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Abstract
The global burden caused by cardiovascular disease is substantial, with heart disease representing the most common cause of death around the world. There remains a need to develop better mechanistic models of cardiac function in order to combat this health concern. Heart rhythm disorders, or arrhythmias, are one particular type of disease which has been amenable to quantitative investigation. Here we review the application of quantitative methodologies to explore dynamical questions pertaining to arrhythmias. We begin by describing single-cell models of cardiac myocytes, from which two and three dimensional models can be constructed. Special focus is placed on results relating to pattern formation across these spatially-distributed systems, especially the formation of spiral waves of activation. Next, we discuss mechanisms which can lead to the initiation of arrhythmias, focusing on the dynamical state of spatially discordant alternans, and outline proposed mechanisms perpetuating arrhythmias such as fibrillation. We then review experimental and clinical results related to the spatio-temporal mapping of heart rhythm disorders. Finally, we describe treatment options for heart rhythm disorders and demonstrate how statistical physics tools can provide insights into the dynamics of heart rhythm disorders.
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Affiliation(s)
- Wouter-Jan Rappel
- Department of Physics, University of California San Diego, La Jolla, CA 92037
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2
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Shahi S, Marcotte CD, Herndon CJ, Fenton FH, Shiferaw Y, Cherry EM. Long-Time Prediction of Arrhythmic Cardiac Action Potentials Using Recurrent Neural Networks and Reservoir Computing. Front Physiol 2021; 12:734178. [PMID: 34646159 PMCID: PMC8502981 DOI: 10.3389/fphys.2021.734178] [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: 06/30/2021] [Accepted: 08/27/2021] [Indexed: 11/13/2022] Open
Abstract
The electrical signals triggering the heart's contraction are governed by non-linear processes that can produce complex irregular activity, especially during or preceding the onset of cardiac arrhythmias. Forecasts of cardiac voltage time series in such conditions could allow new opportunities for intervention and control but would require efficient computation of highly accurate predictions. Although machine-learning (ML) approaches hold promise for delivering such results, non-linear time-series forecasting poses significant challenges. In this manuscript, we study the performance of two recurrent neural network (RNN) approaches along with echo state networks (ESNs) from the reservoir computing (RC) paradigm in predicting cardiac voltage data in terms of accuracy, efficiency, and robustness. We show that these ML time-series prediction methods can forecast synthetic and experimental cardiac action potentials for at least 15–20 beats with a high degree of accuracy, with ESNs typically two orders of magnitude faster than RNN approaches for the same network size.
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Affiliation(s)
- Shahrokh Shahi
- School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, GA, United States
| | - Christopher D Marcotte
- School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, GA, United States
| | - Conner J Herndon
- School of Physics, Georgia Institute of Technology, Atlanta, GA, United States
| | - Flavio H Fenton
- School of Physics, Georgia Institute of Technology, Atlanta, GA, United States
| | - Yohannes Shiferaw
- Department of Physics & Astronomy, California State University, Northridge, CA, United States
| | - Elizabeth M Cherry
- School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, GA, United States
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3
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Liu J, Fu Z, Gong Y, Xia L. Investigating two kinds of cellular alternans and corresponding TWA induced by impaired calcium cycling in myocardial ischemia. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2021; 18:7648-7665. [PMID: 34814268 DOI: 10.3934/mbe.2021379] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
BACKGROUND The utility of T wave alternans (TWA) in identifying arrhythmia risk has been demonstrated. During myocardial ischemia (MI), TWA could be induced by cellular alternans. However, the relationship between cellular alternans patterns and TWA patterns in MI has not been investigated thoroughly. METHODS We set MI conditions to simulate alternans. Either prolonging Ca2+ release or increasing spark-induced sparks (secondary sparks) can give rise to different patterns of APD alternans and TWA. In addition, different ischemic zones and reduced conduction velocity are also considered in one dimensional simulation. RESULTS Delay of Ca2+ release can produce discordant Ca2+-driven alternans in single cell simulation. Increasing secondary sparks leads to concordant alternans. Correspondingly, morphology and magnitude of TWA vary in two different cellular alternans. Epi ischemia results in alternans concentrating in the first half of T wave. Endo and transmural ischemia lead to fluctuations in the second half of T wave. In addition, slowing conduction velocity has no effect on TWA magnitude. CONCLUSION Specific ionic channel dysfunction and ischemic zones affect TWA patterns.
