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Wülfers EM, Moss R, Lehrmann H, Arentz T, Westermann D, Seemann G, Odening KE, Steinfurt J. Whole-heart computational modelling provides further mechanistic insights into ST-elevation in Brugada syndrome. INTERNATIONAL JOURNAL OF CARDIOLOGY. HEART & VASCULATURE 2024; 51:101373. [PMID: 38464963 PMCID: PMC10924145 DOI: 10.1016/j.ijcha.2024.101373] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/11/2023] [Revised: 02/08/2024] [Accepted: 02/21/2024] [Indexed: 03/12/2024]
Abstract
Background Brugada syndrome (BrS) is characterized by dynamic ST-elevations in right precordial leads and increased risk of ventricular fibrillation and sudden cardiac death. As the mechanism underlying ST-elevation and malignant arrhythmias is controversial computational modeling can aid in exploring the disease mechanism. Thus we aim to test the main competing hypotheses ('delayed depolarization' vs. 'early repolarization') of BrS in a whole-heart computational model. Methods In a 3D whole-heart computational model, delayed epicardial RVOT activation with local conduction delay was simulated by reducing conductivity in the epicardial RVOT. Early repolarization was simulated by instead increasing the transient outward potassium current (Ito) in the same region. Additionally, a reduction in the fast sodium current (INa) was incorporated in both models. Results Delayed depolarization with local conduction delay in the computational model resulted in coved-type ST-elevation with negative T-waves in the precordial surface ECG leads. 'Saddleback'-shaped ST-elevation was obtained with reduced substrate extent or thickness. Increased Ito simulations showed early repolarization in the RVOT with a descending but not coved-type ST-elevation. Reduced INa did not show a significant effect on ECG morphology. Conclusions In this whole-heart BrS computational model of both major hypotheses, realistic coved-type ECG resulted only from delayed epicardial RVOT depolarization with local conduction delay but not early repolarizing ion channel modifications. These simulations provide further support for the depolarization hypothesis as electrophysiological mechanism underlying BrS.
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Affiliation(s)
- Eike M Wülfers
- Institute for Experimental Cardiovascular Medicine, University Heart Center Freiburg - Bad Krozingen, and Faculty of Medicine, University of Freiburg, Freiburg, Germany
- Department of Physics and Astronomy, Faculty of Sciences, Ghent University, Ghent, Belgium
| | - Robin Moss
- Institute for Experimental Cardiovascular Medicine, University Heart Center Freiburg - Bad Krozingen, and Faculty of Medicine, University of Freiburg, Freiburg, Germany
| | - Heiko Lehrmann
- Department of Cardiology and Angiology, University Heart Center Freiburg - Bad Krozingen, and Faculty of Medicine, University of Freiburg, Freiburg, Germany
| | - Thomas Arentz
- Department of Cardiology and Angiology, University Heart Center Freiburg - Bad Krozingen, and Faculty of Medicine, University of Freiburg, Freiburg, Germany
| | - Dirk Westermann
- Department of Cardiology and Angiology, University Heart Center Freiburg - Bad Krozingen, and Faculty of Medicine, University of Freiburg, Freiburg, Germany
| | - Gunnar Seemann
- Institute for Experimental Cardiovascular Medicine, University Heart Center Freiburg - Bad Krozingen, and Faculty of Medicine, University of Freiburg, Freiburg, Germany
| | - Katja E Odening
- Translational Cardiology, Department of Cardiology and Institute of Physiology, University Hospital Bern, University of Bern, Switzerland
| | - Johannes Steinfurt
- Department of Cardiology and Angiology, University Heart Center Freiburg - Bad Krozingen, and Faculty of Medicine, University of Freiburg, Freiburg, Germany
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2
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Means SA, Roesler MW, Garrett AS, Cheng L, Clark AR. Steady-state approximations for Hodgkin-Huxley cell models: Reduction of order for uterine smooth muscle cell model. PLoS Comput Biol 2023; 19:e1011359. [PMID: 37647265 PMCID: PMC10468033 DOI: 10.1371/journal.pcbi.1011359] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2022] [Accepted: 07/14/2023] [Indexed: 09/01/2023] Open
Abstract
Multi-scale mathematical bioelectrical models of organs such as the uterus, stomach or heart present challenges both for accuracy and computational tractability. These multi-scale models are typically founded on models of biological cells derived from the classic Hodkgin-Huxley (HH) formalism. Ion channel behaviour is tracked with dynamical variables representing activation or inactivation of currents that relax to steady-state dependencies on cellular membrane voltage. Timescales for relaxation may be orders of magnitude faster than companion ion channel variables or phenomena of physiological interest for the entire cell (such as bursting sequences of action potentials) or the entire organ (such as electromechanical coordination). Exploiting these time scales with steady-state approximations for relatively fast-acting systems is a well-known but often overlooked approach as evidenced by recent published models. We thus investigate feasibility of an extensive reduction of order for an HH-type cell model with steady-state approximations to the full dynamical activation and inactivation ion channel variables. Our effort utilises a published comprehensive uterine smooth muscle cell model that encompasses 19 ordinary differential equations and 105 formulations overall. The numerous ion channel submodels in the published model exhibit relaxation times ranging from order 10-1 to 105 milliseconds. Substitution of the faster dynamic variables with steady-state formulations demonstrates both an accurate reproduction of the full model and substantial improvements in time-to-solve, for test cases performed. Our demonstration here of an effective and relatively straightforward reduction method underlines the particular importance of considering time scales for model simplification before embarking on large-scale computations or parameter sweeps. As a preliminary complement to more intensive reduction of order methods such as parameter sensitivity and bifurcation analysis, this approach can rapidly and accurately improve computational tractability for challenging multi-scale organ modelling efforts.
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Affiliation(s)
- Shawn A. Means
- Auckland Bioengineering Institute, University of Auckland, Auckland, New Zealand
| | - Mathias W. Roesler
- Auckland Bioengineering Institute, University of Auckland, Auckland, New Zealand
| | - Amy S. Garrett
- Auckland Bioengineering Institute, University of Auckland, Auckland, New Zealand
| | - Leo Cheng
- Auckland Bioengineering Institute, University of Auckland, Auckland, New Zealand
| | - Alys R. Clark
- Auckland Bioengineering Institute, University of Auckland, Auckland, New Zealand
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3
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Scacchi S, Colli Franzone P, Pavarino LF, Gionti V, Storti C. Epicardial Dispersion of Repolarization Promotes the Onset of Reentry in Brugada Syndrome: A Numerical Simulation Study. Bull Math Biol 2023; 85:22. [PMID: 36790516 PMCID: PMC9931802 DOI: 10.1007/s11538-023-01124-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2022] [Accepted: 01/17/2023] [Indexed: 02/16/2023]
Abstract
The Brugada syndrome (BrS) is a cardiac arrhythmic disorder responsible for sudden cardiac death associated with the onset of ventricular arrhythmias, such as reentrant ventricular tachycardia and fibrillation. The mechanisms which lead to the onset of such electrical disorders in patients affected by BrS are not completely understood, yet. The aim of the present study is to investigate by means of numerical simulations the electrophysiological mechanisms at the basis of the morphology of electrocardiogram (ECG) and the onset of reentry associated with BrS. To this end, we consider the Bidomain equations coupled with the ten Tusscher-Panfilov membrane model, on an idealized wedge of human right ventricular tissue. The results have shown that: (1) epicardial dispersion of repolarization, generated by the coexistence of regions of early and late repolarization, due to different modulation of the [Formula: see text] current, produces ECG waveforms exhibiting qualitatively the typical BrS morphology, characterized by ST elevation and partially negative T-waves; (2) epicardial dispersion of repolarization promotes the onset of reentry during the implementation of the programmed stimulation protocol, because of the conduction block occurring when a premature beat reaches the border of late repolarizing regions; and (3) the modulation of the [Formula: see text] current affects the duration of reentry, which becomes sustained with a remarkable increase of [Formula: see text] in the subepicardial layers.
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Affiliation(s)
- Simone Scacchi
- Dipartimento di Matematica, Università degli Studi di Milano, Via Saldini 50, 20133, Milan, Italy.
| | - Piero Colli Franzone
- Dipartimento di Matematica, Università degli Studi di Pavia, Via Ferrata 1, 27100, Pavia, Italy
| | - Luca F Pavarino
- Dipartimento di Matematica, Università degli Studi di Pavia, Via Ferrata 1, 27100, Pavia, Italy
| | - Vincenzo Gionti
- Istituto di cura Città di Pavia, via Parco Vecchio 27, 27100, Pavia, Italy
| | - Cesare Storti
- Istituto di cura Città di Pavia, via Parco Vecchio 27, 27100, Pavia, Italy
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4
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Garrett AS, Means SA, Roesler MW, Miller KJW, Cheng LK, Clark AR. Modeling and experimental approaches for elucidating multi-scale uterine smooth muscle electro- and mechano-physiology: A review. Front Physiol 2022; 13:1017649. [PMID: 36277190 PMCID: PMC9585314 DOI: 10.3389/fphys.2022.1017649] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2022] [Accepted: 09/21/2022] [Indexed: 11/13/2022] Open
Abstract
The uterus provides protection and nourishment (via its blood supply) to a developing fetus, and contracts to deliver the baby at an appropriate time, thereby having a critical contribution to the life of every human. However, despite this vital role, it is an under-investigated organ, and gaps remain in our understanding of how contractions are initiated or coordinated. The uterus is a smooth muscle organ that undergoes variations in its contractile function in response to hormonal fluctuations, the extreme instance of this being during pregnancy and labor. Researchers typically use various approaches to studying this organ, such as experiments on uterine muscle cells, tissue samples, or the intact organ, or the employment of mathematical models to simulate the electrical, mechanical and ionic activity. The complexity exhibited in the coordinated contractions of the uterus remains a challenge to understand, requiring coordinated solutions from different research fields. This review investigates differences in the underlying physiology between human and common animal models utilized in experiments, and the experimental interventions and computational models used to assess uterine function. We look to a future of hybrid experimental interventions and modeling techniques that could be employed to improve the understanding of the mechanisms enabling the healthy function of the uterus.
