Stability properties of a Purkinje fiber model

A clincially useful theory of cardiac excitability must be based on an understanding of excitability in the single pacemaker cell. The electrical behavior of these cells is sufficiently complex to demand digital computer simulation as a basic research tool. The most widely used model is that of Noble, which successfully reproduces most of the important intrabeat characteristics. Excitability is also an interbeat phenomenon, though, and the purpose of this investigation is to establish whether this model can serve as the basis for excitability studies. It is found that the limit cycle stability is much too strong to reproduce the experimentally discovered accommodative pattern of post-pacing suppression. By bounding the characteristic multipliers, a quantitative measure of stability is derived which conclusively indicates that this model must be extensively altered to include accommodative mechanisms crucial to excitability studies. One direction for such model improvement is suggested.