Modeling fibrillation potentials--a new analytical description for the muscle intracellular action potential

The single-fiber action potential (SFAP) can be modeled as a convolution of a biolectrical source (the excitation) and a transfer function, representing the electrical volume conduction. In the Dimitrov-Dimitrova (D-D) convolutional model, the first temporal derivative of the intracellular action potential (IAP) is used as the source. In this model, the ratio between the amplitudes of the second and first phases of the SFAP (which we call the PPR, after peak-to-peak ratio) increases invariably with radial distance. This is not the case of real recorded fibrillation potentials (FPs). Moreover, FPs show a wider PPR range than that which the D-D model can provide. These discrepancies suggest that the D-D model should be revised. Since the volume conduction parameters seem to have no apparent effects on the PPR, we assume that the origin of this difference lies in the excitation source. This paper presents a new analytical description of the IAP based on that expressed in the D-D model. The new approximation is shown to model FPs with a range of PPRs comparable to that observed in a set of real FPs which we used as our test signals.