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5
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Gionti V, Scacchi S, Colli Franzone P, Pavarino LF, Dore R, Storti C. Role of Scar and Border Zone Geometry on the Genesis and Maintenance of Re-Entrant Ventricular Tachycardia in Patients With Previous Myocardial Infarction. Front Physiol 2022; 13:834747. [PMID: 35399271 PMCID: PMC8989182 DOI: 10.3389/fphys.2022.834747] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2021] [Accepted: 02/21/2022] [Indexed: 11/23/2022] Open
Abstract
In patients with healed myocardial infarction, the left ventricular ejection fraction is characterized by low sensitivity and specificity in the prediction of future malignant arrhythmias. Thus, there is the need for new parameters in daily practice to perform arrhythmic risk stratification. The aim of this study is to identify some features of proarrhythmic geometric configurations of scars and border zones (BZ), by means of numerical simulations based on left ventricular models derived from post myocardial infarction patients. Two patients with similar clinical characteristics were included in this study. Both patients exhibited left ventricular scars characterized by subendo- and subepicardial BZ and a transmural BZ isthmus. The scar of patient #1 was significantly larger than that of patient #2, whereas the transmural BZ isthmus and the subdendo- and subepicardial BZs of patient #2 were thicker than those of patient #1. Patient #1 was positive at electrophysiologic testing, whereas patient #2 was negative. Based on the cardiac magnetic resonance (CMR) data, we developed a geometric model of the left ventricles of the two patients, taking into account the position, extent, and topological features of scars and BZ. The numerical simulations were based on the anisotropic monodomain model of electrocardiology. In the model of patient #1, sustained ventricular tachycardia (VT) was inducible by an S2 stimulus delivered at any of the six stimulation sites considered, while in the model of patient #2 we were not able to induce sustained VT. In the model of patient #1, making the subendo- and subepicardial BZs as thick as those of patient #2 did not affect the inducibility and maintenance of VT. On the other hand, in the model of patient #2, making the subendo- and subepicardial BZs as thin as those of patient #1 yielded sustained VT. In conclusion, the results show that the numerical simulations have an effective predictive capability in discriminating patients at high arrhythmic risk. The extent of the infarct scar and the presence of transmural BZ isthmuses and thin subendo- and subepicardial BZs promote sustained VT.
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Affiliation(s)
- Vincenzo Gionti
- Divisione di Cardiologia, Istituto di Cura Città di Pavia, Pavia, Italy
| | - Simone Scacchi
- Dipartimento di Matematica, Università degli Studi di Milano, Milan, Italy
- *Correspondence: Simone Scacchi
| | | | - Luca F. Pavarino
- Dipartimento di Matematica, Università degli Studi di Pavia, Pavia, Italy
| | - Roberto Dore
- Divisione di Cardiologia, Istituto di Cura Città di Pavia, Pavia, Italy
| | - Cesare Storti
- Divisione di Cardiologia, Istituto di Cura Città di Pavia, Pavia, Italy
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6
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Khan R, Ng KT. Numerical study of POD-Galerkin-DEIM reduced order modeling of cardiac monodomain formulation. Biomed Phys Eng Express 2021; 8. [PMID: 34808611 DOI: 10.1088/2057-1976/ac3c0b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2021] [Accepted: 11/22/2021] [Indexed: 11/11/2022]
Abstract
The three-dimensional cardiac monodomain model with inhomogeneous and anisotropic conductivity characterizes a complicated system that contains spatial and temporal approximation coefficients along with a nonlinear ionic current term. These complexities make its numerical modeling computationally challenging, and therefore, the formation of an efficient computational approximation is important for studying cardiac propagation. In this paper, a reduced order modeling approach has been developed for the simplified cardiac monodomain model, which yields a significant reduction of the full order dynamics of the cardiac tissue, reducing the required computational resources. Additionally, the discrete empirical interpolation technique has been implemented to accurately estimate the nonlinearity of the ionic current of the cardiac monodomain scheme. The proper orthogonal decomposition technique has been utilized, which transforms a given dataset called 'snapshots' to a new coordinate system. The snapshots are computed first from the original system, and they encapsulate all the information observed over both time and parameter variations. Next, the proper orthogonal decomposition provides a reduced order basis for projecting the original solution onto a low-dimensional orthonormal subspace. Finally, a reduced set of unknowns of the forward problem is obtained for which the solution involves significant computational savings compared to that for the original system of unknowns. The efficiency of the model order reduction technique for finite difference solution of cardiac electrophysiology is examined concerning simulation time, error potential, activation time, maximum temporal derivative, and conduction velocity. Numerical results for the monodomain show that its solution time can be reduced by a significant factor, with only 0.474 mV RMS error between the full order and reduced dimensions solution.
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Affiliation(s)
- Riasat Khan
- Department of Electrical and Computer Engineering, North South University, Dhaka, Bangladesh.,Department of Electrical and Computer Engineering, New Mexico State University, NM, United States of America
| | - Kwong T Ng
- Department of Electrical and Computer Engineering, New Mexico State University, NM, United States of America
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7
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Davidović A, Coudière Y, Bourgault Y. Modelling the action potential propagation in a heart with structural heterogeneities: From high-resolution MRI to numerical simulations. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2021; 37:e3322. [PMID: 32052589 DOI: 10.1002/cnm.3322] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/03/2019] [Revised: 01/28/2020] [Accepted: 02/03/2020] [Indexed: 06/10/2023]
Abstract
Mathematical modelling and numerical simulation in cardiac electrophysiology have already been studied extensively. However, there is a clear lack of techniques and methodologies for studying the propagation of action potential in a heart with structural defects. In this article, we present a modified version of the bidomain model, derived using homogenisation techniques with the assumption of existence of diffusive inclusions in the cardiac tissue. The diffusive inclusions represent regions without electrically active myocytes, for example, fat, fibrosis, and so forth. We present an application of this model to a rat heart. Starting from high-resolution MRI, the geometry of the heart is built and meshed using image processing techniques. We perform a study of the effects of tissue heterogeneities induced by diffusive inclusions on the velocity and shape of the depolarisation wavefront. We present several test cases with different geometries of diffusive inclusions. We reach the conclusion that the conduction velocity is not affected in the best cases, while it is affected by up to 76% in the worst case scenario. Additionally, the shape of the wavefront was affected in some cases.
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Affiliation(s)
- Anđela Davidović
- Carmen Team, Inria Bordeaux-Sud-Ouest, Bordeaux, France
- Calcul scientifique et Modélisation, Institut de Mathématiques de Bordeaux, CNRS UMR 5251, Université de Bordeaux, Bordeaux, France
- L'Institut de RYthmologie et Modélisation Cardiaque-LIRYC, Bordeaux, France
- Department of Computational Biology, CNRS USR 3756, Institut Pasteur, Paris, France
| | - Yves Coudière
- Carmen Team, Inria Bordeaux-Sud-Ouest, Bordeaux, France
- Calcul scientifique et Modélisation, Institut de Mathématiques de Bordeaux, CNRS UMR 5251, Université de Bordeaux, Bordeaux, France
- L'Institut de RYthmologie et Modélisation Cardiaque-LIRYC, Bordeaux, France
| | - Yves Bourgault
- Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario, Canada
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8
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Fresca S, Manzoni A, Dedè L, Quarteroni A. POD-Enhanced Deep Learning-Based Reduced Order Models for the Real-Time Simulation of Cardiac Electrophysiology in the Left Atrium. Front Physiol 2021; 12:679076. [PMID: 34630131 PMCID: PMC8493298 DOI: 10.3389/fphys.2021.679076] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2021] [Accepted: 08/10/2021] [Indexed: 12/22/2022] Open
Abstract
The numerical simulation of multiple scenarios easily becomes computationally prohibitive for cardiac electrophysiology (EP) problems if relying on usual high-fidelity, full order models (FOMs). Likewise, the use of traditional reduced order models (ROMs) for parametrized PDEs to speed up the solution of the aforementioned problems can be problematic. This is primarily due to the strong variability characterizing the solution set and to the nonlinear nature of the input-output maps that we intend to reconstruct numerically. To enhance ROM efficiency, we proposed a new generation of non-intrusive, nonlinear ROMs, based on deep learning (DL) algorithms, such as convolutional, feedforward, and autoencoder neural networks. In the proposed DL-ROM, both the nonlinear solution manifold and the nonlinear reduced dynamics used to model the system evolution on that manifold can be learnt in a non-intrusive way thanks to DL algorithms trained on a set of FOM snapshots. DL-ROMs were shown to be able to accurately capture complex front propagation processes, both in physiological and pathological cardiac EP, very rapidly once neural networks were trained, however, at the expense of huge training costs. In this study, we show that performing a prior dimensionality reduction on FOM snapshots through randomized proper orthogonal decomposition (POD) enables to speed up training times and to decrease networks complexity. Accuracy and efficiency of this strategy, which we refer to as POD-DL-ROM, are assessed in the context of cardiac EP on an idealized left atrium (LA) geometry and considering snapshots arising from a NURBS (non-uniform rational B-splines)-based isogeometric analysis (IGA) discretization. Once the ROMs have been trained, POD-DL-ROMs can efficiently solve both physiological and pathological cardiac EP problems, for any new scenario, in real-time, even in extremely challenging contexts such as those featuring circuit re-entries, that are among the factors triggering cardiac arrhythmias.
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Affiliation(s)
- Stefania Fresca
- MOX, Dipartimento di Matematica, Politecnico di Milano, Milan, Italy
| | - Andrea Manzoni
- MOX, Dipartimento di Matematica, Politecnico di Milano, Milan, Italy
| | - Luca Dedè
- MOX, Dipartimento di Matematica, Politecnico di Milano, Milan, Italy
| | - Alfio Quarteroni
- MOX, Dipartimento di Matematica, Politecnico di Milano, Milan, Italy.,Mathematics Institute, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
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9
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Pagani S, Dede' L, Frontera A, Salvador M, Limite LR, Manzoni A, Lipartiti F, Tsitsinakis G, Hadjis A, Della Bella P, Quarteroni A. A Computational Study of the Electrophysiological Substrate in Patients Suffering From Atrial Fibrillation. Front Physiol 2021; 12:673612. [PMID: 34305637 PMCID: PMC8297688 DOI: 10.3389/fphys.2021.673612] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2021] [Accepted: 05/28/2021] [Indexed: 12/19/2022] Open
Abstract
In the context of cardiac electrophysiology, we propose a novel computational approach to highlight and explain the long-debated mechanisms behind atrial fibrillation (AF) and to reliably numerically predict its induction and sustainment. A key role is played, in this respect, by a new way of setting a parametrization of electrophysiological mathematical models based on conduction velocities; these latter are estimated from high-density mapping data, which provide a detailed characterization of patients' electrophysiological substrate during sinus rhythm. We integrate numerically approximated conduction velocities into a mathematical model consisting of a coupled system of partial and ordinary differential equations, formed by the monodomain equation and the Courtemanche-Ramirez-Nattel model. Our new model parametrization is then adopted to predict the formation and self-sustainment of localized reentries characterizing atrial fibrillation, by numerically simulating the onset of ectopic beats from the pulmonary veins. We investigate the paroxysmal and the persistent form of AF starting from electro-anatomical maps of two patients. The model's response to stimulation shows how substrate characteristics play a key role in inducing and sustaining these arrhythmias. Localized reentries are less frequent and less stable in case of paroxysmal AF, while they tend to anchor themselves in areas affected by severe slow conduction in case of persistent AF.
