Power spectra of extracellular potentials generated by an infinite, homogeneous excitable fibre

The power spectra of the extracellular potentials (EPs) generated under activation of an infinite, homogeneous excitable fibre immersed into an infinite, resistive, isotropic and homogeneous volume conductor are theoretically analysed. The changes in the power spectrum related to the changes in the propagation velocity v, amplitudes Vm and duration Tin of the intracellular action potential (IAP) are analytically determined. It is found that in the ultra-low-frequency region the EP spectral power follows the course of alteration in the square of the modified Bessel function of the second kind and order zero multiplied by the fourth power of the frequency, and the Tin can be assessed by the deviation of the EP power spectrum from this function. It is shown why the sensitivity of the spectral characteristics depends substantially on the radial distance yo from the activated fibre to the point of observation; why the total spectral amplitude depends directly on the IAP wavelength but the total spectral power depends on the IAP wavelength as well as on its duration and propagation velocity; and why the EPs are not proportional to the IAP second spatial derivative even in close proximity to the fibre.