Various ways to make phase singularities by electric shock.
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Computer Simulation↗
Biomedical subjects
A T Winfree
Publications and source records attributed to A T Winfree.
Spatiotemporal evolution of ventricular fibrillation.
Sudden cardiac death is the leading cause of death in the industrialized world, with the majority of such tragedies being due to ventricular fibrillation. Ventricular fibrillation is a frenzied and irregular disturbance of the heart rhythm that quickly renders the heart incapable of sustaining life. Rotors, electrophysiological structures that emit rotating spiral waves, occur in several systems that all share with the heart the functional properties of excitability and refractoriness. These re-entrant waves, seen in numerical solutions of simplified models of cardiac tissue, may occur during ventricular tachycardias. It has been difficult to detect such forms of re-entry in fibrillating mammalian ventricles. Here we show that, in isolated perfused dog hearts, high spatial and temporal resolution mapping of optical transmembrane potentials can easily detect transiently erupting rotors during the early phase of ventricular fibrillation. This activity is characterized by a relatively high spatiotemporal cross-correlation. During this early fibrillatory interval, frequent wavefront collisions and wavebreak generation are also dominant features. Interestingly, this spatiotemporal pattern undergoes an evolution to a less highly spatially correlated mechanism that lacks the epicardial manifestations of rotors despite continued myocardial perfusion.
Electric Stimulation↗
A spatial scale factor for electrophysiological models of myocardium.
In the United States among males 20-64 years old about 1/3 of deaths are classified as 'sudden cardiac death', and 1/4 had no forewarning, nor did autopsy turn up any visible cause. The heart just switches from its normally periodic pumping to an alternative mode called 'fibrillation' more resembling electrical turbulence. In normal tissue its mechanism is a geometrically re-entrant mode of normal propagation. Everything about this spatial pattern depends upon the magnitude of 'D', the one term with dimension involving space in the pertinent biophysical equations. Explicit or implicit estimates in current literature span orders of magnitude. In this article I argue from a diversity of recent experiments for a narrower range of realistic values. It has an important role in the spatio-temporal evolution of fibrillation and in defibrillation.
Adult↗
On measuring curvature and electrical diffusion coefficients in anisotropic myocardium: comments on "effects of bipolar point and line simulation in anisotropic rabbit epicardium: assessment of the critical radius of curvature for longitudinal block".
Notion of "curvature" and "propagation perpendicular to the activation front" inherited from electrophysiological theory of isotropic reaction-diffusion media do not apply directly to experimental data taken in uniformly anisotropic myocardium. They apply directly only after the concept of "curvature" is normalized and propagation is made to look perpendicular to activation fronts by rescaling distances to achieve isotropy. Without rescaling, the curvature-dependence of longitudinal propagation speed turns out counter-intuitively to measure transverse intercellular electrical coupling.
Action Potentials↗
Electrical turbulence in three-dimensional heart muscle.
Rotors or vortex action potentials with a diameter of about 1 centimeter and a rotation period of about 0.1 second occur in normal myocardium just before transition to fibrillation, a disorderly pattern of action potential propagation. Numerical models and corresponding mathematical analysis have recently suggested candidate mechanisms, all two-dimensional, for this transition from periodic electrical activity to something resembling turbulence. However, comparably recent experiments unanimously show that rotors, and the spiral waves they radiate, remain stably periodic in two-dimensional myocardium. This seeming paradox suggests a transition mediated through disorderly dynamics of the electrical vortex in three dimensions, as a "vortex filament."
Action Potentials↗
Persistent tangled vortex rings in generic excitable media.
Excitable media are exemplified by a range of living systems, such as mammalian heart muscle and its cells and Xenopus eggs. They also occur in non-living systems such as the autocatalytic Belousov-Zhabotinsky reaction. In most of these systems, activity patterns, such as concentration waves, typically radiate as spiral waves from a vortex of excitation created by some nonuniform stimulus. In three-dimensional systems, the vortex is commonly a line, and these vortex lines can form linked and knotted rings which contract into compact, particle-like bundles. In most previous work these stable 'organizing centres' have been found to be symmetrical and can be classified topologically. Here I show through numerical studies of a generic excitable medium that the more general configuration of vortex lines is a turbulent tangle, which is robust against changes in the parameters of the system or perturbations to it. In view of their stability, I suggest that these turbulent tangles should be observable in any of the many known excitable media.
Animals↗
Circadian rhythms. Resetting the human clock.
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Circadian Rhythm↗
Vortex action potentials in normal ventricular muscle.
A remarkable feature of healthy ventricular myocardium, exposed by electrical stimulation and high-resolution mapping, is that, despite its gross nonuniformities and structural discontinuities on the submillimeter scale, it behaves electrically so much like a continuous uniformly anisotropic excitable medium. Such media are susceptible to a self-sustaining high-frequency periodic mode of activity in the form of freely movable paired vortices in two dimensions or vortex filaments in three dimensions. These can be evoked by a timely stimulus of the right size, for example, in myocardium by an electrical stimulus during the vulnerable period. Such stimuli may occur at random within complex patterns of stimulation and activation, even in healthy uniform tissue. Discontinuities and heterogeneity apparently make diseased tissue more vulnerable. Such vortices may underlie common reentrant tachycardias that degenerate into ventricular fibrillation, the commonest cause of sudden cardiac death. If the normal mechanism here reviewed also plays a role in diseased tissue, then it provides a quantitative basis for design of improved procedures for management of reentrant ventricular tachycardias that threaten to degrade to fibrillation.