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Affiliation(s)
- S Pagani
- MOX-Department of Mathematics, Politecnico di Milano, Milan, Italy
| | - L Dede'
- MOX-Department of Mathematics, Politecnico di Milano, Milan, Italy
| | - A Frontera
- Department of Arrhythmology, San Raffaele Hospital, Milan, Italy
| | - M Salvador
- MOX-Department of Mathematics, Politecnico di Milano, Milan, Italy
| | - L R Limite
- Department of Arrhythmology, San Raffaele Hospital, Milan, Italy
| | - A Manzoni
- MOX-Department of Mathematics, Politecnico di Milano, Milan, Italy
| | - F Lipartiti
- Department of Arrhythmology, San Raffaele Hospital, Milan, Italy
| | - G Tsitsinakis
- Department of Arrhythmology, San Raffaele Hospital, Milan, Italy
| | - A Hadjis
- Department of Arrhythmology, San Raffaele Hospital, Milan, Italy
| | - P Della Bella
- Department of Arrhythmology, San Raffaele Hospital, Milan, Italy
| | - A Quarteroni
- MOX-Department of Mathematics, Politecnico di Milano, Milan, Italy.,Institute of Mathematics, EPFL, Lausanne, Switzerland
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Pagani S, Manzoni A. Enabling forward uncertainty quantification and sensitivity analysis in cardiac electrophysiology by reduced order modeling and machine learning. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2021; 37:e3450. [PMID: 33599106 PMCID: PMC8244126 DOI: 10.1002/cnm.3450] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Revised: 02/05/2021] [Accepted: 02/07/2021] [Indexed: 06/12/2023]
Abstract
We present a new, computationally efficient framework to perform forward uncertainty quantification (UQ) in cardiac electrophysiology. We consider the monodomain model to describe the electrical activity in the cardiac tissue, coupled with the Aliev-Panfilov model to characterize the ionic activity through the cell membrane. We address a complete forward UQ pipeline, including both: (i) a variance-based global sensitivity analysis for the selection of the most relevant input parameters, and (ii) a way to perform uncertainty propagation to investigate the impact of intra-subject variability on outputs of interest depending on the cardiac potential. Both tasks exploit stochastic sampling techniques, thus implying overwhelming computational costs because of the huge amount of queries to the high-fidelity, full-order computational model obtained by approximating the coupled monodomain/Aliev-Panfilov system through the finite element method. To mitigate this computational burden, we replace the full-order model with computationally inexpensive projection-based reduced-order models (ROMs) aimed at reducing the state-space dimensionality. Resulting approximation errors on the outputs of interest are finally taken into account through artificial neural network (ANN)-based models, enhancing the accuracy of the whole UQ pipeline. Numerical results show that the proposed physics-based ROMs outperform regression-based emulators relying on ANNs built with the same amount of training data, in terms of both numerical accuracy and overall computational efficiency.
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Affiliation(s)
- Stefano Pagani
- MOX, Dipartimento di MatematicaPolitecnico di MilanoMilanItaly
| | - Andrea Manzoni
- MOX, Dipartimento di MatematicaPolitecnico di MilanoMilanItaly
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11
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On the Role of Ionic Modeling on the Signature of Cardiac Arrhythmias for Healthy and Diseased Hearts. MATHEMATICS 2020. [DOI: 10.3390/math8122242] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Abstract
Computational cardiology is rapidly becoming the gold standard for innovative medical treatments and device development. Despite a worldwide effort in mathematical and computational modeling research, the complexity and intrinsic multiscale nature of the heart still limit our predictability power raising the question of the optimal modeling choice for large-scale whole-heart numerical investigations. We propose an extended numerical analysis among two different electrophysiological modeling approaches: a simplified phenomenological one and a detailed biophysical one. To achieve this, we considered three-dimensional healthy and infarcted swine heart geometries. Heterogeneous electrophysiological properties, fine-tuned DT-MRI -based anisotropy features, and non-conductive ischemic regions were included in a custom-built finite element code. We provide a quantitative comparison of the electrical behaviors during steady pacing and sustained ventricular fibrillation for healthy and diseased cases analyzing cardiac arrhythmias dynamics. Action potential duration (APD) restitution distributions, vortex filament counting, and pseudo-electrocardiography (ECG) signals were numerically quantified, introducing a novel statistical description of restitution patterns and ventricular fibrillation sustainability. Computational cost and scalability associated with the two modeling choices suggests that ventricular fibrillation signatures are mainly controlled by anatomy and structural parameters, rather than by regional restitution properties. Finally, we discuss limitations and translational perspectives of the different modeling approaches in view of large-scale whole-heart in silico studies.
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12
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Integration of activation maps of epicardial veins in computational cardiac electrophysiology. Comput Biol Med 2020; 127:104047. [PMID: 33099220 DOI: 10.1016/j.compbiomed.2020.104047] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2020] [Revised: 10/06/2020] [Accepted: 10/06/2020] [Indexed: 12/16/2022]
Abstract
In this work we address the issue of validating the monodomain equation used in combination with the Bueno-Orovio ionic model for the prediction of the activation times in cardiac electro-physiology of the left ventricle. To this aim, we consider four patients who suffered from Left Bundle Branch Block (LBBB). We use activation maps performed at the septum as input data for the model and maps at the epicardial veins for the validation. In particular, a first set (half) of the latter are used to estimate the conductivities of the patient and a second set (the remaining half) to compute the errors of the numerical simulations. We find an excellent agreement between measures and numerical results. Our validated computational tool could be used to accurately predict activation times at the epicardial veins with a short mapping, i.e. by using only a part (the most proximal) of the standard acquisition points, thus reducing the invasive procedure and exposure to radiation.
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14
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Modeling and simulation of cardiac electric activity in a human cardiac tissue with multiple ischemic zones. J Math Biol 2019; 79:1551-1586. [PMID: 31352562 DOI: 10.1007/s00285-019-01403-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2018] [Revised: 04/03/2019] [Indexed: 10/26/2022]
Abstract
In this work, a human ventricular model (ten Tusscher and Panfilov model) coupled with the tissue level monodomain model is used to analyze the influence of multiple myocardial ischemia on the human cardiac tissue. The existence and uniqueness of the ischemic model comprising the monodomain model with a discontinuous ionic model for the human cardiac tissue is discussed. The coupled system of partial differential equation and ordinary differential equations are solved numerically using [Formula: see text] finite elements in space and Backward Euler finite difference scheme in time. The apriori finite element error estimate for the numerical scheme has been shown to be of [Formula: see text]. Essentially, we evaluate the impact of the increasing size of the ischemic region and the presence of the multiple ischemic regions having equal or different intensities on the neighboring healthy part of the cardiac tissue. We examine both the individual and the combined influence of two types of ischemia, Hyperkalemia (with the variation of the extracellular potassium ion concentration, [Formula: see text]) and Hypoxia (with the variation of intracellular Adenosine triphosphate (ATP) concentration via parameter [Formula: see text]) on the cardiac electrical activity of cardiac tissue. We observe that with the increase in the ischemic region size by a factor five times, there is an additional almost 10% drop in the action potential duration (APD) in the neighboring healthy regions. The combined effect of Hyperkalemia and Hypoxia brings an additional 12% drop in APD in the ischemic subregions and an additional 5% drop in APD in the neighboring healthy part of the cardic tissue in comparison to the only Hyperkalemic ischemia. When the Hyperkalemic and/or Hypoxic degeneracy of a ischemic zone is non-uniform then innercore degeneracy has greater influence on resting potential and APD of outercore of variable intensity ischemic zone than the other way. Also, increasing the number of ischemic subregions from 2 to 4 leads to a 4% drop in APD.
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Abstract
BACKGROUND This study estimates atrial repolarization activities (Ta waves), which are typically hidden most of the time from body surface electrocardiography when diagnosing cardiovascular diseases. The morphology of Ta waves has been proven to be an important marker for the early sign of inferior injury, such as acute atrial infarction, or arrhythmia, such as atrial fibrillation. However, Ta waves are usually unseen except during conduction system malfunction, such as long QT interval or atrioventricular block. Therefore, justifying heart diseases based on atrial repolarization becomes impossible in sinus rhythm. METHODS We obtain TMPs in the atrial part of the myocardium which reflects the correct excitation sequence starting from the atrium to the end of the apex. RESULTS The resulting TMP shows the hidden atrial part of ECG waves. CONCLUSIONS This extraction makes many diseases, such as acute atrial infarction or arrhythmia, become easily diagnosed.
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Affiliation(s)
- Wei-Hua Tang
- Division of Cardiology, Department of Internal Medicine, National Yang-Ming University Hospital, Yilan, Taiwan
| | - Wen-Hsien Ho
- Department of Healthcare Administration and Medical Informatics, Kaohsiung Medical University, 100 Shin-Chuan 1st Road, Kaohsiung, 807, Taiwan. .,Department of Medical Research, Kaohsiung Medical University Hospital, Kaohsiung, Taiwan.
| | - Yenming J Chen
- Department of Logistics Management, National Kaohsiung University of Science and Technology, 1 University Road, Yenchao, Kaohsiung, 824, Taiwan.
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Janssen AM, Potyagaylo D, Dössel O, Oostendorp TF. Assessment of the equivalent dipole layer source model in the reconstruction of cardiac activation times on the basis of BSPMs produced by an anisotropic model of the heart. Med Biol Eng Comput 2018. [PMID: 29130137 DOI: 10.1007/sll517-017-1715-x] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/16/2023]
Abstract
Promising results have been reported in noninvasive estimation of cardiac activation times (AT) using the equivalent dipole layer (EDL) source model in combination with the boundary element method (BEM). However, the assumption of equal anisotropy ratios in the heart that underlies the EDL model does not reflect reality. In the present study, we quantify the errors of the nonlinear AT imaging based on the EDL approximation. Nine different excitation patterns (sinus rhythm and eight ectopic beats) were simulated with the monodomain model. Based on the bidomain theory, the body surface potential maps (BSPMs) were calculated for a realistic finite element volume conductor with an anisotropic heart model. For the forward calculations, three cases of bidomain conductivity tensors in the heart were considered: isotropic, equal, and unequal anisotropy ratios in the intra- and extracellular spaces. In all inverse reconstructions, the EDL model with BEM was employed: AT were estimated by solving the nonlinear optimization problem with the initial guess provided by the fastest route algorithm. Expectedly, the case of unequal anisotropy ratios resulted in larger localization errors for almost all considered activation patterns. For the sinus rhythm, all sites of early activation were correctly estimated with an optimal regularization parameter being used. For the ectopic beats, all but one foci were correctly classified to have either endo- or epicardial origin with an average localization error of 20.4 mm for unequal anisotropy ratio. The obtained results confirm validation studies and suggest that cardiac anisotropy might be neglected in clinical applications of the considered EDL-based inverse procedure.