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Affiliation(s)
- Jiaqi Liu
- Key Laboratory for Biomedical Engineering of Ministry of Education, Institute of Biomedical Engineering, Zhejiang University, Hangzhou 310027, China
| | - Zhenyin Fu
- Key Laboratory for Biomedical Engineering of Ministry of Education, Institute of Biomedical Engineering, Zhejiang University, Hangzhou 310027, China
| | - Yinglan Gong
- Key Laboratory for Biomedical Engineering of Ministry of Education, Institute of Biomedical Engineering, Zhejiang University, Hangzhou 310027, China
| | - Ling Xia
- Key Laboratory for Biomedical Engineering of Ministry of Education, Institute of Biomedical Engineering, Zhejiang University, Hangzhou 310027, China
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4
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Barrio R, Martínez MÁ, Pueyo E, Serrano S. Dynamical analysis of early afterdepolarization patterns in a biophysically detailed cardiac model. CHAOS (WOODBURY, N.Y.) 2021; 31:073137. [PMID: 34340346 DOI: 10.1063/5.0055965] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/05/2021] [Accepted: 06/28/2021] [Indexed: 06/13/2023]
Abstract
Arrhythmogenic early afterdepolarizations (EADs) are investigated in a biophysically detailed mathematical model of a rabbit ventricular myocyte, providing their location in the parameter phase space and describing their dynamical mechanisms. Simulations using the Sato model, defined by 27 state variables and 177 parameters, are conducted to generate electrical action potentials (APs) for different values of the pacing cycle length and other parameters related to sodium and calcium concentrations. A detailed study of the different AP patterns with or without EADs is carried out, showing the presence of a high variety of temporal AP configurations with chaotic and quasiperiodic behaviors. Regions of bistability are identified and, importantly, linked to transitions between different behaviors. Using sweeping techniques, one-, two-, and three-parameter phase spaces are provided, allowing ascertainment of the role of the selected parameters as well as location of the transition regions. A Devil's staircase, with symbolic sequence analysis, is proposed to describe transitions in the ratio between the number of voltage (EAD and AP) peaks and the number of APs. To conclude, the obtained results are linked to recent studies for low-dimensional models and a conjecture is made for the internal dynamical structure of the transition region from non-EAD to EAD behavior using fold and cusp bifurcations and maximal canards.
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Affiliation(s)
- Roberto Barrio
- Department of Applied Mathematics and IUMA, Computational Dynamics Group, University of Zaragoza, E-50009 Zaragoza, Spain
| | - M Ángeles Martínez
- Department of Applied Mathematics and IUMA, Computational Dynamics Group, University of Zaragoza, E-50009 Zaragoza, Spain
| | - Esther Pueyo
- I3A, University of Zaragoza, IIS Aragón and CIBER-BBN, E-50018 Zaragoza, Spain
| | - Sergio Serrano
- Department of Applied Mathematics and IUMA, Computational Dynamics Group, University of Zaragoza, E-50009 Zaragoza, Spain
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5
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Kulkarni K, Walton RD, Armoundas AA, Tolkacheva EG. Clinical Potential of Beat-to-Beat Diastolic Interval Control in Preventing Cardiac Arrhythmias. J Am Heart Assoc 2021; 10:e020750. [PMID: 34027678 PMCID: PMC8483541 DOI: 10.1161/jaha.121.020750] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Life‐threatening ventricular arrhythmias and sudden cardiac death are often preceded by cardiac alternans, a beat‐to‐beat oscillation in the T‐wave morphology or duration. However, given the spatiotemporal and structural complexity of the human heart, designing algorithms to effectively suppress alternans and prevent fatal rhythms is challenging. Recently, an antiarrhythmic constant diastolic interval pacing protocol was proposed and shown to be effective in suppressing alternans in 0‐, 1‐, and 2‐dimensional in silico studies as well as in ex vivo whole heart experiments. Herein, we provide a systematic review of the electrophysiological conditions and mechanisms that enable constant diastolic interval pacing to be an effective antiarrhythmic pacing strategy. We also demonstrate a successful translation of the constant diastolic interval pacing protocol into an ECG‐based real‐time control system capable of modulating beat‐to‐beat cardiac electrical activity and preventing alternans. Furthermore, we present evidence of the clinical utility of real‐time alternans suppression in reducing arrhythmia susceptibility in vivo. We provide a comprehensive overview of this promising pacing technique, which can potentially be translated into a clinically viable device that could radically improve the quality of life of patients experiencing abnormal cardiac rhythms.
