Radial changes of extracellular potential amplitude and integral characteristics and the inverse problem in electroneurography

The possibility of solving the inverse problem in electroneurography, i.e. of estimating the main parameters specifying the activated fibre's functional state, using the amplitude and integral characteristics of the surface potentials generated by infinite homogeneous fibres, has been analysed. An analytical expression has been found for the amplitude of the negative phase A_nph of the single fibre extracellular action potential (SFEAP) as a function of the wavelength b, the fibre-electrode distance y and a scale factor A_o proportional to the intracellular action potential amplitude V_m, to the square of the fibre radius a and to the ratio of the axoplasm conductivity τ_a and volume conductor conductivity τ_e. For a large fibre-electrode distance, typical of surface recordings, an analytical expression of the integral of the negative phase I_nph of the SFEAP as a function of A_o, b, y and the propagation velocity v was also found. Simple methods are proposed for estimating v, the location of the electrical centre of the activated fibres' territory and the product of the number of activated fibres N, duration T_in of the intracellular action, potential and of the factor A_o. The estimation errors due to the temporal and spatial dispersion of the activated fibres were analysed as a function of the fibre-electrode distance and the territory shape.