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Affiliation(s)
- Arno M Janssen
- The Netherlands Heart Institute, Utrecht, The Netherlands
- The Donders Institute for Brain, Cognition and Behaviour, Radboud University Medical Centre, Nijmegen, The Netherlands
| | - Danila Potyagaylo
- The Institute of Biomedical Engineering, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany.
| | - Olaf Dössel
- The Institute of Biomedical Engineering, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
| | - Thom F Oostendorp
- The Netherlands Heart Institute, Utrecht, The Netherlands
- The Donders Institute for Brain, Cognition and Behaviour, Radboud University Medical Centre, Nijmegen, The Netherlands
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Janssen AM, Potyagaylo D, Dössel O, Oostendorp TF. Assessment of the equivalent dipole layer source model in the reconstruction of cardiac activation times on the basis of BSPMs produced by an anisotropic model of the heart. Med Biol Eng Comput 2017; 56:1013-1025. [PMID: 29130137 PMCID: PMC5978848 DOI: 10.1007/s11517-017-1715-x] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2016] [Accepted: 08/17/2017] [Indexed: 12/25/2022]
Abstract
Promising results have been reported in noninvasive estimation of cardiac activation times (AT) using the equivalent dipole layer (EDL) source model in combination with the boundary element method (BEM). However, the assumption of equal anisotropy ratios in the heart that underlies the EDL model does not reflect reality. In the present study, we quantify the errors of the nonlinear AT imaging based on the EDL approximation. Nine different excitation patterns (sinus rhythm and eight ectopic beats) were simulated with the monodomain model. Based on the bidomain theory, the body surface potential maps (BSPMs) were calculated for a realistic finite element volume conductor with an anisotropic heart model. For the forward calculations, three cases of bidomain conductivity tensors in the heart were considered: isotropic, equal, and unequal anisotropy ratios in the intra- and extracellular spaces. In all inverse reconstructions, the EDL model with BEM was employed: AT were estimated by solving the nonlinear optimization problem with the initial guess provided by the fastest route algorithm. Expectedly, the case of unequal anisotropy ratios resulted in larger localization errors for almost all considered activation patterns. For the sinus rhythm, all sites of early activation were correctly estimated with an optimal regularization parameter being used. For the ectopic beats, all but one foci were correctly classified to have either endo- or epicardial origin with an average localization error of 20.4 mm for unequal anisotropy ratio. The obtained results confirm validation studies and suggest that cardiac anisotropy might be neglected in clinical applications of the considered EDL-based inverse procedure.
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Affiliation(s)
- Arno M Janssen
- The Netherlands Heart Institute, Utrecht, The Netherlands.,The Donders Institute for Brain, Cognition and Behaviour, Radboud University Medical Centre, Nijmegen, The Netherlands
| | - Danila Potyagaylo
- The Institute of Biomedical Engineering, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany.
| | - Olaf Dössel
- The Institute of Biomedical Engineering, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
| | - Thom F Oostendorp
- The Netherlands Heart Institute, Utrecht, The Netherlands.,The Donders Institute for Brain, Cognition and Behaviour, Radboud University Medical Centre, Nijmegen, The Netherlands
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Barone A, Fenton F, Veneziani A. Numerical sensitivity analysis of a variational data assimilation procedure for cardiac conductivities. CHAOS (WOODBURY, N.Y.) 2017; 27:093930. [PMID: 28964111 DOI: 10.1063/1.5001454] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
An accurate estimation of cardiac conductivities is critical in computational electro-cardiology, yet experimental results in the literature significantly disagree on the values and ratios between longitudinal and tangential coefficients. These are known to have a strong impact on the propagation of potential particularly during defibrillation shocks. Data assimilation is a procedure for merging experimental data and numerical simulations in a rigorous way. In particular, variational data assimilation relies on the least-square minimization of the misfit between simulations and experiments, constrained by the underlying mathematical model, which in this study is represented by the classical Bidomain system, or its common simplification given by the Monodomain problem. Operating on the conductivity tensors as control variables of the minimization, we obtain a parameter estimation procedure. As the theory of this approach currently provides only an existence proof and it is not informative for practical experiments, we present here an extensive numerical simulation campaign to assess practical critical issues such as the size and the location of the measurement sites needed for in silico test cases of potential experimental and realistic settings. This will be finalized with a real validation of the variational data assimilation procedure. Results indicate the presence of lower and upper bounds for the number of sites which guarantee an accurate and minimally redundant parameter estimation, the location of sites being generally non critical for properly designed experiments. An effective combination of parameter estimation based on the Monodomain and Bidomain models is tested for the sake of computational efficiency. Parameter estimation based on the Monodomain equation potentially leads to the accurate computation of the transmembrane potential in real settings.
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Affiliation(s)
- Alessandro Barone
- Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia 30322, USA
| | - Flavio Fenton
- Department of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - Alessandro Veneziani
- Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia, USA; School of Advanced Studies IUSS, Pavia, Italy
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BeatBox-HPC simulation environment for biophysically and anatomically realistic cardiac electrophysiology. PLoS One 2017; 12:e0172292. [PMID: 28467407 PMCID: PMC5415003 DOI: 10.1371/journal.pone.0172292] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2016] [Accepted: 02/02/2017] [Indexed: 01/16/2023] Open
Abstract
The BeatBox simulation environment combines flexible script language user interface with the robust computational tools, in order to setup cardiac electrophysiology in-silico experiments without re-coding at low-level, so that cell excitation, tissue/anatomy models, stimulation protocols may be included into a BeatBox script, and simulation run either sequentially or in parallel (MPI) without re-compilation. BeatBox is a free software written in C language to be run on a Unix-based platform. It provides the whole spectrum of multi scale tissue modelling from 0-dimensional individual cell simulation, 1-dimensional fibre, 2-dimensional sheet and 3-dimensional slab of tissue, up to anatomically realistic whole heart simulations, with run time measurements including cardiac re-entry tip/filament tracing, ECG, local/global samples of any variables, etc. BeatBox solvers, cell, and tissue/anatomy models repositories are extended via robust and flexible interfaces, thus providing an open framework for new developments in the field. In this paper we give an overview of the BeatBox current state, together with a description of the main computational methods and MPI parallelisation approaches.
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CALDWELL BRYANJ, TREW MARKL, LEGRICE IANJ, SMAILL BRUCEH. Development of 3-D Intramural and Surface Potentials in the LV: Microstructural Basis of Preferential Transmural Conduction. J Cardiovasc Electrophysiol 2017; 28:692-701. [DOI: 10.1111/jce.13207] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 11/13/2016] [Revised: 02/27/2017] [Accepted: 03/13/2017] [Indexed: 11/29/2022]
Affiliation(s)
- BRYAN J. CALDWELL
- Auckland Bioengineering Institute; The University of Auckland; New Zealand
| | - MARK L. TREW
- Auckland Bioengineering Institute; The University of Auckland; New Zealand
| | - IAN J. LEGRICE
- Auckland Bioengineering Institute; The University of Auckland; New Zealand
- Department of Physiology; The University of Auckland; New Zealand
| | - BRUCE H. SMAILL
- Auckland Bioengineering Institute; The University of Auckland; New Zealand
- Department of Physiology; The University of Auckland; New Zealand
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Aswath Kumar AK, Drahi A, Jacquemet V. Fitting local repolarization parameters in cardiac reaction-diffusion models in the presence of electrotonic coupling. Comput Biol Med 2016; 81:55-63. [PMID: 28012295 DOI: 10.1016/j.compbiomed.2016.12.008] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2016] [Revised: 11/15/2016] [Accepted: 12/14/2016] [Indexed: 10/20/2022]
Abstract
BACKGROUND Repolarization gradients contribute to arrhythmogenicity. In reaction-diffusion models of cardiac tissue, heterogeneities in action potential duration (APD) can be created by locally modifying an intrinsic membrane kinetics parameter. Electrotonic coupling, however, acts as a confounding factor that modulates APD dispersion. METHOD We developed an algorithm based on a quasi-Newton method that iteratively adjusts the spatial distribution of a membrane parameter to reproduce a pre-defined target APD map in a coupled tissue. The method assumes that the relation between the adjustable parameter and APD is bijective in an isolated cell. Each iteration of the algorithm involved simulating the cardiac reaction-diffusion system with the updated parameter profile for one beat and extracting the APD map. The algorithm was extended to simultaneous estimation of two parameter profiles based on two APD maps at different repolarization thresholds. RESULTS The method was validated in 1D, 2D and 3D atrial tissues using synthetic target APD maps with controllable total variation and maximum APD gradient. The adjustable parameter was local acetylcholine concentration. The iterations converged provided that APD gradients were not too steep. Convergence was found to be faster 2-5 iterations) when the maximal gradient was less steep, when APD range was smaller and when tissue conductivity was reduced. CONCLUSION This algorithm provides a tool to automatically generate arrhythmogenic substrates with controllable repolarization gradients and possibly incorporate experimental APD maps into computer models.
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Affiliation(s)
- Akshay Kota Aswath Kumar
- Université de Montréal, Département de Pharmacologie et Physiologie , Institut de Génie Biomédical, Montréal, Canada; Hôpital du Sacré-Coeur de Montréal, Centre de Recherche, Montréal, Canada
| | - Angelina Drahi
- Université de Montréal, Département de Pharmacologie et Physiologie , Institut de Génie Biomédical, Montréal, Canada; Hôpital du Sacré-Coeur de Montréal, Centre de Recherche, Montréal, Canada
| | - Vincent Jacquemet
- Université de Montréal, Département de Pharmacologie et Physiologie , Institut de Génie Biomédical, Montréal, Canada; Hôpital du Sacré-Coeur de Montréal, Centre de Recherche, Montréal, Canada.
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Adeniran I, MacIver DH, Garratt CJ, Ye J, Hancox JC, Zhang H. Effects of Persistent Atrial Fibrillation-Induced Electrical Remodeling on Atrial Electro-Mechanics - Insights from a 3D Model of the Human Atria. PLoS One 2015; 10:e0142397. [PMID: 26606047 PMCID: PMC4659575 DOI: 10.1371/journal.pone.0142397] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2015] [Accepted: 10/21/2015] [Indexed: 11/28/2022] Open
Abstract
Aims Atrial stunning, a loss of atrial mechanical contraction, can occur following a successful cardioversion. It is hypothesized that persistent atrial fibrillation-induced electrical remodeling (AFER) on atrial electrophysiology may be responsible for such impaired atrial mechanics. This simulation study aimed to investigate the effects of AFER on atrial electro-mechanics. Methods and Results A 3D electromechanical model of the human atria was developed to investigate the effects of AFER on atrial electro-mechanics. Simulations were carried out in 3 conditions for 4 states: (i) the control condition, representing the normal tissue (state 1) and the tissue 2–3 months after cardioversion (state 2) when the atrial tissue recovers its electrophysiological properties after completion of reverse electrophysiological remodelling; (ii) AFER-SR condition for AF-remodeled tissue with normal sinus rhythm (SR) (state 3); and (iii) AFER-AF condition for AF-remodeled tissue with re-entrant excitation waves (state 4). Our results indicate that at the cellular level, AFER (states 3 & 4) abbreviated action potentials and reduced the Ca2+ content in the sarcoplasmic reticulum, resulting in a reduced amplitude of the intracellular Ca2+ transient leading to decreased cell active force and cell shortening as compared to the control condition (states 1 & 2). Consequently at the whole organ level, atrial contraction in AFER-SR condition (state 3) was dramatically reduced. In the AFER-AF condition (state 4) atrial contraction was almost abolished. Conclusions This study provides novel insights into understanding atrial electro-mechanics illustrating that AFER impairs atrial contraction due to reduced intracellular Ca2+ transients.
