Current sources and sinks

Current sources and sinks are analysis formalisms which distinguish points, areas, or volumes through which current enters or exits a system. While current sources or sinks are abstract elements used for analysis, generally they have physical counterparts in real-world applications; e.g. the anode or cathode in a battery. In all cases, each of the opposing terms (source or sink) may refer to the same object, depending on the perspective of the observer and the sign convention being used; there is no intrinsic difference between a source and a sink.

In some cases, the term current source refers to a boundary where current flows from locations where it is not measured to locations where it is measured. In a similar fashion, a current sink may refer to the boundary where current flows from locations where it is measured to locations where it is not measured. By analogy to the flow of water, a current source would be like a mountain spring - water flows from its source (a hidden location underground) to the surface where it is easily observed. Using the same analogy, a current sink would be like water flowing down a drain - water travels from where it is observed to where it is not observed.

Two-compartment model illustrating the definition of a current sink vs source.

Shown at right is a general two-compartment model to help illustrate the definition of current sources or sinks. In this two-compartment model, the compartments are separated by a semi-conductive barrier (gray). An observer, symbolized by the eye, can "see" only one compartment at a time. Red arrows indicate the direction of flow of positive charges, while black arrows indicate the direction of flow of negative charges. The pink and green backgrounds are meant to symbolize different configurations, configuration 1 when charges are flowing in one direction and configuration 2 when they are flowing in the opposite direction. The difference between the left and right panels is simply the location of the "eye".

A source or a sink is defined by which compartment is viewable by the observer.

• A source is:
  • A flow of positive charges from the "invisible" to the "visible" compartment (i.e. toward the eye), or...
  • A flow of negative charges from the "visible" to the "invisible" (away from the eye).
• A sink is:
  • A flow of positive charges "away from the eye", or...
  • A flow of negative charges "toward the eye".

In biology, the schematic barrier in the figure could represent a cell membrane, and as a result, the two compartments could represent the inside and the outside of the cell. Generally speaking the point of observation would be outside the cell. Thus the cell would be termed a sink with respect to any flow of positive charges into it, and the cell would act as a source for any positive charges flowing out of it. Note that when considering the flow of negative charges, the definitions are reversed.

Current sources and sinks in neurobiology

Current sources and sinks have proven to be very valuable in the study of brain function. Both have particular relevance in electrophysiology. Two examples of the study of sources and sinks are Electroencephalography (EEG) and Current Source Density Analysis (extracellular field potentials).

Current source density analysis

Current source density analysis^[1] (which could more accurately be called current source and sink density analysis) is the practice of placing a microelectrode in proximity to a nerve or a nerve cell to detect current sourcing from or sinking into their plasma membranes. When positive charges, for example, flow quickly across a plasma membrane to the inside of a cell (sink) this creates a transient cloud of negativity in the vicinity of the sink. This is because the flow of positive charges into the interior of the cell leaves behind uncompensated negative charges. A nearby micro-electrode with substantial tip resistance (on the order of 1 MΩ) can detect that negativity because a voltage difference will develop across the tip of the electrode (between the negativity outside the electrode, and the electroneutral environment inside the electrode). Put another way, the electrode internal solution will donate some of the positive charge needed to compensate the negativity caused by the current sink. Thus, the inside of the electrode will become negative relative to ground for as long as the extracellular negativity persists. The extracellular negativity will persist as long as the current sink is present. Thus, by measuring a negativity relative to ground, the electrode indirectly reports the presence of a nearby current sink. The size of the recorded negativity will vary directly with the size of the current sink and inversely with the distance between the electrode and the sink.

The relationship between the sum of the current sources and sinks and the voltage measured by the microelectrode probe may be calculated analytically if it is assumed that the quasi-static assumption holds, that the medium is spherically symmetric, homogeneous, isotropic, and infinite, and if the current source or sink is modeled as a point source.^[2] The relationship is given by:

$\Phi(r)={I \over 4 \pi r \sigma}$

where Φ is the potential at radius r from the source or sink, which passes current I through a medium with conductivity σ.

See also

• Current source
• Current mirror

References

1. ^ Nicholson, C; Freeman, JA (1975). "Theory of current source-density analysis and determination of conductivity tensor for anuran cerebellum.". Journal of Neurophysiology Mar;38(2): 356–68. PMID 805215. 
2. ^ Plonsey; Collins (1961). Principles and Applications of Electromagnetic Fields.