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Am J Physiol Heart Circ Physiol 282: H1534-H1547, 2002. First published November 29, 2001; doi:10.1152/ajpheart.00351.2001
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Vol. 282, Issue 4, H1534-H1547, April 2002

Mathematical analysis of dynamics of cardiac memory and accommodation: theory and experiment

Mari A. Watanabe1,2 and Marcus L. Koller3

1 Institute of Biomedical and Life Sciences, Glasgow University, Glasgow G12 8QQ, United Kingdom; 2 Center for Interdisciplinary and Complex Systems, Northeastern University, Boston, Massachusetts 02115; and 3 Medizinische Klinik der Universität Würzburg, 97080 Würzburg, Germany

Decreasing the slope of the dynamic, but not conventional, restitution curves is antifibrillatory. Cardiac memory/accommodation underlies the difference. We measured diastolic interval (DI) and action potential duration (APD) in epicardial, endocardial, and Purkinje tissue from eight dogs. Consecutive 100-stimulus trains were given to study transitions between basic cycle lengths (BCL) ranging from 400 to 1,300 ms. (DI,APD) pairs aligned immediately on the line DI + APD = BCL (64/67) or oscillated (3/67). The shifting effect of up to 10 extrastimuli on restitution curves was also measured. These curves were fit with the equation APD = alpha  + beta  exp(-DI/tau ), where alpha  is asymptote, beta  is drop, and tau  is time constant. Linear regression of the parameters against the number of extrastimuli showed that premature and postmature stimuli decreased and increased alpha  and beta  and increased and decreased tau , respectively. Analysis of a mathematical model treating memory as an exponentially decreasing shift of restitution curves shows that oscillatory DI,APD is expected with large Delta BCL, steep restitution slope, or increased cardiac accommodation. The model explains phase shifts and suggests a common mechanism for Purkinje and myocardial electrical alternans.

arrhythmias; dynamic restitution; short-term memory; modeling


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