Obituary: Arthur T. Winfree (1942-2002).
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Animals↗
Biomedical subjects
Leon Glass
Publications and source records attributed to Leon Glass.
Complex patterns of abnormal heartbeats.
Individuals having frequent abnormal heartbeats interspersed with normal heartbeats may be at an increased risk of sudden cardiac death. However, mechanistic understanding of such cardiac arrhythmias is limited. We present a visual and qualitative method to display statistical properties of abnormal heartbeats. We introduce dynamical "heartprints" which reveal characteristic patterns in long clinical records encompassing approximately 10(5) heartbeats and may provide information about underlying mechanisms. We test if these dynamics can be reproduced by model simulations in which abnormal heartbeats are generated (i) randomly, (ii) at a fixed time interval following a preceding normal heartbeat, or (iii) by an independent oscillator that may or may not interact with the normal heartbeat. We compare the results of these three models and test their limitations to comprehensively simulate the statistical features of selected clinical records. This work introduces methods that can be used to test mathematical models of arrhythmogenesis and to develop a new understanding of underlying electrophysiologic mechanisms of cardiac arrhythmia.
Arrhythmias, Cardiac↗
Chaos in two-loop negative feedback systems.
Multiloop delayed negative feedback systems, with each feedback loop having its own characteristic time lag (delay), are used to describe a great variety of systems: optical systems, neural networks, physiological control systems, etc. Previous investigations have shown that if the number of delayed feedback loops is greater than two, the system can exhibit complex dynamics and chaos, but in the case of two delayed loops only periodic solutions were found. Here we show that a period-doubling cascade and chaotic dynamics are also found in systems with two coupled delayed negative feedback loops.
Biophysics↗
Predicting the entrainment of reentrant cardiac waves using phase resetting curves.
Excitable media, such as the Belousov-Zhabotinsky medium or the heart, are capable of supporting excitation waves that circulate in a closed repetitive path--a phenomenon known as reentrant excitation. A single stimulus, depending on its magnitude, timing, and location, can cause a time shift of the reentrant excitation called resetting. The present study examines the ability of resetting data to predict the effects of periodic stimuli on reentrant excitation circulating on an annular domain. We compare the results of the theoretical models with experiments carried out in an animal model of a dangerous reentrant cardiac rhythm. The current work may lead to improved approaches to therapy through a better understanding of how typical clinical stimuli interact with abnormal reentrant cardiac rhythms.
Animals↗
Spiral wave generation in heterogeneous excitable media.
As the coupling in a heterogeneous excitable medium is reduced, three different types of behavior are encountered: plane waves propagate without breaking up, plane waves break up into spiral waves, and plane waves block. We illustrate these phenomena in monolayers of chick embryonic heart cells using calcium sensitive fluorescent dyes. Following the addition of heptanol, an agent that reduces the electrical coupling between cells, we observe breakup of spiral waves. These results are modeled in a heterogeneous cellular automaton model in which the neighborhood of interaction is modified.
Animals↗
A mathematical model of human atrioventricular nodal function incorporating concealed conduction.
This work develops a mathematical model for the atrioventricular (AV) node in the human heart, based on recordings of electrical activity in the atria (the upper chambers of the heart) and the ventricles (the lower chambers of the heart). Intracardiac recordings of the atrial and ventricular activities were recorded from one patient with atrial flutter and one with atrial fibrillation. During these arrhythmias, not all beats in the atria are conducted to the ventricles. Some are blocked (concealed). However, the blocked beats can affect the properties of the AV node. The activation times of the atrial events were regarded as inputs to a mathematical model of conduction in the AV node, including a representation of AV nodal concealment. The model output was compared to the recorded ventricular response to search for and identify the best possible parameter combinations of the model. Good agreement between the distribution of interbeat intervals in the model and data for durations of 5 min was achieved. A model of AV nodal behavior during atrial flutter and atrial fibrillation could potentially help to understand the relative roles of atrial input activity and intrinsic AV nodal properties in determining the ventricular response.
Atrial Fibrillation↗
Introduction: Mapping and control of complex cardiac arrhythmias.
