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Proceedings - 19th International Conference IEEE/EMBS Oct. 30 - Nov. 2, 1997 Chicago, IL. USA
A MODEL OF SYMPATHETIC NEURAL CONTROL OF CARDIAC PACEMAKER ACTIVITY Socrates Dokos*, Member IEEE, Branko G.-Celler*, Member IEEE, Nigel H. Lovell, Member IEEE *Biomedical Systems Laboratory, School of Electrical Engineering, University of New South Wales, Sydney, Australia, 2052. -Graduate School of Biomedical Engineering, University of New South Wales, Sydney, Australia, 2052. *E-mail:
[email protected] Abstract - We have modijied an existing mathematical model of single cell rabbit sinoatrial node activity to incorporate the dynamic modulation of its membrane currents by sympathetic neural stimulation. The resulting model was able to reproduce the experimentally observed changes in action potential waveform as well as the time course of the positive chronotropic response following sympathetic stimulation.
INTRODUCTION The increase in heart rate elicited by sympathetic neural stimulation is mediated by the action of neurotransmitter norepinephrine (NE) on pacemaker cells of the sinoatrial (SA) node. NE is known to enhance at least three membrane currents of SA node myocytes: the L-type Ca current the hyperpolarization-activatedcurrent $ and the delayed rectifier K current iK [l]. In order to examine the dynamic contribution of each of these currents to the overall response of SA node cells to sympathetic stimulation, we have modified our single cell mathematical model of rabbit SA electrical activity [2] to include timedependent modulation of band iK by NE.
current by NE has not been conclusively demonstrated [7], and was therefore not modelled in this study. Enhancement of i(:a,L and iK were formulated as a time-dependent increase in their membrane conductance, whilst i/ activation was modelled as a time-dependent positive voltage shift in its basal kinetics. Onset activation of both and if by NE were sigmoidal in characteristic, with half-activation times of the order of 10 s and recovery time constants of 20 s following NE decline. In contrast, activation and recovery of iK was much slower with a time constant of 60 s. Main NE Store I
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METHODS NE released into sympathetic neuroeffector junctions binds to P-adrenergic receptors on the membranes of SA node cells to enhance i/. and iK via cytosolic second messenger pathways. As a result, NE-enhancement of these currents exhibits slow activation and recovery kinetics of the order of tens of seconds. On cessation of stimulation, NE in the neuroeffector junction has been reported to decline with a half-time of 460 ms [3]. Even slower rates of decline are observed at higher stimulus frequencies, suggesting that NE uptake saturates at high NE levels [3]. We have fitted the data pertaining to NE uptake with second order kinetics based on a three-compartment model as shown in figure 1, with the rate of uptake k , decreasing at high NE. Time-dependent kinetics describing NE-activation of ica,L, $ and iK were formulated from data described in the literature [ l , 4, 5, 61. NE-activation of the Na-K pump
Extrajunctional Space
Figure 1. Schematic diagram of modelled NE kinetics in sympathetic neuroeffector junction. Three-Eompartment model consists of a main neuronal store of NE ([NE],,,J, a neuroeffector junction compartment ([NE]) and an extrajunctional space ([NEIJ in difisive contact with the neuroeflectorjunction. RESULTS Figure 2 illustrates the effects of sympathetic stimulation on the action potential waveform of the SA node model. Following 10 Hz stimulation for 60 s, the dominant effects on SA node electrical activity are an increase in the rate of diastolic depolarisation and a decrease in the upstroke threshold. Both effects are due to
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Neuroeffector Junction
Proceedings - 19th International Conference - IEEE/EMBS Oct. 30 - Nov. 2, 1997 Chicago, IL. USA the enhancement of the dominant upstroke current, i , , , by NE. 20 r
half-widths of the response, defined as the interval in which sinus rate is greater than 50% of its peak value, were 30 s, 24 s, 22 s and 21 s for the corresponding frequencies of 10 Hz, 5 Hz, 2 Hz and 1 Hz. All these findings are in close agreement with experimental observations in the literature [4]. The incorporation of saturation of the rate of NE uptake in the model allowed the half-width of the response to increase with increase in sympathetic frequency. Without this saturation, the half-width of the response remained fixed and independent of stimulus frequency.
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Figure 2. Modulation of spontaneous pacemaker activity of model following 60 s of sympathetic stimulation at IO Hz. Dashed line represents pre-stimulus rhythmic activity (control).
