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Consider a typical experimental protocol in which one end of a one-dimensional fiber of cardiac tissue is periodically stimulated, or paced, resulting in a train of propagating action potentials. There is evidence that a sudden change in the pacing period can initiate abnormal cardiac rhythms. In this paper, we analyze how the fiber responds to such a… (More)

Action potential duration (APD) restitution, which relates APD to the preceding diastolic interval (DI), is a useful tool for predicting the onset of abnormal cardiac rhythms. However, it is known that different pacing protocols lead to different APD restitution curves (RCs). This phenomenon, known as APD rate dependence, is a consequence of memory in the… (More)

- David G Schaeffer, John W Cain, Daniel J Gauthier, Soma S Kalb, Robert A Oliver, Elena G Tolkacheva +2 others
- Bulletin of mathematical biology
- 2007

Many features of the sequence of action potentials produced by repeated stimulation of a patch of cardiac muscle can be modeled by a 1D mapping, but not the full behavior included in the restitution portrait. Specifically, recent experiments have found that (i) the dynamic and S1-S2 restitution curves are different (rate dependence) and (ii) the approach to… (More)

If spatial extent is neglected, ionic models of cardiac cells consist of systems of ordinary differential equations (ODEs) which have the property of excitability, i.e., a brief stimulus produces a prolonged evolution (called an action potential in the cardiac context) before the eventual return to equilibrium. Under repeated stimulation, or pacing, cardiac… (More)

It is known, from both experiments and simulations, that cardiac action potentials are shortened near a non-conducting boundary. In the present paper, this effect is studied in a simple, two-current ionic model, with propagation restricted to a 1D fibre. An asymptotic approximation for the dependence of action potential duration on distance to the boundary… (More)

- John W Cain, Angela M Reynolds
- 2015

We model electrical wave propagation in a ring of cardiac tissue using an mth-order difference equation, where m denotes the number of cells in the ring. Under physiologically reasonable assumptions, the difference equation has a unique equilibrium solution. Applying Jury's stability test, we prove a theorem concerning the local asymptotic stability of this… (More)

- Carolyn M Berger, John W Cain, Joshua E S Socolar, Daniel J Gauthier
- Physical review. E, Statistical, nonlinear, and…
- 2007

Experimental studies have linked alternans, an abnormal beat-to-beat alternation of cardiac action potential duration, to the genesis of lethal arrhythmias such as ventricular fibrillation. Prior studies have considered various closed-loop feedback control algorithms for perturbing interstimulus intervals in such a way that alternans is suppressed. However,… (More)

- John W Cain
- 2015

O n his website, University of Utah mathematics professor James Keener poses the question, " Did you know that heart attacks can give you mathematics!? " Indeed, there are a host of important research problems in cardiology that appear ideal for unified attack by mathematicians, clinicians, and biomedical engineers. What follows is a survey of six ongoing… (More)

- Advait A Apte, John W Cain, Danail G Bonchev, Stephen S Fong
- Journal of biological engineering
- 2008

BACKGROUND
Feed-forward motifs are important functional modules in biological and other complex networks. The functionality of feed-forward motifs and other network motifs is largely dictated by the connectivity of the individual network components. While studies on the dynamics of motifs and networks are usually devoted to the temporal or spatial… (More)