TY - JOUR
AU - Ilmoniemi, Risto J.
AU - Mäki, Hanna
AU - Saari, Jukka
AU - Salvador, Ricardo
AU - Miranda, Pedro C.
PY - 2016
M3 - 10.3389/fncel.2016.00194
SP - 194
TI - The Frequency-Dependent Neuronal Length Constant in Transcranial Magnetic Stimulation
JO - Frontiers in Cellular Neuroscience
UR - https://www.frontiersin.org/article/10.3389/fncel.2016.00194
VL - 10
SN - 1662-5102
N2 - Background: The behavior of the dendritic or axonal membrane voltage due to transcranial magnetic stimulation (TMS) is often modeled with the one-dimensional cable equation. For the cable equation, a length constant λ_{0} is defined; λ_{0} describes the axial decay of the membrane voltage in the case of constant applied electric field. In TMS, however, the induced electric field waveform is typically a segment of a sinusoidal wave, with characteristic frequencies of the order of several kHz.Objective: To show that the high frequency content of the stimulation pulse causes deviations in the spatial profile of the membrane voltage as compared to the steady state.Methods: We derive the cable equation in complex form utilizing the complex frequency-dependent representation of the membrane conductivity. In addition, we define an effective length constant λ_{eff}, which governs the spatial decay of the membrane voltage. We model the behavior of a dendrite in an applied electric field oscillating at 3.9 kHz with the complex cable equation and by solving the traditional cable equation numerically.Results: The effective length constant decreases as a function of frequency. For a model dendrite or axon, for which λ_{0} = 1.5 mm, the effective length constant at 3.9 kHz is decreased by a factor 10 to 0.13 mm.Conclusion: The frequency dependency of the neuronal length constant has to be taken into account when predicting the spatial behavior of the membrane voltage as a response to TMS.
ER -