A mathematical model of the effects of acetylcholine pulses on sinoatrial pacemaker activity.

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Abstract
A mathematical model of dynamic vagus-sinus interactions was devised based on Hodgkin and Huxley-type equations of time- and voltage-dependent membrane currents. Brief vagal pulses were modeled with a concentration-dependent, acetylcholine-activated, potassium current. Single acetylcholine ("vagal") pulses scanning the sinus cycle induced changes in pacemaker rhythm that depended on pulse magnitude, duration, and time of occurrence during the cycle. Phase-response curves summarizing these effects are strikingly similar to experimental results. Notably, appropriately timed acetylcholine pulses could produce an acceleratory response. With repetitive acetylcholine input, the model produced various patterns of synchronization of the sinus pacemaker. There was stable entrainment at harmonic (i.e., 1:1, 2:1, etc.) relations, as well as more complex arrhythmic patterns that depended on the relationship between the acetylcholine cycle length and the sinus pacemaker period. In some cases, shortening of the acetylcholine input cycle length led to "paradoxical" acceleration of the sinus pacemaker. Simulations suggest that many clinically observed sinus rhythm disturbances can be explained by dynamic vagus-sinus interactions.