909 research outputs found

    Multiple mechanisms of spiral wave breakup in a model of cardiac electrical activity

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    It has become widely accepted that the most dangerous cardiac arrhythmias are due to re- entrant waves, i.e., electrical wave(s) that re-circulate repeatedly throughout the tissue at a higher frequency than the waves produced by the heart's natural pacemaker (sinoatrial node). However, the complicated structure of cardiac tissue, as well as the complex ionic currents in the cell, has made it extremely difficult to pinpoint the detailed mechanisms of these life-threatening reentrant arrhythmias. A simplified ionic model of the cardiac action potential (AP), which can be fitted to a wide variety of experimentally and numerically obtained mesoscopic characteristics of cardiac tissue such as AP shape and restitution of AP duration and conduction velocity, is used to explain many different mechanisms of spiral wave breakup which in principle can occur in cardiac tissue. Some, but not all, of these mechanisms have been observed before using other models; therefore, the purpose of this paper is to demonstrate them using just one framework model and to explain the different parameter regimes or physiological properties necessary for each mechanism (such as high or low excitability, corresponding to normal or ischemic tissue, spiral tip trajectory types, and tissue structures such as rotational anisotropy and periodic boundary conditions). Each mechanism is compared with data from other ionic models or experiments to illustrate that they are not model-specific phenomena. The fact that many different breakup mechanisms exist has important implications for antiarrhythmic drug design and for comparisons of fibrillation experiments using different species, electromechanical uncoupling drugs, and initiation protocols.Comment: 128 pages, 42 figures (29 color, 13 b&w

    Cardiac cell modelling: Observations from the heart of the cardiac physiome project

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    In this manuscript we review the state of cardiac cell modelling in the context of international initiatives such as the IUPS Physiome and Virtual Physiological Human Projects, which aim to integrate computational models across scales and physics. In particular we focus on the relationship between experimental data and model parameterisation across a range of model types and cellular physiological systems. Finally, in the context of parameter identification and model reuse within the Cardiac Physiome, we suggest some future priority areas for this field

    Asymptotics of conduction velocity restitution in models of electrical excitation in the heart

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    We extend a non-Tikhonov asymptotic embedding, proposed earlier, for calculation of conduction velocity restitution curves in ionic models of cardiac excitability. Conduction velocity restitution is the simplest non-trivial spatially extended problem in excitable media, and in the case of cardiac tissue it is an important tool for prediction of cardiac arrhythmias and fibrillation. An idealized conduction velocity restitution curve requires solving a non-linear eigenvalue problem with periodic boundary conditions, which in the cardiac case is very stiff and calls for the use of asymptotic methods. We compare asymptotics of restitution curves in four examples, two generic excitable media models, and two ionic cardiac models. The generic models include the classical FitzHugh–Nagumo model and its variation by Barkley. They are treated with standard singular perturbation techniques. The ionic models include a simplified “caricature” of Noble (J. Physiol. Lond. 160:317–352, 1962) model and Beeler and Reuter (J. Physiol. Lond. 268:177–210, 1977) model, which lead to non-Tikhonov problems where known asymptotic results do not apply. The Caricature Noble model is considered with particular care to demonstrate the well-posedness of the corresponding boundary-value problem. The developed method for calculation of conduction velocity restitution is then applied to the Beeler–Reuter model. We discuss new mathematical features appearing in cardiac ionic models and possible applications of the developed method

    Advancing the Early Detection of Atrial Fibrillation Through In Silico Tissue Modeling

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    Atrial fibrillation (AF) is a widely prevalent arrhythmia which affects approximately 4.5 million people in Europe and the US, reducing quality of life and increasing risk of stroke and death. Considerable research effort is currently directed to the arrhythmia because the mechanisms causing its initiation, maintenance, and termination are not well understood. This study addresses, at a tissue level, the basic descriptors of atrial fibrillation, known causes, and a model to utilize in analyzing heart wave characteristics such as propagation velocity, action potential duration and others for potential use in developing early detection methods of AF. The tissue model methodology, based on epicardial tissue and kinetics from a cellular model, utilized the MATLAB PDEPE solver on a 1 X .0011 cm tissue strip, enabling research into complex action potential (AP) and AP propagation characteristics. The model represented left atrial tissue sinus rhythm (SR) and AF states as defined in Grandi et al.23 with comprehensive state variables and ionic currents as well as complete cellular physiology including excitation contraction coupling with sarcoplasmic reticulum Ca2+ ATPase, calcium-induced calcium release, Ca2+ and Na+ buffer fluxes, subcellular sections and diffusion factors, Based on following the nonlinear response cascade of the potassium channels during the progression to AF, the tissue model study provides insight into wave propagation velocity, atrial AP amplitude, action potential duration, non-refractory periods, in addition to other wave characteristics through rates of change, greater then 50%. Regardless of the many known forms of AF, which often involve polygenetic and other cardiac pathologies, this human tissue model study, with its completeness of cardiac cell and tissue representation, provides a basis for further analysis research and modeling because the cardiac structures used can be modified to represent or independently model other potential pathologies that represent early risk warning indicators

    Using Delay-Differential Equations for Modeling Calcium Cycling in Cardiac Myocytes

