Spatial organization, predictability, and determinism in ventricular fibrillation
Washington University, St. Louis, Missouri 63130. Chaos (Woodbury, N.Y.)
(Impact Factor: 1.95).
03/1998; 8(1):103-115. DOI: 10.1063/1.166291
The degree of spatial organization of ventricular fibrillation (VF) is a fundamental dynamical property of the arrhythmia and may determine the success of proposed therapeutic approaches. Spatial organization is closely related to the dimension of VF, and hence to its predictability and controllability. We have explored several techniques to quantify spatial organization during VF, to predict patterns of activity, and to see how spatial organization and predictability change as the arrhythmia progresses. Epicardial electrograms recorded from pig hearts using rectangular arrays of unipolar extracellular electrodes (1 mm spacing) were analyzed. The correlation length of VF, the number of Karhunen-Loeve modes required to approximate data during VF, the number, size and recurrence of wavefronts, and the mean square error of epicardial potential fields predicted 0.256 seconds into the future were all estimated. The ability of regularly-timed pacing stimuli to capture areas of fibrillating myocardium during VF was confirmed by a significant increase in local spatial organization. Results indicate that VF is neither "low-dimensional chaos" (dimension <5) nor "random" behavior (dimension= infinity ), but is a high-dimensional response with a degree of spatial coherence that changes as the arrhythmia progresses. (c) 1998 American Institute of Physics.
Available from: Kenneth Stein
- "   ) will be able to control fibrillation in the human heart; fibrillation is high-dimensional and spatiotemporal, meaning that multiple variables are required for full-characterization and that its dynamics occur in both space and time. Such dynamics are not accounted for by low-dimensional temporal control techniques  . However, there currently appear to be at least three possible means by which nonlinear dynamics could have an impact in arrhythmia control. "
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ABSTRACT: The field of nonlinear dynamics has made important contributions toward a mechanistic understanding of cardiac arrhythmias. In recent years, many of these advancements have been in the area of arrhythmia control. This paper reviews the literature on analytical, modeling, and experimental nonlinear dynamical arrhythmia control with a focus on stimulation and pharmacologic techniques that have been developed, and in some cases used in experiments, to control reentrant rhythms (including spiral and scroll waves) and fibrillation. Although such approaches currently have practical limitations, they offer hope that nonlinear dynamical control techniques will be clinically useful in the coming years.
Heart Disease 09/1999; 1(4):190-200.
Available from: mcgill.ca
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ABSTRACT: It is well known that there is considerable spatial inhomogeneity in the electrical properties of heart muscle, and that the many interventions that increase this initial degree of inhomogeneity all make it easier to induce certain cardiac arrhythmias. We consider here the specific example of myocardial ischemia, which greatly increases the electrical heterogeneity of ventricular tissue, and often triggers life-threatening cardiac arrhythmias such as ventricular tachycardia and ventricular fibrillation. There is growing evidence that spiral-wave activity underlies these reentrant arrhythmias. We thus investigate whether spiral waves might be induced in a realistic model of inhomogeneous ventricular myocardium. We first modify the Luo and Rudy [Circ. Res. 68, 1501-1526 (1991)] ionic model of cardiac ventricular muscle so as to obtain maintained spiral-wave activity in a two-dimensional homogeneous sheet of ventricular muscle. Regional ischemia is simulated by raising the external potassium concentration ([K(+)](o)) from its nominal value of 5.4 mM in a subsection of the sheet, thus creating a localized inhomogeneity. Spiral-wave activity is induced using a pacing protocol in which the pacing frequency is gradually increased. When [K(+)](o) is sufficiently high in the abnormal area (e.g., 20 mM), there is complete block of propagation of the action potential into that area, resulting in a free end or wave break as the activation wave front encounters the abnormal area. As pacing continues, the free end of the activation wave front traveling in the normal area increasingly separates or detaches from the border between normal and abnormal tissue, eventually resulting in the formation of a maintained spiral wave, whose core lies entirely within an area of normal tissue lying outside of the abnormal area ("type I" spiral wave). At lower [K(+)](o) (e.g., 10.5 mM) in the abnormal area, there is no longer complete block of propagation into the abnormal area; instead, there is partial entrance block into the abnormal area, as well as exit block out of that area. In this case, a different kind of spiral wave (transient "type II" spiral wave) can be evoked, whose induction involves retrograde propagation of the action potential through the abnormal area. The number of turns made by the type II spiral wave depends on several factors, including the level of [K(+)](o) within the abnormal area and its physical size. If the pacing protocol is changed by adding two additional stimuli, a type I spiral wave is instead produced at [K(+)](o)=10.5 mM. When pacing is continued beyond this point, apparently aperiodic multiple spiral-wave activity is seen during pacing. We discuss the relevance of our results for arrythmogenesis in both the ischemic and nonischemic heart. (c) 1998 American Institute of Physics.
Chaos (Woodbury, N.Y.) 04/1998; 8(1):157-174. DOI:10.1063/1.166286 · 1.95 Impact Factor
Available from: thevirtualheart.org
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ABSTRACT: Wave propagation in ventricular muscle is rendered highly anisotropic by the intramural rotation of the fiber. This rotational anisotropy is especially important because it can produce a twist of electrical vortices, which measures the rate of rotation (in degree/mm) of activation wavefronts in successive planes perpendicular to a line of phase singularity, or filament. This twist can then significantly alter the dynamics of the filament. This paper explores this dynamics via numerical simulation. After a review of the literature, we present modeling tools that include: (i) a simplified ionic model with three membrane currents that approximates well the restitution properties and spiral wave behavior of more complex ionic models of cardiac action potential (Beeler-Reuter and others), and (ii) a semi-implicit algorithm for the fast solution of monodomain cable equations with rotational anisotropy. We then discuss selected results of a simulation study of vortex dynamics in a parallelepipedal slab of ventricular muscle of varying wall thickness (S) and fiber rotation rate (theta(z)). The main finding is that rotational anisotropy generates a sufficiently large twist to destabilize a single transmural filament and cause a transition to a wave turbulent state characterized by a high density of chaotically moving filaments. This instability is manifested by the propagation of localized disturbances along the filament and has no previously known analog in isotropic excitable media. These disturbances correspond to highly twisted and distorted regions of filament, or "twistons," that create vortex rings when colliding with the natural boundaries of the ventricle. Moreover, when sufficiently twisted, these rings expand and create additional filaments by further colliding with boundaries. This instability mechanism is distinct from the commonly invoked patchy failure or wave breakup that is not observed here during the initial instability. For modified Beeler-Reuter-like kinetics with stable reentry in two dimensions, decay into turbulence occurs in the left ventricle in about one second above a critical wall thickness in the range of 4-6 mm that matches experiment. However this decay is suppressed by uniformly decreasing excitability. Specific experiments to test these results, and a method to characterize the filament density during fibrillation are discussed. Results are contrasted with other mechanisms of fibrillation and future prospects are summarized. (c)1998 American Institute of Physics.
Chaos (Woodbury, N.Y.) 04/1998; 8(1):20-47. DOI:10.1063/1.166311 · 1.95 Impact Factor
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