Many investigators work with the Hodgkin-Huxley model of membrane behavior or extensions thereof. In these models action potentials are found as solutions of simultaneous nonlinear differential equations which must be solved using numerical techniques on a digital computer. Recent membrane models showing pacemaker activity, such as that of McAllister, Noble, and Tsien, involve solutions covering long periods of time, up to five seconds, and many ionic currents. Those added requirements make it desirable to have an efficient algorithm to minimize computer costs, and a systematic and simple solution method to keep the program writing and debugging to manageable levels. This paper shows that an iterative procedure using only one differential equation is possible and desirable and that the simplest numerical integration method is adequate. Graphical solutions for the action potentials and all nine components of the membrane ionic current over four action potential cycles are provided for the McAllister, Noble, and Tsien model; these are of intrinsic interest and helpful as a program debugging aid. A specific procedure for adjusting step-size during the iterative solution is given and it is shown that 4.5 minutes of repetitive membrane activity requires only 4 minutes of computer time. The procedure and model is shown to be intrinsically stable over this time duration with respect to computer and numerical integration errors. Copyright © 1978 by The Institute of Electrical and Electronics Engineers. Inc.