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Affiliation(s)
- Kanchan Kulkarni
- IHU-LIRYC, Electrophysiology and Heart Modeling InstituteFondation Bordeaux Université Pessac, Bordeaux France.,Centre de Recherche Cardio-Thoracique de Bordeaux University of Bordeaux France.,Centre de Recherche Cardio-Thoracique de Bordeaux INSERM Bordeaux France
| | - Richard D Walton
- IHU-LIRYC, Electrophysiology and Heart Modeling InstituteFondation Bordeaux Université Pessac, Bordeaux France.,Centre de Recherche Cardio-Thoracique de Bordeaux University of Bordeaux France.,Centre de Recherche Cardio-Thoracique de Bordeaux INSERM Bordeaux France
| | - Antonis A Armoundas
- Cardiovascular Research Center Massachusetts General Hospital Boston MA.,Institute for Medical Engineering and Science Massachusetts Institute of Technology Cambridge MA
| | - Elena G Tolkacheva
- Department of Biomedical Engineering University of Minnesota-Twin Cities Minneapolis MN
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6
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Muñoz LM, Ampofo MO, Cherry EM. Controllability of voltage- and calcium-driven cardiac alternans in a map model. CHAOS (WOODBURY, N.Y.) 2021; 31:023139. [PMID: 33653066 DOI: 10.1063/5.0040064] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2020] [Accepted: 02/02/2021] [Indexed: 06/12/2023]
Abstract
Certain cardiac arrhythmias are preceded by electrical alternans, a state characterized by beat-to-beat alternation in cellular action potential duration. Cardiac alternans may arise from different mechanisms including instabilities in voltage or intracellular calcium cycling. Although a number of techniques have been proposed to suppress alternans, these methods have mainly been tested using models that do not support calcium-driven alternans. Therefore, it is important to understand how control methods may perform when alternans is driven by instabilities in calcium cycling. In this study, we applied controllability analysis to a discrete map of alternans dynamics in a cardiac cell. We compared two different controllability measures to determine to what extent different control strategies could suppress alternans and tested these predictions using three feedback controllers. We found a modal controllability measure, unlike the minimum singular value of the controllability matrix, consistently indicated the control strategies requiring the least control effort and yielding the smallest closed-loop eigenvalue. In addition, action potential duration was identified as the most effective variable through which control can be applied, regardless of alternans mechanism, although sarcoplasmic reticulum calcium load was also useful for the calcium-driven alternans cases.
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Affiliation(s)
- Laura M Muñoz
- School of Mathematical Sciences, Rochester Institute of Technology, Rochester, New York 14623-5602, USA
| | - Mark O Ampofo
- School of Mathematical Sciences, Rochester Institute of Technology, Rochester, New York 14623-5602, USA
| | - Elizabeth M Cherry
- School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-4017, USA
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7
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Biasci V, Sacconi L, Cytrynbaum EN, Pijnappels DA, De Coster T, Shrier A, Glass L, Bub G. Universal mechanisms for self-termination of rapid cardiac rhythm. CHAOS (WOODBURY, N.Y.) 2020; 30:121107. [PMID: 33380016 DOI: 10.1063/5.0033813] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/20/2020] [Accepted: 11/14/2020] [Indexed: 06/12/2023]
Abstract
Excitable media sustain circulating waves. In the heart, sustained circulating waves can lead to serious impairment or even death. To investigate factors affecting the stability of such waves, we have used optogenetic techniques to stimulate a region at the apex of a mouse heart at a fixed delay after the detection of excitation at the base of the heart. For long delays, rapid circulating rhythms can be sustained, whereas for shorter delays, there are paroxysmal bursts of activity that start and stop spontaneously. By considering the dependence of the action potential and conduction velocity on the preceding recovery time using restitution curves, as well as the reduced excitability (fatigue) due to the rapid excitation, we model prominent features of the dynamics including alternation of the duration of the excited phases and conduction times, as well as termination of the bursts for short delays. We propose that this illustrates universal mechanisms that exist in biological systems for the self-termination of such activities.
