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Power Laws from Linear Neuronal Cable Theory: Power Spectral Densities of the Soma Potential, Soma Membrane Current and Single-Neuron Contribution to the EEG

Figure 3

Schematic illustration of the ball and stick neuron model and its filtering properties.

(A) Schematic illustration of the ball and stick neuron model with a single input at a given position . The lumped soma is assumed iso-potential and located at . (B) Frequency-dependent current-density envelopes of return currents for a ball and stick neuron with input at . The somatic return currents are illustrated as current densities from a soma section with length placed below the stick. For 1 Hz, 10 Hz, 100 Hz and 1000 Hz the amplitudes of the somatic return currents are about 1/7.3, 1/7.5, 1/22 and 1/3100 of the input current, respectively. Parameters used for the ball and stick neuron model: stick diameter , somatic diameter , stick length mm, specific membrane resistance , inner resistivity m and specific membrane capacitance of . This parameter set is the default parameter set used in the present study, see Table 1. (C) Representative log-log plot for a PSD when input is homogeneously distributed across the entire neuron model. The low frequency (lf), intermediate frequency (if) and high frequency (hf) regimes are stipulated. The regimes are defined relatively to describing the asymptotic value of the exponent of the respective power-law transfer functions (, or ), with both uncorrelated and correlated input (‘all’ types of input) onto both the soma and the stick.

doi: https://doi.org/10.1371/journal.pcbi.1003928.g003