A mathematical model was derived that describes peak force of contraction as a function of stimulus interval and stimulus number in terms of Ca2+ transport between three hypothetical Ca2+ compartments. It includes the conventional uptake and release compartments and recirculation of a fraction r of the activator Ca2+. Peak force is assumed to be proportional to the amount of activator Ca2+ released from the release compartment into the sarcoplasm. A new extension is a slow exchange of Ca2+ with the extracellular space via an exchange compartment. Six independent parameters were necessary to reproduce the different effects of postextrasystolic potentiation, frequency potentiation, and post-rest potentiation in isolated heart muscle from the rat. The normalized steady state peak force (F/Fmax) under standard conditions varied by a factor of ten between preparations from rat heart. Analysis with the model indicated that most of this variation was caused by two variables: the Ca2+ influx per excitation and the recirculating fraction of activator Ca2+. The influence of the Ca2+ antagonist nifedipine of the force-interval relationship was reproduced by the model. It is concluded that the model may serve to analyze the variability of contractile force and the mode of actions of drugs in heart muscle.
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