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Affiliation(s)
- Valentina Biasci
- Division of Physiology, Department of Experimental and Clinical Medicine, University of Florence, 50134 Florence, Italy
| | - Leonardo Sacconi
- National Institute of Optics, National Research Council, 50125 Florence, Italy
| | - Eric N Cytrynbaum
- Department of Mathematics, UBC, Vancouver British Columbia V6T 1Z2, Canada
| | - Daniël A Pijnappels
- Department of Cardiology, Leiden University Medical Center, Albinusdreef 2 2333 ZA Leiden, The Netherlands
| | - Tim De Coster
- Department of Cardiology, Leiden University Medical Center, Albinusdreef 2 2333 ZA Leiden, The Netherlands
| | - Alvin Shrier
- Department of Physiology, McGill University, 3655 Promenade Sir William Osler, Montreal, Quebec H3G 1Y6, Canada
| | - Leon Glass
- Department of Physiology, McGill University, 3655 Promenade Sir William Osler, Montreal, Quebec H3G 1Y6, Canada
| | - Gil Bub
- Department of Physiology, McGill University, 3655 Promenade Sir William Osler, Montreal, Quebec H3G 1Y6, Canada
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8
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Parthiban P, Newell S, Tolkacheva EG. Effect of constant-DI pacing on single cell pacing dynamics. CHAOS (WOODBURY, N.Y.) 2020; 30:103122. [PMID: 33138461 DOI: 10.1063/5.0022066] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2020] [Accepted: 10/02/2020] [Indexed: 06/11/2023]
Abstract
Cardiac alternans, beat-to-beat alternations in action potential duration, is a precursor to fatal arrhythmias such as ventricular fibrillation. Previous research has shown that voltage driven alternans can be suppressed by application of a constant diastolic interval (DI) pacing protocol. However, the effect of constant-DI pacing on cardiac cell dynamics and its interaction with the intracellular calcium cycle remains to be determined. Therefore, we aimed to examine the effects of constant-DI pacing on the dynamical behavior of a single-cell numerical model of cardiac action potential and the influence of voltage-calcium (V-Ca) coupling on it. Single cell dynamics were analyzed in the vicinity of the bifurcation point using a hybrid pacing protocol, a combination of constant-basic cycle length (BCL) and constant-DI pacing. We demonstrated that in a small region beneath the bifurcation point, constant-DI pacing caused the cardiac cell to remain alternans-free after switching to the constant-BCL pacing, thus introducing a region of bistability (RB). The size of the RB increased with stronger V-Ca coupling and was diminished with weaker V-Ca coupling. Overall, our findings demonstrate that the application of constant-DI pacing on cardiac cells with strong V-Ca coupling may induce permanent changes to cardiac cell dynamics increasing the utility of constant-DI pacing.