Action Potentials↗
Electrical instability in cardiac muscle: phase singularities and rotors.
A dynamical system is "excitable" at some stage in its behavior (e.g. at a rest state or while it is nearly at rest prior to a spontaneous event) if a small, but not too small, stimulus of the right kind elicits an immediate big reaction that eventually leads back to the original state. During this return to excitability a typical system is not excitable. An excitable system need not have an attracting rest state; a spontaneous oscillator can be excitable, too, as is common in biological and in chemical excitable kinetics. In a medium characterized by such excitable dynamics at every point, the excitation can propagate as a travelling pulse. Undamaged cardiac muscle shares with other excitable media certain features of such pulse propagation in two and three dimensions. Among the new electrophysiological phenomena thus anticipated are paired mirror-image vortices ("rotors") organized around phase singularities. These should arise in the myocardium near the intersection of a moving critical contour of phase in the normal cycle of excitation and recovery with a momentary critical contour of local stimulus strength. Such intersections, and the corresponding aftermath of paired rotors, should only occur following certain combinations of stimulus size and stimulus timing. Plotting those combinations on a "vulnerability diagram", one delineates a domain for creation of rotors (corresponding to tachycardia) surrounded on all sides by a halo of combinations at which just a few repetitive responses follow stimulation. The experiments called for to check these implications have now been carried out in the special case of electrically-induced tachycardia in healthy canine ventricle. They support the two-dimensional theory, so a new experiment is suggested to demonstrate wholly intramural three-dimensional vortex filaments.
Animals↗
Discontinuities in phase-resetting experiments.
The effects of perturbing an on-going biological oscillation with a single brief stimulus are considered. If the time from some observable event before the stimulus to the next event after the stimulus is plotted as a function of the phase of the stimulus, then there may be discontinuities in this plot. The discontinuities reflect the size of the stimulus and the topological properties of the biological oscillation. The implications for experiments are discussed.
Animals↗
Sudden cardia death: a problem in topology.
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Action Potentials↗
Impact of a circadian clock on the timing of human sleep.
This paper redescribes some recordings of human sleep and waking made in several laboratories during the past decade under conditions of temporal isolation. Since 1972 it has been noticed that sleep duration depends mainly on the timing of prior sleep onset relative to a rhythm of 24- to 25-h duration. The present paper emphasizes four additional points: 1) that the dependence sometimes includes a remarkable discontinuity, 2) that such dependence is characteristic of a rhythmically modulated threshold process; 3) that the rhythm's period gradually changes in some experiments; and 4) that no comparable regularity has been detected in the timing of sleep onset. This last impugns the reliability of models that treat sleep onset and wake onset as complementary but comparable processes.
Circadian Rhythm↗
A three-oscillator model of the human circadian system controlling the core temperature rhythm and the sleep-wake cycle.
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Adult↗
Human body clocks and the timing of sleep.
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Aerospace Medicine↗
The tides of human consciousness: descriptions and questions.
A Rosetta Stone has appeared in our midst in the form of R. A. Wever's monograph The Circadian System of Man (New York: Springer-Verlag, 1979), describing the results of 20 years' experiments with J. Aschoff. In the January 1982 issue of this journal, Kronauer, Czeisler, Pilato, Moore-Ede, and Weitzman offer their decipherment: a mathematical description of man's circadian temperature rhythm and sleep timing based on their own experimental observations in the Bronx, confirming and substantially extending Wever's in Bavaria. This paper might have been as happily received by the Journal of Mathematical Biology or Biological Cybernetics. Accordingly I here attempt to disentangle numerical description from physiological hypothesis, emphasizing items that seem, at least in principle, susceptible to experimental test.
Body Temperature Regulation↗
Circadian timing of sleepiness in man and woman.
Men and women living contentedly in long-term isolation from the usual time-of-day cues have revealed surprising new regularities about the timing of human sleep/wake alternations. Contemporary effort to ferret out and articulate these regularities in quantitative terms lead to a diversity of mathematical models. If these eventually acquire predictive competence then we may expect practical improvements of therapy for insomnia, jet lag, and some kinds of psychiatric depression.
Body Temperature↗
A single spiral artefact in arthropod cuticle.
Spirals are often seen in sections transverse to the axes of bumped structures in arthropod cuticle. (Sections through arthropod cornea or exocones yield excellent examples.) As arthropod cuticle has a helicoidal architecture (Bouligand, 1965), it might be expected that the spirals are a simple consequence of that structure. According to a symmetry argument, the spirals thus predicted must be double spirals. In contrast, the observed spirals are usually single. We propose that the single spirals result from an interaction between the microtome knife and the cuticle architecture. The direction of knife travel defines an orientation within the cuticle, subverting the symmetry arguments that require double spirals. Bouligand (1972) presented a model for the interaction of the knife with the cuticle. However, we offer arguments and observations show that Bouligand's model is incorrect. We argue from detailed observations of the single spiral that it is indeed a knifing artifact and that its explanation probably lies within a certain class of models. Two related models based on relative movements of cuticle components are examined via computer techniques.
Animals↗
Phase control of neural pacemakers.
An electrical stimulus resets the phase of a spontaneously rhythmic neuron. The "new phase" versus "old phase" curve shows either of two distinct topological characters, depending on the stimulus magnitude. These features, and a phase singularity implicit in them, are common to many stable oscillations deriving from continuous feedback between two or more biophysical quantities.
Action Potentials↗