The conducted action potential. Models and comparison to experiments

Propagation of the action potential is a complex process, and the relationships among the various factors involved in conduction have not been clear. We use three mathematical models of uniform conduction in a cable to clarify some of these relationships. One model is newly derived here, and two have been previously derived by Hunter et al. (1975, Prog. Biophys. Mol. Biol., 30:99-144). These models were able to simulate individual experimental action potential upstrokes previously obtained (Walton and Fozzard, 1983, Biophys. J., 44:1-8). The models were then utilized to provide relationships between measures of conduction. Among these were that maximal upstroke velocity (Vmax) is directly proportional to peak inward ionic current normalized by capacitance that is filled during the upstroke (I/Cf), and that conduction velocity was directly related to the square root of either Vmax or I/Cf. These relationships were shown to be model independent and to predict the experimental results, thus providing validated quantitative relationships that were not discernible through use of experimental data alone. The concept of safety factor was considered and a parameter was proposed that may be related to safety factor.