Potential fields from cardiac strands of cylindrical geometry
Clark, John W.
Master of Science
This paper deals with the classical forward and inverse volume conductor field problems associated with the isolated active cardiac strand. The Purkinje fiber and the atrial trabeculum are chosen as specific examples of cardiac tissue that may be well modeled by cylindrical geometry. The electrical behavior of these strands is modeled in terms of the electrical activity of an equivalent single cell, with a representative membrane that separates an anisotropic intracellular medium from an isotropic extracellular medium. The isolated single atrial muscle fiber is also studied as an interesting special case. A Potential theory model is developed for the strand, that is based on a solution of Laplace's equation in the media of interest, subject to appropriate boundary conditions. The solution for potential at an arbitrary point in the extracellular medium is in the form of a Fourier integral; the equation is subsequently reformulated into a more convenient computational form using a discrete Fourier transform (DFT) method. Implementation of this method using a Fast Fourier Transform (FFT) technique, results in a fast and efficient numerical algorithm for the calculation of volume conductor potentials. A benefit of this approach is that the classical forward and inverse problems in electrophysiology may be viewed as equivalent filtering problems. Thus not only can volume conductor field potentials at varions distances from the strand be easily and rapidly computed, but given field potential data, good estimates of the action potential waveform can also be obtained provided the signal to noise ratio is adequate.