Identification procedure in a model of single fibre action potential – Part II: Global approach and experimental results

Abstract 

The present paper describes a global procedure for estimating all the synthesis parameters that generate a single fibre action potential (SFAP) in the Dimitrov–Dimitrova (D–D) convolutional model. We call this inverse problem Identification Procedure, and it is presented in two parts, this paper being the second. The procedure incorporates the candidate pair (CP) method developed in Part I, which provides the values of radial distance r and fibre diameter d of the simulated SFAP that best matches a potential under study. The CP-method required prior knowledge of all the excitation parameters. However, since the Identification Procedure makes no assumption about the excitation, multiple combinations of the synthesis parameters result in very similar SFAPs whose shape is close the signal under study. Analysis of the possible combinations reveals that r and d can be modelled as two jointly Gaussian random variables. The interest of the Identification Procedure is that, for a certain SFAP, it provides estimates of r and d, along with estimates of different parameters that determine the IAP waveform. Moreover, the procedure is able to determine the degree of error that accompanies the estimation of r and d.

Keywords: Single fibre action potential, Inverse problem, SFAP modeling, Radial distance, Fibre diameter