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Affiliation(s)
- Ismail Adeniran
- Biological Physics Group, School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom
| | - David H. MacIver
- Biological Physics Group, School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom
- Taunton & Somerset Hospital, Somerset, United Kingdom
| | - Clifford J. Garratt
- Manchester Heart Centre, Manchester Royal Infirmary, Manchester, United Kingdom
| | - Jianqiao Ye
- Department of Engineering, Lancaster University, Lancaster, United Kingdom
| | - Jules C. Hancox
- Biological Physics Group, School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom
- School of Physiology and Pharmacology, and Cardiovascular Research Laboratories, University of Bristol, Bristol, United Kingdom
| | - Henggui Zhang
- Biological Physics Group, School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom
- * E-mail:
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Simulating Cardiac Electrophysiology Using Unstructured All-Hexahedra Spectral Elements. BIOMED RESEARCH INTERNATIONAL 2015; 2015:473279. [PMID: 26583112 PMCID: PMC4637157 DOI: 10.1155/2015/473279] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/14/2014] [Revised: 03/20/2015] [Accepted: 04/09/2015] [Indexed: 11/17/2022]
Abstract
We discuss the application of the spectral element method to the monodomain and bidomain equations describing propagation of cardiac action potential. Models of cardiac electrophysiology consist of a system of partial differential equations coupled with a system of ordinary differential equations representing cell membrane dynamics. The solution of these equations requires solving multiple length scales due to the ratio of advection to diffusion that varies among the different equations. High order approximation of spectral elements provides greater flexibility in resolving multiple length scales. Furthermore, spectral elements are extremely efficient to model propagation phenomena on complex shapes using fewer degrees of freedom than its finite element equivalent (for the same level of accuracy). We illustrate a fully unstructured all-hexahedra approach implementation of the method and we apply it to the solution of full 3D monodomain and bidomain test cases. We discuss some key elements of the proposed approach on some selected benchmarks and on an anatomically based whole heart human computational model.
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LU WEIGANG, LI JIE, YANG FEI, LUO CUNJIN, WANG KUANQUAN, ADENIRAN ISMAIL, ZHANG HENGGUI. EFFECTS OF ACUTE GLOBAL ISCHEMIA ON RE-ENTRANT ARRHYTHMOGENESIS: A SIMULATION STUDY. J BIOL SYST 2015. [DOI: 10.1142/s0218339015500114] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Sudden cardiac death is mainly caused by arrhythmogenesis. For a functional abnormal heart, such as an ischemic heart, the probability of arrhythmia occurring is greatly increased. During myocardial ischemia, re-entry is prone to degenerate into ventricular fibrillation (VF). Therefore it has important meaning to investigate the intricate mechanisms underlying VF under an ischemic condition in order to better facilitate therapeutic interventions. In this paper, to analyze the functional influence of acute global ischemia on cardiac electrical activity and subsequently on re-entrant arrhythmogenesis, we take into account three main pathophysiological consequences of ischemia: hyperkalaemia, acidosis, and anoxia, and develop a 3D human ventricular ischemic model that combines a detailed biophysical description of the excitation kinetics of human ventricular cells with an integrated geometry of human ventricular tissue which incorporates fiber direction anisotropy and the stimulation activation sequence. The results show that under acute global ischemia, the tissue excitability and the slope of ventricular cellular action potential duration restitution (APDR) are greatly decreased. As a result, the complexity of VF activation patterns is reduced. For the three components of ischemia, hyperkalaemia is the dominant contributor to the stability of re-entry under acute global ischemia. Increasing [K+]o acts to prolong the cell refractory period, reduce the tissue excitability and slow the conduction velocity. Our results also show that VF can be eliminated by decreasing cellular excitability, primarily by elevating the concentration value of extracellular K+.
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Affiliation(s)
- WEIGANG LU
- Department of Educational Technology, Ocean University of China, Qingdao, P. R. China
| | - JIE LI
- School of Electrical Engineering, Yanshan University, Qinhuangdao, P. R. China
| | - FEI YANG
- School of Mechanical, Electrical & Information Engineering, Shandong University, Weihai, P. R. China
| | - CUNJIN LUO
- School of Computer Science and Technology, Harbin Institute of Technology, Harbin, P. R. China
| | - KUANQUAN WANG
- School of Computer Science and Technology, Harbin Institute of Technology, Harbin, P. R. China
| | - ISMAIL ADENIRAN
- School of Physics and Astronomy, University of Manchester, Manchester, UK
| | - HENGGUI ZHANG
- School of Physics and Astronomy, University of Manchester, Manchester, UK
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Calvetti D, Cheng Y, Somersalo E. A spatially distributed computational model of brain cellular metabolism. J Theor Biol 2015; 376:48-65. [PMID: 25863266 DOI: 10.1016/j.jtbi.2015.03.037] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/26/2014] [Revised: 03/06/2015] [Accepted: 03/31/2015] [Indexed: 11/29/2022]
Abstract
This paper develops a three-dimensional spatially distributed model of brain cellular metabolism and investigates how the locus of the synaptic activity in reference to the capillaries and diffusion affects the behavior of the model, a type of analysis which is impossible to carry out in spatially lumped models, which are shown to be consistent spatially averaged approximations of the distributed model. To avoid a geometrically detailed modeling of the complex structure of the tissue consisting of different cell types and the extracellular space, the distributed model is based on a novel multi-domain formulation of reaction-diffusion equations, accounting also for separate mitochondria. The model reduction relating the spatially distributed model and lower dimensional reduced models, including the well-mixed spatially lumped compartment model, is carefully explained. We illustrate the effects of losing the spatial resolution with a computed example which is based on a reduced one-dimensional distributed radial model, and look into how the model behaves when the locus of the synaptic activity in reference to the capillaries is changed. By averaging the fluxes and concentrations in the distributed radial model to correspond to quantities in a lumped model, and further by estimating the parameters in the lumped, we conclude that varying the locus of the synaptic activity in reference to the capillaries alters significantly the lumped model parameters. This observation seems to be consequential for parameter estimation procedures from data when the spatial resolution is insufficient to determine the locus of the activity, indicating that the model uncertainty is an inherent feature of lumped models.
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Affiliation(s)
- Daniela Calvetti
- Department of Mathematics, Applied Mathematics and Statistics, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, OH 44106, United States of America.
| | - Yougan Cheng
- Department of Mathematics, Applied Mathematics and Statistics, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, OH 44106, United States of America.
| | - Erkki Somersalo
- Department of Mathematics, Applied Mathematics and Statistics, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, OH 44106, United States of America.
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Adeniran I, MacIver DH, Hancox JC, Zhang H. Abnormal calcium homeostasis in heart failure with preserved ejection fraction is related to both reduced contractile function and incomplete relaxation: an electromechanically detailed biophysical modeling study. Front Physiol 2015; 6:78. [PMID: 25852567 PMCID: PMC4367530 DOI: 10.3389/fphys.2015.00078] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2014] [Accepted: 02/26/2015] [Indexed: 01/08/2023] Open
Abstract
Heart failure with preserved ejection fraction (HFpEF) accounts for about 50% of heart failure cases. It has features of incomplete relaxation and increased stiffness of the left ventricle. Studies from clinical electrophysiology and animal experiments have found that HFpEF is associated with impaired calcium homeostasis, ion channel remodeling and concentric left ventricle hypertrophy (LVH). However, it is still unclear how the abnormal calcium homeostasis, ion channel and structural remodeling affect the electro-mechanical dynamics of the ventricles. In this study we have developed multiscale models of the human left ventricle from single cells to the 3D organ, which take into consideration HFpEF-induced changes in calcium handling, ion channel remodeling and concentric LVH. Our simulation results suggest that at the cellular level, HFpEF reduces the systolic calcium level resulting in a reduced systolic contractile force, but elevates the diastolic calcium level resulting in an abnormal residual diastolic force. In our simulations, these abnormal electro-mechanical features of the ventricular cells became more pronounced with the increase of the heart rate. However, at the 3D organ level, the ejection fraction of the left ventricle was maintained due to the concentric LVH. The simulation results of this study mirror clinically observed features of HFpEF and provide new insights toward the understanding of the cellular bases of impaired cardiac electromechanical functions in heart failure.
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Affiliation(s)
- Ismail Adeniran
- Biological Physics Group, School of Physics and Astronomy, The University of Manchester Manchester, UK
| | - David H MacIver
- Biological Physics Group, School of Physics and Astronomy, The University of Manchester Manchester, UK ; Department of Cardiology, Taunton and Somerset Hospital Musgrove Park, Taunton, UK
| | - Jules C Hancox
- Biological Physics Group, School of Physics and Astronomy, The University of Manchester Manchester, UK ; School of Physiology and Pharmacology and Cardiovascular Research Laboratories, School of Medical Sciences Bristol, UK
| | - Henggui Zhang
- Biological Physics Group, School of Physics and Astronomy, The University of Manchester Manchester, UK ; School of Computer Science and Technology, Harbin Institute of Technology Harbin, China
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Eriksson TSE, Prassl AJ, Plank G, Holzapfel GA. Modeling the dispersion in electromechanically coupled myocardium. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2013; 29:1267-84. [PMID: 23868817 PMCID: PMC3970090 DOI: 10.1002/cnm.2575] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2012] [Revised: 05/08/2013] [Accepted: 06/06/2013] [Indexed: 05/05/2023]
Abstract
We present an approach to model the dispersion of fiber and sheet orientations in the myocardium. By utilizing structure parameters, an existing orthotropic and invariant-based constitutive model developed to describe the passive behavior of the myocardium is augmented. Two dispersion parameters are fitted to experimentally observed angular dispersion data of the myocardial tissue. Computations are performed on a unit myocardium tissue cube and on a slice of the left ventricle indicating that the dispersion parameter has an effect on the myocardial deformation and stress development. The use of fiber dispersions relating to a pathological myocardium had a rather big effect. The final example represents an ellipsoidal model of the left ventricle indicating the influence of fiber and sheet dispersions upon contraction over a cardiac cycle. Although only a minor shift in the pressure-volume (PV) loops between the cases with no dispersions and with fiber and sheet dispersions for a healthy myocardium was observed, a remarkably different behavior is obtained with a fiber dispersion relating to a diseased myocardium. In future simulations, this dispersion model for myocardial tissue may advantageously be used together with models of, for example, growth and remodeling of various cardiac diseases.
