The time constants for cathodic make stimulation of electrical syncytia: an application to cardiac pacing

In the framework of cardiac pacing, measured chronaxies are different for current and for voltage pulses. They increase with the distance between the pacing cathode and the myocardium, and with the size of the electrode. Mathematical formulae that relate the time constants (and the chronaxies) of the strength duration curves with the parameters of the system composed by the electrode, the volume conductor and the myocardium are used to explain the aforementioned experimental results and to discuss, from an engineering standpoint, some aspects related with thresholds for cardiac pacing, both for unipolar and bipolar pacing. These formulae are derived from a mathematical model of the electric stimulation of a syncytium framed in the bidomain theory. The time constants are given as increasing functions of a non dimensional number, equal to the quotient between a a certain characteristic length and myocardium's space constant. In the case of pacing electrodes, the characteristic length is a function of the size and shape of a region of influence of the cathode on the excitable tissue located adjacent to the electrode.