A Mathematical Model of the Vagally Driven SA Nodal Pacemaker

A model is developed for the vagal control of SA nodal activity in the heart and consists essentially of a modified Bonhoeffer-Van der Pol (BVP) model of the ``free-running'' SA node and a lumped model of the neural terminations in that region. The model is capable of mimicking both the driven transient behavior of the node in terms of pacemaker and inhibition curves, as well as steady-state entrainment phenomena. The model data also agree very well with experimental data from dog experiments performed in our laboratory. The model is described by a set of nonlinear, third-order, ordinary differential equations and provides a relatively uncomplicated functional model of heart period changes due to vagal stimulation patterns.