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Affiliation(s)
- Thomas S E Eriksson
- Institute of Biomechanics, Center of Biomedical Engineering, Graz University of Technology, 8010 Graz, Austria; Department of Biophysics, Medical University of Graz, 8010 Graz, Austria
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Adeniran I, Hancox JC, Zhang H. In silico investigation of the short QT syndrome, using human ventricle models incorporating electromechanical coupling. Front Physiol 2013; 4:166. [PMID: 23847545 PMCID: PMC3701879 DOI: 10.3389/fphys.2013.00166] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2013] [Accepted: 06/14/2013] [Indexed: 11/13/2022] Open
Abstract
INTRODUCTION Genetic forms of the Short QT Syndrome (SQTS) arise due to cardiac ion channel mutations leading to accelerated ventricular repolarization, arrhythmias and sudden cardiac death. Results from experimental and simulation studies suggest that changes to refractoriness and tissue vulnerability produce a substrate favorable to re-entry. Potential electromechanical consequences of the SQTS are less well-understood. The aim of this study was to utilize electromechanically coupled human ventricle models to explore electromechanical consequences of the SQTS. METHODS AND RESULTS The Rice et al. mechanical model was coupled to the ten Tusscher et al. ventricular cell model. Previously validated K(+) channel formulations for SQT variants 1 and 3 were incorporated. Functional effects of the SQTS mutations on [Ca(2+)] i transients, sarcomere length shortening and contractile force at the single cell level were evaluated with and without the consideration of stretch-activated channel current (I sac). Without I sac, at a stimulation frequency of 1Hz, the SQTS mutations produced dramatic reductions in the amplitude of [Ca(2+)] i transients, sarcomere length shortening and contractile force. When I sac was incorporated, there was a considerable attenuation of the effects of SQTS-associated action potential shortening on Ca(2+) transients, sarcomere shortening and contractile force. Single cell models were then incorporated into 3D human ventricular tissue models. The timing of maximum deformation was delayed in the SQTS setting compared to control. CONCLUSION The incorporation of I sac appears to be an important consideration in modeling functional effects of SQT 1 and 3 mutations on cardiac electro-mechanical coupling. Whilst there is little evidence of profoundly impaired cardiac contractile function in SQTS patients, our 3D simulations correlate qualitatively with reported evidence for dissociation between ventricular repolarization and the end of mechanical systole.
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Affiliation(s)
- Ismail Adeniran
- Computational Biology, Biological Physics Group, School of Physics and Astronomy, The University of Manchester Manchester, UK
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Hubbard ML, Henriquez CS. Microscopic variations in interstitial and intracellular structure modulate the distribution of conduction delays and block in cardiac tissue with source-load mismatch. Europace 2013; 14 Suppl 5:v3-v9. [PMID: 23104912 DOI: 10.1093/europace/eus267] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
AIMS Reentrant activity in the heart is often correlated with heterogeneity in both the intracellular structure and the interstitial structure surrounding cells; however, the combined effect of cardiac microstructure and interstitial resistivity in regions of source-load mismatch is largely unknown. The aim of this study was to investigate how microstructural variations in cell arrangement and increased interstitial resistivity influence the spatial distribution of conduction delays and block in poorly coupled regions of tissue. METHODS AND RESULTS Two-dimensional 0.6 cm × 0.6 cm computer models with idealized and realistic cellular structure were used to represent a monolayer of ventricular myocytes. Gap junction connections were distributed around the periphery of each cell at 10 μm intervals. Regions of source-load mismatch were added to the models by increasing the gap junction and interstitial resistivity in one-half of the tissue. Heterogeneity in cell shape and cell arrangement along the boundary between well-coupled and poorly coupled tissue increased variability in longitudinal conduction delays to as much as 10 ms before the onset of conduction block, resulting in wavefront breakthroughs with pronounced curvature at distinct points along the boundary. Increasing the effective interstitial resistivity reduced source-load mismatch at the transition boundary, which caused a decrease in longitudinal conduction delay and an increase in the number of wavefront breakthroughs. CONCLUSION Microstructural variations in cardiac tissue facilitate the formation of isolated sites of wavefront breakthrough that may enable abnormal electrical activity in small regions of diseased tissue to develop into more widespread reentrant activity.
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Adeniran I, Hancox JC, Zhang H. Effect of cardiac ventricular mechanical contraction on the characteristics of the ECG: A simulation study. ACTA ACUST UNITED AC 2013. [DOI: 10.4236/jbise.2013.612a007] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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31
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Boulakia M, Schenone E, Gerbeau JF. Reduced-order modeling for cardiac electrophysiology. Application to parameter identification. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2012; 28:727-744. [PMID: 25364848 DOI: 10.1002/cnm.2465] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2011] [Revised: 12/19/2011] [Accepted: 12/23/2011] [Indexed: 06/04/2023]
Abstract
A reduced-order model based on proper orthogonal decomposition (POD) is proposed for the bidomain equations of cardiac electrophysiology. Its accuracy is assessed through electrocardiograms in various configurations, including myocardium infarctions and long-time simulations. We show in particular that a restitution curve can efficiently be approximated by this approach. The reduced-order model is then used in an inverse problem solved by an evolutionary algorithm. Some attempts are presented to identify ionic parameters and infarction locations from synthetic electrocardiograms.
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Affiliation(s)
- M Boulakia
- LJLL UMR 7598, UPMC-University Paris 6, Paris, F-75005, France.
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32
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Arthurs CJ, Bishop MJ, Kay D. Efficient simulation of cardiac electrical propagation using high order finite elements. JOURNAL OF COMPUTATIONAL PHYSICS 2012; 231:3946-3962. [PMID: 24976644 PMCID: PMC4067136 DOI: 10.1016/j.jcp.2012.01.037] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/13/2011] [Revised: 01/20/2012] [Accepted: 01/30/2012] [Indexed: 05/10/2023]
Abstract
We present an application of high order hierarchical finite elements for the efficient approximation of solutions to the cardiac monodomain problem. We detail the hurdles which must be overcome in order to achieve theoretically-optimal errors in the approximations generated, including the choice of method for approximating the solution to the cardiac cell model component. We place our work on a solid theoretical foundation and show that it can greatly improve the accuracy in the approximation which can be achieved in a given amount of processor time. Our results demonstrate superior accuracy over linear finite elements at a cheaper computational cost and thus indicate the potential indispensability of our approach for large-scale cardiac simulation.
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Affiliation(s)
| | - Martin J. Bishop
- Department of Computer Science, University of Oxford, Oxford, United
Kingdom
- Department of Biomedical Engineering, King’s College London, London,
United Kingdom
| | - David Kay
- Department of Computer Science, University of Oxford, Oxford, United
Kingdom
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Adeniran I, McPate MJ, Witchel HJ, Hancox JC, Zhang H. Increased vulnerability of human ventricle to re-entrant excitation in hERG-linked variant 1 short QT syndrome. PLoS Comput Biol 2011; 7:e1002313. [PMID: 22194679 PMCID: PMC3240585 DOI: 10.1371/journal.pcbi.1002313] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2011] [Accepted: 11/02/2011] [Indexed: 11/24/2022] Open
Abstract
The short QT syndrome (SQTS) is a genetically heterogeneous condition characterized by abbreviated QT intervals and an increased susceptibility to arrhythmia and sudden death. This simulation study identifies arrhythmogenic mechanisms in the rapid-delayed rectifier K+ current (IKr)-linked SQT1 variant of the SQTS. Markov chain (MC) models were found to be superior to Hodgkin-Huxley (HH) models in reproducing experimental data regarding effects of the N588K mutation on KCNH2-encoded hERG. These ionic channel models were then incorporated into human ventricular action potential (AP) models and into 1D and 2D idealised and realistic transmural ventricular tissue simulations and into a 3D anatomical model. In single cell models, the N588K mutation abbreviated ventricular cell AP duration at 90% repolarization (APD90) and decreased the maximal transmural voltage heterogeneity (δV) during APs. This resulted in decreased transmural heterogeneity of APD90 and of the effective refractory period (ERP): effects that are anticipated to be anti-arrhythmic rather than pro-arrhythmic. However, with consideration of transmural heterogeneity of IKr density in the intact tissue model based on the ten Tusscher-Noble-Noble-Panfilov ventricular model, not only did the N588K mutation lead to QT-shortening and increases in T-wave amplitude, but δV was found to be augmented in some local regions of ventricle tissue, resulting in increased tissue vulnerability for uni-directional conduction block and predisposing to formation of re-entrant excitation waves. In 2D and 3D tissue models, the N588K mutation facilitated and maintained re-entrant excitation waves due to the reduced substrate size necessary for sustaining re-entry. Thus, in SQT1 the N588K-hERG mutation facilitates initiation and maintenance of ventricular re-entry, increasing the lifespan of re-entrant spiral waves and the stability of scroll waves in 3D tissue. Sudden cardiac death may arise in individuals with diseased heart tissue, or in apparently healthy subjects who suffer from genetic defects in ‘ion channel’ proteins, which increase cardiac arrhythmia risk and are associated with significant morbidity and mortality. One rare, though serious, genetic condition is the ‘short QT syndrome’ (SQTS). Although it is now known that the KCNH2-encoded N588K-hERG mutation is associated with the main (SQT1) variant of the SQTS, the mechanisms by which ventricular arrhythmia is initiated and sustained are still unclear due to lack of genotypically accurate experimental models. In this study, we used sophisticated multi-scale computer models of human ventricles in order to investigate the pro-arrhythmic effects of the N588K hERG mutation. It was found that the mutation accelerated the ventricular repolarization process, produced augmented electrical heterogeneity in some local regions of the tissue, leading to increased risk of arrhythmia genesis. It was also found that accelerated ventricular repolarization reduced the substrate size of the tissue required to sustain re-entrant circuits in both two and three dimensions. This study provides new mechanistic insight into understanding of how changes to hERG channel function in SQT1 lead to exacerbated ventricular arrhythmia risk in this inherited arrhythmia syndrome.