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Affiliation(s)
- P Parthiban
- Department of Biomedical Engineering, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - S Newell
- Department of Biomedical Engineering, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - E G Tolkacheva
- Department of Biomedical Engineering, University of Minnesota, Minneapolis, Minnesota 55455, USA
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9
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Thakare S, Mathew J, Zlochiver S, Zhao X, Tolkacheva EG. Global vs local control of cardiac alternans in a 1D numerical model of human ventricular tissue. CHAOS (WOODBURY, N.Y.) 2020; 30:083123. [PMID: 32872833 DOI: 10.1063/5.0005432] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/24/2020] [Accepted: 07/17/2020] [Indexed: 06/11/2023]
Abstract
Cardiac alternans is a proarrhythmic state in which the action potential duration (APD) of cardiac myocytes alternate between long and short values and often occurs under conditions of rapid pacing of cardiac tissue. In the ventricles, alternans is especially dangerous due to the life-threatening risk of developing arrhythmias, such as ventricular fibrillation. Alternans can be formed in periodically paced tissue as a result of pacing itself. Recently, it has been demonstrated that this pacing-induced alternans can be prevented by performing constant diastolic interval (DI) pacing, in which DI is independent of APD. However, constant DI pacing is difficult to implement in experimental settings since it requires the real-time measurement of APD. A more practical way was proposed based on electrocardiograms (ECGs), which give an indirect measure of the global DI relaxation period through the TR interval assessment. Previously, we demonstrated that constant TR pacing prevented alternans formation in isolated Langendorff-perfused rabbit hearts. However, the efficacy of "local" constant DI pacing vs "global" constant TR pacing in preventing alternans formation has never been investigated. Thus, the purpose of this study was to implement an ECG-based constant TR pacing in a 1D numerical model of human ventricular tissue and to compare the dynamical behavior of cardiac tissue with that resulted from a constant DI pacing. The results showed that both constant TR and constant DI pacing prevented the onset of alternans until lower basic cycle length when compared to periodic pacing. For longer cable lengths, constant TR pacing was shown to exhibit greater control on alternans than constant DI pacing.
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Affiliation(s)
- Sanket Thakare
- Department of Biomedical Engineering, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Joseph Mathew
- Department of Biomedical Engineering, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Sharon Zlochiver
- Department of Biomedical Engineering, Tel-Aviv University, Tel-Aviv 69379, Israel
| | - Xiaopeng Zhao
- Department of Mechanical, Aerospace and Biomedical Engineering, University of Tennessee, Knoxville, Tennessee 37996, USA
| | - Elena G Tolkacheva
- Department of Biomedical Engineering, University of Minnesota, Minneapolis, Minnesota 55455, USA
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10
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Hoffman MJ, Cherry EM. Sensitivity of a data-assimilation system for reconstructing three-dimensional cardiac electrical dynamics. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2020; 378:20190388. [PMID: 32448069 PMCID: PMC7287341 DOI: 10.1098/rsta.2019.0388] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 02/25/2020] [Indexed: 05/21/2023]
Abstract
Modelling of cardiac electrical behaviour has led to important mechanistic insights, but important challenges, including uncertainty in model formulations and parameter values, make it difficult to obtain quantitatively accurate results. An alternative approach is combining models with observations from experiments to produce a data-informed reconstruction of system states over time. Here, we extend our earlier data-assimilation studies using an ensemble Kalman filter to reconstruct a three-dimensional time series of states with complex spatio-temporal dynamics using only surface observations of voltage. We consider the effects of several algorithmic and model parameters on the accuracy of reconstructions of known scroll-wave truth states using synthetic observations. In particular, we study the algorithm's sensitivity to parameters governing different parts of the process and its robustness to several model-error conditions. We find that the algorithm can achieve an acceptable level of error in many cases, with the weakest performance occurring for model-error cases and more extreme parameter regimes with more complex dynamics. Analysis of the poorest-performing cases indicates an initial decrease in error followed by an increase when the ensemble spread is reduced. Our results suggest avenues for further improvement through increasing ensemble spread by incorporating additive inflation or using a parameter or multi-model ensemble. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.
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Affiliation(s)
- Matthew J. Hoffman
- School of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY 14623, USA
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11
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Welsh AJ, Delgado C, Lee-Trimble C, Kaboudian A, Fenton FH. Simulating waves, chaos and synchronization with a microcontroller. CHAOS (WOODBURY, N.Y.) 2019; 29:123104. [PMID: 31893636 PMCID: PMC7195869 DOI: 10.1063/1.5094351] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/01/2019] [Accepted: 10/22/2019] [Indexed: 05/12/2023]
Abstract
The spatiotemporal dynamics of complex systems have been studied traditionally and visualized numerically using high-end computers. However, due to advances in microcontrollers, it is now possible to run what once were considered large-scale simulations using a very small and inexpensive single integrated circuit that can furthermore send and receive information to and from the outside world in real time. In this paper, we show how microcontrollers can be used to perform simulations of nonlinear ordinary differential equations with spatial coupling and to visualize their dynamics using arrays of light-emitting diodes and/or touchscreens. We demonstrate these abilities using three different models: two reaction-diffusion models (one neural and one cardiac) and a generic model of network oscillators. These models are commonly used to simulate various phenomena in biophysical systems, including bifurcations, waves, chaos, and synchronization. We also demonstrate how simple it is to integrate real-time user interaction with the simulations by showing examples with a light sensor, touchscreen, and web browser.
