A Prototype Inverse Solution in One-Dimension to Find the Origin of Excitation, Strand Radius, Intracellular Resistivity, or Distance from the Surface

Can extracellular waveforms from a one-dimensional strand be used to find the site of origin of excitation (xs0), strand radius (a0), intracellular resistivity (Ri0), or distance of the electrodes from the strand (b0)? A computer simulation of a strand 11.8 mm long was used to examine this question. The Ebihara-Johnson equations were used to model the membrane's behavior. Extracellular waveforms simulated at two of 60 points along the strand were taken as "measurements." The inverse calculations had the objective of finding one or two of the variables xs0, a0, Ri0, or b0 with the others known. The solution procedure compared the "measured" waveforms to trial waveforms obtained by varying all unknown parameters through their physiological range. For example, waveforms from two electrodes separated by 5.6 mm were sufficient to determine xs0 within 200 μm at an error level of 150 μV rms if the stimulus site lay along the strand between the electrodes, and a0, Ri0, and b0 were given. A major objective was a systematic exploration of the errors as a function of the values of the trial parameters. The error curves were frequently found to have several relative minima. In general, however, no combination of unknowns other than the correct one led to rms errors within experimental noise levels, a result in marked contrast to that of most other inverse calculations in electrocardiography.