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Affiliation(s)
- Ismail Adeniran
- Biological Physics Group, School of Physics & Astronomy, The University of Manchester, Manchester, UK
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34
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Niederer SA, Kerfoot E, Benson AP, Bernabeu MO, Bernus O, Bradley C, Cherry EM, Clayton R, Fenton FH, Garny A, Heidenreich E, Land S, Maleckar M, Pathmanathan P, Plank G, Rodríguez JF, Roy I, Sachse FB, Seemann G, Skavhaug O, Smith NP. Verification of cardiac tissue electrophysiology simulators using an N-version benchmark. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2011; 369:4331-51. [PMID: 21969679 PMCID: PMC3263775 DOI: 10.1098/rsta.2011.0139] [Citation(s) in RCA: 143] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/18/2023]
Abstract
Ongoing developments in cardiac modelling have resulted, in particular, in the development of advanced and increasingly complex computational frameworks for simulating cardiac tissue electrophysiology. The goal of these simulations is often to represent the detailed physiology and pathologies of the heart using codes that exploit the computational potential of high-performance computing architectures. These developments have rapidly progressed the simulation capacity of cardiac virtual physiological human style models; however, they have also made it increasingly challenging to verify that a given code provides a faithful representation of the purported governing equations and corresponding solution techniques. This study provides the first cardiac tissue electrophysiology simulation benchmark to allow these codes to be verified. The benchmark was successfully evaluated on 11 simulation platforms to generate a consensus gold-standard converged solution. The benchmark definition in combination with the gold-standard solution can now be used to verify new simulation codes and numerical methods in the future.
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Affiliation(s)
- Steven A Niederer
- Department of Biomedical Engineering, Division of Imaging Sciences and Biomedical Engineering, King's College London, UK.
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35
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Bishop MJ, Plank G. Bidomain ECG simulations using an augmented monodomain model for the cardiac source. IEEE Trans Biomed Eng 2011; 58:10.1109/TBME.2011.2148718. [PMID: 21536529 PMCID: PMC3378475 DOI: 10.1109/tbme.2011.2148718] [Citation(s) in RCA: 41] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
The electrocardiogram (ECG) is an essential clinical tool for the non-invasive assessment of cardiac function. Computational simulations of ECGs using bidomain models are considered the biophysically most detailed approach, but computational costs are significant. Alternatively, pseudo-bidomain formulations can be used, combining a monodomain model with an infrequent bidomain solve to obtain full extracellular potential (φ(e)) distributions and traces. However, previous attempts at such approaches did not see the expected significant decrease in compute time and did not include important effects of bath-loading on activation wavefront morphology (present in full bidomain models), representing a less accurate source term for φ(e) solution. ECG traces can also be derived from computationally cheaper φ(e) recovery techniques, whereby the time-course of φ(e) is approximated at a particular point using the monodomain transmembrane potential as source term. However, φ(e) recovery methods also assume tissue to be immersed in an unbounded conductive medium; not the case in most practical scenarios. We recently demonstrated how bath-loading effects in bidomain simulations could be replicated using an augmented monodomain model, faithfully reproducing bidomain wavefront shapes and activation patterns. Here, a computationally-efficient pseudobidomain formulation is suggested which combines the advantages of an augmented monodomain method with an infrequent bidomain solve, providing activation sequences, ECG traces and φ(e) distributions in a bounded medium surrounding the heart which closely match those of the full bidomain, but at ≈ 10% the computational cost. We demonstrate the important impact of both bath-loading and a finite surrounding bath on spatiotemporal φ(e) distributions, thus demonstrating the utility of our novel pseudo-bidomain model in ECG computation with respect to previous pseudo-bidomain and φ(e) recovery approaches.
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Affiliation(s)
| | - Gernot Plank
- Institute of Biophysics, Medical University of Graz, Graz, Austria and Oxford e-Research Centre, University of Oxford, Oxford, UK
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36
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Reumann M, Fitch BG, Rayshubskiy A, Pitman MC, Rice JJ. Orthogonal recursive bisection as data decomposition strategy for massively parallel cardiac simulations. BIOMED ENG-BIOMED TE 2011; 56:129-45. [PMID: 21657987 DOI: 10.1515/bmt.2011.100] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
We present the orthogonal recursive bisection algorithm that hierarchically segments the anatomical model structure into subvolumes that are distributed to cores. The anatomy is derived from the Visible Human Project, with electrophysiology based on the FitzHugh-Nagumo (FHN) and ten Tusscher (TT04) models with monodomain diffusion. Benchmark simulations with up to 16,384 and 32,768 cores on IBM Blue Gene/P and L supercomputers for both FHN and TT04 results show good load balancing with almost perfect speedup factors that are close to linear with the number of cores. Hence, strong scaling is demonstrated. With 32,768 cores, a 1000 ms simulation of full heart beat requires about 6.5 min of wall clock time for a simulation of the FHN model. For the largest machine partitions, the simulations execute at a rate of 0.548 s (BG/P) and 0.394 s (BG/L) of wall clock time per 1 ms of simulation time. To our knowledge, these simulations show strong scaling to substantially higher numbers of cores than reported previously for organ-level simulation of the heart, thus significantly reducing run times. The ability to reduce runtimes could play a critical role in enabling wider use of cardiac models in research and clinical applications.
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Affiliation(s)
- Matthias Reumann
- IBM T. J. Watson Research Center, Yorktown Heights, NY 10598, USA.
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37
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Colli-Franzone P, Pavarino L, Scacchi S. Exploring anodal and cathodal make and break cardiac excitation mechanisms in a 3D anisotropic bidomain model. Math Biosci 2011; 230:96-114. [DOI: 10.1016/j.mbs.2011.02.002] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2010] [Revised: 02/04/2011] [Accepted: 02/09/2011] [Indexed: 01/09/2023]
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38
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Myles RC, Bernus O, Burton FL, Cobbe SM, Smith GL. Effect of activation sequence on transmural patterns of repolarization and action potential duration in rabbit ventricular myocardium. Am J Physiol Heart Circ Physiol 2010; 299:H1812-22. [PMID: 20889843 DOI: 10.1152/ajpheart.00518.2010] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Abstract
Although transmural heterogeneity of action potential duration (APD) is established in single cells isolated from different tissue layers, the extent to which it produces transmural gradients of repolarization in electrotonically coupled ventricular myocardium remains controversial. The purpose of this study was to examine the relative contribution of intrinsic cellular gradients of APD and electrotonic influences to transmural repolarization in rabbit ventricular myocardium. Transmural optical mapping was performed in left ventricular wedge preparations from eight rabbits. Transmural patterns of activation, repolarization, and APD were recorded during endocardial and epicardial stimulation. Experimental results were compared with modeled data during variations in electrotonic coupling. A transmural gradient of APD was evident during endocardial stimulation, which reflected differences previously seen in isolated cells, with the longest APD at the endocardium and the shortest at the epicardium (endo: 165 ± 5 vs. epi: 147 ± 4 ms; P < 0.05). During epicardial stimulation, this gradient reversed (epi: 162 ± 4 vs. endo: 148 ± 6 ms; P < 0.05). In both activation sequences, transmural repolarization followed activation and APD shortened along the activation path such that significant transmural gradients of repolarization did not occur. This correlation between transmural activation time and APD was recapitulated in simulations and varied with changes in intercellular coupling, confirming that it is mediated by electrotonic current flow between cells. These data suggest that electrotonic influences are important in determining the transmural repolarization sequence in rabbit ventricular myocardium and that they are sufficient to overcome intrinsic differences in the electrophysiological properties of the cells across the ventricular wall.
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Affiliation(s)
- Rachel C Myles
- British Heart Foundation Glasgow Cardiovascular Research Centre, University of Glasgow, Glasgow, United Kingdom
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39
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Zaniboni M, Riva I, Cacciani F, Groppi M. How different two almost identical action potentials can be: a model study on cardiac repolarization. Math Biosci 2010; 228:56-70. [PMID: 20801131 DOI: 10.1016/j.mbs.2010.08.007] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2009] [Revised: 08/18/2010] [Accepted: 08/23/2010] [Indexed: 11/24/2022]
Abstract
Spatial heterogeneity in the properties of ion channels generates spatial dispersion of ventricular repolarization, which is modulated by gap junctional coupling. However, it is possible to simulate conditions in which local differences in excitation properties are electrophysiologically silent and only play a role in pathological states. We use a numerical procedure on the Luo-Rudy phase 1 model of the ventricular action potential (AP1) in order to find a modified set of model parameters which generates an action potential profile (AP2) almost identical to AP1. We show that, although the two waveforms elicited from resting conditions as a single AP are very similar and belong to membranes sharing similar passive electrical properties, the modified membrane generating AP2 is a weaker current source than the one generating AP1, has different sensitivity to up/down-regulation of ion channels and to extracellular potassium, and a different electrical restitution profile. We study electrotonic interaction of AP1- and AP2- type membranes in cell pairs and in cable conduction, and find differences in source-sink properties which are masked in physiological conditions and become manifest during intercellular uncoupling or partial block of ion channels, leading to unidirectional block and spatial repolarization gradients. We provide contour plot representations that summarize differences and similarities. The present report characterizes an inverse problem in cardiac cells, and strengthen the recently emergent notion that a comprehensive characterization and validation of cell models and their components are necessary in order to correctly understand simulation results at higher levels of complexity.
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Affiliation(s)
- Massimiliano Zaniboni
- Dipartimento di Biologia Evolutiva e Funzionale, Sezione Fisiologia, Università degli Studi di Parma, V.le G.P. Usberti 11 A, 43124 Parma, Italy.
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40
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Keller DUJ, Weber FM, Seemann G, Dössel O. Ranking the Influence of Tissue Conductivities on Forward-Calculated ECGs. IEEE Trans Biomed Eng 2010; 57:1568-76. [PMID: 20659824 DOI: 10.1109/tbme.2010.2046485] [Citation(s) in RCA: 88] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- David U J Keller
- Institute of Biomedical Engineering, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany.
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41
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Fernández MA, Zemzemi N. Decoupled time-marching schemes in computational cardiac electrophysiology and ECG numerical simulation. Math Biosci 2010; 226:58-75. [DOI: 10.1016/j.mbs.2010.04.003] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2009] [Revised: 04/14/2010] [Accepted: 04/16/2010] [Indexed: 10/19/2022]
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Models of cardiac tissue electrophysiology: progress, challenges and open questions. PROGRESS IN BIOPHYSICS AND MOLECULAR BIOLOGY 2010; 104:22-48. [PMID: 20553746 DOI: 10.1016/j.pbiomolbio.2010.05.008] [Citation(s) in RCA: 290] [Impact Index Per Article: 20.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/14/2009] [Revised: 04/09/2010] [Accepted: 05/19/2010] [Indexed: 01/03/2023]
Abstract
Models of cardiac tissue electrophysiology are an important component of the Cardiac Physiome Project, which is an international effort to build biophysically based multi-scale mathematical models of the heart. Models of tissue electrophysiology can provide a bridge between electrophysiological cell models at smaller scales, and tissue mechanics, metabolism and blood flow at larger scales. This paper is a critical review of cardiac tissue electrophysiology models, focussing on the micro-structure of cardiac tissue, generic behaviours of action potential propagation, different models of cardiac tissue electrophysiology, the choice of parameter values and tissue geometry, emergent properties in tissue models, numerical techniques and computational issues. We propose a tentative list of information that could be included in published descriptions of tissue electrophysiology models, and used to support interpretation and evaluation of simulation results. We conclude with a discussion of challenges and open questions.