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Affiliation(s)
- Andrea J Welsh
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - Cristian Delgado
- Facultad de Ciencias, Universidad Nacional Autònoma de México, Distrito Federal 04510, Mexico
| | | | - Abouzar Kaboudian
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - Flavio H Fenton
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
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12
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Veasy J, Lai YM, Coombes S, Thul R. Complex patterns of subcellular cardiac alternans. J Theor Biol 2019; 478:102-114. [PMID: 31220466 DOI: 10.1016/j.jtbi.2019.06.016] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/04/2019] [Revised: 06/12/2019] [Accepted: 06/16/2019] [Indexed: 10/26/2022]
Abstract
Cardiac alternans, in which the membrane potential and the intracellular calcium concentration exhibit alternating durations and peak amplitudes at consecutive beats, constitute a precursor to fatal cardiac arrhythmia such as sudden cardiac death. A crucial question therefore concerns the onset of cardiac alternans. Typically, alternans are only reported when they are fully developed. Here, we present a modelling approach to explore recently discovered microscopic alternans, which represent one of the earliest manifestations of cardiac alternans. In this case, the regular periodic dynamics of the local intracellular calcium concentration is already unstable, while the whole-cell behaviour suggests a healthy cell state. In particular, we use our model to investigate the impact of calcium diffusion in both the cytosol and the sarcoplasmic reticulum on the formation of microscopic calcium alternans. We find that for dominant cytosolic coupling, calcium alternans emerge via the traditional period doubling bifurcation. In contrast, dominant luminal coupling leads to a novel route to calcium alternans through a saddle-node bifurcation at the network level. Combining semi-analytical and computational approaches, we compute areas of stability in parameter space and find that as we cross from stable to unstable regions, the emergent patterns of the intracellular calcium concentration change abruptly in a fashion that is highly dependent upon position along the stability boundary. Our results demonstrate that microscopic calcium alternans may possess a much richer dynamical repertoire than previously thought and further strengthen the role of luminal calcium in shaping cardiac calcium dynamics.
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Affiliation(s)
- Joshua Veasy
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK
| | - Yi Ming Lai
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK
| | - Stephen Coombes
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK
| | - Rüdiger Thul
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK.
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13
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Mora MT, Gomez JF, Morley G, Ferrero JM, Trenor B. Mechanistic investigation of Ca2+ alternans in human heart failure and its modulation by fibroblasts. PLoS One 2019; 14:e0217993. [PMID: 31211790 PMCID: PMC6581251 DOI: 10.1371/journal.pone.0217993] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2019] [Accepted: 05/22/2019] [Indexed: 11/18/2022] Open
Abstract
Background Heart failure (HF) is characterized, among other factors, by a progressive loss of contractile function and by the formation of an arrhythmogenic substrate, both aspects partially related to intracellular Ca2+ cycling disorders. In failing hearts both electrophysiological and structural remodeling, including fibroblast proliferation, contribute to changes in Ca2+ handling which promote the appearance of Ca2+ alternans (Ca-alt). Ca-alt in turn give rise to repolarization alternans, which promote dispersion of repolarization and contribute to reentrant activity. The computational analysis of the incidence of Ca2+ and/or repolarization alternans under HF conditions in the presence of fibroblasts could provide a better understanding of the mechanisms leading to HF arrhythmias and contractile function disorders. Methods and findings The goal of the present study was to investigate in silico the mechanisms leading to the formation of Ca-alt in failing human ventricular myocytes and tissues with disperse fibroblast distributions. The contribution of ionic currents variability to alternans formation at the cellular level was analyzed and the results show that in normal ventricular tissue, altered Ca2+ dynamics lead to Ca-alt, which precede APD alternans and can be aggravated by the presence of fibroblasts. Electrophysiological remodeling of failing tissue alone is sufficient to develop alternans. The incidence of alternans is reduced when fibroblasts are present in failing tissue due to significantly depressed Ca2+ transients. The analysis of the underlying ionic mechanisms suggests that Ca-alt are driven by Ca2+-handling protein and Ca2+ cycling dysfunctions in the junctional sarcoplasmic reticulum and that their contribution to alternans occurrence depends on the cardiac remodeling conditions and on myocyte-fibroblast interactions. Conclusion It can thus be concluded that fibroblasts modulate the formation of Ca-alt in human ventricular tissue subjected to heart failure-related electrophysiological remodeling. Pharmacological therapies should thus consider the extent of both the electrophysiological and structural remodeling present in the failing heart.
