The Simulation of Repolarization Events of the Cardiac Purkinje Fiber Action Potential

A mathematical model based on the formalism of the Hodgkin-Huxley equations was implemented on a microcomputer system and used to simulate the membrane action potential of cardiac Purkinje fibers. The complete model is a modification of the representation used by McAllister et al. [1], mainly with respect to the outward current components during the late plateau, the repolarization phase, and the slow repolarization phase of the action potential. A new formulation of the potassium conductance was used, involving two distinct types of ionic channels corresponding, respectively, to the experimentally observed inward-going and outward-going rectification properties of the Purkinje fiber membrane. A unified representation of the Purkinje fiber current components was thus obtained which provides a more satisfactory interpretation of experimental results than was possible with the original model of McAllister et al. [1]. The membrane channel for the potassium pacemaker current is characterized by a set of first-order activation?inactivation variables and a constant fully activated conductance. The other channel carries the potassium current involved in the late plateau and repolarization phase of the action potential.     

Using Vmax to estimate changes in the sodium membrane conductance in cardiac cells

Relative changes in the sodium conductance of the resting cardiac cell membrane are often estimated from relative changes in the maximum rate of rise of the action potential (Vmax). This approach has given rise to some controversy and it has not been possible so far to test it directly on an experimental basis. We have examined here the validity of this estimation using three different Hodgkin-Huxley representations of the cardiac membrane sodium current. The two basic requirements are a constant membrane capacitance and a negligible relative value of the nonsodium membrane currents at the time of Vmax. It is shown further that the approach leads to a satisfactory estimation only when the latency of Vmax is kept constant and a correction factor for the sodium driving force is applied to Vmax measurements. This conclusion applies either to a nonpropagated action or to an action potential propagated at constant velocity, provided that the membrane is not too strongly depolarized. It is valid for a wide range of sodium equilibrium potentials and a range of maximum sodium conductances limited to about 50% of the nominal value.     

A Simulation Study of the Ventricular Myocardial Action Potential

A mathematical model based on the formalism of the Hodgkin?Huxley equations was implemented on a microcomputer system and used to simulate the membrane action potential of ventricular myocardial fibers. The complete model is constituted in part from the representation used by Beeler and Reuter [1] and from a simplified version of a model used by us to simulate the Purkinje fiber action potential [3]. The experimental results from the frog ventricular myocardial preparation were reconstructed successfully in the present study. It was also shown that the Purkinje fiber and ventricular myocardial action potentials could be simulated by means of qualitatively similar models. The major differences are a simpler representation of the potassium current and a more prominent role of the calcium current in the representation used for the ventricular myocardial fiber.     

Revised formulation of the Hodgkin-Huxley representation of the sodium current in cardiac cells

The purpose of this paper is to revise the parameters of the Hodgkin-Huxley formulation for the Na+ current in ventricular myocardial cells. To this end we have assembled much of the recent voltage clamp data on cardiac preparations obtained with modern voltage clamp and patch clamp techniques. The selected activation and inactivation characteristics of the Na+ channel and other membrane parameters represent a good compromise between available experimental measurements and lead to a reasonable average representation of the cardiac Na+ membrane current. The resulting Na+ conductance changes during the action potential upstroke are much larger than in earlier models, so that the upstroke is much faster and the peak depolarization is close to the Na+ equilibrium potential. The firing threshold level is nearly constant for resting potentials in the range of -70 and -90 mV. The maximum rate of rise of the action potential displayed by the new model is quite comparable to experimental observations.