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Mathematical modeling of electrocardiograms: a numerical study. Ann Biomed Eng 2009; 38:1071-97. [PMID: 20033779 DOI: 10.1007/s10439-009-9873-0] [Citation(s) in RCA: 60] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2009] [Accepted: 12/09/2009] [Indexed: 01/13/2023]
Abstract
This paper deals with the numerical simulation of electrocardiograms (ECG). Our aim is to devise a mathematical model, based on partial differential equations, which is able to provide realistic 12-lead ECGs. The main ingredients of this model are classical: the bidomain equations coupled to a phenomenological ionic model in the heart, and a generalized Laplace equation in the torso. The obtention of realistic ECGs relies on other important features--including heart-torso transmission conditions, anisotropy, cell heterogeneity and His bundle modeling--that are discussed in detail. The numerical implementation is based on state-of-the-art numerical methods: domain decomposition techniques and second order semi-implicit time marching schemes, offering a good compromise between accuracy, stability and efficiency. The numerical ECGs obtained with this approach show correct amplitudes, shapes and polarities, in all the 12 standard leads. The relevance of every modeling choice is carefully discussed and the numerical ECG sensitivity to the model parameters investigated.
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Towards accurate numerical method for monodomain models using a realistic heart geometry. Math Biosci 2009; 220:89-101. [DOI: 10.1016/j.mbs.2009.05.003] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2008] [Revised: 04/23/2009] [Accepted: 05/01/2009] [Indexed: 11/18/2022]
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Caldwell BJ, Trew ML, Sands GB, Hooks DA, LeGrice IJ, Smaill BH. Three distinct directions of intramural activation reveal nonuniform side-to-side electrical coupling of ventricular myocytes. Circ Arrhythm Electrophysiol 2009; 2:433-40. [PMID: 19808500 DOI: 10.1161/circep.108.830133] [Citation(s) in RCA: 73] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
BACKGROUND The anisotropy of cardiac tissue is a key determinant of 3D electric propagation and the stability of activation wave fronts in the heart. The electric properties of ventricular myocardium are widely assumed to be axially anisotropic, with activation propagating most rapidly in the myofiber direction and at uniform velocity transverse to this. We present new experimental evidence that contradicts this view. METHODS AND RESULTS For the first time, high-density intramural electric mapping (325 electrodes at approximately 4x4x1-mm spacing) from pig left ventricular tissue was used to reconstruct 3D paced activation surfaces projected directly onto 3D tissue structure imaged throughout the same left ventricular volume. These data from 5 hearts demonstrate that ventricular tissue is electrically orthotropic with 3 distinct propagation directions that coincide with local microstructural axes defined by the laminar arrangement of ventricular myocytes. The maximum conduction velocity of 0.67+/-0.019 ms(-1) was aligned with the myofiber axis. However, transverse to this, the maximum conduction velocity was 0.30+/-0.010 ms(-1), parallel to the myocyte layers and 0.17+/-0.004 ms(-1) normal to them. These orthotropic conduction velocities give rise to preferential activation pathways across the left ventricular free wall that are not captured by structurally detailed computer models, which incorporate axially anisotropic electric properties. CONCLUSIONS Our findings suggest that current views on uniform side-to-side electric coupling in the heart need to be revised. In particular, nonuniform laminar myocardial architecture and associated electric orthotropy should be included in future models of initiation and maintenance of ventricular arrhythmia.
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Affiliation(s)
- Bryan J Caldwell
- Auckland Bioengineering Institute, Faculty of Medical and Health Sciences, University of Auckland, Auckland, New Zealand
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Linge S, Sundnes J, Hanslien M, Lines GT, Tveito A. Numerical solution of the bidomain equations. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2009; 367:1931-1950. [PMID: 19380319 DOI: 10.1098/rsta.2008.0306] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
Knowledge of cardiac electrophysiology is efficiently formulated in terms of mathematical models. However, most of these models are very complex and thus defeat direct mathematical reasoning founded on classical and analytical considerations. This is particularly so for the celebrated bidomain model that was developed almost 40 years ago for the concurrent analysis of extra- and intracellular electrical activity. Numerical simulations based on this model represent an indispensable tool for studying electrophysiology. However, complex mathematical models, steep gradients in the solutions and complicated geometries lead to extremely challenging computational problems. The greatest achievement in scientific computing over the past 50 years has been to enable the solving of linear systems of algebraic equations that arise from discretizations of partial differential equations in an optimal manner, i.e. such that the central processing unit (CPU) effort increases linearly with the number of computational nodes. Over the past decade, such optimal methods have been introduced in the simulation of electrophysiology. This development, together with the development of affordable parallel computers, has enabled the solution of the bidomain model combined with accurate cellular models, on geometries resembling a human heart. However, in spite of recent progress, the full potential of modern computational methods has yet to be exploited for the solution of the bidomain model. This paper reviews the development of numerical methods for solving the bidomain model. However, the field is huge and we thus restrict our focus to developments that have been made since the year 2000.
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Affiliation(s)
- S Linge
- Simula Research Laboratory, PO Box 134, 1325 Lysaker, Norway
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Pitt-Francis J, Bernabeu MO, Cooper J, Garny A, Momtahan L, Osborne J, Pathmanathan P, Rodriguez B, Whiteley JP, Gavaghan DJ. Chaste: using agile programming techniques to develop computational biology software. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2008; 366:3111-3136. [PMID: 18565813 DOI: 10.1098/rsta.2008.0096] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
Cardiac modelling is the area of physiome modelling where the available simulation software is perhaps most mature, and it therefore provides an excellent starting point for considering the software requirements for the wider physiome community. In this paper, we will begin by introducing some of the most advanced existing software packages for simulating cardiac electrical activity. We consider the software development methods used in producing codes of this type, and discuss their use of numerical algorithms, relative computational efficiency, usability, robustness and extensibility. We then go on to describe a class of software development methodologies known as test-driven agile methods and argue that such methods are more suitable for scientific software development than the traditional academic approaches. A case study is a project of our own, Cancer, Heart and Soft Tissue Environment, which is a library of computational biology software that began as an experiment in the use of agile programming methods. We present our experiences with a review of our progress thus far, focusing on the advantages and disadvantages of this new approach compared with the development methods used in some existing packages. We conclude by considering whether the likely wider needs of the cardiac modelling community are currently being met and suggest that, in order to respond effectively to changing requirements, it is essential that these codes should be more malleable. Such codes will allow for reliable extensions to include both detailed mathematical models--of the heart and other organs--and more efficient numerical techniques that are currently being developed by many research groups worldwide.
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Affiliation(s)
- Joe Pitt-Francis
- Oxford University Computing Laboratory, Wolfson Building, University of Oxford, Parks Road, Oxford OX1 3QD, UK.
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Colli Franzone P, Pavarino LF, Scacchi S, Taccardi B. Modeling ventricular repolarization: effects of transmural and apex-to-base heterogeneities in action potential durations. Math Biosci 2008; 214:140-52. [PMID: 18621065 DOI: 10.1016/j.mbs.2008.06.006] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2007] [Accepted: 06/04/2008] [Indexed: 12/22/2022]
Abstract
Heterogeneities in the densities of membrane ionic currents of myocytes cause regional variations in action potential duration (APD) at various intramural depths and along the apico-basal and circumferential directions in the left ventricle. This work extends our previous study of cartesian slabs to ventricular walls shaped as an ellipsoidal volume and including both transmural and apex-to-base APD heterogeneities. Our 3D simulation study investigates the combined effect on repolarization sequences and APD distributions of: (a) the intrinsic APD heterogeneity across the wall and along the apex-to-base direction, and (b) the electrotonic currents that modulate the APDs when myocytes are embedded in a ventricular wall with fiber rotation and orthotropic anisotropy. Our findings show that: (i) the transmural and apex-to-base heterogeneities have only a weak influence on the repolarization patterns on myocardial layers parallel to the epicardium; (ii) the patterns of APD distribution on the epicardial surface are mostly affected by the apex-to-base heterogeneities and do not reveal the APD transmural heterogeneity; (iii) the transmural heterogeneity is clearly discernible in both repolarization and APD patterns only on transmural sections; (iv) the apex-to-base heterogeneity is clearly discernible only in APD patterns on layers parallel to the epicardium. Thus, in our orthotropic ellipsoidal wall, the complex 3D electrotonic modulation of APDs does not fully mix the effects of the transmural and apex-to-base heterogeneity. The intrinsic spatial heterogeneity of the APDs is unmasked in the modulated APD patterns only in the appropriate transmural or intramural sections. These findings are independent of the stimulus location (epicardial, endocardial) and of Purkinje involvement.
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Affiliation(s)
- P Colli Franzone
- Dipartimento di Matematica, Istituto di Analisi Nuerica-C.N.R., Università di Pavia, Via Ferrata 1, 27100 Pavia, Italy.
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An Efficient Technique for the Numerical Solution of the Bidomain Equations. Ann Biomed Eng 2008; 36:1398-408. [DOI: 10.1007/s10439-008-9513-0] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/08/2008] [Accepted: 05/01/2008] [Indexed: 10/22/2022]
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Weiss DL, Keller DUJ, Seemann G, Dössel O. The influence of fibre orientation, extracted from different segments of the human left ventricle, on the activation and repolarization sequence: a simulation study. Europace 2008; 9 Suppl 6:vi96-104. [PMID: 17959700 DOI: 10.1093/europace/eum213] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
AIMS This computational study examined the influence of fibre orientation on the electrical processes in the heart. In contrast to similar previous studies, human diffusion tensor magnetic resonance imaging measurements were used. METHODS The fibre orientation was extracted from distinctive regions of the left ventricle. It was incorporated in a single tissue segment having a fixed geometry. The electrophysiological model applied in the computational units considered transmural heterogeneities. Excitation was computed by means of the monodomain model; the accompanying pseudo-electrocardiograms (ECGs) were calculated. RESULTS The distribution of fibre orientation extracted from the same transversal section showed only small variations. The fibre information extracted from the equal circumferential but different longitudinal positions showed larger differences, mainly in the imbrication angle. Differences of the endocardial myocyte orientation mainly affected the beginning of the activation sequence. The transmural propagation was faster in areas with larger imbrication angles leading to a narrower QRS complex in pseudo-ECGs. CONCLUSION The model can be expanded to simulate electrophysiology and contraction in the whole heart geometry. Embedded in a torso model, the impact of fibre orientation on body surface ECGs and their relation to local pseudo-ECGs can be identified.
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Affiliation(s)
- Daniel L Weiss
- Institute of Biomedical Engineering, Karlsruhe Institute of Technology, Kaiserstrasse 12, 76131 Karlsruhe, Germany.
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