Low dimensional chaos in cardiac tissue

Abstract

CHAOS is a term uvd to characterize aperiodic activity arising in a dynamical system, or in a set of equations describing the system's temporal evolution as a result of a deterministic mechanism that has sensitive dependence on initial conditions¹. Chaos, in that sense, has been proposed to make an important contribution to normal and abnormal cardiac rhythms^2–6. To date, however, descriptions of chaos in heart tissue have been limited primarily to periodically forced cardiac pacemakers^2,6. Because many cardiac rhythm disturbances, particularly those initiated or perpetuated by re-entrant excitation, originate from within non-pacemaker cardiac tissues^7–9, demonstrations of chaos in non-pacemaker tissue might provide a deterministic explanation for a wide variety of complex dysrhythmias. Here we report experimental evidence for chaotic patterns of activation and action potential characteristics in externally driven, non-spontaneously active Purkinje fibres and ventricular muscle. The results indicate that there is an apparent link between the mechanism of low dimensional chaos and the occurrence of reflected responses which could lead to more spatially disorganized phenomena. A detailed mechanism for the low dimensional chaos observed experimentally is pursued using a difference equation model. Critical features of the model include a non-monotonic relationship between recovery time during rhythmic stimulation and the state of membrane properties, and a steeply sloped recovery of membrane properties over certain ranges of recovery times. Besides explaining our results, the analytical model may pertain to irregular dynamics in other excitable systems, particularly the intact dysrhythmic heart.