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Affiliation(s)
- Maria T. Mora
- Centro de Insvestigación e Innovación en Bioingeniería, Universitat Politècnica de València, Valencia, Spain
| | - Juan F. Gomez
- Centro de Insvestigación e Innovación en Bioingeniería, Universitat Politècnica de València, Valencia, Spain
| | - Gregory Morley
- Leon H. Charney Division of Cardiology, New York University School of Medicine, New York, New York, United States of America
| | - Jose M. Ferrero
- Centro de Insvestigación e Innovación en Bioingeniería, Universitat Politècnica de València, Valencia, Spain
| | - Beatriz Trenor
- Centro de Insvestigación e Innovación en Bioingeniería, Universitat Politècnica de València, Valencia, Spain
- * E-mail:
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14
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Landaw J, Qu Z. Control of voltage-driven instabilities in cardiac myocytes with memory. CHAOS (WOODBURY, N.Y.) 2018; 28:113122. [PMID: 30501225 PMCID: PMC6274634 DOI: 10.1063/1.5040854] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/21/2018] [Accepted: 10/29/2018] [Indexed: 06/09/2023]
Abstract
Sudden cardiac death is known to be associated with dynamical instabilities in the heart, and thus control of dynamical instabilities is considered a potential therapeutic strategy. Different control methods were developed previously, including time-delayed feedback pacing control and constant diastolic interval pacing control. Experimental, theoretical, and simulation studies have examined the efficacy of these control methods in stabilizing action potential dynamics. In this study, we apply these control methods to control complex action potential (AP) dynamics under two diseased conditions: early repolarization syndrome and long QT syndrome, in which voltage-driven instabilities occur in the presence of short-term cardiac memory. In addition, we also develop a feedback pacing method to stabilize these instabilities. We perform theoretical analyses using iterated map models and carry out numerical simulations of AP models. We show that under the normal condition where the memory effect is minimal, all three methods can effectively control the action potential duration (APD) dynamics. Under the two diseased conditions where the memory effect is exacerbated, constant diastolic pacing control is least effective, while the feedback pacing control is most effective. Under a very strong memory effect, all three methods fail to stabilize the voltage-driven instabilities. The failure of effective control is due to memory and the all-or-none AP dynamics which results in very steep changes in APD.
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Affiliation(s)
- Julian Landaw
- Department of Medicine (Cardiology), University of California, Los Angeles, California 90095, USA
| | - Zhilin Qu
- Department of Medicine (Cardiology), University of California, Los Angeles, California 90095, USA
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Zaniboni M. Short-term action potential memory and electrical restitution: A cellular computational study on the stability of cardiac repolarization under dynamic pacing. PLoS One 2018; 13:e0193416. [PMID: 29494628 PMCID: PMC5832261 DOI: 10.1371/journal.pone.0193416] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2017] [Accepted: 02/09/2018] [Indexed: 01/24/2023] Open
Abstract
Electrical restitution (ER) is a major determinant of repolarization stability and, under fast pacing rate, it reveals memory properties of the cardiac action potential (AP), whose dynamics have never been fully elucidated, nor their ionic mechanisms. Previous studies have looked at ER mainly in terms of changes in AP duration (APD) when the preceding diastolic interval (DI) changes and described dynamic conditions where this relationship shows hysteresis which, in turn, has been proposed as a marker of short-term AP memory and repolarization stability. By means of numerical simulations of a non-propagated human ventricular AP, we show here that measuring ER as APD versus the preceding cycle length (CL) provides additional information on repolarization dynamics which is not contained in the companion formulation. We focus particularly on fast pacing rate conditions with a beat-to-beat variable CL, where memory properties emerge from APD vs CL and not from APD vs DI and should thus be stored in APD and not in DI. We provide an ion-currents characterization of such conditions under periodic and random CL variability, and show that the memory stored in APD plays a stabilizing role on AP repolarization under pacing rate perturbations. The gating kinetics of L-type calcium current seems to be the main determinant of this safety mechanism. We also show that, at fast pacing rate and under otherwise identical pacing conditions, a periodically beat-to-beat changing CL is more effective than a random one in stabilizing repolarization. In summary, we propose a novel view of short-term AP memory, differentially stored between systole and diastole, which opens a number of methodological and theoretical implications for the understanding of arrhythmia development.
