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Branched semi-infinite axon Next, we considered a bent semi-infinite axon in a uniform EF to establish a relationship between terminal polarization and fibre morphology, extending previous derivations (Tranchina & Nicholson, 1986; Basser & Roth, 2000; Miranda http://www.selleckchem.com/products/byl719.html et al. 2007). We previously derived the analytical steady-state solution to the classic cable equation for a passive terminating straight branch of an axon (eqn (1); for a complete derivation, see Arlotti et al. 2012). (1) The terminal polarization varies with the physical length ? of the final segment and depends on the angle �� of the EF, E, relative to the final branch and the membrane polarization at the bend V0. The relative contribution of E�� vs. V0 depends on the electrotonic (dimensionless) length ?/��. Straight semi-infinite axon A simple analytical solution of polarization of a straight semi-infinite axon in a uniform EF is well known (and is in fact a special case of the axon branch with infinite length); eqn (2) relates polarization at the fibre terminal with the membrane space constant �� (Hause, 1975). The terminal membrane polarization is a function of the uniform extracellular EF relative to the axon, such that ��= 0 corresponds to an EF along the longitudinal http://www.selleck.cn/products/gsk-j4-hcl.html axis of the fibre. Interestingly, in this formulation �� is analogous to the coupling constant, and we intend to establish if and when this approximation is valid for realistic axon morphologies. (2) The overall goal of this study was to systematically characterize the cellular target of action for DCS. Our approach was to first determine the prevalence of radial and tangential EFs in the cortex using MRI-derived computational models. Secondly, the effects of radial and tangential DC fields on synaptic efficacy were characterized http://www.selleckchem.com/products/BEZ235.html in cortical brain slices in four distinct synaptic pathways corresponding to different orientations of afferent axons. Synaptic efficacy was shown to be pathway specific, and synaptic terminal polarization by tangential fields can lead to facilitation/inhibition independent of somatic polarization. These findings motivated us to determine a general rule to describe sensitivity of axon terminals to polarization in the form of a coupling constant. Consistent with previous computational studies, tDCS and HD-tDCS are predicted to generate weak EFs (