A theoretical analysis of extracellular punctate stimulation around dendrites.
The polarization of neuronal trees by external point stimulation is modelled. In one form of model, an almost spheroidal field encloses the dendritic tree. Radially projecting, electrically linear dendrites, along with extracellular medium, are considered to occupy the entire field. The spheroid is modified by a penetrating cone that can surround the stimulating microelectrode; here, and in the rest of the infinite volume outside the field, there is only extracellular medium. A second form of linear electrical model, representing sections of membrane and cytoplasm by means of lumped electrical components commonly known as compartments, is used to validate the field construct. A similar spatial distribution of induced steady-state membrane potential emerges from the two forms of model, for a given morphology and electrophysiology. Compartmental models are also used to demonstrate time-courses of membrane charging. At the soma, if the point source is nearby, charging proves to be essentially complete in less than one time-constant. The soma thresholds under steady-state polarization from different electrode distances are plotted for field models of various electrical space-constant, size and shape of spheroid, and eccentricity of the soma. Characteristic cathodal or anodal thresholds, depending on the particular cell parameters, are revealed for specific electrode trajectories. The range of threshold-distance relations obtained in previously published experiments match those given by the models, when the time-course of charging is taken into account.
Hentall
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ID
Department of Physiology and Biophysics, University of Puerto Rico, San Juan 00936.
D000818:Animals; D003712:Dendrites / Q000502:physiology*; D004558:Electric Stimulation; D008959:Models, Neurological; D009474:Neurons / Q000502:physiology*