Low-frequency dielectric dispersion of brain tissue due to electrically long neurites

The dielectric properties of brain tissue are important for understanding how neural activity is related to local field potentials and electroencephalograms. It is known that the permittivity of brain tissue exhibits strong frequency dependence (dispersion) and that the permittivity is very large in the low-frequency region. However, little is known with regard to the cause of the large permittivity in the low-frequency region. Here, we postulate that the dielectric properties of brain tissue can be partially accounted for by assuming that neurites are of sufficient length to be "electrically long." To test this idea, we consider a model in which a neurite is treated as a long, narrow body, and it is subjected to a stimulus created by electrodes situated in the region external to it. With regard to this electric stimulus, the neurite can be treated as a passive cable. Assuming adequate symmetry so that the tissue packed with multiple cables is equivalent to an isolated system consisting of a single cable and a surrounding extracellular resistive medium, we analytically calculate the extracellular potential of the tissue in response to such an externally created alternating-current electric field using a Green's function that we obtained previously. Our results show that brain tissue modeled by such a cable existing within a purely resistive extracellular medium exhibits a large effective permittivity in the low-frequency region. Moreover, we obtain results suggesting that an extremely large low-frequency permittivity can coexist with weak low-pass filter characteristics in brain tissue.