Transmission line models for ion-selective membranes in cardiology simulated with SPICE

Ion-selective membranes are a key component of cardiovascular micro-electrodes used to study ischemic events in vivo. This paper presents and compares two circuit models for charged species transport by diffusion in ion-selective membranes. One is a conventional, finite transmission line with resistors in series along the line and capacitors running crosswise to ground. The other circuit is the BBB (Barkel-Brumleve-Buck) circuit. The similarities and differences of these circuits are discussed and the impedance functions are compared. For both circuits discretized SPICE models were developed to verify the impedance functions and to investigate the behavior of the circuits for a variety of component values. The comparison showed that the BBB circuit can provide a more general model than the conventional transmission line. However, in many cases the two circuits can be converted into each other. The corresponding relations between the component values were derived