Finding the Site of Origin and Velocity of Propagation in a Short One-Dimensional Strand from Two Extracellular Waveforms

In cardiac muscle times of excitation, the site of origin of excitation and propagation velocity usually are determined from the intrinsic deflections of a collection of extracellular waveforms. Separate waveforms are measured from each site for which an excitation time is to be found. Most of the information in each measured waveshape is discarded, even though waveshape features have been shown to be closely related to propagation characteristics. The objective of this paper is to examine the possibility of more fully utilizing all of the information in the extracellular waveform. Would a small number of measured waveforms, used more completely, be sufficient to find the site of origin, propagation velocity, and excitation times? A computer simulation of intra-and extracellular excitation along a one-dimensional cylindrical cardiac strand provided the framework for the evaluation. The dimensions and the-conductivity of the strand and the action potential shape were assumed known. Extracellular waveforms were simulated at 2 of 51 points on the strand and thereafter taken to be "measurements.?" The objectives were to calculate, from the "measured" waveforms, the site of origin of excitation (possibly anywhere along the strand), the speed of propagation, and the times of excitaion at all 51 points. Propagation speed was assumed constant, but of unknown magnitude, in both directions away from the site of excitation. Notable results of the study include correctly differentiating among different sequences of excitation having identical time differences between the intrinsic deflections of the two known extracellular waveforms.