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A minimal model of the dynamics of internal calcium concentration of the mammalian cardiac Purkinje fiber is examined in order to identify the cause of certain arrhythmias of the heart. The effect of inhibition of the sodium/potassium pump is modeled by an elevated value of internal sodium concentration. Effects of pump inhibition are examined at different clamp voltages. Such conditions mimic those which have been examined experimentally and which are known to cause oscillatory calcium release [W.J. Lederer, PhD thesis, Yale University, New Haven, CT (1976), 168 pp.; R.S. Kass, W.J. Lederer, R.W. Tsien and R. Weingart, J. Physiol. (London) 281 (1978) 187-208]. System dynamics are investigated using numerical continuation methods. Results of these analyses predict the existence of stable periodic oscillations of internal calcium over a range of voltage-clamp values. The emergence of these oscillations depends on the intracellular sodium concentration.
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