MODIFICATION OF DIFRANCESCO-NOBLE EQUATIONS TO SIMULATE THE EFFECTS OF VAGAL-STIMULATION ON IN-VIVO MAMMALIAN SINOATRIAL NODE ELECTRICAL-ACTIVITY

We present a new mathematical model for vagal control of rabbit sinoat rial (SA) node electrical activity based on the DiFrancesco-Noble equa tions. The original equations were found to be unstable, resulting in progressive cycle by cycle depletion or accumulation of ions in intra- and extracellular compartments. This problem was overcome by modifyin g the maximum Na-K pump current and the time constant for uptake of in tracellular calcium. We also included a formulation for the acetylchol ine (ACh)-activated potassium current which was consistent with experi mental data. This formulation was based on kinetics first proposed by Osterrieder and later modified by Yanagihara. The resulting model exhi bits cycle-cycle ionic stability, and includes an ACh-activated potass ium current which accurately reproduces experimentally observed effect s of vagal stimulation on both the membrane potential and its time-der ivative. Simulations were performed for both brief-burst and prolonged vagal stimulation using simplified square wave profiles for the conce ntration of ACh in the synaptic cleft space. This protocol permits the isolation of cardiac period dynamics caused by changes in membrane po tential and intra- and extracellular ionic concentrations from those c aused by other mechanisms including the dynamics of ACh release, diffu sion, hydrolysis and washout. Simulation results for the effects of br ief-burst single cycle stimulation on the cardiac period agree closely with experimental data reported in the literature, accurately reprodu cing changes in membrane potential and the phasic dependency of the re sponse to the position of vagal stimulus bursts within the cycle. Simu lation of the effects of prolonged vagal stimulation accurately reprod uced the steady-state characteristics of heart period response, but di d not yield the complex multimodal dynamics of the recovery phase, or the pronounced post vagal tachycardia observed experimentally at the t ermination of the stimulus. Our results show that the major chronotrop ic effects of vagal stimulation on the SA cell membrane can be explain ed in terms of the ACh-activated potassium current. The effects of thi s membrane current however are generally fast acting and cannot contri bute to any long lasting dynamics of the cardiac period response. The modified DiFrancesco-Noble model presented in this article provides a valuable theoretical tool for further analysis of the dynamics of vaga l control of the cardiac pacemaker.