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    The cycling of calcium at the intracellular level of cardiac cells plays a key role in the excitation-contraction process. The interplay between ionic currents, buffering agents, and calcium release from the sarcoplasmic reticulum (SR) is a complex system that has been shown experimentally to exhibit complex dynamics including period-2 states (alternans) and higher-order rhythms. Many of the calcium cycling activities involve the sensing, binding, or diffusion of calcium between intracellular compartments; these are physical processes that take time and typically are modeled by “relaxation” equations where the steady-state value and time course of a particular variable are specified through an ordinary differential equation (ODE) with a time constant. An alternative approach is to use delay-differential equations (DDEs), where the delays in the system correspond to non-instantaneous events. In this thesis, we present a thorough overview of results from calcium cycling experiments and proposed intracellular calcium cycling models, as well as the context of alternans and delay-differential equations in cardiac modeling. We utilize a DDE to model the diffusion of calcium through the SR by replacing the relaxation ODE typically used for this process. The relaxation time constant τa is replaced by a delay δj, which could also be interpreted as the refractoriness of ryanodine receptor channels after releasing calcium from the sarcoplasmic reticulum. This is the first application of delay-differential equations to modeling calcium cycling dynamics, and to modeling cardiac systems at the cellular level. We analyzed the dynamical behaviors of the system and focus on the factors that have been shown to produce alternans and irregular dynamics in experiments and models with cardiac myocytes. We found that chaotic calcium dynamics could occur even for a more physiologically revelant SR calcium release slope than comparable ODE models. Increasing the SR release slope did not affect the calcium dynamics, but only shifted behavior down to lower values of the delay, allowing alternans, higher-order behavior, and chaos to occur for smaller delays than in simulations with a normal SR release slope. For moderate values of the delay, solely alternans and 1:1 steady-state behavior were observed. Above a particular threshold value for the delay, chaos appeared in the dynamics and further increasing the delay caused the system to destabilize under broader ranges of periods. We also compare our results with other models of intracellular calcium cycling and suggest promising avenues for further development of our preliminary work

    Models of the cardiac L-type calcium current: A quantitative review

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    The L-type calcium current (ICaL) plays a critical role in cardiac electrophysiology, and models of ICaL are vital tools to predict arrhythmogenicity of drugs and mutations. Five decades of measuring and modeling ICaL have resulted in several competing theories (encoded in mathematical equations). However, the introduction of new models has not typically been accompanied by a data-driven critical comparison with previous work, so that it is unclear which model is best suited for any particular application. In this review, we describe and compare 73 published mammalian ICaL models and use simulated experiments to show that there is a large variability in their predictions, which is not substantially diminished when grouping by species or other categories. We provide model code for 60 models, list major data sources, and discuss experimental and modeling work that will be required to reduce this huge list of competing theories and ultimately develop a community consensus model of ICaL. // This article is categorized under: Cardiovascular Diseases > Computational Models Cardiovascular Diseases > Molecular and Cellular Physiolog

    A TIME-AND-SPACE PARALLELIZED ALGORITHM FOR THE CABLE EQUATION

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    Electrical propagation in excitable tissue, such as nerve fibers and heart muscle, is described by a nonlinear diffusion-reaction parabolic partial differential equation for the transmembrane voltage V(x,t)V(x,t), known as the cable equation. This equation involves a highly nonlinear source term, representing the total ionic current across the membrane, governed by a Hodgkin-Huxley type ionic model, and requires the solution of a system of ordinary differential equations. Thus, the model consists of a PDE (in 1-, 2- or 3-dimensions) coupled to a system of ODEs, and it is very expensive to solve, especially in 2 and 3 dimensions. In order to solve this equation numerically, we develop an algorithm, extended from the Parareal Algorithm, to efficiently incorporate space-parallelized solvers into the framework of the Parareal algorithm, to achieve time-and-space parallelization. Numerical results and comparison of the performance of several serial, space-parallelized and time-and-space-parallelized time-stepping numerical schemes in one-dimension and in two-dimensions are also presented

    ISOGEOMETRIC OVERLAPPING ADDITIVE SCHWARZ PRECONDITIONERS IN COMPUTATIONAL ELECTROCARDIOLOGY

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    In this thesis we present and study overlapping additive Schwarz preconditioner for the isogeometric discretization of reaction-diffusion systems modeling the heart bioelectrical activity, known as the Bidomain and Monodomain models. The cardiac Bidomain model consists of a degenerate system of parabolic and elliptic PDE, whereas the simplified Monodomain model consists of a single parabolic equation. These models include intramural fiber rotation, anisotropic conductivity coefficients and are coupled through the reaction term with a system of ODEs, which models the ionic currents of the cellular membrane. The overlapping Schwarz preconditioner is applied with a PCG accelerator to solve the linear system arising at each time step from the isogeometric discretization in space and a semi-implicit adaptive method in time. A theoretical convergence rate analysis shows that the resulting solver is scalable, optimal in the ratio of subdomain/element size and the convergence rate improves with increasing overlap size. Numerical tests in three-dimensional ellipsoidal domains confirm the theoretical estimates and additionally show the robustness with respect to jump discontinuities of the orthotropic conductivity coefficients

    Splitting a heart

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    This thesis investigates and numerically solves the Wohlfart-Arloch equations describing the electrical activity in the atrial part of the heart. This is done through operator splitting that is allowing the diffusion of ionic currents, and the local voltage-driven reactions in each cell to be de-coupled. The local reactions can be solved in closed form, and the diffusion part is solved with a spectral method by interpolating using eigenmodes. The problem of initiating the system is solved by introducing time-dependent boundary conditions and solving these parts as a series. Systematic investigations are carried out both concerning the numerical errors and also the wave speed, multiple pulse shape, and other characteristics relevant to ascertaining the validity of the numerical method used
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