertainties and variability make it very difficult to extrapolate predictions from these models, since current AP models have single parameter values and thus produce a single AP trace. We aim to re-parameterise existing AP models to fit experimental data, and to quantify uncertainty associated with ion current densities when measuring and modelling these APs. We then wish to propagate this uncertainty into model predictions, such as ion channel block effected by a pharmaceutical compound. We perform an in silico study using synthetic data generated from different sets of parameters. We then 'forget' these parameter values and re-infer their distributions using hierarchical Markov chain Monte Carlo methods. We find that we can successfully infer the 'correct' distributions for most ion current densities for each AP trace, along with an approximation to the higher-level distribution from which these parameter values were sampled. There is, however, some level of unidentifiability amongst some of the current densities.
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Affiliation(s)
- Ross H Johnstone
- Computational Biology, Dept. of Computer Science, University of Oxford, Oxford, UK
| | | | - David J Gavaghan
- Computational Biology, Dept. of Computer Science, University of Oxford, Oxford, UK
| | | | | | - Gary R Mirams
- Computational Biology, Dept. of Computer Science, University of Oxford, Oxford, UK
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90
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Gemmell P, Burrage K, Rodríguez B, Quinn TA. Rabbit-specific computational modelling of ventricular cell electrophysiology: Using populations of models to explore variability in the response to ischemia. PROGRESS IN BIOPHYSICS AND MOLECULAR BIOLOGY 2016; 121:169-84. [PMID: 27320382 PMCID: PMC5405055 DOI: 10.1016/j.pbiomolbio.2016.06.003] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/21/2016] [Accepted: 06/13/2016] [Indexed: 11/04/2022]
Abstract
Computational modelling, combined with experimental investigations, is a powerful method for investigating complex cardiac electrophysiological behaviour. The use of rabbit-specific models, due to the similarities of cardiac electrophysiology in this species with human, is especially prevalent. In this paper, we first briefly review rabbit-specific computational modelling of ventricular cell electrophysiology, multi-cellular simulations including cellular heterogeneity, and acute ischemia. This mini-review is followed by an original computational investigation of variability in the electrophysiological response of two experimentally-calibrated populations of rabbit-specific ventricular myocyte action potential models to acute ischemia. We performed a systematic exploration of the response of the model populations to varying degrees of ischemia and individual ischemic parameters, to investigate their individual and combined effects on action potential duration and refractoriness. This revealed complex interactions between model population variability and ischemic factors, which combined to enhance variability during ischemia. This represents an important step towards an improved understanding of the role that physiological variability may play in electrophysiological alterations during acute ischemia.
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Affiliation(s)
- Philip Gemmell
- Department of Computer Science, University of Oxford, Oxford, UK
| | - Kevin Burrage
- Department of Computer Science, University of Oxford, Oxford, UK; School of Mathematical Sciences and ARC Centre of Excellence, ACEMS, Queensland University of Technology, Brisbane, Australia
| | - Blanca Rodríguez
- Department of Computer Science, University of Oxford, Oxford, UK
| | - T Alexander Quinn
- Department of Physiology and Biophysics, Dalhousie University, 5850 College St, Lab 3F, Halifax, NS B3H 4R2, Canada; School of Biomedical Engineering, Dalhousie University, 5850 College St, Lab 3F, Halifax, NS B3H 4R2, Canada.
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91
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Hill AP, Perry MD, Abi-Gerges N, Couderc JP, Fermini B, Hancox JC, Knollmann BC, Mirams GR, Skinner J, Zareba W, Vandenberg JI. Computational cardiology and risk stratification for sudden cardiac death: one of the grand challenges for cardiology in the 21st century. J Physiol 2016; 594:6893-6908. [PMID: 27060987 PMCID: PMC5134408 DOI: 10.1113/jp272015] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/10/2015] [Accepted: 03/16/2016] [Indexed: 12/25/2022] Open
Abstract
Risk stratification in the context of sudden cardiac death has been acknowledged as one of the major challenges facing cardiology for the past four decades. In recent years, the advent of high performance computing has facilitated organ-level simulation of the heart, meaning we can now examine the causes, mechanisms and impact of cardiac dysfunction in silico. As a result, computational cardiology, largely driven by the Physiome project, now stands at the threshold of clinical utility in regards to risk stratification and treatment of patients at risk of sudden cardiac death. In this white paper, we outline a roadmap of what needs to be done to make this translational step, using the relatively well-developed case of acquired or drug-induced long QT syndrome as an exemplar case.
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Affiliation(s)
- Adam P Hill
- Victor Chang Cardiac Research Institute, 405 Liverpool Street, Darlinghurst, NSW, 2010, Australia.,St. Vincent's Clinical School, University of New South Wales, Sydney, NSW, 2052, Australia
| | - Matthew D Perry
- Victor Chang Cardiac Research Institute, 405 Liverpool Street, Darlinghurst, NSW, 2010, Australia.,St. Vincent's Clinical School, University of New South Wales, Sydney, NSW, 2052, Australia
| | - Najah Abi-Gerges
- AnaBios Corporation, 3030 Bunker Hill St., San Diego, CA, 92109, USA
| | | | - Bernard Fermini
- Global Safety Pharmacology, Pfizer Inc, MS8274-1347 Eastern Point Road, Groton, CT, 06340, USA
| | - Jules C Hancox
- School of Physiology, Pharmacology and Neuroscience, University of Bristol, Bristol, UK
| | - Bjorn C Knollmann
- Vanderbilt University School of Medicine, 1285 Medical Research Building IV, Nashville, Tennessee, 37232, USA
| | - Gary R Mirams
- Computational Biology, Department of Computer Science, University of Oxford, Oxford, United Kingdom
| | - Jon Skinner
- Cardiac Inherited Disease Group, Starship Hospital, Auckland, New Zealand
| | - Wojciech Zareba
- University of Rochester Medical Center, Rochester, NY, 14642, USA
| | - Jamie I Vandenberg
- Victor Chang Cardiac Research Institute, 405 Liverpool Street, Darlinghurst, NSW, 2010, Australia.,St. Vincent's Clinical School, University of New South Wales, Sydney, NSW, 2052, Australia
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