A mathematical analysis of SFAP convolutional models

In this paper we compare, from a mathematical point of view, two well-recognized single fiber action potential (SFAP) convolutional models: the Nandedkar-Stalberg (N-S) model and the Dimitrov-Dimitrova (D-D) model. Junction waves appear in N-S SFAPs due to the onset and extinction of the monopoles whereas in D-D SFAPs these waves appear only when the dipoles reach the fiber/tendon junctions. D-D junction waves model more accurately the out-of-the-main-spike waveforms that appear in experimental SFAPs. The origin of junction waves lies in the discontinuities of the impulse responses. There are two kinds of these waves caused by the two types of existing discontinuities (in the impulse response function and in its derivative). We model each kind of discontinuity with a different mathematical function. Using these functions, the N-S and D-D impulse responses can be split and, therefore, the junction waves can be separated from the spike component of the SFAP. The expansion of the impulse response helps us to understand the differences between the N-S and D-D junction waves.