This paper serves as an introduction to the Focus Issue on mapping and control of complex cardiac arrhythmias. We first introduce basic concepts of cardiac electrophysiology and describe the main clinical methods being used to treat arrhythmia. We then provide a brief summary of the main themes contained in the articles in this Focus Issue. In recent years there have been important advances in the ability to map the spread of excitation in intact hearts and in laboratory settings. This work has been combined with simulations that use increasingly realistic geometry and physiology. Waves of excitation and contraction in the heart do not always propagate with constant velocity but are often subject to instabilities that may lead to fluctuations in velocity and cycle time. Such instabilities are often treated best in the context of simple one- or two-dimensional geometries. An understanding of the mechanisms of propagation and wave stability is leading to the implementation of different stimulation protocols in an effort to modify or eliminate abnormal rhythms. (c) 2002 American Institute of Physics.
Journal Article↗
Scroll waves in spherical shell geometries.
The evolution of scroll waves in excitable media with spherical shell geometries is studied as a function of shell thickness and outer radius. The motion of scroll wave filaments that are the locii of phaseless points in the medium and organize the wave pattern is investigated. When the inner radius is sufficiently large the filaments remain attached to both the inner and outer surfaces. The minimum size of the sphere that supports spiral waves and the maximum number of spiral waves that can be sustained on a sphere of given size are determined for both regular and random initial distributions. When the inner radius is too small to support spiral waves the filaments detach from the inner surface and form a curved filament connecting the two spiral tips in the surface. In certain parameter domains the filament is an arc of a circle that shrinks with constant shape. For parameter values close to the meandering border, the filament grows and collisions with the sphere walls lead to turbulent filament dynamics. (c) 2001 American Institute of Physics.
Journal Article↗
Dynamics of Parkinsonian tremor during deep brain stimulation.
The mechanism by which chronic, high frequency, electrical deep brain stimulation (HF-DBS) suppresses tremor in Parkinson's disease is unknown. Rest tremor in subjects with Parkinson's disease receiving HF-DBS was recorded continuously throughout switching the deep brain stimulator on (at an effective frequency) and off. These data suggest that the stimulation induces a qualitative change in the dynamics, called a Hopf bifurcation, so that the stable oscillations are destabilized. We hypothesize that the periodic stimulation modifies a parameter affecting the oscillation in a time dependent way and thereby induces a Hopf bifurcation. We explore this hypothesis using a schematic network model of an oscillator interacting with periodic stimulation. The mechanism of time-dependent change of a control parameter in the model captures two aspects of the dynamics observed in the data: (1) a gradual increase in tremor amplitude when the stimulation is switched off and a gradual decrease in tremor amplitude when the stimulation is switched on and (2) a time delay in the onset and offset of the oscillations. This mechanism is consistent with these rest tremor transition data and with the idea that HF-DBS acts via the gradual change of a network property. (c) 2001 American Institute of Physics.
Journal Article↗
Dynamical disease: Identification, temporal aspects and treatment strategies of human illness.
Dynamical diseases are characterized by sudden changes in the qualitative dynamics of physiological processes, leading to abnormal dynamics and disease. Thus, there is a natural matching between the mathematical field of nonlinear dynamics and medicine. This paper summarizes advances in the study of dynamical disease with emphasis on a NATO Advanced Research Worshop held in Mont Tremblant, Quebec, Canada in February 1994. We describe the international effort currently underway to identify dynamical diseases and to study these diseases from a perspective of nonlinear dynamics. Linear and nonlinear time series analysis combined with analysis of bifurcations in dynamics are being used to help understand mechanisms of pathological rhythms and offer the promise for better diagnostic and therapeutic techniques. (c) 1995 American Institute of Physics.
Journal Article↗
Cardiac arrhythmias and circle maps-A classical problem.
The periodic forcing of nonlinear oscillations can often be cast as a problem involving self-maps of the circle. Consideration of the effects of changes in the frequency and amplitude of the periodic forcing leads to a problem involving the bifurcations of circle maps in a two-dimensional parameter space. The global bifurcations in this two-dimensional parameter space is described for periodic forcing of several simple theoretical models of nonlinear oscillations. As was originally recognized by Arnold, one motivation for the formulation of these models is their connection with theoretical models of cardiac arrhythmias originating from the competition and interaction between two pacemakers for the control of the heart.
Journal Article↗
Nonlinear dynamics of physiological function and control.
Complex rhythms are observed in the physiological systems that control and carry out vital bodily functions. Theoretical approaches to analyze the physiological systems include control theory and computation theory. Complementary to these approaches is nonlinear dynamics, which offers ways to classify both normal and abnormal dynamics, and to analyze bifurcations occurring in physiological dynamics.
Journal Article↗