AJP - Heart and Circulatory Physiology, Vol 256, Issue 2 520-H526, Copyright © 1989 by American Physiological Society
Mathematical model of dependence of heart rate on tissue concentration of acetylcholine
F. Dexter, G. M. Saidel, M. N. Levy and Y. Rudy
Department of Biomedical Engineering, Case Western Reserve University, Cleveland, Ohio 44106.
The change in sinus period elicited by vagal stimulation depends on the
rate of acetylcholine (ACh) release from the nerve endings, the rate of ACh
degradation in the nodal tissue, and the responsiveness of the sinus node
to ACh. Vagal stimulation in anesthetized dogs prolonged sinus period.
After cessation of vagal stimulation, the sinus period returned to the
prestimulation period. We developed a mathematical model to analyze the
dynamics of ACh degradation in the neuroeffector junction and the
dependence of sinus period on the concentration of ACh. From the in vitro
reaction kinetics of acetylcholinesterase, we derived an analytical
expression for the rate of ACh degradation in the intact animal. Our model
represents the electrical behavior of the sinus node by the electrical
activity of one pacemaker cell with six membrane ionic currents. This model
predicts the decline in sinus period of the intact anesthetized dog as
acetylcholinesterase degrades ACh in the neuroeffector junction. The
half-life of ACh after cessation of vagal stimulation was estimated to be
2.7 s. We conclude that following termination of vagal stimulation, the
sinus node of the intact animal responds to ACh as if the sinus node were
one oscillator.