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The time course of this positive chronotropic response as well as associated time-dependent changes in action potential waveshape are illustrated in the panels of figure 3. Following the onset of sympathetic stimulation, SA node cycle length begins to decrease after a latency of -2 s, in agreement with experimental observation [4, 61. Also in agreement with experimental observation is the biphasic time course of the maximum diastolic potential (MDP) of the model during prolonged sympathetic stimulation [4]. During the initial phase of sympathetic stimulation, the MDP becomes less negative due to the gradual activation of ij by NE. This reduction in MDP is reversed by the slower activation of outward iK so that the steady-state MDP is more negative than control. Activation of by NE leads to an increase in upstroke velocity of the action potential, as well as a slight increase in action potential duration. This increase is eventually counterbalanced by the activation of iK which tends to promote repolarisation. In our simulations, we have found that modest enhancement of outward iK significantly decreases the duration of the action potential, whilst having a negligible effect on cycle length. Thus it appears from our simulation studies that activation of iK in sinus node cells serves to limit the increase in action potential duration due to activation of The time course of recovery of the model following sympathetic stimulation is illustrated in figure 4. After the onset of 10 s sympathetic stimulation at frequencies of 1, 2, 5 and 10 Hz, sinus node rate peaks at some 15-20 s before declining to basal rate with a time constant of -20 s. The
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Figure 3. Time course of the positive chronotropic response and associated action potential parameters of the model to continuous I O Hz sympathetic stimulation applied at the time shown by the arrow in the top panel. In order from top to bottom, the panels illustrate the time course of cycle length (CL), change in MDP ( M D P ) , upstroke velocity (Uv),overshoot (OS) and action potential duration (APD).
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Proceedings - 19th International Conference - IEEE/EMBS Oct. 30 - Nov. 2, 1997 Chicago, IL. USA
chronotropic response at high frequencies of sympathetic stimulation.
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REFERENCES
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A. Noma, H. Kotake and H. Irisawa, “Slow inward current and its role mediating the chronotropic effect of epinephrine in the rabbit sinoatrial node”, Pfliigers , 1-9, 1980. Arch., ~ 0 1 3 8 8pp. [2] S . Dokos, B.G. Celler and N.H. Lovell, “Ion currents underlying sinoatrial node pacemaker activity: a new single cell mathematical model”, J. theor. Biol., vol 181, pp. 245-272, 1996. [3] F. Gonon, M. Msghina and L. Stjame, “Kinetics of noradrenaline released by sympathetic nerves”, Neuroscience, vol56, pp. 535-538, 1993. [4] J.K. Choate, F.R. Edwards, G.D. Hirst and J.E. OShea, “Effects of sympathetic nerve stimulation on the sino-atrial node of the guinea-pig”, J. Physiol. (Lond), vol471, pp. 707-727, 1993. [SI A. Zaza, R.B. Robinson and D. DiFrancesco, “Basal responses of the L-type Ca” and hyperpolarizationactivated currents to autonomic agonists in the rabbit sino-atrial node”, J. Physiol. (Lond), vol 491, pp. 347-355, 1996. [6] H. Tanaka, R.B. Clark and W.R. Giles, “Positive chronotropic responses of rabbit sino-atrial node cells to flash photolysis of caged isoproterenol and cyclic AMP”, Proc. R. Soc. Lond. B, vol 263, pp. 241-248, 1996. [7] M.J. Main and M.B. Cannell, “Effects of padrenergic stimulation on the Na+-K+ pump and Na+-Ca2+exchanger in isolated guinea-pig ventricular myocytes”, Abstract, J. Physiol. (Lond), vol. 483P, p. 12P, 1995. [l]
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Figure 4. Positive chronotropic response and recovety of SA model following I O s sympathetic stimulation at frequencies of 10, 5, 2 and I Hz. Time of stimulation is shown in the bar in upper left corner. Data has been plotted as beats per minute for comparison with experimental observations [4].
CONCLUSION The ionic mechanisms underlying the positive chronotropic response of the cardiac pacemaker to sympathetic neural stimulation were examined in this study using a mathematical model of SA node electrical activity. The model was able to simulate the experimentally observed time course of the positive chronotropic response along with changes in action potential characteristics. It was found that activation of ico,L by NE lowered the threshold and increased the rate of action potential upstroke. Activation of i/ by NE led to an initial reduction in the MDP which was completely reversed by the slower activation of iK. Saturation of the rate of NE uptake allowed the model to produce a longer lasting positive
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