The inverse problem in electroneurography. I. Conceptual basis and mathematical formulation

A mathematical technique for the analysis of the compound action potential (CAP) of a peripheral nerve is presented. The procedure deals with the estimation of the number of active fibers contributing to the CAP and the distribution of their conduction velocities. The CAP is described as a filtered Poisson process, the (time-varying) filter representing the single-fiber action potential waveshapes. The estimation procedure consists of two parts. The first part, related to the fast conducting fibers contributing to the CAP main complex, uses least-squares optimization techniques for the reconstruction of the CAP waveshape. The second part, applying to the small late components of the CAP due to slowly conducting fibres, explicitly uses the Poisson process formulism and is based on reconstructing the energy for variance in the CAP.