Determination of the electrical impedance of neural tissue from its microscopic cellular constituents.
The electrical properties of neural tissue are important in a range of dierent applications in biomedical engineering and basic science. These properties are characterized by the electrical admittivity of the tissue, which is the inverse of the specic tissue impedance. Here we derived analytical expressions for the admittivity of various models of neural tissue from the underlying electrical and morphological properties of the constituent cells. Three models are considered: parallel bundles of bers, bers contained in stacked laminae and bers crossing each other randomly in all three-dimensional directions. An important and novel aspect that emerges from considering the underlying cellular composition of the tissue is that the resulting admittivity has both spatial and temporal frequency dependence, a property not shared with conventional conductivity-based descriptions. The frequency dependence of the admittivity results in non-trivial spatiotemporal ltering of electrical signals in the tissue models. These eects are illustrated by considering the example of pulsatile stimulation with a point source electrode. It is shown how changing temporal parameters of a current pulse, such as pulse duration, alters the spatial prole of the extracellular potential. In a second example, it is shown how the degree of electrical anisotropy can change as a function of the distance from the electrode, despite the underlying structurally homogeneity of the tissue. These eects are discussed in terms of dierent current pathways through the intra- and extra-cellular spaces, and how these relate to near- and far-eld limits for the admittivity (which reduce to descriptions in terms of a simple conductivity). The results highlight the complexity of the electrical properties of neural tissue and provide mathematical methods to model this complexity.