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Amplitude equations are derived that describe the spatiotemporal dynamics ofcardiac alternans during periodic pacing of one- and two-dimensionalhomogeneous tissue and one-dimensional anatomical reentry in a ring ofhomogeneous tissue. These equations provide a simple physical understanding ofarrhythmogenic patterns of period-doubling oscillations of action potentialduration with a spatially varying phase and amplitude as well as explicitquantitative predictions that can be compared to ionic model simulations orexperiments. The form of the equations is expected to be valid for a largeclass of ionic models but the coefficients are only derived analytically for atwo-variable ionic model and calculated numerically for the original Noblemodel of Purkinje fiber action potential.In paced tissue, the main result isthe existence of a linear instability that produces a periodic pattern ofdiscordant alternans. Moreover, the patterns of alternans can be eitherstationary, with fixed nodes, or travelling, with moving nodes and hencequasiperiodic oscillations of action potential duration, depending on therelative strength of the destabilizing effect of CV-restitution and thestabilizing effect of diffusive coupling. In both the paced geometries and thering, the onset of alternans is different in tissue than for a paced isolatedcell. The implications of these results for alternans dynamics duringtwo-dimensional reentry are briefly discussed.Comment: 55 pages, 13 figures, to appear in Phys. Rev.

Amplitude equation approach to spatiotemporal dynamics of cardiac alternans