General Network Theory, the Black-Box

In many cases, we will regard our biological material, together with the necessary electrode arrangements, as an unknown black box. By electrical measurement, we want to characterize the content of the box (we do not have direct access to the key to open the lid ). We want to use the data to describe the electrical behavior, and perhaps even explain some of the physical or chemical processes going on in the box, and perhaps discern between electrode and tissue contributions. The description must necessarily be based upon some form of model (e.g., in the form of an equivalent electric circuit), mimicking measured electric behavior. We may also want to link properties to distinct tissue parts or organ parenchyma behavior. A basic problem is that always more than one model fits reasonably the measured electric behavior. 

The equivalent circuit is the tool of the electronic engineers and facilitates their interpretation of the results, simply because they are trained and used to interpret such diagrams. As discussed in Section 9.1, the equivalent model may also go further and be of a more explanatory nature. 

The black box may be assumed to contain the whole body, a part of the body, just an organ, or just a cell, together with the electrodes. It may also be assumed to contain not the real things, just the equivalent model circuit of the tissue of interest. 

We will now give a very general description of the black box and how to characterize it electrically, irrespective of the box content. The black box may be considered to contain the real tissue with electrodes for excitation and response measurement, or our model in the form of an electric network as a combination of lumped (discrete) electrical components. The network may be with two, three, or four external terminals (compare the number of electrodes used). A pair of terminals for excitation or recording is called a port. The treatment is so general that the content can be characterized with global variables not particularly linked with electrophysiology. 

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