Identification Procedure in a model of single fibre action potential – Part I: Estimation of fibre diameter and radial distance

The Dimitrov–Dimitrova (D–D) model generates a single fibre action potential (SFAP) as the convolution of an excitation function and a filter impulse function. We propose a method to estimate the parameters involved in these functions from a SFAP waveform (inverse problem) and call it Identification Procedure. The Identification Procedure comprises two parts. The present paper, Part I, is centred on the estimation of the radial distance, r, and the fibre diameter, d, of a given SFAP. To this end we develop a technique which we call the candidate pair method (CP-method), and we test it on fibrillation potentials (FPs) as experimental data. We found that the D–D model cannot synthesize all the SFAP waveforms observed in the experimental recordings, but in the cases where it can, the CP-method then provides the values of r and d that are more likely to have synthesized the SFAP. Having a method that provides information about the fibre diameter straight from a SFAP waveform is very desirable as this parameter has clinical and physiological relevance. Moreover, the CP-method plays a major role in the Identification Procedure that is carried out in Part II.