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Affiliation(s)
- Massimiliano Zaniboni
- Department of Chemistry, Life Sciences and Environmental Sustainability - University of Parma Parco Area delle Scienze, Parma, Italy
- Center of Excellence for Toxicological Research (CERT) - University of Parma, Parma, Italy
- * E-mail:
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Real-Time Closed Loop Diastolic Interval Control Prevents Cardiac Alternans in Isolated Whole Rabbit Hearts. Ann Biomed Eng 2018; 46:555-566. [PMID: 29356998 DOI: 10.1007/s10439-018-1981-2] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2017] [Accepted: 01/12/2018] [Indexed: 10/18/2022]
Abstract
Cardiac alternans, a beat-to-beat alternation in action potential duration (APD), can lead to fatal arrhythmias. During periodic pacing, changes in diastolic interval (DI) depend on subsequent changes in APD, thus enhancing cardiac instabilities through a 'feedback' mechanism. Recently, an anti-arrhythmic Constant DI pacing protocol was proposed and shown to be effective in suppressing alternans in 0D and 1D in silico studies. However, previous experimental validation of Constant DI pacing in the heart has been unsuccessful due to the spatio-temporal complexity of 2D cardiac tissue and the technical challenges in its real-time implementation. Here, we developed a novel closed loop system to detect T-waves from real-time ECG data, enabling successful implementation of Constant DI pacing protocol, and performed high-resolution optical mapping experiments on isolated whole rabbit hearts to validate its anti-arrhythmic effects. The results were compared with: (1) Periodic pacing (feedback inherent) and (2) pacing with heart rate variability (HRV) (feedback modulation) introduced by using either Gaussian or Physiological patterns. We observed that Constant DI pacing significantly suppressed alternans in the heart, while maintaining APD spatial dispersion and flattening the slope of the APD restitution curve, compared to traditional Periodic pacing. In addition, introduction of HRV in Periodic pacing failed to prevent cardiac alternans, and was arrhythmogenic.
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Otani NF. Theory of the development of alternans in the heart during controlled diastolic interval pacing. CHAOS (WOODBURY, N.Y.) 2017; 27:093935. [PMID: 28964128 DOI: 10.1063/1.5003250] [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
The beat-to-beat alternation in action potential durations (APDs) in the heart, called APD alternans, has been linked to the development of serious cardiac rhythm disorders, including ventricular tachycardia and fibrillation. The length of the period between action potentials, called the diastolic interval (DI), is a key dynamical variable in the standard theory of alternans development. Thus, methods that control the DI may be useful in preventing dangerous cardiac rhythms. In this study, we examine the dynamics of alternans during controlled-DI pacing using a series of single-cell and one-dimensional (1D) fiber models of alternans dynamics. We find that a model that combines a so-called memory model with a calcium cycling model can reasonably explain two key experimental results: the possibility of alternans during constant-DI pacing and the phase lag of APDs behind DIs during sinusoidal-DI pacing. We also find that these results can be replicated by incorporating the memory model into an amplitude equation description of a 1D fiber. The 1D fiber result is potentially concerning because it seems to suggest that constant-DI control of alternans can only be effective over only a limited region in space.
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Affiliation(s)
- Niels F Otani
- Department of Mathematical Sciences, Rochester Institute of Technology, Rochester, New York 14623, USA
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